Multiscale Investigation of Shear Relaxation in Shock Loading—A Top-Down Perspective

It is known that shock loaded metals exhibit shear stress relaxation at the plastic wave front, i.e., the stress state of the material deviates substantially from the yield surface when longitudinal stress or pressure reaches the peak value, but no consensus has ever been reached on its origin and mechanisms due to the multiscale nature of plasticity. To this end, the current study takes a top-down approach by conducting a theoretical and numerical investigation on the macroscale (continuum scale) and simulations on the mesoscale with crystal plasticity (CP), followed by an analysis of the microscale factors based on molecular dynamics (MD) investigations from the literature. On the macroscale, theoretical derivation uncovers that the total strain rate of less than 1.5 times the equivalent plastic strain rate is the critical condition for shear stress relaxation in the isotropic elasticity and von Mises plasticity framework. Evolutions of stress and strain during dynamic deformation of aluminum under shock loading is then examined via continuum finite element simulations, assuming Johnson-Cook (JC) constitutive relation, and considering the nonlinear elastic behavior and equation of state (EOS) at high pressures. The results suggest that strain rate hardening is responsible for the appearance of shear relaxation, and verify that relaxation begins exactly as the theoretical condition predicts. Other factors play subsidiary roles; thermal effect is negligible under low pressure and its promotion of relaxation becomes remarkable when approaching melting, and strain hardening slightly suppresses relaxation. These findings are all echoed in meso-scale simulations with the CP model and hyperelastic constitutive equation. The role and contributions of strain rate hardening, strain hardening and thermal softening to shear relaxation agree well with macroscopic observations. In addition, contribution of deformation heterogeneity is investigated on the mesoscale, and the simulation results show that the additional dissipation induced by grain boundaries' interference with dislocation slip has a subordinate stimulative effect. Results of both macro- and meso-scopic analysis indicate that mechanisms related to strain rate effect should also be the dominant factor for relaxation on the microscale, and the contribution or connection to strain rate hardening should be the guideline for evaluating the relevance and importance of each microscopic mechanism. Consequently, nucleation and multiplication of dislocations are identified as the main cause of shear relaxation on the microscale, based on existing MD simulations and analysis from dislocation theory. In summary, a top-down perspective of the cause and a full picture of shear relaxation during shock loading is established, which reveals that the strain rate effect plays a vital role while contributions of other effects are limited.