New Approaches to Ultrasonic Equivalent Sizing for Small Flaws

Abstract

Ultrasonic equivalent flaw sizing methods size defects in a material by ohtaining a best-lit simple defect shape (such as an ellipsoid or ellipse) from relatively SIll,11I amounts of ultrasonic data. In these cquivulcnt flaw sizing methods. it is essential that the origin of time he determined precisely with respect 10 a fixed spatial location. Current methods for this determination arc not entirely adequate. leading to an important "zero-of-time" problem.In this work, two new approaches to equivalent Ilaw sizing for relatively smalillaws arc developed: (I) an amplitude-based equivalent (AilE) sizing method for obtaining best-lit equivalentllaws by the use of amplitude ratios measured at different transducer orientations, and (2) a first moment (FM) method for estimating the equivalent radius from a first moment calculation of the time domain flaw response. We show how these approaches can address the zero-of-time problem and demonstrate the performance of these methods with experiments.

Ultrasonic flaw sizing inverse problems

“…Equation ( 27) can be used as the basis for a flaw sizing algorithm by making a series of relative amplitude measurements of the leading edge response [25]. To see this, let a 'reference' leading edge response at a particular incident direction, e 0 i , be denoted as a α o ≡ a α (e 0 i , t) where the corresponding effective radius is r e0 .…”

“…Song and Schmerr [25] have termed this sizing approach the amplitude-based equivalent (ABE) sizing method and demonstrated its use on both synthetic and experimental data, including the sizing of a 380 µm circular crack using 13 measured values of r e . The method still relies on a series of zero of time determinations, but these are only used to obtain the single scaling parameter, r e0 , through the use of equation ( 29) and the averaging process involved in that equation helps to reduce the effect of errors.…”

“…Thus, by calculating the FM of a measured response according to equation ( 35) and finding the time δt 0 when this FM is zero, the effective radius, r e , can be obtained from equation (37). This sizing method was called the FM method by Song and Schmerr [25]. Using equation (34) over the entire lit surface as opposed to the more exact result of equation ( 23) produces a bias in the estimated values of r e when using the FM method.…”

Ultrasonic Equivalent Flaw Sizing - A Time-of-Flight Approach

“…Recently, we have also developed some new methods that do work for "small" flaws where TOFE will fail. [6] Thus, equivalent flaw sizing is a viable technique that can treat flaws over a wide range of sizes.…”

“…Once the C parameters are obtained in this manner, the solution of the eigenvalue problem C-,,-I=O (6) then yields the best-fit ellipsoid and its orientation since, as Chiou and Schmerr [3] have shown, the eigenvalues of ~ are just the squares of the three principal ellipsoidal axes (a 2 , b 2 , c 2 ) and the corresponding eigenvectors are the three unit vectors along these axes. Although minimizing I in eq.…”