PSI - Issue 25

Fatima Majid et al. / Procedia Structural Integrity 25 (2020) 430–437 Author name / Structural Integrity Procedia 00 (2019) 000–000

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By using the equation (5), we determined the ultimate number of cycles N f . Then, we calculated the number of cycle for each studied specimen. The figure 4 gives the (ε-N) curve evolution to predict the lifetime of HDPE material through the extracted specimens from an old pipe. From the curve, figure 4, we notice that the ultimate number of cycles is between 10 5 and 10 6 cycles. The obtained lifetime of the studied old HDPE pipes is reduced from a total number of cycles of 10 6 for a virgin material to 10 5 cycles for the old one. The damage is different from one specimen to another and so is the number of cycle. This variability allowed us to establish the Wöhler curve. According to the ISO code, the HDPE material is manufactured to work for 50 years. The most degraded specimen shows that it was working for 15.4 years. In fact, we were able to reproduce the consumed lifetime of the studied pipe through the tensile tests of the studied specimens only.

Fig. 4. (ε-N) curve for old HDPE specimens.

5. Discussion In this paper, we evaluated the static damage of the studied HDPE pipes. The discrepancies between them show that the material behavior is not the same for the main used parameters, as shown in Figure 5. For the stresses, we have noticed that the model is conservative in the propagation phase of the damage because of the stresses’ evolution. However, we have discussed for the energy parameter that the material is releasing its energy according to its mechanical behavior. While the material is shifting to embrittlement, the released energy is maximal. Furthermore, we were able to confirm the critical life fraction around 52% of the HDPE material. The damage curve of the strain model is below the half-life curve corresponding to the critical life fraction. From all the curves, we notice a fluctuation, which have a symmetrical form around βc, representing the damage of the old HDPE pipes as shown in the figure 5 below. The energy model represents the maximum limit of it. Meanwhile, the strain one represents its minimum limit. By analyzing this loop, we obtain the variation of the damage at the critical life fraction ΔD. This variation is almost constant in the second phase of damage. The damage evolution has three stages. The first one, initiation phase, corresponds to an interval of β between 0 and 20% with a slip of 4%. Then, the second one, propagation phase, corresponds to a value of β between 20% and 75% with a slip of 10%. Finally, the last stage, acceleration phase, is considered for a life fraction more than 75%. Therefore, by crossing the reliability loop and the damage one we define the experimental intervals for the stages of the HDPE material from, [0- βc1] for the stage I, [βc1- βc3] for the stage II and [βc3- 1] for the third one.