PSI - Issue 39

Davide Leonetti et al. / Procedia Structural Integrity 39 (2022) 9–19 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4. Conclusion The paper presented an analytical approach to determine the SIFs and therefore estimate the fatigue crack growth rate of rolling contact fatigue defects in a LEFM framework using the weight function method. The stress state in the beam supported by an elastic foundation are calculated by superposition principle of local stresses due to contact and the stress state calculated using the beam theory and resulting from internal forces and moments. The equation of the elastic line of the Winkler beam under a spatially distributed load has been solved on the basis of the solution available for a concentrated force. The stresses due to the line load are obtained from existing theoretical solution from theory of elasticity. The proposed approach allows an acceptable estimation of the stress distribution within the Winkler beam, also in the vicinity of the line load, making it possible the calculation of the Stress Intensity Factors for mode I and mode II loading for an inclined edge crack subjected to a moving distributed load, a case often associated with RCF cracks using the weight functions. The trend of the Stress Intensity Factors, resulting from the applications of the proposed approach resulted in good agreement with similar simulations from literature. As compared to extensive numerical simulation, the proposed approach is significantly less expensive from a computational point of view. References Magel, E. E., 2011. Rolling contact fatigue: a comprehensive review, U.S. Department of Transportation, Report n. DOT/FRA/ORD-11/24 Sadeghi, F., Jalalahmadi, B., Slack, T. S., Raje, N., and Arakere, N. K., 2009. "A Review of Rolling Contact Fatigue." ASME. J. Tribol. October 2009; 131(4): 041403. Zerbst, U., Lundén, R., Edel, K. O., & Smith, R. A., 2009. Introduction to the damage tolerance behaviour of railway rails–a review. Engineering fracture mechanics, 76(17), 2563-2601. Li, Z., Zhao, X., Esveld, C., Dollevoet, R., & Molodova, M., 2008. An investigation into the causes of squats - Correlation analysis and numerical modeling. Wear, 265(9-10), 1349-1355. Li, Z., Dollevoet, R., Molodova, M., & Zhao, X., 2011. Squat growth - Some observations and the validation of numerical predictions. Wear, 271(1 2), 148-157. Pal, S., Valente, C., Daniel, W., & Farjoo, M., 2012. Metallurgical and physical understanding of rail squat initiation and propagation. Wear, 284, 30-42. Olzak, M., Stupnicki, J., &Wojcik, R., 1991. Investigation of crack propagation during contact by a finite element method. Wear, 146(2), 229-240. Bogdanski, S., Olzak, M., & Stupnicki, J., 1996. Numerical stress analysis of rail rolling contact fatigue cracks. Wear, 191(1-2), 14-24. Bogdański, S., Stupnicki, J., Brown, M. W., & Cann on, D. F. (1999). A two dimensional analysis of mixed-mode rolling contact fatigue crack growth in rails. In European Structural Integrity Society (Vol. 25, pp. 235-248). Elsevier. Wong, S. L., Bold, P. E., Brown, M. W., & Allen, R. J., 1996. A branch criterion for shallow angled rolling contact fatigue cracks in rails. Wear, 191(1-2), 45-53. Ringsberg, J. W., & Bergkvist, A., 2003. On propagation of short rolling contact fatigue cracks. Fatigue & Fracture of Engineering Materials & Structures, 26(10), 969-983. Farjoo, M., Pal, S., Daniel, W., & Meehan, P. A., 2012. Stress intensity factors around a 3D squat form crack and prediction of crack growth direction considering water entrapment and elastic foundation. Engineering Fracture Mechanics, 94, 37-55. Trollé, B., Gravouil, A., Baietto, M. C., & Nguyen-Tajan, T. M. L., 2012. Optimization of a stabilized X-FEM formulation for frictional cracks. Finite elements in analysis and design, 59, 18-27. Trollé, B., Baietto, M. C., Gravouil, A., Mai, S. H., & Nguyen-Tajan, T. M. L., 2013. XFEM crack propagation under rolling contact fatigue. In 5th Fatigue Design Conference, Fatigue Design 2013. Vol. 66, pp. 775-782. Maljaars, J., Steenbergen, H. M. G. M., & Vrouwenvelder, A. C. W. M., 2012. Probabilistic model for fatigue crack growth and fracture of welded joints in civil engineering structures. International journal of fatigue, 38, 108-117. Carpinteri, A., Brighenti, R., Huth, H. J., & Vantadori, S., 2005. Fatigue growth of a surface crack in a welded T-joint. International Journal of Fatigue, 27(1), 59-69. Tada, H., Paris, P., & Irwin, G., 2000. The analysis of cracks handbook. New York: ASME Press, 2, 1. Bueckner, H. F., 1970. Novel principle for the computation of stress intensity factors. Zeitschrift fuer Angewandte Mathematik &Mechanik, 50(9). Wu, X. R., & Carlsson, J., 1991. Weight functions and stress intensity factor solutions. Pergamon Press. Fett, T., & Munz, D., 1997. Stress intensity factors and weight functions. Computational Mechanics Publications. Pucillo, G. P., Carrabs, A., Cuomo, S., Elliott, A., & Meo, M., 2021. Cold expansion of rail-end-bolt holes: finite element predictions and experimental validation by DIC and strain gauges. International Journal of Fatigue, 106275. Leonetti, D., Maljaars, J., & Snijder, H. H., 2021. Fracture mechanics based fatigue life prediction for a weld toe crack under constant and variable amplitude random block loading - Modeling and uncertainty estimation. Engineering Fracture Mechanics, 242, 107487. Beghini, M., Bertini, L., & Fontanari, V., 1999. Weight function for an inclined edge crack in a semiplane. International Journal of fracture, 99(4), 281-292.