Issue 64

F. Gugouch et alii, Frattura ed Integrità Strutturale, 64 (2023) 218-228; DOI: 10.3221/IGF-ESIS.64.14

P

  0.7713 1.4838 0.4812 e

ur u



(9)

P

Fig. 7 shows the drop in dimensionless burst pressure according to the life fraction. From Fig. 7, we see there is a progressive decrease in the burst pressure of the tubes as the critical life fraction increases. Damage The appearance of damage affects the physical and mechanical properties of the materials. Therefore, the damage theory aims to studying the evolution of the material behavior of the virgin state to the initiation of macroscopic cracks of the size of the representative volume element [30-31]. There are numerous types of laws in the literature that can model the damage from experimental results, but we limit ourselves here to the ERISMANN model [32]. ERISMANN postulates that at each moment in the life of a material, the damage is modeled as an entire configuration of certain significant physical parameters such as (load drop, hardness, strength... etc.). It is given by the following equation [33]:                0 0 R x x D x x (10) ϕ (x): Well-defined monotonic function of x. x: Property value of the damage. O, R: index of beginning and end of life. The function ɸ represents the variation of some parameters, for example (load drop, hardness, toughness, etc.). Our approach in this work is based on the artificial damage of tubes under pressure. As the notch depth increases; the ultimate pressure decreases. Therefore, by analogy with the law’s ERISEMANN, we can consider that the variation of the residual ultimate pressure redresented by the function ɸ and X represents the fraction of life, i.e. ɸ (x) = Uur ( β ) from which the static damage by pressure is given by the following expression:             0 1 0 ur u a u P P D P P (11)

Pu: the ultimate pressure of the tube when the material is virgin. Pur: the material ultimate residual pressure when it is artificially damaged Pa: the value of pressure just before rupture. The damage evolution in function of the fraction of life is given in Fig. 8.

Figure 8: The static damage evolution based on the bursting pressures as a function of the fraction of life.

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