Spatial Constitutive Modeling of AA7050-T7451 with Anisotropic Stress Transformation

The mechanical properties of anisotropic materials are generally characterized based on the orthotropy or transverse isotropy. However, the two-dimensional plane stress problems cannot comprehensively characterize the anisotropy of materials. In this study, based on the theory of elasticity and the transformation of the three-dimensional space coordinate system, combined with the projection relationship of the Cauchy stress tensor of an arbitrary section, the transformation relationship of the elastic modulus, shear modulus, and stress–strain between the orthogonal and load coordinate systems are obtained. The orthotropic Johnson-Cook (JC) constitutive model of AA7050-T7451 aluminum alloy is modified by fitting, and the constitutive relationship at any spatial angle is theoretically calculated by combining the obtained spatial coordinate transformation matrix. The generated spatial constitutive model is verified and modified through experiments. The results demonstrate that the theoretical mechanical properties and the modified spatial constitutive model can accurately reflect the effect of the spatial angle on the material stress distribution.