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This article presents a review of the sheet metal formability analysis based on the theory of damage mechanics. Specifically, the damage anisotropy is considered. Forming limit analyses based on the anisotropic damage are summarized, including the accumulative critical damage method, the damage-coupled vertex theory and the damage-coupled acoustic tensor method. The accumulative critical damage method postulates that the critical damage at the localized necking is strain-path or loading history independent. It can be applied to predict the forming limit diagrams under either proportional or nonproportional loading. The vertex theory considers that localized necking is associated with the vertex developed on yield surface. The theory is applicable to engineering materials exhibiting the strain-hardening and/or strain-rate dependent behaviors. The acoustic tensor method, on the other hand, can only be applied to the strain-softening materials, which are often observed in warm/hot sheet metal forming or hydroforming.

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ABSTRACT--Under in-plane loading conditions, two independent modes contribute to the failure of a spot weld: the in-plane shear mode and the in-plane rotational mode. In this work, the failures of both modes under large static load are examined individually. To study the combined failure of these two modes, two special test coupons are designed. The first coupon contains one spot weld. The second coupon contains five spot welds. Tests conducted in this work show that a very simple force-based failure criterion can be used to predict the failure of a spot weld under large in-plane combined static loads. Current multiaxial failure theory cannot explain this combined failure. This force-based spot weld failure criterion fits current automotive industry needs for body shell finite element application very well.KEY WORDS---Spot weld, force-based failure criterion, multi--spot weld test verification, spot weld crack, spot weld failure To understand and accurately predict spot weld failure attracts both industrial and academic researchers' attention. Numerous efforts have been devoted to estimating the fatigue life of a spot weld.l-4 Few stress-based mull/axial failure criteria have been published 5-7 for spot weld fatigue failure prediction. These criteria, in general, are concluded from high-cycle/low-stress fatigue tests. Spot weld failure criteria for low-cycle/high-streSs (say, 102 cycles at yield) or smile loads are extremely rare.In real structural designs, spot welds may fail after very low cycle or smile loading. For instance, spot weld cracks are often found in auto body structures after few-hundred-cycles road tests or even in body structural component smile tests. In either case, the above-mentioned fatigue research results cannot provide much design assistance. In 1998, Lee and colleagues 8 developed a test fixture for spot weld combined load failure studies and found that a simple criterion could be used effectively for predicting statically loaded spot weld failure. In their work, spot weld failure due to the combined normal pull, bending peel and tensile shear was studied. However, spot weld failure with in-plane rotation was not considered. Actually, rotational failure of spot welds does exist in complex auto body structures. For instance, failure of a front body apron panel at an engine-mounting bracket

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