Analysis of size effects based on a symmetric lower-order gradient plasticity model

Size effects become significant as soon as strain gradients are high. For instance the stress state around the crack tip cannot be described using conventional plasticity theory due to the extreme strain gradients and micro-structural metallurgical changes. To give an accurate prediction of the structure integrity and to quantify the material failure process, it is necessary to combine the strain gradients into constitutive equations. The present paper deals with developing a symmetric lower-order gradient-dependent constitutive model, which contains only the first-order gradient of equivalent plastic strain as regulator and introduces an intrinsic material length scale to take into account the micro-structure characteristics of materials. The flow stress is assumed linearly depending on the square root of first gradient of the equivalent plastic strain. Our analytical solutions for bending, torsion, void growth and interface stress fields show that the present model is computationally efficient to implement and may catch size effects in different geometries, in comparing with the known experiments. Furthermore, we are briefly discussing the micro-indentation based on the gradient plasticity. The quadratic dependence of the hardness on the inverse of the indentation depth is confirmed. The introduced intrinsic material length can be identified from the micro-indentation test.