An analytical solution for the inverted four-point bending test in orthotropic specimens

Analytical solutions are derived for interfacial energy release rate and mode mixity angle in the inverted four-point bending test. In the test, the loads applied in the classical four-point bending test are inverted so that the crack faces come into contact at the midspan and mode mixity with an important mode II component is produced. The contact forces are evaluated by employing a beam model and imposing that the two delaminated arms undergo the same deflection at the contact point. Friction is accounted for within an approximate Coulomb model. Both Timoshenko and Euler-Bernoulli beam theories are applied and local 2D effects due to near tip deformations are introduced through suitable analytically derived crack tip root rotations and displacements. The results are verified by comparison with finite element results. The model accurately estimates energy release rate and mode mixity angle in orthotropic specimens, also for short/intermediate delaminations, and defines the minimum length of the crack ensuring a steady state propagation under a constant value of energy release rate and mode mixity. Steady state propagation under different mode mixity conditions is demonstrated by varying the relative thickness of the delaminated arms.