Applicability of the displacement discontinuity method to curvilinear crack growth and interaction problems

We studied the applicability of numerical methods based on the discontinuous displacement method to the simulation of curvilinear crack growth and interaction under complex loads. We examined how the resolution of the numerical method and the accuracy of stress intensity factor approximation affect the accuracy of a predicted crack growth path. We considered a low computational complexity method under the assumptions of linear elasticity, plane-strain conditions, and quasi-static crack growth. We selected the zero-order accuracy discontinuous displacement method and approximated stress intensity factors using displacement discontinuity values in elements closest to the crack tip. We demonstrated high accuracy in determining stress intensity factors for single-crack cases. For multiple cracks, we obtained criteria of the method applicability: high accuracy in approximating stress intensity factors occurs when the distance between cracks exceeds the size of the boundary element. The numerically calculated growth trajectory coincided with the experimental one for a plexiglass sample under shear load. We observed a weak dependence of the crack trajectory on the boundary element size and the crack length increment at each step under quasi-static growth. We also showed that the crack trajectory remains stable under small deviations in the presence of stress gradients. Based on these results, we concluded the applicability limits of zero-order methods for modeling the growth and interaction of curvilinear cracks.