Skip to main content
SpringerLink
Log in

Finite Element Modeling of Tensile Instability of Sheet Metals Considering Nonuniform Mechanical Properties

  • Technical Article
  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

In theoretical analyses, such as numerical simulations of the large plastic deformation of sheet metal forming, the material is usually assumed to be ideally uniform; thus, the actual material response during the process cannot be properly characterized. In this paper, a finite element method (FEM) model considering nonuniform material properties is proposed. In the model, the dispersion degree of mechanical parameters is characterized by the microhardness tested from sheet metal samples, and the discrete material properties conforming to the random distribution functions are automatically assigned to the elements in FEM by Python script. The digital image correlation (DIC) method is used to check the tensile instability deformation of sheet metal in the physical experiments of uniaxial tensile tests. The results show that the nonuniform finite element model can reveal the strain transfer and reproduce the diffuse instability in a wide range of plate samples. The deformation feature, crack and its direction are in good consistency with the experiment, and the predicted critical diffuse instability strain is of high accuracy compared with the DIC results. In addition, the influences of random distributions of mechanical properties and the mesh size effects on the simulation results of tensile instability are addressed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. M.A. Dib, N.J. Oliveira, A.E. Marques, M.C. Oliveira, J.V. Fernandes, B.M. Ribeiro and P.A. Prates, Single and Ensemble Classifiers for Defect Prediction in Sheet Metal Forming under Variability, Neural Comput. Appl., 2020, 32, p 12335–12349.

    Article  Google Scholar 

  2. A. Considère, Mémoire sur l’emploi du fer et de l’acier dans les constructions, Annals des Ponts et Chaussées, 1885, 9, p 574.

    Google Scholar 

  3. H.W. Swift, Plastic Instability under Plane Stress, J. Mech. Phys. Solids, 1952, 1, p 1–18.

    Article  Google Scholar 

  4. D. Banabic and E. Dannenmann, Prediction of the Influence of Yield Locus on the Limit Strains in Sheet Metals, J. Mater. Process. Tech., 2001, 109, p 9–12.

    Article  Google Scholar 

  5. D.W.A. Rees, Factors Influencing the FLD of Automotive Sheet Metal, J. Mater. Process. Tech., 2001, 118, p 1–8.

    Article  Google Scholar 

  6. S.C. Heo, T.W. Ku, J. Kim, B.S. Kang and W.J. Song, Application of Forming Limit Criteria Based on Plastic Instability Condition to Metal Forming Process, Int. J. Mod. Phys. B, 2008, 22, p 5680–5685.

    Article  Google Scholar 

  7. F. Labbé and R.R. Cordero, Detecting the Beginning of the Shear Band Formation in Uniaxial Tensile Tests by out-of-plane Displacement Measurements, Opt. Laser Eng., 2007, 45, p 153–159.

    Article  Google Scholar 

  8. M. Micunovic and L. Kudrjavceva, Diffuse Instability of Anisotropic Inelastic Plates by J2 and QRI Models, Theor. Appl. Fract. Mec., 2019, 104, p 1–8.

    Article  Google Scholar 

  9. Z.J. Wang and Y. Liu, Investigation on Deformation Behavior of Sheet Metals in Viscous Pressure Bulging based on ESPI, J. Mater. Process. Tech., 2010, 210, p 1536–1544.

    Article  Google Scholar 

  10. Y.J. Wang, A.X. Sha, X.W. Li, C.L. Jia and W.F. Hao, Experimental Study on the Forming Limit of GH605 Superalloy Sheet Using Digital Image Correlation, J. Mater. Eng. Perform., 2021, 30, p 1420–1429.

    Article  CAS  Google Scholar 

  11. Z.K. Mu, J. Zhao, G.C. Yu, X.Y. Huang, Q.D. Meng and R.X. Zhai, Hardening Model of Anisotropic Sheet Metal during the Diffuse Instability Necking Stage of Uniaxial Tension, Thin-Walled Struct., 2020, 159, p 107198.

    Article  Google Scholar 

  12. R. Hill, On Discontinuous Plastic States, with Special Reference to Localized Necking in Thin Sheets, J. Mech. Phys. Solids, 1952, 1, p 19–30.

    Article  Google Scholar 

  13. Z. Marciniak and K. Kuczyński, Limit Strains in the processes of Stretch-Forming Sheet Metal, Int. J. Mech. Sci., 1967, 9, p 609–620.

    Article  Google Scholar 

  14. J.S. Chen, P.H. Gong and L. Yang, Forming Limit Evaluation for AA5182 Aluminum Alloy at Warm Temperatures based on M-K Model, J. Mater. Eng. Perform., 2020, 29, p 1176–1184.

    Article  CAS  Google Scholar 

  15. X.Q. Li, N. Song and G.Q. Guo, Experimental Measurement and Theoretical Prediction of Forming Limit Curve for Aluminum Alloy 2B06, Trans. Nonferrous Met. Soc. China, 2012, 22, p 335–342.

    Article  Google Scholar 

  16. K. Sato, Q. Yu, J. Hiramoto, T. Urabe and A. Yoshitake, A Method to Investigate Strain Rate Effects on Necking and Fracture Behaviors of Advanced High-Strength Steels Using Digital Imaging Strain Analysis, Int. J. Impact Eng., 2015, 75, p 11–26.

    Article  Google Scholar 

  17. F. Abed-Meraim, T. Balan and G. Altmeyer, Investigation and Comparative Analysis of Plastic Instability Criteria Application to Forming Limit Diagrams, Int. J. Adv. Manuf. Technol., 2014, 71, p 1247–1262.

    Article  Google Scholar 

  18. H.W. Li, X.X. Sun and H. Yang, A Three-Dimensional Cellular Automata-Crystal Plasticity Finite Element Model for Predicting the Multiscale Interaction among Heterogeneous Deformation, DRX Microstructural Evolution and Mechanical Responses in Titanium Alloys, Int. J. Plasticity, 2016, 87, p 154–180.

    Article  CAS  Google Scholar 

  19. A. Milenin, E. Velikoivanenko, G. Rozynka, and N. Pivtorak, Residual Strength and Reliability of Corroded Pipelines-Monte-Carlo Approach for Consideration of Spatially Nonuniform Material Properties, ICTAEM, E.E. Gdoutos (Ed.), June 23-26, (Corfu, Greece), 2019, p 321-326.

  20. T. Furushima, T. Nakayama and K. Sasaki, A New Theoretical Model of Material Inhomogeneity for Prediction of Surface Roughening in Micro Metal Forming, CIRP Ann.-Manuf. Techn., 2019, 68, p 257–260.

    Article  Google Scholar 

  21. S. Dumoulin, O.S. Hopperstad and T. Berstad, Investigation of Integration Algorithms for Rate-Dependent Crystal Plasticity Using Explicit Finite Element Codes, Comp. Mater. Sci., 2009, 46, p 785–799.

    Article  CAS  Google Scholar 

  22. X.H. Hu, D.S. Wilkinson, M. Jain, P.D. Wu and R.K. Mishra, The Impact of Particle Distributions and Grain-Level Inhomogeneities on Post-Necking Deformation and Fracture in AA5754 Sheet Alloys during Uniaxial Tension, Mat. Sci. Eng. A, 2011, 528, p 2002–2016.

    Article  Google Scholar 

  23. Y.L. Liu, Y.X. Zhu, W.Q. Dong and H. Yang, Springback Prediction Model Considering the Variable Young’s Modulus for the Bending Rectangular 3A21 Tube, J. Mater. Eng. Perform., 2013, 22, p 9–16.

    Article  CAS  Google Scholar 

  24. L.C. Guo and N. Noda, Modeling Method for A Crack Problem of Functionally Graded Materials with Arbitrary Properties—Piecewise-Exponential Model, Int. J. Solids Struct., 2007, 44, p 6768–6790.

    Article  Google Scholar 

  25. J.W. Leggoe, Developing Techniques for Modeling Spatially Heterogeneous Materials, Trans. Eng. Sci., 2003, 43, p 145–154.

    Article  Google Scholar 

  26. H. Xue, Y.Q. Bi, S. Wang, J.L. Zhang and S.Y. Gou, Compilation and Application of UMAT for Mechanical Properties of Heterogeneous Metal Welded Joints in Nuclear Power Materials, Adv. Mater. Sci. Eng., 2019, 2, p 1–12.

    Google Scholar 

  27. K.E. N’souglo and J.A. Rodríguez-Martínez, Non-uniform Distributions of Initial Porosity in Metallic Materials Affect the Growth rate of Necking Instabilities in Flat Tensile Samples Subjected to Dynamic Loading, Mech. Res. Commun., 2018, 91, p 87–92.

    Article  Google Scholar 

  28. K.M. Zhao, L.M. Wang, Y. Chang and J.W. Yan, Identification of Post-Necking Stress-Strain Curve for Sheet Metals by Inverse Method, Mech. Mater., 2016, 92, p 107–118.

    Article  Google Scholar 

  29. S.C. Krishna, N.K. Gangwar, A.K. Jha and B. Pant, On the Prediction of Strength from Hardness for Copper Alloys, J. Mater., 2013, 2013, p 1–6.

    Google Scholar 

  30. M.X. Yang, Y. Pan, F.P. Yuan, Y.T. Zhu and X.L. Wu, Back Stress Strengthening and Strain Hardening in Gradient Structure, Mater. Res. Lett., 2016, 4, p 145–151.

    Article  CAS  Google Scholar 

  31. Y. Bouktir, H. Chalal, and F. Abed-Meraim, Prediction of Necking in Thin Sheet Metals Using an Elastic-Plastic Model Coupled with Ductile Damage and Bifurcation Criteria, Int. J. Damage Mech., 2017, 0, p 1-39.

  32. H. Petryk, Plastic Instability: Criteria and Computational Approaches, Arch. Comput. Method E., 1997, 4, p 111–151.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Natural Science Foundation of Chongqing, China (cstc2020jcyj-msxmX0420) and the National Natural Science Foundation of China (Grant No. 51575066).

Author information

Authors and Affiliations

  1. College of Materials Science and Engineering, Chongqing University, Chongqing, 400044, China

    Haoxing Tang, Tong Wen, Yin Zhou, Fan Yang & Yu Zheng

Authors
  1. Haoxing Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tong Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yu Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tong Wen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, H., Wen, T., Zhou, Y. et al. Finite Element Modeling of Tensile Instability of Sheet Metals Considering Nonuniform Mechanical Properties. J. of Materi Eng and Perform 31, 3753–3762 (2022). https://doi.org/10.1007/s11665-021-06492-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-021-06492-8

Keywords

Search

Navigation