Circumferential surface cracks in pipes

As is well-known, many cracks in structural components need to be studied by means of three-dimensional Fracture Mechanics. In two-dimensional problems the crack tip is considered as a point and the crack as a segment of a line, while in three-dimensional problems the flaw is a discontinuity surface delimited by the emerging crack on the external surface of the body and by the crack front internally. Because of the complexities of the 3D crack configurations, exact solutions of the stress-intensity factor KI are often not available for these problems. Therefore, numerical techniques or approximate analyses have to be used to obtain the variation of KI along the crack front [1-6]. Edge flaws in pipes have a three-dimensional nature. A number of KI-solutions for both straight crack front and curved crack front under different loading conditions have been deduced by using several methods [7,8,9]. In the present study, an elliptical-arc surface flaw with aspect ratio a/b (crack depth / semi-major axis of the ellipse) is assumed to be subjected to a constant amplitude cyclic axial loading. The relative crack depth x of the flaw's deepest point is equal to the ratio between the maximum crack depth a and the wall thickness t. The aspect ratio of the initial flaw is made to vary from 0.0 (straight front) to 1.0 (circular-arc front), while the relative crack depth x ranges from 0.1 to 0.6. Moreover, the ratio R/t of internal radius to wall thickness ranges from 1 to 10. The stress-intensity factor variation along the crack front is determined through a finite element analysis carried out with 20-node isoparametric solid elements. The stress singularity is obtained by shifting the finite element midside nodes near the crack front to quarter-point positions. Then the Paris-Erdogan law [10] is applied to analyze the fatigue flaw propagation. The problem is complex since the flaw is an elliptical arc during the whole propagation but the aspect ratio changes. Several authors have shown that the surface flaws in flat plates tend to follow preferred propagation paths, that is, the aspect ratio is a function of the relative crack depth (crack depth/plate thickness) for both axial and bending cyclic loading [1,11-12]. An analogous conclusion has also been drawn for surface flaws in round bars [1,13]. The purpose of the present study is to analyze the growth patterns for edge flaws in pipes. In particular, it will be shown that, for each initial flaw configuration being considered, the propagation pattern converges to an inclined asymptote, with a/b included in the range 0.6 ~ 0.7 for x = 0.6. The range of variation for a/b is related to different materials, loading conditions and initial crack configurations.