General J integral solution for specimens loaded by moments, axial forces and residual stresses – A unifying stiffness formulation

An exact, general solution for the J integral is derived and applied to a cracked double cantilever beam specimen loaded with axial forces in combination with bending moments (including residual stresses). Apart from the loads and the specimen width, the solution depends only on the extensional stiffness and the bending stiffness of the specimen beams. The elastic properties and expansion coefficients may vary continuously in the height direction (functionally graded material) or be piecewise constant within a layered structure. The stiffness formulation unifies analytical fracture mechanics solutions in terms of stiffness referring to the elastic centre, of stiffness per width referring to the mid-height (laminate beam theory), and of deformations (strain and curvature approach). The derived J integral solution is particularly useful for the determination of mixed mode cohesive laws for large-scale crack bridging problems.