Issue 43

F. Majid et alii, Frattura ed Integrità Strutturale, 43 (2018) 97-105; DOI: 10.3221/IGF-ESIS.43.07 102 rupture). Moreover, the damage-reliability curves, Fig. 6, allowed us to define precisely the critical life fraction for both of them. Indeed, the critical life fractions are 52% and 58% for both HDPE and PPR respectively. The damage stages of them are different. Therefore, the first stage limit is 20% and 38%, the second one 75% and 78% and third over the last values for HDPE and PPR respectively. The performance of HDPE and PPR have a similar performance regarding the damage behavior and the criticism of thickness reduction. However, the two materials are very different considering the elastic and the rupture limits and the time to failure. In fact, the neat PPR reaches the burst pressure of 135 bars in 14 s. Meanwhile, the HDPE reaches the burst pressure of 69.5 bars at 49 s. The range of each pipe can explain the discrepancies of these values, the PPR pipes are PN20 and those of HDPE are PN16, and the thickness differences. In fact, we used the existing pipes in the market. Furthermore, we were able to validate previous researches done over HDPE, by comparing the HDPE and PPR performances and developing the modified version of the static damage model based on the burst pressures instead of the stresses as published in the literature [7,14]. Unlike the damage, reliability begins with the value of one, corresponding to the absence of damage, and decreases gradually as the notch depth increases; the total failure of the material is indicated by the zero value. The superposition of damage and reliability curves defines the life fraction at 52% and 58% of reliability for HDPE and PPR respectively. This point is located at the end of stage II and allows the maintenance department to decide on the time of reparation or even the change of the defected pipe. Figure 6 : PPR and HDPE’s damage-reliability evolution in function of the life fraction. Unified theory damage The variation of the unified theory damage in function of the fraction life  is given in the Fig. 7. The unified damage is indicated by a set of curves associated with a constant pressure ratio / u u a P P   ( u P =129.3bars and a P = 20bars) and variable parameter / ur a P P   . Therefore, each curve is associated with a separate level of applied pressure. In the direction of increasing of γ, the curves of the unified theory damage grow to reach the linear tendency for high loading levels. Comparison of static and unified theory damages Fig. 8 shows the variation of experimental and unified theory damages ( 6.46 u   ) and that proposed by Miner in function of the β the life fraction. For low life fractions (0% <β<16%), experimental damage and unified theory damage at a loading level γ = 1.27 are similar. With the increase of the life fraction β, the curve of static damage approaches tend to reach the unified damage corresponding to the loading level γ = 1.9 until they overlay at the end of Stage I. Then, in the beginning