Investigation of the Size Effect in Compression Test by Combined Hill-Taylor Theory

In this paper, first the crystal plasticity notions developed by Taylor are combined with the mathematical form of Hill’s yield criterion for the anisotropic materials and a novel model is developed for description of mechanical response of grains in a specimen, based on their orientation. The advantage of the proposed model compared to other crystal plasticity finite element techniques is that in the conventional crystal plasticity codes, the deformation taken to be consisted of slip on all slip systems which is not valid assumption, yet here, the deformation taken to be consisted of slip on 5 slip systems. Using the proposed model which is called combined Hill-Taylor model, compression test of specimens with different number of grains are simulated and the state of strain in each grain and the condition for elimination of size effect in the final geometry of specimen is studied. The results suggest that the state of strain in each grain is individual and depends on the orientation of that gain which changes abruptly by passing through the grain boundaries. It is also observed that as the number of grains increases, the final geometry approaches to the expected ideal geometry. This trend is studied in statistical point of view and it became clear that as the number of grains increases the average of the state of strain approaches the ideal condition while the scatter in the state of strain in grains continue to maintain.