A minimal gradient-enhancement of crystal plasticity theory

Abstract eng:
A minimal gradient-enhancement of the continuum multislip theory of crystal plasticity for incorporating size effects is proposed. The concept of the tensorial density of geometrically necessary dislocations generated by in-plane slip gradients is combined with the classical Taylor formula for a flow stress. The derived internal length scale is expressed through standard parameters so that no extra assumption is needed to define a characteristic length. It is shown that this internal length scale is related to the mean free path of dislocations and hence possesses physical interpretation which is frequently missing in other gradient-plasticity models. While the resulting gradientenhancement is extremely simple and involves no adjustable length-scale parameter, its verification by 3D finite element simulations of spherical indentation in a Cu single crystal shows good agreement with the experimentally observable size effect.

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