Theory and Application of a Superposition Model of Internal Friction and Creep

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Abstract
Energy dissipation in solids is important in both transient and steady‐state measurements. The results of such measurements can be associated with a distribution of relaxation times provided the material is linear. In the present work, general relations are derived for the attenuation factor, phase factor, and specific dissipation function 1/Q pertaining to transmission of small amplitude stress waves in a material describable by a distribution of relaxation times. Next, a specific, physically realizable relaxation time distribution is used to obtain a creep function and to relate transient creep and frequency response measurements. Curves of 1/Q vs frequency are calculated with a digital computer and show a region approximately proportional to frequency at sufficiently low relative frequencies, a region of virtual frequency independence, and a final region proportional to inverse frequency at high relative frequency. The relation of the present work to other treatments of creep and internal friction is discussed, and the applicability is examined of the analytic and numeric results to creep measurements on metals and rocks, to low‐frequency wave transmission in the earth, to other damping results for the earth as a whole, and to higher‐frequency wave transmission and vibration results for geophysical and other solids. Good agreement between theory and experiment is found for frequency regions where adequate data are available, indicating that all the damping phenomena considered may be well described by a linear theory in the range of very small strain.

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