Mode II weight functions for isotropic and orthotropic double cantilever beams

Approximate weight functions are derived and validated numerically for isotropic and orthotropic double cantilever beams loaded in mode II. They define the stress intensity factor at the crack tip due to a pair of unit point forces acting tangentially to the crack surfaces and have been deduced using asymptotic matching through finite elements and an orthotropy rescaling technique. Along with the related mode I weight functions, which are recalled in the paper, the functions can be used to formulate mixed mode problems in beams and plates as integral equations so avoiding the limitations imposed on accuracy by approximations based on structural theories. An accurate method such as the weight function method becomes necessary when dealing with short cracks, crack initiation and large scale bridging delamination problems with crack wake mechanisms acting over several scales. The accuracy of modes I and II solutions based on beam theory approximations is shown to be strongly influenced by the length of Dugdale type cohesive regions, with short lengths giving rise to large errors in the fracture parameters. Stress intensity factors obtained using the proposed functions for special problems agree with solutions from the literature.