Stress analysis of bonded lap joints using fracture mechanics and energy balance

Abstract This paper uses fracture mechanics and energy balance to develop simple closed-form equations for the peak adhesive shear and normal stresses at the end of the bondline for flat and curved lap joints with adhesives with linear and non-linear material behaviour and variable adherend thickness. By using energy balance, explicit relationships between the strain energy release rate, mode ratio, and adhesive shear and normal stress are developed. The approach is shown to give identical results to the traditional beam-on-an-elastic-foundation approach for adhesive stresses in the special cases where closed-form solutions exist in the literature. The simplicity and ability to obtain closed-form expressions for joints with non-linear adhesives and variable adherend thickness makes the approach suitable for engineering analysis and preliminary design.