Dynamic Acousto-elastic testing

Pioneering measurements of elastic nonlinearity were static methods leading to the thermodynamic diagram that shows the relations between pressure, volume, and temperature (p-v-T diagram) [1]. The dependence of the bulk elastic modulus on the pressure, i.e., a measure of nonlinear elasticity, was deduced from this diagram. In the beginning of the twentieth century, resonance spectroscopy [2, 3] or methods based on interferometry [4] were proposed to measure the elastic moduli as functions of temperature and hydrostatic pressure. Finally, with the possibility of generating an ultrasonic short pulse [5, 6], acousto-elastic testing became an alternative way to assess elastic nonlinearity. Acousto-elastic testing consists in measuring changes of the speed of sound (by the determination of the travel time of an ultrasonic short pulse) induced by a hydrostatic or uniaxial stress (or strain). For metals and polymers, the relative variation in ultrasound wave-speed is found between 10^-5 and 10^-4 per MPa of the applied stress. In cracked or granular media, contacts between the two lips of cracks or contacts between grains can greatly increase the variation in ultrasound wave-speed up to about 10^-2 per MPa of applied stress, i.e., orders of magnitude larger than in metals and polymers [7].