16 Generalization of Integral Parameters to Fatigue Loading in Room Temperature 119 Table 16.2 Paris-Erdogan’s coefficients C m RMSE 3.45 10 13 3.64 0.14 life of the standard Al7075-T6 tensile test specimen. The numerical results can be enhanced using others crack growth models which allows to take into account the crack closure and/or the mean stress effects. 16.5 Conclusions In this paper, a numerical methodology coupling independent path integral and crack growth model is developed to evaluate the fatigue life. The results in term of SIF, given by the M-integral approach, are in good agreement with the analytical reference solutions since the relative error is very small. Unfortunately, Paris-Erdogan’s model underestimates the fatigue crack growth life of the tested specimen. Thus, more accurate crack growth models, such as Walker and Forman laws, should be investigated. In addition, the coming work will be focused on the analysis of crack growth under random loading, where crack retardation phenomena will be closely investigated. Finally, probabilistic approach will be used in order to take into account the effect of uncertainties of the material properties, the crack geometry and the loading conditions, on the variability of the fatigue crack growth. References 1. Paris, P., Erdogan, F.: A critical analysis of crack propagation laws. J. Basic Eng. 85, 528–534 (1963) 2. Bui, H.D., Proix, J.M.: Découplage des modes mixtes de rupture en thermoélasticité linéaire par les intégrales indépendantes du contour. In: Actes du troisième colloque Tendances Actuelles en Calcul de Structure, Bastia, pp. 631–643 (1985) 3. Riahi, H., Moutou Pitti, R., Dubois, F., Chateauneuf, A.: Mixed-mode fracture analysis combining mechanical thermal and hydrological effects in an isotropic and orthotropic material by means of invariant integrals. Theor. Appl. Fract. Mech. 85(Part B), 424–434 4. Suo, X.G., Combescure, A.: On the application of the G™method and its comparison with the Lorenzi’s approach. Nucl. Eng. Des. 135, 207–224 (1992) 5. Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Crack Handbook, 3rd edn. ASME, New York (2000) 6. Grandt Jr., A.F.: Stress intensity factors for some through-cracked fastener holes. Int. J. Fract. 11(2), 283–294 (1975)
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