Numerical simulations of Nakazima formability tests with prediction of failure


  • Dmytro Lumelskyj
  • Jerzy Rojek
  • Marek Tkocz


sheet forming, formability, forming limit curve, numerical simulation


This paper presents results of numerical simulations of the Nakazima test with determination of formability without using the forming limit curve. The onset of localized necking has been determined using the criterion based on analysis of the major principal strain and its first and second time derivatives in the most strained zone. The strain localization has been determined by the maximum of strain acceleration which corresponds to the inflection point of the strain velocity versus time. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering a whole range of the strain paths typical for sheet forming processes. This has allowed us to construct the numerical FLC. The numerical FLC has been compared with the experimental one. It has been shown that the numerical FLC predicts higher formability limits but the differences are not large so the method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.


DICK, R.E., YOON, J.W., STOUGHTON, T.B., Path-independent forming limit models for multistage forming processes, International Journal of Material Forming (Thematic Issue: Formability of Metallic Materials), pp. 1–11, 2015.

ZHANG, J., XU, Y., HU, P., ZHAO, K., Development and applications of forming-conditionbased formability diagram for split concerns in stamping, Journal of Manufacturing Processes, 17, pp. 151–161, 2015.

ABSPOEL, M., SCHOLTING, M.E., DROOG, J.M., A new method for predicting forming limit curves from mechanical properties, Journal of Materials Processing Technology, 213, 5, pp. 759–769, 2013.

ISO 20482, Metallic materials – Sheet and strip – Erichsen cupping test, 2003.

ISO 12004-2, Metallic materials – Sheet and strip – Determination of forming- limit curves. Part 2: Determination of forming-limit curves in the laboratory, 2008.

BANABIC, D., LAZARESCU, L., PARAIANU, L., CIOBANU, I., NICODIM, I., COMSA, D., Development of a new procedure for the experimental determination of the forming limit curves, {CIRP} Annals – Manufacturing Technology, 62, 1, pp. 255–258, 2013.

SWIFT, H.W., Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, 1, 1, pp. 1–18, 1952.

HILL, R., On discontinuous plastic states with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 1, 1, pp. 19–30, 1952.

MARCINIAK, Z., Stability of plastic shells under tension with kinematic boundary condition, Archiwum Mechaniki Stosowanej, 17, pp. 577–592, 1994.

SITU, Q., JAIN, M., METZGER, D., Determination of forming limit diagrams of sheet materials with a hybrid experimental-numerical approach, Int. Journal of Mechanical Sciences, 53, 4, pp. 707–719, 2011.

BANABIC, D., Sheet Metal Forming Processes Constitutive Modelling and Numerical Simulation, Springer, 2010.

VEERMAN, C.C., NEVE, P.F., Some aspects of the determination of the FLD – onset of localized necking, Sheet Metal Industries, 49, pp. 421–423, 1972.

BRAGARD, A., BARET, J., BONNARENS, H., A simplified technique to determine the FLD at onset of necking, Centre for Research in Metallurgy, 33, pp. 53–63, 1972.

D’HAYER, R., BRAGARD, A., Determination of the limiting strains at the onset of necking, Centre for Research in Metallurgy, 42, pp. 33–35, 1975.

KOBAYASHI, T., ISHIGAKI, H., Effect of strain ratios on the deforming limit of steel sheet and its application to the actual press forming, Proceedings of the IDDRG Congress, Amsterdam, 1972, pp. 8.1–8.4.

HECKER, S.S., Simple technique for determining forming limit curves, Sheet Metal Industries, 5, pp. 671–676, 1975.

SITU, Q., JAIN, M., BRUHIS, M., A suitable criterion for precise determination of incipient necking in sheet materials, Materials Science Forum, 519–521, pp. 111–116, 2006.

MAMUSI, H., MASOUMI, A., MAHDAVINEZHAD, R., Numerical simulation for the formability prediction of the laser welded blanks (TWB), Int. J. of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 6, 7, pp. 111–116, 2012.

LUMELSKYY, D., ROJEK, J., PECHERSKI, R., GROSMAN, F., TKOCZ, M., Numerical simulation of formability tests of pre-deformed steel blanks, Archives of Civil and Mechanical Engineering, 12, 2, pp. 133–141, 2012.

ROJEK, J., ZIENKIEWICZ, O., ONATE, E., POSTEK, E., Advances in FE explicit formulation for simulation of metal forming processes, Journal of Materials Processing Technology, 119, 1–3, pp. 41–47, 2001.

KOWALCZYK, P., ROJEK, J., STOCKI, R., BEDNAREK, T., TAUZOWSKI, P., LASOTA, R., LUMELSKYY, D., WAWRZYK, K., Numpress – integrated computer system for analysis and optimization of industrial sheet metal forming processes, HUTNIK – WIADOMOSCI HUTNICZE, 81, 1, pp. 56–63, 2014.

ROJEK, J., ONATE, E., Sheet springback analysis using a simple shell triangle with translational degrees of freedom only, International Journal of Forming Processes, 1, 3, pp. 275–296, 1998.

HILL, R., A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 193, 1033, pp. 281– 297, 1948.

LUMELSKYY, D., ROJEK, J., PECHERSKI, R., GROSMAN, F., TKOCZ, M., Influence of friction on strain distribution in nakazima formability test of circular specimen, 4th International Lower Silesia – Saxony Conference on Advanced Metal Forming Processes in Automotive Industry AutoMetForm, Freiberg, November 3th –5th, 2014, pp. 214–217.