PSI- Issue 9

Fatima Majid et al. / Procedia Structural Integrity 9 (2018) 229–234 Fatima MAJID et al / Structural Integrity Procedia 9 (2018) 229 – 234

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used to evaluate the damage and reliability such as stress, strain, energy and burst pressure. Therefore, many approaches have been developed to assess the damage of metal and plastic materials. These models are not directly applicable to both of them without studying their behavior. Miner (1945) has proposed a linear model for cumulative damage evolution, which is proportional to the life fraction (ratio between the residual and the ultimate lifetime. Meanwhile others, such as Bui Quoc (1971) have proposed nonlinear models taking into consideration characteristic parameters of the studied material and the life fraction. Moreover, we developed for thermoplastic materials many simplified models based on those proposed in the literature. They are using the residual time, the stress, and the burst pressure as main parameters for damage evaluation Majid (2016,2017). For HDPE pipes, it has been found that the life fraction, which is the thickness fluctuation over the initial one, becomes critical while exceeding 52% of the thickness reduction. Other researches has studied the HDPE pipes from another point of view by taking other degradation effect such as UV and accelerated damages L.P. Real (2003). Nomenclature γ is the instantaneous non-dimensional endurance limit. W ur is the ultimate residual pressure. W u is the ultimate pressure corresponding to an undamaged HDPE specimen. W a is the pressure just before the rupture. W 0 is the endurance limit’s corresponding pressure. 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. In this paper, we are leading a new approach based on the energy parameter in order to assess the damage of thermoplastic HDPE pipes through two categories of specimens, which are notched and aged HDPE pipes. For the first category, artificial notches have been created to evaluate their effect over the damage evolution while for the second a natural degradation has been considered, which highlight the fluctuating service pressure from 3 to 6 bars during 15 years in a buried HDPE piping network, the expected chemical attacks and the severe usage environment of these pipes. The results of the burst test and the tensile tests have been discussed, regarding different kinds of solicitations and loadings, in order to analyze the general behavior of the HDPE material. 2. Static damage models and energetic modeling The unified theory assesses the cumulative damage of materials subjected to fatigue phenomena completed by a simple static tensile test until getting to failure. Indeed, the residual endurance limit at failure, after a predefined number of fatigue cycles, is estimated at each step. In our case, a simplified approach, based on artificial notches that have been undertaken as a fatigue preloading, has been developed. It is directly using the burst pressure test’ s results of neat and notched pipes instead of stresses for newly produced pipes. For old pipes, the natural damage, which is different from one specimen to another, is considered as the preloading of the material. Then, standard specimens are subjected to tensile tests as per the unified theory principles. Therefore, the notch depth and the consumed number of cycles are proportional. In the next steps of this paper, the internal pressure and the ( σ , ɛ ) curves evolutions will be considered for energy evaluation and the damage calculations based on it. The static damage using the stresses is expressed as follows:

1





(1)

D



ec e

1





With : γ e = σ ur / σ u and γ ec = σ a / σ u Considering the proportionality between the energy parameter and the stresses, we obtain the static damage based on energy as shown by the equation (2):