Numerical simulations of mixed-mode (I and II) notch tip fields in basal-textured magnesium alloys

Abstract

Crystal plasticity based finite element (CPFE) simulations employing Taylor homogenization for a basal-textured Mg alloy are performed under plane strain, small scale yielding (SSY) conditions to study mixed-mode (I and II) notch tip fields. Two notch orientations are considered. In one case, the notch line and normal to the flat surfaces of the notch are taken parallel to the transverse direction (TD) and rolling direction (RD), whereas in the other, they are aligned with normal direction (ND) and TD. The results are compared against those obtained from an isotropic (von Mises) plasticity model with identical stress–strain behavior under RD tension. The maximum plastic zone size at a given level of effective stress intensity factor |K|, enhances with mode II component (i.e., with decrease in mode mixity parameter Me), and is larger for ND–TD orientation. Further, {101̄2} or tensile twinning (TT) occurs near the stretched part of the notch surface, and is more profuse as Me reduces especially for the ND–TD case. It is found that for a given Me, the notch orientation can profoundly affect the distribution of equivalent plastic strain and hydrostatic stress around the notch tip, which underscores the importance of plastic anisotropy of Mg alloys. Finally, by employing appropriate fracture criteria and the computed near-tip fields, the variations of fracture toughness and operative fracture mechanism with Me are predicted for the TD–RD case, which corroborate well with a recent experimental study.