Characterizing geometrically necessary dislocations using an elastic-plastic decomposition of Laplace stretch (Q2025459)

The paper studies the geometric dislocation density tensor and Burgers vector using an elastic-plastic decomposition of Laplace stretch which arises from a QR decomposition of the deformation gradient and allows for direct experimental measurement. The geometric dislocation density tensor is obtained using the classical argument of failure of a Burgers circuit in a suitable configuration, in which the deformation of the body is solely due to the movement of dislocations. The derived dislocation tensor is used as a measure of the torsion, i.e., incompatibility in the model space and vanishes when it is compatible. A balance law for geometric dislocations is derived taking into account the effect of the dislocation flux and source dislocations. The physical meaning of the plastic Laplace stretch, and consequently, of the derived geometric dislocation tensor proves to be particularly useful in the classification of dislocations. Finally, the significance of the dislocation density tensor is discussed. The derived geometric dislocation density tensor could be specifically useful in developing a strain-gradient and size-dependent theory of plasticity. With its 22 pages and 49 references the text provides a detailed and mathematically rigorous study of the problem, begining with an introduction including exhaustive systematic review of the corresponding scientific literature. Then, the authors revise the QR kinematics in a rather pedagogical manner, after which the configuration space is defined and its geometric properties are studied. In Section 5 the Burges vector is introduced while the following sections provide a balance law for geometrically necessary dislocations and classification results, as well as assessment of the significance of the derived dislocation density tensor.