Bifurcation theory of plasticity, damage and failure

Abstract

I developed a comprehensive theory of plasticity, damage and failure, which is independent of the micromechanical mechanism of plasticity. It includes all major components of the mechanical behavior of ductile materials, e.g. strain/work-hardening and Bauschinger effect, and covers all regimes of viscoplastic tensile/compressive loading/unloading. The theory is based on the concepts of free energy and damage parameter and has the attributes of both rate-dependent and rate-independent plasticity, kinematic and isotropic hardening. The ultimate failure of a specimen is defined as a point of critical value of the damage parameter. The theory provides justification for Drucker’s ad hoc condition of instability. The theory describes diverse phenomena of Lüders stress, creep, internal friction, and fatigue on the same self-consistent basis. In quasi-static low-cycle fatigue, I derive a Paris-type equation between the rate of degradation and cyclic plastic work and reveal a Coffin-Manson power-law relationship between the number of cycles to failure and plastic-strain amplitude. In dynamic fatigue, I find two regimes—low-cycle and high-cycle—whose loading amplitudes are separated by the yield point. The two regimes have significantly different dependencies on the frequency and viscosity. In this publication, I present the theory and computer simulations of a homogeneous viscoplastic body subjected to various conditions of isothermal strain-controlled uniaxial loading. In the follow-up publications, I will expand the theory on the cases of inhomogeneous three-dimensional bodies subjected to multiaxial loading at variable temperatures and compare the results to the experiments. Complete version of the theory can be used for the full-cycle cradle-to-grave design of new materials in service.