Measurement of the Dynamic Modulus of Rubber at Very Small Amplitudes with an Optical Interferometer

Abstract

Abstract A method of measuring very small differences of optical path using light modulation by an interferometer has been described. This enables one to measure amplitudes of mechanical vibrations of the order of 0.01 A or even smaller. We have used this method to measure the dynamic modulus of rubber at very small amplitudes. It is desirable to use this method for measuring the dynamic modulus of rubber and other highly elastic substances, firstly because in accuracy and simplicity it has certain advantages over existing acoustic methods. In the second place, it enables one to work at very small amplitudes and, in association with other methods, over a very wide range of amplitudes of deformation. This is of interest in connection with the general theory of the dynamic properties of rubber, and in particular, for checking the linearity of these properties, that is, the independence of the modulus and the loss on the amplitude, in particular for filled rubbers. We will briefly describe the apparatus with which the measurements were made. It consists of a Michelson interferometer and a source of monochromatic light. The interference pattern (lines of equal width) is projected onto the cathode of a photomultiplier. The output of the photo multiplier is fed to the input of a narrow-band filter, to the output of which the measuring instrument is connected. The mirror on the interferometer is set up so that the whole of the interference pattern, or the greater part of it, is uniformly illuminated. If now one of the mirrors vibrates with a frequency ω and an amplitude of z, then the difference in path between the interference beams will vary with a frequency of ω and the intensity of the light falling on the photomultiplier will also change. The current through the photomultiplier will be modulated with a frequency of ω. The first harmonic of the photocurrent will be I1=AJ1(4τz/λ), where λ is the wavelength of light; A is a coefficient depending on the intensity of the interfering beams and on their difference of path with the mirror at rest; I1 is a first order Bessel function.