Defect Sizing Using Distance-Gain-Size Diagrams for Flat-Bottomed Holes in a Solid: Theoretical Analysis and Experimental Verification

Weight, J.
Hussein, S.
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Although there are a number of potential pitfalls, the classical method of relating defect area to echo amplitude is still the most widely used method to size defects using ultrasonic pulse-echo techniques. In 1959 Krautkramer [1] was the first to introduce a set of curves (DGS diagrams) showing the variation of echo amplitude with range and target size. As Krautkramer made clear, such curves are dependent on transducer pulse shape. For the very far field he gave theoretical results assuming a fluid-like medium of propagation, but he had to resort to a large number of experimental measurements to construct the near field portion of the curves. Well known problems in using DGS diagrams include the sensitivity of echo amplitudes to target angular and lateral alignment and the need to construct a new set of curves for each transducer pulse shape. Furthermore, when sizing targets in solids there are likely to be errors if curves constructed assuming a fluid medium are used. In 1987, McLaren and Weight [2] gave an impulse-response method to predict echo amplitudes for arbitrary target position in the field and for any transducer pulse shape. Normally-aligned, flat-ended cylindrical targets and a fluid medium were assumed. More recently, Schmerr and Sedov [3,4] have calculated single frequency DGS diagrams for flat-bottomed holes (FBH’s), for both direct and water coupling, but the holes are assumed to be in a fluid-like material. Their method takes account of diffraction and refraction effects but not mode conversion. A more exact treatment of the effect of a solid medium of propagation on DGS diagrams has been given by Sumbatyan and Buyove [5] who developed DGS diagrams for disc-like targets using a boundary element method to solve the elastodynamic equations, but again, only for the case of continuous sinusoidal waves. One disadvantage of such an approach is that the calculations can be rather time consuming.