Issue 49

D. E. Belhadri et alii, Frattura ed Integrità Strutturale, 49 (2019) 599-613; DOI: 10.3221/IGF-ESIS.49.55 601   3 4            3 / 1   Plane strain k Plane stress         (3) For three dimensional models, different subscripts are used to designate the stress intensity factor for the three different modes. These factors are formally defined as [13]   0  lim 2 ,0 I yy r K r r       0  lim 2 ,0 II yx r K r r     (4)   0  lim 2 ,0 III yz r K r r     For cylinders subjected to axisymmetric loading, a decomposition of stresses in a polynomial form of third or fourth degree is usually used [14–18]. The SIF can be written in the form:   1,2,3 j j j j j a K i a j t            (6) Recently an interesting study, published in 2018 has been proposed for rapidly estimating notch stress intensity factors using the singular linear elastic peak constraints named: peak stress method (PSM) [19,20]. G EOMETRY AND LOADING OF CRACKED PIPE he pipe analyzed in this study is shown in Fig. 2 where R=350mm, L is the longitudinal length L= 1000 mm, and t =12.7mm is the wall's thickness. The crack was repaired by using a glass-epoxy composite patch bonded cylinder form with an adhesive cylinder e adh =02mm ,L adh =Lp=100mm, e p =4mm . The end sections pipeline was subjected to no displacement in the longitudinal direction (u3=0). The material properties of the pipeline, patch, and adhesive are summarized in Tab. 1. The pipe was made of X65 grade steel per API 5L PSL2 [21] specifications. The pipe is subjected to an internal pressure of 7MPa. The material model is considered as an elastic material. Figure 2: Geometry of the pipe with an external axial crack of semi-elliptical shape. A range of ratios of a/t, c/t, patch length (L p ), patch thickness(ep) as well as single and multi-laps of composite are highlighted in this study. T