Continuum damage modeling through theoretical and experimental pressure limit formulas

Abstract

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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