2. Characteristics of Diffusionless Transformations The Solid Solution of Carbon in Steels Martensite Crystallography The Bain Model of FCC to BCT Transformation

1

Characteristics of Diffusionless Transformations

•The Solid Solution of Carbon in Steels

Martensite Crystallography

The Bain Model of FCC to BCT Transformation

Comparison of Crystallographic Theory With Experimental Results

Theories of Martensite Nucleation

•Formation of Coherent Nuclei of Martensite

•Role of Dislocation in Martensite Nucleation

•Dislocation Strain Energy Assisted Transformation

Characteristics of Diffusionless Transformations

•The Solid Solution of Carbon in Steels


The Bain Model of FCC to BCT Transformation

Comparison of Crystallographic Theory With Experimental Results


•Formation of Coherent Nuclei of Martensite

•Role of Dislocation in Martensite Nucleation

•Dislocation Strain Energy Assisted Transformation

TopicsTopics

INTRODUCTION

• Maraging steels

• Trip Steels

• Ausforming Steels

• Dual phase steels

• Military transformation: Individual atom

movements are less than one interatomic spacing.

Characteristics of Difusionless Transformations

• Lens/Plate shape

• Elastic stress on the surface: Surface relief

• Continuity across the lens on the surface

• Speed of transformation: speed of the sound in solid,

completion in 10-7s.

• No thermal activation needed except for a Fe-Ni alloy.

• Ms: 500°C in low carbon steel, decreases with carbon content.

• Mf: Retained austenite due to elastic stress in between the

transformed plates.

• Driving force for the nucleation of martensite:

• Ordered alloys need small ΔG.

• Solid solution of carbon in Iron


Fig. 6.1 (a), (b) Growth of martensite with increasing cooling below Ms. (c)-(e)

Different martensite morphologies in iron alloys: (c) low C (lath), (d) medium C

(plate), (e) Fe-Ni (plate).


Fig. 6.2 Illustrating how a martensite plate remains (macroscopically coherent with the surrounding austenite and even the surface it intersects.


Fig. 6.3 Various ways of showing the

martensite transformation. (a) Free

energy temperature diagram for

austenite and martensite of fixed

carbon concentration (C0 in (b)). (b)

Free energy-composition diagram for

the austenite and martensite phases

at the Ms temperature. (c) Iron-

carbon phase diagram with T0 as

defined in (a), Ms and Mf

superimposed. (d) Ms and Mf in

relation to the TTT diagram for alloy

C0 in (c).


Fig. 6.5 Illustrating (a) possible sites for interstitial atoms in bcc lattice, and (b)

the large distortion necessary to accommodate a carbon atom (1.54 A diameter)

compared with the space available (0.346 A). (c) Variation of a and c as a function

of carbon content.


• Interface of α/γ: Sound speed, but not always associated with

dislocations

• Habit plane: Undistorted (direction and angular separation unchanged)

• No rotation. • Transformation strains: Homogeneous, shear parallel to

the habit plane. Dilatation (4%, γ to α′) normal to the habit plane. Analogy

to twinning, Fig 6.6.

• Invariant plane strain: Homogeneous shear parallel to the habit plane

(or the twinning planes) and the dilatation normal to the habit plane do

not change the positions or the magnitudes of the vectors on the habit

plane (or twinning plane).


Fig. 6.6 (a) Showing the

twinning of an fcc structure.

Black and white circles

represent atoms on different

levels (b) Graphical

representation of a twinning

shear occurring on a plane K1

in a direction d

The Bain Model of the fcc-bcc transformation

• 1924, Bain

• Two fcc unit cells to one bcc unit cell, see F. 6.7

• Contraction along z-direction: 20%

• Expansion along the x- and y-directions: 12%

• Carbon atoms: <100>/2 position (z-axes) expands the lattice.

The carbon atoms need to be shuffled to become the right

positions in the bct.

• Orientation relationship in the Bain model:

– Bain: (111)γ // (011)α′ [-101]γ // [-1-11]α′

[1-10]γ // [100]α′ [11-2]γ // [01-1]α′

– KS: (111)γ // (011)α′ <-101>γ // <1-11>α′

– NW: (111)γ // (011)α′ <1-10>γ // <101>α′,

about 5° rotation about [111]γ


Fig. 6.7 Bain correspondence for

the α → α′ transformation. Possible

interstitial sites for carbon are

shown by crosses. To obtain α′

the γ unit cell is contracted about

20% on the C axis and expanded

about 12% on the a axes.


• Does the Bain model fit the observation of the undistorted (invariant)

habit plane?

• Refer to the sphere/ellipsoid model in F. 6.8

• Two vectors are needed to form a plane:

Vector OA or OA′ is invariant but OY′ is deformed by 12%. Therefore

the Bain model does not provide the condition of the habit plane.

Fig. 6.8 The Bain deformation is

here simulated by the pure

deformation in compressing a

sphere elastically to the shape of

an oblate ellipsoid. As in the Bain

deformation, this “transformation”

involves two expansion axes and

one contraction axis.

Question on the Bain Model

Modification of the Bain Model

• Internally twinned martensite model: The deformation of the OY′ axis

can be made to zero by introducing twinning or slip, see F. 6.9. This can

form by having alternate regions in the austenite undergo the Bain strain

along different contraction axes such that the net distortions are

compensated. Then the habit plane becomes a macroscopically invariant

plane.

• Experimental data on the habit planes: {111} to {225} to {259}

transition with increasing C content or Ni content. Also, a transition

occurs from dislocated martensite to twinned martensite with increasing

C or Ni. Thickness of twins in high carbon {259} martensite: approx.

3nm.

Role of slip and twinning in martensitic transformation

Fig. 6.9 This figure illustrates

schematically how dislocation glide or

twinning of the martensite can

compensate such as a Bain deformation

and thereby reduce the strain of the

surrounding austenite. The

transformation shear (s) is defined. Note

how s can be reduced by slip or twinning


Fig. 12.5 (a) Formation of a martensite platelet in a crystal of austenite, (b) the

inhomogeneous twinning shear within the platelet


Martensite transformation (a) to (d) of a crystal region. Its external shape can be restored approximately by slip (c) or twinning (d).

Scratches on the surface (a) are sheared in the martensitic transformation (b) resulting in surface relief


Fig. 6.11 Martensite habit planes in various types of steel


Fig. 6.12 Transmission electron micrographs of (a) lath martensite and (b) twinned

martensite. Note the midrib in the twinned martensite, which is thought to be the

first part of the plate to grow.


• Speed of nucleation: 800-1100m/s

• Initial martensite nucleus is coherent with the parent austenite.

• Gibbs energy change for nucleation of coherent nucleus:

– ΔGs is significantly larger than γ.


• A lenticular martensite nucleus with radius a and thickness c:

e.g.) s=0.2, γ=20mJ/m2, ΔGv=174mJ/m3 then, c*/a*=1/40,

ΔG*=20eV (unable to overcome by thermal fluctuation)

• Heterogeneity of Martensite nucleation: Dislocation,

Inclusions but not GB and free surface


Fig. 6.14 Schematic representation of a martensite nucleus


Fig. 6.14 Schematic representation of a martensite nucleus

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2. Characteristics of Diffusionless Transformations The Solid Solution of Carbon in Steels Martensite Crystallography The Bain Model of FCC to BCT Transformation