Prediction of Yield Loci for a Magnesium Alloy Sheet using Crystal‐Plasticity Finite‐Element Method

This paper presents the prediction of yield loci for an AZ31 magnesium alloy sheet using a rate‐dependent crystal‐plasticity finite‐element method. A differential work‐hardening behavior was clearly observed; the contour of plastic work was initially rather flattened in the vicinity of equi‐biaxial tension, but thereafter severely bulged. The variation of the relative activity of each family of slip systems was examined to investigate the mechanism of the differential work‐hardening behavior. During uniaxial tension, the work hardening was determined mainly by the basal slip in the very beginning, while by both the prismatic slip and the basal slip in the subsequent deformation. On the other hand, during equi‐biaxial tension, the activity of the basal slip systems was predominant throughout the deformation, while the relative activity of the prismatic slip systems was smaller than that in the uniaxial tension. We concluded that this difference in the relative activities of the slip systems depending on the biaxial‐stress ratio eventually resulted in the differential work‐hardening behavior of the contour of plastic work. The mechanism that the activity of the prismatic slip systems decreased as the biaxial‐stress ratio approached to one was also discussed using a simple analytical model.