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International audienceContinuum theory of moving dislocations is used to set up a non-local constitutive law for crystal plasticity in the form of partial differential equations for evolving dislocation fields. The concept of single-valued dislocation fields that enables to keep track of the curvature of the continuously distributed gliding dislocations with line tension is utilized. The theory is formulated in the Eulerian as well as in so-called dislocation-Lagrangian forms. The general theory is then specialized to a form appropriate to formulate and solve plane-strain problems of continuum mechanics. The key equation of the specialized theory is identified as a transport equation of diffusion-convection type. The numerical instabilities resulting from the dominating convection are eliminated by resorting to the dislocation-Lagrangian approach. Several examples illustrate the application of the theory

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The problem of simple shearing of a constrained thin crystalline strip posed by Shu et al. ͓J. Mech. Phys. Solids 49, 1361 ͑2001͔͒ is reanalyzed using a nonlocal continuum dislocation-based model of plastic deformation that accounts for the flexibility of curved dislocations carrying the plastic deformation. Attention is paid to the inhomogeneous profiles of plastic slip and lattice rotation as well as to the size-dependent material response of the strip in single slip and symmetric double slip. Additional boundary conditions and an internal length scale with a clear physical interpretation appear quite naturally in the analysis.

The formation of subgrains in the course of plastic deformation is explained as a result of a trend to make the deformation easier by locally reducing the number of active slip systems. Local preference of one slip system changes the crystal orientation with respect to stress (Schmid factor), thus leading to geometrical softening or hardening. The trend to subgrain formation is treated in the framework of continuum mechanics as an instability against internal bending for the simple case of a crystal originally oriented for symmetric double slip. Once formed, the boundaries of the subgrains lead to hardening as they induce long-range internal back stresses in the interior of the subgrains by forcing the mobile dislocations to take a bowed configuration. Simple dislocation-based and Cosserat models are recalled to explain the size-dependent subgrain hardening, where smaller subgrains are stronger.