On flow and work hardening expression correlations in metallic single crystal plasticity

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Abstract
From a comparison of the main phenomenological models describing the single crystal plastic flow (Schmid law, rate dependent approach, percolation model) and work hardening (strain hardening law,generalized hardening), one proposes a general frame of which the usual plastic flow-hardening law associations can be interpreted as particular cases associated with assumptions one tries to specify. To justify this general formulation, one proposes a microstructural description of the involved mechanisms, based on the introduction, in the primary dislocation density and in the slip expressions on the different systems, of a dislocation segment distribution on each slip system to be activated. It mainly comes out that, within the Schmid law frame, the strain hardening law is the limit case of this representation, corresponding with a Dirac distribution for the dislocation segments - the displacement law of which also obeying to such a Dirac function - while for any other distribution, a generalized hardening law is more convenient. Such a generalized hardening law, where the slip rates are no more the only hardening parameters, appears necessary to account for the hardening contribution of the inactive systems, what justifies previous works performed with this aim. A rate dependency of the flow is here expressed by a segment displacement law which is no more a Dirac like function. If the plastic flow threshold is assumed only asymptotically reached, one finds again a known type of rate dependent representation

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