The Change in the SIF of an Internal Semi-Elliptical Surface Crack Due to the Presence of an Adjacent Nonaligned Corner Quarter-Circle Crack in a Semi-Infinite Plate Under Remote Bending
Authors: Ma Qin , Levy Cesar , Perl Mordechai 
Published: November 2023

Abstract
Fracture mechanics-based failure theory has been used for analyzing structural integrity in Fitness-for-Service assessments of structures containing cracks. The stress intensity factors (SIFs) along the crack front are the key information in order to assess the remaining service life of a cracked component. In the case of a multiply cracked component, according to Fitness-for-Service (FFS) standards, these cracks must be first identified as to whether they are on the same cross-sectional plane, to be considered aligned cracks, or whether they are on parallel planes and thus be considered non-aligned parallel cracks. Extensive studies have been carried out on the mutual influence of adjacent parallel cracks. However, the scenario of a semi-elliptical surface crack under the influence of a quarter corner circular crack under remote bending has never been addressed. The present analysis addresses this problem by evaluating the effect of a corner circular crack of length a2 on the SIF of an adjacent nonaligned parallel semi-elliptical surface crack of length 2a1 and depth b1. A parametric study of the effect on the SIF as a function of the horizontal separation (S) and vertical gap (H) distances between the two cracks and the crack length ratio a2/a1 is conducted. Mode I SIFs are evaluated for a wide range of the normalized crack gaps of H/a2 = 0.4∼2, and normalized crack separation distances S/a2 = −0.5∼2.
As in the case of tension, the presence of the corner quarter-circle crack affects the stress intensity factor along the semi-elliptical crack front. The present results clearly indicate that the effect of the corner quarter-circle crack on the surface semi-elliptical crack is weaker in the case of bending, when compared to the tension case. The largest percentage differences (5–22%) occur at the farthest crack tip of the semi-elliptical surface crack from the corner crack. The largest percent differences occur for a2/a1 &lt; 1. In general, the deeper the semi-elliptical crack, the lower this percentage difference. When comparing maximal absolute values of the SIF, that normally occurs when b1/a1 = 1 for the cases undertaken. In general, the maximum values are found at the closest tip of the semi-elliptical crack to the corner quarter-circle crack. When b1/a1 is different from 1, then the maximum’s location can depend on the value of H/a2 and S/a2 irrespective of the ratio a2/a1. In these cases, the absolute maximum can occur in the vicinity of the deepest point or in the vicinity of the farthest crack tip of the semi-elliptical crack.
As in the case of tension, in the case of bending the presence of the Corner Quarter-Circle Crack changes the stress intensity factor along the semi-elliptical crack front. The change reaches its maximum at the tip of the semi-elliptical crack closest to the corner crack, and it monotonically decreases moving away from this tip for the case b1/a1 = 1. For most of the cases b1/a1 &lt; 1, the maximum occurs in the vicinity of the midpoint of the semi-elliptical crack and decreases monotonically in both directions from the midpoint.