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In this paper, analytical stress intensity factor solutions for spot welds with ideal geometry in lap-shear specimens of different materials and thicknesses are presented as functions of the applied load, the elastic material property parameters, and the geometric parameters of the weld and specimen. The analytical stress intensity factor solutions are selectively validated by the results of a three-dimensional finite element analysis for a dissimilar spot weld with ideal geometry in a lap-shear specimen. Finally, selected stress intensity factor solutions at the critical locations of spot welds in lap-shear specimens of dissimilar magnesium, aluminum and steel sheets with equal and different thicknesses are presented in the normalized forms as functions of the ratio of the specimen width to weld diameter.

Fatigue behavior of spot friction welds or friction stir spot welds in lap-shear specimens of dissimilar aluminum 5754-O and 7075-T6 sheets is investigated based on experimental observations and two fatigue life estimation models. Optical micrographs of the 5754/7075 and 7075/5754 welds after failure under cyclic loading conditions are examined to understand the failure mechanisms of the welds. The micrographs show that the 5754/7075 welds mainly fail from the kinked fatigue crack through the lower sheet thickness. Also, the micrographs show that the 7075/5754 welds mainly fail from the kinked fatigue crack through the lower sheet thickness and from the fracture surface through the upper sheet thickness.

Ultrasonic spot welds were made between sheets of 0.8-mm-thick hot-dip-galvanized mild steel and 1.6-mm-thick AZ31B-H24. Lap-shear strengths of 3.0-4.2 kN were achieved with weld times of 0.3-1.2 s. Failure to achieve strong bonding of joints where the Zn coating was removed from the steel surface indicate that Zn is essential to the bonding mechanism. Microstructure characterization and microchemical analysis indicated temperatures at the AZ31-steel interfaces reached at least 344°C in less than 0.3 s. The elevated temperature conditions promoted annealing of the AZ31-H24 metal and chemical reactions between it and the Zn coating.

Failure mode and fatigue behavior of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets made with different processing conditions are investigated based on the experimental results and a structural stress fatigue life estimation model. Lap-shear specimens with FDS joints without clearance hole and lap-shear specimens with stripped FDS joints with clearance hole were made and then tested under quasi-static and cyclic loading conditions. Optical micrographs show the failure modes of the FDS joints without clearance hole (with gap) and the stripped FDS joints with clearance hole under quasi-static and cyclic loading conditions. The fatigue failure mode of the FDS joints without clearance hole (with gap) in lap-shear specimens is similar to those with clearance hole. The fatigue lives of lap-shear specimens with FDS joints without clearance hole are lower than those with clearance hole for given load ranges under cyclic loading conditions.

Fatigue behavior of dissimilar ultrasonic spot welds in lap-shear specimens of magnesium AZ31B-H24 and hot-dipped-galvanized mild steel sheets is investigated based on experimental observations, closed-form stress intensity factor solutions, and a fatigue life estimation model. Fatigue tests were conducted under different load ranges with two load ratios of 0.1 and 0.2. Optical micrographs of the welds after the tests were examined to understand the failure modes of the welds. The micrographs show that the welds mainly fail from kinked fatigue cracks growing through the magnesium sheets. The optical micrographs also indicate that failure mode changes from the partial nugget pullout mode under low-cycle loading conditions to the transverse crack growth mode under high-cycle loading conditions. The closed-form stress intensity factor solutions at the critical locations of the welds are used to explain the locations of fatigue crack initiation and growth.

Fatigue behavior of self-piercing rivets (SPRs) and clinch joints in lap-shear specimens of 6111-T4 aluminum sheets is investigated based on experimental observations and a fatigue life estimation model. Lap-shear specimens with SRPs and clinch joints were tested under cyclic loading conditions. Under cyclic loading conditions, fatigue cracks start from the curved interfacial surface of the upper sheet and then grow into the upper sheet thickness for both self-piercing rivets and clinch joints. The self-piercing rivets and clinch joints fail finally through the circumferential/transverse crack growth in the upper sheets and inner button crack growth, respectively. The structural stress solution and the experimental stress-life data for aluminum 6111-T4 sheets are adopted to estimate the fatigue lives of both types of joints. The fatigue life estimations based on the structural stress model show good agreement with the experimental results.

In this investigation, dissimilar 5754/7075 and 7075/5754 spot friction welds were first made under different processing conditions. The spot friction welds in lap-shear specimens were tested under quasi-static loading conditions. The optimal processing times to maximize the failure loads of the 5754/7075 and 7075/5754 welds under lap-shear loading conditions are identified. The maximum failure load of the 7075/5754 welds is about 40% larger than that of the 5754/7075 welds. Optical micrographs of both types of spot friction welds made at different processing times before and after failure are examined. The micrographs show different weld geometries and different failure modes of spot friction welds made at different processing times. The failure modes of the 5754/7075 and 7075/5754 spot friction welds appear to be quite complex and strongly depend on the geometry and the strength of the interfacial surface between the two deformed sheet materials.

A failure prediction methodology that can predict sheet metal failure under arbitrary deformation histories including rotating principal stretch directions and bending/unbending with consideration of damage evolution is reviewed in this paper. An anisotropic Gurson yield criterion is adopted to characterize the effects of microvoids on the load carrying capacity of sheet metals where Hill’s quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The evolution of the void damage is based on the growth, nucleation and coalescence of microvoids. Mroz’s anisotropic hardening rule, which was proposed based on the cyclic plastic behavior of metals observed in experiments, is generalized to characterize the anisotropic hardening behavior due to loading/unloading with consideration of the evolution of void volume fraction. The effects of yield surface curvature are also included in the plasticity model.

A new closed-form structural stress solution for a spot weld in a square thin plate under central bending conditions is derived based on the thin plate theory. The spot weld is treated as a rigid inclusion and the plate is treated as a thin plate. The boundary conditions follow those of the published solution for a rigid inclusion in a square plate under counter bending conditions. The new closed-form solution indicates that structural stress solution near the rigid inclusion on the surface of the plate along the symmetry plane is larger than those for a rigid inclusion in an infinite plate and a finite circular plate with pinned and clamped outer boundaries under central bending conditions. When the radius distance becomes large and approaches to the outer boundary, the new analytical stress solution approaches to the reference stress whereas the other analytical solutions do not.

Functioning as an introduction to modern mechanics principles and various applications that deal with the science, mathematics and technical aspects of sheet metal forming, Mechanics Modeling of Sheet Metal Forming details theoretically sound formulations based on principles of continuum mechanics for finite or large deformation, which can then be implemented into simulation codes. The forming processes of complex panels by computer codes, in addition to extensive practical examples, are recreated throughout the many chapters of this book in order to benefit practicing engineers by helping them better understand the output of simulation software.