The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain and cyclic plastic strain. However, little research has attempted to systematically consider the sensitivity of overall cyclic stressstrain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation [1]. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain-or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures.
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