Hybrid crack-tip element and its applications

A hybrid crack-tip element with a distribution of traction along the crack surfaces is developed. Following the Hellinger-Reissner variational principle, the reduced form of functional that involves only line integral is used. Linear superposition and approximate functions based on the linear elasticity theory are employed in the formulation. The accuracy of the developed special crack-tip element is demonstrated through comparison with the analytical results for a crack in an infinite (large) plate. The efficiency of the method is verified against numerical results obtained by ABAQUS through an edge-crack boundary value problem. The developed crack-tip element is also applied to problems involving interaction of a main crack with random arrays of micro-cracks subjected to a constant traction on the crack surfaces. The effect of constant traction on the stress intensity factors of the main crack is analyzed.