[SY-A9] Physically based strain gradient plasticity model for length scale dependent yield strength
Many experimental studies have shown a plastic strengthening effect for structural length scales approaching microstructural dimensions. Both increases in initial yield strength and strain hardening have been observed. Over the last 30 years different strain gradient plasticity (SGP) theories have been developed in order to capture these length scale dependences. However, up to now no generally accepted theory has emerged. In the present paper, focus is directed into a physically based SGP model for initiation of plastic deformation. The plastic behavior is governed by a dissipative part that primarily controls the hardening at moderate plastic strains and an energetic part that is of importance for the initiation of plastic flow. It is shown that a model based on the self-energies of dislocations can be translated into an internal free energy in terms of plastic strain gradients. In this way a physical connection is made between the SGP framework and dislocation mechanics. A microstructural length scale can then be defined as the Burgers vector divided by the strain for initiation of plastic deformation. When structural length scales approach this microstructural length scale, strengthening effects result. It the Taylor model is used for the dissipative part, the same microstructural length scale appears. The so developed three-dimensional SGP model is specialized to the simple load cases of tensile tension with a passivation layer that prohibits plastic deformation on surfaces as well as pure bending with free and fixed boundary conditions for plastic strain. Simulations for varying thicknesses are compared to experimental observations reported in the literature. It is shown that the model in a good way can capture the length scale dependences. Suggestions for improvement of the dislocation theory based model for the internal free energy are discussed.