Thermodynamic considerations on a class of dislocation-based constitutive models

TL;DR

This paper examines the thermodynamic consistency of dislocation-based constitutive models in crystal plasticity, highlighting potential violations of thermodynamic laws and proposing constraints to ensure physical plausibility.

Contribution

It provides a thermodynamic framework for evaluating and improving dislocation-based constitutive models in crystal plasticity.

Findings

Failure to account for dislocation energy increases can violate thermodynamic laws.

Constraints can be formulated to ensure models are thermodynamically consistent.

Examples demonstrate the importance of thermodynamic considerations in model formulation.

Abstract

Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of dislocation microstructure evolution and plastic flow. Typically, such constitutive models are not formulated in a thermodynamic framework. Nevertheless, fundamental considerations of thermodynamic consistency impose constraints on the admissible range of model parameters and/or on the range of application of such models. In particular, it is mandatory to ensure that the internal energy increase associated with dislocation accumulation is properly accounted for in the local energy balance. We demonstrate on some examples taken from the literature how failure to do so can lead to constitutive equations that violate the first and second laws of thermodynamics either generally or in some particular limit cases, and we discuss how to formulate constraints that recover thermodynamic consistency.