Determination of higher order coefficients and zones of dominance using a singular integral equation approach

Abstract

A method to determine higher order coefficients from the solution of a singular integral equation is presented. The coefficients are defined by σ rr ( r , 0 ) = ∑ n = 0 ∞ k n ( 2 r ) n - 1 2 + T n ( 2 r ) n , which gives the radial stress at a distance, r, in front of the crack tip. In this asymptotic series the stress intensity factor, k 0, is the first coefficient, and the T-stress, T 0, is the second coefficient. For the example of an edge crack in a half space, converged values of the first 12 mode I coefficients ( k n and T n , n = 0, … , 5) have been determined, and for an edge crack in a finite width strip, the first six coefficients are presented. Coefficients for an internal crack in a half space are also presented. Results for an edge crack in a finite width strip are used to quantify the size of the k-dominant zone, the kT-dominant zone and the zones associated with three and four terms, taking into account the entire region around the crack tip.