An elastic-viscoplastic based finite element model has been developed to study the necking behavior of tube expansion for rate independent materials, rate dependent monolithic materials, and laminated materials during dynamic loading. A numerical study shows that for rate independent materials, the dynamic loading will not delay diffused necking but localized necking; for rate dependent materials, high strain rate sensitivity can significantly delay the onset of localized necking for both monolithic and laminated sheets and affect the multiple-neck formation in high-speed dynamic loading. The model also shows that a higher volume fraction of a clad layer with positive rate sensitivity material in a laminated sheet improves the sheet ductility.
Issue Section:
Research Papers
References
1.
Madsen
, P.
, and Niordson
, F. I.
, 1970
, “Material Properties at High Strain Rates
,” U.S. Air Force Material Lab, Progress Report No. 8.2.
Fyfe
, I. M.
, and Rajendran
, A. M.
, 1980
, “Dynamic Pre-Strain and Inertia Effects on the Fracture of Metals
,” J. Mech. Phys. Solids
, 28
, pp. 17
–26
.10.1016/0022-5096(80)90009-53.
Grady
, D. E.
, and Bensen
, D. A.
, 1983
, “Fragmentation of Metal Rings by Electromagnetic Loading
,” Exp. Mech.
, 12
, pp. 393
–400
.10.1007/BF023300544.
Altynova
, M.
, Hu
, X.
, and Daehn
, G. S.
, 1996
, “Increased Ductility in High Velocity Electromagnetic Ring Expansion
,” Metall. Mater. Trans. A
, 27A
, pp. 1837
–1844
.10.1007/BF026519335.
Zhang
, H.
, and Ravi-Chandar
, K.
, 2006
, “On the Dynamics of Necking and Fragmentation: I. Real-Time and Post-Mortem Observations in Al 6061-O
,” Int. J. Fract.
, 142
, pp. 183
–217
.10.1007/s10704-006-9024-76.
Zhang
, H.
, and Ravi-Chandar
, K.
, 2008
, “On the Dynamics of Necking and Fragmentation: II. Effect of Material Properties, Geometrical Constraints and Absolute Size
,” Int. J. Fract.
, 150
, pp. 3
–36
.10.1007/s10704-008-9233-37.
Zhang
, H.
, Liechti
, K. M.
, and Ravi-Chandar
, K.
, 2009
, “On the Dynamics of Localization and Fragmentation: III. Effect of Cladding With a Polymer
,” Int. J. Fract.
, 155
, pp. 101
–118
.10.1007/s10704-009-9332-98.
Mott
, N. F.
, 1947
, “Fragmentation of Shell Cases
,” Proc. R. Soc. London, Ser. A
, 189
, pp. 300
–308
.10.1098/rspa.1947.00429.
Kipp
, M. E.
, and Grady
, D. E.
, 1985
, “Dynamic Fracture Growth and Interactions in One Dimension
,” J. Mech. Phys. Solids
, 33
, pp. 399
–415
.10.1016/0022-5096(85)90036-510.
Miller
, O.
, Freund
, L. B.
, and Needleman
, A.
, 1999
, “Modeling and Simulation of Dynamic Fragmentation in Brittle Materials
,” Int. J. Fract.
, 96
, pp. 101
–125
.10.1023/A:101866631744811.
Shenoy
, V.
, and Kim
, K. S.
, 2003
, “Disorder Effects in Dynamic Fragmentation of Brittle Materials
,” J. Mech. Phys. Solids
, 51
, pp. 2023
–2035
.10.1016/j.jmps.2003.09.01012.
Han
, J. B.
, and Tvergaard
, V.
, 1995
, “Effect of Inertia on the Necking Behaviour of Ring Specimens Under Rapid Radial Expansion
,” Eur. J. Mech. A/Solids
, 14
, pp. 287
–307
.13.
Pandolfi
, A.
, Krysl
, P.
, and Ortiz
, M.
, 1999
, “Finite Element Simulation of Ring Expansion and Fragmentation: The Capturing of Length and Time Scales Through Cohesive Models of Fracture
,” Int. J. Fract.
, 95
, pp. 279
–297
.10.1023/A:101867292273414.
Becker
, R.
, 2002
, “Ring Fragmentation Predictions Using the Gurson Model With Material Stability Conditions as Failure Criteria
,” Int. J. Solids Struct.
, 39
, pp. 3555
–3580
.10.1016/S0020-7683(02)00170-115.
Xue
, Z.
, and Hutchinson
, J. W.
, 2007
, “Neck Retardation and Enhanced Energy Absorption in Metal-Elastomer Bilayers
,” Mech. Mater.
, 39
, pp. 473
–487
.10.1016/j.mechmat.2006.08.00216.
Xue
, Z.
, Vaziri
, A.
, and Hutchinson
, J. W.
, 2008
, “Material Aspects of Dynamic Neck Retardation
,” J. Mech. Phys. Solids
, 56
, pp. 93
–113
.10.1016/j.jmps.2007.04.00317.
Chen
, X. X.
, Wu
, P. D.
, Embury
, J. D.
, Huang
, Y.
, 2010
, “Enhanced Ductility in Round Tensile Bars Produced by Cladding a Ductile Ring
,” Modell. Simul. Mater. Sci. Eng.
, 18
, 025005
.10.1088/0965-0393/18/2/02500518.
Chen
, X. X.
, Wu
, P. D.
, Lloyd
, D. J.
, Embury
, J. D.
, Huang
, Y.
, 2010
, “Enhanced Ductility in Sheet Metals Produced by Cladding a Ductile Layer
,” ASME J. Appl. Mech.
, 77
(4), p. 041015
.10.1115/1.400092619.
Hutchinson
, J. W.
, and Neale
, K. W.
, 1977
, “Influence of Strain-Rate Sensitivity on Necking Under Uniaxial Tension
,” Acta Metall.
, 25
, pp. 839
–846
.10.1016/0001-6160(77)90168-720.
Ghosh
, A. K.
, 1977
, “Tensile Instability and Necking in Materials With Strain Hardening and Strain-Rate Hardening
,” Acta Metall.
, 25
, pp. 1413
–1424
.10.1016/0001-6160(77)90072-421.
Hutchinson
, J. W.
, and Neale
, K. W.
, 1978
, “Sheet Necking-III, Strain-Rate Effects
,” Mechanics of Sheet Metal Forming
, D. P.
Koistinen
and N.-M.
Wang
, eds., Springer
, New York
, pp. 269
–285
.22.
Peirce
, D.
, Shih
, C. F.
, and Needleman
, A.
, 1984
, “A Tangent Modulus Method for Rate Dependent Solids
,” J. Comput. Struct.
, 18
, pp. 875
–887
.10.1016/0045-7949(84)90033-623.
Hu
, X. H.
, Wu
, P. D.
, Lloyd
, D. J.
, and Embury
, J. D.
, 2013
, “Enhanced Formability in Sheet Metals Produced by Cladding a High Strain-Rate Sensitive Layer
,” ASME J. Appl. Mech.
, 81
(2), p. 021007
.10.1115/1.402441024.
Weber
, G.
, and Anand
, L.
, 1990
, “Finite Deformation Constitutive Equations and a Time Integration Procedure for Isotropic, Hyperelastic-Viscoplastic Solids
,” J. Comp. Methods Appl. Mech. Eng.
, 79
, pp. 173
–202
.10.1016/0045-7825(90)90131-525.
Abaqus Inc.
, 2012
, “ABAQUS Manual Version 6-12
,” Abaqus Inc., Providence, RI.26.
Shi
, Y.
, Wu
, P. D.
, Lloyd
, D. J.
, and Embury
, J. D.
, 2010
, “Crystal Plasticity Based Analysis of Localized Necking in Aluminum Tube Under Internal Pressure
,” Eur. J. Mech. A/Solids
, A29
, pp. 475
–483
.10.1016/j.euromechsol.2010.03.00527.
Kapuria
, S.
, and Kumari
, P.
, 2012
, “Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates
,” ASME J. Appl. Mech.
, 79
(6), p. 061018
.10.1115/1.400649528.
Manoharan
, M.
, Ellis
, L.
, and Lewandowski
, J. J.
, 1990
, “Laminated Composites With Improved Toughness
,” Script. Metall. Mater.
, 24
, pp. 1515
–1519
.10.1016/0956-716X(90)90424-F29.
Lloyd
, D. J.
, Gallerneault
, M.
, and Wagstaff
, R. B.
, 2010
, “The Deformation of Clad Aluminum Sheet Produced by Direct Chill Casting
,” Metall. Mater Trans. A.
, 519–521A
, pp. 2093
–2103
.10.1007/s11661-010-0298-z30.
Li
, T.
, and Suo
, Z.
, 2006
, “Deformability of Thin Metal Films on Elastomer Substrates
,” Int. J. Solids Struct.
, 43
, pp. 2351
–2363
.10.1016/j.ijsolstr.2005.04.03431.
Kim
, K. J.
, Kim
, D.
, Choi
, S. H.
, Chung
, K.
, Shin
, K. S.
, Barlat
, F.
, Oh
, K. H.
, and Youn
, J. R.
, 2003
, “Formability of AA5182/Polypropylene/AA5182 Sandwich Sheets
,” J. Mater. Process. Technol.
, 139
, pp. 1
–7
.10.1016/S0924-0136(03)00173-032.
Chen
, A. Y.
, Zhang
, J. B.
, Lu
, J.
, Lun
, W.
, and Song
, H. W.
, 2007
, “Necking Propagated Deformation Behavior of Layer-Structured Steel Prepared by Co-Warm Rolled Surface Nanocrystallized 304 Stainless Steel
,” Mater. Lett.
, 61
, pp. 5191
–5193
.10.1016/j.matlet.2007.04.027Copyright © 2014 by ASME
You do not currently have access to this content.
