On the thermo-mechanical theory of field dislocations in transient heterogeneous temperature fields

Abstract

A strong coupling between the field theory of dislocation mechanics and heat conduction is proposed. The novel model, called the Thermal Field Dislocation Mechanics (T-FDM) model, is designed to study the dynamics of dislocations during rapid or gradual temperature changes in a body having a heterogeneous temperature distribution; for example, such conditions occur in a heat-affected crystalline solid during an additive manufacturing process. Thermal strains are uniquely separated into compatible and incompatible components via the Stokes-Helmholtz decomposition and the curl of the incompatible part of thermal strains is directly related to the areal dislocation density tensor. A dislocation density evolution (including transport) law is developed and shown to be related to the evolution of the curl of incompatible thermal strains. This relationship demonstrates that dislocation generation, annihilation, motion and/or interactions with other defects can be triggered due to transient temperature changes, and conversely an evolving dislocation density induces temperature changes. The model development is completed with constitutive laws derived from energetic and dissipative considerations. The advantages and consequences of the assumptions of the T-FDM model under rapidly changing temperatures, both spatially and temporally, are discussed. The T-FDM model is intended for application at the length scale where individual dislocations can be characterized. At this level, local thermodynamic equilibrium is found to be a reasonable assumption even for high rates of change of temperature such as those occurring during an additive manufacturing process. Some illustrative examples are presented to demonstrate the applicability of the model and to better understand some of the novel concepts proposed in this work.