Application of Similarity to Anelasticity

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KE1 has shown that, when the internal friction and relaxation of rigidity for very pure aluminium are measured as functions of grain size (D), temperature (T) and frequency of vibration (ω), the effects of these three variables can be stated in terms of a single parameter : where H is an activation energy of 32,000 cal./mol. The exponential term represents2 the temperature variation of the coefficient of intergranular viscosity. This parameter has the disadvantage that it is not dimensionless, so that it is not possible to transfer the results of Ke's experiments to other metals. It is therefore of interest to apply dimensional analysis to this system in the attempt to derive a dimensionless criterion for the ratio of the relaxation time to the vibration time l/ω. Lord Rayleigh3 has pointed out that fundamental laws can frequently be derived by such dimensional analysis.

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    Ke, T. S., Phys. Rev., 72, 41 (1947).

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    Ke, T. S., Phys. Rev., 71, 533 (1947).

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    Rayleigh, Nature, 95, 66 (1918).

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    Zener, C. M., "Elasticity and Anelasticity of Metals", 43 (Chicago, 1948).

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    Thring, M. W., Nature, 162, 193 (1948).

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    Zener, C. M., Phys. Rev., 60, 906 (1941).

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    Mott, N. F., Proc. Phys. Soc., 60, 391 (1948).

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THRING, M. Application of Similarity to Anelasticity. Nature 163, 772–773 (1949) doi:10.1038/163772b0

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