Derivation of the exponential relation for the effect of ellipsoidal porosity on elastic modulus

Journal of the American Ceramic Society

Volumn 79, Issue 8, 1996, Pages 2181-2184

  Andersson, Clarence A ^a,b  

^a American Ceramic Society ^*

^b AMERICAN CERAMIC SOCIETY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRACKS; ELASTIC MODULI; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; POROSITY; STRESSES;

ELLIPSOIDAL POROSITY; EXPONENTIAL CONSTANT; FRACTION POROSITY; PORE ORIENTATION; PORE SHAPE; PORE SIZE; STRESS AXIS;

POROUS MATERIALS;

EID: 0030216184     PISSN: 00027820     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1151-2916.1996.tb08955.x     Document Type: Article

References (42)

1. Z. Hashin, "Elastic Moduli of Heterogeneous Materials," J. Appl. Mech., 29 [1] 143-50 (1962).
2. D. P. H. Hasselman, "On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials," J. Am. Ceram. Soc., 45 [9] 452-53 (1962).
3. Z. Hashin and S. Strikman, "A Variational Approach to the Elastic Behavior of Multiphase Materials," J. Mech. Phys. Solids, 11 [2] 127-40 (1963).
4. R. Hill, "A Self-Consistent Mechanics of Composite Materials," J. Mech. Phys. Solids, 13 [4] 213-22 (1965).
5. B. Budianski, "On the Elastic Moduli of Some Heterogeneous Materials," J. Mech. Phys. Solids, 13 [4] 223-27 (1965).
6. T. T. Wu. "The Effect of the Inclusion Shape on the Elastic Modulus of a Two-Phase Material," Int. J. Solids Struct., 3 [1] 1-8 (1966).
7. R. C. Rossi, "Prediction of Elastic Moduli of Composites," J. Am. Ceram. Soc., 51 [8] 433-39 (1968).
8. R. B. Martin and R. R. Haynes, "Theoretical Analysis of the Effects of Air Voids in Concrete," J. Am. Concr. Inst., 68 [1] 36-41 (1971).
9. J. G. Berryman, "Long-Wavelength Propagation in Composite Elastic Media. I. Spherical Inclusions," J. Acoust. Soc. Am., 68 [6] 1809-19 (1980).
10. J. G, Berryman, "Long-Wavelength Propagation in Composite Elastic Media. II. Ellipsoidal Inclusions," J. Acoust. Soc. Am., 68 [6] 1820-31 (1980).
11. L. F. Nielsen, "Elastic Properties of Two-Phase Materials," Mater. Sci. Eng., 52 [1] 39-62 (1982).
12. E. A. Dean, "Elastic Moduli of Porous Sintered Materials as Modeled by a Variable-Aspect Ratio Self-Consistent Oblate-Spheroidal-Inclusion Theory," J. Am. Ceram. Soc., 66 [12] 847-54 (1983).
13. T. Mori and K. Tanaka, "Average Stress in Matrix and Average Elastic : Energy f Materials and Misfitting Inclusions," Acta Metall., 21, 571-79 (1983).
14. L. F. Nielsen, "Elasticity and Damping of Porous Materials and Impregnated Materials," J. Am. Ceram. Soc., 67 [2] 93-98 (1984).
15. N. Ramakrishnan and V. S. Arunachalam, "Effective Elastic Moduli of Porous Solids," J. Mater. Sci., 25 [9] 3930-37 (1990).
16. N. Ramakrishnan and V. S. Arunachalam, "Effective Elastic Moduli of Porous Ceramic Materials," J. Am. Ceram. Soc., 76 [11] 2745-52 (1993).
17. R. M. Spriggs, "Expression for the Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials, Particularly Alumina," J. Am. Ceram. Soc., 44 [12] 628-29 (1961).
18. F. P. Knudsen, "Effect of Porosity on Young's Modulus of Alumina," J. Am. Ceram. Soc., 45 [2] 94-95 (1962).
19. (a) R. M. Spriggs, "Expression for the Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials, Particularly Aluminum Oxide," J. Am. ' Ceram. Soc., 44 [12] 628-29 (1961);
20. (b) R. M. Spriggs, "Effect of Open and Closed Pores on Elastic Moduli of Polycrystalline Alumina," J. Am. Ceram. Soc., 45 [9] 454 (1962).
21. D. P. H. Hasselman and R. M. Fulrath, "Effect of Small Fraction of Spherical Porosity on Elastic Moduli of Glass," J. Am. Ceram. Soc., 47 [1] 52-53 (1964).
22. 4," J. Am. Ceram. Soc., 58 [1-2] 78-79 (1975).
23. R. W. Rice, "Effects of Inhomogeneous Porosity on Elastic Properties of Ceramics," J. Am. Ceram. Soc., 58 [9-10] 458-59 (1975).
24. W. S. Coblenz, "Elastic Moduli of Boron-Doped Silicon Carbide," J. Am. Ceram. Soc., 58 [11-12] 530-31 (1975).
25. R. W. Rice and T. J. Donahue, "Effect of Inhomogeneous Porosity Distribution on Elastic Moduli of Ceramics," J. Am. Ceram. Soc., 62 [5-6] 306-307 (1979).
26. D. F. Porter, J. S. Reed, and D. Lewis III, "Elastic Moduli of Refractory Spinels," J. Am. Ceram. Soc., 60 [7-8] 345-49 (1977).
27. E. A. Dean and J. A. Lopez, "Empirical Dependence of Elastic Moduli on Porosity for Ceramic Materials," J. Am. Ceram. Soc., 66 [5] 366-70 (1983).
28. K. K. Phani and S. K. Niyoga, "Elastic Modulus-Porosity Relation in Polycrystalline Rare-Earth Oxides," J. Am. Ceram. Soc., 70 [12] C-362-C-366 (1987).
29. F. P. Knudsen, "Dependence of Mechanical Strength of Brittle Polycrystalline Specimens on Porosity and Grain Size," J. Am. Ceram. Soc., 42 [8] 376-87 (1959).
30. C. A. Andersson, "The Deformation and Fracture of Several Polycrystalline Graphites"; Ph.D. Thesis. University of Pittsburgh, Pittsburgh, PA, 1970.
31. A. E. Green and I. N. Sneddon, "The Distribution of Stress in the Neighborhood of a Flat Elliptical Crack in an Elastic Solid," Proc. Cambridge Philos. Soc., 46, 159-63 (1954).
32. G. R. Irwin, "Crack-Extension Force for a Part-Through Crack in a Plate," Trans. ASME, Series E, 84, 651-54 (1962).
33. G. E. Bacon, "A Method of Determining the Degree of Orientation of Graphite," J. Appl. Chem., 6, 477-81 (1956).
34. G. R. Irwin, "Analysis of the Stresses and Strains near the End of a Crack Traversing a Plate," Trans. ASME, Series E, 79, 361-64 (1957).
35. B. D. Eshelby, "The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems," Proc. R. Soc. London, A, 241, 376-96 (1957).
36. S. Boucher, Review M, 22 [1] (1976).
37. R. McLaughlin, "A Study of the Differential Scheme for Composite Materials," Int. J. Eng. Sci., 15, 237-44 (1977).
38. Z. Hashin, "The Differential Scheme and its Application to Cracked Materials," J. Mech. Phys. Solids, 36, 719-34 (1988).
39. B. Budianski and R. J. O'Connell, "Elastic Moduli of a Cracked Solid," Int. J. Solids Struct., 12, 81-97 (1976).
40. I. N. Sneddon, "The Distribution of Stress in the Neighborhood of a Crack in an Elastic Field," Proc. R. Soc. London, A, 187, 229-60 (1946).
41. R. C. Rossi, J. R. Cost, and K. R. Janowski, "Influence of the Shape of Dispersed Particles on the Elastic Behavior of Composite Materials," J. Am. Ceram. Soc., 55 [5] 234-37 (1972).
42. R. W. Rice, "Evaluating Porosity Parameters for Porosity-Property Relations," J. Am. Ceram. Soc., 76 [7] 1801-808 (1993).