Stress intensity factor solutions for spot welds in square overlap parts of cross-tension specimens of different thicknesses and materials

Closed-form stress intensity factor solutions for spot welds in square overlap parts of cross-tension specimens are investigated in this paper. The opposite outer edges of the square overlap parts of cross-tension specimens are under combined opening and counter bending conditions. The closed-form analytical structural stress solutions for a rigid inclusion in a square plate under the combined opening and counter bending conditions are first reviewed. Then, the J integral and stress intensity factor solutions for spot welds between square plates of different thicknesses and materials under the combined opening and counter bending conditions are developed in terms of the closed-form structural stress solutions for a strip model. The results of three-dimensional finite element analyses for spot welds between square plates of different thicknesses and materials under the combined opening and counter bending conditions are then presented. The analytical stress intensity factor solutions at the critical locations for spot welds based on the structural stress solutions with the equivalent and fitting coefficients are compared with the computational results. The results indicate that the computational stress intensity factor solutions agree well with those based on the structural stress solutions with only the equivalent coefficients. Based on the closed-form structural stress solutions, complete sets of the normalized in-plane stress intensity factor solutions at the critical locations of spot welds in square overlap parts of cross-tension specimens as functions of the ratio of the plate width to the spot weld diameter are presented for combinations of steel, aluminum and magnesium sheets and combinations of aluminum and copper sheets for convenient engineering applications.