Mathematical Modelling for Understanding the Effect of Stress State on Relative Slip Activity in HCP Titanium

Abstract: In the present work, the effect of applied stress tensor on relative slip activity as a function of crystallographic orientation on the HCP α-titanium is studied. In this statistical model, a discrete set of thousand uniformly distributed orientations are used to calculate the relative contribution of slip activity for the dominant slip systems in terms of Von Mises strain. The total plastic strain is plotted on the standard IPF triangle as a colour contours map, which enables the predictions of the dominant contribution of activity among several slip systems. The model further concludes that statistically the basal and prismatic slip systems are principal slip systems Furthermore, the relative contribution to total strain from prismatic slip system activity is high as compared to basal slip system activity. This behavior can be explained by the lowest critical resolve shear stress of the prismatic slip system for completely random textured HCP titanium.