Failure of laterally crushed aluminum tubes under combined bending and tension
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This thesis is concerned with the accurate numerical simulation of localized deformation that can develop into necking and failure, induced by combined bending and tension in aluminum alloy shell structures. The study is motivated by the need to establish the onset and evolution of such failures in imploding underwater cylindrical aluminum alloy shell structures. However, failure under combined bending and tension is also of concern in sheet metal forming. Such localized zones of deformation are shown to develop under controlled conditions in specially designed crushing experiments of Al-6061-T6 cylindrical shells. In these experiments shells of finite length and radially constrained ends are crushed laterally by rigid punches. The crushing, which is conducted under displacement control, causes the shell to develop bending and stretching stresses that lead to arcs of localized wall thinning to appear near the radially constrained locations. The local wall thinning develops into depressions with a width of the order of the shell wall thickness. As crushing progresses the depressions deepen, increase their span, become neck-like and develop inclined failures. The crushing was terminated when the first of four such depressions ruptured. After unloading, the shell was sliced along the principal plane of crushing and the most deformed cross sections of the necks were measured using an optical microscope. The crushing experiments were simulated numerically using solid FE models. The material was modeled as a finitely deforming elastic-plastic solid that hardens isotropically using three constitutive models: the first is based on the von Mises yield function, the second on the non-quadratic isotropic Hosford yield function and the third on the anisotropic Yld04-3D yield function. The models were calibrated to the same stress-strain response and to data from a set of radial biaxial experiments conducted on the same alloy tubes. The overall structural response was reproduced well by all models. Apparently such global responses smear out local differences introduced by the shape of the yield function adopted. However, differences between the three constitutive models were observed in the evolution of localization in the depressions. For the von Mises yield function, the localized deformation was significantly milder than in the experiments. The isotropic Hosford yield function produced necks that were closer to the experimental ones, while Yld04-3D produced results that were very close to the measurements. Clearly, and in concert with other applications, the adoption of a non-quadratic yield function is necessary for reproduction of localization and other challenging deformation histories in Al alloys. The addition of anisotropy in such models improves further the predictions. The results also demonstrated that accurate simulation of the evolution of the depressions in the presence of normal contact stresses requires the use of solid elements. Localization is clearly a three-dimensional phenomenon and shell elements reproduce most of the structural response well, but not the depressions and their evolution that eventually cause failure.