Bhadeshia H.K.D.H., Honeycombe R. Steels: Microstructure and Properties

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98 CHAPTER 5 FORMATION OF MARTENSITE

parallel or nearly parallel, and it is usually the case that corresponding directions

within these planes are roughly parallel:

{111}

{011}

<10

<111>

Kurdjumov–Sachs

{111}

{011}

<10

about 5.3

◦

from<111>

towards <111>

Nishiyama–Wasserman

{111}

about 0.2

◦

from {011}

<10

about 2.7

◦

from <111>

towards <111>

Greninger–Troiano

Note that these have been stated approximately: the true relations are

irrational, meaning that the indices of the parallel planes and directions cannot

be expressed using rational numbers.

5.2.3 Structure of the interface

Any process that contributes to the formation of martensite cannot rely on

assistance from thermal activation. There must, therefore, exist a high level of

continuity across the interface between martensite and austenite. The interface

must be coherent or semicoherent;in the latter case,the dislocations in the inter-

face must be able to glide as the martensite grows. It turns out that a stress-free

coherent interface cannot be found between austenite and martensite, the best

that can be achieved is semicoherency, with one direction within the interface

remaining fully coherent. This direction is known as an invariant-line since it is

unrotated and undistorted.

5.2.4 The shape deformation

The passage of a slip dislocation through a crystal causes the formation of a step

where the glide plane intersects the free surface (Figs 5.2a, b). The passage of

many such dislocations on parallel slip planes causes macroscopic shear (Figs

5.2c, d). 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.

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. The dislocations responsible for the deformation

5.2 GENERAL CHARACTERISTICS 99

Fig. 5.2 (a) and (b) Step caused by the passage of a slip dislocation. (c) and (d) Many slip

dislocations, causing a macroscopic shear. (e) An invariant-plane strain with a uniaxial dilatation.

(f) An invariant-plane strain which is a simple shear. (g) An invariant-plane strain which is the

combined effect of a uniaxial dilatation and a simple shear.

are in the α

′

/γ interface, with Burgers vectors such that in addition to deforma-

tion they also cause the change in crystal structure.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 con-

nected at the α

′

/γ interface. These observations, and others, conﬁrm that the

measured shape deformation belongs to a class of deformations know as invari-

ant plane strains (Figs. 5.2e–g), with martensite being the most general case in

this class with a combined shear and dilatational strain (δ ≃0.03) normal to the

habit plane.

Evidencethat the transformationinvolves largeshears caneasily beobtained

by polishing a surface, or better two surfaces at right angles, prior to transform-

ation. After martensite plates form, the surface reveals relief including large

shear displacements (Fig. 5.3) and any scratches present prior to transforma-

tion are themselves displaced (Fig. 5.4). The characteristic surface relief can also

be analysed by using two-beam interferometry or atomic force microscopy, and

quantitative data obtained from the displacement of the fringe patterns or sur-

face contours, respectively. Experiments like these reveal that the shear strain

100 CHAPTER 5 FORMATION OF MARTENSITE

Fig. 5.3 Martensite in a Fe–0.4C–4Ni wt% steel shown in relief on a pre-polished surface,

×3400.

Fig. 5.4 Fe–30.5Ni–0.3C wt% illustrating the displacement of surface scratches by the

martensitic shear. Nomarski interference contrast, ×650.

is of the order of s ≃0.22 and the dilatational strain normal to the habit plane

is typically δ ≃0.03.

5.3 THE CRYSTAL STRUCTURE OF MARTENSITE

Martensite in steels is a supersaturated solid solution of carbon in ferritic iron.

For alloys which have a low martensite-start temperature or a high carbon con-

centration,the carbon atoms tend to order in such a waythat thecrystal structure

5.3 THE CRYSTAL STRUCTURE OF MARTENSITE 101

changes from body-centred cubic (bcc) to body-centred tetragonal (bct). The

tetragonality of the ordered martensite, measured by the ratio between the axes,

c/a, increases with carbon content:

= 1 + 0.045 wt% C (5.2)

implying that at zero carbon content the structure would be bcc, free of distor-

tion. The effect of carbon on the lattice parameter of austenite, and on the c and

a parameters of martensite is shown in Fig. 5.5.

Fig. 5.5 Effect of carbon on the lattice parameters of austenite and of martensite (after

Roberts, in Cohen,Transactions of the Metallurgical Society of AIME 224, 638, 1962).

102 CHAPTER 5 FORMATION OF MARTENSITE

Fig. 5.6 Martensite bct lattice illustrating the three sets of octahedral interstices. The z-set

is fully occupied by carbon atoms (Cohen,Transactions of the Metallurgical Society of AIME 224,

638, 1962).

It is interesting to note that carbon in interstitial solid solution expands the

fcc iron lattice uniformly, but with bcc iron the expansion is non-symmetrical

giving rise to tetragonal distortion. To understand this important difference

in behaviour, it is necessary to compare the interstitial sites for carbon in the

two lattices. In each case, carbon atoms occupy octahedral sites, indicated for

martensite in black in Fig. 5.6, and have six near-neighbour iron atoms. In the fcc

lattice the six iron atoms around each interstitial carbon atoms form a regular

octahedron,whereas in thebcccase the correspondingoctahedra arenot regular,

being shortened along the z-axis (Figs 1.4e,f).These compressed octahedra only

have four-fold symmetry along the shortened axis in each case, in contrast to

the fcc structure in which the regular octahedra have three four-fold axes of

symmetry.

Analysis of the distortion produced by carbon atoms in the several types of

site available in the fcc and bcc lattices, has shown that in the fcc structure the

distortion is completely symmetrical,whereas in the bcc one,interstitial atoms in

z positions will give rise to much greater expansion of iron–iron atom distances

along z than in the x and y positions.

5.4 THE CRYSTALLOGRAPHY OF MARTENSITIC TRANSFORMATIONS 103

Assuming that the face-centred cubic (fcc) →bcc transformation occurs in

a diffusionless way, there is no opportunity for carbon atoms to move. The

ferrite contains three octahedral interstices per iron atom whereas the austenite

has only one octahedral interstice per iron atom. Each of the three sets of

octahedral interstices (the three sublattices) in the ferrite is associated with one

of the cube edges of the ferrite unit cell. Upon diffusionless transformation,

all the carbon atoms in the austenite end up on just one of the octahedral

sublattices of ferrite, causing a tetragonal distortion of the bcc lattice into a bct

lattice. Thus, in Fig. 5.6, since only the z sites are common to both the fcc and

bcc lattices, on transformation the z-axis becomes the c-axis of the tetragonal

form.

Therefore, the tetragonality of martensite arises as a direct result of inter-

stitial solution of carbon atoms in the bcc lattice, together with the preference

for a particular type of octahedral site imposed by the diffusionless character of

the reaction.

5.4 THE CRYSTALLOGRAPHY OF MARTENSITIC

TRANSFORMATIONS

Martensitic transformation is diffusionless so the change in crystal structure

is achieved by a homogeneous deformation of austenite. The strain needed

to transform the fcc lattice of γ into the bcc or bct lattice of α

′

was ﬁrst

proposed by Bain in 1924 and hence is known as the ‘Bain strain’ (Fig. 5.7).

There is a compression of about 17% along the [0 0 1]

corresponding to the

c-axis of the martensite cell, and a uniform expansion of about 12% in the

(001)

plane.

The Bain strain implies the following orientation relationship between the

parent and the product lattices:

[001]

[001]

′

10]

[1 0 0]

′

[110]

[0 1 0]

′

but this is inconsistent with the observed orientation relationship which is irra-

tional,and has correspondingclosest-packed planesand close-packeddirections

approximately parallel. The reason is that the Bain strain on its own is not

the complete deformation because it is necessary to ensure a high degree of

coherency in the interface. It is a requirement that the deformation which

changes austenite into martensite must leave one line fully coherent, i.e. it must

be unrotated and undistorted, an invariant line. Such a deformation is said to

be an invariant-line strain (ILS).

In Figs 5.8a, b, the austenite is represented as a sphere which, as a result of

the Bain strain B, is deformed into an ellipsoid of revolution which represents

the martensite. There are no lines which are left undistorted or unrotated by B.

There are no lines in the (0 0 1)

plane which are undistorted. The lines wx

104 CHAPTER 5 FORMATION OF MARTENSITE

Fig. 5.7 The lattice correspondence for formation of martensite from austenite: (a) tetragonal

unit cell outlined in austenite, (b) lattice deformation (compression along c-axis) to form

martensite of correct c/a ratio Bain strain (Christian, in Martensite: Fundamentals andTechnology

(ed. Petty, E. R.), Longmans, UK, 1970).

Fig. 5.8 (a) and (b) show the effect of the Bain strain on austenite, which when undeformed

is represented as a sphere of diameter wx =yz in three-dimensions. The strain transforms it

to an ellipsoid of revolution. (c) shows the ILS obtained by combining the Bain strain with a

rigid body rotation through an angle θ.a

and a

refer to [100]

, [010]

and [001]

axes

respectively.

5.4 THE CRYSTALLOGRAPHY OF MARTENSITIC TRANSFORMATIONS 105

and yz are undistorted but are rotated to the new positions w

′

and y

′

. Such

rotated lines are not invariant. However, the combined effect of the Bain strain

B and the rigid body rotation R is indeed an ILS because it brings yz and y

′

into

coincidence (Fig. 5.8c).This is the reason why theobserved irrationalorientation

relationship differs from that implied by the Bain strain. Indeed, the rotation

required to convert B into an ILS precisely corrects the Bain orientation into

that which is observed experimentally.

There remains a further discrepancy.As can be seen from Fig. 5.8c,there is no

rotation which canmake B into an invariant-plane strain sincethis wouldrequire

two non-parallel invariant lines. It follows that austenite cannot be transformed

into martensite by a homogeneous strain which leaves a plane invariant. And

yet, the observed shape deformation leaves the habit plane undistorted and

unrotated, i.e. it is an invariant-plane strain.

The phenomenological theory of martensite crystallography elegantly solves

this remaining problem (Fig. 5.9). The Bain strain converts the structure of the

parent phase into that of the product phase. When combined with an appro-

priate rigid body rotation, the net homogeneous lattice deformation RB is an

ILS (step a to c in Fig. 5.9). However, the observed shape deformation is an

Fig. 5.9 The phenomenological theory of martensite crystallography.

106 CHAPTER 5 FORMATION OF MARTENSITE

invariant-plane strain P

(step a to b in Fig. 5.9), but this gives the wrong crystal

structure. If a second homogeneous shear P

is combined with P

(step b to c),

then the correct structure is obtained but the wrong shape since:

= RB.

These discrepancies areall resolved ifthe shape changingeffect of P

iscancelled

macroscopicallyby an inhomogeneouslattice-invariant deformation,which may

be slip or twinning as illustrated in Fig. 5.9.

The theory explains all the observed features of the martensite crystallogra-

phy.The orientation relationship is predictedby deducingthe rotationneeded to

change the Bain strain into an ILS.The habit planedoes not have rational indices

because the amount of lattice-invariant deformation needed to recover the cor-

rect macroscopic shape is notusually rational.The theory predicts asubstructure

in plates of martensite (either twins or slip steps) as is observed experimentally.

The transformation goes to all the trouble of ensuring that the shape deforma-

tion is macroscopically an invariant-plane strain because this reduces the strain

energy when compared with the case where the shape deformation might be

an ILS.

Figure 5.10 shows schematically the two types of lattice invariant deform-

ation occurring within a martensite plate. It should be noted that the block

of martensite formed has produced a surface tilt and that the observed habit is

preserved by the accommodation provided by either slip (Fig. 5.10a) or twinning

(Fig. 5.10b).The result is a macroscopically planar interface which would clearly

have irregularities on a very ﬁne scale.

The above theoretical approach had considerable success in predicting the

observed habit planes, the orientation relationships between matrix and the

martensite, as well as the shape deformation for a number of martensitic trans-

formations including ferrous martensites. It is, however, necessary to have

accurate data, so that the habit planes of individual martensite plates can be

directly associated with a speciﬁc orientation relationship of the plate with

the adjacent matrix. For example, Greninger and Troiano used an iron–22

nickel–0.8 wt% carbon alloy in which austenite was retained in association with

martensite to predict successfully the correct habit plane, which in this alloy is

an irrational plane near {3 10 15}

and also the shape change and the orientation

relationship between martensite and austenite.

5.5 THE MORPHOLOGY OF FERROUS MARTENSITES

The two-shear theory of martensite formation was ﬁrst conﬁrmed by crystallo-

graphic measurements on the two phases, but the existence of the inhomo-

geneous lattice invariant deformation could only be directly established by

microscopic examination. Examination of a number of non-ferrous martensite

5.5 THE MORPHOLOGY OF FERROUS MARTENSITES 107

Fig. 5.10 Formation of martensite plate, illustrating two types of lattice deformation: slip

and twinning (Christian, in Martensite: Fundamentals and Technology (ed. Petty, E. R.), Longmans,

UK, 1970).

transformations in the optical microscope revealed that the martensite lamellae

contained numerous very ﬁne twins in uniform arrays. For example,the marten-

site reaction in the indium–thallium system has some similar characteristics to

ferrous martensites in so far as the transformation is from fcc to a tetragonal

lattice (face-centred). The martensitic lamellae are very uniform, and contain

ﬁne twins on a single variant (101) [10

1] in one lamella.

Martensitic plates in steel are frequently not parallel sided, instead they

are lenticular as a result of constraints in the matrix which oppose the shape

change resulting from the transformation. This is one of the reasons why it is

difﬁcultto identify precisely habitplanes inferrous martensite. However,it is not

responsible for the irrational planes, but rather the scatter obtained in experi-

ments. Another feature of higher carbon martensites is the burst phenomenon,