A micromechanics-based yield criterion is developed for a porous ductile material deforming by localized plasticity in combined tension and shear. The new criterion is primarily intended to model void coalescence by internal necking or internal shearing. The model is obtained by limit analysis and homogenization of a cylindrical cell containing a coaxial cylindrical void of finite height. Plasticity in parts of the matrix is modeled using rate-independent J2 flow theory. It is shown that for the discontinuous, yet kinematically admissible trial velocity fields used in the limit analysis procedure, the overall yield domain exhibits curved parts and flat parts with no vertices. Model predictions are compared with available finite-element (FE) based estimates of limit loads on cubic cells. In addition, a heuristic modification to the model is proposed in the limit case of penny-shape cracks to enable its application to materials failing after limited void growth as well as to situations of shear-induced void closure.
Issue Section:
Research Papers
References
1.
Bao
, Y.
, and Wierzbicki
, T.
, 2004
, “On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space
,” Int. J. Mech. Sci.
, 46
(1
), pp. 81
–98
.10.1016/j.ijmecsci.2004.02.0062.
Barsoum
, I.
, and Faleskog
, J.
, 2007
, “Rupture Mechanisms in Combined Tension and Shear-Experiments
,” Int. J. Solids Struct.
, 44
(6
), pp. 1768
–1786
.10.1016/j.ijsolstr.2006.09.0313.
Haltom
, S. S.
, Kyriakides
, S.
, and Ravi-Chandar
, K.
, 2013
, “Ductile Failure Under Combined Shear and Tension
,” Int. J. Solids Struct.
, 50
(10
), pp. 1507
–1522
.10.1016/j.ijsolstr.2012.12.0094.
Johnson
, G. R.
, Hoegfeldt
, J. M.
, Lindholm
, U. S.
, and Nagy
, A.
, 1983
, “Response of Various Metals to Large Torsional Strains Over a Large Range of Strain Rates—Part 1: Ductile Metals
,” ASME J. Eng. Mater. Technol.
, 105
(1
), pp. 42
–47
.10.1115/1.32256175.
Bai
, Y.
, and Wierzbicki
, T.
, 2008
, “A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence
,” Int. J. Plast.
, 24
(6
), pp. 1071
–1096
.10.1016/j.ijplas.2007.09.0046.
Nahshon
, K.
, and Hutchinson
, J. W.
, 2008
, “Modification of the Gurson Model for Shear Failure
,” Eur. J. Mech.
, 27
(1
), pp. 1
–17
.10.1016/j.euromechsol.2007.08.0027.
Barsoum
, I.
, and Faleskog
, J.
, 2007
, “Rupture Mechanisms in Combined Tension and Shear-Micromechanics
,” Int. J. Solids Struct.
, 44
(17
), pp. 5481
–5498
.10.1016/j.ijsolstr.2007.01.0108.
Achouri
, M.
, Germain
, G.
, Dal Santo
, P.
, and Saidane
, D.
, 2013
, “Experimental Characterization and Numerical Modeling of Micromechanical Damage Under Different Stress States
,” Mater. Des.
, 50
, pp. 207
–222
.10.1016/j.matdes.2013.02.0759.
Needleman
, A.
, 1987
, “A Continuum Model for Void Nucleation by Inclusion Debonding
,” ASME J. Appl. Mech.
, 54
(3
), pp. 525
–531
.10.1115/1.317306410.
Fleck
, N. A.
, Hutchinson
, J. W.
, and Tvergaard
, V.
, 1989
, “Softening by Void Nucleation and Growth in Tension and Shear
,” J. Mech. Phys. Solids
, 37
(4
), pp. 515
–540
.10.1016/0022-5096(89)90027-611.
Siruguet
, K.
, and Leblond
, J.-B.
, 2004
, “Effect of Void Locking by Inclusions Upon the Plastic Behavior of Porous Ductile Solids—I: Theoretical Modeling and Numerical Study of Void Growth
,” Int. J. Plast.
, 20
(2
), pp. 225
–254
.10.1016/S0749-6419(03)00018-412.
Weck
, A.
, and Wilkinson
, D. S.
, 2008
, “Experimental Investigation of Void Coalescence in Metallic Sheets Containing Laser Drilled Holes
,” Acta Mater.
, 56
(8
), pp. 1774
–1784
.10.1016/j.actamat.2007.12.03513.
Tvergaard
, V.
, 2008
, “Shear Deformation of Voids With Contact Modeled by Internal Pressure
,” Int. J. Mech. Sci.
, 50
(10–11
), pp. 1459
–1465
.10.1016/j.ijmecsci.2008.08.00714.
Tvergaard
, V.
, 2012
, “Effect of Stress-State and Spacing on Voids in a Shear-Field
,” Int. J. Solids Struct.
, 49
(22
), pp. 3047
–3054
.10.1016/j.ijsolstr.2012.06.00815.
McClintock
, F. A.
, 1966
, “Ductile Fracture by Hole Growth in Shear Bands
,” Int. J. Fract. Mech.
, 2
(4
), pp. 614
–627
.10.1007/BF0018455816.
Fleck
, N. A.
, and Hutchinson
, J. W.
, 1986
, “Void Growth in Shear
,” Proc. R. Soc. London A
, 407
(1833
), pp. 435
–458
.10.1098/rspa.1986.010417.
Nielsen
, K. L.
, Dahl
, J.
, and Tvergaard
, V.
, 2012
, “Collapse and Coalescence of Spherical Voids Subject to Intense Shearing: Studied in Full 3D
,” Int. J. Fract.
, 177
(2
), pp. 97
–108
.10.1007/s10704-012-9757-418.
Dunand
, M.
, and Mohr
, D.
, 2014
, “Effect of Lode Parameter on Plastic Flow Localization After Proportional Loading at Low Stress Triaxialities
,” J. Mech. Phys. Solids
, 66
(1
), pp. 133
–153
.10.1016/j.jmps.2014.01.00819.
Rice
, J. R.
, and Tracey
, D. M.
, 1969
, “On the Enlargement of Voids in Triaxial Stress Fields
,” J. Mech. Phys. Solids
, 17
(3
), pp. 201
–217
.10.1016/0022-5096(69)90033-720.
Gurson
, A. L.
, 1977
, “Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
,” ASME J. Eng. Mater. Technol.
, 99
(1
), pp. 2
–15
.10.1115/1.344340121.
Chu
, C.
, and Needleman
, A.
, 1980
, “Void Nucleation Effects in Biaxially Stretched Sheets
,” ASME J. Eng. Mater. Technol.
, 102
(3
), pp. 249
–256
.10.1115/1.322480722.
Tvergaard
, V.
, and Needleman
, A.
, 1984
, “Analysis of the Cup–Cone Fracture in a Round Tensile Bar
,” Acta Metall.
, 32
(1
), pp. 157
–169
.10.1016/0001-6160(84)90213-X23.
Shen
, Y.
, Morgeneyer
, T. F.
, Garnier
, J.
, Allais
, L.
, Helfen
, L.
, and Crepin
, J.
, 2013
, “Three-Dimensional Quantitative In Situ Study of Crack Initiation and Propagation in AA6061 Aluminum Alloy Sheets Via Synchrotron Laminography and Finite-Element Simulations
,” Acta Mater.
, 61
(7
), pp. 2571
–2582
.10.1016/j.actamat.2013.01.03524.
Kondori
, B.
, 2015
, “Ductile Fracture of Magnesium Alloys: Characterization and Modeling
,” Ph.D. thesis, Texas A&M University, College Station, TX.25.
Benzerga
, A. A.
, Besson
, J.
, and Pineau
, A.
, 1999
, “Coalescence–Controlled Anisotropic Ductile Fracture
,” ASME J. Eng. Mater. Technol.
, 121
(2
), pp. 221
–229
.10.1115/1.281236926.
Benzerga
, A. A.
, and Leblond
, J.-B.
, 2010
, “Ductile Fracture by Void Growth to Coalescence
,” Adv. Appl. Mech.
, 44
, pp. 169
–305
.10.1016/S0065-2156(10)44003-X27.
Benzerga
, A. A.
, and Leblond
, J.-B.
, 2014
, “Effective Yield Criterion Accounting for Microvoid Coalescence
,” ASME J. Appl. Mech.
, 81
(3
), p. 031009
.10.1115/1.402490828.
Koplik
, J.
, and Needleman
, A.
, 1988
, “Void Growth and Coalescence in Porous Plastic Solids
,” Int. J. Solids Struct.
, 24
(8
), pp. 835
–853
.10.1016/0020-7683(88)90051-029.
Scheyvaerts
, F.
, Onck
, P. R.
, Tekoglu
, C.
, and Pardoen
, T.
, 2011
, “The Growth and Coalescence of Ellipsoidal Voids in Plane Strain Under Combined Shear and Tension
,” J. Mech. Phys. Solids
, 59
(2
), pp. 373
–397
.10.1016/j.jmps.2010.10.00330.
Richelsen
, A. B.
, and Tvergaard
, V.
, 1994
, “Dilatant Plasticity or Upper Bound Estimates for Porous Ductile Solids
,” Acta Metall. Mater.
, 42
(8
), pp. 2561
–2577
.10.1016/0956-7151(94)90198-831.
Pardoen
, T.
, and Hutchinson
, J. W.
, 2000
, “An Extended Model for Void Growth and Coalescence
,” J. Mech. Phys. Solids
, 48
(12
), pp. 2467
–2512
.10.1016/S0022-5096(00)00019-332.
Gologanu
, M.
, Leblond
, J.-B.
, and Devaux
, J.
, 1993
, “Approximate Models for Ductile Metals Containing Non-Spherical Voids—Case of Axisymmetric Prolate Ellipsoidal Cavities
,” J. Mech. Phys. Solids
, 41
(11
), pp. 1723
–1754
.10.1016/0022-5096(93)90029-F33.
Gologanu
, M.
, Leblond
, J.-B.
, and Devaux
, J.
, 1994
, “Approximate Models for Ductile Metals Containing Non-Spherical Voids—Case of Axisymmetric Oblate Ellipsoidal Cavities
,” ASME J. Eng. Mater. Technol.
, 116
(3
), pp. 290
–297
.10.1115/1.290429034.
Ponte Castañeda
, P.
, and Zaidman
, M.
, 1994
, “Constitutive Models for Porous Materials With Evolving Microstructure
,” J. Mech. Phys. Solids
, 42
(9
), pp. 1459
–1495
.10.1016/0022-5096(94)90005-135.
Danas
, K.
, and Ponte Castañeda
, P.
, 2009
, “A Finite-Strain Model for Anisotropic Viscoplastic Porous Media: I—Theory
,” Eur. J. Mech.
, 28
(3
), pp. 387
–401
.10.1016/j.euromechsol.2008.11.00236.
Keralavarma
, S. M.
, and Benzerga
, A. A.
, 2010
, “A Constitutive Model for Plastically Anisotropic Solids With Non-Spherical Voids
,” J. Mech. Phys. Solids
, 58
(6
), pp. 874
–901
.10.1016/j.jmps.2010.03.00737.
Madou
, K.
, and Leblond
, J.-B.
, 2012
, “A Gurson-Type Criterion for Porous Ductile Solids Containing Arbitrary Ellipsoidal Voids—I: Limit-Analysis of Some Representative Cell
,” J. Mech. Phys. Solids
, 60
(5
), pp. 1020
–1036
.10.1016/j.jmps.2011.11.00838.
Madou
, K.
, Leblond
, J.-B.
, and Morin
, L.
, 2013
, “Numerical Studies of Porous Ductile Materials Containing Arbitrary Ellipsoidal Voids—II: Evolution of the Length and Orientation of the Void Axes
,” Eur. J. Mech.
, 42
, pp. 490
–507
.10.1016/j.euromechsol.2013.06.00539.
Benzerga
, A. A.
, Besson
, J.
, and Pineau
, A.
, 2004
, “Anisotropic Ductile Fracture: Part I: Experiments
,” Acta Mater.
, 52
(15
), pp. 4623
–4638
.10.1016/j.actamat.2004.06.02040.
Benzerga
, A. A.
, Besson
, J.
, and Pineau
, A.
, 2004
, “Anisotropic Ductile Fracture: Part II: Theory
,” Acta Mater.
, 52
(15
), pp. 4639
–4650
.10.1016/j.actamat.2004.06.01941.
Thomason
, P. F.
, 1985
, “Three-Dimensional Models for the Plastic Limit-Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids
,” Acta Metall.
, 33
(6
), pp. 1079
–1085
.10.1016/0001-6160(85)90201-942.
Benzerga
, A. A.
, 2002
, “Micromechanics of Coalescence in Ductile Fracture
,” J. Mech. Phys. Solids
, 50
(6
), pp. 1331
–1362
.10.1016/S0022-5096(01)00125-943.
Leblond
, J.-B.
, and Mottet
, G.
, 2008
, “A Theoretical Approach of Strain Localization Within Thin Planar Bands in Porous Ductile Materials
,” C. R. Mec.
, 336
(1–2
), pp. 176
–189
.10.1016/j.crme.2007.11.00844.
Gologanu
, M.
, Leblond
, J.-B.
, Perrin
, G.
, and Devaux
, J.
, 2001
, “Theoretical Models for Void Coalescence in Porous Ductile Solids. I. Coalescence in ‘Layers'
,” Int. J. Solids Struct.
, 38
(32–33
), pp. 5581
–5594
.10.1016/S0020-7683(00)00354-145.
Gologanu
, M.
, Leblond
, J.-B.
, Perrin
, G.
, and Devaux
, J.
, 2001
, “Theoretical Models for Void Coalescence in Porous Ductile Solids. II. Coalescence in ‘Columns'
,” Int. J. Solids Struct.
, 38
(32–33
), pp. 5595
–5604
.10.1016/S0020-7683(00)00355-346.
Tekoglu
, C.
, Leblond
, J.-B.
, and Pardoen
, T.
, 2012
, “A Criterion for the Onset of Void Coalescence Under Combined Tension and Shear
,” J. Mech. Phys. Solids
, 60
(7
), pp. 1363
–1381
.10.1016/j.jmps.2012.02.00647.
Morin
, L.
, Leblond
, J.-B.
, and Benzerga
, A. A.
, 2015
, “Coalescence of Voids by Internal Necking: Theoretical Estimates and Numerical Results
,” J. Mech. Phys. Solids
, 75
, pp. 140
–158
.10.1016/j.jmps.2014.11.00948.
Morin
, L.
, Leblond
, J.-B.
, Benzerga
, A. A.
, and Kondo
, D.
, 2015
, “A Unified Criterion for the Growth and Coalescence of Microvoids
,” J. Mech. Phys. Solids
(submitted).49.
Benzerga
, A. A.
, Besson
, J.
, Batisse
, R.
, and Pineau
, A.
, 2002
, “Synergistic Effects of Plastic Anisotropy and Void Coalescence on Fracture Mode in Plane Strain
,” Modell. Simul. Mater. Sci. Eng.
, 10
(1
), pp. 73
–102
.10.1088/0965-0393/10/1/30650.
Kondori
, B.
, and Benzerga
, A. A.
, 2014
, “Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31
,” Metall. Mater. Trans. A
, 45
(8
), pp. 3292
–3307
.10.1007/s11661-014-2211-751.
Gologanu
, M.
, 1997
, “Etude de Quelques Problèmes de Rupture Ductile des Métaux
,” Ph.D. thesis, Université Paris 6, Paris, France.52.
Collins
, I. F.
, and Houlsby
, G. T.
, 1997
, “Application of Thermomechanical Principles to the Modelling of Geotechnical Materials
,” Proc. R. Soc. London A
, 453
(1964
), pp. 1975
–2001
.10.1098/rspa.1997.010753.
Einav
, I.
, and Carter
, J. P.
, 2007
, “On Convexity, Normality, Pre-Consolidation Pressure, and Singularities in Modelling of Granular Materials
,” Granular Matter
, 9
(1–2
), pp. 87
–96
.10.1007/s10035-006-0025-zCopyright © 2015 by ASME
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