Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses

Abstract

When a sample is cyclically loaded under a mean stress or strain, incremental strain ratcheting or mean stress relaxation phenomena are usually observed. Experiments show that for metallic materials there is generally no full mean stress relaxation as well as saturation of macroscopic strain ratcheting. In contrast, most macroscopic constitutive models produce both quantities in excess, and complex sets of additional internal variables must be introduced to improve the modeling. Little attention has been paid to model such phenomena using polycrystal aggregates especially going up to the regime of cyclic mechanical stability. In this work based on an elementary crystal plasticity model for FCC crystals and large scale finite element simulations, it is shown that the interaction between different grains is sufficient to cater for such complex phenomena. Light is shed on how different regions of the polycrystal accommodate each other and how the classical definition of constant rate strain ratcheting or a zero mean stress is nearly impossible to apply to a polycrystalline aggregate. In addition, it is shown that even if a macroscopic stable hysteresis stress strain loop is observed, ratcheting phenomena can still be observed at the local scale. The distributions of different constitutive quantities within a polycrystal are also analyzed which gives a new insight into what is happening inside a polycrystal in terms of stress and strain redistribution. In particular, the existence of evolving bimodal distributions of stress and accumulated plastic strain is evidenced and related to the occurrence of plastic shakedown and incomplete mean stress relaxation. Two numerical criteria to detect strain ratcheting are finally proposed and discussed.