0
Research Papers

M–K Analysis of Forming Limit Diagram Under Stretch-Bending

[+] Author and Article Information
Ji He, Shuhui Li

State Key Laboratory of Mechanical System and Vibration,
Shanghai 200240, China;
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China

Z. Cedric Xia

Ford Motor Company,
Dearborn, MI 48121
e-mail: zxia@ford.com

Danielle Zeng

Ford Motor Company,
Dearborn, MI 48121

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received September 18, 2012; final manuscript received April 15, 2013; published online July 17, 2013. Assoc. Editor: Jyhwen Wang.

J. Manuf. Sci. Eng 135(4), 041017 (Jul 17, 2013) (10 pages) Paper No: MANU-12-1282; doi: 10.1115/1.4024536 History: Received September 18, 2012; Revised April 15, 2013; Accepted April 17, 2013

Since the forming limit diagram (FLD) was introduced by Keeler, etc., five decades ago, it has been intensively studied by researchers and engineers. Most work has focused on the in-plane deformation which is considered as the dominant mode of the majority forming processes. However the effect of out-of-plane deformation becomes important in the accurate prediction of formability when thick sheet metals and/or smaller forming radii are encountered. Recent research on the stretch-bending induced FLD (BFLD) has been inconclusive. Some studies indicated that the bending effect will enhance a sheet metal's formability while others suggested otherwise. In this paper, we present an in-depth study of the through-thickness bending effect on the forming limits. The Marciniak–Kuczynski (M–K) analysis is extended to include bending, and models based on both flow theory and deformation theory of plasticity are proposed. The study is limited to the right-hand-side of FLD where the bending is along the major stretch direction. The radial return method is adopted as the framework to integrate constitutive equations. The results show that the bending process decreases the sheet metal formability with the flow-theory based model, while the opposite is true if the deformation theory based analysis is adopted. A detailed examination of the deformation histories from those two models reveals that the loading–unloading-reverse loading process during stretch-bending holds the key to the understanding of the conflicting results. The insight gained from the proposed FLD prediction model in this paper provides a new understanding of how the bending process affects the FLD, which can be used to predict and explain the localized necking phenomenon under the stretch-bending condition.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Keeler, S., 1965, “Determination of Forming Limits in Automotive Stampings,” SAE Technical Paper, Paper No. 650535. [CrossRef]
Keeler, S. P., and Backofen, W. A., 1963, “Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches,” ASM Trans. Q, 56(1), pp. 25–48.
Goodwin, G. M., 1968, “Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop,” SAE Technical Paper No. 680093.
Hill, R., 1952, “On Discontinuous Plastic States, With Special Reference to Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 1(1), pp. 19–30. [CrossRef]
Marciniak, Z., and Kuczynski, K., 1967, “Limit Strains in the Processes of Stretch-Forming Sheet Metal,” Int. J. Mech. Sci., 9(9), pp. 609–612, IN1–IN2, 613–620. [CrossRef]
Storen, S., and Rice, J., 1975, “Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 23(6), pp. 421–441. [CrossRef]
Hutchinson, J., and Neale, K., 1978, “Sheet Necking-II: Time-Independent Behavior,” Proceedings of a Symposium of Mechanics of Sheet Metal Forming, D. P.Koistinen and N. M.Wang, eds., pp. 127–150.
Hutchinson, J., and Neale, K., 1978, “Sheet Necking-III: Strain-Rate Effects,” Proceedings of a Symposium of Mechanics of Sheet Metal Forming, D. P.Koistinen and N. M.Wang, eds., pp. 269–285.
Hutchinson, J., Neale, K., and Needleman, A., 1978a, “Sheet Necking-Validity of Plane Stress Assumptions of the Long-Wavelength Approximation,” Proceedings of a Symposium of Mechanics of Sheet Metal Forming, D. P.Koistinen and N.M.Wang, eds., pp. 111–126.
Aghaie-Khafri, M., Mahmudi, R., and Pishbin, H., 2002, “Role of Yield Criteria and Hardening Laws in the Prediction of Forming Limit Diagrams,” Metall. Mater. Trans. A, 33(5), pp. 1363–1371. [CrossRef]
Cao, J., Yao, H., Karafillis, A., and Boyce, M. C., 2000, “Prediction of Localized Thinning in Sheet Metal Using a General Anisotropic Yield Criterion,” Int. J. Plast., 16(9), pp. 1105–1129. [CrossRef]
Laukonis, J. V., and Ghosh, A. K., 1978, “Effects of Strain Path Changes on the Formability of Sheet Metals,” Metall. Mater. Trans. A, 9(12), pp. 1849–1856. [CrossRef]
Butuc, M. C., Da Rocha, A. B., Duarte, J. F., Barlat, F., and Gracio, J. J., 2002, “Forming Limit Diagram for 6016-T4 Aluminium Alloy Deformed along Linear and Complex Strain Paths,” Key Eng. Mater., 230, pp. 529–532. [CrossRef]
Lu, Z., and Lee, D., 1987, “Prediction of History-Dependent Forming Limits by Applying Different Hardening Models,” Int. J. Mech. Sci., 29(2), pp. 123–137. [CrossRef]
Shi, M., and Gerdeen, J., 1991, “Effect of Strain Gradient and Curvature on Forming Limit Diagrams for Anisotropic Sheets,” J. Mater. Shaping Technol., 9(4), pp. 253–268. [CrossRef]
Assempour, A., Nejadkhaki, H. K., and Hashemi, R., 2010, “Forming Limit Diagrams With the Existence of Through-Thickness Normal Stress,” Comput. Mater. Sci., 48(3), pp. 504–508. [CrossRef]
Eyckens, P., Van Bael, A., and Van Houtte, P., 2011, “An Extended Marciniak-Kuczynski Model for Anisotropic Sheet Subjected to Monotonic Strain Paths with through-Thickness Shear,” Int. J. Plast., 27(10), pp. 1577–1597. [CrossRef]
Triantafyllidis, N., 1980, “Bifurcation Phenomena in Pure Bending,” J. Mech. Phys. Solids, 28(3-4), pp. 221–245. [CrossRef]
Triantafyllidis, N., Needleman, A., and Tvergaard, V., 1982, “On the Development of Shear Bands in Pure Bending,” Int. J. Solids Struct., 18(2), pp. 121–138. [CrossRef]
Sriram, S., Yao, H., and Ramisetti, N., 2012, “Development of an Empirical Model to Characterize Fracture Behavior During Forming of Advanced High Strength Steels Under Bending Dominated Conditions,” ASME J. Manuf. Sci. Eng., 134(3), p. 031003. [CrossRef]
Simha, C. H., Grantab, R., and Worswick, M. J., 2008, “Application of an Extended Stress-Based Forming Limit Curve to Predict Necking in Stretch Flange Forming,” ASME J. Manuf. Sci. Eng., 130(5), p. 051007. [CrossRef]
Lin, G., Hu, S. J., and Cai, W., 2009, “Evaluation of Formability in Bending/Hemming of Aluminum Alloys Using Plane-Strain Tensile Tests,” ASME J. Manuf. Sci. Eng., 131(5), p. 051009. [CrossRef]
Salandro, W. A., Jones, J. J., McNeal, T. A., Roth, J. T., Hong, S. T., and Smith, M. T., 2010, “Formability of Al 5xxx Sheet Metals Using Pulsed Current for Various Heat Treatments,” ASME J. Manuf. Sci. Eng., 132(5), p. 051016. [CrossRef]
Xia, Z., Cedric, and Danielle Zeng, 2008, “Sheet Metal Forming Limit Under Stretch-Bending,” Proceedings of the ASME International Manufacturing Science and Engineering Conference.
Tharrett, M., and Stoughton, T., 2003, “Stretch-Bend Forming Limits of 1008 Ak Steel, 70/30 Brass, and 6010 Aluminum,” Dislocations Plast. Met. Form., pp. 199–201.
Tharrett, M. R., and Stoughton, T. B., 2003, “Stretch-Bend Forming Limits of 1008 Ak Steel,” SAE Paper No. 01-1157.
Kitting, D., Koplenig, M., Ofenheimer, A., Pauli, H., and Till, E., 2009, “Application of a “Concave-Side Rule” Approach for Assessing Formability of Stretch-Bent Steel Sheets,” Int. J. Mater. Form., pp. 427–430. [CrossRef]
Kitting, D., Ofenheimer, A., Pauli, H., and Till, E., 2010, “A Phenomenological Concept to Predict Formability in Stretch-Bending Forming Operations,” Int. J. Mater. Form., pp. 1163–1166. [CrossRef]
Hutchinson, J., 1970, “Elastic-Plastic Behaviour of Polycrystalline Metals and Composite,” Proc. R. Soc. London, Ser. A, 319(1537), pp. 247–272. [CrossRef]
Xia, Z. C., 2001, “Failure Analysis of Tubular Hydroforming,” ASME J. Eng. Mater. Technol., 123 (4), 423–429. [CrossRef]
He, J., Xia, Z. C., Zeng, D., and Li, S. H., 2013, “Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading,” ASME J. Eng. Mater. Technol., 135 (3), p. 031009. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A thin sheet metal with M–K analysis

Grahic Jump Location
Fig. 2

A cross section of sheet metal with bending radius RDie

Grahic Jump Location
Fig. 3

Validate deformation theory based model with Hutchinson M–K analysis results

Grahic Jump Location
Fig. 4

Validate flow theory based model with Hutchinson M–K analysis results

Grahic Jump Location
Fig. 5

Effect of Defect Size on limit strain FLD0 in deformation theory

Grahic Jump Location
Fig. 6

Effect of Defect Size on limit strain FLD0 in flow theory

Grahic Jump Location
Fig. 7

Bending Effect on right-hand side of FLD in flow theory

Grahic Jump Location
Fig. 8

Bending Effect on right-hand side of FLD in deformation theory

Grahic Jump Location
Fig. 9

Illustration of the stress condition with loading and unloading processes in flow theory

Grahic Jump Location
Fig. 10

Illustration of the stress condition in deformation theory

Grahic Jump Location
Fig. 11

Top surface strain at the onset of localized necking in flow theory

Grahic Jump Location
Fig. 12

Effect of Anisotropy r-values on right-hand side of deformation theory based BFLD

Grahic Jump Location
Fig. 13

Effect of Anisotropy r-values on right-hand side of flow theory based BFLD

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In