Internal Friction in Solids IV. Relation Between Cold Work and Internal Friction

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Abstract
Previous investigators have found that cold working of metals has a marked effect upon internal friction, increasing it, in certain cases, by a factor of more than ten. In the present paper it is assumed that the effect of cold work upon internal friction is due to the residual internal stresses which it produces. During vibration these residual stresses give rise to fluctuations in temperature, and thus to local heat currents, which are inevitably associated with a rise in entropy, i.e., with internal friction. A formula is obtained for this internal friction in terms of the energy associated with the residual stresses, and the temperature variation of the modulus of rigidity. It gives the observed order of magnitude. According to the theory developed in this paper, the measurement of the internal friction of a cold worked specimen over a wide frequency range and for various types of vibration will give not only the mean square of the residual stresses, but also their preferred axes, if any, and the mean linear dimensions of their inhomogeneities.