Effects of Test Temperature and Grain Size on the Charpy Impact Toughness and Dynamic Toughness (KID) of Polycrystalline Niobium

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL 2003—967

Effects of Test Temperature and Grain Size on the CharpyImpact Toughness and Dynamic Toughness (KID) ofPolycrystalline Niobium

D. PADHI and J.J. LEWANDOWSKI

The effects of changes in test temperature (2196 °C to 25 °C) and grain size (40 to 165 mm) onthe dynamic cleavage fracture toughness (KID) and Charpy impact toughness of polycrystallineniobium (Nb) have been investigated. The ductile-to-brittle transition was found to be affected byboth changes in grain size and the severity of stress concentration (i.e., notch vs fatigue-precrack).In addition to conducting impact tests on notched and fatigue-precracked Charpy specimens, ex-tensive fracture surface analyses have been performed in order to determine the location of ap-parent cleavage nucleation sites and to rationalize the effects of changes in microstructure and ex-perimental variables on fracture toughness. Existing finite element analyses and the stress fielddistributions ahead of stress concentrators are used to compare the experimental observations withthe predictions of various fracture models. The dynamic cleavage fracture toughness, KID, wasshown to be 37 6 4 MPa and relatively independent of grain size (i.e., 40 to 105 mm) andtest temperature over the range 2196 °C to 25 °C.

1m

D. PADHI, Process Engineer-III, is with Applied Materials Inc., SantaClara, CA 95054. J.J. LEWANDOWSKI, Leonard Case Jr. Professor ofEngineering, is with the Department of Materials Science and Engi-neering, Case Western Reserve University, Cleveland, OH 44106. Con-tact e-mail: [email protected] and [email protected]

Manuscript submitted June 19, 2002.

I. INTRODUCTION

THE continuing desire for increasing the efficiency ofturbine engines via operating at elevated temperatures hasled to exploration into various materials systems. Niobium(Nb) is a refractory metal with the distinction of pos-sessing excellent ductility at low temperature, high-temperature strength, and liquid metal corrosion resis-tance. These properties have encouraged researchers toinvestigate a variety of Nb-base systems for potentialaerospace applications. Recently, a number of researchgroups[1–6] have investigated the fracture and fatigue be-havior of Nb-Si systems, which combine a refractory metalintermetallic, Nb5Si3, with the terminal refractory metalphase (i.e., Nb with Si in solid solution).

Recent research studies[1–6] have demonstrated that Nbcan be used as a tough reinforcement in ductile-phase-toughened Nb5Si3 composites. The success of such a sys-tem is significantly affected by the mechanical behaviorof the toughening phase (Nb) as well as the interfacialstrength between the brittle constituent (Nb5Si3) and thetoughening phase. Considerable efforts have been directedin the past toward understanding the effects of changes ingrain size, test temperature, and strain rate on the tensileflow behavior, cleavage fracture stress, and static planestrain fracture toughness of Nb.[7–12] However, the ductile-to-brittle transition and fracture toughness of Nb underdynamic testing conditions, key considerations for struc-tural applications, have not been investigated to the sameextent. The present investigation examines the effects ofchanges in test temperature and grain size on the Charpyimpact and dynamic impact toughness (KID) of polycrys-

talline Nb. The studies reported have been conducted onmaterials identical to those reported previously,[7,8] en-abling direct comparison.

II. EXPERIMENTAL PROCEDURES

A. Materials Tested, Heat Treatments, and SpecimenDetails

Commercial purity Nb (i.e., Nbcp) was obtained fromCabot Corporation (Bethlehem, PA) in the form of hot-rolled square plates having a nominal thickness of 10.5mm. The composition, determined viawet chemical analy-sis, was identical to that tested previously[7,8] (i.e., oxy-gen 165 ppm, nitrogen 63 ppm, silicon 0.03 at. pct, bal.Nb). Unnotched bend bar specimens (dimensions: 55 310.5 3 10.5 mm3) were machined from the plates so thatthe long axis of the bend bar was along the rolling direc-tion. Each bend bar was wrapped in tantalum foil and heattreated in a vacuum of 1025 torr to minimize oxidation.The temperature and time of annealing were varied inorder to obtain a range of grain sizes, measured via thelinear intercept method, and are reported in Table I. Thespecimens were furnace cooled to 500 °C under high vac-uum followed by cooling in N2 atmosphere to room tem-perature. The heat-treated specimens were cut in three mu-tually perpendicular directions, ground, polished, andetched using a solution of 62.5 vol pct distilled water,31.25 vol pct nitric acid, and 6.25 vol pct hydrofluoricacid for approximately 200 seconds. Representative mi-crographs of the specimens are shown in Figure 1. Mea-surements of grain size on the three mutually perpendic-ular directions revealed homogeneity in grain structureindicating complete recrystallization.

Subsized tension specimens (i.e., gage diameter 53 mm, and gage length 5 12 mm) were machined alongthe original rolling direction following ASTM E8M-94.[13]

Standard Charpy specimens were machined from the heat-treated bars in the L-S[13] orientation such that the notch

968—VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS TRANSACTIONS A

Table I. Summary of the Heat Treatments and GrainSizes of Nbcp

Heat Treatment

Temperature Time Grain Size Material (°C) (Min) (mm)

Nbcp 1200 45 57 6 71200 60 39 6 31300 90 104 6 161300 120 165 6 28

Fig. 1—Microstructures of recrystallized Nbcp specimens.

was along the long transverse direction, in accordance withASTM E23.[13] The dynamic fracture toughness test spec-imens (i.e., fatigue-precracked Charpy specimens) wereobtained by introducing a starter notch of approximately3-mm depth using a diamond-impregnated wire saw. Thiswas followed by fatigue precracking at 2125 °C in a three-point bend (3PB) configuration, in accordance with ASTME399.[13] The fatigue precracking was conducted on a20 Kip MTS (Minneapolis, MN) servohydraulic machineusing an MTS 442 controller and a DEC (Maynard, MA)PDP-11 computer at a frequency of 20 Hz and a stressratio (R) of 0.1. Based on previous results for this mater-ial,[8] fatigue precracking was conducted to achieve a totalcrack length between 0.45 and 0.55 W at 2125 °C. This

ensured a small plastic zone size ahead of the fatigue cracktip due to the significantly higher yield stress at 2125 °C(e.g., 426 MPa) compared to 25 °C (e.g., 160 MPa).[8,16]

B. Mechanical Testing

Individual tension tests were conducted at a strain rateof 6(1024) s21 at temperatures ranging from 2196 °C to25 °C on the Nbcp specimens using an Instron 1142 screw-driven machine and an MTS servohydraulic machine fit-ted with an ATS low-/high-temperature cabinet. The lowtemperatures were obtained by injecting liquid N2 vaporinto the cabinet at intervals controlled by a thermocouple.Temperature variation during the tests was ,1 °C. Theload-load point displacement traces were used to calcu-late the 0.2 pct offset yield strength (sy).

The notched Charpy and fatigue precracked impactspecimens were tested in a Wiedemann Baldwin (Summit,NJ) instrumented impact tester. Load, deflection, absorbedenergy, and velocity of the tup were acquired as a func-tion of time via the DYNATUP* instrumentation pack-

*DYNATUP is a trademark of INSTRON Company, Canton, MA.

age. The impact tests were conducted in the temperaturerange of 2196 °C to 25 °C by using a mixture of 2-methyl


(a) (b)

Fig. 2—Schematic of the fracture surface analyses for (a) fatigue-precracked impact test specimen and (b) Charpy impact test specimen.

Fig. 3—Effect of changes in grain size on 0.2 pct offset yield stress ofNbcp.

butane and liquid nitrogen in varying proportions. A non-instrumented Charpy impact tester with a tup of higher ca-pacity (325.4 J) was used for tests at temperatures wherethe absorbed impact energy was greater than 81.4 J. Thepeak load, initial crack length measured from fracturedspecimens, and specimen geometry were used to computethe dynamic fracture toughness (KID) according to ac-cepted procedures[14] and Kcalibrations.[13]

C. Fracture Surface Analyses

The fracture surfaces of the notched Charpy specimensand the fatigue-precracked Charpy test specimens wereanalyzed using a Hitachi (San Jose, CA) 4500 S high-resolution field emission gun scanning electron micro-scope. For each sample, a montage consisting of severalmicrographs was taken in the central 7 mm (thickness di-rection) of the specimen in order to exclude the area underplane stress condition, as shown in Figure 2. Each mon-tage was examined to identify the potential nucleation sitesof cleavage fracture. This was achieved by tracing the“cleavage river lines” back to a region from where all the“river lines” appeared to emanate, as conducted previ-ously.[7,8,15] In some cases, multiple sites of apparent frac-ture nucleation were identified. The distances of these po-tential cleavage fracture nucleation sites from the notchtip/precrack front were measured. The relative amounts ofbrittle (i.e., cleavage) and ductile (i.e., dimpled) fracturewere also quantified for the entire specimen cross sections.

III. EXPERIMENTAL RESULTS

A. Mechanical Tests

The 0.2 pct offset yield strength of Nbcp for differentgrain size/test temperature combinations are plotted as afunction of average grain radius21/2 (d21/2) in Figure 3.No yield points were observed in any of the tension tests.At a given test temperature and strain rate, the yieldstrength of Nbcp is found to be essentially independent ofgrain size in the range of current investigation (i.e., 40 to165 mm) and a strong function of test temperature. From

the current investigation, the calculated values for theHall–Petch slope (ky) for Nbcp were found to be verylow, i.e., 5.6(104) N/m3/2, 2.65(104) N/m3/2, and 4.35(104)N/m3/2 at 2196 °C, 275 °C, and 25 °C, respectively.Adams et al.[9] reported a ky value of 2.76(104) N/m3/2 at20 °C under a strain rate of 2(1024) s21. Johnson[10] in-vestigated the effects of grain size (37 to 138 mm) and testtemperature (2196 °C to 220 °C) on the tensile proper-ties of commercially pure sintered niobium at a strain rateof 1024 s21. No effect of variation in grain size on yieldstrength was observed. Churchman[11] conducted tensiontests on high-purity Nb over the temperature range of2180 °C to 280 °C. His results showed that the yieldstrength was unaffected by the change in grain size fromapproximately 13 to 395 mm. The lack of yield points inthe present and previous tests[9,10,11]suggests that the lackof impurity-induced pinning of dislocations is one poten-tial reason for the low value of ky obtained presently andreported previously. The yield strength increased with in-creasing strain rate,[16] in agreement with results reportedelsewhere.[12,18]


Fig. 4—Ductile-to-brittle transition behavior of Nbcp (Charpy impacttest). Arrows indicate specimens did not fail.

Fig. 5—Absorbed impact energy normalized by initial uncracked liga-ment area.

Fig. 6—Effect of strain rate and test temperature on the yield stress ofNbcp. *Using empirical constitutive equation.[18]

The impact energy (Cv) obtained from the dial readingon the Charpy impact machine is plotted as a function oftest temperature in Figure 4. Two specimens (for eachgrain size) were tested at each test temperature for re-peatability. The lower shelf regime is associated with alow value of absorbed impact energy (#6.5 J), while theupper shelf energy values for the 40 and 105 mm Nbcp arefound to be nearly equal (,258 J). At 225 °C test tem-perature, the impact energy decreases with an increase ingrain size. The other test temperatures did not produce aslarge a change as that obtained at 225 °C.

The impact energy normalized by the area of initial un-cracked ligament is plotted as a function of temperaturein Figure 5 for both the notched and fatigue-precrackedspecimens. It appears from this plot that the complete tran-sition to the upper shelf regime has not occurred at 25 °Cin the fatigue-precracked specimens. Alternatively, theductile-to-brittle transition temperature of fatigue-

precracked specimens is found to be higher than that ofthe notched specimens regardless of grain size.

The dynamic fracture toughness (KID) was computedaccording to accepted procedures.[13,14] The validity of lin-ear elastic fracture mechanics (LEFM) conditions wasverified using standard ASTM procedures[13,14] adoptedfor dynamic testing conditions[17]:

[1]

where

calculated fracture toughness, and

dynamic yield strength at a strain ratej̇.

The strain rate achieved during the impact test ( j̇) can beestimated as[18,19]

[2]

where

W 5 specimen width;S 5 span of loading points (<40 mm for Charpy test);Q 5 1.94 and 2.57 for V-notch and fatigue-pre-

cracked Charpy specimens, respectively; and

load point displacement rate.

Equation [2] yields ̇j values of approximately 380 and505 s21, respectively, for notched and fatigue-precrackedCharpy impact tests. Considering the dearth of data onyield stress of Nbcp at these strain rates, the empirical de-pendence of flow stress of Nbcp on strain rate and test tem-perature, determined recently by Nemat-Nasser andGuo,[18] was used for computations. Work conducted atCase Western Reserve University over a more limitedrange of strain rates is in agreement with the results of

d

t5

#j 5 c 3WQ

2(S>2)2 dBd

tR

s#

jyd 5

KO 5

LEFM: 4p

aKQ

s#jyd

b2

# B, a0, (W 2 a0)

Table II. Dynamic Fracture Toughness and Corresponding Plastic Zone Size Calculations for Fatigue-PrecrackedImpact Tests

Impact PlaneEnergy Strain Validity

Grain Thickness Width (J)2 KID Plastic CriteriaSize Temperature aavg (B) (W) Pmax (Dial (MP a Zone Size (L)(mm) (°C) (mm) (mm) (mm) (kg)* Reading) **) (mm)† (mm)‡ L , B L , aavg L , (W 2 aavg)

40 2195 5.9 10.4 10.1 314.1 3.1 41.4 91 2.2 Y Y Y40 2150 5.5 9.3 10.1 299.3 3.1 39.1 119 2.9 Y Y Y40 2125 5.6 10.4 10.2 329.8 4.4 38.2 142 3.4 Y Y Y40 275 5.0 10.4 10.2 288.2 12.2 27.5 102 2.5 Y Y Y40 275 5.7 10.3 10.1 297.9 5.3 36.7 182 4.4 Y Y Y40 250 6.0 10.3 10.1 309.5 8.1 43.1 291 7.0 Y N N40 250 5.1 10.3 10.1 337.1 16.4 33.7 178 4.3 Y Y Y40 225 5.6 10.4 10.1 315.4 13.9 37.6 260 6.2 Y N N40 225 5.4 10.3 10.1 373.4 18.6 41.8 321 7.7 Y N N40 0 3.8 10.3 10.1 540.3 35.6 37.2 297 7.1 Y N N40 25 4.4 10.4 10.1 423.1 77.6 34.8 302 7.2 Y N N

105 2195 5.6 10.5 10.2 351.2 3.4 40.6 88 2.1 Y Y Y105 2125 5.4 10.4 10.2 354.3 4.4 38.1 113 2.7 Y Y Y105 275 5.3 10.3 10.1 316.9 9.8 34.0 156 3.7 Y Y Y105 275 4.8 10.3 10.1 351.4 4.6 32.6 144 3.4 Y Y Y105 250 5.3 10.4 10.2 322.7 13.7 33.9 180 4.3 Y Y Y105 225 4.6 10.4 10.2 358.4 14.6 30.9 149 3.6 Y Y Y105 225 5.0 10.3 10.1 368.2 22.4 35.9 237 5.7 Y N N105 0 4.7 10.3 10.0 378.6 37.8 34.7 258 6.2 Y N N105 25 4.4 10.4 10.2 396.2 41.0 31.8 253 6.1 Y N N

*Instrumented tup reading.**Using Pmax

†Using dynamic yield strength at a strain rate of 500 s21.[18]

‡Using Eq. [1].

1m


Fig. 7—Effect of test temperature and grain size on dynamic precrackedfracture toughness (KID).

Validity Criteria Satisfied

Nemat-Nasser and Guo’s work[18] [Figure 6]. The KID andthe corresponding plastic zone size data are presented inTable II. The LEFM criteria are violated at the highesttemperatures tested (e.g., 225 °C to 25 °C), and the KID

values provide a lower bound estimate for dynamic frac-ture toughness of the material in this regime. However, itis important to note that both crack length and specimenthickness satisfied the LEFM criteria at the highest tem-peratures, as shown in Table II. The LEFM criteria at thehighest temperatures were only violated in some of thecases by L. aavg and (W2 aavg), as shown in Table II.In the lower shelf regime, the KID is found to be relativelyunaffected by changes in test temperature and grain sizeover the range tested, as shown in Figure 7.

B. Fracture Surface Analyses

Scanning electron microscopy (SEM) fracture analy-ses at low magnification revealed that all the fatigue-precracked Charpy impact specimens exhibited a pre-dominance of cleavage fracture up to test temperaturesof 25 °C. However, above approximately 250 °C, thefine- and coarse-grained specimens exhibited small“stretch zones” (e.g., ,100 mm) along some portions ofthe fracture surface adjacent to the fatigue precrack.Representative SEM fracture surface montages for the40-mm grain size Nbcp precracked specimens tested at2196 °C and 25 °C are presented in Figures 8(a) and

(b), respectively. For the Charpy V-notch specimens, thefracture surface was predominantly cleavage in thelower shelf regime, as shown in Figure 9. Tables III(a)and (b) present the distances of the apparent cleavagefracture nucleation sites from the stress concentrator(i.e., notch and precrack, respectively), while Figures10(a) and (b) plot these data. Quantification of theamount of cleavage vs ductile fracture present on thenotched Charpy impact fracture surfaces[16] indicated


(a)

Fig. 8—Fracture surface montage of an Nbcp 40-mm fatigue-precracked Charpy specimen. (a) test temperature 5 2196 °C and (b) test temperature 525 °C. Apparent cleavage fracture nucleation sites are shown inside the boxes.

that the transition from predominantly cleavage fractureto ductile fracture occurred between 250 °C (i.e.,.80 pct cleavage) and 225 °C (i.e., 100 pct ductile—did not fail) for the 40-mm grain size Nbcp. In contrast,the 105-mm grain size Nbcp Charpy specimens revealedthis transition to occur between 225 °C (i.e., 75 pctcleavage) and 0 °C (i.e., 100 pct ductile—did notfail).[16] The specimens tested on the upper shelf did notfracture into two pieces; the extensive plasticity in thesecases permitted the intact specimen to exit the impactmachine (Figure 4).

IV. DISCUSSION

The present work has investigated the effects of changesin microstructure, specimen geometry, and stress state onthe ductile-to-brittle transition, as well as the energy ab-sorbed/toughness under such testing conditions. The ini-tial discussion will focus on observations related to theductile-to-brittle transition, followed by a discussion ofthe magnitude of fracture toughness possible in the lowershelf regime for such materials, despite the appearance ofcleavage fracture.

(b)


Fig. 9—Fracture surface montage of a Nbcp 40-mm notched Charpy specimen tested at 275 °C. Apparent cleavage fracture nucleation site is showninside the box.

A. Ductile-to-Brittle Transition

Early concepts of the ductile-to-brittle transition behav-ior of a material consider the competition between flow andfracture.[20–27] As originally proposed by Ludwik,[20] brittlefracture occurs when the local stresses exceed the brittlefracture stress. Considerable work has investigated the ef-fects of changes in various microstructural features on themagnitude of the cleavage fracture stress in ferrous-basedsystems.[15,23–28]Work on Nb[7,8] reveals a strong effect ofgrain size on the cleavage fracture stress, with an increasein the cleavage fracture stress arising through the decrease

in grain size. Temperature-independent cleavage fracturestresses in the range 1150 to 1500 MPa were reported bySamant and Lewandowski[7,8] on material of nearly identi-cal chemistry and grain size as that tested presently.

1. Smooth tensile specimensFigure 11 illustrates the effect of changes in test tem-

perature on reduction in area for the smooth tension spec-imens and reveals significant ductility (i.e., RA .50 pct)at 2196 °C, despite the appearance of 100 pct cleavagefracture at 250 °C in the notched/precracked specimens.This is consistent with Ludwik’s concept,[20] because the

Table III(a). Summary of Locations of Apparent Cleavage Fracture Nucleation Sites: Charpy Impact Test

Distance of Apparent Sites of Average Location of Peak Grain Test Cleavage Fracture Nucleation from Measured Tensile Stress Size Temperature Notch Distance from Ahead of Notch (mm) (°C) (mm) Notch (mm) (mm)[30]

40 2195 182 173 77 93 208 221 230 169 6 61 17040 2125 514 216 192 336 384 168 — 302 6 134 25040 275 239 231 239 296 — — — 251 6 30 340

105 2195 215 239 92 110 110 — — 153 6 68 62105 2125 240 275 178 384 240 309 — 271 6 70 212105 275 374 392 — — — — — 383 6 13 320105 225 637 263 519 — — — — 473 6 191 310

Table III(b). Summary of Locations of Apparent Cleavage Fracture Nucleation Sites: Fatigue Precracked Impact Test

Distance of Apparent Sites of Average Location of Peak Grain Test Cleavage Fracture Nucleation from Measured Tensile Stress Size Temperature Fatigue Precrack Distance from Ahead of Crack (mm) (°C) (mm) Precrack (mm) (mm)[39]

40 2195 115 18 100 61 61 79 79 73 6 31 7640 275 154 134 189 64 — — — 135 6 53 10140 225 269 96 198 243 192 — — 200 6 66 —40 25 239 155 183 — — — — 192 6 43 —

105 2195 183 163 127 258 139 136 150 165 6 45 148105 275 489 367 165 49 — — — 267 6 198 183105 25 377 — — — — — — 377 —


(a) (b)

Fig. 10—Effect of test temperature on the location of apparent cleavage fracture nucleation sites: (a) Charpy impact test and (b) precracked impact test.

Fig. 11—Effect of test temperature on RA at fracture (?j 5 6(1024) s21).

yield stress at 2196 °C (approximately 730 MPa) is wellbelow the cleavage fracture stress (i.e., 1150 to1500 MPa), as determined elsewhere.[7,8]

2. Notched charpy specimensThe two important considerations in analyzing the tran-

sition behavior of Charpy impact specimens are (a) thedistribution of stress ahead of the notch and (b) the criti-cal cleavage fracture stress as a function of test tempera-ture. Prior to general yield, the strain rate (?

j) experiencedby the specimen can be estimated using Eq. [2] and themeasured velocity of the impacting tup (i.e., 5.24 m/s),producing?

j value of 380 s21, several orders of magnitudehigher than that experienced during a static test. There-fore, the effect of changes in strain rate on the stress dis-tribution ahead of the notch and sF is required. Green andHundy[29] have studied the profile of the stress field aheadof a Charpy notch under static and impact conditions andshowed that the stress field ahead of the notch is unaf-fected by the impacting conditions, provided the mode of

deformation was unaltered. However, the increase in theyield stress due to the increased strain rate experienced bythe material in the vicinity of the notch increases the mag-nitude of stresses ahead of the notch tip.

More recent finite element model work[30] has charac-terized the magnitude and distribution of stresses in anotched Charpy bar loaded in 3PB to various fractions ofgeneral yield, analogous to work by Griffith and Owen[31]

on notched four-point bend bars. The maximum stress in-tensification for a notched Charpy bar at general yield wasshown to be 2.57 for the slip line field solution,[32] whilean analysis of a notched four-point bend specimen testedto general yield for a material with moderate linear workhardening revealed the maximum stress intensification tobe 2.6.[31] Other work[33,34] on notched four-point bendbars has shown that higher rates of linear or power-lawwork hardening, beyond those exhibited presently, in-crease these values. The maximum stress intensificationat general yield in a notched Charpy bar calculated usingthree-dimensional FEM[30] for a material with power-lawhardening (i.e., n5 0.15) was 2.5. This information isused subsequently to estimate the Nil Ductility Tempera-ture (NDT) and is then compared to the present results.

At the NDT, the conditions for general yield and brit-tle fracture are satisfied[28]:

[3]

[4]

where

maximum stress intensification ratio ahead ofa Charpy notch,maximum principal stress along the directionof loading,dynamic yield strength, andcleavage fracture stress. sF 5

syd 5

smax11 5

R 5

R 5smax

ll

syd

Rsyd 5 sF


Fig. 12—SEM photograph of the fracture surface of a Nbcp 105-mmCharpy impact test specimen tested at 225 °C. The presence of a stretchzone prior to cleavage fracture nucleation is clearly evident.

Considering that Cottrell’s model for grain size controlof the brittle fracture stress is obeyed for Nb as shownearlier,[7] it is estimated that the sF values for 40- and105-mm grain size Nbcp specimens are approximately 1800and 1300 MPa, respectively. Using the values for sF (i.e.,1800 MPa and 1300 MPa) and the values for R (i.e.,approximately 2.6) in Eq. [3], calculated values for syd atthe NDT are 690 and 500 MPa for Nbcp Charpy specimenshaving 40- and 105-mm grain size, respectively. FromNemat-Nasser and Guo’s work,[18] the yield strengths ofNbcp at 2100 °C and 225 °C are approximately 675 and525 MPa, respectively, at a strain rate of 380 s21 (Figure 6).Similarly, from Briggs and Campbell’s experimentaldata,[12] the yield strengths of Nb at 275 °C and 225 °Care found to be 706 and 517 MPa, respectively, at a strainrate of 100 s21. This estimates that the NDT of a 40-mmgrain size Nbcp should lie in the vicinity of 275 °C, whereasthe NDT of 105-mm grain size Nb should be near 225 °C.

The data reported in Figure 4 are qualitatively consistentwith the preceding arguments. The NDT, defined as thetemperature at which the Charpy impact energy first be-gins to rise, appears to be near 250 °C for the 40-mm grainsize Nbcp and is near 225 °C for the 105-mm grain sizeNbcp. Quantification of the amount of cleavage vs ductilefracture present on fracture surfaces[16] indicated that thetransition from predominantly cleavage fracture to ductilefracture occurred between 250 °C (i.e., .80 pct cleav-age) and 225 °C (i.e., 100 pct ductile—did not fail) forthe 40-mm grain size Nbcp. In contrast, the 105-mm grainsize Nbcp Charpy specimens revealed this fracture modetransition occurred between 225 °C (i.e., 75 pct cleav-age) and 0 °C (i.e., 100 pct ductile—did not fail).[16] Inthe present studies, the transition from lower shelf to uppershelf for Nbcp 40-mm grain size occurs at approximately250 °C to 225 °C and takes place between 225 °C and0 °C for 105-mm grain size material. Fracture surfaceanalyses revealed that all the Charpy specimens fracturedvia cleavage mode at test temperatures below the NDT.However, as the test temperature increased beyond theNDT, specimens of both grain sizes showed appreciableamounts of ‘stretch zones’ immediate to the notch tip(Figure 12). In addition, increasing amounts of localplasticity were observed at the apparent cleavage fracturenucleation sites (Figure 13), where evidence of limitedamounts of ductile fracture was present both at the ap-parent nucleation site (Figure 13(a)) and along one of thecleavage river lines (Figure 13(b)). Such features werenonexistent at the lower temperatures. In the upper shelfregion, impact specimens exited the machine intact due tothe extensive plasticity exhibited (Figure 4).

The profiles of load vstime obtained from theinstrumentation package for tests conducted at temper-atures up to the NDT were linear to maximum load. Inthese cases, the maximum load (Lmax) recorded duringthe impact tests conducted below the NDT can be con-sidered as the load at which cleavage fracture started toinitiate/propagate. Using Lmax, the nominal applied stressat fracture for each of the test conditions can be calcu-lated as[35]

[5]snom 56M

b(W 2 a)2

[6]

where

M 5 bending moment experienced by the bar (N.m),B 5 specimen thickness (m),W 5 specimen width (m),a 5 notch depth (m),

Lmax 5 load to failure (N), andS 5 span of loading in Charpy impact test (m).

Using this approach, it is possible to qualitativelycompare the location of apparent sites of cleavage frac-ture nucleation with that of the peak stress in a mannerdescribed elsewhere[7] for specimens loaded under sta-tic conditions. Recent work on Nb[18] is combined withpresently reported effects of changes in strain rate onyield stress in Figure 7, showing reasonable justifica-tion in using an empirical prediction of yield stress ofNbcp as a function of strain rate and test temperature.[18]

Using Eq. [5] and [6] and the yield stress of Nbcp at 380s21 (during the Charpy test), the snom/sy values are com-puted for Nbcp specimens having 40- and 105-mm grainsize for test temperatures near and below the NDT. Com-bining this information with the stress field analyses ofWang et al.,[30] the distances of the potential nucleationsites are calculated and summarized in Table III(a); theexperimentally observed distances of fracture nucleationsites are found to be close to the location of the peaktensile stress, providing evidence of a tensile stress con-trolled brittle fracture process, in agreement with sev-eral investigators.[7,15,23,31]As the test temperature is in-creased above 2196 °C, the yield stress decreases anda higher nominal bending stress needs to be applied inorder to achieve the temperature-independent criticalbrittle fracture stress (sF) for Nb.[7] Thus, snom/sy in-creases and the location of the peak tensile stress movesfarther away from the notch tip, consistent with the datapresented in Figure 10(a).

M 5LmaxS

4


(a) (b)

Fig. 13—Higher magnification view of a cleavage fracture nucleation site in a Nbcp 105-mm Charpy impact specimen tested at 225 °C, illustratinglocal plasticity (inside the boxes): (a) nucleation site and (b) cleavage river line.

3. Fatigue-precracked charpy specimensFrom the plot of absorbed impact energy (normalized

by initial uncracked ligament area) vstest temperature(Figure 5), it appears that complete transition into the duc-tile regime is not achieved even at room temperature forthe fatigue precracked specimens. Furthermore, whencompared with the absorbed energy values from the V-notch Charpy tests normalized by initial uncracked liga-ment area, it is clear that for a given grain size, the tran-sition temperature of Nbcp specimen is higher for theprecracked specimens tested in impact. This is consistentwith the higher stress intensification (R) achieved in aprecracked impact test due to the very small root radius(r V 1 mm) of the fatigue precrack in contrast to that ofa Charpy notch (r, 250 mm). The location of apparentcleavage sites ahead of the fatigue precrack (Table III(b))is discussed in Section B.

B. Dynamic Plane Strain Fracture Toughness (KID)

It appears from Table II that the LEFM criteria (calcu-lated using the sy values at a strain rate of 500 s21[18] areonly violated for specimens tested at temperatures above250 °C and 225 °C for Nbcp specimens having 40- and105-mm grain size, respectively. In addition, the load-timehistory of the specimens tested at 250 °C for the 40-mmgrain size Nbcp specimen did not exhibit any nonlinearityprior to fracture. In contrast, the instrumented load-timetrace for specimens tested at 225 °C revealed some evi-dence of nonlinearity, indicative of plasticity or stablecrack growth. Similar observations were made for the 105-mm grain size Nbcp specimens tested at 225 °C or highertemperatures. Beyond the LEFM validity regime, the KID

values probably underestimate the actual dynamic tough-ness of the material due to the increased plasticity or sta-ble crack growth.

Over the range of LEFM validity (i.e., 2196 °C to250 °C for 40-mm Nbcp and 2196 °C to 225 °C for105-mm Nbcp), Figure 7 revealed that KID is virtually in-

dependent of test temperature and grain size. Over thatrange, Figure 10(b) further revealed that the location ofthe apparent cleavage fracture nucleation sites were notas affected by changes in test temperature as demon-strated in the notched Charpy specimens shown in Fig-ure 10(a). This observation can be rationalized followingarguments used in the cleavage fracture of steels[23,36–38]

and for polycrystalline Nb,[7,8] where a specimen havinga sharp crack, as in the case of a fatigue precrack, wouldfail via cleavage when the maximum principal tensilestress (smax

yy ) ahead of the crack exceeded the criticalcleavage fracture stress (sF) over a microscopically sig-nificant (characteristic) distance. The severity of stressstate provided by a sharp crack results in high stress in-tensification ahead of the crack tip. Finite element analy-ses of the stress field ahead of a sharp crack[39,41,42]showthat the maximum stress intensification achieved in aspecimen having a sharp crack is higher than in a blunt-notched specimen, and depends on the work-hardeningbehavior of the material. Thus, the issue of exceeding thesF becomes secondary, while extending the smax

yy abovethe sF over the characteristic distance becomes the con-trolling event.

To rationalize the results of the present investigationin light of the preceding arguments, it is important to con-sider the distance of apparent cleavage fracture nucleationsites from the crack tip (x). From fracture surface analy-ses of fatigue-precracked specimens (Figure 10(b) andTable III(b), it appears that x is slightly dependent on testtemperature in the range 2196°C to 225°C for speci-mens having 40- and 105-mm grain size. At the highesttest temperatures, this probably arises due to crack tipblunting and the appearance of stretch zones at the cracktip (Figure 12). In precracked specimens, the cleavagefracture can nucleate, stochastically, anywhere in the re-gion where smax

yy exceeds the sF. Thus, it is reasonable toargue that xis indicative of the characteristic distance.Previous work has shown that sF is independent of tem-perature for Nb.[7] The present work indicates that the


Fig. 14—Comparison of the experimentally obtained dynamic fracturetoughness (KID) data with the predicted values using Tracey’s stress fieldanalyses.[39]

global stress (i.e., applied dynamically) required to prop-agate a crack in a brittle manner is unaffected by changesin test temperature (in the range-196 °C to 225 °C), pro-ducing a nominally temperature-independent value for thedynamic fracture toughness over the range of tempera-tures tested.

Early work[37] has suggested that the plane strain frac-ture toughness (KIC) of metals that fail via slip-inducedcleavage can be predicted using sF, x, and the distribu-tion of stress field ahead of the crack. The stress analysisdue to Tracey[39] is used for the present estimation in themanner used previously by Samant and Lewandowski:[7,8]

for static fracture toughness measurements made on es-sentially identical Nb materials. It should be noted thatthe work-hardening exponent (n) has a strong effect onthe stress field profile. From the tensile tests in the pre-sent investigation, nwas found to be between 0.05 and0.08 in the temperature range of 2196 °C to 2125 °C andbetween 0.15 to 0.2 in 275 °C from room temperature.Based on this, nis assumed to be zero for the testtemperature range of 2196 °C to 2125 °C and 0.2 forhigher test temperatures. The yield stress (at 500 s21) val-ues used in the estimation are calculated using the em-pirical equation from Nemat-Nasser and Guo’s work.[18]

The temperature-independent sF values for the 40 and105-mm grain size specimens are estimated from datafrom Samant and Lewandowski[7] as discussed earlier inthis article.

Figure 14 compares the effect of changes in test tem-perature and grain size on the predicted plane strain dy-namic fracture toughness (KID) and the experimentally ob-tained data shown earlier in Figure 7. It is evident thatTracey’s model predicts reasonably well for the low-temperature (2196°C to 275 °C) tests. This is consistentwith the observations of catastrophic crack propagation,without any stable crack growth at these temperatures.However, at higher temperatures (i.e. T . 225 °C), themodel’s prediction of fracture toughness is significantlyhigher than that obtained experimentally. At these temper-atures, the criteria for linear elastic fracture mechanics are

violated, as shown in Table III, and the experimentally ob-tained KID values underestimate the predicted toughness inthe manner demonstrated by Samant and Lewandowski[7,8]

for static tests on similar materials. Attempts at using crackgages to document/record any stable crack growth duringthe instrumented impact tests at 275 °C were unsuccess-ful due to the difficulty and space limitations provided bythe impacting tup and specimen holder.[16] However, crackgages were successfully used to record stable cracking ofthese materials at high testing velocities and low tempera-tures on a servohydraulic testing machine. These tests werenot conducted under the impact conditions used presentlyand are reported elsewhere.[16,40]

V. CONCLUSIONS

1. Smooth Nbcp tension specimens having grain sizesranging from 40 to 165 mm exhibited ductile fracturewhen tested at a strain rate of 6(1024) s21 over the testtemperature range of 25 °C to 2196 °C. Over thisrange, the Hall–Petch slope (ky) was found to vary be-tween 2.65(104) and 5.6(104) N ? m23/2.

2. The ductile-to-brittle transition temperature of notchedNbcp Charpy specimens was grain size dependent. TheNDT of 40-mm grain size Nbcp Charpy specimens wasnear 250 °C, while that of 105-mm grain size Nbcp

Charpy specimens was near 225 °C. The NDT of thefatigue-precracked impact specimens was much higherthan that of notched Charpy specimens, consistent withthe differences in stress state between the specimenstested.

3. All specimens tested at temperatures below the NDTexhibited cleavage fracture with multiple sites of ap-parent cleavage fracture nucleation located ahead ofthe notch tip, consistent with tensile-stress-controlledcleavage fracture. Increases in test temperature pro-duced large increases in the distance ahead of thenotch where the apparent cleavage nucleation siteswere located, in rough agreement with the locationof peak tensile stress available from FEM analyses.At temperatures above the NDT, local plasticity atthe notch and at the apparent cleavage fracture nu-cleation sites was clearly evident. Extensive plastic-ity was exhibited on the upper shelf without cata-strophic fracture.

4. The plane strain dynamic cleavage fracture toughness(KID) was essentially independent of test temperature(over the range 2196 °C to 250 °C for 40-mm grainsize Nbcp and 2196 °C to 225°C for 105-mm grainsize Nbcp) and grain size (40 to 105 mm). Despite thepredominance of cleavage fracture, the dynamiccleavage fracture toughness was approximately 37 64 MPam.

5. The average distances of apparent cleavage fracture nu-cleation sites from the fatigue precrack exhibited aslight dependence on test temperature and grain sizeover the range tested. At the highest test temperatures,this likely results from crack-tip blunting and thechanges in stress distribution that are produced. Com-parisons to available models of cleavage fracturetoughness revealed reasonable agreement for temper-atures below the NDT.


ACKNOWLEDGMENTS

The authors thank AFOSR (Grant No. F49620-96-1-0164 and F49620-00-1-0067) for partial support of thiswork. Partial support by Reference Metals Companyand supply of materials by Cabot Corporation are alsoappreciated.

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TITLE: Effects of Test Temperature and Grain Size on theCharpy Impact Toughness and Dynamic Toughness (KID)of Polycrystalline Niobium

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Effects of Test Temperature and Grain Size on the Charpy Impact Toughness and Dynamic Toughness (KID) of Polycrystalline Niobium