Size-dependent yield function for single crystals with a consideration of defect effects

In this work, a size-dependent yield function for a single crystal is developed by considering defect effects, including dislocation pile-up, dislocation starvation, and source exhaustion, especially for micro-pillars. It is found that the proposed yield function compares well with the experimental data, and the proposed model is the extension of a single-arm source model to describe the yielding behavior under a more complicated loading case, not only the uniaxial compression test. Our quantitative conclusions suggest that the stacking-fault energy (SFE), the crystallographic orientation, and the slip system are significant factors for the shape of the yield surface: the slip system determines the number of the edges of the yield surface; the crystallographic orientation controls the angles between the adjacent edges but does not change the number of the edges; the low SFE can make sharp corners rounded and contract the shape of the yield surface, or even curve the edge of the yield surface. Moreover, we investigate the explicit relationship among the stacking-fault energy, the dislocation pile-up effect inside the sample, and the shape of the yield surface: materials with a low stacking-fault energy exhibit pronounced dislocation pile-up effects, and their yield surfaces tend to display rounded vertices, corresponding to the v. Mises yield criterion for the single-crystal sample with a {1 1 1} slip system for example; those with a high stacking-fault energy show typical Tresca criterion-type yield surfaces displaying sharp vertices for the single-crystal sample with a {1 1 1} slip system for example. We also show that this yield function can describe the size-dependent yield surface by considering the stochastic length of the dislocation source and the dislocation pile-up length in single-crystalline micro-pillars.