Calculations of the Reflection and Transmission of Ultrasound by Rough, Planar Defects Containing Water, Manganese Sulphide or Alumina, in a Steel Host

摘要

Results are presented for the transmission of ultrasound through, and the reflection from, defects in steel. The defects considered are of infinite length, and consist of two parallel planes separated by some width of included material. Two cases are considered: firstly that of smooth, parallel faces and, secondly, faces which have a roughness associated with them. The particular type of roughness chosen is that of infinite striations parallel to the wavefront and with root mean square slope of 45 deg. The two faces of the defect are assumed to be highly correlated, as is, in general, the case for crack-like defects. A crack has highly correlated faces because the two sides are torn apart from the parent metal. On a macroscopic scale the two faces match each other; craters on one face correspond to mountains on the other. This is true down to microscopic levels where shearing, or tearing, causes a redistribution of material as the crack is created. All three independent polarizations of ultrasound, denoted P, SV and SH are considered. Results are presented for water, manganese sulphide and alumina. The frequency of the ultrasound considered is 2.25 MHz. Defect widths of 1 micron up to 200 micron are considered in the smooth case, and from 20 micron up to 200 micron in the rough case. The roughness is included in perturbation theory to first order in the root mean-square roughness height, which is taken to be 10 micron. All angles of incidence between 0 and 90 deg., measured from the normal to the defect plane, are considered.