Stress model and strain energy release rate of a prescribed crack in scarf joint/repair of composite panels

An analytical model for stress distribution was derived and an analytical model for determining the strain energy release rate of a prescribed crack in a scarf joint or a bonded scarf repair of a composite panel was developed. The crack closure method was used to calculate the strain energy release rate at the crack tip after a prescribed crack was inserted at high adhesive stress locations. In the stress model, the first-order laminated plate theory was applied to the composite panels, including the following: (1) scarfed parent substrate and corresponding repair panel for a bonded scarf repair or (2) both adherend panels for a scarf joint, assuming a linear elastic adhesive. The bondline was presumed to be thin, so the adhesive stresses were presumed to be uniform through the thickness. The coupled second-order differential equations obtained via kinematics and force equilibrium were solved semi-numerically using the symbolic computational tool Maple. Finite element analyses using the commercial software ABAQUS™ were conducted for comparison purposes, and results correlated well with the developed analytical model. Experimental strain data of the bonded scarf repairs was also used to verify the developed model. It can be seen that the highest adhesive stresses occur at locations where high-stiffness plies are discontinued. The obtained strain energy release rate can be used for failure analysis if appropriate critical energy release rates in conjunction with proper mode mixture rule are used.