Calculations of amplitude-distance-diameter diagrams

An efficient approach to approximation and practical application of DGS diagrams

“…This is due to the linear behavior, with respect to parameter η, of asymptotics (x, η) at x ∞. This also agrees with the well-known results published in other works [3][4][5][6][7][8][9][10][11].…”

“…We assume, first, that the majority of the physical, mechanical, electric, and geometric working parameters defining the NTI's EAC is fixed, i.e., that they range within rather narrow intervals. Then, according to published data [3][4][5][6][7][8][9][10][11], only three parameters vary in the process of testing: (1) where V ' = -20 (dB) is the attenuation (dB) of the ultrasonic signal reflected by a flaw without taking into account its attenuation in the TO material [4]; | P 0 | and | P ' | are pressure amplitudes of the emitted ultrasonic pulse and of the pulse reflected (scattered) by the flaw; δ l is the attenuation coefficient for ultrasonic oscillations in the TO material; r is the depth at which the flaw is located; d is the diameter of an equivalent flat-bottomed hole simulating the flaw; A ', B ', C ', r ', d ' and d '' are normalization constants;…”

“…It is known [3][4][5][6][7][8][9][10][11] that, for fixed values of d, f, α, D, and other parameters of the electroacoustic channel, the asymptotics of functions V'(x) and y(x) for x ∞ (r ∞) have the following form:…”

“…Note that such situations can occur when a TO is scanned by either a normal or angle PP using beams of longitudinal and transversal waves [3][4][5]. Taking into account the structure of the theoretical attenuation asymptotics of V' in the far-field zone [3][4][5][6][7][8][9][10][11], it is reasonable to introduce logarithmic variables in addition to the main variables (1): …”

“…Note that, in our opinion, attempts to find attenuation in a purely calculative way based on analytical and numerical solutions of model electroacoustic problems [6][7][8][9][10][11] do not yield the required accuracy because of the large number of simplifying theoretical assumptions. Because of all of these circumstances, the problem of approximating the basis DGS functions y mn (x) is hardly solvable and inaccessible for a wide circle of ultrasonic NDT specialists.…”