Martensitic transformation or

Shear transformation or
Displacive transformation.
 Low C - lath

Medium C - plate Fe-Ni - plate

Size of interstitial sites in austenite

Size of interstitial sites in ferrite

Octahedral sites in BCC

c/a = 1.005 + 0.045 (wt% C)

Experimental facts about martensite

1. Diffusionless Character

Evidence 1: Martensite form at very low temperatures,

At these temperatures diffusion, even of interstitial atoms is difficult

However, a low transformation temperature is not sufficient

evidence for diffusionless transformation.
Evidence 2: Martensite plates can grow at speeds which approach
that of sound in the metal. In steel this can be as high as
1100ms−1,

However, in shape memory alloys, the interface velocity is

small enough to observe.

Evidence 3: The chemical composition of martensite can be

measured and shown to be identical to that of the parent
austenite
2. Athermal Nature of Transformation

The extent of reaction is found to be virtually independent

of time

Vα’ is the fraction of martensite and T is a temperature below MS

3. Structure of the Interface

Formation of martensite cannot rely on assistance from

thermal activation

There must therefore exist a high level of continuity across the

interface, which must be coherent or semi–coherent

A semi–coherent interface must be such that the interfacial

dislocations can glide as the interface moves (climb is not
permitted).

Also, Burgers vectors of the interface dislocations must not lie in

the interface plane unless the dislocations are screw in character.
There is an additional condition for a semi–coherent interface to be
glissile. The line vectors of the interfacial dislocations must lie along
an invariant–line, i.e. a line which joins the parent and product
crystals without any rotation or distortion.

It follows that for martensitic transformation to be possible, the

deformation which changes the parent into the product must leave
one or more lines invariant (unrotated, undistorted).

A deformation which leaves one line invariant is called an ‘invariant–

line strain’.
4. Orientation Relationships

The formation of martensite involves the coordinated

movement of atoms which require intimate
relationship between the parent and product phases..

Kurdjumow-Sachs (24 variants)

K-S: {111}A // {011}M and <01-1>A // <11-1>M

Nishiyama-Wassermann
N-W: {111}A // {011}M and <11-2>A // <01-1>M

12 variants

the true relations are irrational

5. The Habit Plane

This is the interface plane between austenite and martensite as

measured on a macroscopic scale

y
Flat

x
z
Curved

strain energy minimisation

introduces some curvature when the
transformation is constrained by its
surroundings.
Habit plane indices for martensite (approximate)
5. The Shape Deformation

During martensitic transformation, the pattern in which the atoms in

the parent crystal are arranged is deformed into that appropriate for
martensite, there must be a corresponding change in the macroscopic
shape of the crystal undergoing transformation

α’

γ γ

Shape deformation is macroscopically homogeneous and leaves

habit plane as invariant plane (no rotation and no distortion)
The deformation is such that an initially flat surface becomes uniformly tilted
about the line formed by the intersection of the interface plane with the free
surface.

Any scratch traversing the transformed region is similarly deflected though the
scratch remains connected at the α’/γ interface.

These observations, and others, confirm that the measured shape

deformation is an invariant–plane strain with a large shear component ( 0.22)
and a small dilatational strain (0.03) directed normal to the habit plane.

Invariant plane
strain

Any distortion or
rotation will result in
discontinuity across Loss of coherency Elastic distortion
the interface
at interface in habit plane
 Invariant–plane strain (IPS)

Slip causes a change in shape

but not a change in the crystal
structure, because the Burgers
vectors of the dislocations are
also lattice vectors.

Macroscopic shear

y
IPS

x
z
Bain model – Martensite transformation

Bain proposed first model - To explain transformation of one crystal

structure to another without any diffusion

Austenite (fcc) Martensite (bcc/bct)

In Bain model one BCT unit cell is carved out from two adjacent fcc unit cells

FCC – BCT(austenite)
Bain model – Martensite transformation

What will be the lattice parameter of BCT (austenite)?

Compression
(20%)
bcc/bct martensite
bct austenite

Homogeneous
Lattice deformation
Bain strain (B)
Expansion
 0 0 0
Expansion
(12%)
B   0 0 
2a '  a
(12%)
0 0 
 0 0  0'  a
Principal distortions a '  a
1.12, 1.12, 0.8 0 
'

a
 What is wrong with Bain model?

Orientation relationship are not what is observed experimentally

Bain model
K-S N-W
(111)fcc // (011)bcc
{111}fcc // {011}bcc {111}fcc // {011}bcc
[001]fcc // [001]bcc
<10-1>fcc // <11-1>bcc <-1-12>fcc // <0-11>bcc
[1-10]fcc // [100]bcc
[110]fcc // [010]bcc

Does it leave at least one line invariant?

 Graphical representation of simple shear

Sphere is sheared on an equatorial plane K1 in the direction d

Taking Analogy! a1
a1
a1
x’ m’
x m x x’

a2 a3
FCC a3
y y’
n y
n’ y’
BCC Rigid body rotation R
Bain strain B No invariant line One invariant line

BR Invariant line strain (homogeneous lattice deformation)

Austenite cannot be transformed into martensite by a homogeneous strain

which is an IPS.
But,
Experimentally observed shape deformation leaves the habit plane
undistorted and unrotated, i.e. it is an invariant–plane strain.
 Phenomenological Theory of Martensite Crystallography (PTMC)

To get an undistorted plane from a homogeneous distortion, one of the

principal distortions must be greater then unity, one must be less then
unity and the third one must be unity
a1
a1 a1

Simple shear
x,x’
FCC a2
y,y’ a2
a3

Crystallographic analysis of martensite transformation postulates an

additional distortion in the from of simple shear which makes the lattice
deformation satisfy above condition
 Phenomenological Theory of Martensite Crystallography (PTMC)

To get an undistorted plane from a homogeneous distortion, one of the

principal distortions must be grater then unity, one must be less then unity
and the third one must be unity
a1
a1 a1
Simple shear

x,x’
a2
a3 y,y’
a3

Crystallographic analysis of martensite transformation postulates an

additional distortion in the from of simple shear which makes the lattice
deformation satisfy above condition
Another way to look at it

Bain strain
+ Shape deformation to get
Rigid body rotation martensite (RBP)
R- rigid body rotation
B – lattice deformation
P – Simple shear (slip or twin)

Inhomogeneous
lattice invariant
deformation

Shape changing effect of P2 is

cancelled macroscopically by
an inhomogeneous lattice–
invariant deformation, which
may be slip or twinning
Low C – lath martensite High C – plate martensite
dislocation twins
The theory explains all the observed features of the martensite crystallography

The orientation relationship is predicted by deducing the rotation

needed to change the Bain strain into an invariant–line strain.

The habit plane does not have rational indices because the amount
of lattice–invariant deformation needed to recover the correct the
macroscopic shape is not usually rational.

The theory predicts a substructure in plates of martensite (either

twins or slip steps) as is observed experimentally.

Shape deformation is macroscopically an invariant–plane strain

because this reduces the strain energy when compared with the case
where the shape deformation might be an invariant–line strain.