On the theory of dislocation and generalized disclination fields and its application to straight and stepped symmetrical tilt boundaries

Abstract

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.

Revisiting the Application of Field Dislocation and Disclination Mechanics to Grain Boundaries

“…It features crystal defects more general than disclinations, and referred to as generalized disclinations. The differences between a couple-stress disclination theory involving only curvatures and a hyper-stress generalized disclination theory involving both curvatures and strain gradients are discussed in [44]. The mechanical dissipation in the material is the difference between the power of the applied forces and the rate of change of the stored energy:…”

Modeling of experimentally observed topological defects inside bulk polycrystals

“…We leverage this idea to identify, at the scale of the observations, plausible intra-granular orientation discontinuities and use g.disclination theory and associated computational techniques in two dimensions to compute their stress fields [21,22]. Related work can be found in [23,24] focusing on defect kinematics where finite difference approximations are used for inferring the disclination density from observations, but no stress fields are calculated. A notable recent work based on EBSD measurements, and broadly complementary to our work is [25]; however, the rare topologically interesting features in the zirconium sample would be difficult to locate with a surface based measurement.…”