Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

  • J.-H. Yan
  • M. A. Sutton
  • X. Deng
  • Z. Wei
  • Pablo Zavattieri
Original Paper


Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.


Mixed mode I/III fracture Ductile materials Thin sheet Digital image correlation Crack tip fields Growing crack Strain field COD CTOD 


  1. Chan KS (1990) Crack-tip behavior of stationary and growing cracks in Al-Fe-X alloys: part I. Near-tip strain field. Metall Trans A 21A: 69–80ADSGoogle Scholar
  2. Correlated Solutions, Inc (2007) VIC-2D and VIC-3D, 120 Kaminer way parkway suite A, Columbia, SC 29210. http://www.correlatedsolutions.com
  3. Dawicke DS, Sutton MA (1994) CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy. Exp Mech 34(4): 357–368CrossRefGoogle Scholar
  4. Dawicke DS, Sutton MA, Newman JC Jr et al (1995) Measurement and analysis of critical CTOA for thin-sheet aluminum alloy materials. In: Erdogan F (ed) Fracture mechanics 25, ASTM STP 1220, pp 358–79Google Scholar
  5. Deng X (1990) Dynamic crack propagation in elastic-plastic solids. Ph.D dissertation, California Institute of Technology, Pasadena, California, May 1990Google Scholar
  6. Deng X, Rosakis AJ (1991) Dynamic crack propagation in elastic-perfectly plastic solids under plane stress conditions. J Mech Phys Solids 39: 683–722CrossRefADSGoogle Scholar
  7. Deng X, Rosakis AJ (1992a) A finite element investigation of quasi-static and dynamic asymptotic crack tip fields in hardening elastic-plastic solids under plane stress; part I: crack growth in linear hardening materials. Int J Fract 57: 291–308CrossRefADSGoogle Scholar
  8. Deng X, Rosakis AJ (1992b) A finite element investigation of quasi-static and dynamic asymptotic crack tip fields in hardening elastic-plastic solids under plane stress; part II: crack growth in power-law hardening materials. Int J Fract 58: 137–156CrossRefADSGoogle Scholar
  9. Gao X, Shih CF (1998) A parametric study of mixed-mode I/III ductile fracture in tough materials under small scale yielding. Eng Fract Mech 60(4): 407–420CrossRefGoogle Scholar
  10. Hutchinson JW (1968) Plastic stress and strain fields at a crack tip. J Mech Phys Solids 16: 337–347CrossRefADSGoogle Scholar
  11. Jones RH, Li H, Hirth JP (2001) Effect of mixed mode I/III loading on environment-induced cracking. Eng Fract Mech 68: 789–801CrossRefGoogle Scholar
  12. Kamat SV, Hirth JP (1995) Mixed mode fracture toughness of engineering materials. J Engng Mater Technol 117(4): 391–394CrossRefGoogle Scholar
  13. Kamat SV, Srinivas M, Rao PR (1998) Mixed mode I/III fracture toughness of armco iron. Acta Mater 46(14): 4985–4992CrossRefGoogle Scholar
  14. Lan W, Deng X, Sutton MA et al (2006) Study of slant fracture in ductile materials. Int J Fract 141(3–4): 469–496CrossRefGoogle Scholar
  15. Li H, Kurtz RJ, Jones RH (1998) Effect of thickness and loading mode on the fracture properties of V-4Cr-4Ti at room temperature. J Nucl Mater 258–263: 1386–1391CrossRefGoogle Scholar
  16. Liu S, Chao YJ, Zhu X (2004) Tensile-shear transition in mixed mode I/III fracture. Int J Solids Struct 41: 6147–6172MATHCrossRefGoogle Scholar
  17. Ma F, Deng X, Sutton MA et al (1999) A CTOD-based mixed-mode fracture criterion. In: Miller KJ, McDowell DL (eds) Mixed-mode crack behavior, ASTM STP 1359. American Society for Testing and Materials, West Conshohocken, pp 86–110CrossRefGoogle Scholar
  18. Ma L, Kobayashi AS, Atluri SN et al (2002) Crack linkup: an experimental analysis. Exp Mech 42(2): 147–152CrossRefGoogle Scholar
  19. Newman JC Jr, James MA, Zerbst U (2003) A review of the CTOA/CTOD fracture criterion. Eng Fract Mech 70: 371–385CrossRefGoogle Scholar
  20. Pan J (1990) Asymptotic analysis of a crack in a power-law material under combined in-plane and out-of-plane shear loading conditions. J Mech Phys Solids 38(2): 133–159MATHCrossRefADSGoogle Scholar
  21. Pan J, Shih CF (1992) Elastic-plastic analysis of combined mode I, II and III crack-tip fields under small-scale yielding conditions. Int J Solids Struct 29(22): 2795–2814MATHCrossRefGoogle Scholar
  22. Paterson EA, Gungor S (1997) A photoelastic study of an angle crack specimen subject to mixed mode I-III displacements. Eng Fract Mech 56(6): 767–778CrossRefGoogle Scholar
  23. Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power law hardening material. J Mech Phys Solids 16: 13–31CrossRefGoogle Scholar
  24. Sutton MA, Boone ML, Ma F, Helm JD (2000a) A combined modeling-experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mode I/II loading in thin sheet materials. Eng Fract Mech 66: 171–185CrossRefGoogle Scholar
  25. Sutton MA, Deng X, Ma F et al (2000b) Development and application of a crack tip opening displacement-based mixed mode fracture criterion. Int J Solids Struct 37: 3591–3618MATHCrossRefGoogle Scholar
  26. Sutton MA, Helm JD, Boone ML (2001) Experimental study of crack growth in thin sheet material under tension-torsion loading. Int J Fract 109: 285–301CrossRefGoogle Scholar
  27. Sutton MA, Yan J-H, Deng X, Cheng C-S, Zavattieri P (2007) Three-dimensional digital image correlation to quantify deformation and crack-opening displacement in ductile aluminum under mixed-mode I/III loading. Opt Eng 46(5): 051003CrossRefADSGoogle Scholar
  28. Wei Z, Yan J, Deng X et al (2005) Study of mixed-mode I/III fracture in ductile materials. In: Proceedings of the 2005 SEM annual conference and exposition on experimental and applied mechanics, 1651–1655, Portland, Oregon, June 7–9, 2005Google Scholar
  29. Wei Z (2008) Study of fracture in ductile thin sheets under remote I/III loadings. Ph.D dissertation, University of South Carolina, Columbia South Carolina, June 2008Google Scholar
  30. Yan J-H, Sutton MA, Deng X, Cheng C-S (2007) Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading. Int J Fract 144: 297–321CrossRefGoogle Scholar
  31. Zucchini A, Hui CY, Zehnder Alan T (2000) Crack tip stress fields for thin, cracked plates in bending, shear and twisting: a comparison of plate theory and three-dimensional elasticity theory solutions. Int J Fract 104: 387–407CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • J.-H. Yan
    • 1
  • M. A. Sutton
    • 1
  • X. Deng
    • 1
  • Z. Wei
    • 1
  • Pablo Zavattieri
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of South CarolinaColumbiaUSA
  2. 2.GM Research and Development CenterWarrenUSA

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