PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Ultrasonic Spectroscopy to Characterize Flaws, Porosity andAdhesive Bonds
Laszlo Adler
Taine McDougal Professor Emeritus
Ohio State University/Adler Consultants Inc.
Clearwater, Florida, USAABSTRACT
Ultrasonic Spectroscopy is the study of ultrasonic waves resolved into their Fourier frequency components.
Since most material properties manifest themselves as amplitude and phase changes in ultrasonic waves usedto interrogate a specimen, ultrasonic spectroscopy is used in many applications of Nondestructive Evaluation.
In this presentation three methods developed by the author to apply ultrasonic spectroscopy in NDE will bediscussed.
Flaw characterization. refers to the determination of size, orientation, and composition of discontinuities insolid materials. Multifrequency (broad band) ultrasonic wave interaction with artificial and real defects
measurements and subsequent theoretical analysis using diffraction of elastic waves provides these material
discontinuities’ characteristics.
Gas porosity assessment. Measuring pore size and volume fraction from the spectrum of attenuation coefficientwill be discussed. Theoretical analysis is based on the attenuation due to independent scatterer of sphericalvoids. The model prediction of the scattering of ultrasonic waves from porosities is in good agreement withmeasured values in aluminum casts.
Evaluation of Adhesive Layers. Linear and nonlinear spectroscopic systems were developed to determine bothadhesive and cohesive properties of thin bonded layers using multi transducer spectroscopy. Scatteredlongitudinal and transverse waves spectra is used in this method. The method was further enhanced by
combining with a low frequency dynamic load acting as a nonlinear (parametric) enhancement. Ultrasonicmeasurements are in good agreement with actual layer properties.
Keywords: ultrasonics, spectroscopy, nondestructive evaluation

1.

INTRODUCTION

Ultrasonic spectroscopy is the study of ultrasonic waves resolved into Fourier frequency
components. The schematic1 of a multipurpose ultrasonic system is shown on figure 1.

Figure1 - Generalized ultrasonic spectroscopy system8180

In this paper several applications of ultrasonic spectroscopy in NDE will be discussed.

2. FLAW CHARACTERIZATION
The first experimental system was developed by Gericke2 in using a contact method and by Whaley andAdler3 immersion method. Both these methods quickly established the variation of frequency spectrum withflaw characteristics.
2.1 Reflection experiments with metal rods
A flaw in metal may be simulated by using the end of a metal rod in water. In both cases the acoustic
impedances are significantly different from each other thus causing a large reflected signal. Ultrasonicpulses were generated in water with a broadband transducer and received and analyzed after reflectingfrom the ends of sample brass rods. The end of the rods was machined flat and smooth with diameter
ranging from 0.281 to 0.031 inches (7.1 to 079 mm). The positioning and the rotation o f the sample isachieved by a very precise Turntable, see, fig. 1. The transducer, nominally 2.25 MHz and .75 inch indiameter, was used with 6 inch water paths.

Figure 2 - Variations in ultrasonic spectra at various angles of incidence for the 0.125 in. and .281 in diameter
brass reflector.
Figure 2 presents the representative data obtained in these tests showing the angular and size
dependence of the shape of the frequency spectrum of a pulse reflected from brass rod. The shapes ofthe spectrum at normal incidence for all rods were essentially the same as the reflected spectrum from alarge plate normal to the transducer axis. The principal frequency is shifted in position as the angle ofincidence changed.

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2.2

Suggested model for the reflected spectra from discontinuities.
Figure 3 - Schematic diagram of the interference model
In this model it is assumed that when a multifrequency wavefront is generated by a circulartransducer it becomes a plane wave in the far field. A circular reflector with diameter d is placed in thefar field of the transducer and the axes of the transducer and reflector are oriented by an angle θ withrespect to each other. It was assumed that the incident plane wave breaks up into three parts when it isreflected: a specular refection and two wavelets originating from the edges of the reflector. Thewavelets are coherent sources that interfere at the face of the transducer. Because these wavelets
contain a broad range of frequencies, the condition for constructive interference will always be satisfied
for some frequencies. From geometrical considerations, after s ome simplification, one obtains aformula for the difference of two consecutive frequency maxima∆f=v/[dsinθ+dsin(θ+/-α)](1)where v is the velocity of the sound. In order to obtain both size and orientation of the reflector asecond equation like (1) is needed, which can be obtained by carrying out measurement for ᴧf say ᴧf’and position α’. Then∆f’= v/[dsinθ+dsin(θ+/-α’)] (2)from (1) and (2) both d and θ can be evaluated.
2.3 Flaws Embedded in Solids
The determination of size for variously shaped reflectors was applied to randomly shaped shims
shown on figure 4. Notice that in addition to circular, elliptical and rectangular reflectors there areirregular shaped reflectors (see numbers 4, 5 and 8 in figure 29). By aligning the transmitter-receiverplane at various orientations, several dimensions of the reflectors can be determined using equations 35
and 36.

Figure 4 - Photograph of various reflectors used in the experiment8182

In table 1, the actual and measured values of the various dimensions are shown for all the reflectors(simulating flaws) used. The agreement between actual values and measured values of the reflectors isgood –within 10-15%.

Table 1 – Comparison of Actual and Measured Sizes for Simulated “Real Flaws”
Additional samples used to simulate defects in solids. Two cylinders of titanium alloy weremachined and their bases diffusion bonded together in such way that the final longer cylinder containeda cavity in the center. On figure 5 the geometry of the simulated defects is shown.

Figure 5 - Simulated defects of various sizes and shapes in a diffusion bonded titanium disk.
A schematic of the experimental setup used in our scattering measurements is shown on figure 6. For an
incident longitudinal wave both the scattered longitudinal and the scattered shear waves are measured
separately as shown on figure 6.

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Figure 6 - Experimental technique for the study of scattering from defects in immersed specimen.
Experimental and theoretical amplitude spectra of scattered waves from 2500x1250 μm ellipticalcracks are shown in figure 7.
The favorable results from these model experiments indicate that the amplitude spectra of elastic
wave scattering from well-defined geometrical flaws can be predicted by theoretical analysis, of Jan
Adler and Achenbach 4 . in metals.

Figure 7 - Amplitude spectra of scattered longitudinal waves from a 2500x1250μm elliptical crack in titanium
along different azimuthal directions, polar angle is 60o

3. POROSITY ASSESSMENT IN ALUMINUM CASTS
Aluminum casts are used in many parts of airplanes and extensive porosity can cause catastrophic
failure. The frequency dependence of ultrasonic attenuation measurement proved to provide both poreconcentration and average pore size The procedure of the measurement is shown schematically infigure 8 where the front surface, back surface and deconvolved spectrum are shown respectively.

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Figure 8 - Ultrasonic spectra from an aluminum block with porosity immersed in water.
Theoretical consideration 5 from the turning point f p using single spherical scatterer provided two
parameters for the aluminum sample.
R= (v/2π)(1/fp ) (3) and
C= (V/2πK)(α p /fp ) (4)where R is the average pore radius, C is the pore concentration v is the velocity of the ultrasound in
the sample and K is a constant dependent on the material.

Figure 9 - Comparison of theoretical and experimental result for the frequency dependent attenuation
coefficient in an aluminum cast alloy.
Using equation 3 and 4 the ultrasonic results favorably compared to actual values obtained from density
measurement for 11 samples as shown

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Table 2 - Summary of ultrasonic results of cast samples

4. ADHESIVE LAYER EVALUATIONIn the Angle beam Ultrasonic Spectroscopy 6 approach obliquely and normally incident ultrasonicbeam are combined .The two angle measurements allow decoupling the effects of the bond line
thickness. To do this we developed a transducer head schematically shown in figure 10 -. The headaccommodates transducers for the normal and oblique measurements. The ultrasonic wave excited by
the transducer is reflected from the interface toward a reflector and returns back to the transducer. The
procedure used to scan the quality of the thin adhesive layer embedded between two composite plates istwofold. At each point of the scan, the normal and angle beam time domain signals reflected from thelayer are recorded. Then they are analyzed in the Fourier domain and processed using our algorithms toobtain the quality of the bond line.
The time signals are recorded using the transducer head. The transducer head is moved over thesample from point to point and each acquisition is recorded. The collected time domain signals are
stored in the form of a 2-D array corresponding to the sampled scan area.
y-axis motor
x-axis motor

Scanning HeadScan Area

Adhesive Joint

Figure 10 - Transducer head
After acquisition of the time signals, the second step is analysis in the Fourier domain of thesesignals to get the relevant parameters for the layer properties determination. The followi ng procedure isapplied for each point:

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Gating of the useful part of the time domain signal
Computation of the Fast Fourier Transform
Gating of the useful part of the frequency domain signal
Determination of the resonance position (in Mhz) and width.
Model-based computation of the layer properties at the corresponding point.
The final result (bond line quality reconstruction for every scanned points) is displayed as a bondline quality image in color level shown on figure 11 together with their relation to bond strength.

Figure 11 Experimental results.
While the ABUS scan clearly displays the fracture no information is obtained by C scan.

This work was partially supported by a grant from the Emeritus Academy OSU.
REFERENCES
1. Fitting, D. E. and Adler L.: Ultrasonic Spectral Analysis for Nondestructive Evaluation, Plenum Press,
New York, 1981.
2. Gericke, O .R: Determination of the Geometry of Hidden Defects by Ultrasonic Pulse Analysis Testing,
Journal of the Acoustical Society of America, 35 (1963), 364..
3. Whaley, H.L. and Adler, L.: Flaw Characterization by Ultrasonic Frequency Analysis, Materials
Evaluation, 29 (1971)
4. Adler. L. and Achenbach J.D.: Elastic Wave Diffraction by Elliptical Cracks: Theory and Experiment
Journal of Nondestructive Evaluation 1 (1980)
5. Adler. L , Rose J. H. and Mobley C.: Ultrasonic Method to Determine Gas Porosity in Aluminum Alloy
Castings: Theory and Experiment. Journal of Applied Physics 55(19860)
6. Rokhlin. S., Wang. I. Xie. B. Yakovlev. V. and Adler. L. Modulated Angle Beam Ultrasonic Spectroscopy
for Evaluation of Imperfect Interfaces and Adhesive Bonds ) Ultrasonics 42 (2004)
This work was partially supported by8187