Gradient plasticity for thermo-mechanical processes in metals with length and time scales

Abstract

A thermodynamically consistent framework is developed in order to characterize the mechanical and thermal behavior of metals in small volume and on the fast transient time. In this regard, an enhanced gradient plasticity theory is coupled with the application of a micromorphic approach to the temperature variable. A physically based yield function based on the concept of thermal activation energy and the dislocation interaction mechanisms including nonlinear hardening is taken into consideration in the derivation. The effect of the material microstructural interface between two materials is also incorporated in the formulation with both temperature and rate effects. In order to accurately address the strengthening and hardening mechanisms, the theory is developed based on the decomposition of the mechanical state variables into energetic and dissipative counterparts which endowed the constitutive equations to have both energetic and dissipative gradient length scales for the bulk material and the interface. Moreover, the microstructural interaction effect in the fast transient process is addressed by incorporating two time scales into the microscopic heat equation. The numerical example of thin film on elastic substrate or a single phase bicrystal under uniform tension is addressed here. The effects of individual counterparts of the framework on the thermal and mechanical responses are investigated. The model is also compared with experimental results.