Representative Volumes of Composite Materials
Publication: Journal of Engineering Mechanics
Volume 122, Issue 12
Abstract
Representative volume (RV) of a composite material is important not only for experimental determination of materials properties, but also for theoretical analysis of various properties of the materials. RV is a random variable; this is especially true for the composites with heterogeneous microstructures. In the present study, RV is redefined as a relationship among three parameters: the volume under consideration, the measured or predicted value of a property corresponding to the volume, and the scattering of the property from the real effective property. There are two steps involved to determine RV. The first is to determine the relationship among the effective property, the properties of each constituents, and volume fractions, which is the topic in composite mechanics. The second is determination of the local variation of the heterogeneity of the composite because, with increasing size of the local volume, the statistics from the local volume asymptotically approaches the value from the global average. The main purpose of this study is to develop a theoretical model to determine local variation of heterogeneity, which is obviously related to the morphological features of the composites. The model accounts for coarseness of grain sizes, volume fractions, spatial arrangement of the constituents, and properties of each constituents. By combining the model with available composite models for effective properties of composites, RV for various materials properties can be developed. As an example, RV for elastic moduli of cementitious materials is demonstrated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aboudi, J. (1991). Mechanics of composite materials, a unified micromechanical approach . Elsevier Science Publishers BV, Amsterdam, The Netherlands.
2.
Ben-Amoz, M.(1970). “The effective thermal properties of two phase solids.”Int. J. Engrg. Sci., 8, 39–47.
3.
Christensen, R. M. (1979). Mechanics of composite materials . A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, N.Y.
4.
Ditlevsen, O. (1981). Uncertainty modeling . McGraw-Hill Book Co., Inc., New York, N.Y.
5.
Grimvall, G. (1986). Thermophysical properties of materials . North-Holland Publishing Co., Amsterdam, The Netherlands.
6.
Hale, D. K.(1976). “Review of the physical properties of composite materials.”J. Mat. Sci., 11, 2105–2141.
7.
Hashin, Z.(1983). “Analysis of composite materials—a survey.”J. Appl. Mech., 50, 481–505.
8.
Hashin, Z., and Shtrikman, S.(1963). “A variational approach to the theory of the elastic behaviors of multiphase materials.”J. Mech. Phys. Solids, 11, 127–140.
9.
Kumar, S. (1992). “Computer simulation of 3D material microstructure and its application in the determination of mechanical behavior of polycrystalline materials and engineering structures,” PhD thesis, Dept. of Engrg. Sci. and Mech., The Pennsylvania State Univ., University Park, Pa.
10.
Lu, B., and Torquato, S.(1990). “Local volume fraction fluctuation in heterogeneous media.”J. Chemical Phys., 93(5), 3452–3459.
11.
Pielou, E. C. (1977). Mathematical ecology . A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, N.Y.
12.
Rosen, B. W., and Hashin, Z.(1970). “Effective thermal expansion coefficient and specific heats of composite materials.”Int. J. Engrg. Sci., 8, 157–173.
13.
Xi, Y. (1994). “Simulation of multiphase spatial distributions with application to fracture of concrete.”Proc., of Europe-U.S. Workshop on Fracture and Damage in Quasibrittle Struct.: Experiment, Modeling and Comp. Anal., E&FN Spon, London, England, 501–510.
14.
Xi, Y.(1995a). “A model for moisture capacities of composite materials—formulation.”Computational Mat. Sci., 4, 65–77.
15.
Xi, Y.(1995b). “A model for moisture capacities of composite materials—application to concrete.”Computational Mat. Sci., 4, 78–92.
16.
Xi, Y. (1996). “Analysis of internal structures of composite materials by second order property of mosaic patterns.”Mat. Characterization, Jan. 11–25.
17.
Xi, Y., Jennings, H. M., and Tennis, P. (1996). “Mathematical modeling of cement paste microstructure by mosaic pattern, part I: Theory.”J. Mat. Res., 11(8), 1943–1952 .
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 12 • December 1996
Pages: 1159 - 1167
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Dec 1, 1996
Published in print: Dec 1996
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.