Equivalent plastic strain gradient crystal plasticity – Enhanced power law subroutine

A gradient crystal plasticity theory is presented including a defect energy based on the gradient of an equivalent plastic strain measure. Preserving the single crystal slip kinematics, the gradient hardening contribution models dislocation long range interactions adding a back-stress term to the flow rule, similar to other gradient crystal plasticity theories. Owing to a reduced number of four nodal degrees of freedom the finite element implementation can handle systems consisting of an increased number of grains (compared to other theories) without elaborate or costly computer systems. Emphasis is put on the enhancement of the power law material subroutine. The associated implicit Euler scheme is optimized based on an improved starting value for the Newton scheme. Three-dimensional simulations illustrate that the proposed algorithm facilitates significantly larger time steps compared to the standard Newton scheme. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)