**Torsion/simple shear of single crystal copper**

M. F. Horstemeyer, T. J. Lim, W. Y. Lu,, D. A. Mosher, M. I. Baskes, V. C. Prantil, S. J. Plimpton, J of Engineering Materials and Technology (Transactions of the ASME), 124, 322-328 (2002).

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.

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