Limit strains variability with respect to material scatter


  • Liana Paraianu
  • Dan Sorin Comsa
  • Dorel Banabic


metal forming, failure, sheet metal


In this paper a study regarding to the effect of the variability of the mechanical parameters on the prediction of the limit strain have been presented. The necking criterion used in the analyses is the one proposed by Marciniak-Kuczinsky [M-K]. The inelastic behaviour of the sheet metal has been described by BBC2005 yield criterion and Hill48 yield criterion respectively. The Swift’s formulation has been used in order to describe the hardening of the material. The material investigated in this paper is DC04 steel sheet (0.85 mm thickness).


COL, A., Investigation on press forming scatter origin, Proc. of ESAFORM 2003 Conference, Salerno, 2003, pp. 183–186.

GERLACH, J., BLUMMEL, K., PAUL, U., Method to ensure appropriate use of material parameter variations for simulation, Proc. of ICTP Conference, Yokohama, 2002, pp. 841–846.

KARTHIK, V, COMSTOCK, R.-J., HERSHBERGER, D.-L. WAGONER, R.-H., Variability of sheet formability and formability testing, Journal of Materials Processing Technology, 121, 2-3, pp. 350–362, 2002.

CARLEER, B., ZWICKL, T., Robust forming process under the “reality” of process and material scatter, in: New developments in sheet metal forming (ed. K. Siegert), Frankfurt, MATINFO, 2004, pp. 175–192.

CARLEER, B. SIGVANT, M., Process scatter with respect to material scatter, in: New developments in sheet metal forming (ed. M. Liewald), Frankfurt, MATINFO, 2006, pp. 225–239.

CARLEER, B., Applicability of stochastical methods in the control of the scatter influence of constitutive parameters, Proc. of the FLC Conference, Zürich, 2006, pp. 116–122.

CARLEER, B., Robust design of sheet metal forming process, in: Sheet metal forming processes. Constitutive modelling and numerical simulation (ed. D. Banabic), Berlin Heidelberg, Springer, 2010, pp. 255–267.

ATZEMA, E., BROUWER, H., KOMMELT, P., Long and short term strategy to deal with material property variation in sheet metal forming, Proc. of IDDRG Conference, Porto, 2006, pp. 121–128.

ATZEMA, E., ABSPOEL, M., KÖMMELT, P., LAMBRIKS, M., Towards robust simulations in sheet metal forming, International Journal of Material Forming, 2, pp. 351–354, 2009.

ROJEK, J., KLEIBER, M., PIELA, A., STOCKI, R. KNABEL, J., Deterministic and stochastic analysis of failure in sheet metal forming operations, Steel Grips, 2, pp. 29–34, 2004.

ZHANG, W., SHIVPURI, R., Investigating reliability of variable blank holder force control in sheet drawing under process uncertainties, Journal of Manufacturing Science and Engineering, 130, 4, pp. 1–8, 2008.

MARRETTA, L., DI LORENZO, R., Influence of material properties variability on springback and thinning in sheet stamping processes: a stochastic analysis, The International Journal of Advanced Manufacturing Technology, 51, 1–4, pp. 117–134, 2010.

ASPENBERG, D., LARSSON, R. NILSSON, L., An evaluation of the statistics of steel material model parameters, Journal of Materials Processing Technology, 212, 6, pp. 1288–1297, 2012.

VAN MINH, H., SOWERBY, R., DUNCAN, J.L., Variability of forming limit curves, International Journal of Mechanical Sciences, 16, 1, pp. 34–44, 1974.

JANSSENS, K., LAMBERT, F., VANROSTENBERGHE, S., VERMEULEN, M., Statistical evaluation of the uncertainty of experimentally characterized forming limits of sheet steel, Journal of Materials Processing Technology, 112, 2–3, pp. 174–184, 2001.

STRANO, M., COLOSIMO, B.-M., Logistic regression analysis for experimental determination of forming limit diagrams, International Journal of Machine Tools and Manufacture, 46, 6, pp. 673–682, 2006.

BANABIC, D., VOS, M., Modelling of the Forming Limit Band –A new Method to Increase the Robustness in the Simulation of Sheet Metal Forming Processes, CIRP Annals – Manufacturing Technology, 56, 1, pp. 249–252, 2007.

FYLLINGEN, Ø., HOPPERSTAD, O.S., LANGSETH, M., Stochastic simulations of forming limit diagrams, Proc. of ESAFORM Conference, 2007, pp. 293–296.

FYLLINGEN, Ø., HOPPERSTAD, O.S., LADEMO, O-G, LANGSETH, M., Estimation of forming limit diagrams by the use of the finite element method and Monte Carlo simulation, Computers and Structures, 87, 1–2, pp. 128–139, 2009.

NARASIMHAN, K., ZHOU, D., WAGONER, R.H., Application of the Monte Carlo and finite element methods to predict the scatter band in forming limit strains, Scripta Metallurgica Materialia, 26, 1, pp. 41–46, 1992.

KIM, J., KANG, B.-S., LEE, J.K., Statistical evaluation of forming limit in hydroforming process using plastic instability combined with FORM, The International Journal of Advanced Manufacturing Technology, 42, 1–2, pp. 53–59, 2009.

P?R?IANU, L., BICHIS, I., BANABIC, D., Variability analysis of the mechanical parameters in order to determine the Forming Limit Band, Proc. of ESAFORM Conference, 2011, pp. 1511–1516.

P?R?IANU, L., COMSA, D.S., BANABIC, D., Forming limit band prediction based o modified maximum force criterion model, FTF Conference, Zurich, 2012, pp. 135–138.

CHIBA, R., Reliability analysis of forming limits of anisotropic metal sheet with uncertain material properties, Computational Materials Science, 69, pp. 113–120, 2013.

WIEBENGA, J.H., Robust design and optimization of forming processes, PhD Thesis, University of Twente, Enschede, 2014.



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