On the Measurement of Nakazima Testing Based Out-of-Plane Forming Limit Curves using 2D Digital Image Correlation


Akshat Agha
Fadi Abu-Farha


The strain compensation method for measuring in-plane forming limit curves (FLCs) using 2D digital image correlation developed previously [A method of measuring in-plane forming limit curves using 2D Digital Image Correlation, SAE Int. J. Mater. Manf., 2023] was modified and extended to more versatile and popular out-of-plane FLCs. The current study introduces a straightforward strain compensation technique for measuring Nakazima testing based out-of-plane FLCs utilizing an affordable single-camera (2D) DIC system. In this study, forming tests are performed on two automotive-grade sheet metal alloys: DP980 steel and a 6xxx series aluminum alloy using the Nakazima test method. The experiments are conducted on a customized setup that allows for simultaneous optical strain measurements using both a stereo DIC and a 2D DIC system. The FLCs are obtained by applying a temporal FLC computation approach to the two measurement sets. The results show that 2D DIC FLC points match those obtained by stereo DIC for both the materials after applying the proposed strain correction method.


How to Cite
Agha, A., & Abu-Farha, F. (2023). On the Measurement of Nakazima Testing Based Out-of-Plane Forming Limit Curves using 2D Digital Image Correlation. International Journal of Pioneering Technology and Engineering, 2(01), 120–127. https://doi.org/10.56158/jpte.2023.42.2.01


  1. Marciniak Z. and Kuczyński K., 1967, Limit strains in the processes of stretch-forming sheet metal, Int J Mech Sci, vol. 9, no. 9, pp. 609–620, Sep., doi: 10.1016/0020-7403(67)90066-5.
  2. Nakazima, K., Toshio Kikuma, and Kaname Hasuka, 1968, Study on the formability of steel sheets, Yawata Tech Rep, Sept, vol. 264, pp. 8517–8530, 1968.
  3. Agha A., 2022, Effectiveness of 2D Digital Image Correlation in Capturing the Fracture Behavior of Sheet Metal Alloys, SAE International Journal of Materials and Manufacturing, vol. 16, no. 2, doi: 10.4271/05-16-02-0009.
  4. A. Agha and F. Abu-Farha, 2023, A Method for Measuring In-Plane Forming Limit Curves Using 2D Digital Image Correlation, SAE International Journal of Materials and Manufacturing, vol. 16, no. 3, doi: 10.4271/05-16-03-0019.
  5. “ISO 12004-2:2021 - Metallic materials — Determination of forming-limit curves for sheet and strip — Part 2: Determination of forming-limit curves in the laboratory”.
  6. G. Huang, S. Sriram, and B. Yan ,2008, Digital image correlation technique and its application in forming limit curve determination, in Proceedings of the IDDRG 2008 International Conference, Olofstrom, Sweden, pp. 16–18.
  7. W. Volk and P. Hora, 2011, Evaluation of Experimental Forming Limit Curves and Investigation of Strain Rate Sensitivity for the Start of Local Necking, AIP Conf Proc, vol. 1383, no. 1, p. 99, doi: 10.1063/1.3623598.
  8. W. Hotz, M. Merklein, A. Kuppert, H. Friebe, and M. Klein, 2013, Time Dependent FLC Determination Comparison of Different Algorithms to Detect the Onset of Unstable Necking before Fracture, Key Eng Mater, vol. 549, pp. 397–404, 2013, doi: 10.4028/www.scientific.net/kem.549.397.
  9. M. Merklein, A. Kuppert, and M. Geiger, 2010, Time dependent determination of forming limit diagrams, CIRP Annals, vol. 59, no. 1, pp. 295–298, doi: 10.1016/J.CIRP.2010.03.001.
  10. A. J. Martínez-Donaire, F. J. García-Lomas, and C. Vallellano, 2014, New approaches to detect the onset of localised necking in sheets under through-thickness strain gradients, Mater Des, vol. 57, pp. 135–145, May 2014, doi: 10.1016/j.matdes.2014.01.012.
  11. J. Min, T. B. Stoughton, J. E. Carsley, and J. Lin, 2017, An improved curvature method of detecting the onset of localized necking in Marciniak tests and its extension to Nakazima tests, Int J Mech Sci, vol. 123, pp. 238–252, doi: 10.1016/J.IJMECSCI.2017.02.011.
  12. K. Wang, J. E. Carsley, B. He, J. Li, and L. Zhang, 2014 ,Measuring forming limit strains with digital image correlation analysis, J Mater Process Technol, vol. 214, no. 5, pp. 1120–1130, doi: 10.1016/j.jmatprotec.2014.01.001.
  13. J. Min, T. B. Stoughton, J. E. Carsley, and J. Lin, 2017, Comparison of DIC Methods of Determining Forming Limit Strains, Procedia Manuf, vol. 7, pp. 668–674, doi: 10.1016/j.promfg.2016.12.099.
  14. L. Huang and M. Shi, 2017, Determination of the Forming Limit Curve Using Digital Image Correlation - Comparison of Different Approaches to Pinpoint the Onset of Localized Necking, SAE Technical Papers, vol. -March, doi: 10.4271/2017-01-0301.
  15. Volk, W., & Hora, P. 2011, New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination. International journal of material forming, 4, 339-346.
  16. M. A. Sutton, J. H. Yan, V. Tiwari, H. W. Schreier, and J. J. Orteu, 2008, The effect of out-of-plane motion on 2D and 3D digital image correlation measurements, Opt Lasers Eng, vol. 46, no. 10, pp. 746–757, doi: 10.1016/j.optlaseng.2008.05.005.