Constitutive equations for thermo-elasto-plastic metallic materials undergoing large temperature variations

In the present work, a framework for the development of constitutive models for metallic materials in a thermomechanical context is proposed. Such a framework provides some guidelines to deal with processes involving large temperature variations, which is typical of manufacturing operations or severe service situations. The proposed framework relies on the additive decomposition of the logarithmic strain tensor to include the contributions of elasticity, plasticity and thermal expansion to deformation. Also, the classical internal variable concept is used to describe the history effects (e.g., hardening and recovery) associated with the development of plasticity. Particular attention is given to considering the impact of temperature on thermophysical properties. For the purpose of illustration, the proposed framework is used to build a constitutive model for polycrystalline copper. The resulting set of constitutive equations allows investigating the thermomechanical behavior of this specific material for some simple deformation histories. The corresponding results are finally used to evaluate the temperature-dependence of common thermophysical properties. The importance of the different heat sources that contribute to the heat diffusion equation is also discussed