PSI - Issue 42

Vítor M. G. Gomes et al. / Procedia Structural Integrity 42 (2022) 1552–1559 V.M.G. Gomes et al. / Structural Integrity Procedia 00 (2019) 000–000

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of these spots was found by implementing an optimization algorithm, which determines the critical plane where the resolved shear stress is maximum. The numerical model included an elastoplastic analysis for the master leaf and elastic for the rest of the components. Combined hardening was introduced with parameters estimated by the monotonic properties of 51CrV4 steel. Regarding the boundary conditions attributed to the model, these took into account the actual fixation of a parabolic leaf spring in a two-axle freight wagon, as well as the imposed random displacement. Two scenarios for the imposed displacement were considered for analysis. From the application of the maximum variance method to the two scenarios under analysis, the following main remarks can be enumerated: • The places of greatest variation were created for both scenarios in the middle zone of the leaf spring. However, when an initial lateral displacement is applied (scenario 2), a potential for failure at the ends where the fibers are most active is verified; • Greater variability in the value of the amplitude of the vertical and lateral displacements (scenario 1) induces a greater potential for failure in the central zone of the notch. However, the same result for scenario 2, whose the variability of the components of lateral and vertical displacement is lower was not verified; • The zones closest to the fixing supports are almost symmetrical across the leaf width in both scenarios. Moreover, the maximum value of the variance of the resolved shear shears appears to occur at nearby of x = -60 mm and x = 60 mm. Additionally, significant changes do not exist between the two scenarios and this may conduct to the conclusion that the maximum value of the resolved shear stress will be influenced mainly by the vertical oscillation of the load.

Acknowledgments

The authors thank to MEDWAY (Maintenance and Repair), AI0181 - Research Project - FERROVIA 4.0 - POCI 01-0247-FEDER-046111, doctoral programme iRail- Innovation in Railway Systems and Technologies funding by the Portuguese Foundation for Science and Technology, IP (FCT) through the PhD grant (PD / BD / 143141 / 2019). Also, a thank you to the Python, Julia, and Ansys community.

References

Susmel, L., 2010. A simple and e ffi cient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems. International Journal of Fatigue, 32, 11, 1875–1883, http: // dx.doi.org / 10.3221 / IGF-ESIS.33.38. Snyman, J. A., 2005. Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms. Springer Publishing, http: // dx.doi.org / 10.1007 / b105200. UIC of Railways, 2007. Wagons – suspension gear – standardisation. International Organization for Standardization, 2004. Heat-treatable steels, alloy steels and, free-cutting steels part 14: Hot-rolled steels for quenched and tempered springs. Simo, J. C., Taylor, R. L., 1985. Consistent Tangent Operators for Rate-Independent Elastoplasticity, Computer Methods in Applied Mechanics and Engineering, 48, 101–118, http: // dx.doi.org / 10.1016 / 0045-7825(85)90070-2. Krieg, R. D., Krieg, D. B., 1977. Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model, Journal of Pressure Vessel Technology. Transactions of the ASME, 99, 4, 510–515, http: // dx.doi.org / 10.1115 / 1.3454568. Bathe, K. J., 1996. Finite Element Procedures. Prentice-Hall. Englewood Cli ff s. George, A., Liu, J. W. H., 1981. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Inc, http: // dx.doi.org / 10.1002 / bimj.4710260217. Simo, J. C., Laursen, T., 1992. An augmented lagrangian treatment of contact problems involving friction, Computers and Structures, 42, 97–116. http: // dx.doi.org / 10.1016 / 0045-7949(92)90540-G. Belytschko, T., Neal, M. O., 1991. Contact-impact by the pinball algorithm with penalty and Lagrangian methods, International Journal for Nu merical Methods in Engineering, 31, 3, 547–572. http: // dx.doi.org / 10.1002 / nme.1620310309. Muralidharan, U., Manson, S. S., 1988. A modified universal slopes equation for estimation of fatigue characteristics of metals, Journal of Engi neering Materials and Technology, 110, 1, 55–58. http: // dx.doi.org / 10.1115 / 1.3226010. Martins, J. R. R. A., Ning, A. 2021. Engineering Design Optimization. Cambridge University Press, 2021. ISBN:9781108833417. Stephens, R. I., Fatemi, A., Stephens, R. R., Fuchs, H. O. 2001.Metal Fatigue in Engineering, ISBN: 978-0-471-51059-8. Chaboche, L., 2008. A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity, 24, 10, 1693–1693., http: // dx.doi.org / 10.1016 / j.ijplas.2008.03.009. Matsumoto, M., Nishimura, T., 1998. Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modeling and Computer Simulation, 8, 1, 3–30. http: // dx.doi.org / 10.1145 / 272991.272995. Nocedal, J., Wright, S. J., 2006. Numerical Optimization. Springer New York, NY, 2nd Edition, http: // dx.doi.org / 10.1007 / 978-0-387-40065-5.

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