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In this paper, we developed a mathematical modeling to represent the damage of thermoplastic pipes. On the one hand, we adapted the theories of the rupture pressure to fit the High Density Polyethylene (HDPE) case. Indeed, the theories for calculating the rupture pressure are multiple, designed originally for steels and alloys. For polymer materials, we have found that these theories can be adapted using a coefficient related to the nature of the studied material. The HDPE is characterized by two important values of pressure, deduced from the ductile form of the internal pressure's evolution until burst. For this reason, we have designed an alpha coefficient taking into account these two pressures and giving a good approximation of the evolution of the experimental burst pressures through the theoretically corrected ones, using Faupel's pressure formula. Then, we can deduce the evolution of the theoretical damage using the calculated pressures. On the other hand, two other mathematical models were undertaken. The first one has given rise to an adaptive model referring to an expression of the pressure as a function of the life fraction, the characteristic pressures and the critical life fraction. The second model represents a continuum damage model incorporating the pressure equations as a function of the life fraction and based on the burst pressure's static damage model. These models represent important tools for industrials to assess the failure of thermoplastic pipes and proceed quick checks.

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ABSTRACT. This paper gives a highlight about pressure vessel (PV) methods of design to initiate new engineers and new researchers to understand the basics and to have a summary about the knowhow of PV design. This understanding will contribute to enhance their knowledge in the selection of the appropriate method. There are several types of tanks distinguished by the operating pressure, temperature and the safety system to predict. The selection of one or the other of these tanks depends on environmental regulations, the geographic location and the used materials. The design theory of PVs is very detailed in various codes and standards API, such as ASME, CODAP ... as well as the standards of material selection such as EN 10025 or EN 10028. While designing a PV, we must design the fatigue of its material through the different methods and theories, we can find in the literature, and specific codes. In this work, a focus on the fatigue lifetime calculation through fracture mechanics theory and the different methods found in the ASME VIII DIV 2, the API 579-1 and EN 13445-3, Annex B, will be detailed by giving a comparison between these methods. In many articles in the literature the uniaxial fatigue has been very detailed. Meanwhile, the multiaxial effect has not been considered as it must be. In this paper we will lead a discussion about the biaxial fatigue due to cyclic pressure in thick-walled PV. Besides, an overview of multiaxial fatigue in PVs is detailed.