Estimating High Cycle Fatigue Lifetime using Chaboche-Lemaitre Damage Model
Authors
Abstract
This article predicts lifetime of high cycle fatigue loading using Chaboche-Lemaitre damage model. The Chaboche-Lemaitre damage model takes into account mean stress effect as well as compressive stresses effect, making crack to close. In the this paper, a numerical algorithm is offered to integrate this model implicitly and the obtained algorithm is implemented as a user material subroutine of the ABAQUS finite element software. To reduce computation time, Jump-in-Cycles procedure is used based on fatigue loading simulation. To verify the proposed algorithm, a V-notched specimen is chosen under a fatigue loading with different stress ratios, and its lifetime is compared with experiments. Next, an aviation industry part, main rotor spindle of an aircraft blades, subjected to a variable fatigue loading is analysed.
Keywords
1. Lemaitre, J., A Course on Damage Mechanics, 1st Edition, Springer, Berlin, 1992.
2. Fatemi, A., and Yang, L., “Cumulative Fatigue Damage and Life Prediction Theories: A Survey of the State of the Art for Homogeneous Materials”, International Journal of Fatigue, Vol. 20, No. 1, pp. 9-34, 1998.
3. Jing, J. P.,Sun, Y., Xia, S. B., and Feng, G. T., “A Continuum Damage Mechanics Model on Low Cycle Fatigue Life Assessment of Steam Turbine Rotor”, International Journal of Pressure Vessels and Piping, Vol. 78, No. 1, pp. 59-64, 2001.
4. Rinaldi, A., Peralta, P., Krajcinovic, D., and Lai, Y. C., “Prediction of Scatter in Fatigue Properties using Discrete Damage Mechanics”, International Journal of Fatigue, Vol. 28, No. 9, pp. 1069-1080, 2006.
5. Lemaitre, J., Sermage, J., and Desmorat, P. R., “A Two Scale Damage Concept Applied to Fatigue”, International Journal of Fracture, Vol. 97, No. 1, pp. 67-81, 1999.
6. Desmorat, R., Kane, A., Seyedi, M., and Sermage, J. P., “Two Scale Damage Model and Related Numerical Issues for Thermo-Mechanical High Cycle Fatigue”, European Journal of Mechanics A/Solids, Vol. 26, No. 6, pp. 909-935, 2007.
7. Mashayekhi, M., “A Two Scale Damage Model for High Cycle Fatigue Life Prediction of Mechanical Components”, Esteghlal Journal of Engineering, Vol. 31, No. 1, pp. 15-28, 2012. (In persian).
8. Bogard, F., Lestriez, P., and Guo, Y. Q., “Damage and Rupture Simulation for Mechanical Parts under Cyclic Loadings”, Journal of Engineering Materials and Technology, Vol. 132, No. 2, pp. 0210031-0210038, 2010.
9. Zhang, T., McHugh, P. E., and Leen, S. B., “Finite Element Implementation of Multiaxial Continuum Damage Mechanics for Plain and Fretting Fatigue”, International Journal of Fatigue, Vol. 44, pp. 260-272, 2012.
10. Chaboche, J. L., “Une Loi Différentielle D’endommagement de Fatigue Avec Cumulation non Linéaire”, Revue Française de Mécanique, Vol. 50, No. 51, pp. 71-82, 1974.
11. Lemaitre, J., and Plumtree, A., “Application of Damage Concepts to Predict Creep-Fatigue Failures”, Journal of Engineering Materials and Technology, Vol. 101, No. 3, pp. 284-292, 1979.
12. Chaboche, J. L., and Lesne, P. M., “A Non-Linear Continuous Fatigue Damage Model”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 11, No. 1, pp. 1-17, 1988.
13. Lemaitre, J., “Local Approach of Fracture”, Engineering Fracture Mechanics, Vol. 25, No. 5, pp. 523-537, 1986.
14. Wang, J., “A Continuum Damage Mechanics Model for Low-Cycle Fatigue Failure of Metals”, Engineering Fracture Mechanics, Vol. 41, No. 3, pp. 437-441, 1992.
15. Wang, T., and Lou, Z., “A Continuum Damage Model for Weld Heat Affected Zone under Low Cycle Fatigue Loading”, Engineering Fracture Mechanics, Vol. 37, No. 4, pp. 825-829, 1990.
16. Li, C., Qian, Z., and Li, G., “The Fatigue Damage Criterion and Evolution Equation Containing Material Microparameters”, Engineering Fracture Mechanics, Vol. 34, No. 2, pp. 435-443, 1989.
17. Lemaitre, J., and Chaboche, J. L., Mechanics of Solid Materials, 1st Edition, Cambridge University Press, 1990.
18. Marmi, A. K., Habraken, A. M., and Duchene, L., “Multiaxial Fatigue Damage Modelling at Macro Scale of Ti–6Al–4V alloy”, International Journal of Fatigue, Vol. 31, No. 11, pp. 2031-2040, 2009.
19. Dattoma,V., Giancane, S., Nobile, R., and Panella, F. W., “Fatigue Life Prediction under Variable Loading Based on a new Non-Linear Continuum Damage Mechanics Model”, International Journal of Fatigue, Vol. 28, No. 2, pp. 89-95, 2006.
20. Sines, G., Behavior of Metals under Complex Static and Alternating Stresses , Metal fatigue, New York: McGraw-Hill, 1959.
21. 21.Simo, J. C., and Hughes, T. J. R., Computational Inelasticity, Springer, New York, 1998.
22. Lemaitre, J., Desmorat, R., Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, Springer, Berlin, 2005.
23. Van Paepegem, W., Degrieck, J., and Baets, P. De, “Finite Element Approach for Modelling Fatigue Damage in Fibre-Reinforced Composite Materials”, Composites Part B: Engineering, Vol. 32, No. 7, pp. 575-588, 2001.
24. Raje, N., Slack, T., and Sadeghi, F., “A Discrete Damage Mechanics Model for High Cycle Fatigue in Polycrystalline Materials Subject to Rolling Contact”, International Journal of Fatigue, Vol. 31, No. 2, pp. 346-360, 2009.
25. Warhadpande, A., Jalalahmadi, B., Slack, T., and Sadeghi, F., “A New Finite Element Fatigue Modeling Approach for Life Scatter in Tensile Steel Specimens”, International Journal of Fatigue, Vol. 32, No. 4, pp. 685-697, 2010.
26. Naderi, M., Hoseini, S. H., and Khonsari, M. M., “Probabilistic Simulation of Fatigue Damage and Life Scatter of Metallic components”, International Journal of Plasticity, Vol. 43, pp. 101-115, 2013.
27. Military Handbook MIL-HDBK-5H, Metallic Materials and Elements for Aerospace Vehicle Structures, US Department of Defense, 1998.
28. Conradi, K., “Report on the Accident to Aerospatiale (Eurocopter) AS 332L Super Puma Registration G-PUMI at Aberdeen Airport”, Department for Transport, Hampshire, U.K., 2010.
29. Forth, S. C., Everett, R. A., and Newman, J. A., “A Novel Approach to Rotorcraft Damage Tolerance”, 6th Joint FAA/DoD/NASA Aging Aircraft Conference, San Francisco, California, 2002.
2. Fatemi, A., and Yang, L., “Cumulative Fatigue Damage and Life Prediction Theories: A Survey of the State of the Art for Homogeneous Materials”, International Journal of Fatigue, Vol. 20, No. 1, pp. 9-34, 1998.
3. Jing, J. P.,Sun, Y., Xia, S. B., and Feng, G. T., “A Continuum Damage Mechanics Model on Low Cycle Fatigue Life Assessment of Steam Turbine Rotor”, International Journal of Pressure Vessels and Piping, Vol. 78, No. 1, pp. 59-64, 2001.
4. Rinaldi, A., Peralta, P., Krajcinovic, D., and Lai, Y. C., “Prediction of Scatter in Fatigue Properties using Discrete Damage Mechanics”, International Journal of Fatigue, Vol. 28, No. 9, pp. 1069-1080, 2006.
5. Lemaitre, J., Sermage, J., and Desmorat, P. R., “A Two Scale Damage Concept Applied to Fatigue”, International Journal of Fracture, Vol. 97, No. 1, pp. 67-81, 1999.
6. Desmorat, R., Kane, A., Seyedi, M., and Sermage, J. P., “Two Scale Damage Model and Related Numerical Issues for Thermo-Mechanical High Cycle Fatigue”, European Journal of Mechanics A/Solids, Vol. 26, No. 6, pp. 909-935, 2007.
7. Mashayekhi, M., “A Two Scale Damage Model for High Cycle Fatigue Life Prediction of Mechanical Components”, Esteghlal Journal of Engineering, Vol. 31, No. 1, pp. 15-28, 2012. (In persian).
8. Bogard, F., Lestriez, P., and Guo, Y. Q., “Damage and Rupture Simulation for Mechanical Parts under Cyclic Loadings”, Journal of Engineering Materials and Technology, Vol. 132, No. 2, pp. 0210031-0210038, 2010.
9. Zhang, T., McHugh, P. E., and Leen, S. B., “Finite Element Implementation of Multiaxial Continuum Damage Mechanics for Plain and Fretting Fatigue”, International Journal of Fatigue, Vol. 44, pp. 260-272, 2012.
10. Chaboche, J. L., “Une Loi Différentielle D’endommagement de Fatigue Avec Cumulation non Linéaire”, Revue Française de Mécanique, Vol. 50, No. 51, pp. 71-82, 1974.
11. Lemaitre, J., and Plumtree, A., “Application of Damage Concepts to Predict Creep-Fatigue Failures”, Journal of Engineering Materials and Technology, Vol. 101, No. 3, pp. 284-292, 1979.
12. Chaboche, J. L., and Lesne, P. M., “A Non-Linear Continuous Fatigue Damage Model”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 11, No. 1, pp. 1-17, 1988.
13. Lemaitre, J., “Local Approach of Fracture”, Engineering Fracture Mechanics, Vol. 25, No. 5, pp. 523-537, 1986.
14. Wang, J., “A Continuum Damage Mechanics Model for Low-Cycle Fatigue Failure of Metals”, Engineering Fracture Mechanics, Vol. 41, No. 3, pp. 437-441, 1992.
15. Wang, T., and Lou, Z., “A Continuum Damage Model for Weld Heat Affected Zone under Low Cycle Fatigue Loading”, Engineering Fracture Mechanics, Vol. 37, No. 4, pp. 825-829, 1990.
16. Li, C., Qian, Z., and Li, G., “The Fatigue Damage Criterion and Evolution Equation Containing Material Microparameters”, Engineering Fracture Mechanics, Vol. 34, No. 2, pp. 435-443, 1989.
17. Lemaitre, J., and Chaboche, J. L., Mechanics of Solid Materials, 1st Edition, Cambridge University Press, 1990.
18. Marmi, A. K., Habraken, A. M., and Duchene, L., “Multiaxial Fatigue Damage Modelling at Macro Scale of Ti–6Al–4V alloy”, International Journal of Fatigue, Vol. 31, No. 11, pp. 2031-2040, 2009.
19. Dattoma,V., Giancane, S., Nobile, R., and Panella, F. W., “Fatigue Life Prediction under Variable Loading Based on a new Non-Linear Continuum Damage Mechanics Model”, International Journal of Fatigue, Vol. 28, No. 2, pp. 89-95, 2006.
20. Sines, G., Behavior of Metals under Complex Static and Alternating Stresses , Metal fatigue, New York: McGraw-Hill, 1959.
21. 21.Simo, J. C., and Hughes, T. J. R., Computational Inelasticity, Springer, New York, 1998.
22. Lemaitre, J., Desmorat, R., Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, Springer, Berlin, 2005.
23. Van Paepegem, W., Degrieck, J., and Baets, P. De, “Finite Element Approach for Modelling Fatigue Damage in Fibre-Reinforced Composite Materials”, Composites Part B: Engineering, Vol. 32, No. 7, pp. 575-588, 2001.
24. Raje, N., Slack, T., and Sadeghi, F., “A Discrete Damage Mechanics Model for High Cycle Fatigue in Polycrystalline Materials Subject to Rolling Contact”, International Journal of Fatigue, Vol. 31, No. 2, pp. 346-360, 2009.
25. Warhadpande, A., Jalalahmadi, B., Slack, T., and Sadeghi, F., “A New Finite Element Fatigue Modeling Approach for Life Scatter in Tensile Steel Specimens”, International Journal of Fatigue, Vol. 32, No. 4, pp. 685-697, 2010.
26. Naderi, M., Hoseini, S. H., and Khonsari, M. M., “Probabilistic Simulation of Fatigue Damage and Life Scatter of Metallic components”, International Journal of Plasticity, Vol. 43, pp. 101-115, 2013.
27. Military Handbook MIL-HDBK-5H, Metallic Materials and Elements for Aerospace Vehicle Structures, US Department of Defense, 1998.
28. Conradi, K., “Report on the Accident to Aerospatiale (Eurocopter) AS 332L Super Puma Registration G-PUMI at Aberdeen Airport”, Department for Transport, Hampshire, U.K., 2010.
29. Forth, S. C., Everett, R. A., and Newman, J. A., “A Novel Approach to Rotorcraft Damage Tolerance”, 6th Joint FAA/DoD/NASA Aging Aircraft Conference, San Francisco, California, 2002.
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