Effective dislocation lines in continuously dislocated crystals. III. Kinematics

Details Effective dislocation lines in continuously dislocated crystals. III. Kinematics Effective dislocation lines in continuously dislocated crystals. III. Kinematics

2007-09-12

arxiv.org/abs/0709.1802v5

Journal of Technical Physics, vol. 49, 2, pp. 79-99, 2008.

Physics

Mathematical Physics

Keywords. Anholonomity, crystal surfaces, dislocation density, dislocation speed, glide surfaces, instantaneous metric tensor,

Scientific paper

A class of congruences 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 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 the treatment of shear stresses as driving stresses of moving dislocations).

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