An analysis of the viscoplastic behavior of metals

Abstract

The inelastic behavior of polycrystalline metals is deduced from microscopic slip mechanisms in individual crystals. With motion of dislocations as the source of inelastic strain, strain rate equations for a slip system in a crystal are compiled. These equations take into account strain-dependent mobile dislocation density, strain hardening and a non-linear dependence of dislocation velocity on the resolved shear stress. A model of interaction between crystal grains in the aggregate is established by utilizing the concept of a spherical inclusion in a homogeneous matrix. The resulting system of non-linear differential and algebraic equations is solved numerically for some typical cases of loading of a specimen in uniaxial tension at room temperature. The theoretical results obtained in this way reproduce all the known aspects of the inelastic behavior of metals, e.g. the rate dependence of the stress-strain curve, the Bauschinger effect, non-stationary creep and stress relaxation. Quantitative comparison of the theoretical results with the experimental data for two cases of loading (static and dynamic tension tests and a stress relaxation test) reveal good agreement between the theoretical and the experimental curves.