Issue 43

F. Majid et alii, Frattura ed Integrità Strutturale, 43 (2018) 79-89; DOI: 10.3221/IGF-ESIS.43.05 88 experimentally. The same evolution was observed for continuum damage model, which has the same tendency as the adaptive one, Fig. 9. C ONCLUSION he assessment and establishment of the damage of HDPE pipes can’t be considered as a simple task. On the one hand, we propose a new approach based on the calculated pressures through the Faupel formula. This theoretical pressure can substitute the experimental burst pressures of the HDPE pipes, which are exposed to an increasing internal pressure until burst. Nevertheless, the calculations obtained by the Faupel formula must take into account the specificities of the used material since they were originally proposed for metals (steels). In this perspective, we have developed a modified equation based on a factor α that depends strongly on the behavior of the internal pressure used for the bursting of the neat studied pipes. Indeed, we have highlighted the effect of elongation of the pipe during the elastic phase to reach a maximum pressure. After that, the pipe reaches a phase of large strains before getting to another pressure peak representing the pressure of rupture. In the used static damage models presented in this paper, we substitute the experimental pressures by the calculated and modified ones. Then, we obtain a close approximate model more representative of the experimental model. The latter represents a powerful and rapid tool that can be used by manufacturers to launch audits and fast checks by knowing just the value of the coefficient α deduced from the evolution of the internal pressure of a neat pipe. Moreover, we have shown another powerful tool, adaptive damage model, perfectly reproducing the experimental static damage through a single burst test of a neat HDPE pipe. Therefore, if we want to calculate the burst pressure and subsequently the corresponding damage, we simply replace the value of the life fraction in the set of Eq. (6) or (7) knowing that the parameters Pr, Pmax and βc are constants that depend on the thermoplastic material and on the class of the pipeline. For the HDPE PE100 PN16 63 mm x 5.8 mm, we found that the values of these parameters are respectively 49.8 bar, 63.2 bar and 0.52. A theoretical modeling of the damage giving rise to a continuum damage model, Eqs. (8) to (11), showed that the latter could be evaluated by knowing the values of the coefficients α and η. These coefficients are constants of the studied material depending respectively on the pressures Pr and Pmax for the first and on the applied experimental pressure Pa and the rupture pressure Pr for the second as well as the critical life fraction. The continuum model is represented as a function of the theoretical life fraction by choosing an iteration for its evolution according to the wanted accuracy. R EFERENCES [1] Abedini, A., Rahimlou, P., Asiabi, T., Ahmadi, S.R., Azdast, T., Effect of flow forming on mechanical properties of high density polyethylene pipes, J. Manuf. Process., 19 (2015) 155–162. DOI:10.1016/j.jmapro.2015.06.014. [2] Krishnaswamy, R.K., Analysis of ductile and brittle failures from creep rupture testing of high-density polyethylene (HDPE) pipes, Polymer (Guildf). 46 (2005) 11664–11672. DOI:10.1016/j.polymer.2005.09.084. [3] Grigoriadou, I., Paraskevopoulos, K.M., Chrissafis, K., Pavlidou, E., Stamkopoulos, T.G., Bikiaris, D., Effect of different nanoparticles on HDPE UV stability, Polym. Degrad. Stab. 96 (2011) 151–163. DOI:10.1016/j.polymdegradstab.2010.10.001. [4] Zhang, S.H., Chen, X.D., Wang, X.N., Hou, J.X., Modeling of burst pressure for internal pressurized pipe elbow considering the effect of yield to tensile strength ratio, Meccanica, 50 (2015) 2123–2133. DOI:10.1007/s11012-015-0148-6. [5] Choi, B.H., Chudnovsky, A., Paradkar, R., Michie, W., Zhou, Z., Cham, P.M., Experimental and theoretical investigation of stress corrosion crack (SCC) growth of polyethylene pipes, Polym. Degrad. Stab., 94 (2009) 859–867. DOI:10.1016/j.polymdegradstab.2009.01.016. [6] Faupel, J., Furbeck, A., Influence of residual stress on behavior of thick-wall closed-end cylinders, Trans. ASME. (1953). [7] Hill, R., The mathematical theory of plasticity Oxford University Press London Google Scholar, (1950). [8] Nadai, A., Plasticity of Metals, (1950). [9] Klever, F., Formulas for rupture, necking, and wrinkling of octg under combined loads, SPE Annu. Tech. Conf. Exhib. (2006). [10] Brabin, A., Christopher, T., Investigation on failure behavior of unflawed steel cylindrical pressure vessels using FEA, Multidiscipline, (2009). [11] Veritas, D., Offshore standard dnv-os-f101, Submar. Pipeline Syst. (2000). T