Energetic dislocation interactions and thermodynamical aspects of strain gradient crystal plasticity theories

Abstract

This paper focuses on the unification of two frequently used and apparently different strain gradient crystal plasticity frameworks: (i) the physically motivated strain gradient crystal plasticity models proposed by Evers et al. [2004a. Non-local crystal plasticity model with intrinsic SSD and GND effects. Journal of the Mechanics and Physics of Solids 52, 2379–2401; 2004b. Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. International Journal of Solids and Structures 41, 5209–5230] and Bayley et al. [2006. A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity. International Journal of Solids and Structure 43, 7268–7286; 2007. A three dimensional dislocation field crystal plasticity approach applied to miniaturized structures. Philosophical Magazine 87, 1361–1378] (here referred to as Evers–Bayley type models), where a physical back stress plays the most important role and which are further extended here to deal with truly large deformations, and (ii) the thermodynamically consistent strain gradient crystal plasticity model of Gurtin (2002–2008) (here referred to as the Gurtin type model), where the energetic part of a higher order micro-stress is derived from a non-standard free energy function. The energetic micro-stress vectors for the Gurtin type models are extracted from the definition of the back stresses of the improved Evers–Bayley type models. The possible defect energy forms that yield the derived physically based micro-stresses are discussed. The duality of both type of formulations is shown further by a comparison of the micro-boundary conditions. As a result, this paper provides a direct physical interpretation of the different terms present in Gurtin's model.