Consisting of stretchable and flexible cell walls or ligaments, soft elastic foams exhibit extremely high fracture toughness. Using the analogy between the cellular structure and the network structure of rubbery polymers, this paper proposes a scaling law for the fracture energy of soft elastic foam. To verify the scaling law, a phase-field model for the fracture processes in soft elastic structures is developed. The numerical simulations in two-dimensional foam structures of various unit-cell geometries have all achieved good agreement with the scaling law. In addition, the dependences of the macroscopic fracture energy on geometric parameters such as the network connectivity and spatial orientation have also been revealed by the numerical results. To further enhance the fracture toughness, a type of soft foam structures with nonstraight ligaments or folded cell walls has been proposed and its performance studied numerically. Simulations have shown that an effective fracture energy one order of magnitude higher than the base material can be reached by using the soft foam structure.
Issue Section:
Research Papers
References
1.
Maiti
, S. K.
, Gibson
, L. J.
, and Ashby
, M. F.
, 1984
, “Deformation and Energy Absorption Diagrams for Cellular Solids
,” Acta Metall.
, 32
(11
), pp. 1963
–1975
.2.
Han
, F.
, Zhu
, Z.
, and Gao
, J.
, 1998
, “Compressive Deformation and Energy Absorbing Characteristic of Foamed Aluminum
,” Metall. Mater. Trans. A
, 29
(10
), pp. 2497
–2502
.3.
Gibson
, L. J.
, and Ashby
, M. F.
, 1999
, Cellular Solids: Structure and Properties
, Cambridge University Press
, Cambridge, UK
.4.
Maiti
, S. K.
, Ashby
, M. F.
, and Gibson
, L. J.
, 1984
, “Fracture Toughness of Brittle Cellular Solids
,” Scr. Metall.
, 18
(3
), pp. 213
–217
.5.
Gibson
, L. J.
, Ashby
, M. F.
, Zhang
, J.
, and Triantafillou
, T. C.
, 1989
, “Failure Surfaces for Cellular Materials Under Multiaxial Loads—I. Modelling
,” Int. J. Mech. Sci.
, 31
(9
), pp. 635
–663
.6.
Brezny
, R.
, and Green
, D. J.
, 1991
, “Factors Controlling the Fracture Resistance of Brittle Cellular Materials
,” J. Am. Ceram. Soc.
, 74
(5
), pp. 1061
–1065
.7.
Chen
, J. Y.
, Huang
, Y.
, and Ortiz
, M.
, 1998
, “Fracture Analysis of Cellular Materials: A Strain Gradient Model
,” J. Mech. Phys. Solids
, 46
(5
), pp. 789
–828
.8.
Bažant
, Z. P.
, Zhou
, Y.
, Zi
, G.
, and Daniel
, I. M.
, 2003
, “Size Effect and Asymptotic Matching Analysis of Fracture of Closed-Cell Polymeric Foam
,” Int. J. Solids Struct.
, 40
(25
), pp. 7197
–7217
.9.
McIntyre
, A.
, and Anderton
, G. E.
, 1979
, “Fracture Properties of a Rigid Polyurethane Foam Over a Range of Densities
,” Polymer
, 20
(2
), pp. 247
–253
.10.
Lake
, G. J.
, and Thomas
, A. G.
, 1967
, “The Strength of Highly Elastic Materials
,” Proc. R. Soc. London, Ser. A
, 300
(1460
), pp. 108
–119
.11.
Thomas
, A. G.
, 1955
, “Rupture of Rubber. II. The Strain Concentration at an Incision
,” J. Polym. Sci.
, 18
(88
), pp. 177
–188
.12.
Aranson
, I. S.
, Kalatsky
, V. A.
, and Vinokur
, V. M.
, 2000
, “Continuum Field Description of Crack Propagation
,” Phys. Rev. Lett.
, 85
(1
), pp. 118
–121.13.
Karma
, A.
, Kessler
, D. A.
, and Levine
, H.
, 2001
, “Phase-Field Model of Mode III Dynamic Fracture
,” Phys. Rev. Lett.
, 87
(4
), p. 045501
.14.
Hakim
, V.
, and Karma
, A.
, 2009
, “Laws of Crack Motion and Phase-Field Models of Fracture
,” J. Mech. Phys. Solids
, 57
(2
), pp. 342
–368
.15.
Eastgate
, L. O.
, Sethna
, J. P.
, Rauscher
, M.
, Cretegny
, T.
, Chen
, C. S.
, and Myers
, C. R.
, 2002
, “Fracture in Mode I Using a Conserved Phase-Field Model
,” Phys. Rev. E
, 65
(3
), p. 036117
.16.
Wang
, Y. U.
, Jin
, Y. M.
, and Khachaturyan
, A. G.
, 2002
, “Phase Field Microelasticity Theory and Modeling of Elastically and Structurally Inhomogeneous Solid
,” J. Appl. Phys.
, 92
(3
), pp. 1351
–1360
.17.
Marconi
, V. I.
, and Jagla
, E. A.
, 2005
, “Diffuse Interface Approach to Brittle Fracture
,” Phys. Rev. E
, 71
(3
), p. 036110
.18.
Spatschek
, R.
, Hartmann
, M.
, Brener
, E.
, Müller-Krumbhaar
, H.
, and Kassner
, K.
, 2006
, “Phase Field Modeling of Fast Crack Propagation
,” Phys. Rev. Lett.
, 96
(1
), p. 015502
.19.
Miehe
, C.
, Welschinger
, F.
, and Hofacker
, M.
, 2010
, “Thermodynamically Consistent Phase‐Field Models of Fracture: Variational Principles and Multi‐Field FE Implementations
,” Int. J. Numer. Methods Eng.
, 83
(10
), pp. 1273
–1311
.20.
Miehe
, C.
, and Schänzel
, L. M.
, 2014
, “Phase Field Modeling of Fracture in Rubbery Polymers. Part I: Finite Elasticity Coupled With Brittle Failure
,” J. Mech. Phys. Solids
, 65
, pp. 93
–113
.21.
Karma
, A.
, and Lobkovsky
, A. E.
, 2004
, “Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture
,” Phys. Rev. Lett.
, 92
(24
), p. 245510
.22.
Henry
, H.
, and Levine
, H.
, 2004
, “Dynamic Instabilities of Fracture Under Biaxial Strain Using a Phase Field Model
,” Phys. Rev. Lett.
, 93
(10
), p. 105504
.23.
Henry
, H.
, 2008
, “Study of the Branching Instability Using a Phase Field Model of Inplane Crack Propagation
,” Europhys. Lett.
, 83
(1
), p. 16004
.24.
Griffith
, A. A.
, 1921
, “The Phenomena of Rupture and Flow in Solids
,” Philos. Trans. R. Soc. London
, 221
(582–593
), pp. 163
–198
.25.
Bazant
, Z. P.
, 2005
, Scaling of Structural Strength
, Butterworth-Heinemann
, London.26.
Hoagland
, R. G.
, Embury
, J. D.
, and Green
, D. J.
, 1975
, “On the Density of Microcracks Formed During the Fracture of Ceramics
,” Scr. Metall.
, 9
(9
), pp. 907
–909
.27.
Evans
, A. G.
, and Fu
, Y.
, 1985
, “Some Effects of Microcracks on the Mechanical Properties of Brittle Solids—II. Microcrack Toughening
,” Acta Metall.
, 33
(8
), pp. 1525
–1531
.28.
Hutchinson
, J. W.
, 1987
, “Crack Tip Shielding by Micro-Cracking in Brittle Solids
,” Acta Metall.
, 35
(7
), pp. 1605
–1619
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