Model identification and FE simulations: Effect of different yield loci and hardening laws in sheet forming

https://doi.org/10.1016/j.ijplas.2006.05.006Get rights and content

Abstract

The bi-axial experimental equipment [Flores, P., Rondia, E., Habraken, A.M., 2005a. Development of an experimental equipment for the identification of constitutive laws (Special Issue). International Journal of Forming Processes] developed by Flores enables to perform Bauschinger shear tests and successive or simultaneous simple shear tests and plane strain tests. Flores investigates the material behavior with the help of classical tensile tests and the ones performed in his bi-axial machine in order to identify the yield locus and the hardening model. With tests performed on one steel grade, the methods applied to identify classical yield surfaces such as [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic materials. Proceedings of the Royal Society of London A 193, 281–297; Hosford, W.F., 1979. On yield loci of anisotropic cubic metals. In: Proceedings of the 7th North American Metalworking Conf. (NMRC), SME, Dearborn, MI, pp. 191–197] ones as well as isotropic Swift type hardening, kinematic Armstrong–Frederick or Teodosiu and Hu hardening models are explained. Comparison with the Taylor–Bishop–Hill yield locus is also provided. The effect of both yield locus and hardening model choices is presented for two applications: plane strain tensile test and Single Point Incremental Forming (SPIF).

Introduction

In practice, different metal forming processes such as deep drawing, stamping or bending are required to manufacture automotive parts, beverage or food cans, steel sheet panels used in aeronautics or civil engineering applications. Computer models try to replace the expensive and time-consuming trial-and-error methods used in conventional design. The Finite Element Method (FEM) is quite successful to simulate metal forming processes, but accuracy depends both on the constitutive laws used and their material parameters identification.

For instance, the final shape of a product is strongly linked to the plastic material flow and to the springback phenomenon. Plastic anisotropy explains the undulated rims called ears (Yoon et al., 2006), which appear in a cup produced by cylindrical tools applied on a circular blank. The classical isotropic von Mises yield criterion predicts no ears at all. The simple quadratic anisotropic Hill yield criterion often simulates an inaccurate four-earing profile. More complex models relying on the crystal plasticity and a homogenization approach provide results that are closer to the experimental observations, but they are quite greedy from a CPU time point of view.

This paper uses both simple classical phenomenological laws and micro–macro constitutive models based on crystal plasticity. Classical phenomenological models roughly consist in the fitting of functions on experimental results. They provide only crude tools, the quality of which depends both on the complexity of the chosen functions and on the type of experiments used to identify them.

The bi-axial experimental equipment (Flores et al., 2005a) developed by Flores enables to perform successive or simultaneous simple shear tests and plane strain tests (see Fig. 1).

Such experiments applied on samples cut in different directions from the rolling direction investigate the onset of plasticity and identify the initial yield locus. Stress contours at identical plastic work can also be drawn. Such data coupled with the strain field measured by optical extensometer allows checking the associated flow rule. Stoughton and Yoon (2006) shows this usually accepted approach still need confirmation and they propose for aluminum and steel alloys accurate models of non-associated type. Next section shows the difference between experimental points and yield loci defined by a phenomenological model or deduced from texture measurement and crystal plasticity.

Kinematic hardening models are identified by cyclic shear tests showing the Bauschinger effect. Orthogonal tests are performed by successive simple shear and tensile tests. Such experimental results provide the necessary data to support simple models, like the one suggested by Armstrong and Frederick (1966) or more complex ones like the Teodosiu and Hu model (Teodosiu and Hu, 1995, Teodosiu and Hu, 1998, Bouvier et al., 2003, Haddadi et al., 2006). Other deformation modes can be investigated for the identification of material parameters. (Brunet et al., 2001) used metal sheet bending–unbending tests and tensile tests for the identification of their model. (Hu, 2005, Tong, 2006) used standard uni-axial-tension and equal bi-axial-tension tests for the characterization of their models.

After the presentation of the method used to identify the yield locus and the hardening behavior for one material, two applications where the simulation results strongly depend on the model choice and identification are described: a plane strain tensile test and Single Point Incremental Forming (SPIF) process. The description of experimental procedure for all mechanical tests used in this article appears in Flores et al., 2005a, Flores, 2006.

Section snippets

Model identification

The first step is the identification of the initial yield locus shape and the second step is the hardening behavior. As underlined in the described identification approach, both steps cannot be completely decoupled. The case of DC06 IF steel sheet of 0.8 mm thickness is presented because this material shows a quite strong anisotropy. Tensile tests were performed in a standard tensile test machine of 20 kN capacity (with a normalized specimen) while the plane strain and simple shear tests were

Conclusions

This paper underlines that the identification method of models is far from being trivial and without consequence for the accuracy of FEM model predictions. The well-known approach of using the Lankford coefficients to identify Hill parameters has been shown to provide quite rough material parameters and consequently poor FEM results. Another point is the fact that in the adjustment of the constitutive law parameters, one cannot decouple the yield locus shape from the hardening model, even if it

Acknowledgements

As Research Director of the Fund for Scientific Research (Belgium), A.M. Habraken thanks this Belgian research fund for its support. The authors also thank the Belgian Federal Science Policy Office (Contract P5/08), the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT), the Walloon Region and Arcelor industry.

References (37)

  • W. Tong

    A plane stress anisotropic plastic flow theory for orthotropic sheet metals

    International Journal of Plasticity

    (2006)
  • J.W. Yoon et al.

    Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function

    International Journal of Plasticity

    (2006)
  • Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. GEGB Report...
  • B. Banabic et al.

    Formability of Metallic Materials

    (2000)
  • S. Bouvier et al.

    Anisotropic work-hardening behaviour of structural steels and aluminium alloys at large strains

    Journal de Physique IV

    (2003)
  • S. Bouvier et al.

    Simple shear test: experimental techniques and characterizations of the plastic anisotropy of rolled sheets at large strains

    Journal of Material Processing Technology

    (2005)
  • M. Brunet et al.

    Nonlinear kinematic hardening identification for anisotropic sheet metals with bending–unbending tests

    Journal of Engineering Materials and Technology

    (2001)
  • L. Duchêne et al.

    Analysis of texture evolution and hardening behavior during deep drawing with an improved mixed type FEM element

    Proc. of the 6th Inter. Conf. and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, On the Cutting Edge of Technology NUMISHEET, Detroit, MI, USA

    AIP

    (2005)
  • Cited by (84)

    • A high-fidelity simulation of double-sided incremental forming: Improving the accuracy by incorporating the effects of machine compliance

      2021, Journal of Materials Processing Technology
      Citation Excerpt :

      This is a limitation of the current model. Based on the previous studies, the reduction in the predicted forces due to introducing the Bauschinger effect is typically within a range of 20 %–40 %, as demonstrated by Flores et al. (2007) for SPIF using AA3003-O, and by Leem et al. (2019) for DSIF using AA7075-O. Nevertheless, the accuracies of the predicted forces improved dramatically when machine compliance was included in the model; the force errors were reduced by 23.0 %–277 % (see Table 4). For modeling DSIF, incorporating machine compliance is as important, if not more important, as considering the Bauschinger effect, depending on the material system and DSIF machine.

    • Damage characterization in a ferritic steel sheet: Experimental tests, parameter identification and numerical modeling

      2018, International Journal of Solids and Structures
      Citation Excerpt :

      Its microstructure is mostly ferritic with a small amount of cementite (Fig. 1), with a body-centered cubic (BCC) crystal system. Based on methodologies presented in Flores et al. (2007) and Gilles et al. (2011), the plastic behavior of the DC01 steel sheet including anisotropy and hardening, is characterized through a test campaign involving homogeneous stress and strain fields. The selected tests are a uniaxial tensile test, monotonic and Bauschinger (reverse) shear tests and a plane strain test.

    • Calibration of anisotropic yield function by introducing plane strain test instead of equi-biaxial tensile test

      2018, Transactions of Nonferrous Metals Society of China (English Edition)
    View all citing articles on Scopus
    View full text