<CRYSTAL_KINEMATIC>#

Description#

Because the crystal potential models takes into account the strains on the individual slip planes, kinematic hardening represents a linear measure of a slip offset distance Xi, or backstress, on the slip line. As described in the <POTENTIAL> crystal section, the yield criterion on each slip plane i is of the form |τijXij|ri, where τi is the resolved shear stress on slip plane i and ri is the sum of all isotropic hardenings on that slip plane.

The internal variables αi, to which the backstresses are associated, are thus scalar and distinct from the tensorial kinematic hardening laws in the macroscopic potentials. They are related to the backstresses Xi through Xi=x0+Cαi with x0 and C parameters having the dimensions of a stress. Trick: a large negative offset x0 might be used to model unidirectional slip, provided that the same positive offset is added to the corresponding isotropic hardening.

These hardening laws will apply uniquely for the monocrystal potentials. Permissible crystalline kinematic types are with their additional parameters are

linear

α˙i=γ˙

nonlinear

α˙i=γ˙DXi|γ˙|/C

nonlinear_phi
α˙i=γ˙ϕ(vi)D(XiXbar)|γ˙|/C

with

ϕ(vi)=(1phi)+phi edelta vi