Variation of Internal Friction with Grain Size

THEORETICAL considerations by one of the authors have led1 to the prediction that the dynamic internal friction of annealed metals has a broad maximum at a certain grain size. This prediction they have veri-fied2 for alpha brass. In the present paper the theory is extended to include the precise manner in which the internal friction varies with grain size on either side of the maximum. New experimental data are pre¬sented to test this extended theory. The physical basis for the type of internal friction that is being investi-gated lies in the interplay between stress and temperature. Just as local fluctuations in temperature give rise to local fluctuations in stress, so like-wise fluctuations in stress give rise to fluctuations in temperature. But temperature gradients give rise to necessarily irreversible thermal cur-rents, and hence to internal friction. The theory for this type of internal friction has been developed quantitatively,3 and has been experimentally verified,4,5 for the particularly simple case of the transverse thermal cur-rents accompanying transverse vibrations. Of more fundamental impor-tance are the intercrystalline thermal currents accompanying all types of vibration. The variation in stress across grain boundaries arises from the elastic anisotropy and at least partial random orientation of the individual crystallites. An exact quantitative treatment of the internal friction due to these thermal currents is of course out of the question. However, much information can be obtained from general arguments.1,6 Thus when the frequency of vibration f is low, or when the grain size d is small, adja-cent grains remain nearly in thermal equilibrium, and vibration proceeds isothermally with little internal friction. Again, when the frequency is high, or the grain size large, the heat flow per cycle is small, the vibration proceeds adiabatically with little internal friction. The internal friction will become a maximum in the transition region. The degree of adiabatic-