Issue 50

M. Belhamiani et alii, Frattura ed Integrità Strutturale, 50 (2019) 623-637; DOI: 10.3221/IGF-ESIS.50.53 629 The J integral max tends to stablize when c/t > 1 for repaired pipe and the composite overwrap reduces the J integral level for a constante value (1.1 J/mm²) beyond 85% of c/t fig .5a. In the other hand, the J* confirm this observation where J* remain independent to c/t for crack length greater than 1,8 of c/t. This can be explained by the level of reaction of the repair system which reaches 72% of its efficiency. c. Patch length In Fig. 6 the variation of the J integral and J* are presented in function of the patch length, As seen in Fig.6 the J*increases rapidly to reach a upper limit with a patch length of the order of 15.75(L / t) with 51% of its maximum efficiency, than the efficiency of the repair system begins to decrease after 15.75 (L/t). This is due to the moment created in the end section of the patch which favours the opening of the crack, This remark has also been signaled by Ahmed Shouman et al [25]. Figure 6 : The variation of the J integral and J* with the patch length for repaired and unrepaired pipe. (a/t=0.5) It can be concluded that increasing the patch length may be detrimental to repair when it exceeds 15.75 (L/t). This limit of patch length give us an economic benefic to reduce the global cost of the repair operation. It has been found that the length (of the recovery) of the repair of the composite leads to a bending response of the repaired pipelines and this length L could be taken as a parameter that could increase the efficiency of the repaired pipes. d. Development of a predicting model for the repair system Knowing that the system for repairing pipelines by composite is a function of several parameters, namely the geometry of the crack, the thickness of the pipe, the length of the overlap of the composite, the thickness of the composite. In what follows a nonlinear regression involves all these parameters in a single equation to predict the J integral for a given situation. Nonlinear regression is used to model complex phenomena that do not fall within the linear model. XLSTAT [26], proposes preprogrammed functions among which the user will be able to possibly find the model describing the phenomenon to be modeled.When the desired model is not available, the user has the possibility to define a new model and add it to his personal library. In this part we summarize a testing and validation analysis of the previously developed model to predict the behavior of the integrated composit-cracked pipe structure. The original model is in the form of a nonlinear multiple regression equation. The model proved to be more accurate in simulating the J integral values of repaired three dimensional through wall cracked pipes (fig.1d) based on our results fig. 7. The general form of the nonlinear model represents a rational framework for developing specific models relevant to the composite overwrap repair technic. The predicted model :   2 2 2 1 2 3 4 5 6 7 Exp p l a L L rep J c c c c c c c       (7) where: