Vol 68, No 6 (2016)

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A minimal gradient-enhancement of the classical continuum theory of crystal plasticity. Part II: Size effects

S. Stupkiewicz, H. Petryk

Arch. Mech. 68 (6), 487-513, 2016

Keywords: gradient plasticity; geometrically necessary dislocations; boundary layer; size effects; indentation; finite element method


In our previous paper, a simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip has been proposed for incorporating size effects. A single internal length scale has been derived as an explicit function of the flow stress defined as the isotropic part of critical resolved shear stresses. The present work is focused on verification whether the simplifications involved are not too severe and allow satisfactory predictions of size effects. The model has been implemented in a finite element code and applied to three-dimensional simulations of fcc single crystals. We have found that the experimentally observed indentation size effect in a Cu single crystal is captured correctly in spite of the absence of any adjustable length-scale parameter. The finite element treatment relies on introducing non-local slip rates that average and smoothen on an element scale the corresponding local quantities. Convergence of the finite element solution to the analytical one is also verified for the one-dimensional problem of a boundary layer formed at a constrained interface.

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