Calculation of the elastic strain energy accompanying the precipitation of coherent particles in the solid state phase transformations and its application in real alloy systems

Abstract

Solid-to-solid phase transformations often accompany a coherent elastic strain energy due to a difference in lattice parameters between matrix and coherent precipitate. The resultant elastic strain energy has to be considered as an important factor in solid-to-solid phase transformations. In chapter I, the elastic strain energy of perfectly coherent ellipsoid of revolution, which has the cube-cube orientation relationship with matrix, has been calculated as a function of the orientation of axis of revolution and of shape factor in anisotropic cubic crystalline materials (Al, Cu, Ni and Fe) using the strain energy of coherent ellipsoidal inclusions occurs at specific shapes (sphere, disc and rod) and at specific orientations ($<001>,\; <011>$ and $<111>$) of the axis of revolution. Thus a detailed sturdy has been performed for the effect of the variation of elastic constants of inclusion on the elastic strain energies of the specific shapes and orientations. The results indicate that the elastic strain energies of three specific shapes are differently dependent on the elastic property of inclusion. This difference originates from the difference in the accommodation behavior of three specific shapes. This accommodation behavior of each shape, also, depend strongly on the orientation of the axis of revolution. The results moreover show that there are the three unique crossing points between the different shapes in each specific orientation of a given matrix. Theses unique crossing points appeared as a constant $\mu_1^\ast\;(C_{11}^\ast\, - \,C_12^\ast)/2$ in $<001>$ orientation and $\mu^\ast\, (C_{44}^\ast)$ in $<111>$ orientation while, for the case of $<011>$ orientation, this value only became a constant $\mu^\ast$ at a fixed $A^\ast$. The diagram, predicting the shape and orientation of the minimum elastic strain energy of various precipitates, has been constructed from these results, for Al, Cu, Ni, and Fe matrices. The minimum strain energy condition occurs ...