Anisotropic elastic and elastic–plastic bending solutions for edge constrained beams

In beam-like fracture tests the rotation at the crack tip is a significant factor controlling the energy release rate. The local deformations of a beam ahead of the crack tip where the lower edge constrained by a stiffness is described for an anisotropic elastic material. This is a useful model for composite delamination tests and gives the crack length correction factor and root rotation which are used in determining energy release rate. The solution is calibrated using FE results and found to be accurate to within 2%.The solution is extended by analogy to plasticity where the yielding of the constrained edge is modelled. The assumption that the deformations are controlled by the same parameters as the elastic solution is confirmed numerically. It is shown that in most practical cases the bottom edge remains elastic. This constraint is important in calculating the root rotation.