Modeling of post shock mechanical behaviour of copper in hydrocode calculations

Abstract
Influence of “shock hardening” on the subsequent plastic behavior of both bcc and fcc metals (respectively tantalum and copper) has been presented during the former DYMAT International Conference in Porto. This second paper proposes to focus on the development of a constitutive relation for hydrocodes calculations. It is well known that most conventional models which describe the flow stress as a function of plastic deformation do not estimate correctly post shock mechanical behavior for fcc metals like copper, aluminum... CEA has worked on a viscoplastic constitutive relation called EDD (Evolution of Defects Density) which is mainly based on the previous researches of J.R. Klepaczko. In this modeling approach, flow stress is divided into two components which are internal and effective stresses. They depend on an internal variable (dislocation density) which describes the evolution of material micro or mesostructure with plastic deformation through an evolution law. This one is dependent on loading conditions (strain rate and temperature). The model parameters for copper have been identified using quasi static and dynamic mechanical experimental results under uniaxial compression. The model is used to expertise shock wave effects using post shock mechanical characterization and TEM observations. Hence, it is implemented into the Hesione CEA hydrocode and the results of calculations done on shock wave experiments demonstrate its robustness and efficiency for further developments.