Non-Schmid effects and finite wavelength instabilities in single crystal metals

Abstract

A long standing postulate in crystal plasticity of metals, known as Schmid law, states that yielding commences once the resolved shear stress on a slip plane reaches a critical value. While non-Schmid effects have previously been reported experimentally (mostly in alloys) and in molecular-dynamics simulations, we examine the validity of this assumption through phonon stability analysis. We subject four distinct single crystal metals to a combined shear-hydrostatic deformation and identify the onset of plasticity with the onset of an instability. We find significant shear-normal coupling in single crystal metals, reflecting non-Schmid effects in defect nucleation. Also, it is a widespread assumption in the literature (Liu et al., 2010; Van Vliet et al., 2003) that the instabilities in single crystal metals are of long wavelength. In contrast, we show that short wavelength instabilities are abundant. Our results illustrate the potential pitfalls of relying on the widely used elastic stability analysis for investigating defect nucleation.