Multi-asperity contact: A comparison between discrete dislocation and crystal plasticity predictions

Plane strain indentation of single crystals by a periodic array of flat rigid contacts is analyzed. The calculations are carried out, with the mechanical response of the crystal characterized by conventional continuum crystal plasticity or by discrete dislocation plasticity. The properties used in the conventional crystal plasticity description are chosen so that both theories give essentially the same response in uniform plane strain compression. The indentation predictions are then compared, focusing in particular on the effect of contact size and spacing. The limiting cases of frictionless contacts and of perfectly sticking contacts are analyzed. Conventional continuum plasticity predicts a size-independent response. Unless the contact spacing to size ratio is very small, the predicted deformation mode under the contacts is a wedging mechanism of the type described by slip line theory, which is only weakly sensitive to friction conditions. For the micron scale contacts analyzed, discrete dislocation plasticity predicts a response that depends on the contact size as well as on the contact spacing to size ratio. When contacts are spaced sufficiently far apart, discrete dislocation plasticity predicts that the deformation is localized beneath the contacts, whereas for more closely spaced contacts, deformation occurs by shear bands extending relatively far into the crystal. Unless the contacts are sufficiently close together so that the response is essentially one of plane strain compression, the mean contact pressure predicted by discrete dislocation plasticity is substantially greater than that predicted by conventional continuum crystal plasticity and is more sensitive to the friction conditions.