On the theory of dislocation and generalized disclination fields and its application to straight and stepped symmetrical tilt boundaries
C Fressengeas and XY Sun, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 143, 104092 (2020).
The theory of dislocation and generalized dislocation fields is developed within a second order mechanical framework where the description of the internal state of the body and the balance equations involve the stress and hyper-stress tensors, work-conjugates to the strain and second-order distortion tensors. Consistently, the free energy density depends on the elastic strain and second-order distortion tensors. To obtain a continuous setting, the theory uses the duality between the discontinuity of the elastic displacement vector and distortion tensor fields and the incompatibility of the smooth second- order elastic distortion field. The conservation of these discontinuities across arbitrary patches provides transport relationships for the motion of dislocations and generalized disclinations serving as a kinematic basis for the description of plasticity and phase transformation. Closure of the theory derives from constitutive relationships for the mobility of dislocations and generalized disclinations compatible with the thermodynamic requirement of positive dissipation. In contrast with dislocations, the driving forces for generalized disclinations involve the hyper-stress tensor, not the stress tensor. The resulting theory is able to address boundary value problems for the elasto-plasticity of solids coupled with phase transformation along arbitrary loading paths. We provide examples showing generalized disclination distributions in plane state situations such as straight symmetrical tilt boundaries and symmetrical tilt boundaries involving steps and ledges. (c) 2020 Elsevier Ltd. All rights reserved.
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