On extension of the phenomenological approach in the theory of plasticity

Abstract

Existing constitutive theories are commonly classified into three large groups: continuum, structural and micro structural. As a rule micro structural models, which are often referred to as physical, are based on the concept of crystallographic slip. One of the interesting exceptions is the theory of plasticity which accounts for micro strains. It postulates generalised deformation laws on mesoscale, and therefore has common properties of micro structural theories. However, it does not account for nanoprocesses, such as behaviour and interaction of separate dislocations, leads to the Von Mises initial yield condition, and accounts for Ilyushin’s postulate of isotropy and other macroscopic phenomenological laws of inelastic deformation. Thus, the theory of micro strains has much in common with continuum theories of plasticity and also establishes connection between continuum and micro structural approaches. In this article previous separate results concerning the theory of microstrains are reviewed and united into a single framework. The resulting generalised variant of the theory of micro strains accounts for both slip and twinning deformation mechanisms and also accurately models polycrystalline grain size distribution. Special cases and some important applications of the theory are discussed.