Development and application of the material constitutive model in springback prediction of cold-bending

Abstract The accuracy for cold-bending springback prediction is determined by the sensitivity and accuracy of the material constitutive model. Thus, the material constitutive model is developed and improved by many researchers, and the improved models are applied in the springback calculation with various materials in finite element simulation or theoretical analysis. To provide a reference for the researchers studying cold-bending springback problems, a review of the development and application of the material constitutive models is presented in this paper, which conducts from the elastic behavior, the anisotropy, and the work-hardening. It can be summarized as: (1) Springback prediction result is higher and more accurate when the variable elastic modulus and the nonlinear recovery are considered. (2) The isotropic hardening leads to an overestimation of the springback, which can be avoided by a hardening model describing the Bauschinger effect. (3) The hardening model has greater impact on springback than the yield criterion. (4) Good accuracy of the springback prediction can be achieved when the variable elastic modulus effect, the material anisotropy and the nonlinear hardening are considered together. It is also found the theory development and practical application of the material constitutive models are out of line, due to lacking further experiment, or that the stress loading–reloading history within a bending part may be not so complex as that “ratchetting behavior” discussed.

[1]  R. H. Wagoner,et al.  Simulation of springback , 2002 .

[2]  M. Abdel-Karim,et al.  Effect of elastic modulus variation during plastic deformation on uniaxial and multiaxial ratchetting simulations , 2011 .

[3]  C. H. Cáceres,et al.  Pseudoelastic behaviour of cast magnesium AZ91 alloy under cyclic loading–unloading , 2003 .

[4]  Daniel E. Green,et al.  Semi-implicit numerical integration of Yoshida–Uemori two-surface plasticity model , 2010 .

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

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

[7]  Lakhdar Taleb,et al.  Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models , 2008 .

[8]  J. K. Lee,et al.  Modeling the Bauschinger effect for sheet metals, part II: applications , 2002 .

[9]  Michael Wolff,et al.  Consistency for two multi-mechanism models in isothermal plasticity , 2008 .

[10]  A. Ghosh,et al.  Inelastic effects on springback in metals , 2002 .

[11]  R. H. Wagoner,et al.  Measurement of springback , 2002 .

[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]  Frédéric Barlat,et al.  Advances in anisotropy and formability , 2010 .

[14]  F. Barlat,et al.  Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction , 2012 .

[15]  Frédéric Barlat,et al.  Spring-back evaluation of automotive sheets based on isotropic-kinematic hardening laws and non-quadratic anisotropic yield functions: Part I: theory and formulation , 2005 .

[16]  Farid Abed-Meraim,et al.  Investigation of advanced strain-path dependent material models for sheet metal forming simulations , 2007 .

[17]  R. H. Wagoner,et al.  Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets , 2008 .

[18]  R. H. Wagoner,et al.  Role of plastic anisotropy and its evolution on springback , 2002 .

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

[20]  Zhongqin Lin,et al.  Numerical analysis of dimension precision of U-shaped aluminium profile rotary stretch bending , 2007 .

[21]  Mei Zhan,et al.  Research on the springback of thin-walled tube NC bending based on the numerical simulation of the whole process , 2008 .

[22]  Xueyu Ruan,et al.  An analytical model for predicting springback and side wall curl of sheet after U-bending , 2007 .

[23]  Mehmet Firat,et al.  Sheet metal forming analyses with an emphasis on the springback deformation , 2008 .

[24]  M. Kimchi,et al.  Numerical Modeling for Springback Predictions by Considering the Variations of Elastic Modulus in Stamping Advanced High‐Strength Steels (AHSS) , 2011 .

[25]  Zhen Zhao,et al.  Springback investigation of anisotropic aluminum alloy sheet with a mixed hardening rule and Barlat yield criteria in sheet metal forming , 2010 .

[26]  Toshihiko Kuwabara,et al.  Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations , 2007 .

[27]  Kjell Mattiasson,et al.  On the modelling of the bending–unbending behaviour for accurate springback predictions , 2009 .

[28]  J. K. Lee,et al.  Modeling the Bauschinger effect for sheet metals, part I: theory , 2002 .

[29]  Sami Chatti,et al.  The effect of non-linear recovery on springback prediction , 2011 .

[30]  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 .

[31]  Dorel Banabic,et al.  An improved analytical description of orthotropy in metallic sheets , 2005 .

[32]  Akhtar S. Khan,et al.  Continuum theory of plasticity , 1995 .

[33]  Bertil Enquist,et al.  Identification of material hardening parameters by three-point bending of metal sheets , 2006 .

[34]  Kwansoo Chung,et al.  Optimization of boost condition and axial feeding on tube bending and hydro-forming process considering formability and spring-back , 2009 .

[35]  R. H. Wagoner,et al.  Springback Analysis with a Modified Hardening Model , 2000 .

[36]  R. Hill The mathematical theory of plasticity , 1950 .

[37]  Yannis F. Dafalias,et al.  BOUNDING SURFACE PLASTICITY, I: MATHEMATICAL FOUNDATION AND HYPOPLASTICITY , 1986 .

[38]  H. Yu,et al.  Variation of elastic modulus during plastic deformation and its influence on springback , 2009 .

[39]  J. Yoon,et al.  A nonlinear kinematic hardening model for the simulation of cyclic loading paths in anisotropic aluminum alloy sheets , 2005 .

[40]  C. Guo,et al.  A constitutive model for spring-back prediction in which the change of Young's modulus with plastic deformation is considered , 2007 .

[41]  Frédéric Barlat,et al.  A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material , 2010 .

[42]  Kwansoo Chung,et al.  A practical two-surface plasticity model and its application to spring-back prediction , 2007 .

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

[44]  K. Mattiasson,et al.  On the Modeling of the Unloading Modulus for Metal Sheets , 2010 .

[45]  E Da-xin,et al.  Spring-back deformation in tube bending , 2009 .

[46]  Michael R. Lovell,et al.  Investigation of springback in high strength anisotropic steels , 2005 .

[47]  S. Yonemura,et al.  Elastic-Plastic and Inelastic Characteristics of High Strength Steel Sheets under Biaxial Loading and Unloading , 2010 .

[48]  J. Chaboche,et al.  Modeling of ratchetting: evaluation of various approaches , 1994 .

[49]  V. Schulze,et al.  Texture-Based Modeling of Sheet Metal Forming and Springback , 2009 .

[50]  B. Tang,et al.  U-bending springback prediction of highly anisotropic aluminum alloy sheet by an efficient non-linear combined hardening rule , 2010, 2010 International Conference on Mechanic Automation and Control Engineering.

[51]  C. O. Frederick,et al.  A mathematical representation of the multiaxial Bauschinger effect , 2007 .

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

[53]  Mohammad Bakhshi-Jooybari,et al.  The study of spring-back of CK67 steel sheet in V-die and U-die bending processes , 2009 .

[54]  K. Saï Multi-mechanism models: Present state and future trends , 2011 .

[55]  G. Kinzel,et al.  A New Model for Springback Prediction for Aluminum Sheet Forming , 2005 .

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

[57]  G. B. Broggiato,et al.  The Chaboche nonlinear kinematic hardening model: calibration methodology and validation , 2008 .

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

[59]  R. H. Wagoner,et al.  Complex unloading behavior: Nature of the deformation and its consistent constitutive representation , 2011 .

[60]  Yeong-Maw Hwang,et al.  The bending moment and springback in pure bending of anisotropic sheets , 2009 .

[61]  Odd Sture Hopperstad,et al.  Sensitivity of model parameters in stretch bending of aluminium extrusions , 2001 .

[62]  Jun Bao,et al.  Effect of the material-hardening mode on the springback simulation accuracy of V-free bending , 2002 .

[63]  Jung-Ho Cheng,et al.  NDE of metal damage: ultrasonics with a damage mechanics model , 2003 .

[64]  F. Barlat,et al.  Yielding description for solution strengthened aluminum alloys , 1997 .

[65]  Amit K. Ghosh,et al.  Elastic and Inelastic Recovery After Plastic Deformation of DQSK Steel Sheet , 2003 .

[66]  Jean-Louis Chaboche,et al.  A review of some plasticity and viscoplasticity constitutive theories , 2008 .

[67]  Luc Papeleux,et al.  Finite element simulation of springback in sheet metal forming , 2002 .

[68]  Rosa Di Lorenzo,et al.  Influence of material properties variability on springback and thinning in sheet stamping processes: a stochastic analysis , 2010 .

[69]  Guoqun Zhao,et al.  A mixed hardening rule coupled with Hill48’ yielding function to predict the springback of sheet U-bending , 2008 .

[70]  Ming Yang,et al.  Evaluation of change in material properties due to plastic deformation , 2004 .

[71]  Enying Li,et al.  Reduction of springback by intelligent sampling-based LSSVR metamodel-based optimization , 2013 .

[72]  Stefanie Reese,et al.  Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening , 2009 .

[73]  William Altenhof,et al.  Finite element simulation of springback for a channel draw process with drawbead using different hardening models , 2009 .

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

[75]  R. Perez,et al.  Study of the Inelastic Response of TRIP Steels after Plastic Deformation , 2005 .

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

[77]  J. Moosbrugger,et al.  A substructure mixtures model for the cyclic plasticity of single slip oriented nickel single crystal at low plastic strain amplitudes , 2005 .

[78]  Dorel Banabic,et al.  Non-quadratic yield criterion for orthotropic sheet metals under plane-stress conditions , 2003 .

[79]  Ihab Ragai,et al.  Anisotropy and springback in draw-bending of stainless steel 410: Experimental and numerical study , 2005 .

[80]  F. Barlat,et al.  Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets , 2005 .

[81]  N. Ramakrishnan,et al.  Finite Element Analysis of sheet metal bending process to predict the springback , 2010 .

[82]  Kjell Mattiasson,et al.  An evaluation of some recent yield criteria for industrial simulations of sheet forming processes , 2008 .

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

[84]  Yannis F. Dafalias,et al.  Plastic Internal Variables Formalism of Cyclic Plasticity , 1976 .

[85]  Hiroshi Hamasaki,et al.  Air bending and springback of stainless steel clad aluminum sheet , 2010 .

[86]  Kwansoo Chung,et al.  Springback prediction of TWIP automotive sheets , 2009 .

[87]  Fusahito Yoshida,et al.  A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation , 2002 .

[88]  Fusahito Yoshida,et al.  A Model of Large-Strain Cyclic Plasticity and its Application to Springback Simulation , 2002 .

[89]  A. H. van den Boogaard,et al.  A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states , 2006 .

[90]  Zenon Mróz,et al.  On the description of anisotropic workhardening , 1967 .

[91]  R. H. Wagoner,et al.  Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets : Application to sheet springback , 2009 .

[92]  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 .

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

[94]  Peter Hodgson,et al.  Experimental and numerical studies of springback in air v-bending process for cold rolled TRIP steels , 2006 .

[95]  S. Thuillier,et al.  A model of one-surface cyclic plasticity and its application to springback prediction , 2011 .

[96]  Fabrice Morestin,et al.  Elasto plastic formulation using a kinematic hardening model for springback analysis in sheet metal forming , 1996 .

[97]  Sandrine Thuillier,et al.  Influence of constitutive model in springback prediction using the split-ring test , 2009 .

[98]  David L. McDowell,et al.  A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations , 1985 .

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

[100]  D. A. Oliveira,et al.  Tube bending and hydroforming of aluminium alloy S-rails , 2009 .

[101]  Jean-Louis Chaboche,et al.  On some modifications of kinematic hardening to improve the description of ratchetting effects , 1991 .

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

[103]  Ruan Xue-yu,et al.  Sheet springback prediction based on non-linear combined hardening rule and Barlat89’s yielding function , 2006 .

[104]  Frédéric Barlat,et al.  Anticlastic curvature in draw-bend springback , 2005 .

[105]  Mei Zhan,et al.  Coupling effects of material properties and the bending angle on the springback angle of a titanium alloy tube during numerically controlled bending , 2010 .

[106]  J. K. Lee,et al.  Finite element analysis of the three-point bending of sheet metals , 2002 .

[107]  Kwansoo Chung,et al.  Spring-back evaluation of automotive sheets based on isotropic-kinematic hardening laws and non-quadratic anisotropic yield functions: Part II: characterization of material properties , 2005 .

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

[109]  B. Stok,et al.  Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation , 2009 .

[110]  N. T. Tseng,et al.  Simple Plasticity Model of Two-Surface Type , 1983 .

[111]  Luís Menezes,et al.  Study on the influence of work-hardening modeling in springback prediction , 2007 .

[112]  Gary L. Kinzel,et al.  An experimental investigation of the influence of the Bauschinger effect on springback predictions , 2001 .

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

[114]  Yuli Liu,et al.  ESTABLISHMENT OF SPRINGBACK PREDICTION MODEL FOR THE ROTARY-DRAW BENDING OF THIN-WALLED RECTANGULAR TUBE CONSIDERING VARIATION OF YOUNG'S MODULUS , 2011 .