The deformation behaviour of alloys comprising two ductile phases— I. Deformation theory

Abstract

A topological transformation has been proposed, which allows a two-phase microstructure with any combination of grain-size, grain-shape, and phase distribution, to be translated into a body consisting of three well-defined microstructural elements aligned along a particular direction of interest. The resultant three-element body is shown to be mechanically equivalent to the original body along this direction. The concept of contiguity and allied topological parameters have been combined with Eshelby's continuum transformation theory to determine the internal stresses and strains, the true stress strain curve, and the in situ stress and the in situ plastic strain distribution in the three microstructural elements and thus derive the mechanical properties of the aggregate. This approach incorporates the interaction between particles of the same phase and the effect of phase distribution as well as the effect of volume fraction. Applications of the theory are given in a companion paper.