PSI - Issue 3

Fatima Majid et al. / Procedia Structural Integrity 3 (2017) 387–394

388 388

Fatima Majid et al. / Procedia Structural Integrity 3 (2017) 387 – 394

Nomenclature γ

is the instantaneous non-dimensional endurance limit. is the instantaneous number of cycles under an applied stress.

n

N f P ur

is the total number of cycles at the rupture.

is the ultimate residual pressure.

P u P a P 0 σ θ

is the ultimate pressure corresponding to an undamaged HDPE specimen.

is the pressure just before the rupture.

is the endurance limit’s corresponding pressure.

is the circumferential stress. is the radius of the pipe specimen. is the thickness of the pipe specimen.

R

e

D is the damage (D = 0 for neat material, D = 1 for completely damaged material). β= (∆e/e) = (n/N f ) is the life fraction in which ∆e is corresponding to the thickness fluctuation.

1. Introduction Predicting and evaluating the mechanical behavior have been a serious concern for a long period. Thus, many models have been developed in the literature to quantify the damage of steel materials, either by referring to linear models or non-linear ones. Miner (1945) showed in his studies that the damage evolution is always linear and it is directly proportional to the ratio between the number of cycle of the damaged specimen and the ultimate number of cycles (n/N f ). However, Shaneley, Valuri, Gatts and Henry have developed non-linear damage theories showing a different behavior of the materials and expressing the non-linearly of the damage evolution in function of the life fraction, Bathias and Pineau (2013). Furthermore, Bui-Quoc (1971) was able to establish a unified theory based on Shaneley, Valuri and Gatts ones. The previous theories were widely applied to steel materials and their alloys [8-9]. In order to take benefit from these theories, we intend to apply them over thermoplastic polymers such us HDPE and PPR. So, many researches have been launched over these materials to quantify their mechanical behavior. Thus, Litvinov and Soliman (2005) have studied the fracture modes and the effect of temperature on the rupture time of PPR tubes subjected to hydrostatic pressure tests at different temperatures to investigate the influence of pressure time and temperature on the intrinsic characteristics of PPR. Furthermore, Zgoul et al (2008) have evaluated the convenience of thermoplastic tubes in transporting domestic and industrial hot water by comparing PPR to PEX tubes in terms mechanical strength under pressure. Besides, Greetz et al (2009) have put under hydrostatic pressure pipes in the PPR for a long time, the purpose was the study of the influence of the internal pressure and the temperature on the diffusion of an antioxidant. For HDPE pipes, Majid (2016) has published a paper giving rise to a new concept of damage modeling allowing a reproduction of the burst pressure mathematically through Faupel formulas and established the static damage model. In another work, a validation of the static damage model for A36 and P265GH metals have been done. Majid (2017) has proceeded to the failure analysis and the damage modeling of HDPE pipes subjected to an internal pressure through three damage models using the burst pressure and the residual time to failure. In this paper, we are introducing the results of newly developed non-linear damage models applied to those two materials. In fact, we are basing our study over the obtained burst pressures of groove notched pipes ’ specimens. The developed model is a modified version of the static damage of the unified theory. Besides, the comparison of the internal burst pressure and the notched pipes’ burst pressure evolutions according to time and the notch depth respectively allowed us to predict the mechanical behavior of the two polymers.