Internal Dissipation in Solids for Small Cyclic Strains

This paper presents the results of investigations of dissipation of energy in vibrating solids, mostly metals, by means of longitudinal and torsional vibrations of cylindrical rods. The amplitudes of strain used have been kept between 10−5 cm/cm and 10−8 cm/cm, in which range the dissipation of energy is proportional to the square of the strain. The specific dissipative property of a material is expressed in three different ways: (1) Equivalent viscosity or the ratio of stress to dissipative component of strain rate; (2) hysteretic constant defined as the area in ergs of the cyclic stress-strain diagram; and (3) elastic phase constant defined as the ratio of specific elastic reactance to equivalent viscosity. Within a range of frequencies 100 to 100,000 cycles per second the results show that the hysteretic constant is proportional to some power Δ of the frequency, the numerical value of the exponent Δ varying between the limits − ⅓ and + ½, depending on the kind of material and its internal structural condition. Measurements made with longitudinal and torsional vibration indicate that dissipation is associated with dilatation as well as with pure shear. Preliminary studies are described showing the correlation between internal dissipation in metals and temperature hardness effects of annealing and aging.