Limit load instabilities of anisotropic tubes under combined tension and torsion

Abstract

Under tensile loadings, thin-walled structures such as sheet metal and tubes develop load maxima, or limit loads, beyond which deformation localizes leading to rupture. For uniform stress states, Considère-type estimates of limit loads can serve as forming limits in applications. The paper explores the effect of anisotropy on such estimates for thin-walled Al-alloy tubes under combined tension and torsion. Anisotropy is modeled using Yld04-3D with an exponent of 8. Material hardening originates from a simple shear test using this yield function, taking into account material axes rotation caused by the shearing. A Considère formulation is developed for the problem, which also incorporates the effect of material frame rotation. The analysis is used to establish limit loads for a set of circumferentially constrained tension–torsion experiments tested under radial nominal tension-shear stress paths. The predictions reproduce the strains measured at the limit loads for the range of biaxiality ratios considered. By contrast, corresponding results produced using the isotropic yield functions of von Mises and Hosford(8) increasingly deviate from the measured results as the shear stress increases. Considère-type formulation is also developed for the same tension–torsion loadings for a uniform thickness tube. The results exhibit a similar trend but the limit strains for shear dominant paths are significantly lower, demonstrating the stabilizing effect of the circumferential constraint used in the experiments.