Mode-I, Mode-II, and Mode-III Stress Intensity Factor Estimation of Regular- and Irregular-Shaped Surface Cracks in Circular Pipes

Abstract

Stress intensity factor (SIF) of surface cracks (semi-circular, semi-elliptical, and irregular shapes) located on a circular pipe (hollow) has been determined using numerical method. The irregular-shaped crack geometry was considered in the present work in order to simulate the cracks that are generally developed during service condition. The interaction behavior of multiple cracks on SIF calculation has also been investigated. Crack aspect ratios [a/c; “a” is the crack depth and where “c” is semi-major axis of elliptical crack] ranging between 0.6 and 1.0 and crack depth ratios [(a/d); where “d” diameter of the pipe] ranging between 0.1 and 0.4 were considered. Irregular-shaped cracks were modeled by keeping the crack depth (a) constant. For a regular profile semi-elliptic crack [(a/c) = 0.6], higher SIF was observed at crack middle region [(S/S0) = 0]. In contrast, higher SIF was observed at crack surface region [(S/S0) = ± 1] for semi-circular crack. Asymmetric spreading of SIF was noticed because of added effect of mode-II and mode-III fracture. In addition, the leading mode of fracture at short crack depth [(a/d) ≤ 0.1] was mode-II (in-plane shear) and mode-III (out of plane shear) fractures whereas at deep crack depths [(a/d) ≥ 0.4], the leading mode of fracture was mode-I fracture which is crack opening mode. Marginal influence of crack aspect ratio was noticed at crack surface region [(S/S0) = ± 1] and the effect is significant at crack middle region [(S/S0) = 0]. For a constant crack depth, higher SIF was obtained at the middle region [(S/S0) = 0] compared to regular profile crack. When comparing the observations of regular semi-elliptic crack, higher influence of mode-II and mode-III fracture was observed for irregular-shaped semi-circular crack which may leads to additional crack growth. Thus, approximating the standard crack geometry may over/under predict the SIF values. It is also inferred that the presence of adjacent cracks significantly affects the SIF of middle crack due to interaction effect. The interaction behavior was observed to be more pronounced when multiple cracks are located at closer interval. The interaction effect reduces gradually when the distance between crack centers increases. The improved SIF solutions obtained with consideration of additional fracture modes will be useful during the residual life determination.