脆性材料の高温における理想強度

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Ideal Strength, aid as a function of temperature was found to be approximated by the following formula: σid≥σid=∫TxT3αE/(1-2μ)dT=3αE(Tx-T)/(1-2μ) where Tx stands for the minimum value of transformation points (melting, sublimation, solid to solid, and brittle to ductile), and α, E, μ respectively for the coefficient of linear thermal expansion, Youngs modulus and Poissons ratio. The formulas error is less than 20%, expressed in the term of error compared with whiskers strength at RT. It was also compared with literature data on high temperature strength of sapphire monofilament, which proved the compatibility of the formula. σid is estimated as 9 GPa for SiC and 3.5 GPa for Si3N4 at 1, 400°C, 1 GPa at 2, 200°C for SiC, and 1 GPa at 1, 700°C for Si3N4. These values prove the usefulness of the materials as high temperature gas turbine components. The formula tells also us that the ideal strength can be well approximated by a straight line regardless of material. The Youngs modulus plotted against temperature can be converted to Youngs modulus plotted against strain, ε, by using ε=3∫α/(1-2μ)dT, which can not be given directly from experimental measurement due to the occurrence of fracture in the material. The tangent of the curve for MgO was proved to agree well with the value given by a classical solid state theory. The range of binding force acting across material surface was estimated by using the ideal strength, giving 0.5-1 nm for SiC and Si3N4 and 0.1-0.5 nm for MgO and Al2O3. The allowable atomic distance difference between neighboring layerd material in coherently multilayered films, which has no defect was also estimated to be less than 3% from the ideal fracture strain.
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脆性材料の高温における理想強度

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