DAMAGE MODELING IN GRADED LAYER SYSTEM

Open access

Abstract

The simplified approach to the modelling of low cycle fatigue (LCF) of functionally graded materials (FGM) based on the continuum mechanics is presented. The fatigue damage model takes into account the mechanical part of the load and a constant service temperature. The concept of FGM as a particle-reinforced metal-matrix composite with gradual change of the reinforcement fraction is used. The FGM is considered as a material consisting of homogeneous layers containing different volume fractions of the reinforcement. The variation of the reinforcement fraction changes the material properties for each layer. The different material properties are obtained according to modified rule of mixture. Since the fatigue damage of metal matrix composites is strongly influenced by the inelastic deformation of the metallic matrix, the constitutive equations of LCF damage model are taken into consideration. The combined isotropic/ kinematic hardening model with linear behaviour of isotropic and kinematic parts of hardening is adopted. The damage scalar parameter is associated with the plastic energy dissipation which is used to update the material properties. The fatigue damage model presented in this paper is applied to the fatigue damage analysis of the cooling channel of thruster used in space shuttles and rockets.

1. Andrews J.S., Armstrong W. H, (1974), Thrust Chamber Life Prediction, Boeing AeroSspace Company, (NASA-CB-144048).

2. Baldwin E. E., Sokol G. J., Coffin L. E (1957), Cyclic strain fatigue studies on AISI 347 stainless steel, Proceedings, American Society for Testing and Materials, 57, 567-586.

3. Bennett J. A. (1946), A study of the damaging effect of fatigue stressing on X4130 steel, Proceedings, American Society for Testing and Materials, 46, 693-714.

4. Bernard-Connolly M., Bui-Quoc T., Biron A. (1983), Multilevel strain controlled fatigue on a type 304 stainless steel, ASME Journal of Engineering Materials and Technology, 105, 188-194.

5. Biron A., Bui-Quoc T. (1981), Cumulative damage concepts with interaction effect consideration for fatigue or creep; a perspective, In Transactions of the 6th International Conference on Structural Mechanical Reaction Technology, Paris, France, L9/1.1-7.

6. Bizon P. T., Thoma D. J., Halford G. R. (1985), Interaction of high cycle and low cycle fatigue of Haynes 188 at 1400 F, In Structure Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381. NASA Lewis Research Center, Cleveland, OH, pp. 129-138.

7. Bluhm J. (1962), A note on fatigue damage, Materials Research and Standards.

8. Bui-Quoc T., Dubuc J., Bazergui A., Biron A. (1971), Cumulative fatigue damage under strain controlled conditions, Journal of Materials, 6, 3, 718-737.

9. Bui-Quoc T. (1981), An interaction effect consideration in cumulative damage on a mild steel under torsion loading, Proceedings of the 5th International Conference on Fracture, Pergamon Press, 5, 2625-2633.

10. Bui-Quoc T. (1982), Cumulative damage with interaction effect due to fatigue under torsion loading, Experimental Mechanics, 22, 180-187.

11. Bui-Quoc T. (1982), A simplified model for cumulative fatigue damage with interaction effects, In Proceedings of the 1982 Joint Conference on Experimental Mechanics, Society for Experimental Stress Analysis, Brookfield Center, CT, 144-149.

12. Carpenter R. D., Rabin B. H., Drake J.T. (1993), Finite Element Analysis of Thermal residual Stresses at Graded Ceramic-Metal Interface, Part I. Model Description and Geometrical Effects, J. Appl.Phys., Vol. 74, 2, 13010-1320.

13. Chaboche J. L. (1974), A differential law for nonlinear cumulative fatigue damage, In Materials and Building Research, Paris Institut Technique Du Batiment Et Des Travaus Publies, Annales de l'ITBTP, HS No. 39, 117-124.

14. Chaboche J. L., Kaczmarek H. (1981), On the interaction of hardening and fatigue damage in the 316 stainless steel, In Proceedings of the 5th International Conference on Fracture (ICF 5), Cannes, Vol. 3, Pergamon Press, Oxford, 1381-1393.

15. Chaboche J. L. (1982), Lifetime predictions and cumulative damage under high-temperature conditioned, In Low-cycle Fatigue and Life Prediction, ASTM STP 770, eds. C, Amzallag, B. N, Leis and P.Rabbe, American Society for Testing and Materials, Philadelphia, PA, 81-103.

16. Chaboche J. L., Lesne P. M. (1988), A non-linear continuous fatigue damage model, Fatigue and Fracture of Engineering Materials and Structures, 11, 1, 1-7.

17. Coffin L. F. (1956), Design aspects of high-temperature fatigue with particular reference to thermal stresses, Transactions of the ASME, 78, 527-532.

18. Corten H. T., Dolon T. J. (1956), Cumulative fatigue damage.

In Proceedings of the International Conference on Fatigue of Metals, Institution of Mechanical Engineering and American Society of Mechanical Engineers, 235-246.

19. Dubuc J., Bui-Quoc T., Bazergui A., Biron A. (1971), Unified theory of cumulative damage in metal fatigue. W.R. C. Bulletin, 162, 1-20.

20. Dunne F., Petrinic N. (2005), Introduction to Computational Plasticity,Oxford University Press, New York

21. French H. J. (1933), Fatigue and hardening of steels, Transactions, American Society of Steel Treating, 21, 899-946.

22. Freudenthal A. M. (1956), Physical and statistical aspects of cumulative damage, Springer-Verlag, Berlin, 53-62.

23. Freudenthal A. M., Heller R. A. (1959), On stress interaction in fatigue and a cumulative damage rule, Journal of the Aerospace Sciences, 26, 7, 431-442.

24. Gatts R. R. (1961), Application of a cumulative damage concept to fatigue, ASME Journal of Basic Engineering,83,529-540.

25. Gatts R. R. (1962), Cumulative fatigue damage with random loading, ASME Journal of Basic Engineering, 84, 403-409.

26. Glinka G, Shen G, Plumtree A. (1995), A multiaxial fatigue strain energy density parameter related to the critical plane, Fatigue Fract Eng Mater Struct; 18:37-46.

27. Golos K., Ellyin F. (1987), Generalization of cumulative damage criterion to multilevel cyclic loading, Theoretical and Applied Fracture Mechanics, 7, 169-176.

28. Golos K., Ellyin F. (1988), A total strain energy density theory for cumulative fatigue damage, ASME Journal of Pressure Vessel Technology, 110, 36-41.

29. Golos K., Ellyin F. (1989), Total strain energy density as a fatigue damage parameter, In Advances in Fatigue Science and Technology, Proceedings of the NATO Advanced Study Institute, cd. C. M.Branco and L. G. Rosa. Kluwer Academic, 849-859.

30. Grover H. J. (1960), An observation concerning the cycle ratio in cumulative damage, American Society for Testing and Materials, Philadelphia, PA , 120-124.

31. Halford G. R. (1966), The energy required for fatigue, Journal of Materials, 1(1), 3-18.

32. Halford G. R., Manson S. S. (1985), Reexamination of cumulative fatigue damage laws, In Structure Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381. NASA, 139-145.

33. Henry D. L. (1955), A theory of fatigue damage accumulation in steel, Transactions of the ASME, 77, 913-918.

34. Hua C. T., Socie D., F. (1984), Fatigue damage in 1045 steel under constant amplitude biaxial loading, Fatigue of Engineering Materials and Structures, 7, 3, 165-179.

35. Inglis N. P. (1927), Hysteresis and fatigue of Wohler rotating cantilever specimen, The Metallurgist, 23-27.

36. Kachanov L. M. (1969), Time to the rupture process under creep conditions, Izvestiia AN SSSR, 1984, OTN(8), 26-31.

37. Kommers J. B. (1945), The effect of overstress in fatigue on the endurance life of steel, Proceedings, American Society for Testing and Materials, 45, 532-541.

38. Kujawski D., Ellyin F. (1984), A cumulative damage theory of fatigue crack initiation and propagation, International Journal of Fatigue, 6, 2, 83-88.

39. Lagoda T. (2001), Energy models for fatigue life estimation under uniaxial random loading. Part I: The model elaboration. Int. J.Fatigue; 23:467-80.

40. Langer B. F. (1937), Fatigue failure from stress cycles of varying amplitude, ASME Journal of Applied Mechanics, 59, AI60-AI62.

41. Leis B. N. (1988), A nonlinear history-dependent damage model for low cycle fatigue, Low Cycle Fatigue, ASTM STP 942.

42. Leis B. N. (1997), An energy-based fatigue and creep-fatigue damage parameter, Journal of Pressure Vessel and Technology, ASME Transactions, 99(4), 52-+-533.

43. Lemaitre J., Chaboche J. L. (1978), Aspect phenomenologique de la ruptutre par endommagement, Journal Mecanique Appliquee, 2(3), 317-365.

44. Lemaitre J., Plumtree A. (1979), Application of damage concepts to predict creep-fatigue failures, ASME Journal of Engineering Materials and Technology, 101, 284-292.

45. Lemaitre J., Chaboche J. L. (1990), Mechanics of Solid Materials, trans. B. Shrivastava, Cambridge University Press, Cambridge, UK.

46. Li C., Qian Z. and Li G. (1989), The fatigue damage criterion and evolution equation containing material microparameters, Engineering Fracture Mechanics, 34(2), 435-443.

47. LLorca J. (2002), Fatigue of particle-and whisker-reinforced metalmatrix composites, Progress in Materials Science, 47, 283-353.

48. Machlin E. S. (1949), Dislocation theory of the fatigue of metals, N.A.C.A. Report 929.

49. Manson S. S. (1966), Interfaces between fatigue, creep, and fracture, International Journal of Fracture Mechanics, 2, 328-363.

50. Manson S. S., Halford G. R. (1981), Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage, International Journal of Fracture, 17(2), 169-192.

51. Manson S. S., Halford G. R. (1983), Complexities of hightemperature metal fatigue: some steps toward understanding, Israel Journal of Technology, 21, 29-53.

52. Marco S. M., Starkey W. L. (1954), A concept of fatigue damage, Transactions of the ASME, 76, 627-632.

53. Miner M. A. (1945), Cumulative damage in fatigue. Journal of Applied Mechanics, 67, AI59-AI64.

54. Morrow J. D. (1965), Cycle plastic strain energy and fatigue of metals. In Internal Friction, Damping, and Cyclic Plasticity, ASTM STP 378, American Society for Testing and Materials, Philadelphia, PA, 45-84.

55. Niu X. D. (1987), Memory behavior of stress amplitude responses and fatigue damage model of a hot-rolled low carbon steel. In Mechanical Behavior of Materials-V, Proceedings of the Fifth International Conference, Vol. 1, ed. M. G. Yan, S. H. Zhang and Z.

M. Zheng., Pergamon Press, Oxford, 685-690.

56. Niu X., Li G. X., Lee H. (1987), Hardening law and fatigue damage of a cyclic hardening metal, Engineering Fracture Mechanics, 26(2), 163-170.

57. Palmgren A. (1924), Die Lebensdauer von Kugellagern, Veifahrenstechinik, Berlin, 68, 339-341.

58. Plumtree A. and O'Connor B. P. D. (1989), Damage accumulation and fatigue crack propagation in a squeeze-formed aluminum alloy, International Journal of Fatigue, 11, 4, 249-254.

59. Rabotnov Y. N. (1969), Creep Problems in Structural Members, North-Holland, Amsterdam.

60. Radhakrishnan V. M. (1978), Cumulative damage in low-cycle fatigue, Experimental Mechanics, 18, 8, 292-296.

61. Radhakrishnan V. M. (1980), An analysis of low cycle fatigue based on hysteresis energy, Fatigue of Engineering Materials and Structures, 3, 75-84.

62. Richart F. E., Newmark N. M. (1948), A hypothesis for the determination of cumulative damage in fatigue, Proceedings, American Society for Testing and Materials, 48, 767-800.

63. Seweryn A, Buczyński A, Szusta J. (2008), Damage accumulation model for low cycle fatigue, Int. J. Fatigue, 1, 30:756-65.

64. Shanley F. R. (1952), A theory of fatigue based on unbonding during reversed slip, Report P-350, The Rand Corporation, Santa Monica.

65. Socie D. F., Fash J. W., Leckie F. A. (1983), A continuum damage model for fatigue analysis of cast iron, In Advances in Life Prediction Methods, ed, D. A. Woodford and J, R. Whitehead, The American Society of Mechanical Engineers, New York, 59-64.

66. Sutton Ch. E. (2009), Fatigue damage assessment of particlereinforced metal matrix composite materials under uniaxial and multiaxial loadings conditions, Digital Commons @ Ryerson, Toronto, Ontario.

67. Tamura I., Tomota Y., Ozawa H. (1973), Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength, Proceedings of the Third International Conference on Strength of Metals and Alloys, Vol. 1. Cambridge: Institute of Metals; 611-5.

68. Valluri S. R. (1961), A unified engineering theory of high stress level fatigue, Aerospace Engineering, 20, 18-19.

69. Valluri S. R. (1961), A theory of cumulative damage in fatigue.

Report No. ARL 182, Aeronautical Research Laboratory, Office of Aerospace Research, United States Air Force.

70. Weinacht D. J., Socie D. F. (1987), Fatigue damage accumulation in grey cast iron, International Journal of Fatigue, 9, 2, 79-86.

71. Wheeler O. E. (1972), Spectrum loading and crack growth, ASME Journal of Basic Engineering, D94(1), 181-186.

72. Willenborg J., Engle R. M., Wood H. A. (1971), A crack growth retardation model using an effective stress concept, AFFDL TM71-IFBR.

73. Williamson R. L., Rabin B. H., Drake J. T. (1993), Finite Element Analysis of Thermal residual Stresses at Graded Ceramic-Metal Interface, Part I. Model Description and Geometrical Effects, J. Appl. Phys., Vol. 74, 2, 13010-1320.

74. Zuchowski R. (1989), Specific strain work as both failure criterion and material damage measure, Res Mechanica, 27(4), 309-322.

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