Abstract
Calculation of the effective elastic constants of a material with irregularly shaped porous space is discussed. It is shown that isolated pores of irregular shapes may be approximated, with good accuracy, by the spheroidal ones. Procedure of evaluation of the average aspect ratio from the photomicrograph is described. Several commonly used approximate schemes are applied to predict effective Young’s and shear moduli of a material with spheroidal pores. Comparisons of these predictions with the experimentally measured elastic constants for completely sintered hydroxyapatite exhibit reasonably good accuracy. The best agreement is given by self-consistent and effective field methods.
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References
Y. Benveniste (1986) ArticleTitleOn the Mori-Tanaka’s method in cracked bodies Mechanics Research Communications 13 IssueID4 193–201 Occurrence Handle0625.73110 Occurrence Handle10.1016/0093-6413(86)90018-2
R. Hill (1965) ArticleTitleA self-consistent mechanics of composite materials Journal of the mechanics and physics of solids 13 IssueID4 213–222 Occurrence Handle10.1016/0022-5096(65)90010-4 Occurrence Handle1965JMPSo..13..213H
M. Kachanov I. Sevostianov (2005) ArticleTitleOn quantitative characterization of microstructures and effective properties International Journal of Solids and Structures 42 309–336 Occurrence Handle1101.74013 Occurrence Handle10.1016/j.ijsolstr.2004.06.016
M. Kachanov I. Tsukrov B. Shafiro (1994) ArticleTitleEffective moduli of solids with cavities of various shapes Applied Mechanics Reviews 47 IssueID1 S151–74 Occurrence Handle10.1115/1.3122810
Kanaun, S. & Levin, V. (1994). in: K. Markov (Ed.) Advances in Mathematical Modeling of Composite Materials, World Scientific, Singapore, p.1.
B. Kibbel A. Heuer (1989) ArticleTitleAnisometric shape factors for microstructures Journal of American Ceramic Society 72 517–19 Occurrence Handle10.1111/j.1151-2916.1989.tb06170.x
V. Laraia I. Rus A. Heuer (1994) ArticleTitleMicrostructural shape factors: relation of random planar section to three dimensional microstructures Journal of American Ceramic Society 78 IssueID6 1532–36 Occurrence Handle10.1111/j.1151-2916.1995.tb08848.x
Markov, K. (2000). in: Markov, K, Preziozi, L.(Eds.), Heterogeneous Media: Micromechanics Modeling Methods and Simulations, Birkhauser, Boston, p.1
R. McLaughlin (1977) ArticleTitleA study of the differential scheme for composite materials International Journal of Engineering Science 15 IssueID4 237–44 Occurrence Handle0349.73050 Occurrence Handle10.1016/0020-7225(77)90058-1
T. Mori K. Tanaka (1973) ArticleTitleAverage stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metallurgica 21 IssueID5 571–74 Occurrence Handle10.1016/0001-6160(73)90064-3
Prokopiev, O & Sevostianov, I. (2006) Materials Science and Engineering A. (In press)
C Russ Dehoff (2000) Practical Stereology EditionNumber2 Plenum Press NY
Sevostianov, I., Kovàčik, J. & Simančík (2006). Elastic and electric properties of closed-cell aluminium foams Cross-property connection. Materials Science and Engineering A. 420 87-99, 2006.
Skorohod, V. (1961). Calculation of the effective isotropic moduli of disperse solid systems, Poroshkovaja Metallurgija (Powder Metall.) 1, 50-55. (in Russian).
R. Zimmerman (1991) ArticleTitleElastic moduli of a solid containing spherical inclusions Mechanics of Materials 12 IssueID1 17–24 Occurrence Handle10.1016/0167-6636(91)90049-6
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Prokopiev, O., Sevostianov, I. On the Possibility of Approximation of Irregular Porous Microstructure by Isolated Spheroidal Pores. Int J Fract 139, 129–136 (2006). https://doi.org/10.1007/s10704-006-8370-9
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DOI: https://doi.org/10.1007/s10704-006-8370-9