Assessing Engineered Materials via Non-Destructive Impact
Acoustics
Yishan DONG; Shahram TAHERZADEH; David B SHARP; James BOWEN
School of Engineering and Innovation, The Open University, Milton Keynes, UK

ABSTRACT
Acoustic testing allows inspection of the quality of engineered products without affecting their
final use. It is an example of non-destructive testing (NDT), a wide group of analytical techniques used
to evaluate the properties of a material, component or system without causing damage. Acoustic
testing is becoming increasingly popular, particularly across the civil engineering, healthcare,
automotive, and aviation industries. One early example originated via the wheeltappers during theIndustrial Revolution when railways came into prominence. An impact between two solid bodies
produces surface and body waves, the velocity and characteristics of which depend on material
properties and the nature of the contact. Parameters such as density, modulus, and surface roughness
influence the properties of these waves. Measurement of these waves can therefore be used in theevaluation of material and surface properties. This work reports on recent attempts to develop a
non-destructive method for assessing the structure and quality of engineered materials. The protocol
involves delivering a low kinetic energy impact to a sample, allowing correlation between theproperties of the specimen and the specimen surface with the a coustic output from the impact event.
Keywords: impact, materials, roughness, surface

1. INTRODUCTION
There are many types of non-destructive testing (NDT) used in engineering, most of which havebeen developed as a means to monitor the condition of components, to undertake structure inspection,or to evaluate the physical properties of a material without causing any damage (1). Many traditional
materials characterisation methods are partially or wholly destructive, carried out until the failure of asample, in order to obtain physically meaningful information. For example, tensile testing is
performed in order to obtain Young's modulus and yield stress. In general, a destructive testing (DT)method is easier to perform than a NDT method. DT results usually re quire less complex dataprocessing post-acquisition. In most cases DT methods provide accurate results, but there aresituations where DT is not possible or desirable; this is where NDT can offer a significant advantage,
particularly when rare and/or expensive samples require consideration.
Acoustic NDT methods such as acoustic emission and ultrasound testing are becoming more andmore popular in preventative maintenance strategies. During the Industrial Revolution, when railways
came into prominence, a wheeltapper (2) was a person who would hit the train wheel with along-handled hammer, listening carefully to the audible response. Experienced wheeltappers could use
this method to diagnose cracks and wheel damage; these inspections helped to minimize downtime andkeep companies ahead of their competitors. Acoustic NDT methods have come a long way since then,but the principle which underlies the wheeltappers' success is intrinsic to modern techniques.
Ongoing research regarding acoustic testing of materials includes investigation of physicalproperties such as porosity (3) and Young’s modulus. The work presented here involves delivering a
low kinetic energy impact to a specimen. The surface topography of the specimen will affect themechanics of contact between the two impacting bodies. This will influence the squeezing of air out
from between the two approaching bodies, and also the amount of air trapped between the bodies at the
point of maximum deformation. Hence, it is anticipated that the acoustic output caused by the impact
might also be influenced by surface topography of the specimen (4).
Surface topography is described by the surface roughness, a quantitative measure of the deviations(in the direction of the normal vector) of a real surface from its ideal form. If these deviations are large,
then the surface is considered rough; if they are small, the surface is considered smooth (5). Surface
roughness is important since it can predict the performance of a mechanical component. For exa mple

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in tribology, a rough surface wears out quickly due to higher friction, however roughness promotes oil
adhesion. Surface topography is typically measured by a profilometer, which has high capital cost andrequires specialist training. There are also usually size restrictions on the samples such instruments
can accommodate.
The aim of the work presented here is to investigate the possibility of developing a new method of
impact-based non-destructive testing. Such a technique could be used to define the physicalcharacteristics of a specimen and the specimen surface.

2. EXPERIMENTAL
2.1 Materials
Aluminum sheet (AL104119, 99.5%H/H; Advent Research Materials, UK) was cut into plates ofdimensions 100.0 mm × 100.0 mm × 2.0 mm. The Young’s modulus of the aluminum, measured bytensile testing, was 70 GPa. The density of the aluminum was assumed to be 2,700 kg m-3 , and theaverage mass of each plate was measured to be 54 g. Solid nylon spheres of radius 6.25 mm werepurchased from Dejay Distribution, UK; the density of the nylon was measured at 1,156 kg m-3 , eachsolid sphere having mass 1.2 g. The Young’s modulus of the nylon was measured to be 1.21 GPa.
2.2 Profilometry
The surface topography of each Al plate and nylon sphere was measured using an opticalprofilometer (DCM3D, Leica Microsystems, UK). Six of the Al plates were roughened using different
grades of SiC polishing paper, of grades P4000, P1200, P500, P240, P120 and P80 (Buehler, Germany).
Each Al plate was roughened until a uniform surface was achieved. After polishing, the surface
topography of each specimen was measured through a 10X lens. Five measurements were taken oneach specimen, at non-overlapping locations. The average roughness of the surface, S a (6) was
calculated using Mountainsmap software (Digital Surf, France) after performing a tilt correction.
2.3 Impact Event and Acoustic Recording
Impact events were generated by dropping a nylon sphere onto an Al plate to create a contact
mechanism according to Hertzian mechanics (7). The plate was oriented perpendicularly to thedirection of the approaching sphere, and was simply supported at all four corners. Although the results
are not presented here, it should be noted that nylon spheres gave excellent repeatability of acoustic
data when compared to other polymers tested; these were poly(propylene), poly(tetrafluoroethylene),poly(urethane), and viton. Fifty separate impact events were recorded.
The sphere radius, landing position, microphone position, and the initial height of the sphere above
the Al plate, will all influence the acoustic data generated. In this work, the initial height of the sphere
was 0.965 m, and the sphere was oriented above the centre of the Al plate. The microphone (SM 58
Vocal Microphone, Shure, USA) was held parallel to the Al plate surface; the tip of the microphone isapproximately 5 mm from the plate edge. For each impact, the data was subsequently processed using
Matlab (R2016b, MathWorks, USA) to obtain a sound spectrum. Specifically, the time domain data
was processed via Fourier transform to obtain a frequency-vs-amplitude spectrum; the frequency
range explored in this work is 0.40-20 kHz.
2.4 High Speed Load Cell
High speed recording of the force and duration of impact events was studied separately to acoustic
recording. An Al plate was attached to a 10 N uniaxial load cell (TCA 720397, Procter and Chester
Measurements, UK), shown in Figure 1. The load cell resonant frequency is approximately 1.0 kHz.

Figure 1: Load cell with attached aluminum plate; nylon sphere shown for scale

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The analogue output from the load cell was collected by a DEWE-43A data acquisition instrument,
connected to a desktop PC running DEWESoftX2 software (DEWESoft, Slovenia). The Al plate u sed
for these measurements had dimensions 100.0 mm × 100.0 mm × 0.5 mm; the plate mass was 14 g,
which meant that over 85% of the load cell range was available for measuring the impact force.

3. THEORY AND SIMULATION
3.1 Impact Energy
The nylon sphere is essentially in free fall through ambient air (21°C, 101.3kPa, humidity 20%),
accelerating from zero velocity to its maximum velocity when it impacts the Al plate . The kinetic
energy of the sphere, 𝐸𝑘 , depends on the sphere mass, 𝑚sphere , and its velocity, 𝑣sphere :𝐸k =2𝑚sphere 𝑣sphere2(1)

The sphere velocity at impact, when dropped from an initial height, ℎ, of 0.965m, can be calculated
according to:𝑣sphere = (2𝑔ℎ)0.5(2)-2
where 𝑔 is gravitational acceleration of 9.81 m s .
Given that the sphere has mass 1.2 g, and the impact velocity is 4.351 m s -1 , the kinetic energy at
impact is 11.4 mJ.
3.2 Natural Frequency of a Solid Sphere
The natural frequency of a solid sphere, according to Lautrup (8), is given by:𝑠
tan 𝑠 =⁡𝑠 2
(3)
(1 − 2 )4𝑞
where 𝑠 is a dimensionless variable, and 𝑞 is the ratio between the transverse and longitudinalsound velocity in the material. The value of 𝑞 is 0.5 (9) for nylon.
Upon plotting equation 3, performed using MATLAB, the intersections between the curve and thex-axis are the solutions. The first solution, 𝑠1 , occurs at 𝑠 = 2.82.
The speed of sound, 𝐶𝐿 ⁡, under the experimental conditions employed in this work is 340 m s-1 .
The angular frequency of the sphere oscillation, 𝜔sphere , is calculated using:
𝐶𝐿 𝑠𝑅
where 𝑅 is the sphere radius, yielding 𝜔sphere,1 =153,408 rad s-1 for 𝑠1 = 2.82.
𝜔sphere =The angular frequency is converted to the natural frequency, 𝑓sphere , according to:𝜔𝑓sphere =2𝜋
which gives the first mode of natural frequency of the nylon sphere as⁡𝑓1 = 24.032 kHz.

(4)

(5)

Using Equations 3-5, the second solution is 𝑓sphere,2 = 48.087 kHz, where 𝜔sphere,2 =301,984 rad,and 𝑠2 = 5.64.
3.3 Natural Frequency of a Solid Plate
The natural frequency of a solid plate, 𝑓plate , is given by (9):𝑓plate =2590

𝐾𝑛 𝐷𝑔 0.5()
2𝜋 𝑤𝑑 4(6)

where 𝐾𝑛 is a constant referring to the mode of vibration, 𝑛. The plate thickness is⁡𝑑, the load perunit area is 𝑤, and 𝐷 depends on the physical properties of the plate material:
𝐸plate 𝑑 3𝐷=(7)2
12(1 − 𝜈plate)
where 𝐸plate and 𝜈plate are the Young's modulus and Poisson’s ratio of the plate respectively.
Assuming 𝜈plate = 0.33 and 𝐸plate = 70 GPa, Equation 7 gives⁡𝐷 = 52.37⁡N m.
Values of 𝐾𝑛 are obtained from Roark’s formulae (9) where 𝐾1 =19.7, 𝐾2 = 𝐾3 = 49.3.
The load per unit area is given by:𝑤 =⁡𝑚plate 𝑔
𝐴𝑝𝑙𝑎𝑡𝑒(8)where 𝐴𝑝𝑙𝑎𝑡𝑒 is the cross-sectional area of the plate perpendicular to where load applies.
Therefore, 𝑤 = 52.974 N m-2 , 𝑓plate,1 = 976.9 Hz, and 𝑓plate,2 = 2.444 kHz.
3.4 COMSOL Modelling
COMSOL Multiphysics software (COMSOL, UK) was employed for modelling the natural
frequencies of both the nylon sphere and the Al plate. In each case a fine mesh 3D model was built foran Eigenfrequency study. Boundary conditions were selected to match the experimental conditions;four corners simply supported for the Al plate, and a fixed centre point for the nylon sphere. Material
properties were imported from the COMSOL material library.
For the solid sphere, only three natural frequencies are predicted to be activated over the frequency
range of interest in this work; 10.3 kHz, 10.4 kHz, and 10.7 kHz. In contrast, over fifty natural
frequencies are predicted to be activated for the Al plate, ranging from 403 Hz to 24 kHz. Figure 2
shows examples of where and how the surface displacements are predicted to occur at specified natural
frequencies. All of these calculated values are compared to the calculation results, and to the acoustic
data, in order to interpret the acoustic impact event.

Figure 2: COMSOL simulation of surface displacement; (a) Al plate, natural frequency 1.0 kHz; (b) nylon
sphere, natural frequency 10.3 kHz

4. RESULTS AND DISCUSSION
4.1 Surface Topography
The average roughnesses of the unpolished 'as-received' Al plate and the six polished Al plates areshown in Figure 3. The roughest surface, plate 6, achieved using P80 grade polishing paper, isapproximately four times rougher than the surface of the unpolished plate. Plates 0-6 have thickness d= 2.0 mm whereas Plates 7 and 8 have thickness d = 0.5 mm and d = 1.0 mm respectively.

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Figure 3: Average roughnesses of Al plate surfaces; error bars represent one standard deviation
4.2 Impact Mechanics
The load cell response from an example 'nylon-on-Al plate' impact event is shown in Figure 4. The
mean time between the initial contact, point A, and the maximum normal load, point B, is 1.09 ± 0.05
ms. Point B is thought to be the point at which the rebound starts, and the nylo n sphere begins to travelin the opposite direction to impact. i.e. upwards, away from the Al plate. The mean maximum normalload with which the nylon sphere impacts the Al plate is 8.64 ± 0.38 N.

Figure 4: Load cell response for a nylon sphere impacting an Al plate
The contact area, a, between the sphere and plate and the vertical displacement of the sphere, 𝛿, arecalculable according to Hertzian contact mechanics (7). It is assumed that the majority of deformation
occurs in the nylon sphere, given it has a much lower modulus than the Al plate. The contact radius isgiven by (7, 10):
𝑅𝐹 1/3𝑎=( )𝑘where 𝐹 is the applied normal load, and 𝐾 is the effective elastic modulus, given by:

(9)

−1

2
2
1 − 𝜈plate
4 1 − 𝜈sphere
(10)
𝑘= (
+
)
3
𝐸sphere𝐸platewhere 𝐸sphere and 𝜈sphere are the Young's modulus and Poisson’s ratio of the sphere material
respectively.

Further, the relationship between the vertical displacement, contact radius, and sphere radius is:
𝛿=

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𝑎2
𝑅

(11)

Assuming 𝜈sphere = 0.50 (Poisson's ratio is dimensionless) and 𝐸sphere = 1.21 GPa, at a
maximum normal load of 𝐹 = 8.64 N, Equations 9 and 10 give a maximum contact radius of
𝑎 = 0.268 mm, while Equation 11 gives a maximum vertical displacement of 𝛿 = 13.9 μm. It isuseful to note that the contact pressure at the point of maximum normal load is on the order 30 MPa,
4.3 Impact Acoustics
Figure 5(a) displays time domain acoustic data for an impact event recorded when a nylon sphere
impacts Plate 0, an unpolished Al plate. The acoustic event has a duration of approximately 70 ms, farlonger than the time in which the impact and rebound event occurs according to the load cell data.
Figure 5(b) illustrates how the data is transformed from voltage into sound pressure (by taking Fouriertransform) and a linear trendline is fitted to the data. The gradient of the trendline is termed the 'decay
constant'; the value of the decay constant for the data in Figure 5(b) is 71 log(Pa) s -1 .

Figure 5: Acoustic data for nylon sphere impact on Plate 0; (a) voltage output from microphone, (b)calculating a decay constant for the sound pressure
Figure 6 illustrates the effect of surface topography and plate thickness on the impact acoustics.
The decay constant increases with Al plate surface roughness, shown in Figure 6(a). This means thatthe acoustic event decays more rapidly as the plate topography becomes rougher. Figure 6(b) showsthat the decay constant also increases with increasing plate thickness, which means that the acoustic
response from an impact on an Al plate lasts longer for plates with lower mass, i.e. the plate vibrations
are less damped.

Figure 6: Decay constants for nylon spheres impacting on Al plates; (a) effect of surface topography,(b) effect of plate thickness2593

Figure 7 shows frequency-vs-pressure spectra for Plates 0, 1, 6, and 7, affording a visualcomparison of the transformed acoustic outputs. Plates 0 and 7 are both unpolished, presenting surface
topographies with similar roughness, but differ in their thickness, d = 2.0 mm and d = 0.5 mm
respectively. Correspondingly, their acoustic spectra are markedly different, reflecting the differencein their acoustic output upon impact. Comparison of Plates 0 and 1, which exhibit similar thickness andsurface roughness, Plate 1 having been roughened with grade P4000 polishing paper, demonstrates thata slight change in surface topography did not dramatically alter the acoustic spectra. Comparison of
Plate 1 with Plate 6, a d = 2.0 mm plate roughened with grade P80 polishing paper, illustrates thatchanging the surface roughness by a greater amount results in noticeably different acoustic spectra.

Figure 7: Acoustic spectra for a nylon sphere impacting Al plates: (a) d = 2.0 mm, Sa = 607 nm; (b) d = 0.5mm, Sa = 547 nm; (c) d = 2.0 mm, Sa = 639 nm; (d) d = 2.0 mm, Sa = 2,564 nm
4.4 Comparison of Experiment, Theory, and Simulation
Comparison of the experimentally-acquired acoustic spectra in Figure 7 to theory and simulation
does not reveal close alignment between predicted and measured frequency peaks. However, it should
be noted that the calculated frequencies 𝑓plate,1 = 977 Hz and 𝑓plate,2 = 2.444 kHz match closelywith the frequencies 978 Hz and 2.337 kHz predicted using COMSOL. This suggests that essential
features of the plates and the impact event, which contribute strongly to the acoustic output, are absent
from both the theory and the simulation. Investigating the critical parameters of the impact w hich2594

determine the magnitude and structure of the acoustic output is currently the subject of ongoing
research.

5. CONCLUSION
This work sought to investigate the possibility of developing a new method of impact -based
non-destructive testing, one which could be used to define the physical characteristics of a specimen
and the specimen surface. The results presented in this paper demonstrate that the acoustic output fromthe impact of a nylon sphere on an aluminium plate can be used to determine differences in surface
topography and plate thickness.
Processing and transformation of the recorded acoustic data was conducted in two ways. As a
primary interpretation of the acoustic output from an impact event, the sound pressure wa s calculated
whilst in the time domain, and a decay constant was calculated. This captures the rate at which theacoustic response from the impact event fades. By this method it was possible to determine differencesin plate thickness and surface topography between samples. However, for some samples, use of this'one dimensional' measure may not permit adequate discrimination between two or more changing
physical properties.
Furthermore, a Fourier transformation was used to generate a spectrum in the frequency domain.
By this method it was also possible to determine differences in plate thickness and surface topography
between samples. This output was more time-consuming to generate, but yielded plots which serve asa useful 'two dimensional fingerprint' of the acoustic output from the impact event.
The acoustic spectra presented here are representative of the data collected from dozens of repeat
measurements for the many sphere/plate combinations investigated. Future work will include thedevelopment of a method for assessing the similarity of acoustic spectra, so that the repeatability of atest can be captured and quantified using one, or perhaps two, uniq ue parameters.

ACKNOWLEDGEMENTS
The authors acknowledge the support and valuable contributions made by the following people:
Damian Flack, Stan Hiller, Peter Ledgard, Peter Seabrook, and Alex Stronach.

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