Orthotropic ductile fracture criterion based on linear transformation

Accurate modelling of orthotropic ductile fracture is key to carry out reliable numerical prediction of rupture in plastic deformation of lightweight metals, such as ultra high strength steel, aluminum alloys, titanium alloys and magnesium alloys. Experiments are conducted for an aluminum alloy in shear, uniaxial tension, plane strain tension along the rolling direction, the diagonal direction and the transverse direction. Loading processes are recorded and fracture strain is measured by analysis of deformation with digital image correlation. First, isotropic fracture behavior is modeled by both linear model (Maximum Shear Stress (MSS) plus mean stress) and nonlinear model (Hosford yield function plus mean stress) considering different triaxiality conditions. It is observed that the mean stress model shows significant difference in the compression area compared to Mohr Coulomb-based normal stress model and a new isotropic model with the mean stress term shows a good correlation for AA 6k21. This approach is extended to an anisotropic ductile fracture criterion based on linear transformation. The anisotropic ductile fracture criterion is applied to model orthotropic fracture strain in shear, uniaxial tension and plane strain tension. The predicted anisotropy in ductile fracture is compared with experimental results for the verification of its accuracy. The comparison indicates that the proposed anisotropic ductile fracture criterion accurately models orthotropic ductile fracture in various loading conditions in shear, uniaxial tension and plane strain tension.