Ideal Strength, aid as a function of temperature was found to be approximated by the following formula:
σ
id≥σ
id=∫
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, Young's modulus and Poisson's ratio. The formula's error is less than 20%, expressed in the term of error compared with whisker's strength at RT. It was also compared with literature data on high temperature strength of sapphire monofilament, which proved the compatibility of the formula.
σ
id is estimated as 9 GPa for SiC and 3.5 GPa for Si
3N
4 at 1, 400°C, 1 GPa at 2, 200°C for SiC, and 1 GPa at 1, 700°C for Si
3N
4. 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 Young's modulus plotted against temperature can be converted to Young's 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 Si
3N
4 and 0.1-0.5 nm for MgO and Al
2O
3. 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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