Yield Surfaces and Plastic Potentials for Metals, with Analysis of Plastic Dilatation and Strength Asymmetry in BCC Crystals

Abstract

Since the 1980s, constitutive modeling has steadily migrated from phenomenological descriptions toward approaches that are based on micromechanics considerations. Despite significant efforts, crystal plasticity remains an open field of research. Among the unresolved issues are the anomalous behavior of metals at low temperatures and the stress upturn at extreme dynamics. This work is focused on the low-temperature responses of body-centered-cubic (bcc) metals, among them, molybdenum (Mo). At these conditions, the plastic flow strength is governed by the motion of screw dislocations. The resultant non-planarity of core structures and slip causes the following: the shear stress includes non-glide components, the Schmid law is violated, there is a tension-compression asymmetry, and the yield surface and plastic potential are clearly decoupled. We find that the behavioral complexities can be explained by atomistically resolved friction coefficients in macroscopic yield and flow. The plastic flow mechanisms establish the departure point into the follow-up analysis of yield surfaces. For example, we know that while the von Mises stress is explained based on energy considerations, we will also show that the stress has a clear geometric interpretation. Moreover, the von Mises stress is just one case within a much broader class of equivalent stresses. Possible correlations among non-Schmid effects (as represented macroscopically by friction coefficients), volume change (i.e., residual elastic dilatation) from dislocation lines, and elastic anisotropy are investigated. Extensions to the shock regime are also established.

Keywords

• tensor representations
• friction coefficient
• metal plasticity
• dislocations
• Schmid law