Statistical characterisation of metals from ultrasonic aberrations

Abstract

Materials with random microstructure can have an adverse effect on ultrasonic measurements through scattering and aberration of the acoustic field. We have developed a theoretical and experimental technique for characterising the effect of the material microstructure on the propagation of acoustic waves. The theoretical method predicts propagation of the statistical properties in the random medium. Using this model and a novel experimental technique we can extract materials properties from observations of acoustic aberrations. The microstructure has been modelled as having grains randomly orientated and weakly anisotropic. Moreover, individuals grains are treated to be equiaxed. This is summarised by assuming that the correlation function for the wave number has a Gaussian shape. Under this assumption, the approximated power correlation function for the acoustic field has been obtained using the stochastic wave equation for random media, along with numerical simulation using phase screen theory. The experimental evidence that aberrations are frequency dependent is presented. Multiple c- scans on titanium were performed using a 10MHz transducer as an ultrasonic source. The output of the transducer gives substantial frequency components between 6MHz and 16MHz. The variation of the frequency on a fixed sample enables us to examine different measurement regimes (higher frequencies correspond to large grains). The statistical analysis and estimated power correlation function from measurements are compared to a modelled power correlation function. The correlation length and standard deviation of the wave number define the power correlation function of the field. This function has been fitted to the estimated power correlation from measurements on titanium 6-4, and values for the variance and correlation length were obtained. The paper demonstrate that the stochastic model is capable of quantitative prediction of the predominant wave scattering effect in granular materials. of acoustic waves will be random. The grain microstructure may have various effects on ultrasonic wave propagation. It attenuates, scatter and aberrates ultrasonic waves as they propagate within this medium. Generally speaking aberrations are wavefront distortion of ultrasonic waves propagating in random medium. It would be desirable to quantify the strength of aberrations on a material with random microstructure. The main observation relies on the transverse coherence of the acoustic field as it propagates. The first step is to measure aberrations then the strength by means of transverse power correlation function of the acoustic field, which will be the subject of forthcoming sections. The theoretical description of SAW propagation is based on a scalar stochastic theory for waves in a random medium. Therefore it is possible to obtain an expression for second order moments of the field which carries information of microstructure. The behaviour of power correlation is mainly dictated by the scale of the inhomogeneity which is a rough estimation of grain size. The theoretical derivation is not included in this paper as the main purposes is to show how this technique behaves under different regimes of frequency and also because it has been developed in a previous paper, (3).