Surface Bifurcation in Anisotropic Materials With Application to Aluminum Alloys

Surface bifurcation is an instability mechanism which appears in the form of surface waviness on traction-free surfaces in ductile solids subjected to large strains. In sheet metal forming, the practical interest in this phenomenon stems from the fact that it occurs past the onset of localization, i.e., the forming limit, but prior to the local fracture failure in a quasi-static, monotonic loading process. In this work, we apply the general theory for surface bifurcation in a homogeneously strained, anisotropic, rate-independent, elastoplastic half-space, to study the influence of material anisotropy on the onset of surface instabilities. In particular, we calculate the critical principal strains $ε1cε2c$ and the corresponding eigenmode orientation angle $Ωc$ when the principal strain axes are at a fixed angle a with respect to the rolling direction of the solid. The presented calculations are for a 2024-T3 aluminum alloy, whose constitutive properties have been determined experimentally. It is found that by varying the strain orientation angle α, the surface bifurcation strains can vary up to an order of 80 percent for in-plane principal strains of a different sign, but only up to an order of ten percent for principal strains of the same sign. The eigenmode orientation angle $Ωc$ is calculated for a particular strain orientation $(α=π/6)$⁠, for which case it is found that $Ωc$ is close to the forming limit angle $ψc$ only for positive principal strains. The presentation is concluded by a discussion of the influence of the anisotropy and the yield surface parameters of the constitutive model on surface bifurcation.