Torsion/Simple Shear of Single Crystal Copper

Abstract

We analyze simple shear and torsion of single crystal copper by employing experiments, molecular dynamics simulations, and finite element simulations in order to focus on the kinematic responses and the apparent yield strengths at different length scales of the specimens. In order to compare torsion with simple shear, the specimens were designed to be of similar size. To accomplish this, the ratio of the cylinder circumference to the axial gage length in torsion equaled the ratio of the length to height of the simple shear specimens (0.43). With the [110] crystallographic direction parallel to the rotational axis of the specimen, we observed a deformation wave of material that oscillated around the specimen in torsion and through the length of the specimen in simple shear. In torsion, the ratio of the wave amplitude divided by cylinder circumference ranged from 0.02–0.07 for the three different methods of analysis: experiments, molecular dynamics simulations, and finite element simulations. In simple shear, the ratio of the deformation wave amplitude divided by the specimen length and the corresponding values predicted by the molecular dynamics and finite element simulations (simple shear experiments were not performed) ranged from 0.23–0.26. Although each different analysis method gave similar results for each type boundary condition, the simple shear case gave approximately five times more amplitude than torsion. We attributed this observation to the plastic spin behaving differently as the simple shear case constrained the dislocation activity to planar double slip, but the torsion specimen experienced quadruple slip. The finite element simulations showed a clear relation with the plastic spin and the oscillation of the material wave. As for the yield stress in simple shear, a size scale dependence was found regarding two different size atomistic simulations for copper (332 atoms and 23628 atoms). We extrapolated the atomistic yield stresses to the order of a centimeter, and these comparisons were close to experimental data in the literature and the present study.