PSI - Issue 25

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

433

4

These models will be compared to a damage model based on the burst pressures. It was established for the notched pipes as validated in our paper (Majid and Elghorba, 2016). In order to predict the lifetime, through the prepared specimens of old HDPE pipes, we based our study on the strain controlled unified theory. The material loses its ductility due to the cumulative damage. The strain parameters are defined as shown by the equations (4). / ) ln( 1 0    ur   , / ) ln( 1 0    u f   (4) The number of life cycles is expressed in function of these parameters by:

      

      

(5)

1

1

 c b N K



   1

   

   







f 

K b and c are constant of the studied material determined by empirical formulas. 4. Results

From that on, we will get through to analytical models, based on the burst pressure and time to rupture, usually considered in fatigue and creep phenomenon. These are very simplified models inspired from the unified theory and adapted to a static testing method instead of a dynamic one. By doing this, we can check fastidious parameters of HDPE pipes and other thermoplastic pipes by doing only static tests, like tensile or burst tests, in a cost effective way.

Fig. 1. Damage and reliability curves for an old HDPE Pipe based on the stresses.

The superposition of the curves damage-reliability, for the model based on stresses, as shown in Figure 1, shows that there is an intersection at 23% of the life fraction. Beyond this point, the damage evolution changes its behavior and get under the reliability curve. It shows that we reach the end of the stage I at a maximum value corresponding to βc2 equal to 24%. Meanwhile, the beginning of the stage III starts at value of 75% of the life fraction. Furthermore, the superposition of those of the model based on the energy, as shown in Figure 2, shows that there is an intersection at 21.5% of the life fraction. Beyond this value, the damage evolution changes its behavior and get under the reliability