Under tensile loads thin-walled structures develop load maxima, or limit loads, beyond which deformation localizes leading to rupture. Thus, limit loads constitute forming limits for the structures. For structures such as sheet metal and tubes under uniform stresses, Considère-type estimates of limit loads provide simpler analytical alternatives to numerical calculations. This study developed such estimates for anisotropic Al-alloy thin-walled tubes under combined tension and torsion [1]. The anisotropy is modeled using the Yld04-3D with an exponent of 8 suitably calibrated. The material hardening response is extracted from a simple shear test using this yield function. Shearing causes rotation of the material axes, and is accounted for in the process. For the combined shear-tension stress state of interest here, material frame rotation affects also the equivalent stress and strain on which Considère calculations are based. The analysis developed describes how to account for the material frame rotation in limit load estimates for this biaxial stress state. The analysis is used to establish limit loads for a set of circumferentially constrained tension-torsion experiments tested in [2] under radial nominal tension-shear stress paths. The predictions reproduce the strains measured at the limit loads for the range of biaxiality ratios considered in the experiments. The results are further confirmed and enriched with finite element simulations of this setup. By contrast, corresponding results produced using the isotropic yield functions of von Mises and Hosford (with exponent 8) increasingly deviate from the measured limit strains as the shear stress increases. This indicates that incorporating the effect of material anisotropy is important in such a prediction of such limit loads.For a broader comparison, the anisotropy of the tube is also modeled using the quadratic Hill-48 anisotropic yield function and a corresponding Considère formulation is developed. The addition of anisotropy to the quadratic yield function improved the predictions by comparison to those from the von Mises yield function for the shear dominant stress ratios. However, the results remain much less accurate than those from Yld04-3D yield function. This supports once more that the adoption of a non-quadratic anisotropic yield function in limit load and post-limit load calculations is essential for Al-alloys.A Considère-type formulation is also developed for the same tension-torsion loadings for uniform thickness tubes using the same constitutive framework. The results exhibit a similar trend but the limit strains for shear dominant paths are significantly lower than those from the circumferentially constrained tension-torsion experiments, demonstrating the stabilizing effect of the circumferential constraint used in the experiments.The presentation will present the main features of the Considère formulation for the constitutive modeling framework adopted, and demonstrate the fidelity of the predictions by comparison to limit loads measured in the tension-torsion experiments.References[1] Chen, K., Kyriakides, S., “Limit Load Instabilities of Anisotropic Tubes Under Combined Tension and Torsion.” Int’l J. Solids &amp; Structures (in press). https://doi.org/10.1016/j.ijsolstr.2021.111148[2] Scales, M., Chen, K., Kyriakides, S., “Material Response, Localization and Failure of an Aluminum Alloy Under Combined Shear and Tension: Part I Experiments.” Int’l J. Plasticity 120, 340-360, 2019. http://doi.org/10.1016/j.ijplas.2019.04.004&nbsp;&nbsp;

Limit Load Instabilities in Anisotropic Aluminum Alloy Tubes Under Combined Tension and Torsion

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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