A Continuum-Dislocation Theory for Modeling Dislocation Microstructures and Size Effects in Plasticity (original) (raw)

Plastic deformation of crystalline solids depends to a high degree on the mechanisms related to the dislocation network. In order to accommodate plastic deformation and to reduce the crystal's energy, new dislocations are nucleated and pile up near the grain or phase boundaries, thereby giving rise to material strengthening. The nucleation and motion of dislocations is hence an essential mechanism to explain plastic yielding, work hardening as well as size and hysteresis effects in crystal plasticity and needs embedding into the constitutive framework of modeling materials with microstructure. An important aspect of modeling dislocation microstructures by a continuum approach lies in a sensible representation of those effects stemming from the characteristics of the discrete crystal lattice which, in particular, prohibits high local dislocation concentrations. Such a saturation behavior gives rise to numerous experimentally observed effects. In particular, experimental investigations hint at an essential size-effect of many properties of elasto-plastic crystals (e.g., the size-dependence of the indentation force during nano-indentation experiments, the grain-size dependence of the yield stress of Hall-Petch or other type, etc.)