References are cited in the compilation by Reference Number (Nbr.). The complete list of references in NISTIR 6853 is given in the following table.
| Nbr. | Reference Citation |
|---|---|
| 1 | S. Timoshenko, Theory of Elasticity, McGraw-Hill, 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. 229-269 (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. 846-865 (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. 1221-1238 (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. 4511-4515 (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. 71-98 (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. 459-464 (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. 147-155 (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. 195-207 (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. 2-13 (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. 155-162 (1971). |
| 15 | R. W. Rice, Porosity of Ceramics, Marcel Dekker, New York (1998). |
| 16 | S. M. Lang, Properties of High-Temperature 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 Single-Crystal Data, Physical Acoustics, Vol. 3B, pp. 43-95 (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. 491-524 (1968). |
| 19 | O. L. Anderson, D. Isaak, and H. Oda, High-Temperature Elastic Constant Data on Minerals Relevant to Geophysics, Reviews of Geophysics, Vol. 30, No. 1, pp. 57-90 (1992). |
| 20 | R. W. Rice, Relation of Tensile Strength-Porosity 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. 215-224 (1989). |
| 21 | R. W. Rice, The Porosity Dependence of Physical Properties of Materials: A Summary Review, Key Engineering Materials, Vol. 115, pp. 1-20 (1995). |
| 22 | R. W. Rice, Evaluation and Extension of Physical Property-Porosity Models Based on Minimum Solid Area, Journal of Materials Science, Vol. 31, pp. 102-118 (1996). |
| 23 | R. G. Munro, Mechanical Properties, Handbook of Superconductivity, edited by C. P. Poole, Academic Press, New York, pp. 570-625 (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. 2246-2248 (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. 1754-1759 (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. 553-557 (1966). |
| 28 | W. Kreher, J. Ranachowski, and F. Rejmund, Ultrasonic Waves in Porous Ceramics With Non-Spherical Holes, Ultrasonics, Vol. 15, No. 2, pp. 70-74 (1977). |
| 29 | E. A. Dean, Elastic Moduli of Porous Sintered Materials as Modeled by a Variable-Aspect-Ratio Self-Consistent Oblate-Spheroidal-Inclusion Theory, Journal of the American Ceramic Society, Vol. 66, No. 12, pp. 847-854 (1983). |
| 30 | N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Solids, Journal of Materials Science, Vol. 25, pp. 3930-3937 (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. 187-192 (1997). |
| 32 | A. R. Boccaccini and Z. Fan, A New Approach for the Young's Modulus-Porosity Correlation of Ceramic Materials, Ceramics International, Vol. 23, pp. 239-245 (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. 286-288 (1998). |
| 34 | R. W. Rice, Comparison of Stress Concentration versus Minimum Solid Area Based on Mechanical Property-Porosity Relations, Journal of Materials Science, Vol. 28, pp. 2187-2190 (1993). |
| 35 | R. W. Rice, Comparison of Physical Property-Porosity Behaviour with Minimum Solid Area Models, Journal of Materials Science, Vol. 31, pp. 1509-1528 (1996). |
| 36 | A. K. Mukhopadhyay and K. K. Phani, Young's Modulus-Porosity Relations: an Analysis Based on a Minimum Contact Area Model, Journal of Materials Science, Vol. 33, pp. 69-72 (1998). |
| 37 | A. K. Mukhopadhyay and K. K. Phani, Ultrasonic Velocity-Porosity Relations: An Analysis Based on a Minimum Contact Area Model, Journal of Materials Science Letters, Vol. 18, pp. 1759-1760 (1999). |
| 38 | A. K. Mukhopadhyay and K. K. Phani, An Analysis of Microstructural Parameters in the Minimum Contact Area Model for Ultrasonic Velocity-Porosity Relations, Journal of the European Ceramic Society, Vol. 20, pp. 29-38 (2000). |
| 39 | D. G. Bika, M. Gentzler, and J. N. Michaels, Mechanical Properties of Agglomerates, Powder Technology, Vol. 117, pp. 98-112 (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. 3041-3048 (2000). |
| 41 | A. P. Roberts and E. J. Garboczi, Elastic Moduli of Model Random Three-Dimensional Closed-Cell Cellular Solids, Acta Materialia, Vol. 49, pp. 189-197 (2001). |
| 42 | J. M. Dewey, The Elastic Constants of Materials Loaded with Non-Rigid Fillers, Journal of Applied Physics, Vol. 18, pp. 578-581 (1947). |
| 43 | J. K. Mackenzie, Elastic Constants of a Solid Containing Spherical Holes, Proceedings of the Physical Society, Section B, Vol. 63, pp. 2-11 (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. 452-453 (1962). |
| 46 | O. Ishai and L. J. Cohen, Elastic Properties of Filled and Porous Epoxy Composites, International Journal of Mechanical Sciences, Vol. 9, pp. 539-546 (1967). |
| 47 | J. C. Wang, Young's Modulus of Porous Materials, Part 1, Theoretical Derivation of Modulus-Porosity Correlation, Journal of Materials Science, Vol. 19, pp. 801-808 (1984). |
| 48 | K. K. Phani and S. K. Niyogi, Young's Modulus of Porous Brittle Solids, Journal of Materials Science, Vol. 22, pp. 257-263 (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. 3862-3868 (1991). |
| 50 | M. Kupkova, Porosity Dependence of Material Elastic Moduli, Journal of Materials Science, Vol. 28, pp. 5265-5268 (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. 119-128 (1993). |
| 52 | B. Budiansky, On the Elastic Moduli of Some Heterogeneous Materials, Journal of the Mechanics and Physics of Solids, Vol. 13, pp. 223-227 (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. 366-370 (1983). |
| 54 | K. K. Phani, Young's Modulus- Porosity Relation in Gypsum Systems, American Ceramic Society Bulletin, Vol. 65, No. 12, pp. 1584-1586 (1986). |
| 55 | K. K. Phani, Elastic-Constant-Porosity Relations for Polycrystalline Thoria, Journal of Materials Science Letters, Vol. 5, pp. 747-750 (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. 427-430 (1986). |
| 57 | K. K. Phani and S. K. Niyogi, Elastic Modulus-Porosity Relation in Polycrystalline Rare-Earth Oxides, Journal of the American Ceramic Society, Vol. 70, No. 12, pp. C-362 - C-366 (1987). |
| 58 | N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Ceramic Materials, Journal of the American Ceramic Society, Vol. 76, pp. 2745-2752 (1993). |
| 59 | L. J. Gibson and M. F. Ashby, The Mechanics of Three-Dimensional Cellular Materials, Proceedings of the Royal Society of London, Vol. A382, pp. 43-59 (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. 1190-1192 (2001). |
| 61 | A. Migliori, T. Chen, B. Alavi, and G. Grüner, Ultrasound Anomaly at Tc in YBa2Cu3Oy , Solid State Communications, Vol. 63, No. 9, pp. 827-829 (1987). |
| 62 | Y. Horie, Y. Terashi, H. Fukuda, T. Fukami, and S. Mase, Ultrasonic Studies of the High Tc Superconductor Y2Ba4Cu6O14 , Solid State Communications, Vol. 64, No. 4, pp. 501-504 (1987). |
| 63 | G. Cannelli, R. Cantelli, F. Cordero, G. A. Costa, M. Ferretti, and G. L. Olcese, Anelastic Relaxation in the High-Tc Superconductor YBa2Cu3O7-x , Physical Review B, Vol. 36, No. 16, pp. 8907-8909 (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 YBa2Cu3O7-(delta) Samples of Different Microstructure, Solid State Communications, Vol. 64, No. 8, pp. 1153-1156 (1987). |
| 65 | Y. He, B. Zhang, S. Lin, J. Xiang, Y. Lou, and H. Chen, Ultrasonic Investigation of Lattice Instability and Superconductivity in High-Tc Systems, Journal of Physics F: Metal Physics, Vol. 17, pp. L243-L248 (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 High-Tc Superconductors, Physical Review Letters, Vol. 60, No. 12, pp. 1181-1184 (1988). |
| 67 | M. Suzuki, Y. Okuda, I. Iwasa, A. J. Ikushima, T. Takabatake, Y. Nakazawa, and M. Ishikawa, Sound Velocity and Attenuation in YBa2Cu3Oy , Japanese Journal of Applied Physics, Vol. 27, No. 3, pp. L308-L310 (1988). |
| 68 | M. Saint-Paul, J. L. Tholence, P. Monceau, H. Noel, J. C. Levet, M. Potel, P. Gougeon, and J. J. Capponi, Ultrasound Study of YBa2Cu3O7-(delta) Single Crystals, Solid State Communications, Vol. 66, No. 6, pp. 641-643 (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 High-Tc Superconductors: La1.8Sr0.2CuO4-y and YBa2Cu3O7-(delta), Physical Review B, Vol. 37, No. 10, pp. 5901-5904 (1988). |
| 70 | S. Hoen, L. C. Bourne, C. M. Kim, and A. Zettl, Elastic Response of Polycrystalline and Single-Crystal YBa2Cu3O7, Physical Review B, Vol. 38, No. 16, pp. 11949-11951 (1988). |
| 71 | X. D. Shi, R. C. Yu, Z. Z. Wang, N. P. Ong, and P. M. Chaikin, Sound Velocity and Attenuation in Single-Crystal YBa2Cu3O7-(delta), Physical Review B, Vol. 39, No. 1, pp. 827-830 (1989). |
| 72 | P. K. Choi, H. Koizumi, K. Takagi, and T. Suzuki, Anomalies of Ultrasonic Velocity in High-Tc Ceramics YBa2Cu3Oy and BiSrCaCu2Oy , Solid State Communications, Vol. 70, No. 12, pp. 1175-1178 (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. 199-203 (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. 377-385 (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. 254-260 (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. 94-95 (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. 323-327 (1964). |
| 78 | D.B. Binns and P. Popper, Mechanical Properties of Some Commerical Alumina Ceramics, Proceedings of the British Ceramic Society, Vol. 6, pp. 71-82 (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. 184-190 (1966). |
| 80 | N. Soga and O.L. Anderson, High-Temperature Elastic Properties of Polycrystalline MgO and Al2O3, Journal of the American Ceramic Society, Vol. 49, No. 7, pp. 355-359 (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. 5316-5326 (1968). |
| 82 | A. Nagarajan, Ultrasonic Study of Elasticity-Porosity Relationship in Polycrystalline Alumina, Journal of Applied Physics, Vol. 42, No. 10, pp. 3693-3696 (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. 809-814 (1984). |
| 84 | C.C. Wu and R.W. Rice, Porosity Dependence of Wear and Other Mechanical Properties of Fine-Grain Al2O3 and B4C, Ceramic Engineering and Science Proceedings, Vol. 6, pp. 977-993 (1985). |
| 85 | H. Hagiwara and D.J. Green, Elastic Behavior of Open-Cell Alumina, Journal of the American Ceramic Society, Vol. 70, No. 11, pp. 811-815 (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. 7588-7602 (1989). |
| 87 | D.J. Green, C. Nader, and R. Brezny, The Elastic Behavior of Partially-Sintered Alumina, Ceramic Transactions, Vol. 7, pp. 345-356 (1990). |
| 88 | J. Kubler, Weibull Characterization of Four Hipped/Posthipped Engineering Ceramics Between Room Temperature and 1500 °C, Report Number: EMPA-Nr. 129'747, EMPA Swiss Federal Laboratories for Materials Testing and Research, pp. 1-88 (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. 2113-2117 (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. 541-546 (1994). |
| 91 | K. S. Tan, P. Hing, and P. Ramalingam, The Elastic Moduli and Diametrical Compressive Fracture Stress of Al2O3-ZrO2 Ceramics, Journal of Physics D: Applied Physics, Vol. 30, pp. 1029-1037 (1997). |
| 92 | A. Wolfenden, Measurement and Analysis of Elastic and Anelastic Properties of Alumina and Silicon Carbide, Journal of Materials Science, Vol. 32, pp. 2275-2282 (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. 2561-2568 (2000). |
| 94 | D. Dierickx, I. Houben, J. Lapin, F. Delannay, O. Van Der Biest, Dense Polycrystalline BaZrO3 Substrates for YBa2Cu3O7-x Melt Processing, Journal of Materials Science Letters, Vol. 15, pp. 1573-1576 (1996). |
| 95 | K.C. Goretta, E.T. Park, R.E. Koritala, M.M. Cuber, E.A. Pascual, N. Chen, A.R. de Arellano-Lopez, and J.L. Routbort, Thermomechanical Response of Polycrystalline BaZrO3, Physica C, Vol. 309, pp. 245-250 (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. 329-347 (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. 283-291 (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. 1283-1284 (1990). |
| 99 | R. R. Reddy, M. Muralidhar, V. H. Babu, and P. V. Reddy, The Relationship Between the Porosity and Elastic Moduli of the Bi-Pb-2212 High-Tc Superconductor, Superconductor Science and Technology, Vol. 8, pp. 101-107 (1995). |
| 100 | M. Muralidhar, K.N. Kishore, Y. V. Ramana, and V. H. Babu, Elastic and Plastic Behaviour of Lead and Silver Doped Bi-Sr-Ca-Cu-O Superconductors, Materials Science and Engineering B, Vol. 13, pp. 215-219 (1992). |
| 101 | S. Satyavathi, M. Muralidhar, V. H. Babu, R. R. Reddy, and P. V. Reddy, Elastic Behaviour of Bi-Pb-Ag-Ca2CuO3 Superconducting Composite Materials, Journal of Alloys and Compounds, Vol. 209, pp. 329-335 (1994). |
| 102 | R .J. Topare, K. Ganesh, N. K. Sahuji, S. S. Shah, and P. V. Reddy, Elastic Anomalies in Bi-Pb-2223/Ag Superconducting Composite Materials, Physica C, Vol. 253, pp. 89-96 (1995). |
| 103 | O. O. Oduleye, S. J. Penn, and N. McN. Alford, The Mechanical Properties of (Bi-Pb)SrCaCuO, Superconductor Science and Technology, Vol. 11, pp. 858-865 (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. 227-228 (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. 436-442 (1969). |
| 106 | W. R. Manning and O. Hunter, Jr., Elastic Properties of Polycrystalline Yttrium Oxide, Holmium Oxide, and Erbium Oxide: High-Temperature Measurements, Journal of the American Ceramic Society, Vol. 52, No. 9, pp. 492-496 (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. 2246-2250 (2000). |
| 108 | J. A. Haglund and O. Hunter,Jr., Elastic Properties of Polycrystalline Monoclinic Gd2O3, Journal of the American Ceramic Society, Vol. 56, No. 6, pp. 327-330 (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. 488-490 (1977). |
| 110 | R. W. Scheidecker, O. Hunter,Jr., and F. W. Calderwood, Elastic Properties of Partially-Stabilized HfO2 Compositions, Journal of Materials Science, Vol. 14, pp. 2284-2288 (1979). |
| 111 | S. L. Dole, O. Hunter, Jr., and F. W. Calderwood, Elastic Properties of Stabilized HfO2 Compositions, Journal of the American Ceramic Society, Vol. 63, No. 3, pp. 136-139 (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. C-47-C-49 (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 Tc Superconductors, Advanced Ceramic Materials, Vol. 2, No. 3B, pp. 444-456 (1987). |
| 114 | A. J. Zaleski and J. Klamut, Penetration Depth in Magnetically Oriented, Ceramic, Ni- and Zn-doped La2-xSrxCuO4, Physica C, Vol. 282, pp. 1463-1464 (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. 279-280 (1970). |
| 116 | O. Hunter, Jr. and G. E. Graddy, Jr., Porosity Dependence of Elastic Properties of Polycrystalline Cubic Lu2O3, Journal of the American Ceramic Society, Vol. 59, No. 1, pp. 82-82 (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. 345-349 (1977). |
| 118 | R. L. Stewart and R. C. Bradt, Fracture of Polycrystalline MgAl2O4, Journal of the American Ceramic Society, Vol. 63, No. 11, pp. 619-623 (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. 1624-1630 (1991). |
| 120 | K. W. White and G. P. Kelkar, Fracture Mechanisms of a Coarse-Grained, Transparent MgAl2O4 at Elevated Temperatures, Journal of the American Ceramic Society, Vol. 75, No. 12, pp. 3440-3444 (1992). |
| 121 | C. Baudin, R. Martinez, and P. Pena, High-Temperature Mechanical Behavior of Stoichiometric Magnesium Spinel, Journal of the American Ceramic Society, Vol. 78, No. 7, pp. 1857-1862 (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. 599-603 (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. 465-466 (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. 38-47 (1983). |
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A substantial effort has been made to select data for this database on the basis of sound scientific judgment. However, the National Institute of Standards and Technology (NIST) makes no warranties regarding its use, and NIST shall not be liable for any damage that may result from errors or omissions in the database.
Certain trade names and other commercial designations are used in this work for the purpose of clarity. In no case does such identification imply endorsement by the National Institute of Standards and Technology, nor does it imply that products or services so identified are necessarily the best available for the purpose.
How are data evaluated?
Scientific and technical data may be examined from three viewpoints:
The description of data generation is crucial. The identification and control of all relevant independent variables must be addressed and demonstrated. For mature areas such as thermodynamics and atomic physics, many measurement techniques are well characterized. In these cases, the adherence to physical laws and intercomparisons predominate. For areas in which behavior is not well understood, such as corrosion, data from different experiments are not usually comparable. Consequently, documentation of control of the experimental condition is most important.
All solid materials can deform, stretch, compress, bend, flex, shear, twist, or otherwise deviate from their original unstressed sizes and shapes when subjected to external forces or internal thermal stresses. This propensity of materials to deform under exerted forces is a critically important consideration in the design of any mechanical component whose operation depends on its ability to sustain loads or to maintain dimensions within specified tolerances. Especially important is the condition known as elastic deformation.
The deformation produced by an external force acting on a solid is said to be elastic when removing the external force returns the solid to its original undeformed state.
The present compilation of elastic moduli data for polycrystalline oxide ceramics includes Young's modulus, shear modulus, bulk modulus, and Poisson's ratio. The data have been collected from the technical literature, either as reported in textual or tabular formats or as digitized from graphical formats. Special attention has been given to the dependence of the moduli on porosity and temperature.
NIST Interagency/Internal Report (NISTIR) 6853
Database Reference: NIST Structural Ceramics Database, SRD Database Number 30
Journal Reference:
Elastic Moduli Data for Polycrystalline Ceramics, R. G. Munro, NISTIR 6853, (2002),
National Institute of Standards and Technology, Gaithersburg, Maryland 20899.
Other materials: Elastic Moduli Data
Other materials Properties: Property Data Summaries
| Ref. Nbr. |
Exhibit Type |
Exhibit Number |
Value Type |
Measurement Method |
Matl. Nbr. |
T [°C] |
d [g/cm3] |
p [%] |
VL [km/s] |
VS [km/s] |
E [GPa] |
G [GPa] |
B [GPa] |
nu |
Table Notes |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 98 | Table | 1 | x | ultrasonic velocity | 27 | 6.22 | 4.834 | 2.838 | 124 | 50.1 | 78.5 | 0.24 | 1 | ||
| 98 | Graph | 1 | x | ultrasonic velocity | -256 | 109.12 | 43.4 | 73.89 | 0.2576 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -248 | 108.85 | 43.24 | 73.88 | 0.2584 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -244 | 108.71 | 43.24 | 73.97 | 0.2584 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -239 | 108.83 | 43.34 | 74.05 | 0.2584 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -231 | 109.23 | 43.5 | 74.29 | 0.2581 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -221 | 110.79 | 44.07 | 74.54 | 0.2561 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -211 | 112.1 | 44.76 | 75.03 | 0.2545 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -203 | 114.32 | 45.61 | 75.6 | 0.2525 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -193 | 116.4 | 46.82 | 76.26 | 0.2496 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -185 | 118.62 | 47.98 | 77.17 | 0.2479 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -175 | 120.85 | 48.98 | 78.16 | 0.2456 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -167 | 122.81 | 49.61 | 78.91 | 0.2448 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -157 | 123.71 | 50.03 | 79.39 | 0.2443 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -148 | 124.62 | 50.3 | 79.89 | 0.244 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -140 | 125.14 | 50.56 | 80.13 | 0.2437 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -130 | 125.79 | 50.72 | 80.38 | 0.2437 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -121 | 125.79 | 50.77 | 80.62 | 0.2434 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -111 | 125.77 | 50.76 | 80.7 | 0.2434 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -103 | 125.9 | 50.76 | 80.7 | 0.2437 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -94 | 126.02 | 50.81 | 80.69 | 0.2439 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -84 | 125.87 | 50.81 | 80.68 | 0.2439 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -75 | 125.87 | 50.75 | 80.68 | 0.2439 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -65 | 126 | 50.69 | 80.67 | 0.2436 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -57 | 125.98 | 50.64 | 80.59 | 0.2436 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -48 | 125.71 | 50.58 | 80.42 | 0.2438 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -38 | 125.44 | 50.53 | 80.24 | 0.243 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -30 | 125.3 | 50.52 | 79.83 | 0.2428 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -20 | 125.17 | 50.47 | 79.65 | 0.2423 | 1 | |||||
| 98 | Graph | 1 | x | ultrasonic velocity | -11 | 125.03 | 50.46 | 79.57 | 0.242 | 1 | |||||
| 113 | Table | I | x | ultrasonic velocity | 23 | 6.55 | 157 | 61 | 1 | ||||||
| 114 | Table | I | x | x-ray diffraction | 6.94 | 2 |