Main Features of a Complete Ultrasonic Measurement Model: Formal Aspects of Modeling of Both Transducers Radiation and Ultrasonic Flaws Responses

Abstract

<p class="MsoNormal"> <span lang="EN-US">This paper aims at describing the theoretical fundamentals of a reciprocity-based ultrasonic measurement model. This complete inspection simulation can be decomposed in two modeling steps, one dedicated to transducer radiation and one to flaw scattering and echo synthesis. The physical meaning of the input/output signals used in these two modeling tools is defined and the theoretical principles of both field calculation and echo computation models are then detailed. The influence on the modeling results of some changes in the simulated configuration (as the incident angle) or some input signal parameters (like the frequency) are studied: </span><span lang="EN-US">it is thus theoretically established</span><span lang="EN-US"> that the simulated results can be compared between each other in terms of amplitude for numerous applications when changing some inspection parameters in the simulation but that a calibration for echo calculation is generally required.</span><span lang="EN-US"><o:p></o:p></span> </p

A Study on the Model of Detecting the Liquid Level of Sealed Containers Based on Kirchhoff Approximation Theory

“…At any point B on the actual transducer, the sound pressure ${\mathrm{p}}_{\mathrm{e}}$ radiated by the circular section can be calculated by Equation (1); furthermore, by integrating the sound pressure ${\mathrm{p}}_{\mathrm{e}}$ on the entire surface of the transducer [14,15,16], the average echo sound pressure $\overline{{\mathrm{P}}_{\mathrm{s}}}$ can be obtained approximately by Equation (3):${\overline{\mathrm{p}}}_{\mathrm{normals}}\left(\mathrm{normalR},\mathrm{sans-serif\theta }\right)=\left(\frac{\mathrm{sans-serif\pi }{\left(\mathrm{normald}/2\right)}^2}{\mathrm{sans-serif\lambda }\mathrm{normalR}}\right)\left[\frac{2{\mathrm{J}}_1\left(\mathrm{normalk}\left(\frac{\mathrm{d}}{2}\right)\sin \mathrm{sans-serif\theta }\right)}{\mathrm{normalk}\left(\frac{\mathrm{d}}{2}\right)\sin \mathrm{sans-serif\theta }}\right]·\overline{p_r}·{\mathrm{sans-serif\pi }\mathrm{normala}}^2$ where $\mathsf{\lambda }$ is the wave length of ultrasonic waves in a medium, $\mathrm{a}$ is the transducer radius, $\mathrm{k}$ is the wave number, ${\mathrm{J}}_1$ is the first order Bessel function, $\mathsf{\theta }$ is the angle between R and the Z-axis, ${\mathrm{R}}_{\mathrm{w}}$ is the reflection coefficient at the inner surface of the wall, and $\overline{{\mathrm{p}}_{\mathrm{r}}}={\mathrm{p}}_0{\mathrm{e}}^{-\mathrm{sans-serif\alpha }\mathrm{normalL}}{\mathrm{R}}_{\mathrm{w}}·4{\mathrm{a}}^2/{\mathrm{d}}^2$.…”

A system model for ultrasonic NDT based on the Physical Theory of Diffraction (PTD)

“…The developed model relies on a generic system model [2], based on the reciprocity principle, which is employed in the CIVA software package [18]. CIVA is an expertise platform, developed by CEA-LIST and partners, for NDT simulation [19] and processing NDT data; its generic platform [20] allows to gather and add in the same software modelling tools of different nature and to compare their simulation results for a numerical validation purpose.…”

“…In Non Destructive Testing modelling nowadays plays an important role in assessing detection capability and conceiving inspections. System models have been developed to predict results of ultrasonic inspection in a range of applications [1,2]. These models simulate the propagated beam as well as its interaction with the flaws and reception by the probe of the waves scattered by the flaws.…”

The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane

“…5(a), UAT reproduces the critical GTD peak exactly, while UTD has a smaller amplitude. The discrepancy can be explained by noting that each UTD diffraction coefficient has four poles, one at the incident angle h a , one at the reflection angle (26)] and the UTD diffraction coefficient differs from the corresponding GTD diffraction coefficient. In Fig.…”

“…In NDT, the flaws are usually inspected in the far field of the used probes or else in their focal areas if they are focused. Consequently, often, at each point of the meshed flaw the incident wave-fields can be approximated by a wave that is locally plane 25,26 and GE ray methods and GTD-based models can be easily applied in the probes far field. 27 Since the proposed UTD model relies on the same high-frequency assumptions as GTD, it should prove to be efficient in the far field of the flaw.…”