Elastic analytical solutions and angular distributions near spot weld nugget in lap-shear specimens

Abstract

Spot welding has been a remarkably important joint method for automotive body engineering. Based on a simplified two-dimensional analytical model in a lap-shear specimen, the elastic analytical solutions near spot weld nugget are theoretically derived to analyze stress distributions. A Cartesian coordinate system is centered at the center of the nugget, and the shear or resultant force acting on the nugget is marked as the positive x-direction. The results show that the normalized radial and hoop stresses are negative at the angle intervals between [66.25°, 113.75°] and [246.25°, 293.74°], while the normalized shear stress is negative at the angle intervals between [0°, 90°] and [180°, 270°]. It can be observed that the locations with the initial yielding failure change gradually from the normalized radial distance of 1.34 to the circumference of the spot weld nugget, and finally to the infinity as the angle increases. The normalized effective stress could approach to 1.84 as the normalized radial distance goes to infinity. In addition, the obtained analytical solutions are validated in the comparison with numerical results. The locations with peak Von Mises stresses along the circumference of the spot weld nugget have a good agreement with the analytical solutions. It indicates that the initial yielding locations would likely occur at the four special angles of the spot weld nugget. Therefore, the derived stress distributions in this study are beneficial for analyzing yielding failure behavior or evaluating damage evolution on engineering structures jointed with spot welds.