Ultrasonic Characterization of Porosity Using the Kramers-Kronig Relations

Abstract

A new algorithm i s proposed t o determine the volume f r a c t i o n o f pores i n s o l i d s using the frequency dependent u l t r a s o n i c attenuation. The algorithm was developed by examining the Kramers-Kronig r e l a t i o n between the p o r o s i t y induced u l t r a s o n i c attenuation and the change i n sound v e l o c i t y. The method i s tested using data measured f o r several porous aluminum samples.

Ultrasonic Characterization of Cylindrical Porosity — A Model Study

“…The reduced scattering cross-section r is defined as the total scattering cross-section divided by the geometric cross-section and for an infinitely long cylinder implies y(ka,n) r(ka,n) X 4a (2) It is dependent on the host medium only through the Poisson's ratio which is fixed by n. The reduced scattering cross-sections for 0.4<n <0.6 are shown in Fig. 1.…”

“…Recently, the frequency dependent ultrasonic attenuation bas been used to find the volume fraction and pore size of gas porosity in cast aluminum alloys [1,2]. The question arises as to whether these techniques can be adapted for the characterization of porosity in layered materiala, such as graphite-epoxy composites.…”

Ultrasonic Attenuation Measurement by Backscattering Analysis

“…A more promising technique is based upon the measurement of the ultrasonic attenuation from the backscattered signal which is much less sensitive to the geometry of the sample. This approach for porosity assessment was first suggested by Rose (7] and implemented by Hsu et. al.…”

“…6, we can introduce the spatial frequency distribution Fz(kx,ky) of the acoustic field in the z plane and make the averaging in the kx,ky domain. According to the Parseval theorem, JJI~(x,y,z)l 2 dxdy = JJIFz(kx,ky)l2 dkx dky, -oo -oo (7) where (8) Neglecting the evanescent field components, k2x + k2y < k2 and (9) i.e. the modulus of the spatial frequency spectrum is independent of z, and the averaged intensity is the same in every z plane.…”

“…Recently several studies which discuss the porosity induced ultrasonic attenuation have appeared [1][2][3][4][5][6][7][8]. Porosity assessment by ultrasonic attenuation measurement involves two principal problems: first, how to relate the porosity induced ultrasonic attenuation to porosity parameters such as average pore radius and volume fraction, and second, how to separate the sought porosity induced attenuation from other components contributing to the actually measured total attenuation.…”