Skip to main content
Log in

Mixed mode stable tearing of thin sheet AI 6061-T6 specimens: experimental measurements and finite element simulations using a modified Mohr-Coulomb fracture criterion

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

In this investigation, a combined experimental and computational approach with a Modified Mohr Coulomb (MMC) fracture criterion employing post-initiation element softening is used to simulate stable crack propagation under Mode I, Mode III and combined Mode I/III loading conditions. Results from the studies demonstrate that good correlation exists between the measured load-displacement and the numerically predicted response when the stiffness of the specimen fixture is included in the FE model. The numerical results were able to capture most of the experimentally observed features during crack propagation, such as through-thickness slant fracture, necking, tunneling and local specimen twist, thus confirming that the MMC criterion is suitable for predicting in-plane and out-of-plane tearing of sheets. It was found that in order to predict correctly the load-displacement curve as well as the fracture plane, different amount of softening is needed for Mode I and Mode III loading cases. This observation can be justified on the micro-mechanical level, while there is a competition between the mechanisms of dimple and shear fracture.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amstutz BE, Sutton MA, Dawicke DS, Newman JC Jr (1995) An experimental study of CTOD for Mode I/Mode II stable crack growth in thin 2024-T3 aluminum specimens, fracture mechanics. American Society for Testing Materials (ASTM STP 1256) 26: 256–271

    Google Scholar 

  • Amstutz BE, Sutton MA, Dawicke DS, Boone ML (1997) Effects of mixed mode I/II loading and grain orientation on crack initiation and stable tearing in 2024-T3 aluminum, fatigue and fracture mechanics. American Society for testing Materials (ASTM STP 1296) 27: 105–126

    Google Scholar 

  • Aoki S, Kishimoto K, Yoshida M, Sakata M, Richard HA (1990) Elastic-plastic fracture behavior of an aluminum alloy under mixed mode loading. J Mech Phys Solids 38(2): 195–213

    Article  Google Scholar 

  • Bai Y, Wierzbicki T (2010) Application of extended Mohr-Coulomb criterion to ductile fracture. Int J Fract 161: 1–20

    Article  CAS  Google Scholar 

  • Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46: 81–98

    Article  Google Scholar 

  • Beese AM, Luo M, Li Y, Bai Y, Wierzbicki T (2010) Partially coupled anisotropic fracture model for aluminum sheets. Eng Fract Mech 77: 1128–1152

    Article  Google Scholar 

  • De-Andre A, Perez JL, Ortiz M (1999) Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Int J Solids Struct 36: 2231–2258

    Article  Google Scholar 

  • Gao H, Klein P (1998) Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46(2): 187–218

    Article  CAS  Google Scholar 

  • Gravouil A, Moes N, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets-Part II: level set update. Int J Numer Methods Eng 53: 2569–2586

    Article  Google Scholar 

  • Lan WM, Deng XM, Sutton MA, Cheng CS (2006) Study of slant fracture in ductile materials. Int J Fract 141: 469–496

    Article  CAS  Google Scholar 

  • Lan WM, Deng XM, Sutton MA (2007) Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments. Eng Fract Mech 74: 2498–2517

    Article  Google Scholar 

  • Li Y, Wierzbicki T (2009) Mesh-size effect study of ductile fracture by non-local approach. In: Proceedings of the SEM annual conference. June 1–4, 2009 Albuquerque New Mexico, USA

  • Li Y, Wierzbicki T (2010a) Prediction of plane strain fracture of AHSS sheets with post-initiation softening. Int J Solids Struct 47(17): 2316–2327

    Article  CAS  Google Scholar 

  • Li Y, Luo M, Gerlach G, Wierzbicki T (2010b) Prediction of shear-induced fracture in sheet metal forming. J Mater Process Technol 210: 1858–1869

    Article  CAS  Google Scholar 

  • Luo M, Wierzbicki T (2010) Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model. Int J Solid Struct 47(22–23): 3084–3102

    Article  CAS  Google Scholar 

  • Ma F, Deng XM, Sutton MA, Newman JC Jr (1999) A CTOD-based mixed mode fracture criterion. ASTM STP 1359 on mixed mode crack behavior, pp 86–110

  • Ma F, Deng XM, Sutton MA, Fawaz SA (2001) Plane strain mixed mode crack-tip stress fields characterized by a triaxial stress parameter and a plastic deformation extent based characteristic length. J Mech Phys Solids 49: 292–2953

    Article  Google Scholar 

  • Mahgoub E, Deng XM, Sutton MA (2003) Three-dimensional stress and deformation fields around flat and slant cracks under remote Mode I loading conditions. Eng Fract Mech 70: 2527–2542

    Article  Google Scholar 

  • Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69: 813–833

    Article  Google Scholar 

  • Morrissey JW, Geubelle PH (1997) A numerical scheme for Mode III dynamic fracture problems. Int J Numer Methods Eng 40: 1181–1196

    Article  Google Scholar 

  • Oliver J (1996a) Modeling strong discontinuities in solid mechanics via strain softening constitutive equations part 1: ‘Fudermentals’. Int J Numer Method Eng 39: 3575–3600

    Article  Google Scholar 

  • Oliver J (1996b) Modeling strong discontinuities in solid mechanics via strain softening constitutive equations Part2: numerical simulation. Int J Numer Method Eng 39: 3601–3623

    Article  Google Scholar 

  • Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Method Eng 44: 1267–1282

    Article  Google Scholar 

  • Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17: 201–217

    Article  Google Scholar 

  • Simonsen BC, Tornqvist R (2004) Experimental and numerical modeling of ductile crack propagation in large-scale shell structures. Marine Struct 17: 1–24

    Article  Google Scholar 

  • Sutton MA, Deng X Ma F, Newman JC Jr, James M (2000a) Development and application of a crack tip opening displacement-based mixed mode fracture criterion. Int J Solids Struct 37: 3591–3618

    Article  Google Scholar 

  • Sutton MA, Boone ML, Ma F, Helm JD (2000b) A combined modeling-experimental study of the crack opening displacement criterion for characterization of stable crack growth under mixed mode I/II loading in thin sheet materials. Eng Fract Mech 66: 171–185

    Article  Google Scholar 

  • Sutton MA, Helm JD, Boone ML (2001) Experimental study of crack growth in thin sheet material under tension-torsion loading. Int J Fract 109: 285–301

    Article  CAS  Google Scholar 

  • Sutton MA, Ma F, Deng XM (2002) Mixed mode I/II crack-tip stress fields characterized by a triaxial stress parameter and a plastic deformation extent based characteristic length, fatigue and fracture mechanics: 33rd volume. ASTM STP 1417: 233–268

    Google Scholar 

  • Sutton MA, Yan JH, Deng XM, Cheng CS, Zavattieri P (2007) 3D Digital image correlation to quantify deformation and COD in ductile aluminum under mixed-mode I/III loading. Opt Eng 46(5): 051003-1–051003-17

    Article  Google Scholar 

  • Teng X (2008) Numerical prediction of slant fracture with continuum damage mechanics. Eng Fract Mech 75(8): 2020–2041

    Article  Google Scholar 

  • Thompson KD, Sheppard SD (1992) Fatigue crack-growth in notched and plain shafts subjected to torsion and axial loading. Eng Fract Mech 43: 55–71

    Article  Google Scholar 

  • Xue L (2007a) Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int J Solids Struct 44: 5163–5181

    Article  CAS  Google Scholar 

  • Xue L (2007b) Ductile fracture modeling—theory, experimental investigation and numerical verification. PhD Thesis, Department of Mechanical Engineering, MIT

  • Xue L, Wierzbicki T (2008) Ductile fracture initiation and propagation modeling using damage plasticity theory. Eng Fract Mech 75(11): 3276–3293

    Article  Google Scholar 

  • Xue L, Wierzbicki T (2009) Numerical simulation of fracture mode transition in ductile plates. Int J Solids Struct 46: 1423–1435

    Article  Google Scholar 

  • Yan JH, Sutton MA, Deng XM, Cheng CS (2007) Mixed-mode fracture of ductile thin sheet materials under combined in-plane and out-of-plane loading. Int J Fract 144: 297–321

    Article  CAS  Google Scholar 

  • Yan JH, Sutton MA, Deng X, Wei Z, Zavattieri P (2009a) Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading. Int J Fract 16: 169–188

    Article  Google Scholar 

  • Yan JH, Sutton MA, Deng X, Zavattieri P, Wei Z (2009b) Mixed-mode crack growth in ductile thin sheet materials. In: Proceedings of the SEM annual conference, June 1–4, 2009 Albuquerque New Mexico USA

  • Zhou Q, Wierzbicki T (1996) A tension zone model of blanking and tearing of ductile metal plates. Int J Mech Sci 38(3): 303–324

    Article  Google Scholar 

  • Zuo JZ, Sutton MA, Deng XM (2004) Basic studies of ductile failure processes and implications for fracture prediction. Fatigue Fract Eng Mater Struct 27: 231–243

    Article  Google Scholar 

  • Zuo JZ, Sutton MA, Deng XM (2005) Advances in tetrahedral mesh generation for modeling of three-dimensional regions with complex curvilinear crack shapes. Int J Number Methods Eng 63: 256–275

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yaning Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y., Wierzbicki, T., Sutton, M.A. et al. Mixed mode stable tearing of thin sheet AI 6061-T6 specimens: experimental measurements and finite element simulations using a modified Mohr-Coulomb fracture criterion. Int J Fract 168, 53–71 (2011). https://doi.org/10.1007/s10704-010-9554-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-010-9554-x

Keywords

Navigation