Cavity expansion methods incorporating strain, strain rate, and temperature

Abstract

This dissertation introduces cavity expansion methods (CEM) based on self-similar fields that account for dynamic hardening dependent on strain, strain rate, and temperature. The research focuses on cavity expansion problems with spherical and cylindrical symmetry, considering J2 plasticity in an infinite compressible medium. The plastic strain and temperature gradients are proposed by applying a self-similar transformation to deal with the dynamic hardening model. Some hardening models with an implicit relationship between the effective stress and the plastic strain rate can be generally applied using an inner-loop optimization problem to find the value of the plastic strain gradient. Furthermore, a modified Lim-Huh hardening model with a strain rate-dependent thermal softening term is investigated to determine the validity of the inner-loop optimization problem. The theoretical model shows that both the effective and radial stresses decrease near the cavity surface, but the hardening effect dominates away from the cavity due to the combined effect of hardening and thermal softening. The proposed method precisely evaluates stresses, which are then utilized to compute cavity pressure and conduct penetration analyses with a rigid projectile. For eroded penetration analyses, a target resistance is determined by the integration of a deformed region, where the effective stress is weighted based on its proximity to the cavity surface. The proposed cavity expansion method can incorporate strain, strain rate, and temperature generally because it can calculate the stresses and strains in the cavity surface and deformed regions without modifying or approximating the dynamic hardening model. The rigid penetration test on AA6061-T651 and AA7075-T651 targets by Forrestal et al. was validated by finite element analysis and the proposed cavity expansion method using the modified Johnson-Cook hardening model. In addition to the proposed cylindrical cavity expansion method, the accuracy of the ballistic limit velocity analysis was improved by applying the residual strength considering the weight of the penetration stage using the target and penetrator geometry and the simultaneous penetration depth. The proposed method can be used to evaluate the stress of a target without ballistic testing economically and contributes to reducing the cost of terminal ballistic testing by reducing the scale of laboratory experiments. The conventional Walker-Anderson penetration model is extended by incorporating the effective target flow stress determined by the cylindrical cavity expansion method based on the Johnson-Cook hardening model. The extended model was validated by comparing the penetration test results of the tungsten heavy alloy penetrator into a steel target by Hohler and Stilp with the results of finite element analysis using the Lagrangian-Euler method.