Extension of quasi-plastic-elastic approach to incorporate complex plastic flow behavior - application to springback of advanced high-strength steels

Materials modeling and numerical formulations were conducted to describe the complex material behavior upon strain path change in order to enhance the prediction accuracy of springback in advanced high strength steels (AHSS). An approach without kinematic hardening rule, or the homogeneous anisotropic hardening (HAH) model, was incorporated to the newly conceived quasi-plastic–elastic strain (QPE) formulations. The HAH model is able to capture complex plastic flow behavior of sheet metals such as the Bauschinger effect, transient behavior, work-hardening stagnation and permanent softening. The QPE approach was developed to reproduce the nonlinear elastic behavior during unloading and reloading. The two models were independently validated for predicting springback, with better performance than conventional constitutive models. In this study, the two models are combined and extended to enhance the prediction capability of springback in AHSS. For this purpose, fully implicit numerical algorithms were re-formulated to link the two modeling approaches using general anisotropic yield function and hardening for shell element. The original model was only valid for continuum isotropic element with analytical stress integration procedure. Simulations of 2D draw bending test were performed to validate the developed approach for two AHSS, DP780 and TRIP780, sheets. The springback prediction was significantly improved if most of the complex material behavior relating to elasticity and plasticity were taken into account in the finite element simulations.

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

[2]  H. Aretz.  A simple isotropic-distortional hardening model and its application in elastic-plastic analysis of localized necking in orthotropic sheet metals , 2008 .

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

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

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

[6]  Byung Chai Lee,et al.  GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL , 1996 .

[7]  Han-chin Wu.  On finite plastic deformation of anisotropic metallic materials , 2003 .

[8]  Sylvain Calloch,et al.  An Improvement of Multiaxial Ratchetting Modeling Via Yield Surface Distortion , 2002 .

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

[10]  Hans-Werner Ziegler.  A Modification of Prager's Hardening Rule , 1959 .

[11]  R. H. Wagoner,et al.  Anisotropic hardening equations derived from reverse-bend testing , 2002 .

[12]  Y. Dafalias,et al.  Simple Model for Directional Distortional Hardening in Metal Plasticity within Thermodynamics , 2008 .

[13]  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 .

[14]  David R. Owen,et al.  Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis , 1993 .

[15]  R. H. Wagoner,et al.  A plastic constitutive equation incorporating strain, strain-rate, and temperature , 2010 .

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

[17]  Yannis F. Dafalias,et al.  Directional distortional hardening in metal plasticity within thermodynamics , 2007 .

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

[19]  Frédéric Barlat,et al.  Advances in Sheet Forming—Materials Modeling, Numerical Simulation, and Press Technologies , 2011 .

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

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

[22]  K. Neale,et al.  On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming , 1999 .

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

[24]  Katsuhiko Yamaguchi,et al.  Effects of plastic strain and strain path on youngs modulus of sheet metals , 1998, Metals and Materials.

[25]  Frédéric Barlat,et al.  EXTENSION OF HOMOGENEOUS ANISOTROPIC HARDENING MODEL TO CROSS-LOADING WITH LATENT EFFECTS , 2013 .

[26]  Kjell Mattiasson,et al.  On constitutive modeling for springback analysis , 2010 .

[27]  Frédéric Barlat,et al.  An application of homogeneous anisotropic hardening to springback prediction in pre-strained U-draw/bending , 2012 .

[28]  R. Hill,et al.  An investigation of plastic flow and differential work hardening in orthotropic brass tubes under fluid pressure and axial load , 1994 .

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

[30]  Heung Nam Han,et al.  Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite , 2010 .

[31]  R. Borst,et al.  Studies in anisotropic plasticity with reference to the Hill criterion , 1990 .

[32]  M. Życzkowski,et al.  Evolution equations for distortional plastic hardening , 1996 .

[33]  Dong-Yol Yang,et al.  Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials , 1999 .

[34]  M. François.  A plasticity model with yield surface distortion for non proportional loading , 2001 .

[35]  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 .

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

[37]  Chung-Souk Han,et al.  Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, part II: Applications , 2006 .

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

[39]  Michael Ortiz,et al.  An analysis of a new class of integration algorithms for elastoplastic constitutive relations , 1986 .

[40]  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 .

[41]  A. Matuszak.  Factors influencing friction in steel sheet forming , 2000 .

[42]  R. H. Wagoner,et al.  A sheet tension/compression test for elevated temperature , 2012 .

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

[44]  Taylan Altan,et al.  Evaluation of stamping lubricants in forming advanced high strength steels (AHSS) using deep drawing and ironing tests , 2009 .

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

[46]  Fabrice Morestin,et al.  On the necessity of taking into account the variation in the Young modulus with plastic strain in elastic-plastic software , 1996 .

[47]  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 .

[48]  Frédéric Barlat,et al.  Stress integration schemes for novel homogeneous anisotropic hardening model , 2012 .

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

[50]  G. Voyiadjis,et al.  Anisotropic Distortional Yield Model , 1990 .

[51]  Frédéric Barlat,et al.  A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming , 1999 .

[52]  Chung-Souk Han,et al.  Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, part I: Theory , 2006 .

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

[54]  W. Prager,et al.  A NEW METHOD OF ANALYZING STRESSES AND STRAINS IN WORK - HARDENING PLASTIC SOLIDS , 1956 .

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

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

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

[58]  Han-Chin Wu,et al.  Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening , 2002 .

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

[60]  Han-chin Wu.  On stress rate and plasticity constitutive equations referred to a body-fixed coordinate system , 2007 .

[61]  Haluk Darendeliler,et al.  Effect of variable friction coefficient on sheet metal drawing , 2002 .