Martensite in Steels - Department of Materials Science and Metallurgy

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Note that these have been stated approximately: the true relations are irrational, meaningthat the indices of the parallel planes and directions cannot be expressed using rational numbers(the square root of 2 is not a rational number).Fig. 2: Stereographic representation of the Kurdjumov–Sachs and Nishiyama–Wasserman orientation relationships. The stereograms are both centred on(1 1 1) γ ‖ (0 1 1) α . It is seen that the NW orientation can be generatedfrom KS by an appropriate small rotation (5.25 ◦ ) about [0 1 1] α . Only afew of the poles are marked to allow a comparison with the Bain orientationrelationship. The neighbouring pairs of poles would superpose exactly for theBain orientation.Athermal Nature of TransformationIn the vast majority of cases, the extent of reaction is found to be virtually independentof time:1 − V α′ = exp{β(M S − T)} where β ≃ −0.011 (1)V α′ is the fraction of martensite and T is a temperature below M S . This is the Koistinen andMarburger equation; notice that time does not feature in this relation, so that the fraction ofmartensite depends only on the undercooling below the martensite–start temperature. Thisathermal character is a consequence of very rapid nucleation and growth, so rapid that thetime taken can in normal circumstances be neglected.Isothermal martensite is possible when nucleation is hindered, although the growth rateof individual plates of martensite can still be rapid.4
Structure of the InterfaceAny process which contributes to the formation of martensite cannot rely on assistance fromthermal activation. There must therefore exist a high level of continuity across the interface,which must be coherent and semi–coherent. A stress–free fully coherent interface is impossiblefor the γ → α ′ transformation since the lattice deformation BR is an invariant–line strain. Asemi–coherent interface must be such that the interfacial dislocations can glide as the interfacemoves (climb is not permitted). It follows that the Burgers vectors of the interface dislocationsmust 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 linevectors of the interfacial dislocations must lie along an invariant–line, i.e. a line which joinsthe parent and product crystals without any rotation or distortion. Why is that? If there isany distortion along the dislocation line, then other dislocations are needed to accommodatethat misfit. It will then be necessary to have more than one set of non–parallel dislocationsin the interface. These non–parallel dislocations can intersect to form jogs which render theinterface sessile.It follows that for martensitic transformation to be possible, the deformation which changesthe parent into the product must leave one or more lines invariant (unrotated, undistorted). Adeformation which leaves one line invariant is called an ‘invariant–line strain’.The Shape DeformationThe passage of a slip dislocation through a crystal causes the formation of a step where theglide plane intersects the free surface (Fig. 3a,b). The passage of many such dislocations onparallel slip planes causes macroscopic shear (Fig. 3c,d). Slip causes a change in shape butnot a change in the crystal structure, because the Burgers vectors of the dislocations are alsolattice vectors.During martensitic transformation, the pattern in which the atoms in the parent crystalare arranged is deformed into that appropriate for martensite, there must be a correspondingchange in the macroscopic shape of the crystal undergoing transformation. The dislocationsresponsible for the deformation are in the α ′ /γ interface, with Burgers vectors such that inaddition to deformation they also cause the change in crystal structure. The deformationis such that an initially flat surface becomes uniformly tilted about the line formed by theintersection of the interface plane with the free surface. Any scratch traversing the transformed5
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Page 7 and 8: as the ‘Bain Strain’ (Fig. 4).
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Page 11 and 12: Fig. 7: The distance ac represents

Martensite in Steels - Department of Materials Science and Metallurgy

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