A discrete dislocation plasticity assessment of the effective temperature in thermodynamic dislocation theory

Abstract

In this study, the effective temperature proposed by Thermodynamic Dislocation Theory (TDT) is assessed using Discrete Dislocation Plasticity (DDP): simulations were performed on small samples driven to a saturated dislocation density condition consistent with prior TDT studies that were correlated with experiments, with results for the steady-state effective temperature compared to the Boltzmann formula. The formulation of configurational heat is presented for DDP, which is the term assigned to describe a stored energy associated with the interaction of dislocations, as opposed to being stored in dislocation self-energy and other internal structures. For the calculation of the configurational heat in DDP, excess dislocations are identified from an energetic rather than geometric perspective; the interaction energy of those dislocations is in agreement with the logarithmic defect energy proposed by Berdichevsky. The distribution of configurational heat shows inhomogeneity, in which it is generally high where excess dislocations accumulate, although it can be of high magnitude even in places where there are only a few dislocations. DDP predictions of the steady-state effective temperature are shown to be in good agreement with TDT, providing the first connection between these two established models of plasticity.