Ruiju Huang

Characterization of the system functions of ultrasonic linear phased array inspection systems.

This work characterizes the electrical and electromechanical aspects of an ultrasonic linear phased array inspection system, using a matrix of system functions that are obtained from the measured response of individual array elements in a simple reference experiment. It is shown that for the arrays tested all these system functions are essentially identical, allowing one to use a single system function to characterize the entire array, as done for an ordinary single element transducer. The variation of this single system function with the number of elements firing in the array or with changes of the delay law used is examined. It is also demonstrated that once such a single system function is obtained for an array, it can be used in a complete ultrasonic measurement model to accurately predict the array response measured from a reference reflector in an immersion setup.

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.

Modeling the radiation of ultrasonic phased-array transducers with Gaussian beams

A new transducer beam model, called a multi-Gaussian array beam model, is developed to simulate the wave fields radiated by ultrasonic phased-array transducers. This new model overcomes the restrictions on using ordinary multi-Gaussian beam models developed for large single-element transducers in phased-array applications. It is demonstrated that this new beam model can effectively model the steered and focused beams of a linear phased-array transducer.

Kirchhoff Approximation Revisited—Some New Results for Scattering in Isotropic and Anisotropic Elastic Solids

Through a series of numerical studies that compare the Kirchhoff approximation to more exact scattering theories, it is demonstrated that the Kirchhoff approximation can accurately predict the pulse–echo peak-to-peak responses of spherical pores and circular cracks in isotropic media over a very wide range of cases that extend well beyond the limits normally associated with this approximation. The reason for this good agreement is shown to lie in the ability of the Kirchhoff approximation to model accurately the very early time response of the flaw. It is also shown that in the Kirchhoff approximation the pulse–echo response of an arbitrary traction-free scatterer in an isotropic elastic solid is identical to the same response obtained using a scalar (fluid) scattering model. This leads to simple analytical expressions for the pulse–echo far-field scattering amplitude of some canonical geometries (circular cracks, spherical voids, cylindrical holes) and to simplified numerical expressions for more general scatterers. For general anisotropic volumetric flaws in a anisotropic elastic solid, it is shown that a high-frequency asymptotic evaluation of the Kirchhoff approximation yields an explicit analytical expression for the pulse–echo leading-edge response of the flaw. Explicit expressions are also given for the pitch–catch response of an elliptical-shaped flat crack in a general anisotropic solid.

The Kirchhoff and Born Approximations for Scattering in Both Isotropic and Anisotropic Elastic Solids

It is shown that in the Kirchhoff approximation the pulse echo response of an arbitrary traction free scatterer in an isotropic elastic solid is identical to the same approximate response for a scalar (fluid) scattering model. This leads to simple analytical expressions for the pulse echo far field scattering amplitude for some canonical geometries (cracks and spherical voids). It is also shown that an explicit analytical expression for the early time (leading edge) pulse echo response for volumetric scatterers in general anisotropic elastic solids can be obtained by a high frequency asymptotic evaluation of the Kirchhoff approximation. Finally, it is also demonstrated that the amplitude and phase compensations to the Born approximation give improved Born scattering results for both weak and strong scattering inclusions.

A New Multi‐Gaussian Beam Model for Phased Array Transducers

A new linear‐phased multi‐Gaussian beam model is developed to simulate the wave fields generated by an ultrasonic phased array transducer. Simulation results show that the piecewise linear phasing used in this model produces a radiated wave field similar to the phasing used in actual phased array transducers. A major advantage of this model is that it not limited to beam steering angles exceeding the paraxial approximation limits of about 20 degrees. This limit restricts the amount of beam steering possible with a direct application of a multi‐Gaussian beam model to the simulation of phased array transducers.

2008 ULTRASONIC BENCHMARK STUDIES OF INTERFACE CURVATURE—A SUMMARY

In the 2008 QNDE ultrasonic benchmark session researchers from five different institutions around the world examined the influence that the curvature of a cylindrical fluid‐solid interface has on the measured NDE immersion pulse‐echo response of a flat‐bottom hole (FBH) reflector. This was a repeat of a study conducted in the 2007 benchmark to try to determine the sources of differences seen in 2007 between model‐based predictions and experiments. Here, we will summarize the results obtained in 2008 and analyze the model‐based results and the experiments.

Multi-Gaussian Beam Modeling for Multilayered Anisotropic Media, I: Modeling Foundations

A model is developed for the propagation and reflection/transmission of Gaussian beams in multilayered media where the layer materials can be general anisotropic, homogeneous elastic solids and the layer interfaces can be curved surfaces. It is shown that the Gaussian beams can be simply described in a set of slowness coordinates and that the complications arising from the multiple layers can be efficiently addressed through the use of an ABCD matrix approach. A multi-Gaussian beam model for an ultrasonic piston transducer radiating into very complex media is then developed by superimposing a small number of these propagating Gaussian beams.

Multi-Gaussian Beam Modeling for Multilayered Anisotropic Media, II: Numerical Examples of Slowness Surface and Geometry Effects

A multi-Gaussian beam model is used to simulate an immersion transducer radiating into an anisotropic solid through a curved fluid–solid interface. It is shown that the characteristics of the beam as it propagates in the solid are controlled by the properties of the slowness surface and the interface geometry. Methods are discussed for efficiently extracting the slowness surface properties including the development of an explicit expression for the curvature of the slowness surface. A number of numerical examples are presented to demonstrate the effects that both the slowness surface and interface geometry have on an ultrasonic beam.

SIMPLIFIED SYSTEM EFFICIENCY FUNCTIONS FOR LINEAR PHASED‐ARRAY TRANSDUCERS

Computer models are often used to simulate ultrasonic inspections of industrial components. One ingredient of such simulations is a frequency dependent function which describes the efficiency of the inspection system for converting electrical energy to sound and vice versa. For a phased‐array transducer there are many such efficiency functions, namely one for each independent pair of piezoelectric elements. In this paper we describe a simplified, approximate approach for specifying these functions. Element‐to‐element differences are accounted for by two “residual” parameters: (1) a strength factor which describes the relative “hotness” of an element compared to its peers; and (2) a time delay which describes the extent to which an element fires later or earlier than its peers when all elements are instructed to fire in unison. These residuals are used to relate the system efficiency function for any pair of elements to that of an average efficiency which can be readily measured. The use of this approach i...