Issue 49

D. E. Belhadri et alii, Frattura ed Integrità Strutturale, 49 (2019) 599-613; DOI: 10.3221/IGF-ESIS.49.55 600 recognized, such as ASME B31.4 [6] and B31.8 [7], accept the use of composite materials for the repair function. Most oil and gas pipeline operators are familiar with composites and the health, safety, technical and commercial benefits they provide. Composite repairs are a proven and accepted technology for repairing high pressure pipelines. For example, Clock Spring has completed more than 100,000 repairs in more than 62 countries around the world [5]. Pipeline defects can be permanently repaired using composites technology in a safer, faster and cheaper way than any other technique. C. Alexander and B. Francini [8] had developed a detailed state of the art assessment of composite systems used to repair transmission pipelines. Many researches had used the stress intensity factor as a criterion to evaluate the efficiency of the composite repair system. Many crack configurations are used to calculate the SIF such as the rectangular and the semi elliptical crack. Newman and Raju (1984) [9] detailed an analytical study of the stress intensity factor equations for an embedded elliptical crack, a semi elliptical surface crack, a quarter-elliptical corner crack, a semi elliptical surface. crack along the bore of a circular hole and a quarter elliptical corner crack at the edge of a circular hole in finite plate. The equations give stress intensity factor as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. A. Saffih and S. Hariri studied elliptical cracks in a cylinder with a thickness transition. They found that SIF calculations in the transition, assuming a uniform thickness cylinder are conservative but not precise. The comparative study shows that the cylinder with a thickness transition is more vulnerable to a defect [10]. Another study of the U.S. Department of Transportation presents an investigation to determine the mode I stress-intensity factors, along two symmetric surface cracks emanating from a centrally located hole in a rectangular plate using the domain integral method [11]. Excellent agreement was obtained with those of Newman and Raju (1983). All these researches are focused on the study of the behavior in rupture in opening mode (mode I). The objective of the present work is to highlight the behavior of a semi-elliptic crack governed by the three failure modes in pipe subjected to internal pressure, after that the study extends on the estimation of the efficiency of repair of the pipe by a carbon-epoxy composite. S TRESS INTENSITY FACTORS CALCULATION he stress intensity factor (SIF) is one of the most important parameters in fracture mechanics. Brittle fracture in cracked engineering components is usually examined by SIF. After the crack detection in a structure, SIF can be calculated by various experimental or theoretical methods such as finite element analysis. Once SIF is known the risk of brittle fracture can be evaluated by using an appropriate fracture criterion. The mode I and mode II stress intensity factors (K I and K II ) can be calculated from finite element analysis based on the displacement functions (u and v) in a local coordinate system fixed to the crack tip [12] . Figure 1: Local Cartesian coordinates on crack tip.   2 2 1 I v r G K k r     (1)   2 2 1 II u r G K k r     (2) where r is the radial distance from the crack front in the polar coordinates, G is the shear modulus, υ is Poisson’s ratio, and k can be defined for plane strain and plane stress problems as follows: T