Issue 43

F. Majid et alii, Frattura ed Integrità Strutturale, 43 (2018) 79-89; DOI: 10.3221/IGF-ESIS.43.05 80 and the technological advances of polymer’s applications [1–5]. In this context, several discoveries have been recorded in the history of plastic materials starting with PVC in 1913, Plexiglas in 1924, polystyrene in 1933, polyethylene in 1935, Teflon in 1938, ABS in 1946 and polypropylene in 1954. The polymers are generally classified into three main categories, which are thermosetting, thermoplastic and elastomer. For our case, the High Density Polyethylene (HDPE) materials have gained a huge importance in the industrial field because of their durability and high performances. To contribute to these advances, we led many simplifying approaches of failure assessment and prediction of HDPE pipes [14-16]. All the developed concepts have been based on experimental tensile and burst tests. Indeed, our aim is to assess the degradations through the damage modelling by referring only to static tests and models instead of tedious and very costly dynamic ones Therefore, we are using the results of the burst tests of HDPE pipes for a mathematical modeling of burst pressure evolution and damage evaluation. For that reason, we evaluated the characteristic pressures of these pipes, obtained from the internal pressure curve, which have been integrated in theoretical equations leading to the damage assessment. In this paper, new concepts based on the limit pressure formulas such as Faupel one [6] and continuum equation of pressure have been introduced. These formulas led to three ways of damage modeling of HDPE pipes: • A theoretical model based on the Faupel formula applying a corrective coefficient α; • An adaptive model using the pressure formulation, P (β), as a function of the life fraction and the critical life fraction and assuming that the applied pressure corresponds to the calculated pressure P (β) corresponding to the last experimental life fraction (86%); • A continuum damage model D (β), which takes values as a function of the life fraction β and the constant α and η and assumes an applied pressure equivalent to the experimental one (11.9 bar). This modeling is considering the theoretical calculations of the HDPE pipe’s burst pressure, for different notches’ depths, by either the Faupel or P (β) formulas. Therefore, we consider the burst pressure of a neat pipe as the ultimate rupture pressure, maximum pressure, while the other pressures, related to the notched pipes, are considered as the residual ones for both the theoretical and the adaptive damage models. For the continuum damage, it is taking into consideration the different pressures of the HDPE pipes as a function of the intervals of β. These approaches are validated and compared to the model of static damage obtained through the experimental burst pressures in order to evaluate their accuracy. M ATERIAL AND METHOD o determine the experimental burst pressures of the studied pipes, we used a hydrostatic tester allowing the control of the internal pressure until burst, Fig. 1. This test allowed us to determine the HDPE pipes’ resistance through their burst pressure. Thus, undamaged HDPE pipes and notched pipes, with a groove of 100 mm length, 5 mm width, and a variable depth from 1 to 5 mm, have been exposed to an increasing pressure until burst for the ultimate and residuals burst pressures determination. The specimens have been chosen according the ASTM code D1599 that requires a specimen with a length that should not exceed five times the diameter of the pipe. The specimens are prepared and conditioned at the room temperature (23 ° C) prior to pressurization. The burst pressures were evaluated, according to the notches’ depths experimentally and theoretically, as explained by the methodology shown in the Fig. 2. Then, the experimental burst pressures have been obtained and recorded, Tab. 1. It is having a proportional drop according to the increase of the notch depth. Figure 1 : Bursting of HDPE pipes and the specimen and notch dimensions. T PN 16 bar PE 100 Thickness = 5.8 mm Ultimate stage of failure 100 mm 5 Notch