International Journal of Fracture

, Volume 189, Issue 1, pp 59–75 | Cite as

Simulation of mixed-mode I/III stable tearing crack growth events using the cohesive zone model approach

  • Xin Chen
  • Xiaomin Deng
  • Michael A. Sutton
  • Pablo Zavattieri
Original Paper
  • 393 Downloads

Abstract

A cohesive zone model (CZM) approach is applied to simulate mixed-mode I/III stable tearing crack growth events in specimens made of 6061-T6 aluminum alloy and GM 6208 steel. The materials are treated as elastic–plastic following the \(J_{2}\) flow theory of plasticity, and the triangular cohesive law is employed to describe the traction-separation relation in the cohesive zone ahead of crack front. A hybrid numerical/experimental approach is employed in simulations using 3D finite element method. For each material, CZM parameter values are chosen by matching simulation prediction with experimental measurement (Yan et al. in Int J Fract 144:297–321, 2009), of the crack extension-time curve for the \(30^{\circ }\) mixed-mode I/III stable tearing crack growth test. With the same sets of CZM parameter values, simulations are performed for the \(60^{\circ }\) loading cases. Good agreements are reached between simulation predictions of the crack extension-time curve and experimental results. The variations of CTOD with crack extension are calculated from CZM simulations under both \(30^{\circ }\) and \(60^{\circ }\) mixed-mode I/III conditions for the aluminum alloy and steel respectively. The predictions agree well with experimental measurements (Yan et al. in Int J Fract 144:297–321, 2009). The findings of the current study demonstrate the applicability of the CZM approach in mixed-mode I/III stable tearing simulations and reaffirm the connection between CTOD and CZM based simulation approaches shown previously for mixed-mode I/II crack growth events.

Keywords

Cohesive zone modeling Finite element analysis Crack growth Mixed-mode fracture Stable tearing Plastic deformation 

References

  1. Abaqus 6.11 Analysis User’s ManualGoogle Scholar
  2. Alfaiate J, Wells GN, Sluys LJ (2002) On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture. Eng Fract Mech 69(2002):661–686CrossRefGoogle Scholar
  3. Alfano M, Lubineau G, Furgiuele F, Paulino GH (2011) On the enhancement of bond toughness for Al/epoxy T-peel joints with laser treated substrates. Int J Fract 171(2):139–50CrossRefGoogle Scholar
  4. Amstutz BE, Sutton MA, Dawicke DS, Newman JC Jr (1995) An experimental study of CTOD for mode I/modeII stable crack growth in thin 2024-T3 aluminum specimens. Fracture Mechanics, ASTM, STP 1256, pp 256–271Google Scholar
  5. Anvari M, Scheider I, Thaulow C (2006) Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements. Eng Fract Mech 73:2210–2228CrossRefGoogle Scholar
  6. Barenblatt GI (1959) The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis. Axially-symmetric cracks. Prikl Matem I Mekham 23:434–444Google Scholar
  7. Barenblatt GI (1962) Mathematical theory of equilibrium cracks. Adv Appl Mech, vol 7. Academic Press, New York, pp 55–125Google Scholar
  8. Barpi F, Valente S (1998) Size-effects induced bifurcation phenomena during multiple cohesive crack propagation. Int J Solids Struct 35(16):1851–1861CrossRefGoogle Scholar
  9. Boone ML (1997) Ductile crack growth in an aluminum aircraft fuselage material, Honors College Undergraduate Thesis, University of South Carolina, Columbia, SC, USAGoogle Scholar
  10. Camanho PP, Dávila CG, de Moura MF (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Compos Mater 37:1415–1438CrossRefGoogle Scholar
  11. Chen X, Deng X, Sutton MA (2013) Simulation of Stable Tearing Crack Growth Events Using the Cohesive Zone Model Approach. Eng Fract Mech 99(2):223–238CrossRefGoogle Scholar
  12. Chen X, Deng X, Sutton MA, Zavattieri PD (2014) An inverse analysis of cohesive zone model parameter values for ductile crack growth simulations. Int J Mech Sci 79:206–215CrossRefGoogle Scholar
  13. Cirak F, Ortiz M, Pandolfi A (2005) A cohesive approach to thin-shell fracture and fragmentation. Comput Methods Appl Mech Eng 194:2604–2618CrossRefGoogle Scholar
  14. Deng X, Newman JC Jr (1999) A study of some issues in stable tearing crack growth simulations. Eng Fract Mech 64:291–304CrossRefGoogle Scholar
  15. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–108CrossRefGoogle Scholar
  16. Gullerud AS, Dodds RH, Hampton RW (1999) Dawicke DS. 3-D modeling of ductile crack growth in thin sheet metals: computational aspects and validation. Eng Fract Mech 63:347–374CrossRefGoogle Scholar
  17. Kamat SV, Hirth JP (1995) Mixed mode fracture toughness of engineering materials. J Eng Mater Technol 117:391–394CrossRefGoogle Scholar
  18. Knauss WG (1970) An observation of crack propagation in anti-plane shear. Int J Fract Mech 6(2):183–7Google Scholar
  19. Lan W, Deng X, Sutton MA (2007) Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments. Eng Fract Mech 74:2498–2517CrossRefGoogle Scholar
  20. Li W, Siegmund T (2002) An analysis of crack growth in thin-sheet metal via a cohesive zone model. Eng Fract Mech 69(18):2073–2093CrossRefGoogle Scholar
  21. Liu S, Chao YJ, Zhu X (2004) Tensile-shear transition in mixed mode I/III fracture. Int J Solids Struct 41(2004):6147–6172CrossRefGoogle Scholar
  22. Marat-Mendes RM, Freitas MM (2010) Failure criteria for mixed mode delamination in glass fibre epoxy composites. Compos Struct 92(2010):2292–2298CrossRefGoogle Scholar
  23. Newman JC Jr (1984) An elastic–plastic finite element analysis of crack initiation, stable crack growth, and instability. In: Fracture Mechanics. Philadelphia: American Society for Testing and Materials. ASTM STP, 833, pp 93–117Google Scholar
  24. Rashid F, Banerjee A (2013) Implementation and validation of triaxiality dependent cohesive model: experiments and simulations. Int J Fract 181:227–239CrossRefGoogle Scholar
  25. Siegmund T, Brocks W (2000) A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Eng Fract Mech 67:139–154CrossRefGoogle Scholar
  26. Sommer E (1969) Formation of fracture ‘lances’ in glass. Eng Fract Mech 1:539–546CrossRefGoogle Scholar
  27. Sun C, Thouless MD, Waas AM, Schroeder JA, Zavattieri PD (2008) Ductile-brittle transition in the fracture of plastically-deforming adhesively-bonded structures. Part II: numerical studies. Int J Solids Struct 45(17):4725–4738CrossRefGoogle Scholar
  28. Suresh S, Shih CF, Morrone A, O’Dowd NP (1990) Mixed-mode fracture toughness of ceramic materials. J Am Ceram Soc 73(5):1257–67CrossRefGoogle Scholar
  29. Sutton MA, Deng X, Ma F, Newman JC Jr, James M (2000) Development and application of a crack tip opening displacement-based mixed mode fracture criterion. Int J Solids Struct 37:3591–3618CrossRefGoogle Scholar
  30. Sutton MA, Yan J Deng X, Cheng CS, Zavattieri P, (2007) Three-dimentional digital image correlation to quantify deformation and crack-opening displacement in ductile aluminum under mixed-mode I/III loading. Opt Eng 46(5):051003-1–051003-17Google Scholar
  31. Tvergaard V (2008) Effect of T-stress on crack growth under mixed mode I–III loading. Int J Solids Struct 45(2008):5181–5188CrossRefGoogle Scholar
  32. Tvergaard V (2010) Effect of pure mode I, II or III loading or mode mixity on crack growth in a homogeneous solid. Int J Solids Struct 47(2010):1611–1617CrossRefGoogle Scholar
  33. Wei Z (2008) Study of fracture in ductile thin sheets under remote I/III loading. Doctoral Thesis, University of South Carolina, Columbia, SC, USAGoogle Scholar
  34. Wei Z, Deng X, Sutton MA, Yan J, Cheng CS, Zavattieri P (2011) Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading. Eng Fract Mech 78(2011):3082–3101CrossRefGoogle Scholar
  35. Wells AA (1961) Unstable crack propagation in metals: cleavage and fast fracture. Proc Cranfield Crack Propag Symp 1:210–230Google Scholar
  36. Wells AA (1963) Application of fracture mechanics at and beyond general yielding. Br Weld J 11:563–570Google Scholar
  37. Xu Y, Yuan H (2011) Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods. Eng Fract Mech 78:544–558CrossRefGoogle Scholar
  38. Yan J, Sutton MA, Deng X, Wei Z, Zavattieri P (2009) Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading. Int J Fract 144:297–321CrossRefGoogle Scholar
  39. Zavattieri PD (2006) Modeling of crack propagation in thin-walled structures using a cohesive model for shell elements. J Appl Mech 73:948–958CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Xin Chen
    • 1
  • Xiaomin Deng
    • 1
  • Michael A. Sutton
    • 1
  • Pablo Zavattieri
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of South CarolinaColumbiaUSA
  2. 2.School of Civil EngineeringPurdue UniversityWest LafayetteUSA

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