Stress intensity solutions for the interaction between a hole edge crack and a line crack

Abstract

The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.

Interaction between a rigid inclusion and a line crack under uniform heat flux

“…2) to represent the rational mapping function technique that can generally deals with arbitrary shapes. The rational mapping function with the following general form (Hasebe and Inohara, 1980;Hasebe and Ueda, 1980;Hasebe and Chen, 1996;Yoshikawa and Hasebe, 1999a;Hasebe et al, 2003b):…”

“…The tractions normal ðN D I Þ and tangential ðT D I Þ to the crack line AB for problem D I are obtained (Hasebe and Chen, 1996) …”

Interaction between a cracked hole and a line crack under uniform heat flux

“…A number of papers dealing with the hole edge crack problem are available (Bowie, 1956;Tweed and Rooke, 1973;Hasebe and Ueda, 1980;Schijve, 1983;Hasebe et al, 1988Hasebe et al, , 1994aZhang and Hasebe, 1993;Chao and Lee, 1996;Hasebe and Chen, 1996). Among them, the rational mapping function approach is significant to solve the hole edge crack problem (Hasebe and Ueda, 1980;Hasebe et al, 1988Hasebe et al, , 1994aHasebe and Chen, 1996).…”

“…Hasebe et al (1994a) solved a second mixed boundary value problem analytically and as an example of the solution, the interaction of a square hole with an edge crack and a line crack was investigated for a geometrically symmetric case. Hasebe and Chen (1996) treated a cracked circular hole and a crack when the remote stresses were applied at infinity. The interactions of a hole and a rigid inclusion, respectively, with a crack were considered by Hasebe et al, (2003a).…”

“…Inserting (50) into (48) and (49), and after transformation of integral variable t = −b cos θ , the singular integral equations can be solved using the Gauss-Chebyshev integration formula (Erdogan, 1969;Erdogan and Gupta, 1972;Chen and Hasebe, 1992). Then, the stress intensity factors at the crack tips A, B and C can be obtained by (Chen and Hasebe, 1992;Hasebe and Chen, 1996):…”