A general constitutive theory for linear and nonlinear particulate media with microstructure evolution

Abstract

This work is concerned with the development of a constitutive theory for composite materials with particulate microstructures, which is capable of predicting, approximately, the evolution of the microstructure and its influence on the effective response of composites under general three-dimensional finitestrain loading conditions, such as those present in metal-forming operations. In its present form, the theory is general enough to be used for linearly viscous, nonlinearly viscous and perfectly plastic composites with randomly oriented and distributed ellipsoidal inclusions (or pores), which, in the most general case, can change size, shape and orientation. In addition, the “shape” and “orientation” of their center-to-center statistical distribution functions can also evolve with the deformation. To illustrate the key features of the new theory in the context of a simple example, an application is carried out for plane-strain loading of two-phase systems consisting of random distributions of aligned rigid particles in a power-law matrix phase. The results show that the evolution of the relevant microstructural variables, as well as the effective response, depend in a complex fashion on the initial state of the microstructure, as well as on the specific boundary conditions. In particular, it is found that the changes in orientation of the particles provide a mechanism analogous to “geometric softening” in ductile single crystals, which can lead to significant changes in the instantaneous hardening rate of the composite. This is shown to have important consequences for the possible onset of shear localization in the composite.