Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T06:25:30.409Z Has data issue: false hasContentIssue false

Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet

Published online by Cambridge University Press:  12 October 2015

Minsoo Kim
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Korea
Felix Rickhey
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Korea
Hyungyil Lee*
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Korea
Naksoo Kim
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Korea
*
a)Address all correspondence to this author. e-mail: hylee@sogang.ac.kr
Get access

Abstract

The forming limit strains (FLSs) of zircaloy-4 sheets are studied. After having obtained the true stress–strain curve of zircaloy-4 using the weighted-average method, limit dome height (LDH) tests are performed to establish experimental FLSs. We summarize related theoretical forming limit curves (FLC) and discuss their limitations. Two finite element (FE) models are established for determining FLSs; an LDH test FE model for the negative minor strain sector, and a biaxial tensile FE model for the positive minor strain sector. The numerical FLSs are found to agree well with experimental data. Since the numerical FLC gives the strain at the onset of local thinning (whereas the experimental FLC provides the strain between local necking and ductile fracture), resulting FE FLS values are slightly lower than the experimental ones so that results can be regarded as conservative. Our FE approach substitutes the expensive and time-demanding experimental LDH tests.

Type
Articles
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Yang-T. Cheng

References

REFERENCES

Keeler, S.P.: Determination of forming limits in automotive stampings. Sheet Metal. Ind. 42, 683691 (1965).Google Scholar
Goodwin, G.M.: Application of strain analysis to sheet metal forming problems in the press shop. Metall. Ital. 60, 764774 (1968).Google Scholar
Arrieux, R., Bedrin, C., and Boivin, M.: Determination of an intrinsic forming limit stress diagram for isotropic metal sheets. In Proceedings of the 12th Biennial Congress IDDRG; Genoa, Italy, 1982; pp. 6171.Google Scholar
He, J., Xia, Z., Zhu, X., Zeng, D., and Li, S.: Sheet metal forming limits under stretch–bending with anisotropic hardening. Int. J. Mech. Sci. 75, 244256 (2013).Google Scholar
Inal, K., Neale, K.W., and Aboutajeddine, A.: Forming limit comparisons for FCC and BCC sheets. Int. J. Plast. 21, 12551266 (2005).Google Scholar
Lee, W., Chung, K.H., Kim, D., Kim, J., Kim, C., Okamoto, K., Wagoner, R.H., and Chung, K.: Experimental and numerical study on formability of friction stir welded TWB sheets based on hemispherical dome stretch tests. Int. J. Plast. 25, 16261654 (2009).Google Scholar
Liu, J., Liu, W., and Xue, W.: Forming limit diagram prediction of AA5052/polyethylene/AA5052 sandwich sheets. Mater. Des. 46, 112120 (2013).CrossRefGoogle Scholar
Narayanan, R.G. and Narasimhan, K.: Predicting the forming limit strains of tailor-welded blanks. J. Strain Anal. Eng. Des. 43, 217227 (2008).CrossRefGoogle Scholar
Ozturk, F. and Lee, D.: Analysis of forming limits using ductile fracture criteria. J. Mater. Process. Technol. 147, 397404 (2004).CrossRefGoogle Scholar
Pepelnjak, T. and Kuzman, K.: Numerical determination of the forming limit diagrams. J. Achiev. Mater. Manuf. Eng. 20, 375378 (2007).Google Scholar
Petek, A., Pepelnjak, T., and Kuzman, K.: An improved method for determining a forming limit diagram in the digital environment. J. Mech. Eng. 51, 330345 (2005).Google Scholar
Seong, D.Y., Haque, M.Z., Kim, J.B., Stoughton, T.B., and Yoon, J.W.: Suppression of necking in incremental sheet forming. Int. J. Solids Struct. 51, 28402849 (2014).Google Scholar
Smith, L.M., Averill, R.C., Lucas, J.P., Stoughton, T.B., and Matin, P.H.: Influence of transverse normal stress on sheet metal formability. Int. J. Plast. 19, 15671583 (2003).Google Scholar
Zhang, C., Leotoing, L., Guines, D., and Ragneau, E.: Theoretical and numerical study of strain rate influence on aa5083 formability. J. Mater. Process. Technol. 209, 38493858 (2009).Google Scholar
Zhang, L. and Wang, J.: Modeling the localized necking in anisotropic sheet metals. Int. J. Plast. 39, 103118 (2012).Google Scholar
Graf, A. and Hosford, W.F.: Effect of changing strain paths on forming limit diagram of Al 2008-T4. Metall. Mater. Trans. A 24, 25032512 (1993).Google Scholar
Stoughton, T.B. and Zhu, X.: Review of theoretical models of the strain-based FLD and their relevance to the stress-based. Int. J. Plast. 20, 14631486 (2004).CrossRefGoogle Scholar
Seo, Y., Hyun, H.C., Lee, H., and Kim, N.: Forming limit diagrams of zircaloy-4 and zirlo sheets for stamping of spacer grids of nuclear fuel rods. Trans. Korean Soc. Mech. Eng. A 35, 889897 (2011). [In Korean].Google Scholar
Hill, R.: On discontinuous plastic state, with special reference to localized necking in thin sheets. J. Mech. Phys. Solids 1, 1930 (1952).CrossRefGoogle Scholar
Swift, H.W.: Plastic instability under plane stress. J. Mech. Phys. Solids 1, 116 (1952).CrossRefGoogle Scholar
Marciniak, Z. and Kuczynski, K.: Limits strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609620 (1967).Google Scholar
Stören, S. and Rice, J.R.: Localized necking in thin sheets. J. Mech. Phys. Solids 23, 421441 (1975).CrossRefGoogle Scholar
Bridgman, P.W.: Studies in Large Plastic Flow and Fracture (McGraw Hill, New York, 1952).Google Scholar
Ling, Y.: Uniaxial true stress-strain after necking. AMP. J. Technol. 5, 3748 (1996).Google Scholar
Abaqus: Abaqus User's Manual: Version 6.12 (Dassault Systemes, Providence, RI, 2012).Google Scholar
Hyun, H.C., Kim, M., Bang, S., and Lee, H.: On acquiring true stress-strain curves for sheet specimen using tensile test and fe analysis based on a local necking criterion. J. Mater. Res. 29, 695707 (2014).CrossRefGoogle Scholar
Hecker, S.S.: A simple forming limit curve technique and results on aluminum alloys. In Proceedings of the 7th Biennial Congress IDDRG; Amsterdam, Netherlands, 1972; pp. 5.15.8.Google Scholar
Marciniak, Z.: Stability of plastic shells under tension with kinematic boundary condition. Arch. Mech. Stosow. 17, 577592 (1965).Google Scholar
Hotz, W.: European Efforts in Standardization of FLC (ETH Zürich, Zürich, Switzerland, 2006); pp. 2425.Google Scholar
Ghosh, A.K.: The effect of lateral draw-in on stretch formability. Met. Eng. Q 15, 5364 (1975).Google Scholar
Ayres, R.A., Brazier, W.G., and Sajewski, V.F.: Evaluating the GMR-limiting dome height test as a new measure of press formability near plane strain. J. Appl. Metalwork 1, 4149 (1978).Google Scholar
Bragard, A., Baret, J.C., and Bonnarens, H.: A simplified technique to determine the FLD at onset of necking. Rapport du Centre de Recherches Mettallurgiques 33, 5363 (1972).Google Scholar
Liebertz, H., Duwel, A., Illig, R., Hotz, W., Keller, S., Koehler, A., Kroeff, A., Merklein, M., Rauer, J., Staubwasser, L., Steinbeck, G., and Vegter, H.: Guideline for the determination of forming limit curves. In Proceedings of the IDDRG Conference; Sindelfingen, Germany, 2004; pp. 216224.Google Scholar
ISO 12004: Metallic Materials-sheet and Strip-Determination of the Forming Limit Curves. Part 2: Determination of Forming Limit Curves in the Laboratory (ISO, Geneva, 2006).Google Scholar
Hasek, V.: Research and theoretical description concerning the influences on the FLDs. Blech, Rohre, Profile 25, 213220 (1978). [In German].Google Scholar