2. DIFFUSIONLESS TRANSFORMATIONS

3. Topics 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

4. INTRODUCTION • Maraging steels • Trip Steels • Ausforming Steels
• Dual phase steels
• Military transformation: Individual atom movements are less than one interatomic spacing.

5. 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

6. Characteristics of Difusionless Transformations
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).

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

8. Characteristics of Difusionless Transformations
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).

9. Characteristics of Difusionless Transformations
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.

10. Characteristics of Difusionless Transformations
• 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).

11. Martensite Crystallography
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

12. The Bain Model of the fcc-bcc transformation
• 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

13. The Bain Model of the fcc-bcc transformation
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.

14. The Bain Model of the fcc-bcc transformation
Question on the Bain Model
• 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.

15. 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 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.

16. 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

17. Role of slip and twinning in martensitic transformation
Fig (a) Formation of a martensite platelet in a crystal of austenite, (b) the inhomogeneous twinning shear within the platelet

18. Role of slip and twinning in martensitic transformation
Scratches on the surface (a) are sheared in the martensitic transformation (b) resulting in surface relief
Martensite transformation (a) to (d) of a crystal region. Its external shape can be restored approximately by slip (c) or twinning (d).

19. Fig. 6.11 Martensite habit planes in various types of steel
Role of slip and twinning in martensitic transformation
Fig Martensite habit planes in various types of steel

20. Role of slip and twinning in martensitic transformation
Fig 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.

21. Theories of Martensite Nucleation
• Speed of nucleation: m/s
• Initial martensite nucleus is coherent with the parent austenite.
• Gibbs energy change for nucleation of coherent nucleus:
– ΔGs is significantly larger than γ.

22. Theories of Martensite Nucleation
• 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

23. Theories of Martensite Nucleation
Fig Schematic representation of a martensite nucleus

24. Theories of Martensite Nucleation
Fig Schematic representation of a martensite nucleus