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Research Papers

Localized Necking in Elastomer-Supported Metal Layers: Impact of Kinematic Hardening

[+] Author and Article Information
Mohamed Ben Bettaieb

LEM3, UMR CNRS 7239—Arts et Métiers ParisTech,
4 rue Augustin Fresnel,
Metz Cedex 3 57078, France;
DAMAS,
Laboratory of Excellence on Design of Alloy
Metals for low-mAss Structures,
Université de Lorraine,
Nancy 54000, France
e-mail: Mohamed.BenBettaieb@ensam.eu

Farid Abed-Meraim

LEM3, UMR CNRS 7239—Arts et Métiers ParisTech,
4 rue Augustin Fresnel,
Metz Cedex 3 57078, France;
DAMAS,
Laboratory of Excellence on Design of Alloy
Metals for low-mAss Structures,
Université de Lorraine,
Nancy 54000, France

1Corresponding author.

Manuscript received March 11, 2016; final manuscript received October 29, 2016; published online January 25, 2017. Assoc. Editor: Yannis Korkolis.

J. Manuf. Sci. Eng 139(6), 061008 (Jan 25, 2017) (10 pages) Paper No: MANU-16-1159; doi: 10.1115/1.4035183 History: Received March 11, 2016; Revised October 29, 2016

This paper deals with localized necking in stretched metal sheets using the initial imperfection approach. The first objective is to study the effect of kinematic hardening on the formability of a freestanding metal layer. To this end, the behavior of the metal layer is assumed to follow the rigid-plastic rate-independent flow theory. The isotropic (respectively, kinematic) hardening of this metal is modeled by the Hollomon (respectively, Prager) law. A parametric study is carried out in order to investigate the effect of kinematic hardening on the formability limits. It is shown that the effect of kinematic hardening on the ductility limit is noticeably different depending on the strain path considered. The second aim of this paper is to analyze the effect of an elastomer substrate, perfectly bonded to the metal layer, on the formability of the whole bilayer. It is found that the addition of an elastomer layer substantially enhances the formability of the bilayer, in agreement with earlier studies.

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References

Keeler, S. P. , and Backofen, W. A. , 1963, “ Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches,” Trans. Am. Soc. Met., 56(1), pp. 25–48.
Goodwin, G. M. , 1968, “ Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop,” Metall. Ital., 60, pp. 764–774.
Abed-Meraim, F. , Balan, T. , and Altmeyer, G. , 2014, “ Investigation and Comparative Analysis of Plastic Instability Criteria: Application to Forming Limit Diagrams,” Int. J. Adv. Manuf. Technol., 71(5), pp. 1247–1262. [CrossRef]
Jaamialahmadi, A. , and Kadkhodayan, M. , 2011, “ An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis,” ASME J. Appl. Mech., 78(3), p. 031006. [CrossRef]
Jaamialahmadi, A. , and Kadkhodayan, M. , 2012, “ A Modified Storen-Rice Bifurcation Analysis of Sheet Metal Forming Limit Diagrams,” ASME J. Appl. Mech., 79(6), p. 061004. [CrossRef]
Chow, C. L. , Yang, J. , and Chu, E. , 2002, “ Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Nonproportional Loading,” ASME J. Eng. Mater. Technol., 124(2), pp. 259–265. [CrossRef]
Jalali Aghchai, A. , Shakeri, M. , and Mollaei Dariani, B. , 2013, “ Influences of Material Properties of Components on Formability of Two-Layer Metallic Sheets,” Int. J. Adv. Manuf. Technol., 66(5), pp. 809–823. [CrossRef]
Hutchinson, J. W. , and Neale, K. W. , 1978, Sheet Necking-II, Time-Independent Behavior, Mechanics of Sheet Metal Forming, D. P. Koistinen and N. M. Wang , eds., Plenum, New York, pp. 127–153.
Ghosh, A. , 1977, “ A Tensile Instability and Necking in Materials With Strain Hardening and Strain-Rate Hardening,” Acta Metall., 25(12), pp. 1413–1424. [CrossRef]
Hutchinson, J. W. , and Neale, K. W. , 1978, Sheet Necking-III. Strain-Rate Effects, D. P. Koistinen and N. M. Wang , eds., Plenum, New York, pp. 269–285.
Neale, K. W. , and Chater, E. , 1980, “ Limit Strain Predictions for Strain-Rate Sensitive Anisotropic Sheets,” Int. J. Mech. Sci., 22(9), pp. 563–574. [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]
Kuroda, M. , and Tvergaard, V. , 2000, “ Forming Limit Diagrams for Anisotropic Metal Sheets With Different Yield Criteria,” Int. J. Solids Struct., 37(37), pp. 5037–5059. [CrossRef]
Haddag, B. , Abed-Meraim, F. , and Balan, T. , 2009, “ Strain Localization Analysis Using a Large Deformation Anisotropic Elastic–Plastic Model Coupled With Damage,” Int. J. Plast., 25(10), pp. 1970–1995. [CrossRef]
Mansouri, L. Z. , Chalal, H. , and Abed-Meraim, F. , 2014, “ Ductility Limit Prediction Using a GTN Damage Model Coupled With Localization Bifurcation Analysis,” Mech. Mater., 76, pp. 64–92. [CrossRef]
Tvergaard, V. , 1978, “ Effect of Kinematic Hardening on Localized Necking in Biaxially Stretched Sheets,” Int. J. Mech. Sci., 20(9), pp. 651–658. [CrossRef]
He, J. , Cedric Xia, Z. , Zhu, X. , Zeng, D. , and Li, S. , 2013, “ Sheet Metal Forming Limits Under Stretch-Bending With Anisotropic Hardening,” Int. J. Mech. Sci., 75, pp. 244–256. [CrossRef]
He, J. , Zeng, D. , Zhu, X. , Cedric Xia, Z. , and Li, S. , 2014, “ Effect of Nonlinear Strain Paths on Forming Limits Under Isotropic and Anisotropic Hardening,” Int. J. Solids Struct., 51(2), pp. 402–415. [CrossRef]
Hommel, M. , and Kraft, O. , 2001, “ Deformation Behavior of Thin Copper Films on Deformable Substrates,” Acta Mater., 49(19), pp. 3935–3947. [CrossRef]
Huang, H. B. , and Spaepen, F. , 2000, “ Tensile Testing of Free-Standing Cu, Ag and Al Thin Films and Ag/Cu Multilayers,” Acta Mater., 48(12), pp. 3261–3269. [CrossRef]
Lu, N. , Wang, X. , Suo, Z. , and VIassak, J. , 2007, “ Metal Films on Polymer Substrates Stretched Beyond 50%,” Appl. Phys. Lett., 91(22), p. 221909. [CrossRef]
Morales, S. A. , Albrecht, A. B. , Zhang, H. , Liechti, K. M. , and Ravi-Chandar, K. , 2011, “ On the Dynamics of Localization and Fragmentation—V: Response of Polymer Coated Al 6061-O Tubes,” Int. J. Fract., 172(2), pp. 161–185. [CrossRef]
Guduru, P. R. , Bharathi, M. S. , and Freund, L. B. , 2006, “ The Influence of a Surface Coating on the High-Rate Fragmentation of a Ductile Material,” Int. J. Fract., 137(1), pp. 89–108. [CrossRef]
Jia, Z. , and Li, T. , 2013, “ Necking Limit of Substrate-Supported Metal Layers Under Biaxial In-Plane Loading,” Int. J. Plast., 51, pp. 65–79. [CrossRef]
Stören, S. , and Rice, J. R. , 1975, “ Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 23(6), pp. 421–441. [CrossRef]
Ben Bettaieb, M. , and Abed-Meraim, F. , 2015, “ Investigation of Localized Necking in Substrate-Supported Metal Layers: Comparison of Bifurcation and Imperfection Analyses,” Int. J. Plast., 65, pp. 168–190. [CrossRef]
Marciniak, Z. , and Kuczynski, K. , 1967, “ Limit Strains in the Processes of Stretch-Forming Sheet Metal,” Int. J. Mech. Sci., 9(9), pp. 609–620. [CrossRef]
Hollomon, J. H. , 1945, “ Tensile Deformation,” Trans. AIME, 162(444), pp. 268–290.
Prager, W. , 1955, “ The Theory of Plasticity—A Survey of Recent Achievements,” Proc. Inst. Mech. Eng., 169(1955), pp. 41–57. [CrossRef]
Hunter, S. C. , 1979, “ Some Exact Solutions in the Theory of Finite Elasticity for Incompressible NHeo-Hookean Materials,” Int. J. Mech. Sci., 21(4), pp. 203–211. [CrossRef]
Amirkhizi, A. V. , Isaacs, J. , McGee, J. , and Nemat-Nasser, S. , 2006, “ An Experimentally-Based Viscoelastic Constitutive Model for Polyurea Including Pressure and Temperature Effects,” Philos. Mag., 86(36), pp. 5847–5866. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Illustration of the M–K analysis for a bilayer in its initial configuration

Grahic Jump Location
Fig. 2

Comparison between the stress–strain curves obtained by isotropic hardening and mixed hardening: (a) material 1 (C=100 MPa), (b) material 2 (C=200 MPa), (c) material 3 (C=300 MPa), and (d) material 4 (C=400 MPa)

Grahic Jump Location
Fig. 3

Evolution of the strain ratio ε11B/ε11S as a function of ε11S for the plane-strain state (freestanding metal layer): (a) material 1, (b) material 2, (c) material 3, and (d) material 4

Grahic Jump Location
Fig. 4

Effect of kinematic hardening on the FLDs of freestanding metal layer: (a) material 1, (b) material 2, (c) material 3, and (d) material 4

Grahic Jump Location
Fig. 5

Effect of the initial imperfection factor on the FLDs of freestanding metal layer: (a) material 1, (b) material 2, (c) material 3, and (d) material 4

Grahic Jump Location
Fig. 6

Evolution of strain ratio ε11B/ε11S as a function of ε11S for the plane-strain state (metal/elastomer bilayer): (a) material 1 (mixed hardening), (b) material 2 (mixed hardening), (c) material 3 (mixed hardening), and (d) material 4 (mixed hardening)

Grahic Jump Location
Fig. 7

Effect of the thickness ratio HI/hI on the FLDs of metal/elastomer bilayer: (a) material 1 (isotropic hardening), (b) material 1 (mixed hardening), (c) material 2 (isotropic hardening), (d) material 2 (mixed hardening), (e) material 3 (isotropic hardening), and (f) material 3 (mixed hardening)

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