Finite Element Analysis of Discrete Circular Dislocations

The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence of grain boundaries, interstitial particles, microvoids, thin film constraints and nano-indentation phenomena. The interaction of few dislocations with various inhomogeneities gives rise to size effects in the yield strength which are of great importance in nano-mechanics.