Stress-intensity factor approximations for two-dimensional curvilinear cracks

Two approximations are introduced and assessed that simplify the analytical and numerical treatment of curvilinear cracks in two-dimensional linear elastic fracture-mechanics analyses. The first involves the approximation of the crack trajectory with three segments that maintain a sufficiently accurate description of the near-tip geometry, including the tip's tangent. The second is associated with the use of only two segments, one of which specifies the tip's tangent. Results calculated for several configurations suggest that both approximations lead to accurate stress intensity factors and energy release rates, and can, therefore, be of great use in Monte Carlo-based characterization of random crack growth in brittle materials. An analytical expression is presented for the stress intensity factors of a curvilinear edge crack subjected to uniform far-field tension.