An analysis of geometrically necessary dislocation evolution and plasticity size effects in micro-crystals
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abstract
Mechanism-based discrete dislocation plasticity is used to develop a phenomenological model of plastic flow and work hardening in micro-crystals. The proposal model is based on two ingredients: (a) a dislocation evolution law; (b) a hardening law. The former accounts for dislocation storage and dynamic recovery, just as in classical models, and for geometrically necessary dislocation (GND) density build-up, at the scale of description. The hardening law is novel and accounts for the effect of GND density, In the proposed model, the flow stress is a derived quantity. Its expression in terms of total dislocation and GND densities is rather complex but does reduce to the Taylor equation for a bulk crystal. Model predictions are found to fit remarkably well the discrete dislocation results over a wide range of specimen sizes.
