Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part I: Plasticity

Abstract An extensive experimental program has been carried out to characterize the plastic behavior of 2 mm thick extruded aluminum AA6260-T6 sheets under large deformations. Using a newly-developed dual actuator system, combinations of normal and tangential loads are applied to a flat specimen to investigate the material response under more than 30 different multi-axial stress states. The Yld2000-2d yield criterion with an associated flow rule and an isotropic hardening model has been successfully used to describe the initial yield surface and its evolution. The comparison between the experimental results and finite element simulations shows that this constitutive model provides very accurate predictions for the material response under multi-axial loading. A special extension of the Yld2000-2d yield function for general three-dimensional stress states is also presented. The yield function for three-dimensional stress states is chosen such that it reduces to the Yld2000-2d yield function under plane stress conditions and makes use of the same anisotropy coefficients.

[1]  Jeong Whan Yoon,et al.  A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming , 2010 .

[2]  Jacques Besson,et al.  A yield function for anisotropic materials Application to aluminum alloys , 2004 .

[3]  R. Mises.  Mechanik der festen Körper im plastisch- deformablen Zustand , 1913 .

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

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

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

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

[8]  Frédéric Barlat,et al.  A novel approach for anisotropic hardening modeling. Part I: Theory and its application to finite element analysis of deep drawing , 2009 .

[9]  G Ferron,et al.  Design and development of a biaxial strength testing device , 1988 .

[10]  Fusahito Yoshida,et al.  Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain , 2002 .

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

[12]  Kwansoo Chung,et al.  Spring-back evaluation of automotive sheets based on isotropic–kinematic hardening laws and non-quadratic anisotropic yield functions, part III: applications , 2005 .

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

[14]  Frédéric Barlat,et al.  Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions , 1989 .

[15]  Haowen Liu,et al.  Variable strain rate sensitivity in an aluminum alloy: Response and constitutive modeling , 2012 .

[16]  Thomas B. Stoughton,et al.  Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al) , 2010 .

[17]  Tetsuo Naka,et al.  Effects of temperature on yield locus for 5083 aluminum alloy sheet , 2003 .

[18]  F. Barlat,et al.  A six-component yield function for anisotropic materials , 1991 .

[19]  Tore Børvik,et al.  Evaluation of identification methods for YLD2004-18p , 2008 .

[20]  Jeong Whan Yoon,et al.  Anisotropic hardening and non-associated flow in proportional loading of sheet metals , 2009 .

[21]  R. Hill.  Theoretical plasticity of textured aggregates , 1979, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  Jeong Whan Yoon,et al.  Sheet metal formability analysis for anisotropic materials under non-proportional loading , 2005 .

[23]  Dual-stage nested homogenization for rate-dependent anisotropic elasto-plasticity model of dendritic cast aluminum alloys , 2011 .

[24]  Jeong W Yoon,et al.  Modeling of aluminum alloy sheets based on new anisotropic yield functions , 2006 .

[25]  Geoffrey Ingram Taylor,et al.  The Plastic Distortion of Metals , 1932 .

[26]  W. Hosford.  A Generalized Isotropic Yield Criterion , 1972 .

[27]  D. Mohr,et al.  Macroscopic plasticity modeling of anisotropic aluminum extrusions using a Reduced Texture Methodology , 2012 .

[28]  Thomas B. Stoughton,et al.  A non-associated flow rule for sheet metal forming , 2002 .

[29]  Thomas B. Stoughton,et al.  Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511) , 2009 .

[30]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[31]  Jeong Whan Yoon,et al.  Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystal plasticity , 2009 .

[32]  Larsgunnar Nilsson,et al.  On constitutive modeling of aluminum alloys for tube hydroforming applications , 2005 .

[33]  Željan Lozina,et al.  A finite element formulation based on non-associated plasticity for sheet metal forming , 2008 .

[34]  Dirk Mohr,et al.  Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading , 2010 .

[35]  R. Pearce,et al.  The anomalous behaviour of aluminium sheet under balanced biaxial tension , 1970 .

[36]  Kengo Yoshida,et al.  Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure , 2004 .

[37]  M. Langseth,et al.  An evaluation of yield criteria and flow rules for aluminium alloys , 1999 .

[38]  K. S. Raghavan.  A simple technique to generate in-plane forming limit curves and selected applications , 1995 .

[39]  F. Barlat,et al.  Yield function development for aluminum alloy sheets , 1997 .

[40]  Frédéric Barlat,et al.  Linear transfomation-based anisotropic yield functions , 2005 .

[41]  Frédéric Barlat,et al.  An alternative to kinematic hardening in classical plasticity , 2011 .

[42]  R. Hill.  Constitutive modelling of orthotropic plasticity in sheet metals , 1990 .

[43]  Stelios Kyriakides,et al.  Path-dependent failure of inflated aluminum tubes , 2009 .

[44]  R. Desmorat,et al.  Non-quadratic Kelvin modes based plasticity criteria for anisotropic materials , 2011 .

[45]  An Evaluation of Anisotropic Effective Stress-Strain Criteria for the Biaxial Yield and Flow of 2024 Aluminum Tubes , 1983 .

[46]  Stelios Kyriakides,et al.  Hydroforming of anisotropic aluminum tubes: Part II analysis , 2011 .

[47]  Haowen Liu,et al.  Strain rate and temperature dependent fracture criteria for isotropic and anisotropic metals , 2012 .

[48]  Kjell Arne Malo,et al.  Modelling of plastic anisotropy in heat-treated aluminium extrusions , 2002 .

[49]  William F. Hosford,et al.  Upper-bound anisotropic yield locus calculations assuming 〈111〉-pencil glide , 1980 .

[50]  Stephen W. Banovic,et al.  Experimental observations of evolving yield loci in biaxially strained AA5754-O , 2008 .

[51]  Stelios Kyriakides,et al.  Inflation and burst of aluminum tubes. Part II: An advanced yield function including deformation-induced anisotropy , 2008 .

[52]  Dirk Mohr,et al.  Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture , 2012 .

[53]  J. Chaboche.  Time-independent constitutive theories for cyclic plasticity , 1986 .

[54]  D. Mohr,et al.  Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling , 2008 .

[55]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[56]  John L. Bassani,et al.  Yield characterization of metals with transversely isotropic plastic properties , 1977 .

[57]  Frédéric Barlat,et al.  Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function , 2006 .

[58]  Kenneth W. Neale,et al.  Experimental investigation of the biaxial behaviour of an aluminum sheet , 2004 .

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