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An analytical load distribution solution for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical roller bearings under radial loading is proposed in this paper. The loads exerted by the rolling elements are obtained based on an assumption that the profile of the maximum contact pressures of rolling elements resemble the profile of the contact pressure of the corresponding lumped cylinder. Based on this assumption, an analytical load distribution solution which gives the loads exerted by the rolling elements on the outer raceway is derived based on the non-conforming contact solution of Hertz and the conforming contact solution of Persson. These loads can be calculated from the analytical solution with the total applied load and the normalized contact pressure profile of the corresponding lumped cylinder. Two-dimensional finite element analysis was conducted to validate the proposed analytical solutions.

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.

In this paper, the differences of the residual stresses due to rolling in a finite elastic-plastic plate by rigid and elastic deformable rollers at very high rolling loads are investigated by two-dimensional plane strain finite element analyses using ABAQUS. In the finite element analyses, the rollers are modeled both as rigid and linear elastic, and have frictionless contact with the elastic-plastic finite plate. The plate material is modeled as an elastic-plastic power-law strain hardening material with a non-linear kinematic hardening rule for loading and unloading. Two new numerical schemes are developed to represent the elastic roller to model the indentation and rolling. The results of the contact pressure and subsurface stress distributions from the two numerical schemes are almost identical.

In this paper, residual stresses due to single indentation and rolling on a finite plate at very high rolling loads are investigated by two-dimensional plane strain finite element analyses using ABAQUS. In the finite element analyses, the roller is modeled as rigid and has frictionless contact with the finite plate. The plate material is modeled as an elastic-plastic power-law strain hardening material with a non-linear kinematic hardening rule for loading and unloading. For indentation and rolling at high rolling loads with extensive plastic deformation, the computational results show that the contact pressure distributions are quite different and they are also significantly different from the elastic Hertzian pressure distribution. The computational results for the rolling case show a significantly higher longitudinal compressive residual stress and a lower out-of-plane compressive residual stress along the contact surface when compared to those for the single indentation case.

Failure modes of friction stir spot welds in lap-shear specimens of dissimilar high strength dual phase steel (DP780GA) and hot stamped boron steel (HSBS) sheets are investigated under quasi-static and cyclic loading conditions based on experimental observations. Optical micrographs of dissimilar DP780GA/HSBS friction stir spot welds made by a concave tool before and after failure are examined. The micrographs indicate that the failure modes of the welds under quasi-static and cyclic loading conditions are quite similar. The micrographs show that the DP780GA/HSBS welds mainly fail from cracks growing through the upper DP780GA sheets where the concave tool was plunged into during the welding process. Based on the observed failure modes, a kinked fatigue crack growth model is adopted to estimate fatigue lives.

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.

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.