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Simulation of crack extension in shell structures and prediction of residual strength

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Abstract

Two models for the numerical simulation of ductile crack extension in shell structures are presented and compared. They are based on the crack tip opening angle and a cohesive zone approach. After identification of the model parameters and investigations of the mesh dependence, the models are applied to various specimen configurations and structural components. Their excellent numerical performance favors their application for predicting the residual strength of lightweight components like aircraft fuselages.

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References

  1. ASTM E 1290. Standard test method for crack tip opening displacement (CTOD) fracture toughness measurement. Annual Book of ASTM Standards, vol. 03.01 (1993)

  2. Barenblatt G.I. (1962): The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129

    Article  MathSciNet  Google Scholar 

  3. Brocks W. (2004): Computational fracture mechanics. In: Raabe D., Roters F., Barlat F., Chen L.Q. (eds) Continuum Scale Simulation of Engineering Materials. Wiley-VCH, Weinheim, pp. 621–637

    Chapter  Google Scholar 

  4. Brocks W. (2005): Cohesive strength and separation energy as characteristic parameters of fracture toughness and their relation to micromechanics. Struct. Integr. Durab. 1, 233–244

    Google Scholar 

  5. Brocks W., Cornec A., Scheider I. (2003): Computational aspects of nonlinear fracture mechanics. In: Milne I., Ritchie O., Karihaloo B. (eds) Comprehensive structural integrity Fracture of materials from nano to macro. Elsevier, Oxford, vol. 3, pp. 127–209

  6. Brocks W., Nègre P., Scheider I., Schödel M., Steglich D., Zerbst U. (2003): Structural integrity assessment by models of ductile crack extension in sheet metal. Steel Res. 74, 504–513

    Google Scholar 

  7. Brocks W., Scheider I. (2006): Cohesive elements for thin-walled structures. Comput. Mater. Sci. 37, 101–109

    Article  Google Scholar 

  8. Broek, D.: Concepts of Fracture Control and Damage Tolerance Analysis, vol. 19, pp. 410–419. ASM, New York (1996)

  9. Chabanet O., Steglich D., Besson J., Heitmann V., Hellmann D., Brocks W. (2003): Predicting crack growth resistance of aluminium sheets. Comp. Mater. Sci. 26, 1–12

    Article  Google Scholar 

  10. Congourdeau, F., Journet, B.: Damage tolerance of fuselage welded stiffened panels. In: ICAF 2003, pp. 361–84 (2004)

  11. Cornec A., Scheider I., Schwalbe K.H. (2003): On the practical application of the cohesive model. Eng. Fract. Mech. 70, 1963–1987

    Article  Google Scholar 

  12. Crisfield M.A. (1981): A fast incremental/iteration solution procedure that handles “snap-through”. Comp. Struct. 13, 55–62

    Article  MATH  Google Scholar 

  13. Dugdale D.S. (1960): Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104

    Article  Google Scholar 

  14. Fredriksson, B., Sjöström, L.: The role of mechanics and modelling in advanced product development. Eur. J. Mech. A/Solids 83–86 (1997)

  15. Gullerud A.S., Dodds R.H., Hampton R.W., Dawicke D.S. (1999): 3-D modeling of ductile crack growth in thin metals: computational aspects and validation. Eng. Fract. Mech. 63, 347–374

    Article  Google Scholar 

  16. Heerens J., Schödel M. (2003): On the determination of crack tip opening angle, CTOA, using light microscopy and δ5 measurement technique. Eng. Fract. Mech. 70, 417–426

    Article  Google Scholar 

  17. ISO/TC 164/SC 4-N 413: Method of test for the determination of resistance to stable crack extension using specimens of low constraint. Draft Standard: Metallic Materials (2004)

  18. Kaplan, M.P., Wolff, T.A.: Life Extension and Damage Tolerance of Aircraft, Vol 19, pp. 557–565. ASM, New York (1996)

  19. Newman, J.C.: Advances in fatigue and fracture mechanics analyses for aircraft structures. In: ICAF 2003, pp. 3–42 (1999)

  20. Newman, J.C., Bigelow, C.A., Dawicke, D.S.: Finite-element analyses and fracture simulation in thin-sheet aluminum alloy, Durability of Metal Aircraft Structures. In: Proceedings of the International Workshop on Structural Integrity of Aging Airplanes, p. 167 (1999)

  21. Newman J.C., James M.A., Zerbst U. (2003): A review of the CTOA/CTOD fracture criterion. Eng. Fract. Mech. 70, 371–385

    Article  Google Scholar 

  22. Powell G., Simons J. (1981): Improved iterative strategy for nonlinear structures. Int. J. Num. Methods Eng. 17, 1455–1467

    Article  MATH  Google Scholar 

  23. Ramm E. (1981): Strategies for tracing the nonlinear response near limit points. In: Wunderlich E., Stein E., Bathe K.J. (eds) Nonlinear Finite Element Analysis in Structural Mechanics. Springer, Berlin Heidelberg New York

    Google Scholar 

  24. Roy Y.A., Dodds R.H. (2001): Simulation of ductile crack growth in aluminium panels using 3-D surface cohesive elements. Int. J. Fract. 110, 21–45

    Article  Google Scholar 

  25. Scheider, I.: Simulation of cup-cone fracture in round bars using the cohesive zone model. In: Proceedings of the 1st MIT Conference of an Computational Fluid and Solid Mechanics, pp. 460–462 (2000)

  26. Scheider, I., Brocks, W.: Simulation of crack propagation and failure in shell structures using the cohesive model. In: Ramm, E., Wall, W.A., Bletzinger, K.U., Bischoff, M. (eds.) Proceedings of the 5th International Conference Computation of Shell and Spatial Structures. Salzburg, Austria (2005)

  27. Scheider I., Schödel M., Brocks W., Schönfeld W. (2006): Crack propagation analyses with CTOA and cohesive model: Comparison and experimental validation. Eng. Fract. Mech. 73, 252–263

    Article  Google Scholar 

  28. Scheider, I., Schödel, M., Schönfeld, W., Brocks, W.: Modelling crack extension in biaxially loaded panels. In: 11th International Conference on Fracture, ICF 11, Turin (I), p. 5662 (2005)

  29. Schwalbe K.H. (1995): Introduction of δ5 as an operational definition of the CTOD and its practical use. ASTM STP 1256, 763–778

    Google Scholar 

  30. Schwalbe K.H., Newman J.C., Shannon J.L. (2005): Fracture mechanics testing on specimens with low constraint—standardisation activities within ISO and ASTM. Eng. Fract. Mech. 72, 557–576

    Google Scholar 

  31. Shan G.X., Kolednik O., Fischer F.D., Stüwe H.P. (1993): A 2D-model for the numerical investigations of the stable crack growth in thick smooth fracture mechanics specimens. Eng. Fract. Mech. 45, 99–106

    Article  Google Scholar 

  32. Siegmund, T., Brocks, W.: Simulation of ductile crack growth in thin aluminum alloys. In: Halford G.R., Gallagher, J.P. (eds.) 31st National Symposium on Fatigue and Fracture Mechanics, Cleveland, OH. ASTM STP 1389, pp. 475–485 (2000)

  33. Stampfl J., Scherer S., Berchthaler M., Gruber M., Kolednik O. (1996): Determination of the fracture toughness by automatic image processing. Int. J. Fract. 78, 35–44

    Article  Google Scholar 

  34. Zerbst, U., Brocks, W., Heerens, J., Schödel, M., Scheider, I., Steglich, D., Seib, E., Cornec, A., Schwalbe, K.H.: Failure assessment concepts for thin-walled structures. In: Structural Integrity of Advanced Aircraft and Life Extension for Current Fleets, ICAF 2005, Hamburg, Germany (2005)

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Brocks, W., Scheider, I. & Schödel, M. Simulation of crack extension in shell structures and prediction of residual strength. Arch Appl Mech 76, 655–665 (2006). https://doi.org/10.1007/s00419-006-0041-9

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  • DOI: https://doi.org/10.1007/s00419-006-0041-9

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