A Dilatational Plasticity Theory for Aluminum Sheets

The nucleation, growth and coalescence of micro-voids are important failure mechanisms in ductile materials. Gurson (1977) has developed a dilatation plasticity theory to quantitatively characterize the state of deformation and damage associated with micro-voids in isotropic materials. This theory, however, is not applicable to aluminum sheets because they are highly anisotropic. A dilatational plasticity theory for anisotropic ductile materials is developed in this study. The constitutive law is established for aluminum sheets that contain micro-voids, where the matrix material of aluminum is characterized by an anisotropic constitutive model developed by Barlat et al. (1991). Based on the numerical analysis, an approximate yield function is given in the closed form for anisotropic sheets. It shows that the mean hydrostatic stress plays an important role in the plastic behavior of anisotropic micro-voided aluminum sheets.