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NORTHWESTERN UNIVERSITY
Systems Design of Transformation Toughened Blast-Resistant Naval Hull Steels
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
Field of Materials Science and Engineering
By
Arup Saha
EVANSTON, ILLINOIS
June 2004
ii
© Copyright by Arup Saha 2004 All Rights Reserved
iii
ABSTRACT
Systems Design of Transformation Toughened Blast-Resistant Naval Hull Steels
Arup Saha
A systems approach to computational materials design has
demonstrated a new class of ultratough, weldable secondary hardened plate steels
combining new levels of strength and toughness while meeting processability
requirements. A first prototype alloy has achieved property goals motivated by
projected naval hull applications requiring extreme fracture toughness (Cv > 85 ft-lbs
(115 J) corresponding to KId > 200 ksi.in1/2 (220 MPa.m1/2)) at strength levels of 150-
180 ksi (1034 – 1241 MPa) yield strength in weldable, formable plate steels.
A theoretical design concept was explored integrating the mechanism of
precipitated nickel-stabilized dispersed austenite for transformation toughening in an
alloy strengthened by combined precipitation of M2C carbides and BCC copper both at
an optimal ~3nm particle size for efficient strengthening. This concept was adapted to
plate steel design by employing a mixed bainitic/martensitic matrix microstructure
produced by air-cooling after solution-treatment and constraining the composition to
low carbon content for weldability. With optimized levels of copper and M2C carbide
formers based on a quantitative strength model, a required alloy nickel content of
6.5 wt% was predicted for optimal austenite stability for transformation toughening at
iv
the desired strength level of 160 ksi (1100 MPa) yield strength. A relatively high Cu
level of 3.65 wt% was employed to allow a carbon limit of 0.05 wt% for good
weldability.
Hardness and tensile tests conducted on the designed prototype
confirmed predicted precipitation strengthening behavior in quench and tempered
material. Multi-step tempering conditions were employed to achieve the optimal
austenite stability resulting in significant increase of impact toughness to 130 ft-lb
(176 J) at a strength level of 160 ksi (1100 MPa). Comparison with the baseline
toughness-strength combination determined by isochronal tempering studies indicates
a transformation toughening increment of 60% in Charpy energy. Predicted Cu particle
number densities and the heterogeneous nucleation of optimal stability high Ni 5 nm
austenite on nanometer-scale copper precipitates in the multi-step tempered samples
was confirmed using three-dimensional atom probe microscopy. Charpy impact tests
and fractography demonstrate ductile fracture with Cv > 90 ft-lbs (122 J) down to
− 400C, with a substantial toughness peak at 250C consistent with designed
transformation toughening behavior. The properties demonstrated in this first prototype
represent a substantial advance over existing naval hull steels.
v
ACKNOWLEDGEMENTS
No word or phrase can completely express the gratitude I feel for all the
people who have made this journey such an amazing and wonderful experience. Nor
can I adequately thank all those people who have been directly or indirectly involved,
without writing another document as lengthy as this thesis. I can’t imagine surviving
through all the hardship of “graduate” life without the committed and unfailing help of
many. I would specially like to thank a few of them and apologize to those whom I fail
to mention.
Professor Greg Olson, you are simply the best. I still remember the excitement
on your face when you saw the 3D reconstruction of the austenite particle on the
copper precipitates and uttered spontaneously, “This is as good as it gets…” It is your
constant push towards the very limits in every aspect of research that has been my
inspiration over the years. Thank you for introducing me to the exciting and
challenging world of the systems design approach. I am forever indebted to you for
your guidance, encouragement and friendliness; they have meant a lot to me. Your vast
breadth of knowledge about apparently everything, analytical capability and extremely
sharp memory have always amazed me. I am truly honored to have the opportunity to
work with you, and the interactions with you have been very enriching for me.
My Mom and Dad, your constant enthusiasm in all my efforts and your belief
in me have helped me overcome a lot of pain and hardship. Nothing can appropriately
express my respect and gratitude towards you.
vi
Professors Morris Fine and Mark Asta for agreeing to serve on my committee
and providing helpful insights about this research. I deeply regret the sudden illness of
one of my committee members, Professor Brian Moran. I wish him a speedy recovery
and good luck for his health. I am thankful to Professor Horacio Espinosa for
accepting to be on my committee in such a short notice.
Dr. Gautam Ghosh for your patience and answering every little question I had.
I am thankful to you for helping me out with ThermoCalc and DICTRA during my
initial years.
Rick Kraemer, thank you for the help with the furnaces, seal-off and
dilatometry. Without your help none of the experiments would have been possible. I
would also like to thank Dr. Kathleen Stair for helping me with the salt-pot and
answering much-needed metallography questions, Mark Seniw for the help with tensile
testing and Jerry Carsello for the x-ray diffraction work. I am especially thankful to
Jesse Becker for taking good care of “thor”. Thang Bui in the machine shop for
providing the samples whenever I demanded them.
Dr. Herng-Jeng Jou, for providing useful expert advice about computational
modeling, Dr. Frode Stavehaug and Dr. Charlie Kuehmann for providing useful
experimental tips.
Jim Herman, your help makes all the complicated paperwork look so easy.
Thank you for giving your priority to every small detail and of course, I can’t thank
you enough for all the cups of coffee I had from your office. Thanks, Sharon for all the
vii
help with course registrations and paychecks. Joanna and the MSE staff for all the
administrative help.
Dr. Dieter Isheim, Stephan and Chantal in Seidman Research Group for being
so helpful while I was using the atom-probe. Your expert opinions helped to avoid a lot
of problems.
The Olson Group members, past and present. Jim and Rachel, you have been
excellent office-mates. Jin-won, thanks for all the long hours with the atom-probe and
the TEM. Abhijeet, for the company during lunch and being a good friend. Ben and
Dave you are an enthusiastic bunch and great company. I’ll miss office-basketball and
“would you rather” questions! Michelle, Matt and Yana, good luck with your research.
All my friends in NU, especially, JP, Naveen and Smita. Thanks for the fun
during the “dinner & movie” nights and the “board-game” parties.
My girlfriend, Mayurakshi for always being there for me. Life would have been
much difficult without the motivation and encouragement you provided during the
difficult times. I hope I can bring in the same enthusiasm and excitement in your life.
This research was supported by the Office of Naval Research under grant
number N00014–01–1–0953.
viii
TABLE OF CONTENTS
ABSTRACT iii ACKNOWLEDGEMENTS v LIST OF FIGURES xi LIST OF TABLES xx CHAPTER 1 INTRODUCTION 1
1.1 Goals and Context 4 1.2 Document Outline 8
CHAPTER 2 BACKGROUND 9
2.1 Design Approach 9 2.2 Bainitic Transformation 15 2.2.1 Carbon Redistribution under Paraequilibrium 18 2.2.2 Kinetics of Bainite Transformation 20 2.2.2.1 Bainitic Ferrite Nucleation and Growth 21 2.3 Strengthening Dispersions 29 2.3.1 Carbide Strengthening Dispersion 31 2.3.2 Copper Strengthening Dispersion 36 2.4 Transformation Toughening 45 2.3.1 Retained Austenite 51 2.3.2 Precipitated Austenite 55
CHAPTER 3 ALLOY DESIGN 61
3.1 Modeling Tools 62 3.1.1 ThermoCalc™ 62 3.1.2 CMD™ (Computational Materials Dynamics) 64
3.2 Design Approach 65 3.2.1 Strength Design 68
3.2.1.1 Quantitative Strengthening Contributions 68 3.2.1.2 M2C Carbide Strengthening 74 3.2.1.3 Copper Precipitation Strengthening 81
3.2.2 Transformation Toughening Design 83 3.2.3 Design Integration 90 3.2.4 Processing Considerations 94
ix
3.2.4.1 Solution Treatment Temperature and 94 Allotropic Transformations
3.2.4.2 Scheil Simulation for Microsegregation Behavior 95 3.2.4.3 Optimal Tempering Temperature 99
CHAPTER 4 MATERIALS AND 101
EXPERIMENTAL PROCEDURES
4.1 Materials 101 4.2 Experimental Procedures 102
4.2.1 Heat Treating 102 4.2.2 Metallographic Sample Preparation 103 4.2.3 Dilatometry 104 4.2.4 Microhardness Testing 105 4.2.5 Impact Toughness Testing 106 4.2.6 Tensile Testing 107 4.2.7 X-ray Diffraction (XRD) 109 4.2.8 Magnetometry 110 4.2.9 Electron Microscopy 113 4.2.10 Atom Probe/Field Ion Microscopy (AP-FIM) 114
CHAPTER 5 PROTOTYPE EVALUATION 119 5.1 Microsegregation and Hot-working behavior 119 5.2 Evaluation of Allotropic Kinetics 125 5.3 Isochronal Tempering Response 134 5.4 Toughness Optimization by Multi-step Tempering 143 5.5 Evaluation of Tensile Properties 150 5.6 Toughness – Temperature Dependence 153 5.7 Microstructural Characterization 159
5.7.1 X-ray Diffraction 160 5.7.2 Magnetometry 162 5.7.3 Transmission Electron Microscopy (TEM) 163 5.7.4 Three-Dimensional Atom Probe (3DAP) Microscopy 166
CHAPTER 6 CONCLUSIONS 187 6.1 Alloy Design 187 6.1 Prototype Evaluation 190
x
CHAPTER 7 SUGGESTIONS FOR FUTURE WORK 194 7.1 Further Prototype Evaluation 194 7.2 Next Design Iteration 195 REFERENCE LIST 197 APPENDICES APPENDIX A 214
Design and Evaluation of Concept A Alloy APPENDIX B 226
Assessment of Interfacial Dissipation Effects at Reconstructive Ferrite-Austenite Interfaces
xi
LIST OF FIGURES
Figure 1.1 KIC toughness vs. RC hardness cross-plot for ultra-high strength
martensitic steels 2
Figure 1.2 KIC toughness vs. σy yield strength cross-plot for different classes of materials [10] 5
Figure 2.1 Systems design chart for blast resistant naval hull steels 10
Figure 2.2 Correlation between KIc and CV test results [134] for high Ni steels 12
Figure 2.3 Schematic representation of TTT diagrams illustrating the flat-tops of
bainite C-curves [15] 15
Figure 2.4(a) TEM micrograph of upper bainite with austenite (A) between the lath sub-units in Fe-0.6%C-2.0%Si steel transformed at 4000C (magnification, 40000X) [16] 16
Figure 2.4(b) TEM micrograph of lower bainite with midribs in a 1.10% C steel
transformed at 1900C for 5hours [16] 17
Figure 2.5 Schematic illustration of bainite microstructural features relevant to the kinetic description [15,26] 21
Figure 2.6 Schematic illustration of thermodynamics to determine the driving force
for bainitic transformation [21,26] 22
Figure 2.7 Schematic illustration of nucleation/growth velocity as a function of
bainite sub-unit length [26] 24
Figure 2.8 Schematic representation of potency size distribution for pre-existing
and autocatalytic defects respectively [26,30] 25
xii
Figure 2.9 Schematic representation of transition from shearing to looping mechanism as a function of particle size at constant volume fraction [12] 30
Figure 2.10 M2C carbide precipitation behavior in AF1410 steel as a function of
tempering temperature at 5100C following 1 hour solution treatment at 8300C [42] 33
Figure 2.11 Plot of maximum increase in yield strength vs. (volume fraction of precipitates)1/2. The points represent experimental data and the line is predicted by the theory for dislocation core radius equal to 2b(burgers vector). The arrow indicates the limit of solid solubility [59] 40
Figure 2.12 Lower yield stress of Fe-1.4 at% Cu alloy as a function of aging time at
5000C [60] 40
Figure 2.13 Mean particle diameter of copper precipitates as a function of the
square-root of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]
41
Figure 2.14 Number density of copper precipitates as a function of tempering time
in Fe-1.4 at% Cu alloy at 5000C [60] 42
Figure 2.15 Volume fraction of copper precipitates determined from measured
number density and mean diameter as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C. The relative amounts are coherent and non-coherent precipitates are shown schematically by dashed lines [60]
42
Figure 2.16 Mean composition of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [61] 42
Figure 2.17 Schematic representation of stress-assisted and strain-induced regimes
for mechanically-induced transformation [95] 46
Figure 2.18 J-integral toughness enhancement at Ms
σ for precipitation-hardened metastable austenitic steels [9] 51
xiii
Figure 2.19 Temperature dependence of the 0.2% tensile and compressive flow stresses [100] 54
Figure 2.20 Optimal Ni content vs. normalized austenite particle volume in Fe-
14Co-Ni system [100] 56
Figure 2.21 Conventional TEM dark field image of an interlath austenite film (A)
and dispersed intralath (B) austenite after 5070C/30minute + 4550C/7hour temper in AerMet100 [6] 57
Figure 2.22 Correlation of Cr and Ni from embedded austenite precipitates prior to
partitioning of STEM EDS signal into matrix and precipitate portions [6]. The data points are from multi-step tempered AerMet100 samples aged at 4050C for longer times after a short time 5070C nucleation treatment. 59
Figure 3.1 Schematic of the design optimization procedure 67
Figure 3.2 Power-law relationship relating hardness of related steels to yield stress
from experimental data from Foley [77] (circles), Kuehmann [2] (triangles) and Spaulding [138] (diamonds) shown in comparison to straight-line relationship for ideal plastic material 69
Figure 3.3 Graville diagram for determining susceptibility to HAZ cracking in
plate steels [137] 71
Figure 3.4 Change in hardness as a function of alloy carbon content for M2C
carbide strengthening contribution [12]. The arrows represent hardness increment of 175 VHN is achieved at C level of 0.05 wt% set for the alloy. Experimental results of other secondary hardening steels are shown 73
Figure 3.5 Graphical representation for contributions of the individual mechanisms
to achieve the strength goal equivalent to 389 VHN 73
Figure 3.6 Cr-Mo Phase Diagram at 9000C with alloy composition in atomic %:
Fe-0.234C-1.32Cu-6.21Ni-0.055V. This diagram shows the phase fields of the FCC austenite and FCC+M6C revealing that the M2C stoichiometry (red) line is well within the solubility limit 76
xiv
Figure 3.7 Driving Forces (in kJ/mole) for M2C carbide nucleation contour plot
varying at% (Mo) and at% (Cr) with superimposed M2C stoichiometric (red) line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.21Ni-0.055V 77
Figure 3.8 Driving Force (in kJ/mole) for M2C carbide nucleation contour plot
varying at% (Mo) and at% (V) with superimposed M2C stoichiometric line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.2Ni
79
Figure 3.9 Mo-V Phase Diagram at 9000C with alloy composition in atomic %: Fe-0.234C-1.32Cu-6.2Ni. This diagram shows the phase fields of the FCC austenite and FCC+V3C2 revealing that the M2C stoichiometric (red) line is well within the solubility limit 80
Figure 3.10 Change in hardness as a function of alloy copper content for BCC
copper strengthening contribution [59]. Experimental results of other copper strengthened steels are shown. The dotted line represents the best-fit line for one-half power law given by equation (3.4) 82
Figure 3.11 Room temperature (300K) austenite stability plotted as a function of
Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept B alloy corresponding to yield strength requirement of 150-180 ksi after extrapolation of data from previous alloys, AF1410 and AerMet100 87
Figure 3.12 Fraction of Ni in austenite and phase fraction of austenite in alloy vs.
mole fraction of Ni at 5000C with alloy composition in weight fraction: Fe-0.05C-3.65Cu-1.85Cr-0.6Mo-0.1V 89
Figure 3.13 Equilibrium composition of austenite as a function of alloy Cr content
(wt. fraction) at 5100C 90 Figure 3.14 Quasi-ternary section of the designed multicomponent alloy system at
5100C. Other alloying elements are fixed at Fe – 0.24C – 3.25Cu – 6.26Ni – 0.35Mo – 0.11V. The tie-triangles shown by thin solid lines indicate three-phase equilibrium between BCC Cu, austenite and ferrite. The dashed arrow traces out the trajectory of the austenite phase composition (solid dots) as a function of increasing alloy Cr content
92
xv
Figure 3.15 Equilibrium phase fractions at 5100C as a function of alloy Cr content (wt fraction) 93
Figure 3.16 Plot showing the variation of equilibrium mole fraction of different
phases in the alloy as a function of temperature, showing that the alloy is solution treatable at 9000C 94
Figure 3.17 Scheil simulation for evolution of the fraction solid with cooling for
designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%) in comparison with equilibrium solidification 97
Figure 3.18 Scheil simulation for composition profile of each alloying element after
solidification for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%). Solid fraction corresponds to position relative to dendrite arm center 98
Figure 3.19 Room Temperature (300K) stability of austenite as a function of
tempering temperature. The required stability is predicted for 4900C. 99 Figure 4.1 Charpy V-notch impact specimen dimensions (Standard ASTM E23)
with longitudinal axis corresponding to the L-T orientation 107 Figure 4.2 Tensile test specimen dimensions (Standard ASTM E23) 108 Figure 4.3 An example of magnetometry data processing to determine saturation
magnetization 112 Figure 5.1 Optical micrograph of the as-received plate viewed transverse to the
rolling direction at the oxide-metal interface after etching with 2% nital 120 Figure 5.2 Optical micrograph of the hot-rolled plate viewed transverse to the
rolling direction at the centerline after etching with 2% nital 121 Figure 5.3 Higher magnification optical micrograph of the hot-rolled plate at the
centerline 122 Figure 5.4 Line profile compositions for as-received material from oxide-metal
interface 123 Figure 5.5 Optical micrograph showing the oxide scale in the as-received plate 125
xvi
Figure 5.6 Relative sample length change and temperature trace during heating and cooling (quench) cycle from dilatometry experiment 126
Figure 5.7 Relative sample length change and temperature trace during heating,
cooling and isothermal hold at 3770C from dilatometry experiment 128 Figure 5.8 Volume fraction evolution of bainite as a function of time for isothermal
temperature of 3770C 129 Figure 5.9 Time-temperature-transformation (TTT) curve for bainite
transformation reaction 130 Figure 5.10 Experimental data fit to saturation volume fraction of bainite predicted
by model [26] using ASTM grain size number 15 132 Figure 5.11 Microstructure showing 60% bainite and 40% martensite mix after 2-
hour isothermal hold at 3600C during dilatometry 132 Figure 5.12 TTT diagram representing 1% bainite transformation calculated from
model [26] after calibration to fit experimental data 134 Figure 5.13 Isochronal (1 hour) tempering response of prototype alloy. The arrow
superimposed on the plot shows that the design objective is achieved by tempering at 5000C in agreement with design prediction. 136
Figure 5.14 Isochronal tempering response represented by Charpy toughness –
Vickers hardness trajectory. The label corresponding to each data point indicates the tempering temperature. 138
Figure 5.15 Hollomon-Jaffe Parameter correlating the hardness data obtained for
different tempering conditions in the overaged region 140 Figure 5.16 SEM micrograph of quasi-cleavage fracture surface for prototype
tempered at 4500C for 1 hour 141 Figure 5.17 SEM micrograph of ductile fracture surface for prototype tempered at
5250C for 5 hours 142 Figure 5.18 SEM micrograph of ductile fracture surface representing toughness
enhancement due to transformation toughening for prototype tempered at 5500C for 5 hours 142
xvii
Figure 5.19 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for prototype tempered at 5750C for 5 hours 143
Figure 5.20 Multi-step tempering treatments designed to maximize transformation
toughening response represented by Charpy toughness – Vickers hardness trajectory. The label corresponding to each data point indicates the tempering time during the first tempering step. The condition for the second step is listed on the legend. 145
Figure 5.21 SEM micrograph of ductile fracture surface representing toughness
enhancement due to transformation toughening for the 5500C 30min + 4500C 5hrs multi-step tempering treatment 148
Figure 5.22 SEM micrograph of a primary void in the fracture surface of prototype
for 5500C 30min + 4500C 5hrs multi-step tempering treatment 149 Figure 5.23 True stress – true plastic strain response. The stress (σ) - plastic strain
(εp) behavior is shown by solid lines until uniform elongation and by dotted line after necking. 151
Figure 5.24 Hardness – Yield Strength Correlation developed from previous data.
The heavy black points represent data from current investigation. 153 Figure 5.25 Charpy impact energy absorbed as a function of testing temperature for
prototype tempered at 5500C 30min + 4500C 5hr. Toughness increment of 30ft-lb due to dispersed phase transformation toughening is shown. The toughness band defined by 5 hour and 10 hour single step tempering is superimposed. 155
Figure 5.26 SEM micrograph of quasicleavage fracture surface showing flat facets
with dimples and tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 840C 157
Figure 5.27 SEM micrograph of mixed ductile/brittle mode fracture surface showing
microvoids with some tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 400C 157
Figure 5.28 SEM micrograph of purely ductile mode fracture surface showing
primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 200C 158
xviii
Figure 5.29 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 00C 158
Figure 5.30 SEM micrograph of purely ductile mode fracture surface showing
primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 1000C 159
Figure 5.31 XRD Pattern of prototype tempered at 5500C for 5 hours (lower plot)
scanned from 630 to 670 from 71.50 to 77.50 2θ angles shown in comparison with standard (upper plot) containing 4 vol% austenite
161 Figure 5.32 Bright-field TEM micrograph showing martensite laths in multi-step
tempered prototype at 5500C for 30min + 4500C for 5hrs 164 Figure 5.33 Higher magnification bright-field TEM micrograph showing martensite
laths in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs 164
Figure 5.34 Bright-field TEM micrograph showing dense dislocation structure
within a martensite lath in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs 165
Figure 5.35 3DAP reconstruction for prototype tempered at 4500C for 1 hour. The
elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis. 169
Figure 5.36 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C
5hrs. The elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis. 170
Figure 5.37 3DAP reconstruction for prototype tempered at 4500C for 1 hour
showing copper precipitates defined at 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. All other atoms in the reconstruction are not shown. z is the direction of analysis. 171
Figure 5.38 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C
5hrs showing copper precipitates defined by 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. z is the direction of analysis. 172
xix
Figure 5.39 Example of a cross-section of analyzed volume for prototype tempered at 4500C for 1 hour showing copper precipitates in red. All other atoms in the reconstruction are hidden. 174
Figure 5.40 Example of a cross-section of analyzed volume for prototype tempered
at 5000C 30min + 4500C 5hrs showing copper precipitates in red. All other atoms in the reconstruction are hidden. 174
Figure 5.41 Proxigram of all the solute species detected in the 4500C 1hr temper
specimen with respect to 10 at% copper isoconcentration surface in the analysis volume 180
Figure 5.42 Proxigram of all the solute species detected in the 5000C 30min + 4500C
5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume 181
Figure 5.43 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C
5hrs showing austenite defined by 10 at % Ni level isoconcentration surface overlaid on atomic positions of nickel and copper atoms. z is the direction of analysis. 183
Figure 5.44 One-dimensional composition profile along the atom-probe analysis
direction in the 5000C 30min + 4500C 5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume. z is the direction of analysis. 184
Figure 6.1 Toughness-yield strength comparison plot of Blastalloy160 with other
commercial and experimental steels 191
xx
LIST OF TABLES
Table 3.1: Target Chemical Driving Force (∆Gch) + Frictional Work (Wf) Value 86
Table 3.2: Amplitude of microsegregation with respect to each alloying element predicted by Scheil simulation at 95% solidification 98
Table 4.1A: Designed and Measured Composition (in wt. %) of Concept A alloy 102 Table 4.1B: Designed and Measured Composition (in wt. %) of Concept B alloy 102 Table 5.1: Saturation volume fraction of bainite as a function of isothermal
temperature 129
Table 5.2: Room temperature tensile properties of prototype 151 Table 5.3: Fitting parameters for Hollomon power law equation (5.1) from tensile
data of prototype (Fig. 5.23) 153 Table 5.4: Austenite Volume fraction measured by magnetometry for different
heat treatment conditions 163 Table 5.5: Comparison between the actual composition of prototype and the
compositions determined by 3DAP analysis 168 Table 5.6: Average copper precipitate compositions determined by 3DAP analysis
for selected heat treatment compositions. ND means not detected 176 Table 5.7: Average matrix compositions determined by 3DAP analysis for selected
heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected 177
Table 5.8: Average austenite composition determined by 3DAP analysis for
selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected 185
1
1. INTRODUCTION
Over the years, the multi-institutional university/government/industry
interdisciplinary Steel Research Group (SRG) program has directed its research at
scientific principles for the design of new classes of steels driven by specific property
objectives of importance to the government and industry. With scientific advances in
the past century, the property-driven view of structure and processing for the creation
of value has motivated the development of a systems approach in the design of
materials [1]. The systems approach to computational design of materials combines
materials science, quantum physics and continuum mechanics in the integration of
process/structure/property/performance relations for predictive design of high
performance steels as multilevel dynamic structures.
Throughout the history of materials development, there has been an
ever-increasing need for stronger, tougher, more fracture resistant and easily weldable
plate steels for structural applications at minimal cost. Unfortunately, however, any
increase in strength is rarely achieved without concomitant decreases in toughness and
ductility, which limits the utility of most ultrahigh-strength steels. The best
combinations of strength and toughness have usually been obtained from martensitic
microstructures as shown in Fig.1.1. High strength bainitic steels have not been as
successful in practice because of the coarse cementite particles in bainite that are
detrimental to toughness. If a mixed microstructure consisting of bainitic ferrite
separated by carbon-enriched regions of austenite is developed, it could be an ideal
2
combination for achieving our quantitative property objectives. The primary benefit
motivating the research of air-hardened steels containing bainite/martensite mixtures is
the ease of processing, which finally leads to a product with good performance at a
relatively lower cost. There is then the possibility of improving the strength and
toughness simultaneously using fine-grained bainitic ferrite plates and enhancing the
toughness by transformation toughening effects. Further improvements of strength can
be achieved with co-precipitation of alloy carbides and bcc copper for easily weldable
low-carbon steels [3].
Figure 1.1 KIC toughness vs. RC hardness cross-plot for ultra-high strength martensitic steels
3
It is now well established that the interaction of deformation-induced
martensitic transformation of dispersed austenite with fracture-controlling processes
such as microvoid induced shear localization results in substantial improvements in
fracture toughness called Dispersed Phase Transformation Toughening (DPTT). This is
the toughening mechanism modeled and investigated in this work. Transformation
toughening is partly attributed to modification of the constitutive behavior of the
matrix and partly to a modification of the stress state because of transformation volume
change [100]. Both the transformation behavior and the toughening effects are
controlled by the stability of the austenite dispersion. For transformation toughening,
the required stability of the austenite dispersion is quite high and can be achieved only
by size refinement and compositional enrichment of the austenite particles. The size
influences the characteristic potency of nucleation sites in the particles while the
composition influences the chemical driving force and interfacial friction for the
martensitic transformation. The size refinement and the compositional enrichment of
the austenite can be controlled with heat treatments such as multi-step tempering.
Combining new levels of strength, toughness and hydrogen resistance
while meeting processability requirements, the design addressed here will focus on a
new class of ultratough, weldable secondary-hardened bainitic plate steels for blast
resistant hull materials for the navy to adapt to a new “age of terror”.
4
1.1 Goals and Context
Looking ahead to the projected naval hull material requirements in the
year 2020, the primary design objectives motivating this research will be the
achievement of extreme impact fracture toughness (Cv > 85 ft-lbs corresponding to
fracture toughness, KId > 200 ksi.in1/2 and KIc > 250 ksi.in1/2) at high strength levels of
150-180 ksi yield strength in weldable, formable plate steels with high resistance to
hydrogen stress corrosion cracking (KISCC/KIC > 0.5). Because of difficulties in
measurement of KId and KIc fracture toughness at such extreme levels, toughness of
prototypes has been assessed by Charpy impact energy (CV) absorption measurements;
details of the KIc – CV and KId - CV toughness correlation will be discussed in Chapter
2. The primary design goals are marked by the star in the cross-plot of KIc fracture
toughness and yield strength illustrated in Fig. 1.2. This design aims to substantially
expand the envelope marked as “steels” to the top right corner of the plot.
5
Figure 1.2 KIC toughness vs. σ yield strength cross-plot for different classes of materials [10]
The initial research will focus on secondary hardening mixed
bainitic/martensitic steels produced as air-cooled plates, which appears to be the most
promising candidate class of steels.
Earlier SRG research [5,6] has emphasized achieving acceptable
toughness and hydrogen resistance in much higher strength steels needed for
lightweight aviation applications, integrating quantum mechanical modeling for the
enhancement of hydrogen resistance. With a new priority on toughness, the
“Cybersteel 2020” program of the ONR (Office of Naval Research) Grand Challenge
6
in “Naval Materials by Design”, of which this research is a part, expands quantum
mechanical modeling beyond intergranular hydrogen fracture resistance to address
alloying effects in transgranular cleavage resistance and the role of metal/ceramic
adhesion in voiding/microvoiding phenomena, integrating the latter into multiscale
mechanics of ductile fracture simulation. The resulting toughness models will be
combined with existing computational thermodynamics based models for phase
selection and microstructural dynamics in the integrated systems design of new alloys.
The design approach will build on the primary microstructural strategy ultimately
adding new optimization to both the dispersion geometry and metal/ceramic interfacial
characteristics associated with the combined effect of primary inclusions and
secondary grain-refining dispersions.
Looking at the overall program in a broad perspective, it involves a multi-
disciplinary team working together closely to insure purposeful modeling activities
supporting the materials design strategy of the SRG. Studies on grain-refining particle
dispersions are being performed for different systems starting with TiC by Professor
Freeman’s physics group at Northwestern University for selection of metal/ceramic
interfaces of importance to particle dispersions in steels. Thereafter, CSL-based slab
supercells are being constructed for FLAPW (Full-potential Linearized Augmented
Plane Wave) and FLMTO (Full-potential Linear Muffin-Tin Orbital) total energy
quantum mechanical calculations. Professors Liu and Moran in mechanical
engineering at Northwestern University are focusing on representation of particle
7
dispersion geometries based on current steel microstructures and subsequently assess
the roles of dispersion geometry and interfacial properties in multiscale mechanics
simulation of ductile fracture toughness. In parallel with these efforts, the materials
design synthesis of this thesis research integrates materials science design models such
as precipitation strengthening and dispersed phase transformation toughening. To
achieve the required strength level in weldable low-carbon air-hardened bainitic
structures, this will involve a combination of overaged alloy carbides and precipitated
Cu. Conceptual designs also integrate previous models of transformation toughening.
The ultimate design integration of the ONR project will thus combine new quantum
physics and multiscale mechanics models with our existing suite of computational
materials science design models to address new phase selection and quantitative
microstructural design for a new generation of “cybersteels” to meet the navy’s new
requirements.
8
1.2 Document Outline
This work applies the systems based approach to design ultratough high-
strength weldable plate steels by utilizing existing models where applicable and
developing new models where needed in order extend the properties of the existing
steels to higher performance levels. Chapter 2 gives a detailed description of the
systems based design approach and describes each of the subsystems involved in the
design with the current level of quantitative modeling available. Chapter 3 describes
the alloy design process detailing the concepts used. The material and experimental
procedures used in this study are outlined in Chapter 4. Chapter 5 presents the
properties obtained from the evaluation of the prototype and validates the design based
on microstructural characterization. Chapters 6 and 7 discuss the conclusions of this
investigation and suggestions for future research respectively.
9
2. BACKGROUND
2.1 Design Approach
Based on Cyril Smith’s [7] modern view of materials structure as
“universal multilevel structure with strong interactions among different levels…” this
materials design approach breaks down the complex nature of the structural hierarchy
to better understand the structure and property relations underlying the technological
and economic value of materials. Once the final goal has been set, the structure is
broken down into subsystems with graphical representation of the interactions through
a system flow block diagram. The flow block diagram represents the key
microstructural subsystems, links them to the properties they control and then to the
stages of processing that govern their dynamic evolution. Because of the complex
nature of materials, it should be realized that the interaction between the subsystems is
as important as the subsystems themselves. The systems analysis is then applied to
identify and prioritize the key structure-property and processing-structure relations.
Optimization of such a complicated system can thus be effectively achieved by the
method of systems design. Fig. 2.1 describes the systems approach that will be used in
the thesis to design steel with the specified strength, toughness levels as well as
optimum weldability and hydrogen resistance.
10
PROCESS STRUCTURE PROPERTIES
PERFORMANCE
MatrixBainitic Ferrite / Martensite
Morphology (lower bainite/lath martensite)Composition
Kinetics
MatrixBainitic Ferrite / Martensite
Morphology (lower bainite/lath martensite)Composition
Kinetics
Grain Boundary ChemistryCohesion Enhancement: B,W
Impurity Gettering: La,Zr
Grain Boundary ChemistryCohesion Enhancement: B,W
Impurity Gettering: La,Zr
InclusionsMultiphaseInterface
Distribution
InclusionsMultiphaseInterface
Distribution
Austenite DispersionStability (Size, Composition)
AmountDilatation
Austenite DispersionStability (Size, Composition)
AmountDilatation
Grain Refining Dispersion
d/fMicrovoid Nucleation Resistance TiCx
Grain Refining Dispersion
d/fMicrovoid Nucleation Resistance TiCx
Grain Refining Dispersion
d/fMicrovoid Nucleation Resistance TiCx
Strengthening Dispersion(Mo,Cr,V,Fe)2C
BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6
Strengthening Dispersion(Mo,Cr,V,Fe)2C
BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6
Strengthening Dispersion(Mo,Cr,V,Fe)2C
BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6
Tempering
Cooling Rate
Solidification
Deoxidation
Refining
Solution Treatment
Hot Rolling
Toughness
Strength
Weldability
HydrogenResistance
Figure 2.1 Systems design chart for blast resistant naval hull steels
With toughness being a major priority for this design, the matrix was
chosen as a secondary hardened bainite/martensite mixture, in which cementite
particles should be eliminated, as they are detrimental to the toughness of the steel.
Bainite may have a large variety of morphologies and have intermediate properties
between pearlite and martensite. These intermediate properties of bainite offer more
degrees of freedom by designing the kinetics of formation to achieve the desired matrix
toughness. In addition, an optimum-stability austenite dispersion in the
11
bainitic/martensitic matrix can also help in increasing the toughness of the steel.
Several investigators [8,9] have reported exceptionally large fracture toughness values
in high-strength precipitation-hardened metastable austenitic steels. This remarkable
increase in the fracture toughness is attributable to the process of transformation
toughening which will be discussed in greater detail later. Recent SRG studies [128]
have also shown that fine Ti(C,N) inclusions have contributed to increasing the
fracture resistance by delaying the coalescence of microvoids among the primary
voids. The Ti(C,N) particles also have a grain refining effect helpful for strength and
toughness. Studies by Garrison [140] have suggested that the resistance to primary
void formation and coalescence is proportional to inclusion spacing. It is thus desirable
to reduce the volume fraction of inclusions or coarsen inclusions for a given volume
fraction. This can be achieved by clean melt practices and tight composition control.
However, engineering design fracture toughness parameters like KIc and KId are
difficult and expensive to measure. Thus for preliminary design analyses, small-scale
inexpensive fracture measurements like Charpy V-notch impact energy (CV) values can
be used to estimate KIc and KId. Studies of fracture toughness dependence on loading
rate measured over a temperature range [134] have shown that KIc fracture toughness
values under static and intermediate loading are about 20% higher than the KId
measured under impact loading. On the basis of various previous investigations,
Barsom and Rolfe [134] established a correlation between KIc and CV test results:
(2.1) VIC ACK =2
12
where A is a constant of proportionality. Fitting equation (2.1) to results from high Ni
steels shown in Fig. 2.2, an empirical correlation can be established for the class of
steels explored in this study.
Figure 2.2 Correlation between KIc and CV test results [134] for high Ni steels
According to this relationship, the CV impact toughness objective of 85 ft-lbs
corresponds to a KIc fracture toughness under static loading of 250 ksi.in1/2 and a
dynamic KId of 200 ksi.in1/2.
13
A fine carbide dispersion must be obtained in order to achieve the
desired strength level. Coherent M2C carbides have been used in secondary hardened
steels that are currently in use [11]. Previous work [12] to optimize the carbide particle
size for maximizing the strength has shown that 3nm carbide precipitates provide
minimum distance between particles within the Orowan looping regime for a
maximum barrier to dislocation movement. Thermodynamics and kinetics of carbide
precipitation has to be controlled to obtain fine-enough M2C carbide dispersion. The
driving force for M2C nucleation should be maximized by proper control of the amount
and ratio of carbide formers in the alloy to refine the M2C particle size. Cementite
dissolution must accompany M2C carbide precipitation to attain the desired toughness
levels because coarse cementite particles are extremely deleterious as microvoid
nucleation sites. Tempering times should also be minimized to prevent impurity
segregation at grain boundaries.
Even if we maintain low alloy carbon levels, steels containing higher
alloying content might help in achieving the desired combination of mechanical
properties, but they reduce the weldability of the material by increasing hardenability.
For any structural material, the heat-affected zones (HAZ) adjacent to the welded joints
are considered to be the weakest links. Weldability of steels is controlled by both the
matrix and the strengthening dispersion structures. As a rule of thumb, for adequate
weldability of the steel C content of the alloy should be kept below 0.15 wt %. This in
turn limits the C available for M2C strengthening. For the bainitic matrix, if we modify
14
the hardenability of the steel, we can obtain bainite with a much lower cooling rate.
This becomes a trade off since weldability can deteriorate as the hardenability
increases.
Ultra-high strength steels are prone to a decrease of fracture toughness
in aqueous environments due to hydrogen assisted cracking. This reduction of
toughness is caused by intergranular brittle fracture associated with impurity
segregation to grain boundaries, which may reduce toughness of the steel by as much
as 80% in a corrosive environment. The common impurities in steel are P and S, both
of which are embrittlers since they have lower free energy on a surface than at a grain
boundary. So the most effective way of reducing them is by cleaner processing
techniques or impurity gettering. Impurity gettering can tie up P and S as stable
compounds formed during solidification. La and Zr have been found to be effective
impurity gettering elements. Another approach to minimize impurity effects is by
design of grain boundary chemistry. By placing elements like W and Re [13,14]
preferentially on the grain boundaries that enhance grain boundary cohesion is
beneficial to the stress corrosion cracking resistance. Small amounts of B also help in
grain boundary cohesion.
15
2.2 Bainitic Transformation
Bainite grows from austenite as a non-lamellar aggregate of ferrite laths
or platelets and carbides forming in a coupled manner. These aggregates of bainitic
ferrite laths/platelets are called sheaves and the individual sub-structures are called
sub-units. Within a sheaf, the sub-units tend to be in a common crystallographic
orientation. Bainite forms either during the isothermal transformation condition or
athermal treatments at cooling rates too fast to generate pearlite but not rapid enough to
produce martensite. Fig 2.3 [15] gives a schematic representation of a TTT (Time-
Temperature Transformation) diagram showing flat tops on the bainite curve
representing bainite start (BS) temperature.
Figure 2.3 Schematic representation of TTT diagrams illustrating the flat-tops of
bainite C-curves [15]
16
Depending on the cooling rate or the isothermal hold temperature, there
are two major morphologies of bainite, upper bainite and lower bainite. Upper bainite
forms at temperatures just below that of pearlite formation, while lower bainite forms
at temperatures closer to martensite start (MS) temperature. Fig. 2.4 [16] displays
representative TEM micrographs of upper bainite (a) and lower bainite (b).
Figure 2.4(a) TEM micrograph of upper bainite with austenite (A) between the lath sub-units in Fe-0.6%C-2.0%Si steel transformed at 4000C (magnification, 40000X) [16]
17
Figure 2.4(b) TEM micrograph of lower bainite with midribs in a 1.10% C steel transformed at 1900C for 5hours [16]
The mechanism of bainitic transformation has been the subject of
numerous investigations and studies [17-19]. Bainitic transformation occurs in two
separate stages that consist of the growth of ferrite followed by precipitation of
carbides, unlike pearlite where ferrite and cementite grow cooperatively. This means
that growth rates are coupled in a manner that excess solute displaced during ferrite
growth is incorporated in cementite. The relatively high dislocation density of bainitic
ferrite indicates that it forms by a shear displacive mechanism. But unlike martensitic
transformations, in which concentrations of both interstitial and substitutional atoms
18
are identical to those of parent austenite, bainitic ferrite seems to have different carbon
contents compared to austenite although the substitutional alloy content is the same.
This results from the significant difference in the mobility of carbon atoms and
substitutional atoms in the bainitic transformation range and is known as the
paraequilibrium condition. Thus, bainite is considered to form by a coupled
diffusional/displacive transformation mechanism [20-21]. After nucleation of the
bainitic laths, growth is limited by the partitioning of carbon into the remaining
austenite. As the austenite becomes enriched in carbon, bainitic growth rate slows
down as the austenite carbon content approaches the paraequilibrium limit at which
point bainitic ferrite ceases to grow until carbides precipitate.
2.2.1 Carbon Redistribution under Paraequilibrium
The formation of bainite enriches the carbon content of the residual
austenite. Substitutional alloying elements are unable to partition during transformation
in the time scale of experiments. Since carbon is a fast diffusing interstitial element it
redistributes between phases and reaches equilibrium under “paraequilibrium”
constraint. Bainite formation begins with nucleation of ferrite of paraequilibrium
carbon concentration, so the residual austenite is enriched with respect to carbon [15].
When substitutional alloying elements redistribute during transformation it occurs
under orthoequilibrium. Paraequilibrium is defined as a kinetically constrained
19
equilibrium in which the diffusivity of the substitutional species is negligible compared
to that of the interstitial species.
The paraequilibrium constraint is useful in modeling the
thermodynamics and kinetics at different stages prior to the bainite transformation
[22]. Since substitutional alloying elements are not allowed to partition, the
thermodynamic behavior of these elements is expressed by one hypothetical element
N. Thus, the paraequilibrium model is defined by a uniform carbon potential and
uniform site fraction of substitutional elements across the transforming interface. For
ferrite(α)/austenite(γ) transformation, the thermodynamic conditions for
paraequilibrium are given by
γα µµ CC = (2.2)
γαjj yy = (2.3)
)()( ∑ ∑⇒=⇒j j
jjNjjN yy γγαα µµµµ (2.4)
where µip represents the chemical potential of elements i in phase p and yj represents
the site fraction of the substitutional elements j (= Fe, Al, Co, Cr, Cu, Mn, Mo, Nb, Ni,
Si, Ti, V, W) in the corresponding phase.
20
For a system containing both substitutional(j) and interstitial(C and N)
species, the site fractions are related to the mole fractions(x) by:
C
jj x
xy
−=
1 (2.5)
C
CC x
xqpy
−=
1 (2.6)
where, p=1 and q=3 for ferrite and p=q=1 for austenite, according to the two sublattice
model [23].
2.2.2 Kinetics of Bainite Transformation
Unlike martensitic transformation, the progress of bainite
transformation can be represented by a C curve on a TTT diagram with a well-defined
incubation period before isothermal transformation [24]. Since bainite forms at a more
elevated temperature than martensite, less driving force is available for transformation
of austenite. Ko and Cottrell [25] suggested that coherent growth of bainite can occur if
the strain due to density change is relieved by diffusion of carbon from bainite that
would lead to reduction of free energy. Bhadeshia [15] summarized the bainite reaction
as a coupled mechanism of diffusion and interface migration so that the carbide
precipitation within ferrite (for lower bainite) or carbon rejection to austenite (for upper
bainite) takes place at the moving interface. Fig 2.5 gives a schematic view relevant to
the kinetic description of the bainite reaction.
21
Figure 2.5 Schematic illustration of bainite microstructural features relevant to the kinetic description [15,26]
2.2.2.1 Bainitic Ferrite Nucleation and Growth
As bainite transformation occurs by coupled diffusional/displacive
transformation, the driving force to form bainite consists of two terms: one is to
overcome the critical energy associated with the shape change of lattice from austenite
to bainitic ferrite and the other is the carbon partitioning from supersaturated bainitic
ferrite to retained austenite. This is illustrated schematically in Fig 2.6 and is
represented by equations (2.7) and (2.8) where x0 is the nominal carbon composition,
xα and xI are the carbon concentrations of α and γ at the interface respectively,
is the chemical driving force to form bainite with carbon concentration ),( TxGchem ααγ →∆
22
xα at temperature T, is the energy dissipation associated with carbon diffusion
from bainite to retained austenite,
dG∆
critG∆ is the critical driving force for displacive
transformation.
Figure 2.6 Schematic illustration of thermodynamics to determine the driving force for bainitic transformation [21,26]
)(2),( αµααγ σ xW
ndGGGGTxG el
dcritdchem +++∆=∆+∆=∆ → (2.7)
where is the elastic strain energy per unit volume associated with distortions in the
nucleus interface plane, σ is the nucleus specific interfacial energy, n is the potency of
a nucleation site expressed as thickness in numbers of crystal planes, d is the crystal
interplanar spacing and W
elG
µ is the frictional work of interfacial motion.
23
)()()()()1( 00 ICCIMMd xxxxxxG γγα
γγα µµµµ −+−−=∆ (2.8)
where and are the chemical potentials of alloying elements in γ with
carbon concentrations x
)( 0xMγµ )( IM xγµ
0 and xI respectively.
Bainite transformation starts at heterogeneous nucleation sites of
existing defect embryos in austenite, which grow as individual sub-units coupled with
carbon diffusion at the interface. This transformation accompanied by shear causes
plastic deformation leading to large dislocation density both in the parent and product
phases. The forest dislocation friction stops the motion of the glissile sub-unit, which
grows only to a limited size, much smaller than the austenite grain size. Grujicic et al
[27] established the theory of the detailed mechanism of halt by plastic strain. Thus,
the sheaf as a whole grows by repeated nucleation of new sub-units from the tip of
those already formed. Fig. 2.7 illustrates the nucleation and growth of a sub-unit
showing the dependence of nucleation velocity on the length of sub-unit.
24
Figure 2.7 Schematic illustration of nucleation/growth velocity as a function of
bainite sub-unit length [26]
Heterogeneous nucleation due to the displacive mechanism becomes
more frequent as defects are introduced into austenite by deformation although their
growth is soon terminated as the moving interface encounters accumulated
dislocations. Accelerated transformation rate in the initial stage of transformation can
be explained by the shifted distribution of defect potency in both pre-existing and
autocatalytically formed sites, while the average volume of sub-units is almost constant
and independent of volume fraction [28]. Based on previous studies on potency
distribution of pre-existing nucleation [29] that increases monotonically with
decreasing defect potency following an exponential function, Lin et al [30] found that
25
the autocatalytic defect potency distribution follows a Gaussian function. The defect
potency size distribution of both pre-existing and autocatalytic defects is given in Fig.
2.8 where nm* and nb* are the respective critical defect potency sizes for martensitic
and bainitic phase transformations. Both of these parameters can be determined from
the critical condition of nucleation. The accumulated distributions for the preexisting
and autocatalytic defect potencies can be calculated by equations (2.9) and (2.10)
respectively.
Figure 2.8 Schematic representation of potency size distribution for pre-existing
and autocatalytic defects [26,30]
26
The cumulative density of preexisting nucleation defects is represented
by the exponential function [31]:
).exp()().exp()()( 121
0 nDkknNndnNnN mv
nii αα −+=−=′= −
∞
∫ (2.9)
where Nv0 is the total number density of preexisting defects with all potencies, α is a
factor that represents the distribution shape and k1, k2 and m1 are parameters that
describe the grain-size (D in meters) dependence of Nv0.
The autocatalytic defect size distribution can be described as a Gaussian distribution
[30]:
⎥⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ −−== ∫
∞
σ21
21)()( max
nnerfPndnPnPn
ii (2.10)
where, Pmax, ⎯n and s are the amplitude, mean and standard deviation of the
distribution respectively, each of which depend on the grain size.
Olson et al [21] proposed a kinetic model for bainitic transformation by
considering transformation of the substitutional lattice by a displacive mechanism
while carbon atoms undergo paraequilibrium partitioning between the parent and
product phases. They assumed that the rate at which the ferrite(α)-austenite(γ) interface
moves depends both on the intrinsic mobility and the ease with which the partitioned
solute (i.e., carbon) can diffuse ahead of the moving interface. Since both the processes
are coupled, the interfacial velocity calculated from interfacial mobility must equal that
computed from the diffusion ahead of the interface. As there are three unknowns to
27
)
solve for (supersaturation, austenite composition at the interface and growth rate) but
only two velocity laws available, they attempted a more complete analysis by utilizing
an additional interface response function derived by Aziz [32-34] for the case of solute
trapping during rapid solidification processes. Thus, based on these interface response
functions two kinetic relationships were set up as given by
(2.11) kdn VVnV ==)(
Vn(n) is the nucleation velocity for potency n as discussed earlier;
Vd is the steady-state growth velocity of ferrite of constant composition xα in a steel of
composition⎯x (transformed at temperature T) expressed in terms of carbon
concentration in austenite at the interface xI ; and
Vk is the velocity response function determined from solute trapping law relating
interfacial velocity to the partitioning coefficient kp(=xα/xI).
The set of three non-linear equations, two kinetic equations given by equation (2.11)
and the thermodynamic driving force equation (2.7) are used to solve for the three
unknowns Vn (n), xa and xI.
Considering the sequential growth characteristics of bainite sub-units as
in Fig 2.7, the nucleation velocity of the defect embryo is the rate controlling term in
determining the bainite start kinetics. The number of nucleating defects available to
operate at any given time and temperature per unit volume of alloy has been described
as [35]:
1)(( bvbiit fNfPNN −−+= (2.12)
28
which leads us to the evolution equation for the number of sub-units (Nv) of potency n
)()1)](()()()[()()(
bbvbiinv fVfnNfnPnNnVnCdt
ndN−−′+′= (2.13)
with Nv(n) = 0 for all n > nb* at t = 0.
fb : Volume fraction of bainite, ∑= ))(()( nNfVf vbb
V (fb) : Mean volume of bainite sub-unit
C (n) : Time scaling factor with geometry effects due to defect size (calibrated against
experimental data)
and Ni and Pi are defined in equations (2.9) and (2.10) respectively.
For a small volume fraction of bainite (fb) at the beginning of bainite
transformation, the number density (Nv(n)) of defects already transformed to bainite is
considered negligible. Thus equation (2.13) can be simplified to:
)1)(( bbb fBfA
dtdf
−+= (2.14)
where A and B are coefficients derived by approximating equation (2.13), and the
bainite start time is computed when the volume fraction of bainite (fb) is 0.01.
Based on the evolution equation (2.12), an executable program (“Runbmk”) to predict
bainite transformation kinetics under isothermal condition was developed by Jou et al
[26].
29
2.3 Strengthening Dispersions
The most effective mechanism of strengthening in high strength alloys
is achieved through fine dispersion of precipitates. The extent of strengthening depends
on particle size and volume fraction (mean particle separation distance is defined by
these two factors), particle shape, chemical and mechanical properties and coherency
with the matrix [36]. These factors determine the degree and the means of particle-
dislocation interaction. For cases in which the dislocation shears a particle, the
strengthening mechanisms by precipitate dispersions include coherency strain,
modulus effect, chemical, stacking fault and order hardening. Non-deforming hard
particles that cannot be cut force the dislocations to bow around them by the Orowan
mechanism.
The contribution to strength of the precipitate dispersion depends on
whether dislocation “cutting” or “bowing” is the predominant slip mechanism.
Coherent boundaries of small size or of low elastic modulus precipitates generally
result in dislocations passing through or cutting the particle. As the particles grow or
the particle-matrix interface becomes disordered, shearing becomes more difficult. The
increase in size usually leads to loss of coherency and does not permit the dislocation
to pass through the particle. Thus, there occurs a transition between the shearing
mechanism to Orowan bypass. Dislocations now have to bow around the particles.
While the dislocation is pinned by the particle, the free segments continue to glide
under applied stress. After the particle is circumvented the dislocation ends combine
30
and leave behind a loop. The Orowan mechanism of particle bypass becomes easier as
the particles coarsen at a constant volume fraction and consequently the strength
decreases. This offsets the increase in strength as shearing becomes more difficult with
increasing particle size and we reach a condition of maximum stress to move the
dislocations. Fig. 2.9 [12] illustrates this effect.
Figure 2.9 Schematic representation of transition from shearing to looping mechanism as a function of particle size at constant volume fraction [12]
31
2.3.1 Carbide Strengthening Dispersion
Strengthening in secondary hardened ultrahigh strength steels is
achieved through fine scale precipitation of a carbide (M2C) phase. Many researchers
have extensively studied carbide strengthening of steels due to its importance in the
modern industrial world. An earlier paper by Jack and Jack [37] has comprehensively
summarized previous research of carbides in steels. Gil Speich [38] demonstrated
carbide strengthening in his original research on ultrahigh strength Co-Ni steels.
Alloy carbides precipitate to give substantial strengthening during the
secondary hardening (4500C to 7000C) tempering stage. To achieve a higher
strength/toughness combination, the alloy carbide precipitation reaction must be
carried to completion so that the relatively coarse cementite carbides, which act as
microvoid nucleation sites limiting ductile fracture resistance, are eliminated. The
strength of these overaged precipitation hardened structures is controlled by the
Orowan bypass mechanism. For a given volume fraction of carbides (determined by
carbon content), a fine dispersion provides higher strength since the strength is
determined by the mean free path between the dislocations. However as
aforementioned, dislocations will shear the particles instead of looping them if the
particles are too fine. So an optimal particle size is desired at the transition between
particle shearing and Orowan bypass to maximize strengthening. During the secondary
hardening stage, a variety of alloy carbides form, namely MC, M2C, M7C3, M23C6
(M = Cr, Mo, V, W) depending on the alloy composition thermodynamics and kinetics.
32
Of these carbides, M2C is the preferred strengthening precipitate due to its coherent
nature of precipitation in the martensitic matrix that ensures finer size and helps in
microvoid nucleation resistance. Although, M2C is not the most stable carbide phase at
intermediate tempering temperatures (~5000C), it is the phase with the highest driving
force for precipitation from martensite [39]. It also dissolves the relatively coarse
embrittling cementite phase as carbon partitions to the alloy carbides. Previous
researchers [12,40,41] have determined the optimal size distribution of the carbides for
maximum strengthening at a given carbon content. The critical M2C diameter for peak
strengthening has been found to be 3nm, corresponding to the transition of the
deformation mechanisms.
It is necessary to control the thermodynamics and kinetics of carbide
precipitation in order to obtain a fine M2C carbide dispersion. It is desirable to
maximize the driving force for M2C nucleation to obtain a fine initial dispersion. M2C
nucleation driving force can be increased by controlling the amount and ratio
(stoichiometric balance) of carbide formers in the alloy. Mo2C is more stable than
Cr2C, so Mo has a positive effect on M2C nucleation when substituted for Cr [42].
However, segregation during solidification limits the Mo content in steels. Small
additions of V greatly increase the M2C driving force, but it is limited by V’s low
solubility.
33
Figure 2.10 M2C carbide precipitation behavior in AF1410 steel as a function of tempering temperature at 5100C following 1 hour solution treatment at 8300C [42]
34
Montgomery [40] and Olson [42] have done a comprehensive
investigation with integration of previous research [43-53] on thermodynamics and
kinetics of M2C carbide precipitation in AF1410 alloy. The results are summarized in
Fig 2.10 which shows the M2C carbide particle size, shape, number density, volume
fraction, lattice parameters, composition and overall hardness as a function of
tempering time at a standard secondary tempering temperature of 5100C, following
solution treatment of 1 hour at austenizing temperature of 8300C. The information
obtained from this summary plot (Fig 2.10) helps in improving alloy compositions for
more efficient strengthening from precipitation kinetic theory through control of
appropriate scaling factors.
The average particle size of rod-shaped M2C carbides has been
expressed as equivalent diameter of a sphere of diameter ds. The analysis of the SANS
(Small Angle Neutron Scattering) data and TEM (Transmission Electron Microscopy)
of extracted particles helped in determining the evolution of the carbide aspect ratio, β
smoothly varying from near unity (at initial nucleation) to 4 (near equilibrium). The
time dependence of the average particle size with smooth transition in aspect ratio
evolution indicates transition from nucleation to coarsening with suppressed growth
characteristic of precipitates at high supersaturations as theorized by Langer and
Schwartz [49]. They studied that the average particle size is always close to critical
particle size for growth or dissolution at high supersaturation (work of formation of
critical nucleus, kTW 10* ≤δ ). At high supersaturations, the nucleation rate is high,
35
which in turn reduces the supersaturation rapidly. Now, the critical particle size
increases as supersaturation decreases during the nucleation process. Thus, particles
that were above critical nucleus size now become subcritical and dissolve as
supersaturation decreases. This competition between the nucleating particles and
critical particle size inhibits the growth of the particle distribution. The average particle
size is initially governed by the nucleation process and smoothly transitions to a regime
governed by coarsening, as shown by the top two plots of Fig 2.10. This shows that the
critical particle size and coarsening rate determine the effect of coherency (or particle
size) on precipitation and hence the strength. This fact is supported by plot 3 of Fig
2.10 where a second stage of nucleation, between 1 and 2 hours, reduces the average
particle size through increased number of finer particles, passing the number density
Nv, through a maximum. This observation that the average particle size never differs
greatly from critical size because of suppression of the growth region at high
supersaturation constitutes a useful phenomenon for maintaining the finest possible
particle size at high supersaturation. The volume fraction curve (plot 3) shows that the
precipitation is complete after 10hr tempering with complete dissolution of transient
cementite. The lattice parameter plot (plot 4) gives conclusive information about the
interfacial coherency of the carbide particles. In the coherent state, the precipitate tends
to reduce the elastic energy by shifting composition to reduce the overall lattice
deformation relating the coherent HCP carbide to the BCC matrix. The observed lattice
parameter shift indicates that the precipitates are coherent below 10hr tempering and
36
become fully incoherent beyond 100hr. Based on the M2C composition dependence on
the lattice parameter (plots 4 and 5), the depletion of C and enrichment of Fe are
consistent with observed lattice parameter shifts. The lattice parameter shifts and the
volume fraction measurements also suggest that the carbides are close to coherent
equilibrium after an 8hr tempering treatment. The hardness curve (plot 5) further
verifies the completion of M2C precipitation at 8-10hrs of tempering corresponding to
the overaged state, which controls the strength by Orowan bypass mechanism.
Similar experiments by Yoo and others [54-56] have demonstrated the
tempering evolution of M2C carbides in AerMet100, an alloy having superior
properties than AF1410. The reason for higher strength is attributed to finer particle
size distribution and higher carbide volume fraction in AerMet100 compared to
AF1410. Thus, through the investigative study of evolution characteristics of M2C
carbide precipitation, it can concluded that by the control of the appropriate scaling
factors, improved alloy compositions can be designed which will lead to more efficient
strengthening and hence improved properties.
2.3.2 Copper Strengthening Dispersion
The precipitation of copper as a strengthening dispersion in iron and
steels has been extensively studied in the past [57-70] and has been basis for the
development of high strength, low alloy steels (HSLA) for applications particularly in
shipbuilding, pressure vessels and gas pipelines [71-76]. Copper precipitation is used
37
as an alternative strengthening mechanism in these steels with comparatively low
hardenability, where the limited strengthening by alloy carbides because of low carbon
requirements is partially recovered [77]. The unusual feature of this system is that the
high-work hardening rates associated with overaging is not observed, i.e., the
precipitates stay shearable even in the overaged conditions. Thus, the standard models
associated with peak hardening to the shearing/bypass transition as described in
Section 2.3 cannot be applied in this case.
The precipitation sequence in copper bearing steels has been well
established from several studies [60,63,71,78,79]. Initially, copper precipitates from
the supersaturated solid solution as metastable body centered cubic (BCC) phase,
which is fully coherent with the ferritic/martensitic matrix. These coherent precipitates
with an average diameter of 1-5 nm are not pure copper, containing a significant
amount of iron [61,71]. As these BCC-copper precipitates reach a critical size of 2.3 to
3 nm [71,80], a martensitic transformation to the intermediate 9R structure occurs
[63,69,79,81,82]. The 9R structure can be regarded as a face centered cubic (FCC)
lattice with intrinsic stacking faults on every third close-packed plane [82]. These
intermediate 9R precipitates were observed [65] to grow subsequently as spherical,
multiply-twinned particles up to ~ 17 nm. At sizes larger than 17 nm, a second
transformation to more stable 3R structure occurs. The 3R corresponds to an
untwinned distorted FCC structure. The 3R evolves into the equilibrium FCC ε-phase,
suggesting that lattice relaxation occurs during the diffusional growth of the 3R
38
precipitates. These incoherent equilibrium ε-phase copper precipitates formed at high
aging temperatures and longer aging periods have ellipsoidal [65] or rod-shaped with
hemispherically capped [58] morphology.
The contribution of the precipitates in the strengthening mechanism is
complicated by the precipitation sequence [70]. It is well established that the
strengthening precipitates in the peak aging condition have a BCC structure. However,
studies [60,70] show that maximum strength is reached well before precipitation is
complete. This is attributed to dynamic strain-induced martensitic nucleation and
subsequent growth of the precipitates from the BCC to the 9R structure continuously
throughout the broad age hardening peak. Precipitation hardening in the Fe-Cu system
has been described by the Russell-Brown model [59] in which the strengthening is
related to the difference in the shear modulus between the copper precipitate and the
ferrite matrix. Since BCC copper precipitates are assumed elastically softer than the
matrix, no increase in work hardening results from overaging and the strength is solely
achieved by particle cutting. The strength contribution from chemical hardening caused
by increase in total particle-matrix interfacial energy when a dislocation cuts through a
particle is thought to be much smaller than the contribution from modulus
strengthening. The Russell-Brown model proposed a theory based on interaction
between matrix slip dislocations and copper particles of lower elastic modulus and
accounted for the observed yield strength and work hardening behavior. They
considered a random distribution of spherical precipitates having lower modulus than
39
the matrix and calculated the yield stress dependence both in the underaged and the
overaged state. The peak aging stage is the upper limit of the underaged state when the
radius of the precipitate reaches twice the core radius of the dislocation. So applying
modulus strengthening [83,84] to the stress solution at which a dislocation can move
through an array of softer copper precipitates in the underaged state, they derived that
the maximum strength which can be achieved is proportional to the square root of the
volume fraction of the precipitate phase. Fig. 2.11 is a plot of the experimentally
available data for maximum hardening increment against volume fraction, f1/2. Thus,
according to this model, a copper precipitation strengthened system can be designed by
evaluating the phase fraction of the metastable BCC precipitate at the tempering
temperature. Osamura et al [64] proposed an alternative hardening mechanism by
analyzing structural parameters during the interaction of dislocations with precipitates,
assuming that hardening during initial stages of precipitation is controlled by
coherency strains. Charleux et al [66] also proposed a hardening model combining the
viscous motion of screw dislocations and the dislocation-precipitate interaction.
However, recently Deschamps et al [70] investigated the various models and
confirmed that the Russell-Brown model is in very good agreement with their
experiments.
40
Figure 2.11 Plot of maximum increase in yield strength vs. (volume fraction of atoms)1/2. The points represent experimental data and the line is predicted by the theory for a dislocation core radius equal to 2b(burgers vector). The arrow indicates the limit of solid solubility [59]
Figure 2.12 Lower yield stress of Fe-1.4 at% Cu alloy as a function of aging time at 5000C [60]
41
Goodman et al [60,61] studied the size, number density and
composition evolution of the copper precipitates during the early stages of precipitation
in a Fe-1.4 at. % Cu at 5000C using Field-Ion Microscopy (FIM). Particles as small as
8Å were detected, most of which were spherical with a few rod-shaped exceptions. The
yield stress dependence on the aging time at 5000C is given in Fig 2.12. Fig 2.13 shows
the evolution of the mean size of the particles. It was confirmed that the mean diameter
of the particles at maximum strength is about 2.4nm. The linear dependence of the plot
between mean particle diameter and time (t1/2) shows that the growth of the copper
particles is purely diffusion controlled (slope = 2αD1/2; [84] where α is the growth
coefficient and D is the diffusivity). Fig. 2.14 and Fig. 2.15 give the particle number
density and volume fraction as a function of aging time respectively.
Figure 2.13 Mean particle diameter of copper precipitates as a function of the square-root of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]
42
Figure 2.14 Number density of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]
Figure 2.15 Volume fraction of copper precipitates determined from measured number density and mean diameter as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C. The relative amounts of coherent and non-coherent precipitates are shown schematically by dashed lines [60]
Figure 2.16 Mean composition of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [61]
43
The number density remained nearly constant at 1018 precipitates/cm3
until the peak strength was reached and then decreased to 1016 precipitates/cm3 as the
alloy overaged and softened. The volume fraction of the precipitates was calculated
from the number density and the mean size of the particles. It shows that the volume
fraction increases gradually until the mean particle size reaches 10nm. The mean
composition evolution of the copper precipitates as a function of aging time is given in
Fig 2.16. It shows that during the initial stages of precipitation, the particle
compositions remain constant at nearly 50% Cu until the peak aged condition. This
contradicts values reported by Kampmann and Wagner [62] who suggested by
thermodynamic analysis that precipitates with radius greater than 0.5nm are expected
to be almost pure copper. However, for longer tempering times, the average
composition reached close to 100% Cu although some precipitates were observed to
contain appreciable amounts of iron.
In addition to strengthening by a fine dispersion of coherent
precipitates, copper precipitates act as heterogeneous nucleation sites for other phases
such as, Ni-rich Ni3(Ti,Al) in maraging steels [86] and α-Fe in iron-based amorphous
glass [87,88]. Earlier work by Hornbogen [57] suggested that copper precipitates
nucleate by homogeneous clustering in a matrix of α-iron. However, recent studies by
Dunne et al [75], Maruyama et al [81] and Deschamps et al [70] have shown that
nucleation of copper precipitates is promoted by the presence of dislocations through
TEM and SAXS (Small Angle X-ray Scattering) observations where most of the
44
copper clusters precipitated on martensite laths and dislocations during isothermal
aging.
The influence of copper precipitation on impact toughness in low
carbon steels has been studied by Aroztegui et al [89]. They observed no evidence of
copper precipitates aiding in nucleating cleavage cracks and their influence on fracture
stress was negligible. Copper additions of up to 4% in austenitic steels help improve
corrosion resistance [73]. However, it is also known that copper addition to steels
cause hot shortness during rolling, which can be prevented by the addition of nickel
[90,91]. There has thus been considerable interest in characterizing the effect of nickel
on copper precipitates. Worrall et al [71] and Buswell et al [92] found that for smaller
particle sizes in the underaged condition nickel segregates at the interface of the
coherent BCC copper particles while they found that nickel is not contained in the
overaged FCC precipitates. This was confirmed by Atom Probe studies by Osamura et
al [93]. Recent 3DAP (Three-dimensional Atom Probe) studies of segregation at
coherent precipitate/matrix heterophase interfaces by Isheim [94] also show Ni
segregation with an excess of 1.47 ± 0.43 nm-2 at the interface.
45
2.4 Transformation Toughening
The interaction of deformation-induced martensitic transformation of
dispersed austenite with fracture-controlling processes, such as microvoid induced
shear localization, results in dispersed-phase transformation toughening [95]. In
metastable fully austenitic steels, transformation plasticity is also responsible for
significant enhancement in elongation and fracture strain. The transformation behavior
and toughening effects are controlled by the stability of the austenitic dispersion
determined by size and chemical composition of the austenite particles. The size
affects the probability of finding the nucleation site in the particle and the composition
determines the chemical driving force for martensitic transformation. The stability also
depends on the stress state through interaction of the transformation volume change
with stress triaxiality. The Msσ temperature for the stress-state of interest provides a
single-parameter characterization for the stability of dispersed austenite. It is the
temperature at which there is a transition in the deformation mechanism. Above the
Msσ temperature the initial yield is by slip, while below Ms
σ initial yield is by
transformation. Toughness is increased when austenite particles undergo martensitic
transformation under the crack-tip stress state. This transformation creates a strain
hardening effect, which offsets softening due to microvoid formation and thus delays
the onset of shear localization. The toughening effect is maximum at the crack tip MSσ
temperature [8,9,135]. Thus one would like to have the Msσ temperature around the
46
room temperature for maximum transformation toughening. This can be explained in
greater detail using the schematic diagram in Fig 2.17.
Figure 2.17 Schematic representation of stress-assisted and strain-induced regimes for mechanically-induced transformation [95]
Spontaneous transformation is triggered by pre-existing nucleation sites,
i.e., through stress assisted nucleation above the Ms temperature represented by point A
in Fig 2.17. At the Msσ temperature the stress reaches the yield stress σy level for slip
in the parent phase represented by point C in the diagram. Above Msσ up to Md
(maximum temperature above which martensitic transformation cannot be induced by
deformation), plastic strain introduces new potent nucleation sites, which trigger strain-
47
induced nucleation. As mentioned, Msσ thus creates a boundary between the
temperature regimes where two different modes of transformation operate. Thus below
Msσ, yield stress follows the stress for stress-assisted transformation during
transformation plasticity. The change in the deformation mechanism around Msσ can be
characterized by the difference in the transformation product morphologies: stress-
assisted transformation forms relatively coarse plates while strain-induced
transformation forms fine laths at intersections of shear micro-bands.
• Stress-assisted mode of transformation
In this case, the applied elastic stress modifies the effective potency
distribution of pre-existing nucleation sites, which helps in the transformation kinetics.
Based on the Olson-Cohen [96] dislocation dissociation model of classical
heterogeneous martensitic nucleation by elastic interactions with internal stress
concentrations, the potency distribution of nucleation sites under an applied elastic
stress σ can be expressed by equation (2.15):
str
fch
SVV EWGG
dNN++∆+∆
=)(
/2exp)(max
0
σαγσ σ (2.15)
where γs is the interfacial energy, d is the interplanar spacing and α is a constant. The
force term in the denominator is a sum of the mechanical driving force ∆Gσ(σ),
chemical driving force ∆Gch, elastic strain energy per unit volume Estr and frictional
work of interfacial motion Wf. At a given stress level, the value of the mechanical
driving force changes with the orientation of the nucleus relative to the stress state. The
48
mechanical driving force is related to the applied stress through the Patel-Cohen
criterion [97]:
)(σ
σσ
∂∆∂
=∆GG (2.16)
For considering the stress effects on the potency distribution, the two
extreme cases would be; the operative nucleation sites are of optimum orientation for
maximum interaction with applied stress, i.e., ∆Gσ=∆Gσmax and the other extreme is a
fully random distribution [31]. The actual behavior should be between these two
extremes. Equation 2.15 thus gives the potency distribution under an applied elastic
stress in the case when stress-assisted transformation of a well-spaced dispersion of
metastable particles in a stable matrix is controlled by pre-existing nucleation sites. For
an average particle volume Vp, the fraction of particles to transform due to sufficient
potency of the sites is equal to the probability of finding at least one nucleation site in
the particle, which is given by
(2.17) ).exp(1 pV VNf −−=
assuming that a single initial nucleation event transforms the particle to martensite. NV
is the cumulative number density.
• Strain-assisted mode of transformation
During strain-induced transformation new nucleation sites are created
by plastic strain. In this case, the nucleation sites would be activated by the applied
49
stress and created by the plastic strain simultaneously. The potency distribution can be
found as:
str
fch
SVV EWGG
dNN++∆+∆
=)(
/2exp)()(max
0
σαγεε σ (2.18)
with all variables having their usual meaning. A fully biased distribution was used for
the strain-induced part and Kuroda [98] expressed the strain dependence of NVO for
strain-induced nucleation by non-linear curve fitting:
(2.19) )]exp(1[)(0 nV KNN εε −−=
where K and N are constants.
Since stress-assisted transformation (T<MSσ) takes place in the absence
of any slip, it represents a softening phenomenon relative to the flow behavior of the
parent phase. But for T>MSσ where strain-induced nucleation dominates the
deformation behavior, transformation and slip act in parallel. While a dynamic
softening operates with transformation as a deformation mechanism, a static hardening
effect also arises from the transformation product acting as a slip obstacle. For
transformation plasticity, dynamic softening is dominant at low strains while static
hardening is dominant at high strains as the rate of transformation decreases. This
distorts the usual σ−ε curve into an upward curving shape.
Prior work on austenitic transformation toughened steels investigated
the condition for optimum toughening enhancement, which has led to the development
of TRIP (TRansformation Induced Plasticity) steels [8,9]. Their experiments
50
demonstrated that the flow-stabilizing influence of transformation plasticity could
maximize the toughness at the MSσ temperature for the crack-tip stress state. Fig 2.18
shows the plot of the relative increment of J-integral toughness enhancement as a
function of relative transformation stability represented by a normalized temperature
parameter, θ (=T − MS
σ
Md − MSσ ). The transformation toughening reaches a maximum near
the MSσ temperature, which is consistent with the effect of transformation plasticity on
flow stability.
The dispersed metastable austenite discussed here may either be in the
form of retained austenite or precipitated austenite. The former is the austenite that
remains untransformed after cooling down from the solution temperature, while the
latter forms upon high-temperature tempering or intercritical annealing. Retained
austenite is typically associated with low temperature tempering, whereas precipitated
austenite is found in secondary hardening alloy steels.
51
Figure 2.18 J-integral toughness enhancement at Msσ for precipitation-hardened
metastable austenitic steels [9]
2.4.1 Retained Austenite
Conventionally, this is the austenite that is the leftover from a
martensitic transformation when steels are quenched from the solution temperature.
This austenite can be designed appropriately for the necessary high stability to achieve
the transformation plasticity phenomena under deformation. Previous work [4,99]
shows that the ductility of this class of steels can be increased by the TRIP effect that
led to the design of triple phase steels: ferrite, austenite and bainite being the three
phases. Coarse cementite particles formed during bainitic transformation are
detrimental to the toughness of these steels, but the precipitation of cementite can be
52
suppressed by alloying with about 1.5 wt % Si, which has very low solubility in
cementite. The carbon that is rejected by the bainitic ferrite enriches the residual
austenite thereby stabilizing it. Thus, on slow cooling followed by quenching we
obtain fine plates of bainitic ferrite separated by carbon enriched retained austenite.
This mixed microstructure has high resistance to cleavage fracture and void formation
because of the absence of cementite carbides. The strength and toughness can be
further enhanced by an ultrafine grain size of the bainitic ferrite plates as well as the
TRIP effect.
All the promising properties of this microstructure might not reach full
potential if the large blocky regions of austenite trapped between sheaves of bainite are
unstable. These unstable blocks then tend to transform into coarse high carbon
untempered martensite, leading to an embrittling effect. On the other hand, austenite
trapped between subunits of bainitic ferrite is more stable, not only because they have
higher carbon concentration but also due to a finer particle size. Thus, the aim of the
design should be to maximize the degree of transformation of bainitic ferrite and in the
process reduce the fraction of blocky austenite and increase its stability with respect to
martensitic transformation. Chemical stabilization due to the enrichment of carbon in
retained austenite is the most important operational mechanism for austenite retention.
Both bainitic transformation and the retention of stable austenite after transformation
from ferrite have been explored in considerable detail, which will be described later
(Appendix B). Since the stabilization of austenite largely depends on the kinetics of
53
carbon diffusion and does not involve the larger substitutional atom diffusion, it can be
simulated using paraequilibrium (PE) growth models [22], as described in Section
2.2.1.
Haidemenopoulos [100] has characterized the stability of retained
austenite in terms of the Msσ temperature. The Ms
σ temperature was measured in
uniaxial tension Msσ(u.t.) and uniaxial compression Ms
σ(u.c.). The temperature
dependence of 0.2% flow stress in tension and compression for a material containing
4% retained austenite showed an increase with decreasing temperature. The tensile
flow stress region has a plateau region around the Msσ (u.t.) temperature (Fig 2.19),
which is attributed to the mechanical relaxation due to transformation of retained
austenite. In the stress-assisted nucleation regime (T< Msσ), initial yielding is
controlled by transformation of retained austenite. The stress-strain behavior can be
described by nucleation-site potency distribution models described in the previous
section.
54
Figure 2.19 Temperature dependence of the 0.2% tensile and compressive flow stresses [100]
Strain-induced transformation of retained austenite delays shear
instability during pure shear deformation. Since fracture is often controlled by shear
localization, it is expected that delocalizing effects arising from transformation
plasticity of retained austenite should enhance the fracture toughness. It was found that
retained austenite is sufficiently stable for a pure-shear stress state but too unstable for
a crack-tip stress state when tests are performed at room temperature. A toughening
effect associated with strain-induced transformation would be only observed at or
above the Msσ temperature. Thus, transformation toughening can result only by
lowering the crack-tip Msσ below room temperature by stabilizing the austenite.
55
2.4.2 Precipitated Austenite
Precipitated austenite is the form of dispersed austenite that precipitates
during intercritical annealing or during tempering at high-temperature above ~470OC.
This difference in the mode of formation from retained austenite makes precipitated
austenite very attractive for application of transformation toughening since there are
more easily controllable degrees of freedom. Since it is formed as a result of
precipitation reaction, its amount and distribution can be controlled. Its size and
composition can be varied through heat treatment and its stability can be tuned for
transformation toughening effects.
The most important factors affecting the dispersed-phase transformation
toughening in steels are the stability of the dispersed austenite and the transformation
volume change, both of which depend on the composition of the steel. Studies on
precipitated austenite have been mostly performed on high Ni-Co secondary hardened
martensitic steels [6,100]. Similar to retained austenite, transformation behavior and
toughening effects are controlled by the stability of the austenitic dispersion with the
microstructural parameters again being size and chemical composition of the austenite
particles. Other than that, stability of austenite also depends on the stress state due to
the interaction of the transformational volume change and strength of the matrix.
Haidemenopoulos showed that in order to get a very high stability of dispersed
austenite, so that the Msσ temperature for the crack–tip stress state can be below room
temperature, the austenite has to be very fine and enriched in Ni. By equating the
56
transformation stress (σt) derived from equation (2.15) and the yield stress (σy), he
obtained the Msσ temperature as:
MSσ = σ y[0.121+ 0.0542(σ h /σ )]+
1465.3−4.6 − lnNV
OVP
+ [1418.92 −33.92(wt%Ni) − 0.5(wt%Ni)2/ 3](2.20)
At room temperature (300K) for the crack-tip stress state, the required Ni content of
the austenite particles can be plotted vs. particle size as given in Fig 2.20 for a fixed
yield strength of 1400 MPa.
Figure 2.20 Optimal Ni content vs. normalized austenite particle volume in Fe-14Co-Ni system [100]
57
Precipitated austenite occurs in two competing morphologies: as thin
interlath films and as intralath dispersion of fine precipitates. Fig 2.21 shows the
presence of both interlath films and dispersed intralath austenite in AerMet100 after
two-stage tempering.
Figure 2.21 Conventional TEM dark field image of an interlath austenite film (A) and dispersed intralath (B) austenite after 5070C/30minute + 4550C/7hour temper in AerMet100 [6]
The thin interlath austenite films are located on martensite lath
boundaries. The dispersed austenite precipitates are located at heterogeneous sites
within the martensitic laths. However, both interlath films and dispersed precipitates of
austenite nucleate during tempering above 500OC. The austenite films are enriched by
58
FCC stabilizing elements like Ni. The small width of the film is also responsible for
the resistance to martensitic transformation upon cooling to room temperature. The
competition between the two types of austenitic morphologies is crucial to the
transformation toughening properties of the alloy. The lath boundary films do not
generally possess the requisite stability for effective transformation toughening. The
intralath precipitates are sufficiently enriched with Ni and refined in size to increase
the alloy toughness, provided an adequate volume fraction is present. Lippard [6]
studied the commercial alloy AerMet100 that displays transformation toughening
enhanced properties when given a specific two-stage tempering. The first stage of
treatment precipitates both interlath films and a fine dispersion of intralath precipitates.
But the intralath austenite precipitates have small (~8nm) size with highly enriched Ni
content at the second stage of tempering that provided sufficient stability to produce
transformation toughening properties. Overaging treatments coarsened both the
austenite dispersion and carbide strengthening dispersion. But the dispersed intralath
austenite maintained its composition while the interlath films became enriched with
carbon. Thus, interaction of the carbide dispersion and matrix dislocation network was
found to be important for austenite precipitation.
Lippard consistently found evidence of a high Cr signal much greater
than either the equilibrium matrix or precipitate contents associated with STEM EDS
data gathered from dispersed intralath austenite precipitates as shown in Fig. 2.22.
Based on this indirect evidence, he proposed a mechanism of austenite precipitate
59
nucleation on an M2C carbide or in its immediate coherency strain field. He concluded
that dispersed intralath austenite requires an M2C carbide to provide an energetically
favorable nucleation site. He suggested that direct evidence of the precipitation
sequence and the spatial relationship of the M2C carbides and austenite precipitates
could best be obtained by three-dimensional reconstruction from position sensitive
atom probe microanalysis.
Figure 2.22 Correlation of Cr and Ni from embedded austenite precipitates prior to partitioning of STEM EDS signal into matrix and precipitate portions [6]. The data points are from multi-step tempered AerMet100 samples aged at 4050C for longer times after a short time 5070C nucleation treatment.
60
Grujicic [101] studied stabilization of precipitated austenite in C-Mn
steels via heterogeneous precipitation to produce compositional control of austenite.
He considered two modes of austenite formation under para-equilibrium conditions:
heterogeneous nucleation at a ferrite-cementite interface with subsequent growth into
either ferrite or cementite and heterogeneous precipitation on ferrite grain boundaries.
A reduction of Mn content of cementite below its equilibrium value was found to favor
austenite nucleation at ferrite-cementite interfaces and subsequent conversion of
cementite to austenite. Through thermodynamic calculations, the nucleation of
austenite at ferrite-cementite interfaces and the subsequent conversion of cementite
into austenite are most likely to take place during intercritical or supercritical
treatment. The precipitated austenite is very stable due to higher Mn content. Only at
high temperatures can complete cementite → austenite conversion be achieved. Yet at
such high temperatures the likelihood of formation of less-stable austenite via massive
transformation of ferrite increases. This can be suppressed by adding elements that
lower the activity of C in ferrite such as Mn, Cr, Mo or W.
61
3. ALLOY DESIGN
The design of high toughness plate steels at high strength levels has
been pursued employing transformation toughening phenomena while constraining the
alloy carbon content of the steel for weldability. Two toughening concepts have been
explored, both based on mechanisms of dispersed austenite stabilization for
transformation toughening adapted to weldable bainitic plate steels. Concept A is
based on low alloy, low cost C-stabilized austenite in high Si steels with Cu
precipitation strengthening. This design focuses on precipitation-strengthened bainitic
steels with carbon-stabilized austenite for transformation toughening. Silicon, in this
concept, acts to suppress the precipitation of cementite to keep C available for
austenite stabilization. The second, Concept B, higher strength, lower risk and higher
cost concept is primarily nickel-stabilized austenite, in an alloy strengthened by
precipitation of M2C carbides in combination with copper. These two design concepts
are based on a trade-off between the risk of the design and the cost of the product. The
Concept A prototype proved to be too stable to allow full assessment of the
compatibility of simultaneous bainitic transformation and copper precipitation
strengthening and the design principles and prototype evaluation are described in
Appendix A, while the Concept B prototype proved successful in meeting its
objectives and became the focus of the research effort.
62
3.1 Modeling Tools
Two primary software systems were used for analyzing and integrating
the design parameters: ThermoCalc™ and CMD™ (Computational Materials
Dynamics).
3.1.1 ThermoCalc™
ThermoCalc™ is a generalized thermodynamic database and calculation
package developed by the Royal Institute of Technology in Stockholm, Sweden (KTH)
[102]. The database is comprised of thermodynamic assessments, mostly compiled
from experimental results, of binary, ternary and quaternary systems used to
extrapolate to higher order systems. The program uses the compiled information in the
database to calculate equilibrium (or constrained equilibrium) thermodynamic values
such as phase fractions, phase compositions and driving forces as functions of
chemical composition, temperature, pressure, chemical potential and other user defined
functions by solving for the state of lowest Gibbs free energy. The separation of the
calculation package from the database makes this tool extremely versatile and
powerful, since it allows use of different thermochemical models to describe the
thermodynamics of the system. ThermoCalc™ uses sublattice models to describe the
different lattice sites within a crystalline phase like the general sublattice model [108]
(includes the regular solution model as a special case) and the two sublattice ionic
63
model [109]. For example, a two-sublattice model is used for the description of BCC
iron in the form ApBq where A is the first sublattice (substitutional) consisting of p
sites and B is the second sublattice (interstitial: allowing non-occupied sites or
vacancies) consisting of q sites.
The thermodynamic databases used were created by the Scientific
Group Thermodata Europe (SGTE), a consortium of European research centers
developing databases for inorganic chemistry and metallurgy. For alloy design in this
thesis, the SGTE solution database or SSOL has been primarily used. It includes data
for over 150 binary, 70 ternary and 20 higher systems. In addition to the SSOL
database, two other custom databases developed in SRG research were examined
during the design process. The MART 4 database was developed by Ghosh and Olson
[105] to calculate martensite start temperature. The database includes modified low
temperature thermodynamic parameters for FCC and BCC phases for iron based
systems. This database modification was necessary for a more accurate description of
the lower temperature thermodynamics since the parameters in the SSOL database is
based only on high temperature data. The COHERENT3 database was also used for
modeling the coherent precipitation behavior of M2C carbides from a BCC iron matrix.
This database was modified to include a thermodynamic description of the elastic
strain energy associated with lattice misfit. Since we were aiming at a high martensite
start temperature (>3000C), the SSOL database proved adequate for MS prediction.
Introduction of a miscibility gap in the BCC phase to define the coherent BCC copper
64
phase led to erroneous phase descriptions when the COHERENT 3 database was used.
Thus, the SSOL database was used for all the thermodynamic calculations of the
design.
3.1.2 CMD™ (Computational Materials Dynamics)
CMD™ is a user-friendly computational materials design software
system developed by Questek Innovations LLC, Evanston [103]. It is composed of a
collection of mechanistic models describing both processing-structure and structure-
property relations integrated with their software implementation. The models link up
with ThermoCalc™ and DICTRA™ (DIffusion Controlled TRAnsformation) to gather
all the thermodynamic and mobility information for multicomponent computation. The
user has to establish the material design criteria for using the CMD™ model programs.
The software relies on user’s input and manual optimization guided by parametric
contour plots to meet the design criteria. The process of materials design using CMD™
involves a large number of calculations using different models to study the trade-offs
and perform optimization of the design strategies. For alloy design in this thesis,
CMD™ has been used to optimize the driving force of the M2C carbides for dispersion
refinement with respect to the various carbide formers, Cr, Mo and V within the
stoichiometric balance limit. The model for calculating carbide driving forces from a
supersaturated solid solution of BCC has been primarily used for this purpose.
65
3.2 Design Approach
The objective of this design is to maximize the toughness-strength
combination in weldable and affordable plate steels. The desired microstructure is a
matrix containing a bainite-martensite mix, BCC copper and M2C carbide for
strengthening with a fine dispersion of optimum stability austenite for transformation
toughening. The bainite-martensite mix will be formed by air-cooling from solution
treatment temperature and subsequent aging at secondary hardening temperatures will
precipitate the toughening and strengthening dispersions. The strengthening approach
is based on design concepts of the current Navy HSLA100 steel (Fe-0.06C-0.9Mn-
0.4Si-3.5Ni-1.6Cu-0.6Mo-0.03Nb; in wt%) with a quench and temper processing
treatment. This is integrated with modeling of nickel-stabilized austenite produced by
precipitation as demonstrated in transformation toughened AerMet100 and AF1410
steels with multi-step tempering treatments [2,6,100]. The proposed methods of
toughening and precipitation strengthening have been modeled in this design to assess
theoretical feasibility in order to minimize necessary experimentation.
The structural hierarchy in this alloy system with strong interactions
among levels has been organized by the systems design chart, presented in Fig. 2.1,
through relationships between the processing/structure/property/performance
interactions with adequate description of the substructure present within each
microstructural element. During the design process, the systems approach emphasized
the interaction of the various subsystems and addressed the role of each individual
66
component within the larger system. As outlined by Jenkins [136], a breakdown of the
steps involved in the systems design process can be represented as:
Systems Analysis → Systems Design/Synthesis → Implementation → Operation.
The first step, systems analysis, involves identifying the application and the material
property/performance objectives expressed by the systems design chart. The models
necessary to characterize the subsystems and their interactions are subsequently
decided based on the priorities of the interactions necessary to achieve the properties.
Once the appropriate models are developed, the models are integrated to design a new
material for the specific application. It is important not to optimize a particular
subsystem at the expense of the total system. Moreover, the designed composition
should be robust; all the design parameters are ensured to be insensitive over a range so
that small deviations in the composition will not result in dramatic differences in
properties. Fig. 3.1 presents a schematic process flow of the design optimization
procedure to determine an optimal composition. Once the optimal composition is
determined, a prototype alloy is made and evaluation of the prototype is done.
Prototype evaluation not only characterizes the alloy, but also verifies the effectiveness
of models and their integration in the design. If needed, another design iteration is run
before the material is used for its intended application.
67
igure 3.1 Schematic of the design optimization procedure
CSet Carbon Level
Weldability
CSet Carbon Level
Weldability
Castability Cu, Ni, CrCastability Cu, Ni, Cr
Refine M2C Strengthening Dispersion Mo, V, Cr, C
Maximize M2CDriving Force
SolutionTemperature
Predicted StrengthIncrement
Refine M2C Strengthening Dispersion Mo, V, Cr, C
Maximize M2CDriving Force
SolutionTemperature
Predicted StrengthIncrement
Optimize Transformation Toughening Dispersion
Austenite NickelContent
Austenite PhaseFraction
Meet StabilityRequirement
NiOptimize Transformation Toughening Dispersion
Austenite NickelContent
Austenite PhaseFraction
Meet StabilityRequirement
Ni
Set Matrix Composition Fe, Ni, Cr, Cu
Martensite StartTemperature
BainiticTransformation
CleavageResistance
Set Matrix Composition Fe, Ni, Cr, Cu
Martensite StartTemperature
BainiticTransformation
CleavageResistance
Set Copper for Strengthening Dispersion
Additional StrengthIncrement
Volume fraction ofCopper Precipitates
Cu, Cr
Partitioning of Copper by Chromium
Set Copper for Strengthening Dispersion
Additional StrengthIncrement
Volume fraction ofCopper Precipitates
Cu, Cr
Partitioning of Copper by Chromium
Optim
al Com
position
F
68
.2.1 Strength Design
An efficient approach to strengthen the steel while limiting carbon
content for weldability is co-precipitating M2C carbides and BCC copper. By
optimizing the particle size and the phase fraction of the precipitates, the goal of high-
strength can be achieved.
3.2.1.1 Quantitative Strengthening Contributions
As highlighted by the system design chart (Fig. 2.1), the strength of the
alloy will be designed by using quantitative strengthening models to predict its
dependence on the structure of the steel. To achieve a goal of 160ksi yield strength,
quantitative models will be employed to relate the contribution from dispersions of
M2C carbide precipitates [12] and BCC copper precipitates [59] in secondary-hardened
steels. The levels of M2C carbide formers and copper will be optimized based on the
strength contribution from each of these substructures. In this work, assessment of the
yield strength of the material has been made directly from the hardness data because of
the ease and convenience in measurement of the latter. Hardness of a material is a
direct manifestation of its resistance to plastic flow, monotonically relating to yield
stress. An empirical relationship has been developed between hardness and yield stress
based on experimental data from previous research on related steels: HSLA100 data
from Foley [77], AerMet100 data from Kuehmann [2] and SRG C2 carburizable gear
steel data from Spaulding [138]. The best-fit curve in a log-log plot of hardness vs.
3
69
yield stress has been used to determine the relationship based on strain hardening
associated with the alloy. Fig. 3.2 presents the experimentally measured hardness –
yield stress data from previous research superimposed with the best-fit power-law
relationship and the theoretical straight-line relation describing the same for an ideal
plastic material [107]. The higher hardness of the empirical power-law relationship
relative to the ideally-plastic case represents the effect of strain hardening, which
appears to be more pronounced at lower strength levels. The point at which the two
curves meet represents the prediction limit of the relationship.
Figure 3.2 Power-law relationship relating hardness of related steels to yield stress from experimental data from Foley [77] (circles), Kuehmann [2] (triangles) and Spaulding [138] (diamonds) shown in comparison to straight-line relationship for ideal plastic material
70
Thus, the hardness estimate for the target yield strength of 160 ksi from the power-law
relationship is 389 VHN. The relation obtained is:
(3.1) 8184.0116.6 YSVHN =
where, VHN (Vickers Hardness Number) is in kg/mm2 and YS (Yield Strength) is in
ksi.
The first step in the design involved setting the carbon content of the
alloy to ensure good weldability. Fig. 3.3 presents the Graville diagram of overall
carbon content in the alloy as a function of carbon equivalent. This shows that at 0.05
wt% C, the steel is not susceptible to hydrogen – induced cold cracking in heat affected
zone (HAZ) of weldments. Consistent with the carbon level in current Navy HSLA100
steel, the lower limit C content of 0.05 wt % C was set for the alloy.
71
Figure 3.3 Graville diagram for determining susceptibility to HAZ cracking in plate steels [137]
Based on the effect of M2C carbide precipitates in the Orowon bypass
regime, Wise [12] developed a quantitative strength model to predict the strengthening
achieved for a given carbon level. The predictions assume that a given carbon content
of the alloy specifies the carbide volume fraction and considers carbides of fixed
particle diameter. Based on the change in hardness-carbon content (wt%) plot shown in
Fig. 3.4, at a C level of 0.05 wt% the hardness increment due to M2C carbide
precipitation is estimated to be 175 VHN provided a sufficient driving force is
maintained to achieve the particle size range in Fig. 3.4. The base strength of the lath
72
martensitic substructure was estimated as 63 VHN by Wise [12]. The additional
strength increment of 151 VHN to achieve the strength goal of 389 VHN will be
attained through BCC copper precipitation strengthening, described in Section 3.2.1.2.
The effect of solid solution strengthening is assumed to be negligible for steels having
low carbon and low hardenability. Thus, the total strength of the alloy has been
modeled by breaking it down into its individual mechanisms. The strength is described
by the effects of M2C carbide precipitates, τM2C; BCC copper precipitates, τCu and
matrix martensitic structure, τα’.
VHNCuCM 389'2 ≡∆+∆+∆= αττττ (3.2)
The contributions of the individual mechanisms to achieve the strength goal equivalent
to 389 VHN are graphically presented in Fig. 3.5.
73
Figure 3.4 Change in hardness as a function of alloy carbon content for M2C
carbide strengthening contribution [12]. The arrows represent hardness increment of 175 VHN is achieved at C level of 0.05 wt% set for the alloy. Experimental results of other secondary hardening steels are shown.
Figure 3.5 Graphical representation for contributions of the individual mechanisms to achieve the strength goal equivalent to 389 VHN
74
3.2.1.2 M2C Carbide Strengthening
For the high-strength design, we want to ensure that all of the carbon is
taken up by the M2C carbide formers (Cr, Mo and V) in order to dissolve the cementite
in the matrix. Cementite negatively affects strength and toughness. Therefore, we
want the sum of the atomic concentrations of Cr, Mo, and V to double the
concentration of C for the M2C stoichiometry.
A series of calculations were performed in order to design a steel that
meets the strength requirements. Preliminary compositions were set using the guideline
(consistent with the HSLA100 alloy) that carbon content should be limited to 0.05
weight % for weldability (Fig. 3.3); Cu should be at least 1.5 weight % for significant
strengthening [76,77], minimum Ni content should be at least half that of Cu to avoid
hot shortness, and the relative amounts of carbide formers Cr, Mo and V was initially
set equal in atomic percent. A feasibility study was then performed to ensure that this
strengthening concept, in conjunction with Concept B for toughening (described in
Section 3.2.2) is thermodynamically possible, i.e. all of the phases needed for
precipitation strengthening and nickel-stabilized austenite could coexist at least in
metastable equilibrium at processing temperatures. A BCC Cu-rich precipitate is
necessary for Cu precipitation strengthening, an M2C carbide phase is necessary for
carbide strengthening, and FCC austenite is critical for transformation toughening.
Considering these constraints, thermodynamic feasibility of the preliminary alloy
75
composition was verified by ThermoCalc™ calculations at kinetically reasonable
tempering temperatures of 400-5000C.
After the feasibility study demonstrated that these concepts were
thermodynamically compatible, detailed driving force calculations were performed.
The M2C precipitation driving force determines the degree of particle size refinement
for efficient strengthening. Using the CMD™ interface, the driving force for M2C
carbides with respect to the content of each of the carbide formers was determined,
assuming initial paraequilibrium with cementite (prior precipitation of cementite with
only interstitial carbon partitioning) and neglecting coherency. The tempering
temperature used is 500°C to allow sufficient substitutional diffusion. By increasing
the driving force, a finer dispersion of precipitates is formed in the matrix. Ideally,
therefore, the driving force should be maximized while maintaining an M/C ratio in the
M2C stoichiometry.
Before the driving forces were calculated, a Mo-Cr phase diagram
section at a solution temperature of 900°C was calculated in order to determine the
relative solubility of the carbide formers in the austenite phase at a reasonable solution
temperature. The solubility limit should not be exceeded in order to achieve full
conversion to M2C for maximum carbide strengthening. Recalling that the M2C
stoichiometry must be maintained, the stoichiometric constraint, as well as the
solubility limit, can be superimposed onto a contour plot of driving force vs. Mo and
Cr concentration to optimize the M2C driving force. The Mo-Cr phase diagram section
76
is shown in Fig. 3.6. It is apparent from the phase diagram that solubility is not a
limiting factor in the region of interest, due to the relatively limited C content.
StoichiometricLine
FCC (γ) + M6C
FCC (γ)
Figure 3.6 Cr-Mo Phase Diagram at 9000C with alloy composition in atomic %:
Fe-0.234C-1.32Cu-6.21Ni-0.055V. This diagram shows the phase fields of the FCC austenite and FCC+M6C revealing that the M2C stoichiometry (red) line is well within the solubility limit.
The stoichiometric constraints of the M2C carbide dictated that the total
amount of carbide formers (Cr, Mo, V) needed to balance the carbon content would be
0.468 at%. Using this constraint, initial plots were constructed of the driving force for
M2C nucleation vs. at%(Mo) and at%(Cr), setting V at different levels. Fig.3.7 is a
77
representative plot of driving force contours with varying at%(Mo) and at%(Cr) at an
alloy composition of 0.05at% V and at 5000C. The stoichiometric constraint line has
been drawn on the plot indicating the line of allowed compositions for M2C. This
study indicated that Cr has the least effect on driving force, especially at the higher
contents of interest.
Figure 3.7 Driving Forces (in kJ/mole) for M2C carbide nucleation contour plot
varying at% (Mo) and at% (Cr) with superimposed M2C stoichiometric (red) line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.21Ni-0.055V.
78
Based on this finding, another set of driving force plots were created
varying at%(Mo) and at%(V) while setting the Cr level at fixed values. Due to the
very small Cr dependence, all the plots were very similar and so only a representative
graph (Fig. 3.8) was included at 0 at%(Cr). A similar M2C stoichiometric line was
drawn as before, constraining a maximum driving force at about 14.4 (kJ/mole). This
plot revealed an almost equal effect on driving force for Mo and V, indicating that any
allowed ratio of the two should give a maximum driving force value, so a series of
calculations were done along the stoichiometric line (maximum driving force). We
found a feasible alloy composition where all the desired phases as mentioned before
co-existed, which is indicated by the dot and arrow in Fig. 3.8. An initial feasible alloy
composition in wt % was thus determined without any Cr: Fe-0.05C-1.5Cu-6.5Ni-
0.6Mo-0.1V.
79
Figure 3.8 Driving Force (in kJ/mole) for M2C carbide nucleation contour plot
varying at% (Mo) and at% (V) with superimposed M2C stoichiometric line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.2Ni.
The V-Mo phase diagram section at a solution temperature of 900°C
with the feasible alloy composition was then calculated. Again, the solubility of these
carbide formers is not a limiting factor in the region of interest. This plot is shown in
Fig. 3.9.
80
Stoichiometric Line
FCC (γ) + V3C2
FCC (γ)
Figure 3.9 Mo-V Phase Diagram at 9000C with alloy composition in atomic %:
Fe-0.234C-1.32Cu-6.2Ni. This diagram shows the phase fields of the FCC austenite and FCC+V3C2 revealing that the M2C stoichiometric (red) line is well within the solubility limit
81
3.2.1.2 Copper Precipitation Strengthening
In addition to M2C carbide strengthening, BCC copper precipitation
strengthening will be modeled to control the phase fraction of the precipitates through
the alloy copper content to provide the additional increment of strength (≡ 151 VHN).
As described in Section 2.3.2, the copper precipitates that contribute to strengthening
in steels have a metastable BCC structure, which are fully coherent with the matrix
having an average diameter of 1-5 nm. The strengthening mechanism has been
described by the Russell-Brown model [59] based on the interaction between the
matrix slip dislocation and the second phase copper-rich particle of lower shear
modulus than the matrix. They derived an expression to calculate the minimum
included angle, φ, reached by the arms of a dislocation while cutting the precipitate as a
function of the energy of the dislocation on either side of the precipitate/matrix
interface. This angle is used to calculate the yield stress as a function of interparticle
spacing. Since these coherent copper particles effective for strengthening are small in
size, they calculated the flow stress by considering energy of the dislocation per unit
length in an infinite medium of the matrix. The shear stress has a maximum value, τmax,
given by Equation 3.3.
0
2/1
max041.0
rGbf
=τ (3.3)
where G is the matrix shear modulus, b is the burgers vector, f is the volume fraction of
atoms and r0 is the core radius of the dislocation. Thus the maximum strength that can
82
be achieved is proportional to the square root of the volume fraction of the precipitate.
Based on this volume fraction dependence of the precipitate on yield stress, the
hardening increment from available data of copper precipitation strengthened steels
[59] was plotted as shown in Fig. 3.10. The best-fit line described by a one-half power
law defined the hardening increment dependence on the alloy content (at%) of copper.
(3.4) 2/1807.83)( CuXVHN =∆τ
Based on this relationship, the hardness increment of 151 VHN can be achieved by
addition of 3.25 at% Cu to the alloy composition.
Figure 3.10 Change in hardness as a function of alloy copper content for BCC copper strengthening contribution [59]. Experimental results of other copper strengthened steels are shown. The dotted line represents the best-fit line for one-half power law given by equation (3.4).
83
3.2.2 Transformation Toughening Design
For design of tough steels for such high strength levels (160 ksi YS) we
need to develop a fully secondary hardened microstructure with higher stability
austenite produced by precipitation. At high strength levels we need the higher stability
of precipitated austenite since the mechanical driving force for transformation is very
high. This design seeks to improve the toughness of higher strength steels by utilizing
the beneficial properties of Ni-stabilized precipitated austenite. This form of austenite
can precipitate during annealing or tempering at elevated temperatures above about
470°C. The fact that this dispersed austenite forms by precipitation is significant
because it allows greater overall control of the amount and stability of the austenite.
Further processing and treatments can be used in the form of multi-step tempering to
first nucleate particles in a fine form at a higher tempering temperature and then
complete Ni enrichment during completion of precipitation strengthening (cementite
conversion to 3nm M2C) at a lower final tempering temperature.
Shear localization by microvoid nucleation is known to be the most
dominant fracture mode in high strength steels. As discussed in Section 2.4, studies
[104] have shown that fine particle dispersions with adherent interfaces are optimal for
controlling microvoid nucleation. The most promising microstructure modification is
achieved by nucleating an optimal stability austenite dispersion, which increases
toughness by suppressing microvoid nucleation to higher strain levels. Thus, emphasis
84
will be put on the design of intralath dispersions, as the greater stability associated with
their finer size makes them the primary toughening form of austenite precipitates.
The austenite dispersion must have sufficient stability and proper
formation kinetics to ensure maximum toughening enhancement. Other factors
controlling the stability of austenite are particle size and stress state sensitivity, the
latter being related to the transformational volume change. The Olson-Cohen classical
heterogeneous martensitic model can be applied to describe dispersed austenite
stability for transformation toughening [100]. Stability of an austenite precipitate is
defined by chemical and mechanical driving force terms. According to the model, at
the Msσ temperature for the crack-tip stress state, the total driving force equals the
critical driving force for martensite nucleation, as represented by Equation 3.5.
Combining Equations 2.15, 2.16 and 2.17 in Chapter 2,
⎥⎦⎤
⎢⎣⎡ ++−=
∆+∆ f
cracktipy
ch WGndd
GdG 02γ
σσ
σ
(3.5)
Rearranging the terms and substituting the dependence of defect potency on particle
volume Vp, we can define a convenient stability parameter:
⎥⎥⎦
⎤
⎢⎢⎣
⎡+
∆−=++∆ 0)ln(
GdGd
VKWG
cracktipy
pf
ch
σσ
σ
(3.6)
85
∆Gch is the transformation chemical free energy change and Wf is the athermal
frictional work term described in Section 2.4. ∆Gch is temperature and composition
dependent while Wf is only composition dependent. Wf will vary with tempering
temperature due to the change in austenite composition. σy is the yield stress of the
material, ∆Gσ is set by the stress state and G0 is a nucleus elastic strain energy term. K
is a proportionality constant, γ is the nucleus-specific interfacial energy and d is the
crystal interplanar spacing.
The austenite stability for a given set of conditions or service
temperature for a given dispersion can be assessed by the parameter given by the left-
hand side of Equation 3.6. If we assume an austenite particle size equivalent to that
achieved in previous studies of AF1410 and AerMet100 steels, our austenite stability
parameter becomes the sum of the chemical driving force for transformation of FCC
austenite to BCC martensite at room temperature (300K) and the frictional work term
for martensitic interfacial motion: ∆Gch + Wf. ThermoCalc™ can be used to predict the
temperature and compositional dependence of the chemical energy term. Ghosh and
Olson [105,106] have modeled the composition dependence of the frictional work term
as a power law with an exponent of 0.5 and a fit to experimental data was achieved.
Appropriate superposition laws considering relative strengths of the solutes were
applied for complex systems. The model is represented in Equation 3.7.
2/12/12/12/1 )()()( CoCo
kk
k
jj
j
ii
if XKXKXKXKW +++= ∑∑∑ (3.7)
86
where the K’s represent the coefficients used to fit the solid solution strengthening data
and i = C, N; j = Cr, Mn, Mo, Nb, Si, Ti, V; and k = Al, Cu, Ni, W.
Equation 3.7 further indicates that the stability parameter is a linear function of the
yield strength of the material.
The strength dependence of the optimal stability level was determined
from previous transformation toughening experiments on the AF1410 and AerMet100
steels [6]. Fig. 3.11 gives the plot of the austenite stability parameter, ∆Gch + Wf, at
room temperature against Vickers hardness of the alloy. The room temperature
stability of the austenite dispersion projected from the hardness (or strength)
requirement of the design is marked by the shaded region in the figure and
quantitatively expressed in Table 3.1. To achieve a goal of 160ksi yield strength
equivalent to Vickers hardness of 389 (Rc40 equivalent), the estimated optimum ∆Gch
+ Wf value of 2837 J/mole was found for the required stability.
Table 3.1: Target Chemical Driving Force (∆Gch) + Frictional Work (Wf) Value
Alloy Rockwell C Hardness
Vickers Hardness ∆Gch + Wf
Rc VHN (kg/mm2) J/mol
AerMet 100 54 577 4350
AF1410 48 484 3600
Concept B Steel 40 389 2837
87
RT (300K) Stability of Austenite
0
1000
2000
3000
4000
5000
280 330 380 430 480 530 580 630
Hardness (Vickers)
Gch
+Wf (
J/m
ol)
AerMet 100AF1410
Concept B Design Alloy
Figure 3.11 Room temperature (300K) austenite stability plotted as a function of
Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept B alloy corresponding to yield strength requirement of 150-180 ksi after extrapolation of data from previous alloys, AF1410 and AerMet100.
The design of transformation-toughened austenite has been calibrated
against this stability parameter to determine the optimal level of austenite-stabilizing
nickel in the alloy. Plots of both the phase fraction of austenite and nickel content in
the austenite phase vs. alloy atomic fraction Ni were computed. Fig. 3.12 was
calculated at an estimated final tempering temperature of 500ºC for substitutional
88
diffusion and revealed that a minimum of 3.5at% Ni is required to get austenite and a
maximum fraction of nickel in the austenite of about 0.30 could be obtained. It also
showed that at the 6.25 at% Ni composition from feasibility studies, about a 0.10 phase
fraction of austenite would be formed as shown by the red arrows. This compares well
to the phase fraction of austenite employed in previous transformation toughened
steels. We thus set the alloy Ni level to 6.25at%, which also saturates the austenite Ni
content to 30 at%.
After conducting the feasibility study mentioned previously in Section
3.2.1.1 and verifying that the corresponding austenite stability was within the design
limits given in Fig. 3.11, a thermodynamically viable alloy composition was found
using 6.25 at% Ni. This Ni level was deemed acceptable as it fell well within the
nickel content guidelines, while being low enough to limit the material cost.
89
T= 5000C
Figure 3.12 Fraction of Ni in austenite and phase fraction of austenite in alloy vs.
mole fraction of Ni at 5000C with alloy composition in weight %: Fe-0.05C-3.65Cu-1.85Cr-0.6Mo-0.1V
90
3.2.3 Design Integration
The overall composition was optimized so that all of the phases
necessary for strengthening and toughening are simultaneously present. Since the
maximum M2C driving force is obtained with no chromium, equilibrium phase
calculations were done for the initial feasible composition. For this composition, it was
found that the copper added for precipitation strengthening went instead into the
austenite phase. A study of the equilibrium austenite composition with varying alloy Cr
content was then undertaken as given in Fig.3.13. It was found that Cr partitions Cu
out of austenite and into the BCC precipitate phase effectively at 2wt% and above.
00.050.1
0.150.2
0.250.3
0.350.4
0.450.5
0 0.02 0.04 0.06 0.08 0.1 0.12
Alloy Weight Fraction of Cr
Mol
e fr
actio
n of
ele
men
ts
x(Cu)x(Ni)x(Cr)x(Mo)x(V)x(C)
Ni
Cu
Cr
Figure 3.13 Equilibrium composition of austenite as a function of alloy Cr content
(wt. fraction) at 5100C
91
Further, to understand the effect of Cr on partitioning of Cu out of the
austenite phase, a detailed investigation was done based on a quasi-ternary section of
the multicomponent system at 5100C as presented in Fig. 3.14. The equilibrium Cr and
Cu phase compositions of BCC Cu, austenite and the ferrite phases connected with tie-
triangles are presented for different Cr contents of the alloy. An interesting feature to
note in the figure is that the austenite equilibrium point abruptly shifts to a much lower
Cu level with an increase of alloy Cr level from 1 at% to 1.2 at%. This study confirms
that Cu partitions to the BCC precipitate phase above 1.2 at% Cr. From a robust alloy
design consideration as discussed earlier in the section, 2 at%Cr (equivalent to 1.84
wt% Cr) was set for the alloy to make the copper in the alloy available for precipitation
strengthening.
92
Figure 3.14 Quasi-ternary section of the designed multicomponent alloy system at 5100C. Other alloying elements are fixed at Fe – 0.24C – 3.25Cu – 6.26Ni – 0.35Mo – 0.11V (at%). The tie-triangles shown by thin solid lines indicate three-phase equilibrium between BCC Cu, austenite and ferrite. The dashed arrow traces out the trajectory of the austenite phase composition (solid dots) as a function of increasing alloy Cr content
93
The relative fractions of the different phases in the microstructure were
then calculated as a function of the alloy Cr content to confirm the effect of chromium
as shown in Fig. 3.15 This confirms that at 2wt% Cr, there is sufficient precipitation of
austenite (> 0.1 mole fraction) for transformation toughening and bcc Cu (~0.03 mole
fraction) for strengthening.
0.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
0 0.02 0.04 0.06 0.08 0.1 0.12
Alloy wt. fraction of Cr
Phas
e fr
actio
ns
FCC austenite
BCC copper
M2C
MC
Figure 3.15 Equilibrium phase fractions at 5100C as a function of alloy Cr content
(wt fraction)
94
3.2.4 Processing Considerations
3.2.4.1 Solution Treatment Temperature and Allotropic Transformations
A solution treatment temperature of 9000C was chosen based on
optimization studies [2, 117] of grain size dependence on hardness and toughness on 1
hour solution treated samples in secondary hardened steels. With the increased levels
of Cu and Cr it was confirmed that the alloy was solution treatable at 9000C as shown
by the ThermoCalc™ plot in Fig. 3.16.
Figure 3.16 Plot showing the variation of equilibrium mole fraction of different phases in the alloy as a function of temperature, showing that the alloy is solution treatable at 9000C
95
For this alloy composition, the martensite and bainite kinetic models
predict an MS temperature of 2980C and a bainite start (BS) temperature of 3360C.
These should be sufficiently high to ensure formation of bainite/martensite mixtures
with air-cooling.
3.2.4.2 Scheil Simulation for Microsegregation behavior
Solidification of alloys generally occurs with segregation, which can
have a strong effect on the alloy’s final properties. Thus, it is important to model
segregation to assess the processability of the designed alloy. This investigation uses
thermodynamic modeling to predict microsegregation of the as-cast material.
Macrosegregation effects can also be addressed by modeling liquid buoyancy
associated with the microsegregation amplitude but are not addressed in this
assessment.
Scheil simulation is a fast method of estimating microsegregation [118].
The main approximations are infinite diffusion in the liquid but no diffusion in the
solid phase. This has been coupled to the multicomponent SGTE thermodynamic
database using ThermoCalc™ from which the solid/liquid equilibrium was calculated
repeatedly during the simulation. Fig. 3.17 presents the solidification simulation result
as temperature vs. fraction solid using the non-equilibrium Scheil simulation and
compares it with the full equilibrium case. Fig. 3.18 presents the composition profiles
calculated by the Scheil simulation showing the degree of microsegregation in the solid
96
after solidification. Here, the fraction of solid is equivalent to position relative to a
dendrite arm center. Previous comparison with more rigorous calculations
incorporating solid back diffusion indicate that the Scheil result at 95% solid is a
reasonable estimate of the maximum microsegregation amplitude under typical ingot
solidification conditions. The results presented in Table 3.2 predict that Mo has the
greatest potential for segregation. However, since the level of Mo in the alloy is low,
no serious microsegregation problems are predicted for the designed composition.
97
Figure 3.17 Scheil simulation for evolution of the fraction solid with cooling for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%) in comparison with equilibrium solidification
98
Figure 3.18 Scheil simulation for composition profile of each alloying element after
solidification for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%). Solid fraction corresponds to position relative to dendrite arm center
Table 3.2: Amplitude of microsegregation with respect to each alloying element
predicted by Scheil simulation at 95% solidification
Alloying Elements Ni Cu Cr Mo V Nominal Alloy Composition
Calloy (at %)
6.38 3.31 2.04 0.36 0.11
Microsegregation Amplitude
C0.95 – C0 (at %)
1.29
1.67
0.72
0.34
0.05
99
3.2.4.3 Optimal Tempering Temperature
The austenite stability for this transformation toughened alloy is
dependent on the optimal tempering temperature condition. With the alloy composition
fixed, the austenite stability was then calculated as a function of tempering temperature
as shown in Fig. 3.19. It illustrates that the ∆Gch + Wf value of 2836 J/mole desired for
this alloy is achieved for a tempering temperature of 4900C, very close to the originally
assumed temperature of 5000C.
Figure 3.19 Room Temperature (300K) stability of austenite as a function of tempering temperature. The required stability is predicted for 4900C
100
Based on the design calculations, we derive a composition for the
ultratough, high strength weldable plate steel (in wt%) to be tempered at 4900C:
Fe – 0.05C – 3.65Cu – 6.5Ni – 1.84Cr – 0.6Mo – 0.1V.
The composition should be solution treatable at 9000C, with predicted MS and BS
transformation temperatures of 2980C and 3360C respectively. Based on previous
transformation toughened steels, it is expected that initial tempering at a slightly
elevated temperature will help nucleate the austenite before tempering at 4900C to
enrich the Ni content to the designed level.
101
4. MATERIALS AND EXPERIMENTAL PROCEDURES
4.1 Materials
The compositions of the alloys studied in this research have been
designed using a systems-based approach as presented in Appendix A (Concept A
alloy) and in Chapter 3 (Concept B alloy). The alloys were designed to provide an
effective transformation toughening austenite dispersion and an efficient combination
of carbide and copper strengthening dispersions. Special Metals Corporation in New
Hartford, New York produced the alloys as 34-pound experimental heats by Vacuum
Induction Melting (VIM) from 100% virgin raw materials and cast into 9.5” X 8” X
1.75” (24.1cm X 20.3cm X 4.5cm) slab ingots as a simulation of a continuous casting
process. The as-cast ingots were subsequently homogenized at 22000F (12040C) for 8
hours and then hot rolled to 0.45” (1.1cm) thickness followed by air-cooling to room
temperature by Huntington Alloys in Huntington, West Virginia. The final dimension
of the plate measured roughly 33” X 10” X 0.45” (83.8cm X 25.4cm X 1.1cm). The
hot-rolled plate was annealed at 9000F (4820C) for 10 hours to improve machinability
of the material. The designed and the actual compositions (in wt %) of the Concept A
and Concept B alloys are given in Tables 4.1A and 4.1B respectively. The impurity
levels in the Concept A alloy were measured as 0.002 wt % S, 13 ppm O and 2 ppm N,
and are expected to be similar in the Concept B alloy based on its identical melt
practice. The measured compositions are very close to the designed compositions and
the variations are within the tolerance limits of the design.
102
Table 4.1A: Designed and Measured Composition (in wt. %) of Concept A* alloy
Alloy Fe C Cu Ni Mn Si
Design Bal. 0.10
± 0.01
1.37
± 0.05
0.82
± 0.05
7.6
± 0.2
1.5
± 0.05
Measured Bal. 0.10 1.39 0.84 7.42 1.45
*Prototype Evaluation of Concept A alloy is described in Appendix A
Table 4.1B: Designed and Measured Composition (in wt. %) of Concept B alloy
Alloy Fe C Cu Ni Cr Mo V
Design Bal. 0.05
± 0.01
3.65
± 0.05
6.5
± 0.2
1.84
± 0.05
0.6
± 0.05
0.1
± 0.01
Measured Bal. 0.040 3.64 6.61 1.78 0.58 0.11
4.2 Experimental Procedures
4.2.1 Heat Treating
All samples were solution treated at 9000C for 1 hour and quenched in
water followed by a liquid nitrogen cool for 30 minutes prior to every tempering
treatment to ensure a fully martensitic starting microstructure and eliminate any
retained austenite. Solution treatments were done in an argon atmosphere to prevent
103
oxidation of samples. To ensure rapid heating of the entire sample, the short-time
nucleation stage heat treatments were conducted using a molten salt bath followed by
water-quenching to room temperature. The salt used for the molten bath was Thermo-
Quench Salt (300 – 11000F) produced by Heat Bath Corporation. The residue layer
from the salt pot treatment was ground off before the second step aging treatment. The
standard aging treatments for longer times (1 – 10 hours) were performed in a box
furnace under vacuum (to prevent oxidation and decarburization) and then air-cooled
to room temperature. Vacuum was achieved by encapsulating the samples in 0.75”
diameter pyrex tubes connected to a vacuum system. The pyrex tubes were evacuated
by a mechanical roughing pump followed by a diffusion pump. During evacuation, the
tubes were backfilled with argon three times before reaching a final vacuum of < 5
mtorr. Each tube was then sealed with an oxygen/propane torch.
4.2.2 Metallographic Sample Preparation
All samples were ground and polished directly to 1 µm finish using a
Buehler Ecomet-4 variable speed automatic grinder/polisher. The samples prepared for
measuring hardness were mounted in room temperature curing acrylic, while those
prepared for microsegregation studies were hot mounted with conductive phenolic
resin using a Stuers LaboPress-1 after nickel-plating for edge retention of the oxide
layer during grinding and polishing. Microsegregation samples were etched by
submersion in a 2% nital (2% nitric acid in ethanol) solution for 10 – 30 seconds to
104
reveal the compositional banding close to the metal-oxide interface associated with
scale formation during hot working. Following etching, the samples were viewed with
an optical microscope to study the banded structure in the as-cast material.
4.2.3 Dilatometry
Dilatometry is used to study phase transformations by recording length
changes versus temperature. For these studies a computer controlled MMC Quenching
Dilatometer was used. Specimens were prepared by EDM (Electro-Discharge
Machining) wire cutting into cylindrical rods 10 mm long and 3 mm in diameter. The
samples are heated by an induction furnace and cooled by jets of helium gas. They are
mounted between two low expansion quartz platens, which are lightly spring-loaded
and are connected to an LVDT transducer that records the length. The temperature is
monitored by a Pt-Pt 10%Rh thermocouple spot welded directly to the sample surface.
The sample stage is enclosed in a vacuum chamber connected to a turbo-mechanical
pump and mechanical backing pump capable of achieving a vacuum of 10-4 torr.
Dilatometry was used for determining the martensite start temperature
(MS) and for evaluating the bainite transformation kinetics. For estimating the
experimental MS temperature, samples were heated at a rate of 2-30C/sec to 10500C,
held for 5 minutes for homogenization and then rapidly quenched (> 1000C/sec) to
room temperature. The MS temperature was determined as the transition at which the
sample started expanding on cooling. For studying the bainite kinetics, samples were
105
held isothermally for 2 hours at bainite transformation temperatures between 360 –
4200C after quenching (Cooling rate from 8000C to 5000C, T8/5 = 500C/sec) from the
austenizing temperature. The length change at the isothermal hold temperature is a
measure of the amount of bainitic transformation. All samples were austenized at
10500C for 5 minutes and then rapidly quenched prior to the actual runs of martensite
and bainite transformation in order to ensure uniform starting microstructure.
4.2.4 Microhardness Testing
Vickers hardness was measured for every aging condition as a measure
of strength. The relationship between hardness and yield strength (Fig. 3.2) helped to
assess the mechanical properties directly from the hardness data. Hardness
measurements of materials in this study were performed using the Buehler Micromet II
Micro Hardness Tester based on the method prescribed in ASTM standard E384. A
diamond Vickers pyramidal indenter with face angles of 1360 is used to make the
indentations. After applying a load of 200g for 5 seconds, the diagonals of the indent
were measured at 400X magnification to obtain the Vickers Hardness (VHN)
according to Equation 4.1.
2
854.1d
PVHN = (4.1)
where P is the load in kg. and d is the average length of the diagonal in millimeters of
the indent. Prior to testing, all the heat-treated samples were mounted in acrylic mold
106
and polished to 1 µm. The samples were at least 8mm thick and ground to reveal
opposite surfaces to avoid any errors due to anvil effects. At least ten hardness
measurements were recorded uniformly across the cross-section for every sample
tested and the average was documented as the hardness value.
4.2.5 Impact Toughness Testing
The impact toughness properties for the different heat treatment
conditions of the alloy were measured using a Tinius Olsen 260 ft-lb (352J) impact-
testing machine. Prior to testing, the samples were machined according to the ASTM
standard Charpy V-notch dimensions (1996 ASTM E23) 10mm X 10mm X 55mm
(0.39” X 0.39” X 2.17”) with a 450 notch of depth 2mm and root radius of 0.25mm
placed at the center of the long side. The longitudinal axis of the specimen
corresponded to the L-T orientation. A schematic view of the sample geometry is given
in Fig. 4.1. The impact fracture energy was measured directly on analog scale and the
given impact energy data was mostly based on a two-sample average. Most impact
properties were evaluated at room temperature. For the low temperature impact
fracture properties, the aged samples were held for 20 minutes at the test temperature
in an Instron low temperature furnace connected to a liquid nitrogen supply. Within 5
seconds of removal from the furnace, the samples were placed inside the machine and
struck with the 100-lbf hammer.
107
Rolling Direction
Figure 4.1 Charpy V-notch impact specimen dimensions (Standard ASTM E23) with longitudinal axis corresponding to the L-T orientation
4.2.6 Tensile Testing
Tensile test specimens were machined from blanks measuring
approximately 10mm X 10mm X 70mm (0.39” X 0.39” X 2.76”) from the original
plate parallel to the longitudinal rolling direction. Prior to machining, the samples were
solution-treated and aged as discussed in Section 4.2.1. From each blank, sub-sized
tensile specimens, scaled in accordance to ASTM standards (1996 ASTM E8M) were
machined as shown schematically in Fig. 4.2. The final specimen had a gage diameter
of 6 mm (0.24”) and a gage length of 30 mm (1.18”).
108
Rolling Direction
G (gage length) 30 ± 0.1 mm (1.18” ± 0.004”) D (gage diameter) 6 ± 0.1 mm (0.24” ± 0.004”) R (radius of fillet) 6 mm (0.24”) A (length of reduced section) 36 mm (1.42”) Figure 4.2 Tensile test specimen dimensions (Standard ASTM E23)
All tensile tests were performed at room temperature using a computer
controlled Sintech 20/G screw driven mechanical testing machine with a 20,000 lb
(8896 N) load cell at a constant cross-head speed of 0.005 in/sec (0.127 mm/sec). The
load cell was calibrated prior to every data set using the computer controlled
calibration test. A calibrated extensometer of gage length 1” (25.4 mm) was attached to
the sample during testing to measure the displacement. The load-time response was
recorded using the TestWorks computer software package interfaced with the Sintech
tensile testing machine. The actual cross-sectional areas and gage lengths of the
specimens were measured prior to testing and listed in the testing program. Area
reduction and extension were measured manually upon completion of the test.
Engineering stress-strain curves were obtained directly thorough the TestWorks
109
program. Based on a two-sample average for select processing conditions, the ultimate
tensile strengths, 0.2% offset yield strengths and total elongations were obtained.
4.2.7 X-Ray Diffraction (XRD)
The measurement of the volume fraction of austenite was attempted by
X-ray Diffraction. Metallographically polished samples were centered in a Scintag
diffractometer equipped with CuKα radiation source and a solid-state detector. For
austenite volume fraction measurements the ratio of the integrated intensities of (200)
reflection of martensite and (220) reflection of austenite were compared with that of a
standard specimen of known volume fractions of ferrite and austenite. The 2θ ranges
scanned were from 630 to 670 for the (200) reflection of martensite and from 71.50 to
77.50 for the (220) reflection of austenite. The data collection times were 50s and 100s
for the austenite and the martensite reflection, respectively, at each step with a step size
of 0.0250. The volume fraction of austenite was measured after water quenching from
solution treatment for 1 hour at 9000C followed by liquid nitrogen cooling and
tempering treatment.
In a two phase alloy consisting of martensite (α) and austenite (γ), the
ratio of the diffracted intensities is given by [139]
α
γ
γαα
γ
V
V
ff
RII
220200200
220 = (4.1)
110
where Iγ220 and Iα200 are the integrated intensities and fVγ and fV
α are the volume
fractions of austenite and martensite respectively. The Rij-factor includes the structure
factor, the multiplicity factor, the Lorentz-Polarization factor and the temperature
factor. For a given experimental setup and a selected pair of austenite-ferrite reflection,
the R-factor is a constant relating intensity to volume fraction by Equation 4.1. In this
work, the Rα200γ220 factor for the above experimental condition was evaluated using a
Standard Reference Material (SRM # 485) from the National Bureau of Standards
(NBS) containing 4 ± 0.2 vol% austenite in ferrite. The volume fraction of austenite in
the tempered prototype can then be determined by following the relation:
γγαα
γγαγ
IRIIR
fV += (4.2)
The (220) reflection of austenite was not discernable above the background, attributed
to a very fine particle size established by atom-probe observations.
4.2.8 Magnetometry
Magnetometry measurements were performed to determine the austenite
volume fraction in the heat treated alloys. The difference in the magnetic moments of
the martensite and austenite phases are used to determine the phase fractions based on
the total measured magnetic moment and the rule of mixtures. Magnetometry was
selected in addition to standard X-ray diffraction method because of the matrix strain,
111
texture in the alloys tested, nanometer-sized austenite precipitates and low precipitate
volume fraction which reduces the signal to noise ratio to unacceptable levels.
A Quantum Design Magnetic Property Measurement System with a
superconducting quantum interference device (SQUID) detector was used in these
experiments. The apparatus is equipped with a superconducting magnet capable of
supplying a maximum of 50,000 gauss to the sample. The resulting magnetization was
measured using a SQUID detector. The magnetic signal was measured at 298K by
passing the specimen through the detector with applied magnetic field strengths
ranging from 5000 – 50000 gauss and measuring the response of the detector as a
function of distance within the detector. Each data point was measured three times to
ensure accuracy and provide error estimations. The specimen weight was limited to
less than 5mg to avoid saturating the detector with induced moments of greater than
1.25 emu. To produce samples of this size, thin discs were sectioned from the heat-
treated samples, ground using 600 grit SiC and then finally electro-polished using a
perchloric and acetic acid solution to remove any surface cold work introduced during
sample preparation. The completed specimen is contained in a gelatin capsule and is
suspended with a nonmagnetic plastic rod in the measurement chamber kept under
vacuum. The specific magnetization is calculated from the recorded data and plotted
against the reciprocal of the applied field as shown in Fig. 4.3. The intercept with the
y-axis is taken as the saturation magnetization.
112
σ = mH-1 + σS
σS = 204.21m = -783999R2 = 0.9892
0
50
100
150
200
250
0 0.00005 0.0001 0.00015 0.0002 0.00025
H-1 (gauss-1)
Spec
ific
Mag
netiz
atio
n (e
mu/
g)
Figure 4.3 An example of magnetometry data processing to determine saturation magnetization
The saturation magnetization can be related to the experimentally
measured room temperature magnetic moments by the Miodownik [110]
approximation to the Brillouin-Langevin function represented by Equations 4.2 and
4.3.
⎥⎦
⎤⎢⎣
⎡−= 60 )(1
CSS T
Tσσ T < 0.9 TC (4.2)
⎟⎟⎠
⎞⎜⎜⎝
⎛−
⎟⎠⎞
⎜⎝⎛=
8100
21 CT
T
SS σσ T > 0.9 TC (4.3)
where σS0 is the magnetic moment at absolute zero, TC is the Curie temperature and σS
is the magnetic moment at temperature T. The Bohr magneton moment at absolute zero
113
and the Curie temperature for FCC and BCC phases can be calculated using the
ThermoCalc™ SGTE-SSOL database. The saturation magnetization value at absolute
zero is calculated from the predicted magnetic moment per atom (from ThermoCalc™)
by multiplying the moment per atom by Avagadro’s number and dividing by the
atomic weight of the phase. The contribution from carbides and copper precipitates is
neglected because their magnetic moments are much less that either that of austenite
(γ) or martensite (α). The rule of simple mixtures is then solved to determine the molar
fractions of each phase.
(4.4) γγαα σσσ SmSmalloyS ff +=
where, σSalloy is the measured saturation magnetic moment, fm is the molar fraction of
the denoted phases. The molar fraction is then converted to volume fraction using the
relation:
)( 11
1
−−
−
+=
αα
γγ
γγ
γ
ρρρ
ww
wv ff
ff (4.5)
where ρ is the density of the indicated phase.
4.2.9 Electron Microscopy
A Hitachi S-3500 scanning electron microscope (SEM) with a tungsten
hairpin filament was used to investigate the composition banding in the as-rolled
samples and the fracture surfaces of the Charpy impact specimens. The microscope
uses Quartz PCI Image Management Software for capturing images and for conducting
114
quantitative analysis. For analysis, the samples were mounted on graphite tape and
examined in the SEM with a 20 kV electron beam at a vacuum level of 10-4 torr inside
the specimen chamber. The secondary electron (SE) detector was used for imaging
both the etched and fracture surfaces. The compositionally banded structure of the
etched sample was characterized quantitatively from the metal-oxide interface using
the PGT Energy Dispersive X-ray analyzer with digital pulse processing. Fractography
analysis was done to characterize the fracture surface and micrographs containing
interesting features were taken.
Conventional transmission electron microscopy (TEM) was performed
in a Hitachi H-8100 200kV thermionic-emission (W hairpin filament) TEM. The
samples were obtained by sectioning thin slices approximately 150 µm thick directly
from the hardness specimens. The samples were then ground to a thickness of
approximately 50 µm and then punched into small discs. The discs were then jet-
polished until a small hole was present using a Twin Jet electropolishing system with a
20 vol.% perchloric acid in methanol electrolyte at a temperature of –400C and an
operating voltage in the range of 35-40 V.
4.2.10 Atom Probe/ Field Ion Microscopy (AP-FIM)
A three-dimensional atom probe microscope (MRC Atom-Probe
Facility, Northwestern University) described in [111], was used for characterizing the
size, number-density and composition of nanoscale strengthening (Cu precipitates) and
115
toughening (Ni-stabilized austenite) dispersions in the heat-treated samples. The atom
probe, operated and maintained under an ultra-high vacuum system (10-10- 10-11 torr)
combined with a field ion microscope, operated with imaging gas at a pressure level of
10-5 torr, makes it an extremely high-resolution microscopy technique.
The specimens (atom probe tips) were prepared by a two-step
electropolishing sequence of small rods (100mm long with 200µm X 200µm square
cross-section) cut from heat-treated hardness samples. Initial polishing was done using
a solution of 10% perchloric acid in butoxyethanol at room temperature applying a DC
voltage of 23V until the square rods were shaped into long needles with a small taper
angle. A solution of 2% perchloric acid in butoxyethanol at room temperature was used
for necking and final polishing to produce a sharply pointed tip, with a radius of
curvature less than 50nm. The voltage was gradually decreased from 12V DC to 5V
DC during the final stages of electropolishing.
Each atom probe specimen of tip radius 10 to 50 nm is raised to a high
positive potential of 5-15 kV, resulting in an exceptionally strong electric field on the
order of 50 V/nm. FIM analysis was performed at temperatures between 50K – 80K
with a chamber pressure of 10-5 torr consisting of neon gas. The voltage on the tip was
raised until an FIM image was observed on the monitor. Neon atoms, which are used
as an imaging gas for steel, are ionized in the high electric field causing the positively
charged ions to accelerate to a microchannel plate array. The ionization process occurs
at prominent atomic sites at the edge of a crystallographic plane corresponding to a
116
particular atom. A continuous stream of ions form an image on a phosphorus screen
that represents the nanometer-scale structure of the specimen tip. FIM images were
captured during analysis using the Scion Image imaging software. For atom probe
analysis, the specimen is then rotated towards the reflectron for aligning the primary
detector on the region of interest in the FIM image (usually near a pole or on a
precipitate in the FIM image). Atom probe analysis is then conducted at temperatures
50K and 70K under ultra-high vacuum conditions (10-10- 10-11 torr) for pulsed field-
evaporation with a pulse fraction (pulse voltage/ steady state DC voltage) of 20% at a
pulse frequency of 1500Hz.
Atom probe microanalysis is the study of the specimen composition by
pulsed evaporation. Field evaporation of the specimen occurs at higher electric fields
than ionization of imaging gas ions. The positively charged ions evaporated from the
specimen are accelerated towards a detector. By measuring the time of flight, it is
possible to determine the mass to charge ratio of the ions according to the following
equation [112]:
( )2
0 ⎟⎠
⎞⎜⎝
⎛ ++=
dtt
VVknm
pulsedc βα (4.6)
where m is the atomic mass, n is the charge, k is a constant related to the elementary
charge of an electron, V is the DC or pulse voltage, t is the time, t0 is a time offset from
electronic delays, and α and β are system specific calibration parameters.
117
The standard error, σ, for compositions measured using an atom probe is
calculated using binomial statistics to account for the statistical uncertainty associated
with small sampling sizes according to the equation [113]:
σ =ci 1 − ci( )
N (4.7)
where ci is the measured composition of element i and N is the total number of ions
sampled. This standard error does not account for any overlapping mass to charge
ratios between different elements. Systematic errors that may interfere with the
collection of specific elements such as carbon may be an additional source of error.
Three-dimensional atom probe (3DAP) records the two-dimensional
location of atoms and determines the third dimension (z) by the sequence of arrival of
atoms to the detector, thus providing a three-dimensional reconstruction of the
specimen tip. The evaporated ion collides with a primary detector that records the time
of flight, and the phosphorus screen emits light. The light is split by a partially
silvered mirror at 45° to both a camera and an 8 by 10 array of anodes which determine
the position of the ion.
The data from 3DAP was analyzed and visualized by the software
ADAM developed by Hellman et al [114]. Different elemental isotopes were
distinguished by their mass/charge ratio. The overlap of isotope masses between
elements contributed to the experimental error in addition to the statistical counting
error. A range of tools is available in ADAM to analyze the data from the 3DAP [115].
118
One feature of ADAM is the ability to define planar or cylindrical regions of interest
and to perform analyses such as concentration profiles, ladder diagrams and
composition maps with respect to that region of interest. For the data containing copper
precipitates, varying in composition from the matrix, it was possible to define
isoconcentration surfaces of constant composition. The three-dimensional
representation of these isoconcentration surfaces allows for a qualitative view of the
approximate size and shape of the precipitates being studied. ADAM has been designed
to employ this method by creating a discrete lattice of nodes for which the local
composition is calculated. The isoconcentration surfaces then have discrete positions.
The creation of isoconcentration surfaces allows for another method of 3DAP data
analysis referred to as the proximity histogram, or proxigram [116]. The minimum
distance to an isoconcentration surface is calculated for each ion in the data set and the
ions are then assigned to bins according to distance. The concentration of each bin is
calculated and plotted as a function of distance to the isoconcentration surface. The
standard error of each bin is calculated and displayed on the proxigram.
119
5. PROTOTYPE EVALUATION
Characterization of the Concept B prototype alloy demonstrated the
effectiveness of the systems approach to computational materials design as described
in Chapter 3. The primary goal of prototype evaluation in this study is to
experimentally verify the processing-structure and structure-property relationships
quantified during the alloy design process. This will reveal the strength and
weaknesses of the design models and their integration. The analysis began with
evaluation of the processability characteristics of the designed alloy at an
experimental-heat scale. Optimization of the tempering response of the alloy designed
for multi-step treatment helped to attain a toughness/strength combination exceeding
the design objectives. Characterization of the strengthening and toughening dispersions
related the structure to the properties and verified the prototype design.
5.1 Microsegregation and Hot-working behavior
The achievement of the property objectives begins with meeting the
initial processability requirements, i.e., castability of the steel. Microsegregation is a
common problem observed in high-alloyed castings and hot-worked products, which
limits the mechanical properties. For example, the mechanical properties of the
stainless prototype alloy from a previous project, NASA2, suffered from Cr
segregation resulting in high amounts of retained austenite [117]. This occurs because
of interdendritic segregation of alloying elements during solidification, which leads to
120
a concentration banding in the cast structure. The regions enriched in these elements
are elongated during rolling. When etched, the inherited segregation produces a banded
appearance on both the transverse and the longitudinal sections. Differential etching
effects reveal this banded structure arising from a non-uniform concentration profile
across the sample.
To study the microsegregation behavior in our cast prototype, the as-
received material (homogenized for 8 hours at 12040C, hot-rolled for 75% reduction to
0.45” or 4.5cm thick plate and then annealed at 4820C for 10 hours) in the form of a
10mm X 10mm X 20mm sample, was etched with 2% nital following standard
metallographic polishing to 1µm. Low magnification transverse optical micrographs
revealed both the banded structure oriented along the longitudinal rolling direction and
the oxide-metal interface as shown in Fig. 5.1.
Rolling Direction
Figure 5.1 Optical micrograph of the as-received plate viewed transverse to the rolling direction at the oxide-metal interface after etching with 2% nital
121
The centerline of the hot-rolled plate did not reveal as much of a banded
structure as the surface region, as shown in Fig. 5.2. Higher magnification optical
micrograph at the centerline of the plate presented in Fig. 5.3 shows an equiaxed
microstructure, which is predominantly lath martensite in the form of packets within
the prior austenite grain boundaries of an average size of ~50µm.
Rolling Direction
Figure 5.2 Optical micrograph of the hot-rolled plate viewed transverse to the
rolling direction at the centerline after etching with 2% nital
122
Figure 5.3 Higher magnification optical micrograph of the hot-rolled plate at the
centerline
The composition bands revealed on etching in Fig. 5.1 were estimated
to be of 40-50 µm thickness. The extent of microsegregation within these bands was
determined by measuring the composition profile across the thickness of the plate near
the oxide-metal interface. Composition data was collected every 4µm starting from the
metal-oxide interface and proceeding towards the center of the plate. The composition
variation across the bands with respect to the major alloying elements Ni, Cu, Cr and
Mo is presented in Fig. 5.4. It was found that compositional banding in the plate was
limited to an amplitude of approximately 6 - 7.5 wt% Ni, 3.5 - 5 wt% Cu, 1.6 – 2 wt%
Cr, and 0.2 – 0.5wt% Mo and agree well with the microsegregation predictions
obtained from Scheil simulation in Chapter 3. From the strength model, a variation in
123
the level of Cu across the bands within 3.5 to 5 wt% corresponds to a predicted
hardness variation of 30 VHN equivalent to 6.8 ksi (~47 MPa) in yield strength. This
will promote a smooth yielding behavior as confirmed by the tensile property behavior
in Section 5.5.
Figure 5.4 Line profile compositions for as-received material from oxide-metal
interface
Another important factor determining the processability of an alloy is
the material response during high temperature deformation or formability. Hot
shortness is a common problem associated with high copper steel production. During
the rolling stage of the fabrication process, the effect of hot shortness is observed by
124
the appearance of surface cracks or fissures leading to unacceptable products.
Investigations in the past [119, 120, 121] have shown that copper is a particularly
detrimental element associated with this phenomenon. At hot rolling temperatures
above 10500C in an oxidizing atmosphere, iron is selectively oxidized leaving an
enrichment of copper near the oxide-metal interface. If the composition of the copper
enriched region exceeds the liquid-austenite equilibrium limit, the copper enriched
liquid phase enters the grain boundary of the austenite causing intergranular fracture
during hot rolling. But the advantages of copper addition to steels for strengthening as
well as improving atmospheric-corrosion resistance has led to extensive research [122-
126] to prevent hot-shortness in copper-bearing steels. These studies have explored the
mechanism by which addition of nickel in an amount equal to 0.5 – 1 times that of
copper shows negligible surface cracking. The prevention of hot shortness by Ni in Cu-
steels has been rationalized by several demonstrated theories. Salter [122]
demonstrated that Ni increases the solubility of Cu in austenite while another theory
[126] proposes that Ni raises the melting point of the Cu-rich phase above the
oxidation temperature. However, Fisher [123] later proposed that Ni causes occlusion
into the oxide scale of the enriched Cu-rich layer formed at the oxide-metal interface.
Based on the findings of previous research, a high Ni/Cu ratio of 1.8 was maintained in
our design to prevent any hot-shortness problems during processing. Successful hot
rolling of the designed alloy was demonstrated during processing. As further
verification, the oxide layer of the as-received material was examined carefully for any
125
evidence of Cu-rich regions. Fig. 5.5 shows an optical micrograph of the oxide layer in
the as-received plate. The oxide-metal interface does not show any evidence of hot
shortness. Composition analysis of various regions in the oxide layer did not reveal any
Cu rich phase but did show some Ni-enriched phases varying from 20 to 80% within
the Fe-rich oxide. This study thus supports the ability of Ni to cause occlusion of the
Cu-enriched liquid during oxidation as proposed by Fisher thus preventing hot
shortness in this steel containing 3.64 wt% Cu.
Figure 5.5 Optical micrograph showing the oxide scale in the as-received plate
5.2 Evaluation of Allotropic Kinetics
A dilatometry study was next conducted to determine the allotropic
kinetics of the prototype. The first step involved the measurement of the martensite
start temperature (MS) of the designed alloy. Fig. 5.6 presents a plot of the relative
126
length change vs. temperature, used to determine the transformation points during the
heating and cooling (quench) cycle of a dilatometry experiment. Straight lines are fit to
the single phase portions of heating and cooling curves, the full width between them
defining full transformation. The series of dashed lines superimposed on the length and
temperature trace represent varying degrees of partial martensitic transformation
during rapid quench from an austenizing temperature of 10500C. The threshold for
transformation is taken as 1% [2]. Thus, MS was determined from the 1% martensitic
transformation point as shown in Fig. 5.6.
Figure 5.6 Relative sample length change and temperature trace during heating and
cooling (quench) cycle from dilatometry experiment
127
The MS temperature, averaged over 15 dilatometry runs, is 360 ± 8.4 0C.
The predicted MS temperature from the Ghosh-Olson model [105] using the SSOL
database was 2980C.
Since the alloy was designed to produce a bainite/martensite
microstructure during air-cooling of plates, the bainite kinetics was determined by
studying the isothermal time-temperature-transformation characteristics of the steel
through dilatometry. This information is useful in determining the processing
necessary in order to achieve bainitic transformation of 50%, for example. With the
help of senior project student Jamie Heisserer, the amount of bainitic transformation
was determined by isothermal hold experiments (after an initial quench step)
performed at incremental temperatures above the martensite start temperature. This
data was then compiled and analyzed in order to plot a time-temperature-
transformation (TTT) curve.
The relative length change vs. temperature dilatometry trace for a two-
hour isothermal hold at 377°C is presented in Fig. 5.7. The percent of bainitic
transformation is determined by measuring the length increase upon arrival at the
isothermal hold temperature and dividing it by the total FCC(γ) - BCC(α) length
difference (defined from the martensitic transformation in Fig. 5.6) at the isothermal
hold temperature. In this case, the total bainitic transformation that took place after 2
hours is 44.1%. The evolution of bainitic transformation with respect to time can be
determined from the measurement presented in Fig. 5.7. This behavior at 377 °C is
128
shown in Fig. 5.8. From this plot it is apparent that the volume fraction of bainite is
saturated after a two-hour isothermal hold. Similar analyses were carried out for each
two-hour test performed at isothermal temperatures ranging from 3620C to 4070C.
Table 5.1 summarizes the maximum transformation levels at all the temperatures. The
TTT curve was then determined by analyzing the data at each isothermal hold
temperature. For example, a 1% transformation curve is plotted by finding the time at
which the sample exhibits 1% transformation at different isothermal temperatures. The
TTT curve based on the data from all of the isothermal runs is presented in Fig. 5.9. It
shows that we can achieve a 50% bainite/martensite mix in approximately 4 minutes at
3600C. The experimental BS temperature was determined to be 4100C, 500C higher
than the corresponding MS temperature (3600C).
Figure 5.7 Relative sample length change and temperature trace during heating,
cooling and isothermal hold at 3770C from dilatometry experiment
129
Table 5.1: Saturation volume fraction of bainite as a function of isothermal temperature
Temperature (C) Saturation Volume Fraction of Bainite 362 0.609629 367 0.526697 372 0.5003 377 0.440938 382 0.242981 387 0.265119 392 0.098382 402 0.015628 407 0.007966
Figure 5.8 Volume fraction evolution of bainite as a function of time for isothermal
temperature of 3770C
130
Figure 5.9 Time-temperature-transformation (TTT) curve for bainite
transformation reaction
Based on this experimental data, the thermodynamic model of bainite
kinetics as described in Chapter 2, Section 2.2.2.1 was calibrated to accurately reflect
the actual kinetics of the alloy in preparation for further design iterations. The model
implemented by the bainite kinetics software (“RunBmk”) yields an output of a TTT
curve, volume fraction vs. temperature and other additional plots, when the alloy
composition and other thermodynamic terms are input. The model was calibrated to the
experimental data by employing two factors namely, nucleant potency and strain
energy.
131
One of the terms in the model is the ASTM Grain Size number, as
described in ASTM method E 112. Through the number density of nucleation sites,
grain size is a controlling factor of volume fraction, as well as the concavity of the TTT
model, and thus was used to fit the model volume fraction vs. temperature curve to the
experiment. The ASTM grain size number of 15 allowed for the best fit of the model
to the data. The saturation volume fraction of bainite was fit to the experimental data as
a function of temperature to determine the best fitting nucleation density (grain size)
parameter (Fig. 5.10). Metallographic etching did not reveal the prior austenite grain
boundaries as shown in Fig. 5.11, and thus the grain size used for the fit was not
validated. Based on the nital etching response, the larger blocks that are lighter in
color are potentially martensite with the darker, finer microstructure being that of
bainite. The microstructure contains roughly 60% bainite and 40% martensite mix, as
determined from dilatometry.
132
Figure 5.10 Experimental data fit to saturation volume fraction of bainite predicted by model [26] using ASTM grain size number 15
Figure 5.11 Microstructure showing 60% bainite and 40% martensite mix after 2-hour isothermal hold at 3600C during dilatometry
133
The model initially predicted much slower bainite transformation
kinetics than observed experimentally (Fig. 5.9) because the MS temperature was
underestimated by ~600C. However, the interval between the model BS and the MS
temperatures was in reasonable agreement with the experimental result of 500C. The
model MS temperature was fit to the experimental MS of 3600C by adjusting the strain
energy correction factor G (J/mole) in CMD™ to –384 J/mole. This is equivalent to a
shift of the free energy curve by a constant. The resulting bainite start temperature of
4030C is very close to the experimental BS temperature of 4100C. Fig. 5.12 presents the
TTT curve output from the model after correction of the transformation temperature.
After calibration, the bainite kinetics model curve is in reasonable agreement at lower
temperatures (where the highest bainite saturation levels are achieved) with the start
kinetics of the bainite transformation reaction determined experimentally (Fig. 5.9).
134
Figure 5.12 TTT diagram representing 1% bainite transformation calculated from
model [26] after calibration to fit experimental data
5.3 Isochronal Tempering Response
An isochronal tempering study was conducted to evaluate the tempering
characteristics of the prototype and provide a baseline for later studies of multi-step
tempering treatments. For simplicity, the tempering response investigation was done in
a uniform martensite matrix to minimize retained austenite effects. Deleterious
transformation products from retained austenite decomposition during tempering could
negatively affect the toughness. After a solution treatment at 9000C for 1 hour followed
by a water quench and liquid nitrogen cool, tempering was performed for 1, 5 and 10
hours under vacuum. Samples were finish machined, notched and then tested at room
135
temperature for Charpy impact toughness. Hardness measurements were taken directly
from the polished surface of the Charpy specimens.
The tempering response for 1 hour isochronal tempering was
investigated over a temperature range of 2000C - 6000C in the solution-treated
prototype alloy and is shown in Fig. 5.13. The 1-hour isochronal tempering study
demonstrates that a peak hardness level is reached at 4200C followed by gradual
overaging. This is consistent with the peak aging temperature for 30 minute tempering
reported by Maruyama et al [81] in martensitic steels strengthened by copper
precipitation. The retention of high hardness even after the peak aging condition to
5000C can be attributed to precipitation of M2C carbides and a fine austenite dispersion
observed at secondary hardening temperature of 4820C in carbide strengthened ultra-
high strength steels like AerMet100 and AF1410 [2]. The hardness at 5000C
(represented by an arrow in Fig. 5.13) is in very good agreement with that predicted for
the calculated final tempering temperature (4900C) in Chapter 3 to achieve the design
objectives.
136
Figure 5.13 Isochronal (1 hour) tempering response of prototype alloy. The arrow
superimposed on the plot shows that the design objective is achieved by tempering at 5000C in agreement with design prediction.
After confirming the basic secondary hardening characteristics of the
prototype alloy, a series of isochronal tempering treatments of Charpy specimens were
done for 1, 5 and 10 hours within a temperature range of 400 – 6000C. Fig. 5.14
illustrates the room temperature Charpy toughness (CV) – Vickers hardness (VHN)
trajectory for the indicated tempering temperatures. This establishes the baseline of the
toughness-hardness (strength) combination in tempered martensitic microstructures.
137
The shape of the trajectory is consistent with earlier studies of HSLA100 [77], AF1410
and AerMet100 [2] where the best combination of strength and toughness are obtained
in slightly overaged condition corresponding to complete cementite dissolution.
At the shortest tempering time of 1 hour we see from Fig. 5.14 that
cementite formation limits toughness, and as Cu precipitates in its presence, strength
increases from 4000C to 4500C tempering treatment while there is a sharp decline in
toughness. With further tempering, cementite begins to dissolve as a result of M2C
carbide formation in combination with BCC copper precipitation at the peak aging
condition. This results in an increase of both strength and toughness. The toughness-
hardness trajectory takes a sharp turn thereafter, as the strengthening precipitates begin
to coarsen exceeding their optimum sizes and the strength continues to decrease with
overaging. Fig. 5.14 suggests that peak hardness occurs at 4500C 5 hour tempering and
the corresponding toughness resides on an upper band indicating complete dissolution
of paraequilibrium cementite by precipitation of an optimal size M2C strengthening
dispersion.
138
Figu
re 5
.14
Isoc
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The
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139
The highly overaged region is also likely associated with precipitation
of a fine dispersion of austenite, which increases in stability due to Ni enrichment at
higher tempering times. An interesting feature observed in the toughness-hardness
trajectory for 5 hour tempering in Fig. 5.14 between tempering temperatures of 5250C
and 5750C is a toughness enhancement from the baseline toughness of 144 ft-lbs to 170
ft-lbs respectively, a toughness increment by 18% at a strength level corresponding to
355 VHN. This is characteristic of the transformation toughening phenomenon caused
by the austenite reaching an optimal stability for the lower strength condition.
The tempering response of the hardness (strength) can be correlated to
an empirical Larson-Miller type parameter, known as the Hollomon-Jaffe tempering
parameter [127]. The parameter is defined as T(18 + ln(t)) where T is tempering
temperature in K and t is the tempering time in minutes, and is used for correlation of
hardness data at higher tempering temperatures between 4000C and 6000C. Fig. 5.15
presents the measured values of hardness for different tempering conditions as a
function of the Hollomon-Jaffe tempering parameter. Fairly good agreement with the
parameter is obtained for hardnesses under overaged tempering conditions. The
parameter can provide a simple interpolation scheme to adjust tempering for a desired
strength level.
140
Figure 5.15 Hollomon-Jaffe Parameter correlating the hardness data obtained for different tempering conditions in the overaged region
The fracture surfaces of the broken Charpy impact testing
samples were observed under SEM to characterize the mode of fracture. The fracture
surface for the 4500C 1 hour tempering condition is presented in Fig. 5.16. The SEM
micrograph reveals that the sample failed by quasi-cleavage fracture with signs of
intergranular embrittlement. Quasi-cleavage is characterized by an array of cleavage
failures connected by ductile tear ridges but is a much more desired fracture mode
compared to intergranular fracture. The fracture mode represents relatively brittle
behavior attributed to the presence of undissolved cementite at short tempering times.
141
Figure 5.16 SEM micrograph of quasi-cleavage fracture surface for prototype
tempered at 4500C for 1 hour
For higher tempering times and temperatures, ductile fracture occurred
by microvoid nucleation and coalescence. Representative SEM micrographs showing
ductile mode of fracture for 5 hour tempering marked by toughness enhancement due
to transformation toughening in Fig. 5.14 are presented in order of increasing
tempering temperature in Figs. 5.17 through 5.19. Fig. 5.17 clearly shows that a
completely ductile mode of fracture is achieved with 5 hour 5250C tempering and
micrographs presented in Figs. 5.18 and 5.19 represent fracture surfaces with increased
toughness due to transformation toughening, indicated by the relatively higher degree
of primary void growth.
142
Figure 5.17 SEM micrograph of ductile fracture surface for prototype tempered at
5250C for 5 hours
Figure 5.18 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for prototype tempered at 5500C for 5 hours
143
Figure 5.19 SEM micrograph of ductile fracture surface representing toughness
enhancement due to transformation toughening for prototype tempered at 5750C for 5 hours
5.4 Toughness Optimization by Multi-step Tempering
Heat treatment for stabilization of austenite for dispersed phase
transformation toughening phenomenon is directed towards combined size refinement
and compositional enrichment of the austenite particles. A two-step tempering process
consisting of an initial high temperature, short time treatment followed by a standard
isothermal tempering treatment is employed to achieve this goal. The first step is
designed to nucleate a fine, uniform dispersion of intralath austenite and strengthening
particles of sub-optimal size formed directly by increasing the driving force for
precipitation. This is achieved by a short time, high-temperature tempering step
144
designed to give an underaged state based on the isochronal tempering study. At this
stage, it is important to understand the implications of the kinetic competition between
the precipitation of austenite and strengthening dispersions namely, BCC copper and
M2C carbides. In the prototype alloy, the austenite precipitation kinetics is slower than
the BCC copper precipitation kinetics, which in turn is considerably slower than the
carbide precipitation process at intermediate tempering temperatures. It is, therefore,
critical to optimize the time for the high-temperature austenite nucleation step, since
the carbides might become overaged at higher times and full hardness cannot be
achieved. Yet this uncertainty in loss of strength by overaging of carbides is overcome
in the prototype because of additional strengthening of nearly 40% provided by BCC
copper precipitation (Chapter 3), which has slower coarsening kinetics than the
carbides. The second tempering step is optimized to enhance Ni-enrichment of the
austenite particles coupled with completion of precipitation strengthening for peak
aging condition involving enrichment of the 3nm Cu precipitates and cementite
conversion to 3nm M2C carbides. This is achieved by a longer-time final tempering at
a lower temperature characterized by the peak strengthening condition. Thus, from the
toughness-hardness trajectory for isochronal tempering presented in Fig. 5.14, the
optimal final stage tempering condition was determined to be 5 hours at 4500C, which
produced a peak hardness of 436 VHN. The first step was optimized by varying the
tempering time from 5 to 90 minutes over a temperature range of 5000C to 5750C in
intervals of 250C.
145
Figu
re 5
.20
Mul
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treat
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ts d
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ize
trans
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icke
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ndic
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146
Fig. 5.20 shows the variety of two-step heat treatments investigated to
maximize the toughness-strength combination in comparison with the HSLA100 alloy
and is superimposed on the isochronal tempering plot. The labels in the plot represent
the tempering time in minutes corresponding to the first step and the bold black arrow
points to the condition for maximum strengthening, which is the final step in the
tempering sequence. The short time, high temperature nucleation treatments were
conducted in a molten salt-bath to reduce heating time followed by water quench to
reduce cooling time. The initial solution treatment was conducted in argon atmosphere
and isothermal aging was conducted under vacuum as described in Chapter 4.
The optimal combination of toughness and strength is determined from
Fig. 5.20 to be a 5500C 30 minutes + 4500C 5 hours heat treatment. The apparent
achievement of optimal austenite stability by multi-step tempering results in significant
increase of impact toughness to 130 ft-lbs at a hardness level of 415 VHN. Comparing
with the baseline toughness-strength combination from isochronal tempering data, a
transformation toughening increment of 50% from 87 ft-lbs for the 10 hour isothermal
treatment and 70% from 77 ft-lbs for the 5 hour isothermal treatment is observed at the
same strength level. So an average of 60% toughness increment due to dispersed phase
transformation toughening can be attributed to multi-step tempering when compared to
standard isothermal tempering at the same strength level. This toughness level exceeds
the design goal of 85 ft-lbs by almost 55%.
147
The competition of several substructures begins with the first higher
temperature nucleation treatment. Within the carbide subsystem, cementite has an
initial advantage of precipitation because it involves only rapid interstitial carbon
diffusion. As aging time increases, the more stable but kinetically slower M2C carbides
attract carbon from cementite as they coherently precipitate at heterogeneous sites
provided by the high dislocation density of the martensitic matrix. In parallel, the
copper atoms also partition out of solution and nucleate on the dislocation substructure.
This should promote not only dissolution of cementite but also heterogeneous
nucleation of austenite particles on the carbide and copper strengthening precipitates.
Lippard [6] has demonstrated through microanalytical analysis that high Cr signals
corresponding to M2C are observed near dispersed intralath precipitates suggesting
carbide precipitates act as nucleation sites for the fine austenite. The precipitation
phenomenon is halted after the first step nucleation treatment by water quenching. At
this point, the microstructure consists of embryonic BCC copper and M2C precipitates
acting as nucleation sites for intralath austenite with some undissolved cementite. The
second heat treatment step continues the precipitation of M2C at the expense of
cementite and enriches the fine austenite in Ni while continuing the precipitation of
Cu. The lower temperature of this second tempering step is likely to produce additional
nucleation of the strengthening precipitates as more dislocation sites are activated by
the higher driving force. The embrittling cementite dispersion is eventually consumed
by the very fine dispersion of M2C.
148
SEM analysis of the fracture surfaces for the multi-step treatment
specimens indicate transition from quasi-cleavage to ductile mode of failure as the time
of initial tempering is increased, attributed to transformation toughening increment as
described in the previous section. Fig. 5.21 presents a representative micrograph of the
fracture surface for the optimal toughness-strength combination for tempering
treatment of 5500C 30min + 4500C 5hrs. Fig. 5.22 shows a higher magnification
micrograph of a primary void in the same sample. The relatively higher degree of
primary void growth is consistent with delayed microvoid instability, as expected for
transformation toughening.
Figure 5.21 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for the 5500C 30min + 4500C 5hrs multi-step tempering treatment
149
Figure 5.22 SEM micrograph of a primary void in the fracture surface of prototype for 5500C 30min + 4500C 5hrs multi-step tempering treatment
150
5.5 Evaluation of Tensile Properties
An evaluation of the tensile properties was conducted to determine the
actual yield strength of the prototype under the optimized tempering conditions and to
provide a basis for comparison of the hardness – strength correlation for this class of
steels. Room temperature tensile properties were assessed for the chosen heat treatment
conditions based on the results of the toughness – hardness data from both isochronal
and multi-step tempering response. The tempering conditions were chosen to cover the
full width of the toughness – strength combination plot (Fig.5.20). The same
processing route of solution treatment at 9000C for 1 hour followed by water and liquid
nitrogen quench and isothermal aging (short time aging was done using molten salt
bath) was followed for the tensile samples, prior to final machining into dimensions
described in Section 4.2.6. Duplicate samples for each heat treatment condition were
tested to determine the scatter in the data. Table 5.2 summarizes the results of the
tensile testing for the solution treated and aged samples for each heat treatment
condition and provides hardness values for comparison. Fig. 5.23 presents the true
stress vs. true plastic strain curves for all the samples tested. The curves are
represented as solid lines until the point of tensile instability (necking) or uniform
elongation and by dotted lines thereafter. The tensile data presented in Fig. 5.23 and
Table 5.2 confirms the design of a 160 ksi yield strength steel. The multi-step
tempering treatments helped to achieve the 160 ksi yield strength goal. Thus, the
prototype has been named “BlastAlloy160”.
151
Table 5.2: Room temperature tensile properties of prototype
Figure 5.23 True stress – true plastic strain response. The stress (σ) - plastic strain
(εp) behavior is shown by solid lines until uniform elongation and by dotted line after necking.
152
From data on the reduction in area at fracture and uniform elongation in
Table 5.2, all the heat treatment conditions show reasonably high values of ductility.
The ratio of YS/UTS (strength ratio) is a general measure of work hardening behavior.
The low values of strength ratio for the “transformation toughening optimized” multi-
step treatments compared to that for the single-step treatment condition suggests that
the work hardening of the steel is appreciably improved by the optimal tempering
treatments. The load-displacement curves for all the conditions showed smooth
yielding without any distinguishable upper and lower yield points. Analysis revealed
that the plastic stress strain behavior could be described by the Hollomon power law
equation (Equation 5.1) [129]. The fitting parameters are summarized in Table 5.3.
nplpl Kεσ = (5.1)
n is the strain-hardening exponent and K is the strength coefficient in ksi.
The yield strength and hardness data from Table 5.2 is superimposed on
the hardness – yield strength correlation plot developed earlier in Fig. 5.24. The black
heavy points represent the data from the current tensile properties study of
BlastAlloy160. The data lies within the experimental scatter of the relationship,
supporting the assumptions in specifying the hardness and strength goals.
153
Table 5.3: Fitting parameters for Hollomon power law equation (5.1) from tensile data of prototype (Fig. 5.23)
Figure 5.24 Hardness – Yield Strength Correlation developed from previous data.
The heavy black points represent data from current investigation.
154
5.6 Toughness – Temperature Dependence
To characterize the effect of service temperature on toughness, Charpy
V-notch impact tests were performed over temperatures ranging from – 840C to 1000C
for the tempering condition that optimized the austenite for room-temperature
dispersed phase transformation toughening. Thus, from Fig. 5.20 the tempering
condition displaying the best toughness-strength combination, 5500C 30min + 4500C
5hrs was chosen. The prototypes were solution treated at 9000C for 1 hour, water
quenched, liquid nitrogen cooled and then multi-step tempered. The samples were
thermally equilibrated at the test temperature for 20 minutes prior to testing.
Fig. 5.25 shows the Charpy impact energy of the prototype as a function
of test temperature. The corresponding impact energy values for 5 hour and 10 hour
tempering treatments at room temperature are superimposed on the plot. Consistent
with the concept that our composition and process design optimized the dispersed
phase transformation toughening phenomenon at room temperature (Chapter 3), the
plot shows that there is a 30 ft-lbs toughness increment at 250C compared to the
baseline ductile fracture toughness at lower and higher test temperatures. This supports
our concept that additional toughening occurs in the prototype because of the delay of
microvoid shear localization during ductile fracture by the optimum stability austenite
dispersion. At higher and lower test temperatures austenite becomes less stable than
required for transformation toughening to occur although the fracture still occurs in a
purely ductile mode, as confirmed by fractography.
155
Figure 5.25 Charpy impact energy absorbed as a function of testing temperature for
prototype tempered at 5500C 30min + 4500C 5hr. Toughness increment of 30ft-lb due to dispersed phase transformation toughening is shown. The toughness band defined by 5 hour and 10 hour single step tempering is superimposed.
SEM micrographs of the fracture surfaces presented in Figs. 5.26 to
5.30 at each of the test temperatures establish the mode of fracture. Fig. 5.26 shows
that the fracture surface for the prototype tested at – 840C is representative of
quasicleavage fracture characterized by the array of flat facets with dimples and tear
ridges around the periphery of the facets. This indicates a brittle mode of failure.
However, as the test temperature is increased to – 400C, the fracture surface primarily
156
consists of microvoids. Although most of the fracture surface is characteristic of
ductile mode of fracture, closer investigation of Fig. 5.27 shows that there are a few
tear ridges with facets, indicating a slightly mixed fracture mode. Figs. 5.28, 5.29 and
5.30 are representative micrographs from fracture surfaces of prototypes tested at –
200C, 00C and 1000C respectively showing purely ductile mode of fracture
characterized by primary voids and microvoids without any evidence of flat facets. The
micrographs for the fracture surface of the prototype tested at room temperature are
presented in Figs. 5.21 and 5.22, which contain mostly primary voids with very few
microvoids. The delay of microvoid shear localization caused by the dispersed phase,
transformation toughened, optimal stability austenite at the crack-tip stress state leads
to more extensive growth of the primary voids before they coalesce by microvoiding.
This finding further supports the design for transformation toughening by multi-step
tempering to precipitate an optimal stability dispersion of austenite. Transformation
toughening studies by Leal [9] in fully austenitic steels indicate a toughness
enhancement of 20 – 50 % relative to the toughness of stable austenite depending on
the transformational volume change as shown in Fig. 2.17. Toughness enhancement is
increased by a larger volume change. Fig. 5.25 indicates that the toughness
enhancement in the prototype is 30%. Toughness measurements within closer
temperature intervals need to be done to find the true maximum for toughness
enhancement.
157
Figure 5.26 SEM micrograph of quasicleavage fracture surface showing flat facets with dimples and tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 840C
Figure 5.27 SEM micrograph of mixed ductile/brittle mode fracture surface showing microvoids with some tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 400C
158
Figure 5.28 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 200C
Figure 5.29 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 00C
159
Figure 5.30 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 1000C
5.7 Microstructural Characterization
Optimization of the processing conditions of the prototype for dispersed
phase transformation toughening in combination with a fine dispersion of
strengthening precipitates has been supported by property evaluation in the previous
sections. Microanalytical characterization of the austenite dispersion and the
strengthening precipitates and their interaction with the other substructures in the
prototype was performed next to fully validate the systems design and the results are
presented in this section.
160
5.7.1 X-ray Diffraction (XRD)
X-ray diffraction studies were undertaken to find the volume fraction of
austenite in the prototype as a function of tempering temperature. Since low X-ray
peak intensity is associated with low austenite volume fraction, tempering conditions
that will maximize the austenite content in the prototype were chosen. Corresponding
to the toughness enhancement due to optimal stability austenite as observed during the
5 hour isochronal tempering study (Fig. 5.14), tempering conditions for projected
maximum austenite content were selected; temperatures ranging from 500 – 6000C
aged for 5 hours. All samples were solution treated at 9000C for 1 hour, water and
liquid nitrogen quenched and then tempered prior to XRD measurements.
The Rij-factor described in Section 4.2.6 was estimated by calibration
with the standard (NBS SRM 485) and was used in Equation 4.2 as
⎥⎦
⎤⎢⎣
⎡=
200
220254.0α
γα
γ
II
ff
V
V to find the volume fraction of austenite as a function of tempering
temperature. However, no austenite peak was discernable above background for the
tempered samples and thus the austenite volume fraction could not be estimated. As an
example, Fig. 5.31 presents the raw XRD data (counts/sec vs. 2θ angle) for the
prototype tempered at 5500C for 5 hours (lower plot) in comparison to the data
obtained for the standard (upper plot) containing 4 ± 0.2 volume % austenite. The 2θ
angle ranges scanned were from 630 to 670 for the (200) reflection of martensite and
from 71.50 to 77.50 for the (220) reflection of austenite. It is clear from the figure that
161
the background intensity level is twice of that for the standard specimen. It is well
known that appreciable peak broadening takes place for small crystals resulting in
smearing of the diffraction peak with the background. Since we are expecting a fine
(10nm scale) dispersion of austenite, the absence of the (220) austenite peak in the
diffraction pattern might be attributed to peak broadening effect. Moreover, for a hot-
worked quenched and tempered sample like the prototype, matrix strain and texture
effects may be responsible for reducing the signal to noise ratio to unacceptable levels.
0
20
40
60
80
100
120
62 64 66 68 70 72 74 76 78
2θ (degrees)
Cou
nts
per S
econ
d
(200)α
0
50
100
150
200
250
300
Cou
nts
per S
econ
d
(200)α
(220)γ
Figure 5.31 XRD Pattern of prototype tempered at 5500C for 5 hours (lower plot)
scanned from 630 to 670 from 71.50 to 77.50 2θ angles shown in comparison with standard (upper plot) containing 4 vol% austenite
162
5.7.2 Magnetometry
Because of the limitations of X-ray diffraction technique to characterize
the volume fraction of fine dispersion of austenite, magnetometry specimens were
prepared from the XRD samples to determine the austenite content in the heat treated
alloys. The austenite calculations are based on estimates of BCC and FCC magnetic
moment and Curie point from ThermoCalc™ equilibrium calculations. The results of
the austenite volume fraction measurements are given in Table 5.3. The error bars
indicate ± σ confidence levels. Without calibrations from standard samples or
observations of the actual state of the microstructure, the predicted austenite cannot be
considered accurate, however comparisons among the different tempering conditions
are possible. Absolute values of austenite fraction ranging from 2.3 –3.1 % for the
different tempering conditions are much lower than the equilibrium value of ~10%.
Calibration with respect to fully martensitic standard needs to be done to obtain
accurate estimates of the volume fraction of austenite. However, the variation in the
level of austenite volume fractions observed among different tempering conditions
corresponds very well with the variation of toughness as presented in Fig. 5.14. The
toughness increment due to transformation toughening for the 5500C 5 hours tempering
condition relates very well to the peak austenite volume fraction measured for the same
condition compared to higher (5000C) and lower (6000C) tempering temperatures. A
higher increment in toughness is recorded for varying the tempering temperature from
5000C to 5500C than the decrease in toughness related to changing the tempering
163
temperature from 5000C to 5500C. This correlates with the relative austenite volume
fraction measured.
Table 5.4: Austenite Volume fraction measured by magnetometry for different
heat treatment conditions
Tempering Condition Austenite Volume fraction 5000C 5 hours 0.0233 ± 0.005
5500C 5 hours 0.0308 ± 0.007
6000C 5 hours 0.0295 ± 0.008
5.7.3 Transmission Electron Microscopy (TEM)
Conventional TEM was used to search for austenite at lath boundaries
of the martensitic matrix. Investigations were conducted on the best toughness-strength
condition, corresponding to 5500C 30min + 4500C 5hr tempering treatment, based on
the bulk mechanical property measurement of the prototype. Thin foils with large
electron transparent regions were prepared by mechanical and electro-polishing
(described in Section 2.4.9) from the hardness specimens. Figs. 5.32 and 5.33 show
bright field images of martensite laths at two different magnifications.
164
Figure 5.32 Bright-field TEM micrograph showing martensite laths in multi-step
tempered prototype at 5500C for 30min + 4500C for 5hrs
Figure 5.33 Higher magnification bright-field TEM micrograph showing martensite laths in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs
165
Examination of the substructure inside the martensite laths revealed a highly dislocated
structure as presented in Fig. 5.34. This dense dislocation network within the laths is
known to provide nucleation sites for the strengthening dispersions of BCC copper
precipitates and M2C carbides. Intralath austenite could not be resolved at the
magnification at which the investigation was performed. Conventional dark field
imaging was also done, but the diffraction from austenite could not be clearly
identified because of interactions with signals from other phases and dislocation strain
fields in the microstructure.
Figure 5.34 Bright-field TEM micrograph showing dense dislocation structure within a martensite lath in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs
166
5.7.4 Three-Dimensional Atom Probe (3DAP) Microscopy
The modern 3DAP microscope is a unique ultrahigh resolution
microstructural characterization technique that is capable of identifying and
characterizing individual atoms and then generating three-dimensional reconstructions
of the internal structures. Since XRD, magnetometry and TEM studies were
unsuccessful in identifying the nanometer scale intra-lath austenite and the optimal
3nm particle size strengthening precipitates in the transformation toughened
BlastAlloy160, 3DAP microscopy was chosen to the be the preferred method of
characterization. This characterization tool was used as a means of evaluating the
matrix composition as well as precipitate compositions, sizes, morphologies and their
average number density.
The choice of samples for analysis was based on the condition of
tempering treatment for the highest obtainable number density of the precipitates,
determined from the assessed mechanical properties (Fig. 5.20). Thus, the tempering
condition corresponding to the highest observed strength (Table 5.2) namely, 5000C
30min + 4500C 5hrs was chosen. The 4500C 1 hour tempering condition was also
chosen as a reference for comparison with 3DAP data on similar Cu-strengthened
steels [76] as well as with the other tempering condition. For simplification, the 4500C
1 hour tempering treatment specimen will be referred to as the “single-step temper”
and the 5000C 30min + 4500C 5hrs tempering treatment specimen will be referred to as
167
the “multi-step temper” in this section. The data for both the tempering conditions will
be presented simultaneously for easier comparison.
The analyzed tips were isothermally aged according to their respective
schedules, following solution treatment at 9000C for 1 hour, water quench and liquid
nitrogen quench. The overall composition of the reconstructed volume from atom
probe analysis was obtained and compared with the actual composition of the
prototype as shown in Table 5.5. It is seen that the actual compositions compare well
with that for the elements detected. The error for the concentrations is given by 2σc,
where Nccc /)1( −=σ , with c being the measured composition and N being the total
number of atoms detected. Thus, the statistical error associated with composition
analysis decreases as the total number of atoms detected increases.
168
Table 5.5: Comparison between the actual overall composition of prototype and the overall compositions determined by 3DAP analysis
Overall Composition from 3DAP
Actual Overall
Composition 4500C 1 hr 5000C 30 min + 4500C 5 hrs
Element wt % at % at % at %
Fe 87.2 90 89.90 ± 0.08 88.58 ± 0.18
C 0.04 0.192 0.11 ± 0.24 0.12 ± 0.53
Cu 3.64 3.30 2.37 ± 0.23 1.13 ± 0.53
Ni 6.61 6.49 5.34 ± 0.23 7.01 ± 0.52
Cr 1.78 1.97 1.86 ± 0.23 2.1 ± 0.53
Mo 0.58 0.35 0.31 ± 0.24 0.89 ± 0.53
V 0.11 0.124 0.11 ± 0.24 0.16 ± 0.53
Atom probe analysis of the single-step temper was conducted at 50K
while that for the multi-step temper at 70K with a pulse fraction of 20% at a pulse
frequency of 1.5 kHz from 7kV to 10kV steady state DC voltage. The complete
analysis for the single-step temper contained a total of 751,608 atoms in a
reconstruction volume of dimensions 13nm X 13nm X 84nm. The multi-step temper
169
analysis collected 254,917 atoms in a reconstruction volume dimension of 17nm X
16nm X 28nm. Figs. 5.35 and 5.36 show partial 3D reconstruction of all the atoms
detected after being field evaporated from the specimen with their positions and
elemental identities for single-step and multi-step tempering conditions respectively.
Iron is not shown in any reconstruction in this section for purpose of clarity, enabling
larger microstructural features like precipitates to be seen distinctly.
z
13nm
13nm
84nm
Cu Ni Cr Mo V C
Figure 5.35 3DAP reconstruction for prototype tempered at 4500C for 1 hour. The
elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis.
170
mz
m
m Figure 5.36 3DAP reconstruction for prototype
5hrs. The elements in the reconstruccode. Iron is not shown to provide mz is the direction of analysis.
The regions of high copper concent
Figs. 5.35 and 5.36 confirming the presence of a n
distribution in the microstructure. These copper – r
by an isoconcentration surface at 10 at % copper le
positions of copper atoms as shown in Figs. 5.37 a
28n
16n17n
Cu Ni Cr Mo V C
tempered at 5000C 30min + 4500C tion are indicated by their color ore clarity in viewing the particles.
ration are clearly noticeable in both
anometer sized copper particle
ich precipitates can be represented
vel overlaid with the atomic
nd 5.38. The isoconcentration
171
surfaces clearly outline the Cu-rich precipitates. The size of the copper precipitates for
the single-step temper is relatively smaller than that for the multi-step temper, while
the number density of precipitates for the former is much higher.
Cu11nm
11nm
31nmz
Figure 5.37 3DAP reconstruction for prototype tempered at 4500C for 1 hour
showing copper precipitates defined at 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. All other atoms in the reconstruction are not shown. z is the direction of analysis.
172
Cu Ni Cr Mo V C
z
14nm
14nm
28nm
Figure 5.38 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C
5hrs showing copper precipitates defined by 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. z is the direction of analysis.
The shape of the copper precipitates appears to be elliptical and
stretched in the direction of analysis for both the tempering conditions. The distortion
is an instrument artifact due to a magnification effect caused by the difference in field
evaporation of copper precipitates compared to the matrix. The precipitates are
believed to be spherical in shape as evidenced by other researchers [59, 76,141].
173
Having defined the copper precipitates by the isoconcentration surface,
the size, number densities and compositions of these copper precipitates can be
determined with the help of the 3DAP analysis software, ADAM [114]. Cross-sectional
views from an analyzed volume of the reconstruction were used to measure the size of
the precipitates, examples of which for each tempering condition are shown in Figs.
5.39 and 5.40. For the single-step temper, the average diameter of the copper
precipitates contained completely within the analysis volume was found to be 2.67 ±
0.57 nm while that for the multi-step temper is 3.79 ± 0.13 nm. From the hardness data
it is apparent that the multi-step temper corresponds to the peak aging condition.
However, considering the statistical error of the measurement and a distribution of
particle sizes in the material, the optimal particle size of BCC Cu-precipitates for
maximum particle size lies within 2.5 – 4 nm. This measurement is consistent with the
optimal particle size value of 2.9 nm obtained from atom-probe measurements by
Isheim and Gagliano [76,141] for copper strengthened steel aged for 100 minutes at
4900C and also with the peak aging size of 1 – 5 nm for BCC copper precipitates
determined from previous literature (Section 2.3.2).
174
Cu 5nm
Figure 5.39 Example of a cross-section of analyzed volume for prototype tempered
at 4500C for 1 hour showing copper precipitates in red. All other atoms in the reconstruction are hidden.
Cu 5nm
Figure 5.40 Example of a cross-section of analyzed volume for prototype tempered
at 5000C 30min + 4500C 5hrs showing copper precipitates in red. All other atoms in the reconstruction are hidden.
175
It is apparent from Figs. 5.39 and 5.40 that the number density of
strengthening Cu precipitates is higher for the single-step temper than the multi-step
temper. The number density of the copper precipitates in the analyzed volume was
estimated by equation (5.3) [112]:
Ω
=n
NN p
V
ζ (5.3)
Np and n are the number of particles and the total number of atoms detected in the
volume, Ω is the average atomic volume and ζ is the detection efficiency of a single
ion detector, equal to 0.6 in this case. The number density of copper precipitates for the
single-step temper was calculated to be 5.42 X 1018 precipitates/cm3 while that for
multi-step temper was calculated to be 1.2 X 1018 precipitates/cm3. The high number
density measured for the single-step temper (4.5 times that for multi-step temper) is
consistent with the high Cu content of the alloy. Evidence for cementite dissolution in
the toughness-hardness plots of Fig. 5.20 support the presence of M2C carbides
contributing to the strength of the multi-step tempered material.
The average matrix and precipitate compositions can be determined
from the analyzed volume by calculating the fraction of atoms of each element within
the phase. To analyze the composition of the inner core of the precipitates, a higher
threshold level of 15 at % was set to isolate them. Tables 5.6 and 5.7 give the
composition of the Cu-precipitates and the matrix respectively with 2σ error bar limits
for both the single-step and multi-step conditions. Table 5.7 also compares alloy matrix
176
composition with the homogeneous phase composition of the BCC matrix predicted
using ThermoCalc at the optimal tempering temperature for required austenite stability
(Chapter 3).
Table 5.6: Average copper precipitate compositions determined by 3DAP analysis for selected heat treatment compositions. ND means not detected
BCC Cu Precipitate Composition
from 3DAP analysis
4500C 1 hr 5000C 30 min + 4500C 5 hrs
Element at % at %
Fe 30.25 ± 3.53 43.79 ± 6.52
Cu 63.50 ± 2.55 46.69 ± 6.35
Ni 5.40 ± 4.11 8.76 ± 8.31
C ND ND
Cr 0.40 ± 4.21 0.57 ± 8.67
Mo 0.13 ± 4.22 ND
V ND 0.19 ± 8.69
177
Table 5.7: Average matrix compositions determined by 3DAP analysis for selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected
BCC Matrix Composition
from 3DAP analysis
Equilibrium
Prediction
4500C 1 hr 5000C 30 min + 4500C 5 hrs 4900C
Element at % at % at %
Fe 91.22 ± 0.49 92.01 ± 0.22 94.1
Cu 0.73 ± 0.66 0.22 ± 0.77 0.12
Ni 5.32 ± 1.62 6.33 ± 0.74 3.78
C 0.014 ± 1.67 0.041 ± 0.77 0.000044
Cr 2.18 ± 1.65 0.88 ± 0.76 1.88
Mo 0.44 ± 1.66 0.39 ± 0.77 0.10
V 0.09 ± 1.67 0.12 ± 0.77 0.02
The results of the 3DAP analysis indicate that the matrix composition
for both heat treatment conditions compare reasonably well with the predicted
equilibrium calculations. The matrix Cu composition is near the predicted equilibrium
composition at the earliest evolution stage, indicating a high degree of Cu precipitation
178
and it remains at the equilibrium condition for the multi-step temper composition
analyzed. The relatively higher Ni level observed for both conditions may be
associated with the microsegregation compositional banding described earlier in
Section 5.1. The difference between the homogeneous equilibrium matrix Ni
prediction and the 3DAP microanalysis results is consistent with the level of banding
microsegregation observed with respect to Ni.
From Table 5.6, the Cu composition of the precipitates from 3DAP
analysis is consistent with previous atom-probe results by Goodman [61] (Fig. 2.15)
and Isheim – Gagliano [76, 141] during the early stages of evolution. They reported
values ranging from 50 to 70 % Cu in the precipitates during the initial stages of
precipitation until the peak aged condition is reached. However, these values are much
lower than the equilibrium prediction of 94% Cu in the precipitates. As mentioned by
Gagliano [76] this may be the lower limit of the true concentration value caused by
aberrations of ion trajectories and local magnification effects in 3DAP, which limits
the spatial resolution of this nanoanalytical technique to a few tenths of a nanometer
[131]. It is well established now [132,133] that spatial overlap effects due to the
difference in the field evaporation between the matrix and the precipitate in the Fe-Cu
system leads to matrix atoms being projected into the precipitate, especially for
particles smaller than 5nm in size. The high uncertainty for the concentration values in
the multi-step temper sample is because of the limited data available for analysis.
179
The average matrix and precipitate compositions and the concentration
of the various solute atoms near the matrix/precipitate interface can be investigated by
a proximity histogram, or “proxigram”, available in ADAM, developed and
implemented by Hellman et al [116]. The concentration values were determined by
averaging the concentration in 0.2 nm peripheral shells around all the precipitates with
respect to the 10 at% copper isoconcentration surface, within and outside the
precipitates. The negative values in abscissa represent the matrix composition while
the positive values are indicative of the precipitate compositions. However, the zero
point is not necessarily a correct estimate of the precipitate/matrix interface and serves
as an approximate reference point [116]. The proxigrams obtained from analysis of
copper precipitates in single-step temper and multi-step temper samples are presented
in Figs. 5.41 and 5.42 respectively. The proxigrams indicate that for both cases of
tempering condition, Ni shows considerable partitioning to the precipitate/matrix
interface while that for other solute atoms is within the error limit of estimation. The
level of Ni enrichment at the interface is about 50% higher than the matrix Ni content
for the single-step temper observed in Fig. 5.41, which is consistent with the proxigram
analysis results of Isheim and Gagliano [76,141]. Other researchers have also reported
Ni segregation at the interface of the coherent BCC Cu precipitates as described in
Section 2.3.2.
180
Figure 5.41 Proxigram of all the solute species detected in the 4500C 1hr temper
specimen with respect to 10 at% copper isoconcentration surface in the analysis volume
181
Figure 5.42 Proxigram of all the solute species detected in the 5000C 30min + 4500C
5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume
182
Furthermore, it is interesting to see from Fig. 5.42 that the level of Ni
located near the interface was more than 50% with respect to the matrix Ni content for
the multi-step temper condition. This led to further investigation of the
precipitate/matrix interface region by varying Ni concentration threshold levels in the
3D reconstruction for the multi-step temper. Setting a 10 at % level for Ni, the
isoconcentration surface of a Ni-rich precipitate at the interface of the Cu-rich
precipitates could be identified. Fig. 5.43 shows the isoconcentration surface outlining
the Ni-rich precipitate defined at 10 at % Ni, overlaid with atomic positions of Cu and
Ni from three different orientations. Composition analysis for the Ni-rich precipitate
and its comparison with equilibrium prediction of austenite composition is shown in
Table 5.8. Ni concentration of 19.5 at% in the precipitate strongly supports that the
precipitate is the desired austenite of optimum stability for transformation toughening.
Lower than equilibrium concentration of the Ni in the austenite estimated as 30 at%
may be attributed to the local magnification effects previously mentioned. This
argument is further supported by the higher (twice) Cu level in austenite than
equilibrium prediction due to the possibility of having copper atoms from the adjacent
copper precipitates projected into the austenite precipitate because of the solute overlap
effect. Since only a single austenite particle was observed, the statistical error
associated with the composition estimation is significant. To confirm the Ni content of
austenite, further investigation was done by a one-dimensional composition profile
183
plotted along the atom-probe analysis direction in Fig. 5.44. This confirmed that the Ni
content of austenite is 30 at% and is consistent with equilibrium values.
Figu
re 5
.43
3DA
P re
cons
truct
ion
for p
roto
type
tem
pere
d at
500
0 C 3
0min
+ 4
500 C
5hr
s sho
win
g au
sten
ite d
efin
ed b
y 10
at %
Ni l
evel
isoc
once
ntra
tion
surf
ace
over
laid
on
atom
ic
posi
tions
of n
icke
l and
cop
per a
tom
s. z
is th
e di
rect
ion
of a
naly
sis.
184
Figure 5.44 One-dimensional composition profile along the atom-probe analysis direction in the 5000C 30min + 4500C 5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume. z is the direction of analysis.
185
Table 5.8: Average austenite composition determined by 3DAP analysis for selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected
Austenite Composition
from 3DAP analysis
Equilibrium
Prediction
5000C 30 min + 4500C 5 hrs 4900C
Element at % at %
Fe 65.9 ± 5.6 61.5
Cu 13.9 ± 8.9 6.97
Ni 19.3 ± 8.6 29.8
C ND 0.00068
Cr 0.93 ± 9.6 1.47
Mo ND 0.03
V ND 0.00084
The size and location of the austenite precipitate, measured as 5nm from
Fig. 5.44, confirms that it is intralath austenite nucleated on two adjacent Cu
precipitates. The size of the precipitate is consistent with that from dark-field TEM
observation of intralath austenite of 5-10 nm by Lippard in multi-step tempered
AerMet100 alloy (Fig. 2.20). Lippard also proposed a mechanism of austenite
186
nucleation on an M2C carbide or in its intermediate coherency strain field from
evidence of high Cr signals associated with STEM EDS data gathered from dispersed
austenite intralath precipitates. This result thus provides direct visual evidence of the
heterogeneous nucleation of intralath austenite on a fine dispersion of strengthening
precipitates; Cu precipitates in this case. This finding also strengthens the
transformation toughening design of achieving an optimal stability austenite dispersion
by employing a multi-step tempering treatment to nucleate the austenite in the first
tempering step followed by a Ni-enrichment final tempering step.
Even with the optimized conditions for C ion detection efficiency
suggested by Carinci [50], no M2C carbide precipitate was identified in the atom-probe
reconstructions. Because of the low equilibrium phase fraction of M2C calculated for
the optimal tempering treatment, the precipitates might have been excluded from the
analysis volume of the atom probe. Also, detection of carbide particles is difficult
because of differences in the field evaporation rates between the carbide and the
surrounding matrix that cause the carbide to stick out in relief leading to tip-fracture.
Such a situation was encountered during the multi-step temper atom-probe run, when a
high level of carbon and molybdenum was observed in the in-situ composition profile
during data collection and the tip fractured soon thereafter. No data could thus be
obtained for 3D reconstruction and characterization of M2C carbide in the prototype.
187
6. CONCLUSIONS
A systems approach to computational materials design has been
successfully applied to the creation of an ultratough high-strength weldable plate steel
for naval hull applications, conducted under the ONR (Office of Naval Research)
grand challenge initiative in “Naval Materials by Design”. The systems approach
integrated processing/structure/property/performance relations with mechanistic
models to achieve the desired quantitative property objectives. The alloy design began
with a study of the structure-property relationships, with special emphasis on
understanding each of the structural subsystems to optimize the corresponding
properties. Quantitative models were then used to design the toughening and
strengthening dispersions, which were the two major property requirements to be met
under stringent processability constraints. Prototype evaluation validated the designs
and characterization of the mechanical properties of Blastalloy160 indicates significant
improvement in strength-toughness combination compared to other commercial steels
currently used by the Navy. The success of the prototype alloy reinforces the strengths
of the design models and their integration.
6.1 Alloy Design
The overall strategy behind the thermodynamic modeling has been to
map the mechanical properties objectives to thermodynamic parameters to set goals for
the design of the microstructural subsystems. The Olson-Cohen model for
188
heterogeneous nucleation aided the determination of a thermodynamic stability
parameter for the austenite. The stability of the transformation-toughened austenite was
calibrated against the parameter (∆Gch + Wf) combining thermodynamic driving force
and interfacial friction to obtain the required toughness, which was the top priority of
this design. Then, based on the strength requirement projected to hardness values, the
design space was identified. The alloy composition and the processing conditions were
subsequently determined by conforming to these parametric design requirements.
The explored design concept is based on the mechanism of dispersed
austenite stabilization for transformation toughening adapted to weldable high strength
steels. The concept employs mixed bainitic/martensitic microstructures produced by
air-cooling of solution-treated plate, combined with copper and alloy carbide
precipitation strengthening during lower temperature isothermal treatment, constrained
by a low carbon content for weldability. A fine particle dispersion of optimal ~ 3nm
size for effective strengthening was designed by precipitation of M2C carbides and
BCC copper from a highly supersaturated BCC solution. The carbon content of the
alloy was set at 0.05 wt% to meet weldability constraints. Based on the carbon level
set, a quantitative carbide-strengthening model was used to determine the strength
contribution from M2C carbides, with the driving force for M2C precipitation
maximized at ~14 kJ/mole (while maintaining a stoichiometric balance between carbon
and the carbide formers Mo, Cr, V) to obtain a fine 3-4nm precipitate particle size. The
additional strengthening required to meet the yield strength goal of 160ksi was
189
achieved by setting an optimal level of copper at 3.65 wt% based on a quantitative
copper-strengthening model. This relatively high Cu level was necessary to allow the
low carbon limit. A high Ni/Cu ratio (1.8) was also maintained in the multicomponent
alloy design to prevent hot shortness problems during processing.
Transformation toughening arises from dispersed austenite precipitates,
which undergo a martensitic transformation at the crack-tip stress state. This leads to
impediment of crack growth by delay of microvoid shear localization during ductile
fracture. Thus to achieve high toughening by this mechanism, optimum stability of the
austenite was designed by optimizing Ni as an FCC stabilizer. Thermodynamic
calculations predicted an alloy Ni content of 6.5 wt% to enable the equilibrium nickel
content of 30% in the austenite to meet the requirement for transformation toughening.
The design also revealed that although Cr did not have a strong effect
on the driving force for carbide precipitation, it helped in partitioning Cu out of the
austenite phase for effective copper precipitation strengthening above 1.1 wt%. For a
robust composition design, the alloy Cr level was set at 1.8 wt%. The processability
conditions were then evaluated under stringent restrictions for the designed alloy (Fe-
0.05C-3.65Cu-6.5Ni-1.84Cr-0.6Mo-0.1V) based on solution treatment condition,
microsegregation behavior and optimal tempering condition. A design solution
treatment condition of 9000C for 1 hour was found sufficient to dissolve M2C carbides
without excessive austenite grain growth. No serious microsegregation problems were
predicted for the designed composition based on results from Scheil simulation. An
190
optimal final tempering temperature of 4900C (after a higher temperature austenite
nucleation step) was predicted to achieve sufficient austenite stability for
transformation toughening. Thus, thermodynamic calculations demonstrated feasibility
of combining copper and M2C carbide precipitation for strengthening in combination
with nickel-stabilized austenite for transformation toughening in a relatively low cost
weldable plate steel.
6.2 Prototype Evaluation
The characterization of the first Blastalloy160 prototype yielded very
encouraging results. The principal design objective of toughness-strength combination
was met. Impact toughness of 130ft-lb was achieved at 160ksi yield strength for a
multi-step tempering condition of the prototype, which is a significant improvement of
properties over other conventional alloys. Fig 6.1 graphically represents the toughness-
strength combination of the Blastalloy160 prototype for three different tempering
conditions in comparison to other commercial and experimental alloys.
191
Figure 6.1 Toughness-yield strength comparison plot of Blastalloy160 with other
commercial and experimental steels
To simulate a continuous casting process, a 34lb (15.4kg) Vacuum
Induction Melt (VIM) heat of the Concept B prototype was slab cast as 1.75” (4.45cm)
plate, homogenized for 8 hours at 22000F (12040C), hot-rolled to 0.45” (1.14cm) and
then annealed at 9000F (4820C) for 10 hours. Consistent with microsegregation /
homogenization simulations, compositional banding in the plate was limited to an
amplitude of 6 - 7.5 wt% Ni, 3.5 - 5 wt% Cu, 1.6 – 2 wt% Cr, and 0.2 – 0.5wt% Mo.
Examination of the oxide scale showed no evidence of hot shortness in the alloy during
hot working. The evaluation of the prototype alloy for different tempering conditions
192
was conducted under an initial martensitic condition obtained by austenizing solution
treatment at 9000C for 1hour followed by a water-quench and a liquid nitrogen cool.
Since this was a design for low-cost air-hardenable plate steel, isothermal
transformation kinetics measurements were also conducted, demonstrating
achievement of 50% bainite in 4 minutes at 3600C. Reasonable agreement was
obtained between the experimental and calculated transformation behavior with the
transformation temperatures (MS / BS) higher by ~600C. The experimental data was fit
to saturation volume fraction of bainite predictions to calibrate the kinetic model for
future prediction of bainite start kinetics in this alloy system. Hardness and tensile tests
confirmed predicted precipitation strengthening behavior in quench and tempered
material. Isochronal tempering studies at 1 hour confirmed peak strengthening at
4200C with gradual overaging, consistent with literature findings for copper bearing
systems. Multi-step tempering was employed to optimize the austenite and a
significant enhancement in toughness was observed with minimal loss in strength for a
5500C 30min + 4500C 5hrs tempering condition. An optimal austenite stability was
indicated by a significant increase of impact toughness to 130 ft-lb at a strength level
of 160 ksi. Comparison with the baseline toughness-strength combination determined
by isochronal tempering studies indicates a significant transformation toughening
increment of 60% in Charpy energy, exceeding the actual toughness goal of 85 ft-lbs
by almost 55%. Tensile tests were conducted on the optimum tempering conditions to
confirm the predicted strength levels. Charpy impact tests and fractography
193
demonstrate ductile fracture with Cv > 80 ft-lbs down to –400C, with a substantial
toughness peak at 250C consistent with designed transformation toughening behavior.
Predicted Cu particle number densities and the heterogeneous nucleation of optimal
stability high Ni 5nm austenite on nanometer-scale copper precipitates in the multi-step
tempered samples were confirmed using three-dimensional atom probe microscopy.
The copper precipitate size was verified for peak strengthening at 2-3 nm and
precipitate composition of 50-60% copper for short tempering times agreed with
results from previous studies. The fine austenite showed a Ni content near the
theoretical prediction of 30%.
The properties demonstrated in this first prototype represent a
substantial advance over existing naval hull steels. Achieving these improvements in a
single design iteration is a significant progress in computational materials design
capability.
194
7. SUGGESTIONS FOR FUTURE WORK
Initial evaluation and characterization of the prototype has demonstrated
the success of the systems approach in achieving the design objectives. However, it has
also opened new research horizons to be explored for further enhancement of
properties. In addition, the achievement of major improvements in properties over
current commercial steels in a single design iteration displays the strengths and
robustness of the design models and opens up opportunities to widen their application.
7.1 Further Prototype Evaluation
The amount of optimal stability austenite for the dispersed phase
transformation toughening phenomenon in the initial prototype could not be
characterized appropriately with the techniques used in the present work. Although the
relative variation of austenite volume fraction from magnetometry measurements are
consistent with the toughness results, calibrations with respect to standard samples in
fully martensitic state needs to be done to make accurate measurements. Another
possibility will be to use X-ray diffraction with high-energy synchrotron radiation to
obtain a higher signal to noise ratio over the background for precise estimation of
integrated intensities from austenite diffraction peaks.
A more detailed evaluation of the toughness dependence on temperature
also should be done to accurately define the toughness increment due to transformation
toughening over baseline ductile fracture toughness. The transformation toughening
195
peak then can be redesigned based on the operating temperature of the alloy to achieve
the best property combination under service conditions through a design iteration of
composition and processing.
Further atom-probe investigations should be conducted to detect and
characterize the designed 3-4nm sized M2C carbide particles to validate the strength
model used in the design.
Following the success of the initial prototype, processing of the
designed alloy should be scaled up to larger heats with small elemental additions for
grain refinement and impurity gettering. Addition of B will help improve the grain
boundary cohesion and is beneficial to stress corrosion cracking resistance. A Ti
addition during melt de-oxidation can provide an effective grain refining dispersion
during solution treatment with good interfacial adhesion for toughness. The properties
should also be characterized with bainite/martensite mixtures formed by air-cooling.
7.2 Next Design Iteration
Further exploration with respect to optimal combinations of austenite
stabilizers in the next design iteration can predict leaner alloy compositions leading to
improved weldability and lower cost of the material. Further calibration of the bainite
kinetics model with more experiments is necessary for the design of robust air-cooled
plate steels. Building on this research to study transformation toughening mechanisms,
196
a more radical design concept of a non-magnetic, fully austenitic precipitation-
hardening alloy can be investigated for maximum toughening.
197
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214
APPENDICES
APPENDIX A
Design and Evaluation of Concept A Alloy
The design of the higher risk Concept A alloy was based on a lower cost
low alloy carbon-stabilized austenite in a high silicon steel strengthened by BCC Cu
precipitation. The design focused on precipitation-strengthened, 150 ksi yield strength
bainitic steels with carbon-stabilized austenite for transformation toughening. By
judicious use of Si as an alloying element to suppress the precipitation of cementite
and thus avoiding large regions of unstable austenite, Bhadeshia [4] has achieved
impressive combinations of strength (YS=160ksi) and toughness levels
(KIC=140ksi.in1/2). Design Concept A employs the phenomenon of bainitic
stabilization of austenite during low temperature isothermal treatment on a low
hardenability plate steel air-cooled from solution treatment temperature. The strength
levels will be increased by precipitation of bcc Cu since not enough carbon would be
available for carbide strengthening. Thus the aim of research using this concept was to
combine carbon stabilization of austenite with simultaneous Cu precipitation.
A preliminary composition of the Concept A alloy was set based on
strict design and cost constraints. Since this concept employs carbon stabilization of
austenite for achieving optimal stability for transformation toughening, an upper limit
carbon level of 0.1 wt% was set within the zone to avoid susceptibility to HAZ
215
cracking of weldments, specified by the Graville diagram (Fig. 3.3). As a result,
carbide strengthening is ruled out so that all of the carbon is available for partitioning
into austenite. Thus, the design requires BCC copper precipitation strengthening to
provide the additional strength increment over the solid solution strengthening and the
bainitic substructure strengthening in the alloy. However, initial calculations showed
that C partitions to austenite at low alloy Cu content, so a lower concentration of 1.37
wt%, sufficient for strengthening was selected [76]. Consistent with the Ni level in
similar steels to avoid hot-shortness, the alloy Ni content was set to 0.82 wt%. This
corresponds to the addition of Ni in an amount equal to 0.5 – 1 times that of copper to
prevent surface cracking during hot rolling as discussed in Section 5.1. During the
bainitic stabilization of austenite by isothermal transformation as depicted by the
schematic of the thermal processing route employed in this design (Fig. A1), it is
important to suppress cementite formation in order to allow more carbon to partition
into austenite. Moreover, since cementite negatively affects the toughness of the alloy,
suppression of cementite formation to higher temperature by addition of Si up to 1.5
wt% is well established [4]. Addition of higher Si results in the formation of a thick
oxide layer on the surface of the steel during hot rolling. Mn is usually present in small
amounts in most steels to getter sulfur as sulfides. But Mn addition in this alloy is
crucial since it has a substantial effect on the amount of C in the retained austenite.
The MS temperature is also strongly affected by the alloy Mn content, which in turn
216
sets the lowest temperature at which bainitic transformation can be achieved
isothermally.
Figure A1 A schematic of the thermal processing of Concept A alloy
The calculations performed for Concept A mainly concerned the
optimization of the alloy Mn content. The calculations were performed under para-
equilibrium constraint, where only carbon diffuses during isothermal transformation.
The fixed values of the other alloying elements are shown in Table A1.
Table A1 Initial composition of Concept A steel
Element Fe C Cu Ni Si Mn
wt % Balance 0.1 1.37 0.82 1.5 Optimized
217
Figure A2 shows the effect of alloy Mn content on the MS temperature.
The MS temperature decreases with increase in the alloy Mn content. Since isothermal
treatment just above MS is necessary for bainitic transformation, it is important to
estimate the C content of the austenite at such temperatures. The isothermal bainitic
hold temperature (or processing temperature) was set to be 100C above the MS
temperature. Paraequilibrium calculations were performed to find the C content of
retained austenite for varying isothermal hold temperature corresponding to the
variation in alloy Mn content. The results are shown in Figure A3. This plot shows
that a lower processing temperature or MS is beneficial because more C is partitioned
to the austenite. The amount of C in austenite is a primary measure of the stability of
the austenite phase—more carbon provides more stable austenite. It is shown that Mn
decreases the C content of austenite calculated at the fixed processing (Ms+100C)
temperatures. So Figures A2 and A3 show the importance of Mn in decreasing the Ms
temperature, which increases the C content of austenite and hence the stability for
transformation toughening.
218
Figure A2 Variation of Martensite Start (Ms) temperature with alloy Mn content
(wt%)
Figure A3 Carbon content of retained austenite (wt%) as a function of alloy Mn content (wt%) calculated at processing temperature (Ms+100C) corresponding to Mn content in Figure A2
219
The room temperature stability of dispersed retained austenite for
transformation toughening was calculated by the sum of the chemical and mechanical
driving force terms (∆Gch + Wf) as described in Section 3.2.2. Similar to the
transformation toughening design for Concept B alloy, a linear relation was fit between
the austenite stability parameter and the alloy hardness (Fig. A4), and an estimate of
the required optimum stability was thus obtained. Fig. A4 show that for a yield
strength of 150 ksi, the optimal value of ∆Gch + Wf would be 2.2 kJ/mol, for the
required austenite stability.
RT (300K) Stability of Austenite
0500
100015002000250030003500400045005000
280 330 380 430 480 530 580 630
Vickers Hardness (VHN)
∆G
ch+W
f, J
/mol
AerMet 100AF1410
Concept A Design Alloy
Figure A4 Room Temperature (300K) austenite stability plotted as a function of Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept A alloy corresponding to yield strength requirement of 140-160ksi.
220
Based on the requirement of austenite stability, calculations were performed to
estimate the value of ∆G + Wf with varying alloy Mn content as shown in Fig A5. The
stability calculations were performed maintaining para-equilibrium, so the
compositions of all elements except for C are the same in austenite as they are in the
alloy. Only carbon atoms are diffusing, so the austenite carbon content is determined
from Fig A3. From Fig A5 it was found that the required level of stability (2200
J/mol) was reached at 7.5 wt% Mn. Figure A6 shows the ∆Gch + Wf stability
parameter plotted against processing temperature according to the corresponding Mn
levels and we reach the required austenite stability at 3150C (MS = 3050C).
Figure A5 Room Temperature (300K) stability of austenite as a function of alloy
Mn (wt%). The required stability was achieved at 7.5wt% Mn.
221
Figure A6 Room Temperature (300K) stability of austenite as a function of
processing temperature (Ms+100C). The required stability was achieved at 3150C.
Based on these computed results, the composition of the Concept A steel (in wt%) was
determined as Fe-0.1C-1.37Cu-0.82 Ni-1.5Si-7.5Mn with an isothermal transformation
temperature of 315oC. Steel of this composition and processing should give optimal
performance at a reasonable cost.
Initial evaluation of the prototype to determine the allotropic kinetics
revealed that the austenite is too stable to allow any bainitic transformation.
Dilatometry studies were done to measure the MS temperature of the designed alloy
determined from the 1% martensitic transformation point shown in Fig. A7. The actual
MS averaged over 10 dilatometry runs is 227 ± 8.80C. This is 780C lower than the MS
222
predicted by the Ghosh-Olson model employing the SSOL database. Because of
overestimation of the lower transformation temperature, the kinetics of bainite
transformation were too slow and no discernable length change was observed after 2
hours of isothermal hold at temperatures just above the MS. Thus the bainite kinetics
could not be evaluated.
Figure A7 Relative sample length change and temperature trace during heating and cooling cycle from dilatometry experiment. MS was determined from 1% martensitic transformation point.
223
Since evaluation of the transformation toughening behavior of the
retained austenite in the prototype could not be done by bainitic stabilization, some
preliminary characterization of the retained austenite was performed in the martensitic
state in quenched and tempered samples. To vary the amount of retained austenite in
the sample, one batch of the prototype was cooled in liquid nitrogen following water
quench after solution treatment. Consistent with the peak aging temperature of 4200C
for Cu precipitation strengthening (Fig. A8), 1 hour isochronal tempering response of
the prototype for both the cases exceeded the strength goal of the design. X-ray
diffraction measurement of volume fraction of austenite, confirmed that the liquid
nitrogen cool led to further transformation of retained austenite to martensite. The
decrease in the amount of retained austenite associated with the peak aging condition
indicates that maximum strengthening at 4200C is also contributed by the precipitation
of cementite through decomposition of austenite. This was confirmed by the sharp drop
in Charpy impact toughness as shown by the toughness – hardness trajectory in Fig.A9.
224
Figure A8 Isochronal (1 hour) tempering response of Concept A prototype
Figure A9 Isochronal (1 hour) tempering response of Concept A prototype represented by Charpy toughness – Vickers hardness trajectory.
225
The prototype evaluation demonstrates the shortcoming of the design in
terms of improper estimation of transformation temperatures. Since the actual MS
temperature was much lower than that predicted by the design, the retained austenite
was too stable to transform to bainite for isothermal hold just above MS while it
decomposed to form cementite near peak aging temperature for copper precipitation
strengthening, thus lowering the toughness. Hence, the compatibility of simultaneous
bainitic transformation and copper precipitation strengthening could not be assessed in
the Concept A prototype.
226
APPENDIX B
Assessment of Interfacial Dissipation Effects at Reconstructive
Ferrite-Austenite Interfaces
Accurate prediction of carbon content in austenite is important to
control the stability of austenite for design of “Triple-Phase” steels. The design
Concept A described in Appendix A was adapted from this study employing carbon
stabilization of austenite during isothermal bainitic transformation. This included
investigation of carbon enrichment of austenite during “epitaxial” growth of
reconstructive ferrite. Paraequilibrium growth simulation in a multicomponent system
was run using the DICTRA (DIffusion Controlled Transformation) software to study
the carbon concentration profile at the ferrite-austenite interface during rapid cooling
from an intercritical annealing temperature to a bainitic transformation temperature. A
mobility model was developed from previous literature data to estimate a temperature
dependent interfacial dissipation energy function. Addition of the interfacial
dissipation energy to the ferrite free energy lowers the interface carbon content in
austenite to levels consistent with experimental measurements of retained austenite.
There are two main factors that determine the stability of retained
austenite. The enrichment of austenite with carbon is a widely acknowledged technique
to stabilize retained austenite. Secondly, retained austenite pool size is predicted to
provide a significant stabilizing effect by the Olson-Cohen statistical kinetic model
227
[B1]. In order to control the stability of the retained austenite, it is important to
quantify the evolution of the size and carbon content of austenite pools. This will
define the phase fraction and carbon content distribution in austenite pools at the
isothermal hold temperature, that is, the initial conditions for bainite transformation.
This can be modeled by a spherical simulation of “epitaxial” ferrite growth with carbon
partitioning into the austenite pools using the DICTRA software. The implementation
of the paraequilibrium constraint in the thermodynamic and kinetic calculations is
schematically represented in Fig. B1.
Figure B1 Schematic representation of the Implementation of Paraequilibrium Growth in DICTRA.
The metal sublattice is approximated by a hypothetical element NU
whose thermodynamic and mobility parameters are expressed by the weighted average
of the thermodynamic parameters and mobilities of the substitutional alloying
elements. This allows calculation of the paraequilibrium phase diagrams and the
228
paraequilibrium growth simulations directly in the ThermoCalc and DICTRA software
respectively. In DICTRA the paraequilibrium constraint modifies the different mobility
parameters and diffusion of C in the sublattice, which becomes the rate-controlling
process.
Paraequilibrium Ferrite Growth for an Infinitely Mobile Interface
The evolution of retained austenite stability in triple-phase sheet steels
during rapid cooling to the bainitic transformation temperature after intercritical
annealing has been studied by Brandt [99] in a Fe-0.26C-1.22Mn-1.52Si-0.05Al alloy.
The alloy was intercritically annealed at 1043K followed by rapid cooling to 673K
where isothermal treatment forms bainite. We simulated ferrite growth for the same
alloy under paraequilibrium constraint at the experimental cooling rate of 450C/sec
using the DICTRA diffusion software. The Gibbs energy and the mobility data files
for the austenite and the ferrite phases were rewritten so that the paraequilibrium phase
diagram calculation and the growth simulation can be performed for any composition
of the Fe-C-Mn-Si-Al system. The paraequilibrium phase diagram for ferrite and
austenite in the Fe-xC-1.22Mn-1.52Si-0.05Al system is given in Fig B2.
229
Figure B2 Paraequilibrium phase diagram of Fe-xC-1.22Mn-1.52Si-0.05Al.
At 0.26wt% C and a temperature of 1043K, the phase fractions of
paraequilibrium ferrite and austenite are 0.42 and 0.58 respectively. We considered a
spherical geometry for the austenite grain with an outer shell of ferrite growing
inwards to simulate a uniform microstructure. This is considered a reasonable
approximation for the overall ferrite formation starting from equiaxed austenite pools
[B10, B11]. Our starting cell is set with austenite in the middle covered uniformly by a
layer of ferrite. Based on the ratio of the phase fractions, we set the initial radius of the
austenite cell at 10µm and the ferrite cell as a 2µm thickness shell enclosing the
austenite cell. This is schematically represented in Fig B3.
230
Ferrite (α)
rα+γ = 12µm
rγ = 10µmAustenite (γ)
Figure B3 Schematic representation of the initial ferrite growth cell.
The initial carbon composition for the austenite and ferrite cells were set at those given
by the paraequilibrium phase diagram at 1043K in Fig B2. The simulation result of the
paraequilibrium ferrite growth model at a cooling rate of 450C/sec from 1043K to
673K is shown in Fig B4.
Figure B4 Carbon content profile of an infinitely mobile paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec.
231
It should be noted that at 673K for an infinitely mobile interface, the local carbon
composition of austenite reaches 3.65 wt% C, close to the paraequilibrium value of
3.76 wt% C as predicted by the phase diagram (Fig. B2) at 673K. A steep carbon
concentration profile develops in austenite near the transforming interface because of
much lower diffusivity of C in austenite compared to ferrite while the far-field C level
remains the same as the initial profile. Also, about 40% of the original austenite pool
has been converted to ferrite while cooling from 1043K to 673K. This is in fair
agreement with the results of Brandt [99] who reported 30% conversion and also
consistent with results obtained by Ghosh [B2].
Interfacial Dissipation Energy
Measurement of carbon levels in retained austenite [99] shows that
initially there is a rapid increase in carbon level, which saturates at about 1.4 wt%. We
interpret the retained austenite as representing the highest carbon regions, with the
lower carbon austenite transforming to martensite or bainite on subsequent cooling.
Our predicted level of interface carbon by ferrite growth with infinite interfacial
mobility predicts a much higher value corresponding to the paraequilibrium value.
Additional X-ray diffraction measurements were employed to determine the retained
austenite lattice parameter, using the Ridely, Stuart and Zwell relationship [B3]:
CwtAa %044.0555.3)(0
+= (B1)
232
The austenite carbon content was estimated to be 1.37wt%C. This value is in excellent
agreement with experimentally determined average C content in retained austenite of
1.36 wt% as reported by Brandt [99] for intercritially annealed (at 1043K) and
quenched alloy of same composition. Thus, the DICTRA paraequilibrium ferrite
growth model predicted a much higher value of interface carbon composition. This
higher value may be due to a dissipation energy at the interface neglected in the growth
model simulation.
The velocity of the interface should depend both on its intrinsic mobility
which is related to the process of structural change from austenite to ferrite and on the
diffusion of interstitial carbon ahead of the moving interface. The two processes are
coupled so that interfacial velocity associated with interfacial mobility matches that for
diffusion. The net free energy available for interfacial motion is a sum of the amount of
energy dissipated in the interface process (Gid) and the quantity dissipated in the
diffusion process (Gdd) [B4]. The two dissipation energies Gid and Gdd are then related
by equation (B2):
ddid GGG +=∆ (B2)
When ∆G ≈ Gdd, growth is diffusion-controlled while, interface-controlled growth
occurs when ∆G ≈ Gid. Interfacial motion is generally under mixed control where each
process causes some dissipation of free energy.
233
Figure B5 Constant temperature free energy curves showing ∆G, Gdd and Gid for a ferrite(α)-austenite(γ) interface [B6].
For bainitic transformation, Brandt [99] also considered the addition of an energy term,
which reduces the carbon in austenite by effectively raising the ferrite free energy
curve with respect to the austenite free energy curve (Fig B6). Based on a value
comparable to martensitic transformation critical driving forces, he found a stored
energy term of 1500J/mole modified the level of carbon in austenite to his
experimentally determined value after bainitic transformation.
234
Figure B6 Schematic illustration of the effect of stored energy term added to free energy curve of ferrite upon the carbon content of the austenite as determined by the common tangent construction method [99].
For simulating the reconstructive ferrite growth at higher temperatures, we need to
establish an interfacial dissipation energy function. At high undercooling continuous
reconstructive growth kinetics are expected to follow a linear-viscous behavior [B5]:
idMGV = (B3)
where, V is the interface velocity and M is the interface mobility.
For thermally activated motion, the interfacial dissipation energy is a function of
interface velocity and temperature, where
)*exp(kTHAM ∆
−= (B4)
Thus,
),()*exp(
TVf
kTHA
VMVGid =
∆−
== (B5)
235
where, ∆H* is the enthalpy of activation, T is the temperature in Kelvin and k is the
Universal Boltzmann constant. Thus, the calculation of ferrite growth under conditions
of finite interface mobility requires measures of M. Only two mobility models are
available in the literature as reported by Hillert [B10] and Kierlaart and Van der Zwagg
[B11].
Researchers [B12, B13] have used the two descriptions to estimate the
velocity of the austenite/ferrite interface through its mobility. But unfortunately their
estimates differ by several orders of magnitude. Recently, Inden and Hutchinson [B14]
have shown that the two mobility values at 7000C vary by four orders of magnitude.
Because of this uncertainty in available mobility measures and difficulty to obtain
them experimentally, researchers have often neglected the effect of interfacial
dissipation energy during ferrite growth.
To estimate the mobility of a reconstructive interface we interpret the
kinetics of massive transformation as reconstructive motion in the partitionless limit.
Speich [B6] and Perepezko [B7] performed experimental studies on the kinetics of
massive transformations in the Fe-C and Fe-Ni systems respectively. They fit their
experimental observations to equation (B4) with the mobility for the corresponding
systems by equations (B6) and (B7) assuming an activation of about ½ that for self-
diffusion.
236
For the Fe-C system [B6] this gives,
)10585.1exp(4.21205
RTGVM
id
×−== (B6)
and for the Fe-Ni system [B5, B7] we get,
)10733.1exp(63.1455
RTGVM
id
×−== (B7)
where, R is the universal gas constant.
From these proposed mobility relations, we obtained an upper bound interfacial
dissipation energy function (equation (B5)) employing the same velocities obtained
from the previous diffusional growth simulations and re-ran the simulation with a
temperature-dependent dissipation energy. The carbon profiles for the simulation of the
ferrite growth using the interfacial mobilities proposed by Speich [B6] and Perepezko
[B5, B7] are given in Fig. B7(a) and Fig. B7(b) respectively.
237
(a)
(b)
Figure B7 Carbon content profile of a paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec using interfacial mobilities proposed by (a) Speich et al [B6] (b) Perepezko et al [B5, B7].
238
We find that neither mobility models suppresses the interfacial carbon level close to
that measured experimentally. We then adopted a single mobility law for iron based
alloys by fitting one curve through the two experimentally determined mobility points
(represented by heavy dots) points of Perepezko (at 840K) and Speich (at 1223K) as
shown in Fig. B8.
M = 2120.4e-(158448.2/RT)
M = 145.63e-(173288.7/RT)
M = 7.900E+07e-(265475.5/RT)
1E-121E-111E-101E-091E-081E-071E-061E-05
0.00010.001
0.010.1
10 0.0005 0.001 0.0015
(1/T) in K
Mob
ility
in m
ole.
(N.s
ec)-1
Fe-C(Speich & Szirmae)
Fe-Ni(Perepezko et al)
Mobility Model
Figure B8 Plot of Interface mobility as a function of Inverse Temperature representing the different models [B5-B7].
239
While it is commonly assumed that the enthalpy of activation for the massive mobility
law [B5-B7, B10-B11] is about 50% of that of volume self diffusion, that for our new
empirical model is about 75% corresponding to the high end of reasonable values for a
boundary diffusion controlled process. The new mobility relation is then expressed as:
)106548.2exp(109.75
7
RTGVM
id
×−×== (B8)
A comparison with the various experimental data available on mobility measurements
and those suggested by earlier researchers [B10, B11] with our mobility model adapted
from massive transformation kinetics has been made as shown in Fig. B9. It clearly
suggests that historically all researchers have assumed nearly constant enthalpy of
activation (50% of that of volume self diffusion of α-Fe) while their relationships
varied in terms of pre-factor estimation. Our relation described by equation (B8)
assumes a higher enthalpy of activation and is consistent with most of the experimental
mobility measurements especially with that of Hu [B15] for α-Fe grain growth. These
literature experimental data support our model using activation energy as 75% of that
for self-diffusion of α-Fe.
240
Figure B9 Comparison of current mobility model with experimentally measured mobility [B15-B17] and suggested mobility relationships [B5, B6, B10, B11].
Using the velocity values obtained from the simulation for an infinitely
mobile interface, a fourth order polynomial was fit (R2=0.9975) to describe a
temperature dependent interfacial dissipation energy. This function was then added to
the chemical free energy of ferrite and employed in a paraequilibrium spherical ferrite
growth simulation. To test convergence of the proposed model, the ferrite growth
simulation was run for two more iterations using velocity values from previous
simulations. The temperature dependent interfacial dissipation energy function was
similarly fitted (R2=0.9988 and R2=0.9992 respectively) from the velocity values. The
241
percent ferrite corresponding to the two iterations of simulation was plotted (Fig. B10)
as a function of temperature and compared with experimental values obtained directly
from dilatometry runs by Brandt [99] under identical conditions of 450C/sec cooling
rate. Fig. B10 clearly shows that the iterations converged and gave good agreement
with the measured experimental result.
Figure B10 Comparison of amount of ferrite (%) as a function of temperature (K)
between DICTRA simulation iterations and Dilatometry data from Brandt [99] for cooling rate of 450C/sec.
242
The evolution of the carbon content at the interface during ferrite growth after addition
of interfacial dissipation energy according to the mobility model described by equation
(B8) is given in Fig. B11.
Figure B11 Carbon content profile of a paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec using interfacial dissipation energy function generated by the mobility law given in equation (B8).
243
From Fig. B10 we see that our new dissipation energy function decreases the
interfacial carbon content to about 1.8wt%. Once again due to a much lower diffusivity
of C in austenite, we observe a steep profile in front of the interface. Ghosh and Olson
[B2] have evaluated different methods to estimate the average C content in the
austenite in a steep concentration profile at the interface based on cutoff values of C
levels in regions that will transform to martensite upon quenching to room temperature.
They proposed that the best criterion is to consider the C content that will give 90%
transformation on cooling to room temperature and estimated it to be at 0.8 wt% C. So,
the average (Fig. B11) carbon content at the austenite-ferrite interface applying a
dissipation energy as given by equation (B8) was found to be 1.32 wt% when averaged
from 1.8wt% C at the interface over to 0.8wt% C. This is in excellent agreement with
experimental X-ray diffraction values obtained for the average C content of the
austenite retained on cooling determined to be 1.37wt% in this study and 1.36wt% by
Brandt [99]. For an infinitely mobile interface (Fig. B4), the average carbon content for
90% transformation was determined to be 2.23wt% C at the interface. Thus, comparing
these values the addition of interfacial dissipation energy interpreted from massive
transformation kinetics in the partitionless limit lowers the average carbon content at
the interface by 0.9 wt% to a reasonable level.
244
Conclusions
We have demonstrated that reconstructive mobility can significantly affect the carbon
partitioning level at the ferrite-austenite interface. By adding a temperature dependent
interfacial dissipation energy term we predict a carbon level at the interface close to
values obtained experimentally for the retained austenite. The developed mobility
model will help predict austenite stabilization behavior both by carbon partitioning as
well as the size of the austenite pools. This can be of significant help for designing
optimum austenite stability in triple-phase steels that exploit dispersed-phase
transformation plasticity more effectively.
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245
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