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Effective dislocation lines in continuously dislocated crystals. III. Kinematics

Trzęsowski A.

Journal of Technical Physics

2008

Vol. 49, no 2

79-99

A class of congrunces of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their dislocation densities (tensorial as well as scalar). Moreover, it is shown, basing oneself on a formula defining the mean curvature of glide surfaces for principal edge effective dislocation lines, that the considered kinematics of continuized defective crystals is consistent with some relations appearing in the physical theory of plasticity (e.g. with the Orowan-type kinematic relations and with treatment of the shear stresses as driving stresses of moving dislocations).

Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity

Trzęsowski A.

Journal of Technical Physics

2007

Vol. 48, no 3-4

193-214

A continuous geometric description of Bravais monocrystals with many dislocations and secondary point defects created by the distribution of these dislocations is proposed. Namely, it is distinguished, basing oneself on Kondo and Kröner's Gedanken Experiments for dislocated bodies, an anholonomic triad of linearly independent vector fields. The triad defines local crystallographic directions of the defective crystal as well as a continuous counterpart of the Burgers vector for single dislocations. Next, the influence of secondary point defects on the distribution of many dislocations is modeled by treating these local crystallographic directions, as well as Burgers circuits, as those located in such a Riemannian material space that becomes an Euclidean 3-manifold when dislocations are absent. Some consequences of this approach are discussed.