Belirsizliklerin yorulma ömrü üzerindeki etkilerinin aralık sayılar kullanarak analizi

Yıl 2024, Cilt: 39 Sayı: 2, 909 - 920, 30.11.2023

Ayşe Erdölen , Zafer Kütüğ

https://doi.org/10.17341/gazimmfd.1074423

Öz

Büyüklüğü zamanla değişen yüklemeler altında mühendislik yapılarındaki küçük yorulma çatlakları, daha sonrasında gelişerek ani ve yıkıcı hasarların oluşması gibi tehlikeli sonuçlara ulaşabilmektedir. Yorulma Çatlak Büyümesi (FCG) ömrünün güvenli bir aralıkta tanımlanması, bir sistemin işletme yükleri altında emniyetli bir şekilde çalıştırılması için son derece önemlidir. Bu sayede doğru bir bakım ve servis aralığının tespiti öngörülerek söz konusu hasarların aniden ortaya çıkması önlenebilmektedir. Diğer taraftan tasarım sürecinde yorulma performansının belirlenmesinde, yetersiz bilgilerden ve genellemelerden kaynaklanan bazı belirsizlikler söz konudur. Bu çalışmada, kırılma mekaniğine dayalı yorulma çatlak büyümesi tahmininde yer alan, malzeme, yük ve geometri parametrelerindeki belirsizliklerin etkileri Interval Analizi Yöntemini (Aralık Sayılar) kullanılarak sunulmuştur. Dolayısıyla, farklı türden parametrelerin belirsizlikleri dikkate alınarak, FCG life için alt ve üst sınırları ile belirlenmiş güvenli aralık değerlerin elde edilmesi hedeflenmektedir. Önerilen yöntem, EN-GJS-600-3 malzeme özelliklerine sahip bir plakanın yorulma çatlağı büyüme ömrünün tahminine uygulanmıştır. Matematiksel işlemlerde MatLab ara yüzü için geliştirilen interval toolboxlar kullanılarak, interval aritmetiğine özgün olarak hazırlanan bilgisayar kodu ile birlikte çalışması sağlanmıştır.

Anahtar Kelimeler

Yorulma, FCG, belirsizlik, interval analizi, Paris kanunu

Kaynakça

• 1. Anderson, T. L., Fracture Mechanics Fundamentals and Applications, CRC Pres., New York, USA, 2005.
• 2. Chowdhury P., Sehitoglu H., Mechanisms of fatigue crack growth – a critical digest of theoretical developments, Fatigue Fract Engineering Materials Structures, 39, 652–674, 2016.
• 3. Long X.Y., Jiang C., Liu K., Han X., Gao W., Li B.C., An interval analysis method for fatigue crack growth life prediction with uncertainty, Computers and Structures, 210, 1–1, 2018.
• 4. Besterfield G.H, Liu W.K, Lawrence M.A, Belytschko T., Fatigue crack growth reliability by probabilistic finite elements, Comput. Methods Appl. Mech. Eng., 86, 297–320, 1991.
• 5. Liu W.K, Chen Y, Belytschko T, Lua Y.J., Three reliability methods for fatigue crack growth, Eng. Fract. Mech., 53(5), 733-752, 1996.
• 6. Leonel E., Chateauneuf A., Venturini W., Bressolette P., Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation, Int. J. Fatigue, 32,1823–1834, 2010.
• 7. Sankararaman S., Ling Y., Shantz C.,. Mahadevan S., Model Calibration for Fatigue Crack Growth Analysis under Uncertainty, Proceedings of the IMAC-XXVIII, Jacksonville, Florida USA, February 1–4, 2010.
• 8. Sankararaman S., Ling Y., Shantz C., Mahadevan S., Uncertainty quantification in fatigue crack growth prognosis, International Journal of Prognostics and Health Management, ISSN 2153-2648, 2011.
• 9. Sankararaman S., Ling Y., Mahadevan S., Uncertainty quantification and model validation of fatigue crack growth prediction, Engineering Fracture Mechanics, 78, 1487–1504, 2011.
• 10. Cohen M.L., Kulkarni S.S., Achenbach J.D., Probabilistic approach to growth and detection of a truncated distribution of initial crack lengths based on Paris’ law, Struct. Health Monit., 11 (2), 225–236, 2012.
• 11. Robinson E. I., Marzat J., Raissi T., Model-based Prognosis Algorithms with Uncertainty Propagation: Application to Fatigue Crack Growth, Conference on Control and Fault-Tolerant Systems (SysTol), Barcelona, Spain, Sept. 7-9, 2016.
• 12. Wang L., Wang X.J., Su H., Lin G., Reliability estimation of fatigue crack growth prediction via limited measured data, Int. J. Mech. Sci, 121, 44–57, 2017.
• 13. Long X.Y., Liu K., Jianga C., Xiao Y., Wu S.C., Uncertainty propagation method for probabilistic fatigue crack growth life, Theoretical and Applied Fracture Mechanics, 103, 102268, 2019.
• 14. Mallor C., Calvo S., Núñez J.L., Rodríguez-Barrachina R., Landaberea A., Propagation of uncertainty in fatigue crack growth for probabilistic life estimation, Procedia Structural Integrity, 28, 619–626, 2020.
• 15. Tang H., Guo X., Xue S., Uncertainty quantification in small-timescale model-based fatigue crack growth analysis using a stochastic collocation method, Metals, 10, 646, 2020.
• 16. Ben-Haim Y, Elishakoff I., Convex Models of Uncertainty in Applied Mechanics, Elsevier, New York, USA, 2013.
• 17. Moore, R. E., Interval Analysis, Prentice Hall, Upper Saddle River, USA, 1966.
• 18. Moore, R. E., Methods and Applications of Interval Analysis, PA: SIAM, Philadelphia, USA, 1979.
• 19. Nuding, V. E., Wilhelm, J., Über gleichungen und über lösungen [On equations and solutions], ZAMM, 52:188–190, 1972.
• 20. Rao, S., Berke, L., Analysis of uncertain structural systems using interval analysis, AIAA J, 35 (2), 727–735, 1997.
• 21. Muhanna, R. L., Mullen, R. L., Development of Interval Based Methods for Fuzziness in Continuum Mechanics, Proceeding of the ISUMA-NAFIPS’95, Maryland, USA, 145–150, Sept. 17–20, 1995.
• 22. Mullen, R. L., Muhanna, R. L., Structural Analysis with Fuzzy-Based Load Uncertainty, Proceeding of the 7th ASCE EMD/STD Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, USA, Aug. 7–9, 1996.
• 23. Muhanna, R. L., Mullen, R. L., Formulation of fuzzy finite element methods for mechanics problems, Computer-Aided Civil and Infrastructure Engineering, (Previously Microcomputers in Civil Engineering), 14, 107–117, 1999.
• 24. Koyluoglu, H. U., Elishakoff, I. A, Comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties, Comput. Struct., 67, 91–98, 1998.
• 25. Muhanna, R. L., Mullen, R. L., Uncertainty in mechanics problems- Interval based approach, J. Eng. Mechanic, 127(6), 557–566, 2001.
• 26. Muhanna, R. L., Zhang, H., Mullen, R. L., Combined axial and bending stiffness in interval finite-element methods, Journal of Structural Engineering, 133(9), 1700–1709, 2007.
• 27. Rama R.M.V, Pownuk, A., Design of truss and frame structures with ,interval and fuzzy parameters, NAFIPS, New York, USA, 2008.
• 28. Qiu, Z., Wang, J., Reliability study of fracture mechanics based non-probabilistic interval analysis model, Fatigue and Fracture of Engineering Materials and Structures, 33, 539-548, 2010.
• 29. Zhang, H., Mullen, R., Muhanna, R.L., Interval monte carlo methods for structural reliability, Structural Safety, 32, 183-190, 2010.
• 30. Impollonia, N., Muscolino, G., Interval analysis of structures with uncertain-but-bounded axial stiffness, Comput. Methods Appl. Engrg, 200, 1945-1962, 2011.
• 31. Zhang, M.Q., Beer, M., Koh, C. G., Interval analysis for system identification of linear MDOF structures in the presence of modeling errors, Journal of Engineering Mechanics, 138(11), 1326-1338, 2012.
• 32. Hao, S., Xi, X., Qu, S., Shi, W., The application of interval analsis method in the stability analysis, Applied Mechanics and Materials, 117-119, 48-52, 2012.
• 33. Gau, X., Li, A., Luo, L., Wang, C., A new method for structural non-probabilistic reliability analysis based on interval analysis, Structural Non-Probabilistic Reliability, 73-79, 2015.
• 34. Liu, G., Mao, Z., Structural damage diagnosis with uncertainties quantified using interval analysis, Struct. Control Health Monit, 24, 1-12, 2017.
• 35. Qui, Z., Zhang, Z., Crack propagation in structures with uncertain-but-bounded parameters via interval method, Theoretical and Applied Fracture Mechanics, 98, 95-103, 2018.
• 36. Wanga L., Liang J., Yanga Y., Zheng Y., Time-dependent reliability assessment of fatigue crack growth modeling based on perturbation series expansions and interval mathematics, Theoretical and Applied Fracture Mechanics, 95, 104-118, 2018.
• 37. Wan Z., Zhang S.J., Zhou Y., Interval solution for nonlinear programming of maximizing the fatigue life of v-belt under polymorphic uncertain environment, Math. Problems Eng, 2013.
• 38. Qiu Z., Zhang Z., Crack propagation in structures with uncertain-but-bounded parameters via interval perturbation method, Theoretical and Applied Fracture Mechanics, 98, 95–103, 2018.
• 39. Paris P. C., Erdoğan F., A critical Analysis of crack propagation laws, Transactions of ASME, Journal of Basic Engineering, D85, 528-534, 1963.
• 40. Richard H. A., Sander M., Fatigue Crack Growth, Solid Mechanics and Its Applications, Springer International Publishing, Switzerland, 2016.
• 41. Griffith, A. A., The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc., A 221, 163-198, 1920.
• 42. Newman J.C., A crack opening stress equation for fatigue crack growth, Int. J. Fract., 24:R131–5, 1984.
• 43. Forman RG, Mettu SR., Behavior of Surface and Corner Cracks Subjected to Tensile and Bending Loads in Ti–6Al–4V Alloy, In: Fracture Mechanics: 22nd Symposium, Vol. 1, ASTM STP 1131, Philadelphia, USA, 519–546, 1992.