Issue 43

F. Majid et alii, Frattura ed Integrità Strutturale, 43 (2018) 97-105; DOI: 10.3221/IGF-ESIS.43.07 100 THEORY Damage theories n this paper, we led burst tests over notched pipes for both HDPE and PPR materials. Thus, we prepared standard specimens according the ASTM 1599. Then, we created multi-level grooves in the produced specimens. After that, we exposed neat and notched pipes to an increasing internal pressure until the rupture through a hydrostatic burst tester. The studied specimens of HDPE and PPR have seemingly the same dimensions. Moreover, the internal pressure evolution according to time have been registered for the neat pipe and the notched ones. Besides, the burst pressure and the time of burst have been also got from the hydrostatic tester display. These pressures are considered as the main parameters used in this paper to quantify the damage evolution. On the one hand, we interpreted the internal pressure evolution and the way it is representing the ductile behavior of the thermoplastic materials. On the other hand, the representation of the burst pressure according to the life fraction, which have been chosen as the ratio of the thickness and its fluctuation, have been detailed. The static damage of the unified theory based on the burst pressures has been developed to predict the damage evolution and the artificial preloading impact, which is represented by the notch depth [14, 15]. Static damage The static damage model is presented in the Eq. (1). This model is justified by the proportionality between the stress and the rupture pressure.    1 1 ur u a u p P D p P (1) Unified theory damage By correlation to the expression of the unified theory damage developed by Bui-Quoc, a relationship describing the evolution of the damage depending on the life fraction and pressure is given by Eq. (2):                                   _ 1 1 m u D (2) with: β: Life fraction. m: Empirical constant depending on material (m=1 for our case). / u u a P P   : Parameter reflecting the strength of the material in a virgin state. / ur a P P   : Parameter characterizing the effect of the damage on the mechanical characteristics of the material. Reliability estimation Reliability analysis is an essential part of any safety study. Originally, reliability was related to high-tech systems (nuclear power plants, aerospace). Today, reliability has become a key parameter of quality and decision-making in the study of most components, products and processes for transport, energy, buildings, electronic components and mechanical components. Many industrialists are working to evaluate and improve the reliability of their products during their life cycle, from design to operation in order to develop their knowledge of the report Cost / Reliability and control failure causes [11]. I