Issue 43

F. Majid et alii, Frattura ed Integrità Strutturale, 43 (2018) 79-89; DOI: 10.3221/IGF-ESIS.43.05 89 [12] Bathias, C., Pineau, A., Fatigue of Materials and Structures, (2013). DOI:10.1002/9781118616994. [13] Lemaitre, J., Desmorat, R., Engineering Damage Mechanics, (2005). DOI:10.1007/b138882. [14] Majid, F., Elghorba, M., HDPE pipes failure analysis and damage modeling, Eng. Fail. Anal. (2017). [15] Majid, F., Nattaj, J., Elghorba, M., Pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue, 38 (2016) 273–280. DOI:10.3221/IGF-ESIS.38.37. [16] Majid, F., Ouardi, A., Barakat, M., Elghorba, M., Prediction of PPR and HDPE polymers through newly developed nonlinear damage-reliability models, Procedia Struct. Integr., 3 (2017) 387–394. DOI:10.1016/j.prostr.2017.04.043. N OMENCLATURE Δe Thickness fluctuation of each created notch (groove). e Thickness of the pipe. n Instantaneous number of cycles under an applied stress. N f Total number of cycles at the rupture. β Life fraction representing the thickness fluctuation over the pipe’s thickness (β = Δe/e). βc Critical life fraction. β Pa Life fraction corresponding to the pressure before rupture. P Burst or limit pressure. P u Ultimate pressure corresponding to a neat HDPE specimen. P max Maximum pressure of the internal pressure curve of neat HDPE pipes P r Rupture pressure of HDPE pipes. P ur Ultimate residual burst pressure of notched pipes. Pa Pressure just before the rupture corresponding to the last possible notch. P ur1 , P ur2 , , Pa Ultimate residual burst pressure of notched pipes according to the notch level. α Parameter depending on the studied material (α = Pmax/Pr). η Parameter depending on the applied pressure corresponding to the notch just before rupture (η =Pa/Pr). D 0 , D i External and internal diameters of a cylinder. σ y Yield stress. σ UTS Ultimate stress P (β) Continuum burst pressure as a function of the life fraction β, D (β) Continuum damage as a function of the life fraction β. Ds Static damage based on burst pressures of HDPE pipes. D Linear damage of Miner.