Crystal plasticity with nonassociated flow

Qing Qin, University of Pennsylvania


A new yield criterion, where stresses other than the resolved shear stress on the slip systems (the Schmid stress) are included, is proposed to describe various non-Schmid behaviors experimentally observed in single crystals, particularly intermetallic compounds, such as the orientation dependence of critical resolved shear stress (CRSS) and the tension/compression asymmetry. Time-independent constitutive relations based on the yield criterion are derived for small elastic strain but finite plastic strain. Since the yield function is not the plastic potential, plastic flow is said to be non-associated. This tends to restrict the activation of multiple slip systems, to cause tension/compression asymmetry in strain-hardening, and to increase the tendency for strain localization in the form shear bands. The yield surfaces for single crystals and for polycrystals of randomly oriented FCC (Face-Center-Cubic) single crystals are calculated, where the latter which are based on a self-consistent scheme are shown to be isotropic and are of a Tresca type only when the grains do not have a tension/compression asymmetry. In general, the polycrystal yield surface have asymmetry with respect to the sense of the load if the grains do. The size of the yield surface of polycrystals is a function of the elastic anisotropy of grains and the magnitude of the non-Schmid factors. Due to the restricted slip effects, the polycrystal response can be stiffer than the case when non-Schmid effects are absent.

Subject Area

Mechanics|Mechanical engineering

Recommended Citation

Qin, Qing, "Crystal plasticity with nonassociated flow" (1990). Dissertations available from ProQuest. AAI9026630.