Simulation of fatigue crack growth with a cyclic cohesive zone model

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• 作者：Stephan Roth (1)
  Geralf Hütter (1)
  Meinhard Kuna (1)
  
• 关键词：Cyclic cohesive zone model ; Fatigue crack growth ; Damage mechanics ; Boundary layer model
• 刊名：International Journal of Fracture
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：188
• 期：1
• 页码：23-45
• 全文大小：
• 参考文献：1. Anderson T (2005) Fracture mechanics: fundamentals and applications, 3rd edn. Taylor and Francis, London
  2. Barenblatt G (1962) The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden HL, GKFvdD Th von Kármán, Howarth L (eds) Advances in applied mechanics, vol 7, Elsevier, pp 55-29
  3. Bouvard J, Chaboche J, Feyel F, Gallerneau F (2009) A cohesive zone model for fatigue and creep-fatigue crack growth in single crystal superalloys. Int J Fatigue 31(5):868-79 CrossRef
  4. Brocks W, Cornec A, Scheider I (2003) Computational aspects of nonlinear fracture mechanics. In: Milne I, Ritchie R, Karihaloo B (eds) Comprehensive structural integrity—numerical and computational methods, vol 3. Elsevier, Amsterdam, pp 127-09 CrossRef
  5. Camacho G, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20-2):2899-938 CrossRef
  6. Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2):100-04 CrossRef
  7. Fleck N, Kang K, Ashby M (1994) Overview no. 112: the cyclic properties of engineering materials. Acta Metall Mater 42(2):365-81 CrossRef
  8. Goyal VK, Johnson ER, Davila CG (2004) Irreversible constitutive law for modeling the delamination process using interfacial surface discontinuities. Compos Struct 65(3-):289-05 CrossRef
  9. Haibach E (1989) Betriebsfestigkeit: Verfahren und Daten zur Bauteilberechnung. VDI-Verlag GmbH, Düsseldorf
  10. Hütter G (2013) Multi-scale simulation of crack propagation in the ductile-brittle transition region. Dissertation, TU Bergakademie Freiberg
  11. Hütter G, Mühlich U, Kuna M (2011) Simulation of local instabilities during crack propagation in the ductile–brittle transition region. Eur J Mech A/Solids 30(3):195-03 CrossRef
  12. Kroon M, Faleskog J (2005) Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking. J Mech Phys Solids 53(1):171-96 CrossRef
  13. Lemaitre J (1996) A course on damage mechanics, 2nd edn. Springer, New York CrossRef
  14. Liu J, Yuan H, Liao R (2010) Prediction of fatigue crack growth and residual stress relaxations in shot-peened material. Mater Sci Eng A 527(21-2):5962-968 CrossRef
  15. Lucas L, Black T, Jones D (2008) Use of cohesive elements in fatigue analysis. In: American society of mechanical engineers, pressure vessels and piping division (publication) PVP, ASME, vol 2, pp 13-5
  16. Nguyen O, Repetto E, Ortiz M, Radovitzky R (2001) A cohesive model of fatigue crack growth. Int J Fract 110(4):351-69 CrossRef
  17. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(9):1267-282 CrossRef
  18. Paris P, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng-T Asme 85(4):528-33 CrossRef
  19. Radaj D, Vormwald M (2007) Ermüdungsfestigkeit: Grundlagen für Ingenieure. Springer, London
  20. Rice J (1968) A path-independent integral and approximate analysis of strain concentration by notches and cracks. ASME J Appl Mech 35:379-86 CrossRef
  21. Ritchie R (1988) Mechanisms of fatigue crack propagation in metals, ceramics and composites: role of crack tip shielding. Mater Sci Eng 103(1):15-8 CrossRef
  22. Roe K, Siegmund T (2003) An irreversible cohesive zone model for interface fatigue crack growth simulation. Eng Fract Mech 70(2):209-32 CrossRef
  23. Roth S, Kuna M (2013) Finite element analyses of fatigue crack growth under small scale yielding conditions modelled with a cyclic cohesive zone approach, COMPLAS XII. In: O?ate E, Owen D, Peric D, Suárez B (eds) Computational plasticity XII—fundamentals and applications. CIMNE, Barcelona, pp 1075-086
  24. Roychowdhury S, Arun Roy Y (2002) Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-d surface cohesive elements. Eng Fract Mech 69(8):983-002 CrossRef
  25. Roth S, Hütter G, Mühlich U, Nassauer B, Zybell L, Kuna M (2012) Visualisation of user defined finite elements with ABAQUS/Viewer. GACM Report 7:7-4
  26. Schütz W (1967) über eine Beziehung zwischen der Lebens- dauer bei konstanter und bei ver?nderlicher Beanspruchungs amplitude und ihre Anwendbarkeit auf die Bemessung von Flugzeugbauteilen. Zeitschrift für Flugwissenschaften 15(11):407-19
  27. Smith J (1942) The effect of range of stress on the fatigue strength of metals. In: Engineering experiment station bulletin, vol 334. University of Illinois
  28. Suresh S (1998) Fatigue of materials, 2nd edn. Cambridge University Press, Cambridge CrossRef
  29. Scheider I, Mosler J (2011) Novel approach for the treatment of cyclic loading using a potential-based cohesive zone model. Proc Eng 10:2164-169 CrossRef
  30. Schwalbe KH, Scheider I, Cornec A (2013) Guidelines for applying cohesive models to the damage behaviour of engineering materials and structures. Springer, Berlin CrossRef
  31. Siegmund T (2004) A numerical study of transient fatigue crack growth by use of an irreversible cohesive zone model. Int J Fatigue 26(9):929-39 CrossRef
  32. Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J Mech Phys Solids 40(6):1377-397 CrossRef
  33. Xu XP, Needleman A (1993) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci 1(2):111-32 CrossRef
  34. Xu Y, Yuan H (2009a) Computational analysis of mixed-mode fatigue crack growth in quasi-brittle materials using extended finite element methods. Eng Fract Mech 76(2):165-81 CrossRef
  35. Xu Y, Yuan H (2009b) On damage accumulations in the cyclic cohesive zone model for xfem analysis of mixed-mode fatigue crack growth. Comput Mater Sci 46(3):579-85 CrossRef
  36. Yang B, Mall S, Ravi-Chandar K (2001) A cohesive zone model for fatigue crack growth in quasibrittle materials. Int J Solids Struct 38(22-3):3927-944 CrossRef
  
• 作者单位：Stephan Roth (1)
  Geralf Hütter (1)
  Meinhard Kuna (1)
  
  1. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, 09596?, Freiberg, Germany
  
• ISSN：1573-2673

文摘

Fatigue crack growth is simulated for an elastic solid with a cyclic cohesive zone model (CZM). Material degradation and thus separation follows from the current damage state, which represents the amount of maximum transferable traction across the cohesive zone. The traction–separation relation proposed in the cyclic CZM includes non-linear paths for both un- and reloading. This allows a smooth transition from reversible to damaged state. The exponential traction–separation envelope is controlled by two shape parameters. Moreover, a lower bound for damage evolution is introduced by a local damage dependent endurance limit, which enters the damage evolution equation. The cyclic CZM is applied to mode I fatigue crack growth under \(K_{\mathrm{I}}\) -controlled external loading conditions. The influences of the model parameters with respect to static failure load \(K_{\mathrm{0}}\) , threshold load \(\varDelta K_{\mathrm{th}}\) and Paris parameters \(m, C\) are investigated. The study reveals that the proposed endurance limit formulation is well suited to control the ratio \(\varDelta K_{\mathrm{th}}/K_{\mathrm{0}}\) independent of \(m\) and \(C\) . An identification procedure is suggested to identify the cohesive parameters with the help of W?hler diagrams and fatigue crack growth rate curves.