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Research Papers

Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth

[+] Author and Article Information
Brian Nyvang Legarth

Associate Professor
Department of Mechanical Engineering,
Solid Mechanics,
Technical University of Denmark,
Lyngby DK-2800 Kgs., Denmark
e-mail: bnl@mek.dtu.dk

Viggo Tvergaard

Professor Emeritus
Department of Mechanical Engineering,
Solid Mechanics,
Technical University of Denmark,
Lyngby DK-2800 Kgs., Denmark
e-mail: viggo@mek.dtu.dk

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 25, 2018; final manuscript received January 26, 2018; published online March 14, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(5), 051007 (Mar 14, 2018) (8 pages) Paper No: JAM-18-1052; doi: 10.1115/1.4039172 History: Received January 25, 2018; Revised January 26, 2018

Void growth in an anisotropic ductile solid is studied by numerical analyses for three-dimensional (3D) unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include the effects of different void shapes, including oblate, prolate, or general ellipsoidal voids. Also, other 3D effects such as those of different spacings of voids in different material directions and the effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the response is very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.

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References

McClintock, F. A. , 1968, “ A Criterion for Ductile Fracture by Growth of Holes,” ASME J. Appl. Mech., 35(2), pp. 363–371. [CrossRef]
Rice, J. R. , and Tracey, D. M. , 1969, “ On the Ductile Enlargement of Voids in Triaxial Stress Fields,” J. Mech. Phys. Solids, 17(3), pp. 201–217. [CrossRef]
Garrison , W. M., Jr ., and Moody, N. R. , 1987, “ Ductile Fracture,” J. Phys. Chem. Solids, 48(11), pp. 1035–1074. [CrossRef]
Tvergaard, V. , 1990, “ Material Failure by Void Growth to Coalescence,” Adv. Appl. Mech., 27, pp. 83–151. [CrossRef]
Benzerga, A. A. , and Leblond, J.-B. , 2010, “ Ductile Fracture by Void Growth to Coalescence,” Adv. Appl. Mech., 44, pp. 169–305. [CrossRef]
Benzerga, A. A. , Leblond, J. B. , Needleman, A. , and Tvergaard, V. , 2016, “ Ductile Failure Modeling,” Int. J. Fract., 201(1), pp. 29–80. [CrossRef]
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. [CrossRef]
Tvergaard, V. , 1981, “ Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions,” Int. J. Fract., 17(4), pp. 389–407. [CrossRef]
Tvergaard, V. , and Needleman, A. , 1984, “ Analysis of the Cup-Cone Fracture in a Round Tensile Bar,” Acta Metall., 32(1), pp. 157–169. [CrossRef]
Hill, R. , 1948, “ A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, A, 193(1033), pp. 281–297. [CrossRef]
Hill, R. , 1950, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, UK.
Benzerga, A. A. , and Besson, J. , 2001, “ Plastic Potentials for Anisotropic Porous Solids,” Eur. J. Mech. A, 20(3), pp. 397–434. [CrossRef]
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. [CrossRef]
Morin, L. , Madou, K. , Leblond, J.-B. , and Kondo, D. , 2014, “ A New Technique for Finite Element Limit-Analysis of Hill Materials, With an Application to the Assessment of Criteria for Anisotropic Plastic Porous Solids,” Int. J. Eng. Sci., 74, pp. 65–79. [CrossRef]
Steglich, D. , Wafai, H. , and Besson, J. , 2010, “ Interaction Between Anisotropic Plastic Deformation and Damage Evolution in Al 2198 Sheet Metal,” Eng. Fract. Mech., 77(17), pp. 3501–3518. [CrossRef]
Chien, W. Y. , Pan, J. , and Tang, S. C. , 2001, “ Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals,” ASME J. Eng. Mater. Technol., 123(4), pp. 409–416. [CrossRef]
Wang, D.-A. , Pan, J. , and Liu, S.-D. , 2004, “ An Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals With Planar Anisotropy,” Int. J. Damage Mech., 13(1), pp. 7–33. [CrossRef]
Dæhli, L. E. B. , Faleskog, J. , Børvik, T. , and Hopperstad, O. S. , 2017, “ Unit Cell Simulations and Porous Plasticity Modelling for Strongly Anisotropic FCC Metals,” Eur. J. Mech. A, 65, pp. 360–383. [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(5), pp. 1009–1039. [CrossRef]
Srivastava, A. , and Needleman, A. , 2015, “ Effect of Crystal Orientation on Porosity Evolution in a Creeping Single Crystal,” Mech. Mater., 90, pp. 10–29. [CrossRef]
Legarth, B. N. , and Tvergaard, V. , 2010, “ 3D Analyses of Cavitation Instabilities Accounting for Plastic Anisotropy,” Z. Angew. Math. Mech., 90(9), pp. 701–709. [CrossRef]
Tvergaard, V. , 1976, “ Effect of Thickness Inhomogeneities in Internally Pressurized Elastic-Plastic Spherical Shells,” J. Mech. Phys. Solids, 24(5), pp. 291–304. [CrossRef]
Dafalias, Y. F. , 1985, “ A Missing Link in the Macroscopic Constitutive Formulation of Large Plastic Deformation,” Plasticity Today, Modelling, Methods and Applications, A. Sawczuk and G. Bianchi , eds., Elsevier, Amsterdam, The Netherlands, pp. 135–151.
Dafalias, Y. F. , 1985, “ The Plastic Spin,” ASME J. Appl. Mech., 52(4), pp. 865–871. [CrossRef]
Dafalias, Y. F. , 1993, “ On Multiple Spins and Texture Development. Case Study: Kinematic and Orthotropic Hardening,” Acta Mech., 100(3–4), pp. 171–194. [CrossRef]
Yamada, Y. , and Sasaki, M. , 1995, “ Elastic-Plastic Large Deformation Analysis Program and Lamina Compression Test,” Int. J. Mech., 37(7), pp. 691–707. [CrossRef]
Legarth, B. N. , 2008, “ Necking of Anisotropic Micro-Films With Strain-Gradient Effects,” Acta Mech. Sin., 24(5), pp. 557–567. [CrossRef]
Peirce, D. , Shih, C. F. , and Needleman, A. , 1984, “ A Tangent Modulus Method for Rate Dependent Solids,” Comput. Struct., 18(5), pp. 875–887. [CrossRef]
Kuroda, M. , and Tvergaard, V. , 2001, “ Plastic Spin Associated With a Non-Normality Theory of Plasticity,” Eur. J. Mech. A, 20(6), pp. 893–905. [CrossRef]
McMeeking, R. M. , and Rice, J. R. , 1975, “ Finite-Element Formulations for Problems of Large Elastic-Plastic Deformation,” Int. J. Solids Struct., 11(5), pp. 601–616. [CrossRef]
Legarth, B. N. , 2007, “ Strain-Gradient Effects in Anisotropic Materials,” Modell. Simul. Mater. Sci. Eng., 15(1), pp. S71–S81. [CrossRef]
Budiansky, B. , Hutchinson, J. W. , and Slutsky, S. , 1982, “ Void Growth and Collapse in Viscous Solids,” Mechanics of Solids (Rodney Hill 60th Anniversary Volume, Vol. 90), H. G. Hopkins and M. J. Sewell , eds., Pergamon Press, Oxford, UK, pp. 13–45. [CrossRef]
Tvergaard, V. , 2009, “ Behaviour of Voids in a Shear Field,” Int. J. Fract., 158(1), pp. 41–49. [CrossRef]
Moen, L. A. , Langseth, M. , and Hopperstad, O. , 1998, “ Elastoplastic Buckling of Anisotropic Aluminum, Plate Elements,” J. Struct. Eng., 124(6), pp. 712–719. [CrossRef]
Pardoen, T. , and Hutchinson, J. W. , 2000, “ An Extended Model for Void Growth and Coalescence,” J. Mech. Phys. Solids, 48(12), pp. 2467–2512. [CrossRef]
Cao, T. S. , Mazière, M. , Danas, K. , and Besson, J. , 2015, “ A Model for Ductile Damage Prediction at Low Stress Triaxialities Incorporating Void Shape Change and Void Rotation,” Int. J. Solids Struct., 63, pp. 240–263. [CrossRef]
Legarth, B. N. , 2004, “ Unit Cell Debonding Analyses for Arbitrary Orientations of Plastic Anisotropy,” Int. J. Solids Struct., 41(26), pp. 7267–7285. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Geometry of ellipsoidal void analyzed. Illustrated for w1=2 and w3=1/2 as well as L2/L1=L2/L3=1 for an initial void volume fraction of f0=0.01.

Grahic Jump Location
Fig. 2

Example of mesh used for evenly distributed ellipsoidal voids (w1=2 and w3=1/2 as well as L2/L1=L2/L3=1 for an initial void volume fraction of f0=0.01) using 1536 elements

Grahic Jump Location
Fig. 3

Initial yield surfaces shown in the (σ11,σ22)-plane for σ33=σ12=σ13=σ23=0. Two different anisotropic Hill yield surfaces are shown: (II) F = 0.40 and G = 7.33 (IV) F = 2.50 and G = 0.30, while both have H=1.00,N=L=M=9.60 in Eq. (9). The isotropic Mises yield surface is also shown.

Grahic Jump Location
Fig. 4

Effects of void shape, w1 and w3, for isotropic plasticity, equally distributed voids, L2/L1=L2/L3=1, and κ1=κ3=5/8 (T = 2). (a) Normalized stress–strain response in the primary load direction. (b) Void volume fraction evolution.

Grahic Jump Location
Fig. 5

Effects of void shape, w1 and w3, void spacing, L2/L1 and L2/L3, and stress ratio, κ1 and κ3 for isotropic plasticity. When nothing else is stated, the curves have w1=w3=1,L2/L1=L2/L3=1, and κ1=κ3=5/8 (T = 2). (a) Normalized stress–strain response in the primary load direction. (b) Void volume fraction evolution.

Grahic Jump Location
Fig. 6

Effects of axisymmetric void shape, w1 = w3, for anisotropic plasticity and equally distributed voids, L2/L1=L2/L3=1, κ1=κ3=5/8 (T = 2). (a) Stress–strain response in the primary load direction. (b) Void volume fraction evolution.

Grahic Jump Location
Fig. 7

Contours of effective plastic strain, εp, at an overall strain, E2=0.147, in Fig. 6, for w1=w3=1/4, L2/L1=L2/L3=1,κ1=κ3=5/8 (T = 2) with plastic anisotropy IV (Color figure available online)

Grahic Jump Location
Fig. 8

Effects of general void shape, w1=2 and w3=1/2, for anisotropic plasticity and equally distributed voids, L2/L1=L2/L3=1, κ1=κ3=5/8 (T = 2). (a) Stress–strain response in the primary load direction. (b) Void volume fraction evolution.

Grahic Jump Location
Fig. 9

Effects of spacing, L2/L1 and L2/L3, and stress ratio, κ1 and κ3, for anisotropic plasticity with spherical voids, w1=w3=1. When nothing else is stated, the curves have L2/L1=L2/L3=1 and κ1=κ3=5/8 (T = 2). (a) Stress–strain response in the primary load direction. (b) Void volume fraction evolution.

Grahic Jump Location
Fig. 10

Contours of effective plastic strain, εp, at an overall strain, E2=0.015, in Fig. 9, for w1=w3=1, L2/L1=L2/L3=1, κ1=10/9, and κ3=5/9 (T = 2) with plastic anisotropy II (Color figure available online)

Grahic Jump Location
Fig. 11

Plasticity effects for equally distributed voids, L2/L1=L2/L3=1, of general shape, w1=2 and w3=1/2 with the stress ratios κ1=10/9 and κ3=5/9 (T = 2). (a) Stress–strain response in the primary load direction. (b) Void volume fraction evolution.

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