Research Papers

Analysis of Nonisothermal Deep Drawing of Aluminum Alloy Sheet With Induced Anisotropy and Rate Sensitivity at Elevated Temperatures

[+] Author and Article Information
Michael J. Worswick

Mechanical and Mechatronics Engineering Department,
University of Waterloo,
200 University Avenue West,
Waterloo, ON N2L 3G1, Canada

Manuscript received September 10, 2012; final manuscript received July 22, 2013; published online November 5, 2013. Assoc. Editor: Brad L. Kinsey.

J. Manuf. Sci. Eng 136(1), 011006 (Nov 05, 2013) (16 pages) Paper No: MANU-12-1271; doi: 10.1115/1.4025407 History: Received September 10, 2012; Revised July 22, 2013

In this paper, a finite element model is developed for 3000 series clad aluminum alloy brazing sheet to account for temperature and strain rate dependency, as well as plastic anisotropy. The current work considers a novel implementation of the Barlat YLD2000 yield surface in conjunction with the Bergstrom hardening model to accurately model aluminum alloy sheet during warm forming. The Barlat YLD2000 yield criterion is used to capture the anisotropy while the Bergstrom hardening rule predicts the temperature and strain rate dependency. The results are compared with those obtained from experiments. The measured stress–strain curves of the AA3003 aluminum alloy sheet at elevated temperatures and different strain rates are used to fit the Bergstrom parameters and measured R-values and directional yield stresses are used to fit the yield function parameters. Isothermal uniaxial tensile tests and nonisothermal deep drawing experiments are performed and the predicted response using the new constitutive model is compared with measured data. In simulations of tensile tests, the material behavior is predicted accurately by the numerical models. Also, the nonisothermal deep drawing simulations are able to predict the load–displacement response and strain distributions accurately.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Kaya, S., Spampinato, G., and Altan, T., 2008, “An Experimental Study on Non-Isothermal Deep Drawing Process Using Aluminum and Magnesium Alloys,” ASME J. Manuf. Sci. Eng., 130, p. 061001. [CrossRef]
Tebbe, P. A., and Kridli, G. T., 2004, “Warm Forming of Aluminum Alloys: An Overview and Future Directions,” Int. J. Mater. Prod. Technol., 21, pp. 24–40. [CrossRef]
Shehata, F., Painter, M. J., and Pearce, R., 1978, “Warm Forming of Aluminum/Magnesium Alloy Sheet,” J. Mech. Work. Technol., 2, pp. 279–291. [CrossRef]
Wilson, D. V., 1988, “Aluminum Versus Steel in the Family Car-The Formability Factor,” J. Mech. Work. Technol., 16, pp. 257–277. [CrossRef]
Schmoeckel, D., Liebler, B. C., and Speck, F. D., 1995, “Grundlagen und modellversuche-temperaturgefu hrterstofffluß beim tiefziehen von Al-blech-realversuche,” Bander Bleche Rohre, 36, spp. 14–21.
Li, D., and Ghosh, A., 2003, “Tensile Deformation Behavior of Aluminum Alloys at Warm Forming Temperatures,” Mater. Sci. Eng., A, 352, pp. 279–286. [CrossRef]
Van den Boogaard, A. H., and Huetink, J., 2006, “Simulation of Aluminum Sheet Forming at Elevated Temperatures,” Comput. Methods Appl. Mech. Eng., 195, pp. 6691–6709. [CrossRef]
Mckinley, J., Abedrabbo, N., Worswick, M. J., and Kozards, M., 2008, “Effect of Independent Die and Punch Temperature Control on the Formability of 3003 Aluminum Alloy in Warm Deep Drawing,” Proceedings of the 7th International Conference, Numisheet, Interlaken, Switzerland.
Kim, H. S., Koç, M., Ni, J., and Ghosh, A., 2006, “Finite Element Modeling and Analysis of Warm Forming of Aluminum Alloys-Validation Through Comparisons With Experiments and Determination of a Failure Criterion,” ASME J. Manuf. Sci. Eng., 128, pp. 613–621. [CrossRef]
Tugcu, P., Wu, P. D., and Neale, K. W., 2002, “On the Predictive Capabilities of Anisotropic Yield Criteria for Metals Undergoing Shearing Deformations,” Int. J. Plast., 18, pp. 1219–1236. [CrossRef]
Paquet, D., Dondeti, P., and Gosh, S., 2011, “Dual-Stage Nested Homogenization for Rate-Dependant Anisotropic Elasto-Plasticity Model of Dendritic Cast Aluminum Alloys,” Int. J. Plast., 27, pp. 1677–1701. [CrossRef]
Desmorat, R., and Marukk, R., 2011, “Non-Quadratic Kelvin Modes Based Plasticity for Anisotropic Materials,” Int. J. Plast., 27, pp. 328–351. [CrossRef]
Thomson, W. K., (Lord Kelvin), 1856, “Elements of a Mathematical Theory of Elasticity,” Philos. Trans. R. Soc. London, 166, pp. 481–498.
Segurado, J., Lebensohn, R. A., Lorca, J., and Tome, C. N., 2012, “Multiscale Modeling of Plasticity Based on Embedding the Viscoplastic Self-Consistent Formulation in Implicit Finite Elements,” Int. J. Plast., 28, pp. 124–140. [CrossRef]
Fourmeau, M., Borvki, T., Benallal, A., Lademo, O. G., and Hopperstad, O. S., 2011, “On the Plastic Anisotropy of an Aluminum Alloy and Its Influence on Constrained Multiaxial Flow,” Int. J. Plast., 27, pp. 2005–2025. [CrossRef]
Barlat, F., Aretz, H., Yoon, J. W., Karabin, M. E., Brem, J. C., and Dick, R. E., 2005, “Linear Transformation-Based Anisotropic Yield Functions,” Int. J. Plast., 21, pp. 1009–1039. [CrossRef]
Yoon, J. W., Dick, R. E., and Barlat, F., 2011, “A New Analytical Theory for Earing Generated From Anisotropic Plasticity,” Int. J. Plast., 27, pp. 1165–1184. [CrossRef]
Bagheriasl, R., Ghavam, K., and Worswick, M., 2011, “Formability Analysis of Aluminum Alloy Sheets at Elevated Temperatures With Numerical Simulation Based on the M-K Method,” Proceedings of ESAFORM, Belfast, Ireland.
Farrokh, B., and Khan, A. S., 2009, “Grain Size, Strain Rate, and Temperature Dependence of Flow Stress in Ultra-Fine Grained and Nanocrystalline Cu and Al: Synthesis, Experiment, and Constitutive Modeling,” Int. J. Plast., 25, pp. 715–732. [CrossRef]
Ghavam, K., and Naghdabadi, R., 2011, “Constitutive Modeling of Temperature and Strain Rate Dependent Elastoplastic Hardening Materials Using a Corotational Rate Associated With the Plastic Deformation,” Int. J. Plast., 27, pp. 1445–1455. [CrossRef]
Mahabunphachai, S., Koc, M., and Carsley, J. E., 2011, “Investigations on Deformation Behavior of AA5754 Sheet Alloy Under Warm Hydroforming Conditions,” ASME J. Manuf. Sci. Eng., 133, p. 051007. [CrossRef]
Khan, A. S., and Baig, M., 2011, “Anisotropic Response, Constitutive Modeling and the Effect of Strain-Rate and Temperature on the Formability of an Aluminum Alloy,” Int. J. Plast., 27, pp. 522–538. [CrossRef]
Khan, A. S., and Liang, R., 1999, “Behavior of Three BCC Metal Over a Wide Range of Strain Rates and Temperatures,” Int. J. Plast., 15, pp. 1089–1109. [CrossRef]
Bergstrom, Y., and Hallen, H., 1982, “An Improved Dislocation Model for the Stress-Strain Behavior of Polycrystalline α-Fe,” Mater. Sci. Eng., 55, pp. 49–61. [CrossRef]
Nes, E., 1998, “Modeling of Work Hardening and Stress Saturation in FCC Metals,” Prog. Mater. Sci., 145, pp. 129–193.
Kurukuri, S., van den Boogaard, A. H., Mirox, A., and Holmedal, B., 2009, “Warm Forming Simulation of Al-Mg Sheet,” J. Mat. Process. Technol., 209(15–16), pp. 5636–5645. [CrossRef]
Lee, M. G., Kim, C., Pavlina, E. J., and Barlat, F., 2011, “Advances in Sheet Forming-Materials Modeling, Numerical Simulation, and Press Technologies,” ASME J. Manuf. Sci. Eng., 133, p. 061001. [CrossRef]
Barlat, F., Brem, J. C., Yoon, J. W., Chung, K., and Dick, R. E., 2003, “Plane Stress Yield Function for Aluminum Alloy Sheets—Part 1: Theory,” Int. J. Plast., 19, pp. 1297–1319. [CrossRef]
Abedrabbo, N., Pourboghrat, F., and Carsley, J., 2007, “Forming of AA5182-O and AA5754-O at Elevated Temperatures Using Coupled Thermo-Mechanical Finite Element Models,” Int. J. Plast., 23(5), pp. 841–875. [CrossRef]
Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer, New York, pp. 143–149.
McKinley, J., 2010, “Warm Forming of Aluminum Brazing Sheet,” M.Sc. thesis, University of Waterloo, Waterloo, Ontario, Canada.
Yoon, J., Barlat, F., Dick, R. E., Chung, K., and Kang, T. J., 2004, “Plane Stress Yield Function for Aluminum Alloy Sheets-Part II: FE Formulation and Its Implementation,” Int. J. Plast., 20(3), pp. 495–522. [CrossRef]
Abedrabbo, N., Pourboghrat, F., and Carsley, J., 2006, “Forming of Aluminum Alloys at Elevated Temperatures—Part 1: Material Characterization,” Int. J. Plast., 22(2), pp. 314–341. [CrossRef]
Belytschko, T., and Tsay, C. S., 1981, “Explicit Algorithms for Nonlinear Dynamics of Shells,” AMD, ASME, 48, pp. 209–231.
Takuda, H., Mori, K., Masuda, I., Abe, Y., and Matsuo, M., 2002, “Finite Element Simulation of Warm Deep Drawing of Aluminum Alloy Sheet When Accounting for Heat Conduction,” J. Mater. Process. Technol., 120, pp. 412–418. [CrossRef]


Grahic Jump Location
Fig. 1

Stress–strain curves using fit parameters versus experimental results for different temperatures and strain rates. (a) 25 °C, (b) 100 °C, (c) 200 °C, and (d) 250 °C

Grahic Jump Location
Fig. 2

Yield surface at different temperatures for AA3003: (a) normalized by the RD yield stress for each temperature and (b) without normalization.

Grahic Jump Location
Fig. 3

Geometry of tensile test sample (all dimensions are in mm)

Grahic Jump Location
Fig. 4

Mesh model of tensile test showing the fine mesh

Grahic Jump Location
Fig. 5

Effect of mesh size on numerical results for stress–strain curve

Grahic Jump Location
Fig. 6

Comparison of numerical results with measured engineering stress–strain curves at (a) 0.07, (b) 0.007, and (c) 0.0007 s-1 strain rates

Grahic Jump Location
Fig. 7

Effect of strain rate on predicted stress–strain response and rate sensitivity: (a) simulation and (b) experiments

Grahic Jump Location
Fig. 8

Tooling cross section (a) and close up view of the tooling (b)

Grahic Jump Location
Fig. 9

Mesh model of the quarter tooling (a) and quarter blank mesh (b)

Grahic Jump Location
Fig. 10

(a) Contour plot of temperature distribution for a deep drawn 203.2 mm blank; (b) change in blank temperature versus normalized position on the cup wall from the center to the cup edge for a full, one half and one quarter drawn cup.

Grahic Jump Location
Fig. 11

Comparison of predicted normalized thickness change versus normalized position (along radial direction) on the cup under isothermal conditions at room temperature and 250  °C and nonisothermal forming with punch at 15  °C and dies at 250  °C.

Grahic Jump Location
Fig. 12

Major versus minor strain along x-axis (rolling direction) for experiments [31] and simulations. 228.6 mm (9 in.) blank and 17.8 kN clamping force

Grahic Jump Location
Fig. 13

Major versus minor strain along y-axis (transverse direction) for experiments [31] and simulations. 228.6 mm (9 in.) blank and 17.8 kN clamping force

Grahic Jump Location
Fig. 14

Contour plots of major strain for deep drawn 203 mm blank under isothermal conditions at room temperature (a) and nonisothermal conditions with dies at 250  °C (b), comparison between major strains for a row of elements initially located along an arc of radius 93 mm from the center of the blank (c).

Grahic Jump Location
Fig. 15

Contour plot of minor strain for deep drawing of 203 mm blank under isothermal conditions at room temperature (a) and nonisothermal conditions with dies at 250  °C (b), comparison between minor strains for a row of elements initially located along an arc of radius 93 mm from the center of the blank (c).

Grahic Jump Location
Fig. 16

(a) Wrinkled isothermal and (b) fully drawn nonisothermal parts under blank holder forces of 6.6 and 17.8 kN, respectively. The predicted effective plastic strain distributions are shown for both parts.

Grahic Jump Location
Fig. 17

Punch force versus punch displacement for deep drawing 228.6 mm using Teflon sheet lubricant and 8 mm/s punch speed, comparing results with experiments for room temperature forming and nonisothermal warm forming with dies at 250  °C

Grahic Jump Location
Fig. 18

Punch force versus punch displacement for deep drawing 228.6 mm blank using warm dies and cold punch and Dasco Cast lubricant at different punch speeds

Grahic Jump Location
Fig. 19

Punch force versus punch displacement for nonisothermal, warm deep drawing 228.6 mm blank using Teflon sheet lubricant comparing result with experiment at two blank holder force level

Grahic Jump Location
Fig. 20

Punch force versus punch displacement for nonisothermal warm deep drawing 228.6 mm at 8 mm/s punch speed comparing results with experiment for two different lubricants




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