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

Abstract

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 εθθ 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.

Keywords

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

References

  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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