PSI - Issue 3

Jilali Nattaj et al. / Procedia Structural Integrity 3 (2017) 579–587 Author name / Structural Integrity Procedia 00 (2017) 000–000

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Nomenclature σ a

Amplitude of applied stress; Stress level applied in fatigue;

Δσ σ u σ ur σ 0 σe

Ultimate constraint of the original material; Ultimate stress of the tired material, in static traction; Endurance limit of the original material in controlled stress;

Instantaneous endurance limit;

σ* 0 Critical endurance limit; γ = σ / σ 0 Nondimentional stress parameter; σ y Elastic limit of the material; E Modulus of elasticity; γ e σ e /σ 0 ; γ *e σ *e/ σ 0 ; γ u σ e /σ 0 , ; RRCB Rate of Reduction of Cycle’s number at Break (RRCB); N f0

The number of fracture cycles under a stress Δ σ = σ 0 corresponding to the endurance limit of the material which is close to 10 6 cycles for steel;

N f

Number of breaking cycles which represents a part of N f0; Number of breaking cycles which is given by experimentation; Number of breaking cycles which is given by the equation (11);

N fex N fc

1. Introduction Piping systems made of A36 steel are often subjected to cyclic loads due to pressure fluctuations. These pressure variations lead to fatigue phenomena of the material which is sometimes accelerated by the harmfulness of the defects such notches. From then, a deterioration of the expected lifetime of the impacted material occurs. In this case, a re-estimation of the material’s residual lifetime is required taking into consideration the type and the size of the defect. The new lifetime parameters will help the maintenance staff to make the right decisions. The re estimation of the lifetime involves an evaluation of the damage of the material at any moment. Various theoretical approaches have been developed in the literature to assess the accelerated degradation by focusing over two kind of behavior. On the one hand, Miner (1954) have proposed an approach dealing with the linearity of the damage. On the other hand, Gatts (1961) and Valuri (1965) have proposed a cumulative damage approach which is a nonlinear one. On the basis of the previous models, the unified theory has been developed as a nonlinear damage model taking into consideration the life fraction parameter and the experimental characteristics of the material. This model, have been compared to the RRCB approach developed in our research by calculating a new parameter proportional to the ratio of Nf/Nf0 based on the notched and undamaged specimens. Moreover, we have been able to determine the evolution of the damage as a function of the life fraction and the rate of reduction of the number of cycles to break resulting from fatigue and static tests. From then, we were able to quantify the damage of the notched specimens by the rate of reduction of the lifetime and compare it to the one evaluated through the unified theory approach. 2. Theory 2.1. Unified theory The loss of resistance may be associated with static tensile strength or fatigue strength under the effect of cyclic loading damage. The concept of energy damage associated with cyclic plastic deformation for stresses greater than the endurance limit was originally suggested by Henry and then taken up by Gatts. Using some characteristics of the theories of Shanley (1953) and Valluri (1965), Bui-Quoc (1969) developed the unified theory of fatigue; the author