Nbr.

Reference Citation

1

S. Timoshenko, Theory of Elasticity, McGrawHill, New York (1934).

2

R. Hooke, De Potentia Restitutiva, London (1678).

3

T. Young, On the Equilibrium and Strength of Elastic Substances, Mathematical Elements of Natural Philosophy, Vol. II of Dr. Young's Lectures , Section IX, p. 46 (1807).

4

C. A. Coulomb, Theoretical and Experimental Researches on the Force of Torsion and on the Elasticity of Metal Wires, Histoire de l'Academie des Sciences, Year 1784 , pp. 229269 (1787).

5

ASTM, American Society for Testing and Materials, West Conshohocken, Pennsylvania.

6

G. Pickett, Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders, American Society for Testing and Materials, Proceedings, Vol. 45, pp. 846865 (1945).

7

S. Spinner and W. E. Tefft, A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from These Frequencies, American Society for Testing and Materials, Proceedings, Vol. 61, pp. 12211238 (1961).

8

G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, and O. Van der Biest, Impulse Excitation Apparatus to Measure Resonant Frequencies, Elastic Moduli, and Internal Friction at Room and High Temperature, Reviews of Scientific Instruments, Vol. 68, No. 12, pp. 45114515 (1997).

9

J. T. Richards, An Evaluation of Several Static and Dynamic Methods for Determiing Elastic Moduli, ASTM STP No. 129, American Society for Testing Materials, Philadelphia, pp. 7198 (1952).

10

S. Spinner and R. C. Valore, Jr., Comparison of Theoretical and Empirical Relations Between the Shear Modulus and Torsional Resonance Frequencies for Bars of Rectangular Cross Section, Journal of Research of the National Bureau of Standards, Vol. 60, No. 5, pp. 459464 (1958).

11

S. Spinner, T. W. Reichard, and W. E. Tefft, A Comparison of Experimental and Theoretical Relations Between Young's Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars, Journal of Research of the National Bureau of Standards, Vol. 64A, No. 2, pp. 147155 (1960).

12

J. S. Smith, M. D. Wyrick, and J. M. Poole, An Evaluation of Three Techniques for Determining the Young's Modulus of Mechanically Alloyed Materials, ASTM STP 1045, edited by A. Wolfenden, American Society for Testing and Materials, Philadelphia, pp. 195207 (1990).

13

A. Wolfenden, M. R. Harmouche, G. V. Blessing, Y. T. Chen, P. Terranova, V. Dayal, V. K. Kinra, J. W. Lemmens, R. R. Phillips, J. S. Smith, P. Mahmoodi, and R. J. Wann, Dynamic Young's Modulus Measurements in Metallic Materials: Results of an Interlaboratory Testing Program, Journal of Testing and Evaluation, Vol. 17, No. 1, pp. 213 (1989).

14

R. W. Dickson and J. B. Wachtman, Jr., An Alumina Standard Reference Material for Resonance Frequency and Dynamic Elastic Moduli Measurement, I. For Use at 25 °C, Journal of Research of the National Bureau of Standards, Vol. 75A, No. 3, pp. 155162 (1971).

15

R. W. Rice, Porosity of Ceramics, Marcel Dekker, New York (1998).

16

S. M. Lang, Properties of HighTemperature Ceramics and Cermets, Elasticity and Density at Room Temperature, Monograph 6, National Bureau of Standards, Washington, D.C. (1960).

17

O. L. Anderson, Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates Using SingleCrystal Data, Physical Acoustics, Vol. 3B, pp. 4395 (1965).

18

O. L. Anderson, E. Schreiber, and R. C. Liebermann, Some Elastic Constant Data on Minerals Relevant to Geophysics, Reviews of Geophysics, Vol. 6, No. 4, pp. 491524 (1968).

19

O. L. Anderson, D. Isaak, and H. Oda, HighTemperature Elastic Constant Data on Minerals Relevant to Geophysics, Reviews of Geophysics, Vol. 30, No. 1, pp. 5790 (1992).

20

R. W. Rice, Relation of Tensile StrengthPorosity Effects in Ceramics to Porosity Dependence of Young's Modulus and Fracture Energy, Porosity Character and Grain Size, Materials Science and Engineering, Vol. A112, pp. 215224 (1989).

21

R. W. Rice, The Porosity Dependence of Physical Properties of Materials: A Summary Review, Key Engineering Materials, Vol. 115, pp. 120 (1995).

22

R. W. Rice, Evaluation and Extension of Physical PropertyPorosity Models Based on Minimum Solid Area, Journal of Materials Science, Vol. 31, pp. 102118 (1996).

23

R. G. Munro, Mechanical Properties, Handbook of Superconductivity, edited by C. P. Poole, Academic Press, New York, pp. 570625 (1999).

24

R. G. Munro and S. W. Freiman, Correlation of Fracture Toughness and Strength, Journal of the American Ceramic Society, Vol. 82, No. 8, pp. 22462248 (1999).

25

M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford University, New York (1954).

26

J. B. Wachtman, Jr., W. E. Tefft, D. G. Lam, Jr., and C. S. Apstein, Physical Review, Vol. 122, No. 6, pp. 17541759 (1961).

27

O. L. Anderson, Derivation of Wachtman's Equation for the Temperature Dependence of Elastic Moduli of Oxide Compounds, Physical Review, Vol. 144, No. 2, pp. 553557 (1966).

28

W. Kreher, J. Ranachowski, and F. Rejmund, Ultrasonic Waves in Porous Ceramics With NonSpherical Holes, Ultrasonics, Vol. 15, No. 2, pp. 7074 (1977).

29

E. A. Dean, Elastic Moduli of Porous Sintered Materials as Modeled by a VariableAspectRatio SelfConsistent OblateSpheroidalInclusion Theory, Journal of the American Ceramic Society, Vol. 66, No. 12, pp. 847854 (1983).

30

N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Solids, Journal of Materials Science, Vol. 25, pp. 39303937 (1990).

31

D. N. Boccaccini and A. R. Boccaccini, Dependence of Ultrasonic Velocity on Porosity and Pore Shape in Sintered Materials, Journal of Nondestructive Evaluation, Vol. 16, No. 4, pp. 187192 (1997).

32

A. R. Boccaccini and Z. Fan, A New Approach for the Young's ModulusPorosity Correlation of Ceramic Materials, Ceramics International, Vol. 23, pp. 239245 (1997).

33

F. Wang, W. Gou, X. Zheng, and M. Lu, Effective Elastic Moduli of Ceramics with Pores, Journal of Materials Science and Technology, Vol. 14, pp. 286288 (1998).

34

R. W. Rice, Comparison of Stress Concentration versus Minimum Solid Area Based on Mechanical PropertyPorosity Relations, Journal of Materials Science, Vol. 28, pp. 21872190 (1993).

35

R. W. Rice, Comparison of Physical PropertyPorosity Behaviour with Minimum Solid Area Models, Journal of Materials Science, Vol. 31, pp. 15091528 (1996).

36

A. K. Mukhopadhyay and K. K. Phani, Young's ModulusPorosity Relations: an Analysis Based on a Minimum Contact Area Model, Journal of Materials Science, Vol. 33, pp. 6972 (1998).

37

A. K. Mukhopadhyay and K. K. Phani, Ultrasonic VelocityPorosity Relations: An Analysis Based on a Minimum Contact Area Model, Journal of Materials Science Letters, Vol. 18, pp. 17591760 (1999).

38

A. K. Mukhopadhyay and K. K. Phani, An Analysis of Microstructural Parameters in the Minimum Contact Area Model for Ultrasonic VelocityPorosity Relations, Journal of the European Ceramic Society, Vol. 20, pp. 2938 (2000).

39

D. G. Bika, M. Gentzler, and J. N. Michaels, Mechanical Properties of Agglomerates, Powder Technology, Vol. 117, pp. 98112 (2001).

40

A. P. Roberts and E. J. Garboczi, Elastic Properties of Model Porous Ceramics, Journal of the American Ceramic Society, Vol. 83, No. 12, pp. 30413048 (2000).

41

A. P. Roberts and E. J. Garboczi, Elastic Moduli of Model Random ThreeDimensional ClosedCell Cellular Solids, Acta Materialia, Vol. 49, pp. 189197 (2001).

42

J. M. Dewey, The Elastic Constants of Materials Loaded with NonRigid Fillers, Journal of Applied Physics, Vol. 18, pp. 578581 (1947).

43

J. K. Mackenzie, Elastic Constants of a Solid Containing Spherical Holes, Proceedings of the Physical Society, Section B, Vol. 63, pp. 211 (1950).

44

R. M. Spriggs and T. Vasilos, Effect of Grain Size and Porosity on the Transverse Bend Strength and Elastic Modulus of Hot Pressed Alumina and Magnesia, Journal of the American Ceramic Society, Vol. 40, No. 4, pg. 187 (1961).

45

D. P. H. Hasselman, On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials, Journal of the American Ceramic Society, Vol. 45, pp. 452453 (1962).

46

O. Ishai and L. J. Cohen, Elastic Properties of Filled and Porous Epoxy Composites, International Journal of Mechanical Sciences, Vol. 9, pp. 539546 (1967).

47

J. C. Wang, Young's Modulus of Porous Materials, Part 1, Theoretical Derivation of ModulusPorosity Correlation, Journal of Materials Science, Vol. 19, pp. 801808 (1984).

48

K. K. Phani and S. K. Niyogi, Young's Modulus of Porous Brittle Solids, Journal of Materials Science, Vol. 22, pp. 257263 (1987).

49

A. S. Wagh, R. B. Poeppel, and J. P. Singh, Open Pore Description of Mechanical Properties of Ceramics, Journal of Materials Science, Vol. 26, pp. 38623868 (1991).

50

M. Kupkova, Porosity Dependence of Material Elastic Moduli, Journal of Materials Science, Vol. 28, pp. 52655268 (1993).

51

A. R. Boccaccini, G. Ondracek, P. Mazilu, and D. Windelberg, On the Effective Young's Modulus of Elasticity for Porous Materials: Microstructure Modelling and Comparison Between Calculated and Experimental Values, Journal of the Mechanical Behavior of Materials, Vol. 4, pp. 119128 (1993).

52

B. Budiansky, On the Elastic Moduli of Some Heterogeneous Materials, Journal of the Mechanics and Physics of Solids, Vol. 13, pp. 223227 (1965).

53

E. A. Dean and J. A. Lopez, Empirical Dependence of Elastic Moduli on Porosity for Ceramic Materials, Journal of the American Ceramic Society, Vol. 66, No. 5, pp. 366370 (1983).

54

K. K. Phani, Young's Modulus Porosity Relation in Gypsum Systems, American Ceramic Society Bulletin, Vol. 65, No. 12, pp. 15841586 (1986).

55

K. K. Phani, ElasticConstantPorosity Relations for Polycrystalline Thoria, Journal of Materials Science Letters, Vol. 5, pp. 747750 (1986).

56

K. K. Phani and S. K. Niyogi, Porosity Dependence of Ultrasonic Velocity and Elastic Modulus in Sintered Uranium Dioxide, Journal of Materials Science Letters, Vol. 5, pp. 427430 (1986).

57

K. K. Phani and S. K. Niyogi, Elastic ModulusPorosity Relation in Polycrystalline RareEarth Oxides, Journal of the American Ceramic Society, Vol. 70, No. 12, pp. C362  C366 (1987).

58

N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Ceramic Materials, Journal of the American Ceramic Society, Vol. 76, pp. 27452752 (1993).

59

L. J. Gibson and M. F. Ashby, The Mechanics of ThreeDimensional Cellular Materials, Proceedings of the Royal Society of London, Vol. A382, pp. 4359 (1982).

60

R. G. Munro, Effective Medium Theory of the Porosity Dependence of Bulk Moduli, Journal of the American Ceramic Society, Vol. 84, No. 5, pp. 11901192 (2001).

61

A. Migliori, T. Chen, B. Alavi, and G. Grüner, Ultrasound Anomaly at T_{c} in YBa_{2}Cu_{3}O_{y} , Solid State Communications, Vol. 63, No. 9, pp. 827829 (1987).

62

Y. Horie, Y. Terashi, H. Fukuda, T. Fukami, and S. Mase, Ultrasonic Studies of the High T_{c} Superconductor Y_{2}Ba_{4}Cu_{6}O_{14} , Solid State Communications, Vol. 64, No. 4, pp. 501504 (1987).

63

G. Cannelli, R. Cantelli, F. Cordero, G. A. Costa, M. Ferretti, and G. L. Olcese, Anelastic Relaxation in the HighT_{c} Superconductor YBa_{2}Cu_{3}O_{7x} , Physical Review B, Vol. 36, No. 16, pp. 89078909 (1987).

64

S. Ewert, S. Guo, P. Lemmens, F. Stellmach, J. Wynants, G. Arlt, D. Bonnenberg, H. Kliem, A. Comberg, and H. Passing, Ultrasonic Investigations on Superconducting YBa_{2}Cu_{3}O_{7(delta)} Samples of Different Microstructure, Solid State Communications, Vol. 64, No. 8, pp. 11531156 (1987).

65

Y. He, B. Zhang, S. Lin, J. Xiang, Y. Lou, and H. Chen, Ultrasonic Investigation of Lattice Instability and Superconductivity in HighT_{c} Systems, Journal of Physics F: Metal Physics, Vol. 17, pp. L243L248 (1987).

66

S. Bhattacharya, M. J. Higgins, D. C. Johnston, A. J. Jacobson, J. P. Stokes, D. P. Goshorn, and J. T. Lewandowski, Elastic Anomalies and Phase Transitions in HighT_{c} Superconductors, Physical Review Letters, Vol. 60, No. 12, pp. 11811184 (1988).

67

M. Suzuki, Y. Okuda, I. Iwasa, A. J. Ikushima, T. Takabatake, Y. Nakazawa, and M. Ishikawa, Sound Velocity and Attenuation in YBa_{2}Cu_{3}O_{y} , Japanese Journal of Applied Physics, Vol. 27, No. 3, pp. L308L310 (1988).

68

M. SaintPaul, J. L. Tholence, P. Monceau, H. Noel, J. C. Levet, M. Potel, P. Gougeon, and J. J. Capponi, Ultrasound Study of YBa_{2}Cu_{3}O_{7(delta)} Single Crystals, Solid State Communications, Vol. 66, No. 6, pp. 641643 (1988).

69

S. Bhattacharya, M. J. Higgins, D. C. Johnston, A. J. Jacobson, J. P. Stokes, J. T. Lewandowski, and D. P. Goshorn, Anomalous Ultrasound Propagation in HighT_{c} Superconductors: La_{1.8}Sr_{0.2}CuO_{4y} and YBa_{2}Cu_{3}O_{7(delta)}, Physical Review B, Vol. 37, No. 10, pp. 59015904 (1988).

70

S. Hoen, L. C. Bourne, C. M. Kim, and A. Zettl, Elastic Response of Polycrystalline and SingleCrystal YBa_{2}Cu_{3}O_{7}, Physical Review B, Vol. 38, No. 16, pp. 1194911951 (1988).

71

X. D. Shi, R. C. Yu, Z. Z. Wang, N. P. Ong, and P. M. Chaikin, Sound Velocity and Attenuation in SingleCrystal YBa_{2}Cu_{3}O_{7(delta)}, Physical Review B, Vol. 39, No. 1, pp. 827830 (1989).

72

P. K. Choi, H. Koizumi, K. Takagi, and T. Suzuki, Anomalies of Ultrasonic Velocity in HighT_{c} Ceramics YBa_{2}Cu_{3}O_{y} and BiSrCaCu_{2}O_{y} , Solid State Communications, Vol. 70, No. 12, pp. 11751178 (1989).

73

N.N. Ault and H.F.G. Ueltz, Sonic Analysis for Solid Bodies, Journal of the American Ceramic Society, Vol. 36, No. 6, pp. 199203 (1953).

74

R.L. Coble and W.D. Kingery, Effect of Porosity on Physical Properties of Sintered Alumina, Journal of the American Ceramic Society, Vol. 39, No. 11, pp. 377385 (1956).

75

J.B. Wachtman,Jr. and D.G. Lam,Jr., Young's Modulus of Various Refractory Materials as a Function of Temperature, Journal of the American Ceramic Society, Vol. 42, No. 5, pp. 254260 (1959).

76

F.P. Knudsen, Effect of Porosity on Young's Modulus of Alumina, Journal of the American Ceramic Society, Vol. 45, No. 2, pp. 9495 (1962).

77

R.M. Spriggs, J.B. Mitchell, and T. Vasilos, Mechanical Properties of Pure, Dense Aluminum Oxide as a Function of Temperature and Grain Size, Journal of the American Ceramic Society, Vol. 47, No. 7, pp. 323327 (1964).

78

D.B. Binns and P. Popper, Mechanical Properties of Some Commerical Alumina Ceramics, Proceedings of the British Ceramic Society, Vol. 6, pp. 7182 (1966).

79

E. Schreiber and O.L. Anderson, Pressure Derivatives of the Sound Velocities of Polycrystalline Alumina, Journal of the American Ceramic Society, Vol. 49, pp. 184190 (1966).

80

N. Soga and O.L. Anderson, HighTemperature Elastic Properties of Polycrystalline MgO and Al_{2}O_{3}, Journal of the American Ceramic Society, Vol. 49, No. 7, pp. 355359 (1966).

81

D.H. Chung and G. Simmons, Pressure and Temperature Dependences of the Isotropic Elastic Moduli of Polycrystalline Alumina, Journal of Applied Physics, Vol. 39, No. 11, pp. 53165326 (1968).

82

A. Nagarajan, Ultrasonic Study of ElasticityPorosity Relationship in Polycrystalline Alumina, Journal of Applied Physics, Vol. 42, No. 10, pp. 36933696 (1971).

83

J.C. Wang, Young's Modulus of Porous Materials, Part 2, Young's Modulus of Porous Alumina with Changing Pore Structure, Journal of Materials Science, Vol. 19, pp. 809814 (1984).

84

C.C. Wu and R.W. Rice, Porosity Dependence of Wear and Other Mechanical Properties of FineGrain Al_{2}O_{3} and B_{4}C, Ceramic Engineering and Science Proceedings, Vol. 6, pp. 977993 (1985).

85

H. Hagiwara and D.J. Green, Elastic Behavior of OpenCell Alumina, Journal of the American Ceramic Society, Vol. 70, No. 11, pp. 811815 (1987).

86

T. Goto and O.L. Anderson, Elastic Constants of Corundum up to 1825 K, Journal of Geophysical Research, Vol. 94, No. B6, pp. 75887602 (1989).

87

D.J. Green, C. Nader, and R. Brezny, The Elastic Behavior of PartiallySintered Alumina, Ceramic Transactions, Vol. 7, pp. 345356 (1990).

88

J. Kubler, Weibull Characterization of Four Hipped/Posthipped Engineering Ceramics Between Room Temperature and 1500 °C, Report Number: EMPANr. 129'747, EMPA Swiss Federal Laboratories for Materials Testing and Research, pp. 188 (1992).

89

D.C. Lam, F.F. Lange, and A.G. Evans, Mechanical Properties of Partially Dense Alumina Produced from Powder Compacts, Journal of the American Ceramic Society, Vol. 77, No. 8, pp. 21132117 (1994).

90

J. Piekarczyk, J. Lis, and J. Bialoskorski, Elastic Properties, Hardness and Indentation Fracture Toughness of (beta)Sialons, Key Engineering Materials, Vol. 89, pp. 541546 (1994).

91

K. S. Tan, P. Hing, and P. Ramalingam, The Elastic Moduli and Diametrical Compressive Fracture Stress of Al_{2}O_{3}ZrO_{2} Ceramics, Journal of Physics D: Applied Physics, Vol. 30, pp. 10291037 (1997).

92

A. Wolfenden, Measurement and Analysis of Elastic and Anelastic Properties of Alumina and Silicon Carbide, Journal of Materials Science, Vol. 32, pp. 22752282 (1997).

93

B.D. Flinn, R.K. Borida, A. Zimmermann, and J. Rodel, Evolution of Defect Size and Strength of Porous Alumina During Sintering, Journal of the European Ceramic Society, Vol. 20, pp. 25612568 (2000).

94

D. Dierickx, I. Houben, J. Lapin, F. Delannay, O. Van Der Biest, Dense Polycrystalline BaZrO_{3} Substrates for YBa_{2}Cu_{3}O_{7x} Melt Processing, Journal of Materials Science Letters, Vol. 15, pp. 15731576 (1996).

95

K.C. Goretta, E.T. Park, R.E. Koritala, M.M. Cuber, E.A. Pascual, N. Chen, A.R. de ArellanoLopez, and J.L. Routbort, Thermomechanical Response of Polycrystalline BaZrO_{3}, Physica C, Vol. 309, pp. 245250 (1998).

96

B. A. Chandler, E. C. Duderstadt, and J. F. White, Fabrication and Properties of Extruded and Sintered BeO, Journal of Nuclear Materials, Vol. 8, No. 3, pp. 329347 (1963).

97

R.E. Fryxell and B.A. Chandler, Creep, Strength, Expansion, and Elastic Moduli of Sintered BeO as a Function of Grain Size, Porosity, and Grain Orientation, Journal of the American Ceramic Society, Vol. 47, No. 6, pp. 283291 (1964).

98

Y. He, J. Xiang, S. Jin, A. He, and J. Zhang, Ultrasonic Investigation of the Layered Perovskite Ceramic Superconducting Systems, Physica B, Vol. 165&166, pp. 12831284 (1990).

99

R. R. Reddy, M. Muralidhar, V. H. Babu, and P. V. Reddy, The Relationship Between the Porosity and Elastic Moduli of the BiPb2212 HighT_{c} Superconductor, Superconductor Science and Technology, Vol. 8, pp. 101107 (1995).

100

M. Muralidhar, K.N. Kishore, Y. V. Ramana, and V. H. Babu, Elastic and Plastic Behaviour of Lead and Silver Doped BiSrCaCuO Superconductors, Materials Science and Engineering B, Vol. 13, pp. 215219 (1992).

101

S. Satyavathi, M. Muralidhar, V. H. Babu, R. R. Reddy, and P. V. Reddy, Elastic Behaviour of BiPbAgCa_{2}CuO_{3} Superconducting Composite Materials, Journal of Alloys and Compounds, Vol. 209, pp. 329335 (1994).

102

R .J. Topare, K. Ganesh, N. K. Sahuji, S. S. Shah, and P. V. Reddy, Elastic Anomalies in BiPb2223/Ag Superconducting Composite Materials, Physica C, Vol. 253, pp. 8996 (1995).

103

O. O. Oduleye, S. J. Penn, and N. McN. Alford, The Mechanical Properties of (BiPb)SrCaCuO, Superconductor Science and Technology, Vol. 11, pp. 858865 (1998).

104

W. R. Manning, M. O. Marlowe, and D. R. Wilder, Temperature and Porosity Dependence of Young's Modulus of Polycrystalline Dysprosium Oxide and Erbium Oxide, Journal of the American Ceramic Society, Vol. 49, No. 4, pp. 227228 (1966).

105

W. R. Manning, O. Hunter, Jr., and B. R. Powell, Jr., Elastic Properties of Polycrystalline Yttrium Oxide, Dysprosium Oxide, Holmium Oxide, and Erbium Oxide: Room Temperature Measurements, Journal of the American Ceramic Society, Vol. 52, No. 8, pp. 436442 (1969).

106

W. R. Manning and O. Hunter, Jr., Elastic Properties of Polycrystalline Yttrium Oxide, Holmium Oxide, and Erbium Oxide: HighTemperature Measurements, Journal of the American Ceramic Society, Vol. 52, No. 9, pp. 492496 (1969).

107

A. A. Sharif, F. Chu, A. Mirsa, T. E. Mitchell, and J. J. Petrovic, Elastic Constants of Erbia Single Crystals, Journal of the American Ceramic Society, Vol. 83, No. 9, pp. 22462250 (2000).

108

J. A. Haglund and O. Hunter,Jr., Elastic Properties of Polycrystalline Monoclinic Gd_{2}O_{3}, Journal of the American Ceramic Society, Vol. 56, No. 6, pp. 327330 (1973).

109

S. L. Dole, O. Hunter,Jr., and C. J. Wooge, Elastic Properties of Monoclinic Hafnium Oxide at Room Temperature, Journal of the American Ceramic Society, Vol. 60, No. 11, pp. 488490 (1977).

110

R. W. Scheidecker, O. Hunter,Jr., and F. W. Calderwood, Elastic Properties of PartiallyStabilized HfO_{2} Compositions, Journal of Materials Science, Vol. 14, pp. 22842288 (1979).

111

S. L. Dole, O. Hunter, Jr., and F. W. Calderwood, Elastic Properties of Stabilized HfO_{2} Compositions, Journal of the American Ceramic Society, Vol. 63, No. 3, pp. 136139 (1980).

112

S. L. Dole and O. Hunter, Jr., Elastic Properties of Hafnium and Zirconium Oxides Stabilized with Praseodymium or Terbium Oxide, Journal of the American Ceramic Society, Vol. 66, No. 3, pp. C47C49 (1983).

113

G. W. Crabtree, J. W. Downey, B. K. Flandermeyer, J. D. Jorgensen, T. E. Klippert, D. S. Kupperman, W. K. Kwok, D. J. Lam, A. W. Mitchell, A. G. McKale, M. V. Nevitt, L. J. Nowicki, A. P. Paulikas, R. B. Poeppel, S. J. Rothman, J. L. Roubort, J. P. Singh, C. H. Sowers, A. Umezawa, B. W. Veal, and J. E. Baker, Fabrication, Mechanical Properties, Heat Capacity, Oxygen Diffusion, and the Effect of Alkali Earth Ion Substitution on High T_{c} Superconductors, Advanced Ceramic Materials, Vol. 2, No. 3B, pp. 444456 (1987).

114

A. J. Zaleski and J. Klamut, Penetration Depth in Magnetically Oriented, Ceramic, Ni and Zndoped La_{2x}Sr_{x}CuO_{4}, Physica C, Vol. 282, pp. 14631464 (1997).

115

W. R. Manning and O. Hunter, Jr., Elastic Properties of Polycrystalline Thulium Oxide and Lutetium Oxide from 20 °C to 1000 °C, Journal of the American Ceramic Society, Vol. 53, No. 5, pp. 279280 (1970).

116

O. Hunter, Jr. and G. E. Graddy, Jr., Porosity Dependence of Elastic Properties of Polycrystalline Cubic Lu_{2}O_{3}, Journal of the American Ceramic Society, Vol. 59, No. 1, pp. 8282 (1976).

117

D. F. Porter, J. S. Reed, and D. Lewis, Elastic Moduli of Refractory Spinels, Journal of the American Ceramic Society, Vol. 60, No. 7, pp. 345349 (1977).

118

R. L. Stewart and R. C. Bradt, Fracture of Polycrystalline MgAl_{2}O_{4}, Journal of the American Ceramic Society, Vol. 63, No. 11, pp. 619623 (1980).

119

A. Ghosh, K. W. White, M. G. Jenkins, A. S. Kobayashi, and R. C. Bradt, Fracture Resistance of a Transparent Magnesium Aluminate Spinel, Journal of the American Ceramic Society, Vol. 74, No. 7, pp. 16241630 (1991).

120

K. W. White and G. P. Kelkar, Fracture Mechanisms of a CoarseGrained, Transparent MgAl_{2}O_{4} at Elevated Temperatures, Journal of the American Ceramic Society, Vol. 75, No. 12, pp. 34403444 (1992).

121

C. Baudin, R. Martinez, and P. Pena, HighTemperature Mechanical Behavior of Stoichiometric Magnesium Spinel, Journal of the American Ceramic Society, Vol. 78, No. 7, pp. 18571862 (1995).

122

K. R. Janowski and R. C. Rossi, Elastic Behavior of MgO Matrix Composites, Journal of the American Ceramic Society, Vol. 50, No. 11, pp. 599603 (1967).

123

N. Soga and E. Schreiber, Porosity Dependence of Sound Velocity and Poisson's Ratio for Polycrystalline MgO Determined by Resonant Sphere Method, Vol. 51, No. 8, pp. 465466 (1968).

124

Y. Sumino, O. L. Anderson, and I. Suzuki, Temperature Coefficients of Elastic Constants of Single Crystal MgO between 80 K and 1300 K, Physics and Chemistry of Minerals, Vol. 9, pp. 3847 (1983).

125

D. G. Isaak, O. L. Anderson, and T. Goto, Measured Elastic Moduli of SingleCrystal MgO up to 1800 K, Physics and Chemistry of Minerals, Vol. 16, pp. 704713 (1989).

126

R. A. Penty, D.P.H. Hasselman, and R. M. Spriggs, Young's Modulus of HighDensity Polycrystalline Mullite, Journal of the American Ceramic Society, Vol. 55, No. 3, pp. 169170 (1972).

127

K. S. Mazdiyasni and L. M. Brown, Synthesis and Mechanical Properties of Stoichiometric Aluminum Silicate (Mullite), Journal of the American Ceramic Society, Vol. 55, pp. 548552 (1972).

128

B. L. Metcalfe and J. H. Sant, The Synthesis, Microstructure and Physical Properties of High Purity Mullite, Transactions of the British Ceramic Society, Vol. 74, pp. 193201 (1975).

129

M.G.M.U. Ismail, Z. Nakai, and S. Somiya, Microstructure and Mechanical Properties of Mullite Prepared by the SolGel Method, Journal of the American Ceramic Society, Vol. 70, No. 1, pp. C7C8 (1987).

130

M. I. Osendi and C. Baudin, Mechanical Properties of Mullite Materials, Journal of the European Ceramic Society, Vol. 16, pp. 217224 (1996).

131

C. Baudin, Fracture Mechanisms in a Stoichiometric 3Al_{2}O_{3}Â·2SiO_{2} Mullite, Journal of Materials Science, Vol. 32, pp. 20772086 (1997).

132

H. Ledbetter, S. Kim, D. Balzar, S. Crudele, and W. Kriven, Elastic Properties of Mullite, Journal of the American Ceramic Society, Vol. 81, No. 4, pp. 10251028 (1998).

133

A. K. Yahya and R. AbdShukor, Ultrasonic Velocity Measurements on PrBa_{2}Cu_{3}O_{7(delta)} ((delta) =0.1, 0.5), Physica B, Vol. 252, pp. 237243 (1998).

134

S. L. Dole, O. Hunter, Jr., and F. W. Calderwood, Elastic Properties of Polycrytalline Scandium and Thulium Sesquioxides, Journal of the American Ceramic Society, Vol. 60, No. 3, pp. 167168 (1977).

135

H. J. McSkimin, Measurement of Elastic Constants at Low Temperatures by Means of Ultrasonic Waves  Data for Silicon and Germanium Single Crystals, and for Fused Silica, Journal of Applied Physics, Vol. 24, No. 8, pp. 988997 (1953).

136

S. Spinner, Journal of the American Ceramic Society, Vol. 37, No. 5, pp. 229234 (1954).

137

S. Spinner, Elastic Moduli of Glasses at Elevated Temperatures by a Dynamic Method, Journal of the American Ceramic Society, Vol. 39, pp. 113118 (1956).

138

H. J. McSkimin, Measurement of Ultrasonic Wave Velocities and Elastic Moduli for Small Solid Specimens at High Temperatures, Journal of the Acoustical Society of America, Vol. 31, No. 3, pp. 287295 (1959).

139

E. H. Carnevale, L. C. Lynnworth, and G. S. Larson, Ultrasonic Measurement of Elastic Moduli at Elevated Temperatures, using Momentary Contact, Journal of the Acoustical Society of America, Vol. 36, No. 9, pp. 16781684 (1964).

140

M. Fukuhara and A. Sanpei, High TemperatureElastic Moduli and Internal Dilational and Shear Frictions of Fused Quartz, Japanese Journal of Applied Physics, Vol. 33, pp. 28902893 (1994).

141

M. Fukuhara, A. Sanpei, and K. Shibuki, Low Temperature Elastic Moduli, Debye Temperature and Internal Dilational and Shear Frictions of Fused Quartz, Journal of Materials Science, Vol. 32, pp. 12071211 (1997).

142

S. Spinner, Temperature Dependence of Elastic Constants of Vitreous Silica, Journal of the American Ceramic Society, Vol. 45, No. 8, pp. 394397 (1962).

143

O. Hunter, H. J. Korklan, and R. R. Suchomel, Elastic Properties of Polycrystalline Monoclinic Sm_{2}O_{3}, Journal of the American Ceramic Society, Vol. 57, No. 6, pp. 267268 (1974).

144

S. Spinner, F. P. Knudsen, and L. Stone, Elastic ConstantPorosity Relations for Polycrystalline Thoria, Journal of Research of the National Bureau of Standards, Vol. 67C, No. 1, pp. 3946 (1963).

145

W. P. Minnear and R. C. Bradt, Elastic Properties of Polycrystalline TiO_{2x}, Journal of the American Ceramic Society, Vol. 60, No. 9, pp. 458459 (1977).

146

J. Li, S. Forberg, and L. Hermansson, Evaluation of the Mechanical Properties of Hot Isostatically Pressed Titania and TitaniaCalcium Phosphate Composites, Biomaterials, Vol. 12, pp. 438440 (1991).

147

O. Anderson, C. R. Ottermann, R. Kuschnereit, P. Hess, and K. Bange, Density and Young's Modulus of Thin TiO_{2} Films, Fresenius Journal of Analytical Chemistry, Vol. 358, pp. 315318 (1997).

148

D. G. Isaak, J. D. Carnes, O. L. Anderson, H. Cynn, and E. Hake, Physics and Chemistry of Minerals, Vol. 26, 3143 (1998).

149

J. B. Wachtman, Jr. and M. L. Wheat, Elastic Constants of Single Crystal UO_{2} at 25 °C, Journal of Nuclear Materials, Vol. 16, pp. 3941 (1965).

150

A. Padel and Ch. de Novion, Constantes Elastiques des Carbures, Nitrures et Oxydes d'Uranium et de Plutonium, Journal of Nuclear Materials, Vol. 33, pp. 4051 (1969).

151

J. P. Panakkal and J. K. Ghosh, Ultrasonic Velocity in Sintered Uranium Dioxide Pellets, Journal of Materials Science Letters, Vol. 3, pp. 835836 (1984).

152

V. M. Baranov, Y. K. Bibilashvili, I. S. Golovnin, V. N. Kakurin, T. S. Men'shikova, Y. V. Miloserdin, and A. V. Rimashevskii, InReactor Measurements of the Modulus of Elasticity of Uranium Dioxide, Soviet Atomic Energy, Vol. 40, No. 1, pp. 3739 (1976).

153

J. P. Panakkal, Use of Longitudinal Ultrasonic Velocity as a Predictor of Elastic Moduli and Density of Sintered Uranium Dioxide, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 38, No. 3, pp. 161165 (1991).

154

V. Roque, B. Cros, D. Baron, and P. Dehaudt, Effects of the Porosity in Uranium Dioxide on Microacoustic and Elastic Properties, Journal of Nuclear Materials, Vol. 277, pp. 211216 (2000).

155

D. P. Almond, E. Lambson, G. A. Saunders, and W. Hong, An Ultrasonic Study of the Elastic Properties of the Normal and Superconducting States of YBa_{2}Cu_{3}O_{7(delta)}, Journal of Physics F: Metal Physics, Vol. 17, pp. L221L224 (1987).

156

N. McN. Alford, J. D. Birchall, W. J. Clegg, M. A. Harmer, K. Kendall, and D. H. Jones, Physical and Mechanical Properties of YBa_{2}Cu_{3}O_{7(delta)} Superconductors, Journal of Materials Science, Vol. 23, pp. 761768 (1988).

157

M. Cankurtaran, G. A. Saunders, J. R. Willis, A. AlKheffaji, and D. P. Almond, Bulk Modulus and Its Pressure Derivative of YBa_{2}Cu_{3}O_{7x}, Physical Review B, Vol. 39, No. 4, pp. 28722875 (1989).

158

A. AlKheffaji, M. Cankurtaran, G. A. Saunders, D. P. Almond, E. F. Lambson, and R. C. J. Draper, Elastic Behaviour under Pressure of HighT_{c} Superconductors RBa_{2}Cu_{3}O_{7x} (R = Y, Gd and Eu), Philosophical Magazine B, Vol. 59, No. 5, pp. 487497 (1989).

159

J. P. Singh, H. J. Leu, R. B. Poeppel, E. Van Voorhees, G. T. Goudey, K. Winsley, and D. Shi, Effect of Silver and Silver Oxide Additions on the Mechanical and Superconducting Properties of YBa_{2}Cu_{3}O_{7(delta)} Superconductors, Journal of Applied Physics, Vol. 66, No. 7, pp. 31543159 (1989).

160

B. Bridge and R. Round, Density Dependence of the Ultrasonic Properties of HighT_{c} Sintered YBa_{2}Cu_{3}O_{7x} Superconductors, Journal of Materials Science Letters, Vol. 8, pp. 691694 (1989).

161

M. C. Bhardwaj and A. S. Bhalla, Ultrasonic Characterization of Ceramic Superconductors, Journal of Materials Science Letters, Vol. 10, pp. 210213 (1991).

162

M. Cankurtaran, G. A. Saunders, K. C. Goretta, and R. B. Poeppel, Ultrasonic Determination of the Elastic Properties and Their Pressure and Temperature Dependences in Very Dense YBa_{2}Cu_{3}O_{7x}, Physical Review B, Vol. 46, No. 2, pp. 11571165 (1992).

163

P. V. Reddy, R. R. Reddy, K. B. Reddy, and V. N. Mulay, Ulrasonic Anomalies in YBaCuO HighT_{c} Superconducting Materials, Modern Physics Letters B, Vol. 7, No. 22, pp. 14571465 (1993).

164

M. Cankurtaran, G. A. Saunders, and K. C. Goretta, Ultrasonic Study of the Temperature and Pressure Dependences of the Elastic Properties of Fully Oxygenated YBa_{2}Cu_{3}O_{6.94}, Superconductor Science and Technology, Vol. 7, pp. 49 (1994).

165

P. V. Reddy, S. Shekar, and K. Somaiah, Elasticity Studies of REBaCuO HighT_{c} Superconductors, Materials Letters, Vol. 21, pp. 2129 (1994).

166

H. Ledbetter, M. Lei, A. Hermann, and Z. Sheng, LowTemperature Elastic Constants of Y_{1}Ba_{2}Cu_{3}O_{7}, Physica C, Vol. 225, pp. 397403 (1994).

167

Z. Zhong, Y. Qianjin, T. Xinlu, Z. Lizhong, W. Qimin, and Z. Peiqiang, The Dynamical Mechanical Properties of YBCO Superconductor, Experimental Techniques, Vol. 18, No. 4, pp. 2527 (1994).

168

R. R. Reddy, O. M. Prakash, and R. V. Reddy, The Effect of Porosity on Elastic Moduli of YBa_{2}Cu_{3}O_{7(delta)} High T_{c} Superconductors, Applied Superconductivity, Vol. 3, No. 4, pp. 215222 (1995).

169

Q. Wang, G. A. Saunders, D. P. Almond, M. Cankurtaran, and K. C. Goretta, Elastic and Nonlinear Acoustic Properties of YBa_{2}Cu_{3}O_{7x} Ceramics with Different Oxygen Contents, Physical Review B, Vol. 52, No. 5, pp. 37113726 (1995).

170

L. Masi, E. Borchi, and S. de Gennaro, Porosity Behaviour of Ultrasonic Velocities in Polycrystalline YBCO, Journal of Physics F: Applied Physics, Vol. 29, pp. 20152019 (1996).

171

F. Yu, K. W. White, and R. Meng, Mechanical Characterization of TopSeeded MeltTextured YBa_{2}Cu_{3}O_{7(delta)} Single Crystal, Physica C, Vol. 276, pp. 295308, (1997).

172

F. Tancret, G. Desgardin, and F. Osterstock, Influence of Porosity on the mechanical Properties of Cold Isostatically Pressed and Sintered YBa_{2}Cu_{3}O_{7x} Superconductors, Philosophical Magazine A, Vol. 75, No. 2, pp. 505523 (1997).

173

P. V. Reddy and M. Murakami, Elastic Behavior of MeltPowderMeltGrowth Processed YBa_{2}Cu_{3}O_{7(delta)}, Modern Physics Letters B, Vol. 13, No. 8, pp. 261270 (1999).

174

R. Sreekumar, J. Isaac, J. Philip, K. V. Paulose, M. T. Sebastian, and A. D. Damodaran, Elastic and Thermal Properties of Yttrium Barium Zirconate, Physica Status Solidi (a), Vol. 133, pp. 341347 (1992).

175

M. O. Marlowe and D. R. Wilder, Elasticity and Internal Friction of Polycrystalline Yttrium Oxide, Journal of the American Ceramic Society, Vol. 48, No. 5, pp. 227233 (1965).

176

W. R. Manning and O. Hunter, Jr., Porosity Dependence of Young's and Shear Moduli of Polycrystalline Yttrium Oxide, Journal of the American Ceramic Society, Vol. 51, No. 9, pp. 537538 (1968).

177

O. Yeheskel and O. Tevet, Elastic Moduli of Transparent Yttria, Journal of the American Ceramic Society, Vol. 82, No. 1, pp. 136144 (1999).

178

J. W. Palko, W. M. Kriven, S. V. Sinogeikin, J. D. Bass, and A. Sayir, Elastic Constants of Yttria (Y2O3) Monocrystals to High Temperatures, Journal of Applied Physics, Vol. 89, No. 12, pp. 77917796 (2001).

179

R. W. Dickson and R. C. Anderson, Temperature Dependence of the Elastic Moduli of 91Y_{2}O_{3} + 9ThO_{2} from 25° to 1100°C, Journal of the American Ceramic Society, Vol. 51, No. 4, pp. 233234 (1968).

180

C. E. Holcombe, T. T. Meek, and N. L. Dykes, Unusual Properties of MicrowaveSintered Yttria2wt% Zirconia, Journal of Materials Science Letters, Vol. 7, pp. 881884 (1988).

181

B. R. Powell, Jr., O. Hunter, Jr., and W. R. Manning, Elastic Properties of Polycrystalline Ytterbium Oxide, Journal of the American Ceramic Society, Vol. 54, No. 10, pp. 488490 (1971).

182

L. P. Martin, D. Dadon, and M. Rosen, Evaluation of Ultrasonically Determined ElasticityPorosity Relations in Zinc Oxide, Journal of the American Ceramic Society, Vol. 79, No. 5, pp. 12811289 (1996).

183

A. K. Mukhopadhyay, M. R. Chaudhuri, A. Seal, S. K. Dalui, M. Banerjee, and K. K. Phani, Mechanical Characterization of Microwave Sintered Zinc Oxide, Bulletin of Materials Science, Vol. 24, No. 2, pp. 125128 (2001).

184

C. F. Smith and W. B. Crandall, Calculated HighTemperature Elastic Constants for Zero Porosity Monoclinic Zirconia, Journal of the American Ceramic Society, Vol. 47, No. 12, pp. 624627 (1964).

185

J. W. Adams, R. Ruh, and K. S. Mazdiyasni, Young's Modulus, Flexural Strength, and Fracture of YttriaStabilized Zirconia versus Temperature, Journal of the American Ceramic Society, Vol. 80, No. 4, pp. 903908 (1997).

186

M. A. Ewaida, A. A. Higazy, B. Bridge, and M. M. Abou Sekkina, Elastic Constants of the Iron Oxide Doped YttriaStabilized Zirconia, Journal of Materials Science, Vol. 24, pp. 36603666 (1989).

187

Y. Kubota, M. Ashizuka, E. Ishida, and T. Mitamura, Influence of Temperature on Elastic Modulus and Strength of MgOPartially Stabilized Zirconia (MgPSZ), Journal of the Ceramic Society of Japan, Vol. 102, No. 8, pp. 708712 (1994).

188

W. J. Wei and Y. Lin, Mechanical and Thermal Shock Properties of Size Graded MgOPSZ Refractory, Journal of the European Ceramic Society, Vol. 20, pp. 11591167 (2000).

189

Y. Kubota, M. Ashizuka, and H. Hokazono, Elastic Modulus and Fracture Toughness of CeO_{2}Containing Tetragonal Zirconia Polycrystals, Journal of the Ceramic Society of Japan, Vol. 102, No. 2, pp. 175179 (1994).

190

G. A. Gogotsi, V. P. Zavada, and M. V. Swain, Mechanical Property Characterization of a 9 mol% CeTZP Ceramic Material, I: Flexural Response, Journal of the European Ceramic Society, Vol. 15, pp. 11851192 (1995).

191

Z. Zhang, D. Jin, L. Li, Z. Tu, L. Zhao, P. Zhang, and J. Zhao, Fracture Strength and Dynamic Elastic Modulus of Ce and ErTZP at Low Temperature, Journal of the American Ceramic Society, Vol. 78, No. 9, pp. 25482550 (1995).

192

J. Luo and R. Stevens, PorosityDependence of Elastic Moduli and Hardness of 3YTZP Ceramics, Ceramics International, Vol. 25, pp. 281286 (1999).

193

S. P. Timoshenko, On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Philosophical Magazine, Vol. 41, Sixth Series, pp. 744746 (1921).

194

E. Goens, Über die Bestimmung des Elastizitätsmoduls von Stäben mit Hilfe von Beigungsschwingungen, Annalen der Physik, 5 Folge, Band 11, Reihe 403, Heft 6, 649678 (1931).

195

F. Forster, Ein neues Messverfahren zur Bestimmung des Elastizitätsmoduls und Dampfung, Zeitschrift für Metallkunde, Vol. 29, No. 4, pp. 109115 (1937).
