POWER LAWS AND GENERALISED DIMENSIONAL ANALYSIS IN ULTRASONIC NDE

A number of power laws for ultrasonic attenuation have been proposed in the non-destructive evaluation (NDE) literature empirically or derived analytically, for various regimes of wavelength relative to size of inhomogeneity. In this paper we view these laws in a unifying framework and analyse published data on the dependence of ultrasonic attenuation on inspection frequency and parameters describing the microstructure of an inspected solid by using generalised dimensional analysis based on various "self-similarity hypotheses". We establish universal power laws for newly defined NDE variables, involving attenuation derivatives. These variables are readily accessible to measurement and can be of great importance when characterising the solid's microstructure and, specifically, stages of damage accumulation. All the corresponding powers are found by curve-fitting techniques or by reference to known experimental results. They depend on the conditions of the experiment.