Analytical Modeling of Dynamic Crack Propagation in DCB Specimens

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded medium such as DCB (Double Cantilever Beam) specimen. In the static case, the stress intensity factor (SIF) is derived at the crack tip through the compliance approach for fixed displacement conditions. In the dynamic case, the energy balance criterion is employed to obtain the equation of motion for a running crack and the problem is solved supposing quasi-static crack propagation. Finally, a closed form relation for the crack propagation velocity versus specimen parameters and crack growth resistance of the material is found. Therefore, the effects of various parameters are investigated on the crack growth velocity. It is shown that the reacceleration of crack growth appears when the crack tip approaches the end of specimen under fixed displacement loading. The predicted results are compared with those cited in the literature and a good agreement is observed. It is seen that shear deformation effects are more significant when the small values of a₀/h is considered in the analysis.