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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 normal train Fig. 2. Invariant plain strain s, composed of a shear component y parallel to the habit plane(shaded)and a expansion/contraction E(=An normal to the habit plane. Note that the strain is zero in the direction perpendicular to s and to the habit plane normal. the lattice invariant shear L, a rotation R will be required to ensure that the undis- torted plane is also unrotated So, the shape strain S can be divided(mathematically) into three component strains 1. A lattice invariant shear (LIS)L, which is inhomogeneous on a macroscopic scale, and is the additional strain required to make the overall strain an invariant ane strain 2. The Bain strain B, which is simply the strain required to convert the crystal structure of the parent lattice to that of the product. Note that, in general, B is not an invariant plane strain, although in some cases it may be close to one 3. A rigid body rotation R, which ensures that the habit plane is unrotated The total shape strain (s)is given by the equation S=RBL (2.1) where the order of the strains has no physical significance. Despite the fact that the theory is phenomenological, rather than mechanistic, the steps involved in Eq.(2.1) can be illustrated schematically as shown in Fig 3. ' / ( $ 0 $ 3 4 $ < * 3,04 ' $ / $ ! F ' $ / $ $ I $ % * ' $ $ 34 / < ' $ . E $ $ $ ;/ 3! 4 ' % ! , $ $ $ $ $ 3 4 +$ 9 3J(4 $ I ) $$ $ 12! ,- - . #-"- &! " / , $! ! 0 1 2)344