We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing coated spherical inclusions. The composite is modeled by a four phase pattern consisting of inclusion, interphase, matrix layer, and equivalent homogeneous medium. The overall elastic moduli are obtained using a micromechanical approach based on the Green function techniques and the interfacial operators. The four phase model assumes that all constituents are elastic and perfectly bonded. The model is used to derive the effective elastic properties of representative volume element using classical averaging schemes assuming the isotropy of constituent. Finally, effect of the thickness and stiffness of interphase on the global behavior of real composite materials are examined. Comparisons with experimental results show a good agreement.
Issue Section:
Technical Papers
1.
Walpole
, L. J.
, 1978, “A Coated Inclusion in an Elastic Medium
,” Math. Proc. Cambridge Philos. Soc.
0305-0041, 83
, pp. 495
–506
.2.
Cherkaoui
, M.
, Sabar
, H.
, and Berveiller
, M.
, 1994, “Micromechanical Approach of the Coated Inclusion Problem and Applications to Composite Materials
,” ASME J. Eng. Mater. Technol.
0094-4289, 116
, pp. 274
–278
.3.
Cherkaoui
, M.
, Sabar
, H.
, and Berveiller
, M.
, 1995, “Elastic Composites With Coated Reinforcements: A Micromechanical Approach for Nonhomothetic Topology
,” Int. J. Eng. Sci.
0020-7225, 33
, pp. 829
–843
.4.
Aboutajeddine
, A.
, 2001, “Elaboration de Nouvelles Approches Micromécaniques pour l’Optimisation des Performances Mécaniques des Matériaux Hétérogènes
,” Thèse de doctorat. Université de Sherbrooke (Québec) Canada.5.
Benveniste
, Y.
, Dvorak
, G. J.
, and Chen
, T.
, 1989, “Stress Field in Composite With Coated Inclusions
,” Mech. Mater.
0167-6636, 7
, pp. 305
–317
.6.
Hervé
, E.
, and Zaoui
, A.
, 1993, “N-Layered Inclusion-Based Micromechanical Modeling
,” Int. J. Eng. Sci.
0020-7225, 31
, pp. 1
–10
.7.
Lipinski
, P.
, Barhdadi El
, H.
, and Cherkaoui
, M.
, 2005, “Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion
,” Philos. Mag.
1478-6435, in press.8.
Ramesh
, G.
, Sotelino
, E. D.
, and Chen
, W. F.
, 1996, “Effect of Transition Zone on Elastic Moduli of Concrete Materials
,” Cem. Concr. Res.
0008-8846, 26
, pp. 611
–622
.9.
Hashin
, Z.
, and Monteiro
, P. J. M.
, 2002, “An Inverse Method to Determine the Elastic Properties of the Interphase Between the Aggregate and the Cement Paste
,” Cem. Concr. Res.
0008-8846, 32
, pp. 1291
–1300
.10.
Hervé
, E.
, and Pellegrini
, O.
, 1995, “The Elastic Constants of a Material Containing a Spherical Coated Holes
,” J. Inflamm
1078-7852, 47
, pp. 223
–246
.11.
Bardella
, L.
, and Genna
, F.
, 2001, “On the Elastic Behavior of Syntactic Foams
,” Int. J. Solids Struct.
0020-7683, 38
, pp. 7235
–7260
.12.
Bornert
, M.
, Stolz
, C.
, and Zaoui
, A.
, 1996, “Morphologically Representative Pattern-Based Bounding in Elasticity
,” J. Mech. Phys. Solids
0022-5096, 44
, pp. 307
–331
.13.
Dederichs
, P. H.
, and Zeller
, R.
, 1973, “Variational Treatment of the Elastic Constants of Disordered Materials
,” Z. Phys.
0044-3328, 259
, pp. 103
–113
.14.
Hill
, R.
, 1983, “Interfacial Operators in the Mechanics of Composite Media
,” J. Mech. Phys. Solids
0022-5096, 31
, pp. 347
–357
.15.
Hashin
, Z.
, 1962, “The Elastic Moduli of Heterogeneous Materials
,” ASME J. Appl. Mech.
0021-8936, 29
, pp. 143
–150
.16.
Christensen
, R. M.
, and Lo
, K. H.
, 1979, “Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models
,” J. Mech. Phys. Solids
0022-5096, 27
, pp. 315
–330
.17.
Eshelby
, J. D.
, 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems
,” Proc. R. Soc. London, Ser. A
1364-5021, 241
, pp. 376
–396
.18.
Huang
, J. S.
, and Gibson
, L. J.
, 1993, “Elastic Moduli of a Composite With Hollow Spheres in a Matrix
,” J. Mech. Phys. Solids
0022-5096, 41
, pp. 55
–75
.19.
Amdouni
, N.
, Sautereau
, H.
, and Gerard
, J. F.
, 1992, “Epoxy Composites Based on Glass Beads. II. Mechanical Properties
,” J. Appl. Polym. Sci.
0021-8995, 46
, pp. 1723
–1735
.20.
Shodja
, H. M.
, and Roumi
, F.
, 2005, “Overall Behavior of Composites With Periodic Multi-Inhomogeneities
,” Mechanics of Materials
, 37
, pp. 243
–253
.21.
Neubauer
, C. M.
, Jennings
, E. J.
, and Garboczi
, E. J.
, 1996, “A Three-Phase Model of the Elastic and Shrinkage Properties of Mortar
,” Adv. Cem. Based Mater.
1065-7355, 4
, pp. 6
–20
.22.
Cohen
, M. D.
, Goldman
, A.
, and Chen
, W. F.
, 1994, “The Role of Silica Fume in Mortar: Transition Zone Versus Bulk Paste Modification
,” Cem. Concr. Res.
0008-8846, 24
, pp. 95
–98
.23.
Wang
, J. A.
, Lubliner
, J.
, and Monteiro
, P. J. M.
, 1988, “Effect of Ice Formation on the Elastic Moduli of Cement Paste and Mortar
,” Cem. Concr. Res.
0008-8846, 18
, pp. 874
–885
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
