Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture

Abstract The anisotropic ductile fracture of a 6260-T6 anisotropic aluminum alloy extrusion is investigated using a hybrid experimental–numerical approach. A basic fracture testing program covering a wide range of stress states and different material orientations is carried out. It comprises experiments on notched tensile specimens, tensile specimens with a central hole and butterfly shear specimens. The surface strain fields are obtained using two-dimensional Digital Image Correlation (DIC), while detailed finite element simulations are performed of all experiments to determine the local stress and strain histories inside the specimens. The analysis shows that the use of the newly-proposed extension of the Yld2000 yield function for three-dimensional stress states (see companion paper) together with an isotropic hardening law is able to predict the elasto-plastic behaviors of the present anisotropic aluminum alloy in all experiments. The experimental results show a strong dependency of the strain to fracture on the material orientation with respect to the loading direction. An uncoupled non-associated anisotropic fracture model is proposed which makes use of a stress state dependent weighting function and an anisotropic plastic strain measure. The latter is obtained from applying the von Mises equivalent plastic strain definition after the linear transformation of the plastic strain tensor. It is shown that the use of the isotropic Modified Mohr–Coulomb (MMC) stress state weighting function in this anisotropic fracture modeling framework provides accurate predictions of the onset of fracture for all thirteen fracture experiments.

[1]  J. Leblond,et al.  Ductile Fracture by Void Growth to Coalescence , 2010 .

[2]  Dirk Mohr,et al.  Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading , 2011 .

[3]  D. Mohr,et al.  A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel Sheets , 2008 .

[4]  F. Barlat,et al.  Plane stress yield function for aluminum alloy sheets—part 1: theory , 2003 .

[5]  Ke-Shi Zhang,et al.  Numerical analysis of the influence of the Lode parameter on void growth , 2001 .

[6]  Jean-Baptiste Leblond,et al.  An improved Gurson-type model for hardenable ductile metals , 1995 .

[7]  Tomasz Wierzbicki,et al.  A Comparative Study on Various Ductile Crack Formation Criteria , 2004 .

[8]  Otmar Kolednik,et al.  A note on calibration of ductile failure damage indicators , 1995 .

[9]  Fabrice Morestin,et al.  Failure analysis of anisotropic sheet-metals using a non-local plastic damage model , 2005 .

[10]  J. Hutchinson,et al.  Modification of the Gurson Model for shear failure , 2008 .

[11]  I. Sinclair,et al.  Evolution of voids during ductile crack propagation in an aluminium alloy sheet toughness test studied by synchrotron radiation computed tomography , 2008 .

[12]  Tomasz Wierzbicki,et al.  Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model , 2010 .

[13]  T. Wierzbicki,et al.  A new model of metal plasticity and fracture with pressure and Lode dependence , 2008 .

[14]  A. Needleman,et al.  Void Nucleation Effects in Biaxially Stretched Sheets , 1980 .

[15]  A. P. Karafillis,et al.  A general anisotropic yield criterion using bounds and a transformation weighting tensor , 1993 .

[16]  J. D. Embury,et al.  A model of ductile fracture based on the nucleation and growth of voids , 1981 .

[17]  Mark F. Horstemeyer,et al.  A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence , 2007 .

[18]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[19]  Frédéric Barlat,et al.  Generalization of Drucker's Yield Criterion to Orthotropy , 2001 .

[20]  A. Pineau,et al.  Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain , 2002 .

[21]  Yuanli Bai,et al.  Application of extended Mohr–Coulomb criterion to ductile fracture , 2009 .

[22]  Raja K. Mishra,et al.  Microstructure-based finite element analysis of strain localization behavior in AA5754 aluminum sheet , 2008 .

[23]  Jacques Besson,et al.  Simulation of the ductile tearing for two grades of 2024 aluminum alloy thin sheets , 2006 .

[24]  Jacques Besson,et al.  Anisotropic ductile fracture: Part II: theory , 2004 .

[25]  A. Benzerga,et al.  An approximate yield criterion for anisotropic porous media , 2008 .

[26]  Dirk Mohr,et al.  Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals , 2010 .

[27]  Paul Steinmann,et al.  A theoretical and computational framework for anisotropic continuum damage mechanics at large strains , 2001 .

[28]  Tie-jun Wang.  Unified CDM model and local criterion for ductile fracture—II. Ductile fracture local criterion based on the CDM model , 1992 .

[29]  H. Yang,et al.  Ductile fracture: Experiments and computations , 2011 .

[30]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[31]  Jinkook Kim,et al.  Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity , 2004 .

[32]  T. Pardoena,et al.  An extended model for void growth and coalescence , 2022 .

[33]  L. Xue.  Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading , 2007 .

[34]  Tommaso Coppola,et al.  The effect of stress invariants on ductile fracture limit in steels , 2009 .

[35]  Dirk Mohr,et al.  Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part I: Plasticity , 2012 .

[36]  Jacques Besson,et al.  Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation , 2001 .

[37]  Seogou Choi,et al.  Ductile fracture in axisymmetric extrusion , 1998 .

[38]  D. Karr,et al.  Prediction of ductile fracture in tension by bifurcation, localization, and imperfection analyses , 2009 .

[39]  M. Wilkins,et al.  Cumulative-strain-damage model of ductile fracture: simulation and prediction of engineering fracture tests , 1980 .

[40]  R. E. Dick,et al.  Plane stress yield functions for aluminum alloy sheets , 2002 .

[41]  Yuanli Bai,et al.  Partially coupled anisotropic fracture model for aluminum sheets , 2010 .

[42]  V. monchiet,et al.  Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids , 2008 .

[43]  Liang Xue,et al.  Ductile fracture modeling : theory, experimental investigation and numerical verification , 2007 .

[44]  A. Benzerga,et al.  A constitutive model for plastically anisotropic solids with non-spherical voids , 2010 .

[45]  Jean-Baptiste Leblond,et al.  Theoretical models for void coalescence in porous ductile solids. II. Coalescence “in columns” , 2001 .

[46]  Thomas Pardoen,et al.  Anisotropic ductile fracture of Al 2024 alloys , 2008 .

[47]  C. Chow,et al.  Prediction of forming limit diagrams for AL6111-T4 under non-proportional loading , 2001 .

[48]  J. Chaboche.  Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth , 1988 .

[49]  J. Chaboche.  Continuum Damage Mechanics: Part I—General Concepts , 1988 .

[50]  D. Lloyd,et al.  Notch fracture behaviour of 5754 automotive aluminium alloys , 2002 .

[51]  Viggo Tvergaard,et al.  Ductile shear failure or plug failure of spot welds modelled by modified Gurson model , 2010 .

[52]  K. Ravi-Chandar,et al.  Ductile failure in polycrystalline OFHC copper , 2011 .

[53]  Jacques Besson,et al.  Anisotropic ductile fracture: Part I: experiments , 2004 .

[54]  A. Huespe,et al.  A finite thickness band method for ductile fracture analysis , 2009 .

[55]  A. Needleman,et al.  Analysis of the cup-cone fracture in a round tensile bar , 1984 .

[56]  G. Voyiadjis,et al.  Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior , 2007 .

[57]  Tomasz Wierzbicki,et al.  Prediction of plane strain fracture of AHSS sheets with post-initiation softening , 2010 .

[58]  Michael Brünig,et al.  Simulation of damage evolution in ductile metals undergoing dynamic loading conditions , 2011 .

[59]  Rinze Benedictus,et al.  Formability prediction of high strength aluminum sheets , 2009 .

[60]  Thomas Pardoen,et al.  Micromechanics-based model for trends in toughness of ductile metals , 2003 .

[61]  Stephen F. Corbin,et al.  The influence of iron content on the plane strain fracture behaviour of AA 5754 Al–Mg sheet alloys , 2002 .

[62]  F. A. McClintock,et al.  A Criterion for Ductile Fracture by the Growth of Holes , 1968 .

[63]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[64]  Z. Marciniak,et al.  Limit strains in the processes of stretch-forming sheet metal , 1967 .

[65]  S. M. Graham,et al.  On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule , 2011 .

[66]  C. L. Chow,et al.  An anisotropic theory of continuum damage mechanics for ductile fracture , 1987 .

[67]  K. S. Choi,et al.  Predicting failure modes and ductility of dual phase steels using plastic strain localization , 2009 .

[68]  S. Clift,et al.  Fracture prediction in plastic deformation processes , 1990 .

[69]  Michael Brünig,et al.  A ductile damage criterion at various stress triaxialities , 2008 .

[70]  Raju Sethuraman,et al.  A continuum damage mechanics model for ductile fracture , 2000 .

[71]  J. Besson,et al.  Fracture of 6056 aluminum sheet materials: effect of specimen thickness and hardening behavior on strain localization and toughness , 2005 .

[72]  I. Sinclair,et al.  Experimental and numerical analysis of toughness anisotropy in AA2139 Al-alloy sheet , 2009 .

[73]  Liza Lecarme,et al.  Void growth and coalescence in ductile solids with stage III and stage IV strain hardening , 2011 .

[74]  Xiaosheng Gao,et al.  Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy , 2009 .

[75]  L. Xue,et al.  Constitutive modeling of void shearing effect in ductile fracture of porous materials , 2008 .

[76]  Dirk Mohr,et al.  Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method , 2007 .

[77]  K. L. Nielsen,et al.  Micro-mechanical modelling of ductile failure in 6005A aluminium using a physics based strain hardening law including stage IV , 2010 .