A Unified Constrained Inversion Model for Ultrasonic Flaw Sizing

Abstract

Equivalent flaw sizing using ultrasonic waves is an approach whereby shape and orientation information of a defect are obtained in terms of a best-fit simple geometry that is able to represent the major aspects of the flaw. Separate examples of this approach have previously been developed for volumetric flaws and cracks using the Born and Kirchhoff approximations, respectively. Here, these separate algorithms are unified into a single algorithm capable of sizing both volumetric flaws and cracks. Some examples of the performance of this unified algorithm on both synthetic and experimental data are also given.     

Modeling the Ultrasonic Radiation of a Planar Transducer Through a Plane Fluid—Solid Interface

Three types of transducer beam models are developed for obtaining the bulk waves generated by a plane piston transducer radiating through a planar fluid—solid interface. The first type, called the surface integral model, is based on a Rayleigh—Sommerfeld-like integral that requires a two-dimensional surface integral to be evaluated. The second model, called the boundary diffraction wave (BDW) paraxial model, simplifies the two-dimensional integration of the surface integral model to a one-dimensional line integration. The third type of model, called the edge element model, is shown to be a novel way of efficiently evaluating the two-dimensional surface integration of the surface integral model. The limitations of these models for simulating inspections near critical refracted angles and near the interface are discussed. It is shown that the introduction of the paraxial approximation in the BDW model allows that model to be computed with a very large (300—1) speed advantage over the surface integral while retaining the same accuracy in most cases. The edge element model, while having a smaller (5—1) advantage over the direct numerical integration of the surface integral model, retains the accuracy of the surface integral model in cases where the paraxial approximation fails and can be easily generalized to more complex testing situations (focused probes, curved interfaces, etc.).     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

Determination of an ultrasonic transducer's sensitivity and impedance in a pulse-echo setup

The role that an ultrasonic piezoelectric transducer plays in an ultrasonic measurement system can be described in terms of the transducer's input electrical impedance and its sensitivity. Here, a new model-based approach is proposed to determine both the transducer impedance and sensitivity in a pulse-echo setup. This new method is much simpler to apply than previous "self-reciprocity" calibration methods for determining sensitivity and generalizes those methods. It is demonstrated that sensitivities obtained with this new method agree well with the sensitivities obtained by a three-transducer method commonly used in calibration studies. It is demonstrated that at the megahertz frequencies at which ultrasonic transducers operate it is important to compensate for cabling effects in these measurements. The influence of the pulser/receiver settings on the results obtained also will be discussed.     

A Modified Born Approximation for Scattering in Isotropic and Anisotropic Elastic Solids

A new modified Born approximation (MBA) is presented that significantly extends the range of validity of the Born approximation to include the pulse-echo responses of strongly scattering inclusions in an elastic solid. The MBA also improves on the doubly distorted Born approximation (DDBA), a similar modification of the Born approximation that has been recently developed. These improvements are demonstrated by comparing the MBA, the Born approximation and the DDBA with the exact separation of variables solution for spherical inclusions in isotropic media. Furthermore, it is shown that the form of the MBA remains valid even for the pulse-echo scattering of an anisotropic inclusion in a general anisotropic elastic medium so that it is potentially applicable to a wide class of flaws and materials.     

Modeling and Measuring All the Elements of an Ultrasonic Nondestructive Evaluation System II: Model-Based Measurements

In Part I: Modeling Foundations [1], a comprehensive model of an ultrasonic nondestructive evaluation (NDE) flaw measurement system was developed. Here, it will be shown that this comprehensive model can be used to completely characterize commercial measurement systems where all the elements of the system can be either modeled explicitly or measured, using purely electrical measurements. When combined, these models and measurements are shown to be able to predict accurately the measured signals in an ultrasonic test.     

Ultrasonic beam propagation in highly anisotropic materials simulated by multi-Gaussian beams

The necessity of nondestructively inspecting fiber-reinforced composites, austenitic steels, and other inherently anisotropic materials has stimulated considerable interest in developing beam models for anisotropic media. The properties of slowness surface play a key role in the beam models based on the paraxial approximation. In this paper, we apply a modular muiti-Gaussian beam (MMGB) model to study the effects of material anisotropy on ultrasonic beam profile. It is shown that the anisotropic effects of beam skew and excess beam divergence enter into the MMGB model through parameters defining the slope and curvature of the slowness surface. The overall beam profile is found when the quasilongitudinal (qL) beam propagates in the symmetry plane of a transversely isotropic gr/ep composite. Simulation results are presented to illustrate the effects of these parameters on ultrasonic beam diffraction and beam skew. The MMGB calculations are also checked by comparing the anisotropy factor and beam skew angle with other analytical solutions.     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

Abstract

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

The Flat-Bottom Hole: An Ultrasonic Scattering Model

Abstract

A new model is developed that predicts the pulse-echo compressional wave transducer response from a flat-bottom hole whose axis is aligned with the axis of the transducer. This model uses the Schoch solution for the waves incident on the hole, the Kirchhoff approximation at the hole, and high frequency asymptotics to obtain an approximate analytical expression for the measured response. This solution significantly extends previous scattering models for this problem. For a small hole in the far-field of the transducer this new model is shown to reduce to the more restrictive existing models and numerical results are obtained to illustrate where differences with these earlier models are important. This solution is also used to obtain distance-gain-size (DGS)-like curves that can predict the significant response variations in both the near-and far-field.