P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 important aspects of the theoretical predictions and look at some particular features of martensitic transformations that are relevant to transformation toughening - the correspondence, variants, twins, self-accommodation and the role of stress in indu- cing transformatio 2. Martensitic transformations 2.1. The phenomenological theory The phenomenological theory describes the crystallography of a martensitic transformation in purely mathematical terms, and is not meant to represent the physical mechanism by which one lattice becomes another. The various versions of the theory [20-23, 25, 26), which are all essentially equivalent, are capable of predict ing a number of crystallographic features of the transformation that can be tested experimentally. The basis of the theory is that the overall macroscopic strain associated with the transformed region(the shape strain S) must be an invariant plane strain (i.e. a strain which leaves one particular plane in the two phases the habit plane - undistorted and unrotated during the transformation). The use of an invariant plane strain is intimately linked with the formation of a transformed region that is plate-like in shape with the habit plane of the plate being the invariant plane. In fact, it was the observation that the product of a martensitic transformation invariably consisted of thin, discus-like, lenticular plates that led to using the invariant plane strain concept as the basis for the phenomenological In general, an invariant plane strain(IPS)consists of an expansion(or contrac tion)(E)normal to the invariant plane together with a shear(r)in a direction lying n the invariant plane. This is illustrated in Fig. 2. Note that the strain in the direc tion perpendicular to both the normal to the invariant plane and the shear direction is zero, and that, if there is any volume change(An associated with the transfor mation, then this must be contained in the expansion(or contraction) normal to the invariant plane -i.e. =AV. In more mathematical terms, to ensure that S is an invariant plane strain, one of its principal strains must be zero and the other two must be of opposite sign. In general, the strain required to convert the crystal structure of the parent phase to hat of the product(the Bain strain B)will not satisfy these conditions-ie. B is not itself an invariant plane strain. Hence, in order to ensure that the final, overall strain Sis an IPS, another strain is required. This strain must not alter the crystal structure of the new product phase resulting from the Bain strain B, but it must change the shape of the transformed volume in such a way that it satisfies the conditions for an IPS. This additional strain L is known as the lattice invariant shear (LIs). It is inhomogeneous on a macroscopic scale, but has no effect on the crystal structure on a microscopic or atomic scale-1e it is lattice invariant. Typical examples of a LIs are slip or twinning, both of which leave the structure of the crystalline material subjected to such shears unaltered. Finally, after combining the Bain strain B and$   $      $        $                          $     '   (           (             -<-     !  
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