Modelling of stress gradient effect on fatigue life using Weibull based distribution function

• Autorzy: Karolczuk A. , Palin-Luc T.

Warianty tytułu

PL

Modelowanie efektu gradient naprężeń na trwałość zmęczeniową przy zastosowaniu funkcji bazującej na rozkładzie Weibulla

• Języki publikacji: EN

Abstrakty

EN

In the present paper, a new approach is developed in order to take into account the stress gradient effect on fatigue life of structural components. The proposed approach is based on the weakest link concept in which the shape coefficient of the Weibull distribution becomes a function of a local damage parameter. The function simulates the experimentally observed relationship between the shape of the fatigue life distribution and the stress level. Such an approach allows one to calculate the global probability distribution of the fatigue life for notched structural components in a wide range of fatigue life regime: 10⁴-10⁷ cycles typically. For comparison purposes, the approach is applied to calculate the number of cycles to crack initiation of structural elements under three probability levels: 5%, 63% and 95%. The calculated lifetimes are compared with the lifetimes obtained from experiments performed on notched cruciform specimens and notched round specimens subjected to constant amplitude loading.

PL

W artykule zaprezentowano nową koncepcję uwzględnienia wpływu gradientu naprężeń na trwałość zmęczeniową elementów konstrukcyjnych. Przedstawione podejście bazuje na koncepcji najsłabszego ogniwa, w której współczynnik kształtu rozkładu Weibulla jest funkcją lokalnego parametru uszkodzenia. Zaproponowana funkcja symuluje obserwowany eksperymentalnie związek między kształtem rozkładu trwałości zmęczeniowej a amplitudą naprężenia. Podejście takie umożliwia wyznaczenie globalnego rozkładu prawdopodobieństwa zniszczenia dla elementów z karbem w szerokim zakresie trwałości: 10⁴-10⁷ cykli. Dla celów porównawczych zaproponowane podejście zostało zastosowane do obliczenia liczby cykli do inicjacji pęknięcia dla trzech poziomów prawdopodobieństwa, tj. 5%, 63% oraz 95%. Obliczone trwałości zmęczeniowe zostały porównane z trwałością eksperymentalną otrzymaną dla próbek krzyżowych z karbem oraz dla próbek cylindrycznych z karbem obrączkowym.

Słowa kluczowe

EN

fatigue life; stress gradient effect; weakest link concept

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 2
• Strony: 297--311
• Opis fizyczny: Bibliogr. 38 poz., rys., tab.

Twórcy

autor

Karolczuk A.

• Opole University of Technology, Department of Mechanics and Machine Design, Opole, Poland

autor

Palin-Luc T.

• Universit´e Bordeaux 1, Arts et M´etiers ParisTech, I2M, UMR CNRS 5295, Talence Cedex, France

Bibliografia

• 1. ASTM E739-91, 1998, Standard Practices for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε − N) Fatigue Data, ASTM International, West Conshohocken, PA, www.astm.org
• 2. Banvillet A., Łagoda T., Macha E., Niesłony A., Palin-Luc T., Vittori J.-F., 2004, Fatigue life under non-Gaussian random loading from various models, Int. J. Fatigue, 26, 349-363
• 3. Banvillet A., Palin-Luc T., Lasserre S., 2003, A volumetric energy based high cycle multiaxial fatigue criterion, Int. J. Fatigue, 25, 755-769
• 4. Bastenaire F.A., 1972, New method for the statistical evaluation of constant stress amplitude fatigue-test results. Probabilistic aspects of fatigue, ASTM STP, 511, 3-28
• 5. Bathias C. and Paris P.C., 2005, Gigacycle Fatigue in Mechanical Practice Marcel Dekker Editions, New York
• 6. Bomas H., Mayr P., Schleicher M., 1997, Calculation method for the fatigue limit of parts of case hardened steels, Materials Science and Engineering, A234-236, 393-396
• 7. Bomas H., Linkewitz T. Mayra P., 1999, Application of a weakest-link concept to the fatigue limit of the bearing steel SAE 52100 in a bainitic condition, Fatigue Fract. Engng Mater. Struct., 22, 733-741
• 8. Bomas H., Mayr P. Linkewitz T., 1999, Inclusion size distribution and endurance limit of a hard steel, Extremes, 2, 2, 149-164
• 9. Carpinteri A., Spagnoli A., Vantadori S., 2003, A multiaxial fatigue criterion for random loading, Fatigue Fract. Engng Mater. Struct., 26, 515-522
• 10. COMSOL, 2006, Structural Mechanics Module User’s Guide, version 3.3
• 11. Dang Van K., 1983, Macro-micro approach in high-cycle multiaxial fatigue, [In:] Advances in Multiaxial Fatigue, McDowell D.L. and Ellis R. (Edit.), American Society for Testing and Materials STP 1191, 120-130
• 12. Dang Van K., Cailletaud G., Flavenot J.F., Le Douaron A., Lieurade H.P., 1989, Criterion for high cycle fatigue failure under multiaxial loading, [In:] Biaxial and Multiaxial Fatigue Brown M. and Miller K.J. (Edit.), Mechanical Engineering Publications, 459-478
• 13. Delahay T., Palin-Luc T., 2006, Estimation of the fatigue strength distribution in high-cycle multiaxial fatigue taking into account the stress–strain gradient effect, Int. J. Fatigue, 28, 474-484
• 14. Fatemi A., Zeng Z., Plaseied A., 2004, Fatigue behavior and life predictions of notched specimens made of QT and forged microalloyed steels, Int. J. Fatigue, 26, 663-672
• 15. Flaceliere L., Morel F., 2004, Probabilistic approach in high-cycle multiaxial fatigue: volume and surface effects, Fatigue Fract. Engng Mater. Struct., 27, 1123-1135
• 16. Han F., Billardon R., Beranger A.S., 1996, Fatigue failures maps of heterogeneous materials, Mechanics of Materials, 22, 11-21
• 17. Karolczuk A, Macha E., 2005, A review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials, Int. J. Fract., 134, 267-304
• 18. Karolczuk A., Lachowicz C.T., Rozumek D. Słowik J., 2007, Inicjacja i rozwój pęknięć zmęczeniowych w próbkach krzyżowych z karbem, Przegląd Mechaniczny, 12, 7, 18-23 [In Polish]
• 19. Karolczuk A., 2008,. Non-local area approach for fatigue life evaluation under combined reversed bending and torsion, Int. J. Fatigue, 30, 1985-1996
• 20. Miller K.J., O’Donnell W.J., 1999, The fatigue limit and its elimination, Fatigue Fract. Engng Mater. Struct., 22, 545-557
• 21. Morel F., Huyen N., 2008, Plasticity and damage heterogeneity in fatigue, Theoretical and Applied Fracture Mechanics, 49, 98-127
• 22. Morel F. and Palin-Luc T., 2002,. A non local theory applied to high cycle multiaxial fatigue, Fatigue Fract. Engng Mater. Struct., 25, 649-665
• 23. Murakami Y., Endo M., 1994, Effect of defect, inclusions and inhomogeneities on fatigue strength, Int. J. Fatigue, 16, 163-182
• 24. Papadopoulos I.V., Panoskaltsis V.P., 1996, Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion, Engng Fract. Mech., 55, 4, 513-528
• 25. Papadopoulos I.V., Davoli P., Gorla C., Filippini M., Bernasconi A., 1997, A comparative study of multiaxial high-cycle fatigue criteria for metals, Int. J. Fatigue, 19, 3, 219-235
• 26. Papadopoulos I.V., 2001, Long life fatigue under multiaxial loading, Int. J. Fatigue, 23, 831-849
• 27. Qylafku G., Azari Z., Gjonaj M, Pluvinage G., 1998, On the fatigue failure and life prediction for notched specimens, Materials Science, 34, 5, 604-618
• 28. Schijve J., 1993, A normal distribution or a Weibull distribution for fatigue lives, Fatigue Fract. Engng Mater. Struct., 16, 8, 851-859
• 29. Schijve J., 1994, Fatigue predictions and scatter, Fatigue Fract. Engng Mater. Struct., 17, 381-396
• 30. Schijve J., 2005, Statistical distribution functions and fatigue of structures, Int. J. Fatigue, 27, 1031-1039
• 31. Seweryn A., Mróz Z., 1998, On the criterion of damage evolution for variable multiaxial stress states, Int. J. Solids Structures, 35, 14, 1589-1616
• 32. Sonsino C.M., 2007, Course of SN-curves especially in the high-cycle fatigue regime with regard to component design and safety, Int. J. Fatigue, 29, 2246-2258
• 33. Taylor D., 1999, Geometrical effects in fatigue: a unifying theoretical model, Int. J. Fatigue, 21, 413-420
• 34. Weibull W., 1939, A statistical theory of the strength of materials, Royal Swed. Inst. Engng Res., 151, Sweden
• 35. Weibull W., 1949, A statistical representation of fatigue failures in solids, Transaction of the Royal Institute of Technology, 27, Sweden
• 36. Wormsen A., Sjödin B., Hrkegrd G. Fjeldstad A., 2007, Non-local stress approach for fatigue assessment based on weakest-link theory and statistics of extremes, Fatigue Fract. Engng Mater. Struct., 30, 1214-1227
• 37. Zheng X., Lü B., Jiang H., 1995, Determination of probability distribution of fatigue strength and expressions of P-S-N curves, Engng Fract. Mech., 50, 4, 483-491
• 38. Zheng X., Li Z., Lü B., 1996, Prediction of probability distribution of fatigue life of 15MnVN steel notched elements under variable-amplitude loading, Int. J. Fatigue, 18, 2, 81-86