Inﬂuence of hardening on the cyclic behavior of laminate microstructures in ﬁnite crystal plasticity
We investigate the cyclic behavior of laminate microstructures in ﬁnite-strain crystal plasticity and the resulting stress-strain response, based on a variational, incremental description of the microstructure evolution. The nonconvex free energy density in multiplicative single- and multi-slip plasticity gives rise to the formation of ﬁne-scale deformation structures, experimentally observed as complex material microstructures. Here, we treat ﬁrst-order laminate microstructures and model their origin and their subsequent evolution. Interestingly, the cyclic behavior of such microstructures has been reported to exhibit a gradual degeneration of the laminate as well as of the stress-strain hysteresis loop, leading to an elastic shakedown. However, previous results have predicted the occurrence of this ﬁnal, steady state within a few load cycles, which has appeared physically doubtful. Therefore, we analyze here the inﬂuence of work hardening in single-slip and of latent hardening in double-slip plasticity on the laminate microstructures and the corresponding stress-strain responses during cyclic loading. Results indicate that the amount of hardening considerably affects the rate at which the stress-strain hysteresis and the laminate degenerate.