An ultrasonic method for the determination of the elastic constants of some solids



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Sound waves traveling through an isotropic solid may be considered as elastic wave phenomena. Two expressions relating the transmission velocities of dilational and shear waves to the elastic constants, bulk and shear modulus of rigidity, of an Isotropic solid were developed from elastic wave theory. If these two velocities and the density of such a solid may be obtained in some manner, the two elastic constants may be calculated directly. With the values of these two constants determined, two other dependent constants. Young's modulus and Poisson's ratio, may be calculated. A method for obtaining the velocity of propagation of dllational end shear waves through a plane perallel-sided test plate Immersed in a sound carrying liquid was developed from an Inferred Snell's law of acoustics. Determination of the velocities depended on the location of certain "critical angles" of incidence of sound waves on the plate as the plate was rotated In the liquid with respect to the sound wave front. The critical angles for shear and dllational waves were evidenced by minima of sound transmission through the test plate. A determination of these angles and hence the velocities allowed the calculation of the elastic constants of the test plate. The density of the test plate, which was needed for these calculations, was obtained from published data. An acoustical system and its associated electronic equipment were designed and built for the purpose of determining the elastic constants of plane test plate specimens by the method outlined above. Other exerimenters performing tests by this method heve used the high frequency range of ultrasonic waves (2 to 10 Mcs.) produced by plezoelectris crystal transducers. One purpose of this experiment was to illustrate that low frequency ultrasonic waves (100 Kes.) produced by a magnetostriction transducer might also be used in determining the elastic constants of solids by this method. Low frequency ultrasonic waves in the one-hundred kilocycle range were produced In a tank of distilled water by a magnetostriction transducer. The plate to be tested was mounted in a calibrated rotator which allowed it to be rotated through known angles with respect to the sound waves in the distilled water. A magnetostriction sound receiver was placed in the distilled water on the side of the test plate opposite the sound transducer. With the sound receiver in this position, readings could be taken of the relative amplitude of sound sent through the test piste at various angles of sound incidence on the plate. Data were taken, and graphs made of the relative amplitude of sound sent through eight test plates of six different materials for various angles of sound incidence. The data were taken by a "profiling" method. Interpritatlon of the data and graphs gave the values of the critical angles for shear and dilational waves which were used to calculate the velocities of the waves, end hence the elastic constants of the eight test plates. There is a theoretical minimum thickness of the test plate that will give good results in this experiment. This value of thickness is dependent on the material of the test plate and the operating frequency of the sound source. Two of the test plates used in this experiment were much thinner than the values of minimum thickness calculated for them. They were included as test specimens to illustrate the adverse effect of using very thin plates. Fair results were achieved with other test plates of thicknesses down to one-half of the calculated minimum values how frequency ultrasonic waves were found to be effective for determining the elastic constants of solids, and in some cases may even be superior to high frequency ultrasonic waves for such determinations.