Physically based temperature dependence of elastic-viscoplastic constitutive equations for copper between 20 and 500°C

An anisothermal material model has been established for cyclic mechanical and thermal loading in chill-cast pure copper undergoing creep and cyclic plasticity. The temperature dependences in the model are physically based. The material parameters arising in the model have been determined from a programme of tests carried out on pure copper, enabling the model to be validated over the temperature range 20-500°C, s train range 0-±l-0% and strain rate range 0006-0-6% s^-1. The variations, with inverse temperature, in the viscoplastic strain rate parameter, the cyclically hardened yield stress, and hardening and softening parameters, when considered with respect to logarithmic scales have been shown to be bilinear in nature, over the temperature range considered. The transition temperature, in ail cases, was found to be 209°C. For the viscoplastic strain rate parameter, an activation energy of 200 kJ mol^-1 was determined for temperatures in excess of 209°C, and 33 kJ mol^-1 for temperatures less than 209°C. Deformation mechanisms of bulk diffusion, and dislocation glide and climb, are thought to predominate for the two temperatures ranges respectively. However, in the case of the cyclically hardened yield stress, and the hardening and recovery parameters, activation energies of 34 kJ mol^-1 and 11 kJ mol^-1 were determined for temperatures greater than and less than 209°C respectively. The deformation mechanisms predominating are thought to be dislocation glide and cümb for the case of the higher temperature range, and glide only for the lower temperature range, because of the dependence of dislocation climb on core diffusion which is thought not to occur significantly in copper below about 209°C. The constitutive equations developed have been generalized to multiaxial stress States, and a methodology for the determination of the material parameters given, which ensures that they are physically meaningful.