Effect of Elastic Strain Energy

The elastic energy of a (3 cluster in an a matrix can be calculated by carrying out the following four-stage process [7]  

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an 

The shape could therefore be varied between that of a thin disc (c a) and that of a needle (c a). The strain energy (per unit volume of inclusion) is expressed in the form 

Eshelby treated systems that are both elastically homogeneous and elastically isotropic [7]. Some results for the ellipsoidal inclusion described by Eq. 19.23 are given below. 

Case 1. Pure dilational transformation strain with sxx = s y = ejz. 

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