Analytic Solution of Mode I Stress Intensity Factor for Spot Welds in Lap-Shear Specimens

The analytic solution of the mode I stress intensity factor for spot welds in lap-shear specimens is investigated based on the classical Kirchhoff plate theory for linear elastic materials. Approximate closed-form solutions for a finite square plate containing a rigid inclusion under counter bending conditions are first derived. Based on the J integral, the closed-form structural stress solution is used to develop the analytic solution of the mode I stress intensity factor for spot welds in lap-shear specimens of finite size. Finally, the analytic solution of the mode I stress intensity factor based on the stress solution for a finite square plate with an inclusion is compared with the results of the three-dimensional finite element computations for lap-shear specimens with various ratios of the specimen half width to the nugget radius. The results indicate that the mode I stress intensity factor solution based on a finite square plate with an inclusion agrees well with the computational results for lap-shear specimens.