Ultrasonic guided interface waves at a soft-stiff boundary Jason H. Bostrona) Graduate Program in Acoustics, The Pennsylvania State University, University Park, Pennsylvania 16802
Joseph L. Rose Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802
Clark A. Moose Composite Materials Division, Applied Research Laboratory, P.O. Box 30, State College, Pennsylvania 16804
(Received 18 April 2013; revised 26 August 2013; accepted 3 October 2013) Interface waves traveling along the boundary between two solids have been studied for nearly a century. However, little attention has been given to the case where interface waves travel at the boundary between a soft and stiff solid and when the soft material is relatively light and viscoelastic. In this paper, the characteristics of interface waves that propagate along a soft-stiff boundary are described. These waves are similar to a leaky Rayleigh-like wave on the stiff solid in terms of the wave velocity and displacement wave structure. Analytical and finite element models are used to model and simulate wave propagation. An example problem of bond evaluation for coatings on metal structures is considered. Experiments on 2.5 cm thick steel plate with 2.5 cm viscoelastic coatings show good agreement to models. Additionally, the results of models and experiments show several promising features that may be used to evaluate bonds in a non-destructive evaluation approach. C 2013 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4826177] V PACS number(s): 43.35.Pt, 43.35.Cg, 43.35.Zc [BEA]
I. INTRODUCTION
The general solution for waves that travel along the interface between two solid materials is well known. The solution was first described by Stoneley (1924). This is a good approximation for waves that travel at the interface of two plate-like materials, assuming the frequency is relatively high and/or the structure is relatively thick compared to a wavelength. The range of existence of non-attenuative Stoneley waves is known to be limited to materials with certain material property combinations (Scholte, 1947; Ewing et al., 1957). Outside of this limited range complex solutions are described that imply attenuation of the wave as it propagates along the interface. A variety of papers discuss liquid-solid interfaces (Roever et al., 1959; Strick and Ginzbarg, 1956; Phinney, 1961; Gilbert and Laster, 1962; Gusev et al., 1996) and solidsolid interfaces (Gilbert and Laster, 1962; Phinney, 1961; Yamaguchi and Sato, 1956; Ginzbarg and Strick, 1958; Lee and Corbly, 1977; Barnett et al., 1985; Gusev et al., 1996; Destrade and Fu, 2006). Of these, only two have experiments that consider materials with properties that approximate a relatively soft-stiff boundary. Hsieh and Rosen (1993) consider an aluminum and silicon carbide interface and Mattei et al. (1997) consider a Plexiglas and fused quartz interface. None of these studies consider much softer, less dense, and viscoelastic materials similar to those materials used as coatings for the protection of metal structures.
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Author to whom correspondence should be addressed. Electronic mail: [email protected]
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An example problem of nondestructive evaluation (NDE) of bonds for several viscoelastic coatings on steel is considered to demonstrate the use and characteristics of interface waves at a soft-stiff boundary. Previously, Pilarski and Rose (1992) studied the use of guided wave ultrasound to assess bond integrity. They show that increased sensitivity to bond defects may be achieved by choosing guide wave modes that contain shear-type vibration at the interface. Guided interface waves such as Rayleigh and Stoneley waves can fulfill this requirement. For relatively thick structures and/or relatively high frequencies, we can excite these ultrasonic guided interface waves to evaluate the bond at a coating-metal interface. Additionally, the use of interface waves allows us to generalize the technique for any structures where the metal substrate has low curvature and is above a certain thickness, regardless of internal ribs/structure, condition, and fill level (for tanks, etc.). For this reason, we consider the use of guided interface waves instead of plate waves in this paper. Recently, several authors used guided waves to study bond evaluation. Puthillath et al. (2010) used guided waves to identify adhesive and cohesive defects found in titanium repair patches bonded onto aircraft skin. Van Velsor (2009) used circumferential guided waves to study coating bond integrity on pipe. This paper extends the previous NDE-related work by considering interface waves for bond evaluation in thick structures. The objective of the research reported in this paper is to describe guided ultrasonic interface waves at a soft-stiff boundary and to demonstrate the feasibility of using these waves to evaluate the bond between coatings and metal structures. The research approach is divided into several
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FIG. 1. Sketch of an interface wave propagating in a two-layer structure.
steps. First, we discuss the analytical solution for interface waves and the properties of waves at a soft-stiff boundary. Second, we describe the use of the semi-analytical finite element method with absorbing regions as a tool to assess mode properties. Third, we simulate wave propagation using a finite element model and search for potentially useful physically based wave features. Fourth, we discuss experimental tests with several coatings bonded to steel plate. Results indicate several physically based wave features that are correlated with bond length.
II. BASIS OF MODELS AND SIMULATIONS A. Stoneley wave solution
Consider waves that propagate along the interface of two solid materials as shown schematically in Fig. 1. The solution for waves that travel at an interface between two solids was first described by Stoneley (1924). One of the most detailed analyses of the results when considering different material properties is given by Pilant (1972). One interesting result given by Pilant is the description of the range of existence for Stoneley, attenuative interface, and Rayleigh-like wave regimes based on the relative material properties of the two materials. The range of existence for these wave types is broken into four general regions, illustrated in Fig. 2. Most previous research has focused in the Stoneley and interface wave regimes, in the lower half of Fig. 2. Hsieh and Rosen (1993) and Mattei et al. (1997) considered materials with a shear speed ratio above 4 and a density ratio of about 0.85. These
FIG. 2. Stoneley, interface, and Rayleigh-like wave regimes for materials with a Poisson’s ratio of 0.25 (after Pilant, 1972, Fig. 1). Lines indicate the boundary between wave types. Hidden indicates that there are no propagating solutions. 4352
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studies worked in the upper right region of Fig. 2, where Rayleigh-like and Interface wave types exist. Bulk shear wave speeds in coatings and epoxies are typically two to three or more times less than in steel (giving a squared velocity ratio of at least 5); this puts the waves considered in this paper firmly in the Rayleigh regime and, in the upper left corner of Fig. 2 since these materials are relatively light. In this regime, there is a Rayleigh-like wave propagating on the surface of material 2, leaking energy into the coating (attenuating) at a rate dependent on the relative material properties. The wave is non-dispersive, unless frequency-dependent viscoelasticity is considered. In that case, the wave can have a minor amount of dispersion, which contributes to an increase in pulse width in models and experiments. B. Leaky Rayleigh-like wave solution
True Rayleigh waves, which exist on the surface of an elastic half space in a vacuum, are non-attenuative, so intuitively, as the coating density and wave velocities tend toward zero, we expect the leaky Rayleigh-like wave to have less attenuation (leak less). In contrast, as the density and wave velocities in the coating material increase, we expect the leaky Rayleigh-like wave to couple better to the coating so more energy will leak away, attenuating the interface wave. This is the case in the Rayleigh region at the top of Fig. 2. Alternatively, we may plot the attenuation (in dB/m) for the leaky Rayleigh-like wave by considering the imaginary component of the solution to the Stoneley wave equation. This is plotted in Fig. 3. When the two materials become more dissimilar in either density or wave velocity [move left or up in Fig. 3(b)], the attenuation decreases. Likewise, the attenuation increases as the materials become more similar in material properties.
FIG. 3. (Color online) (a) Normalized velocity, c/cR, and (b) attenuation (dB/m) of leaky Rayleigh-like waves at 1 MHz for materials with a Poisson’s ratio of 0.25. Bostron et al.: Interface waves at a soft-stiff boundary
TABLE I. Parameters for the SAFE method with absorbing regions (AR) used to calculate the solution for a leaky Rayleigh-like wave at 1 MHz. Layer 1 2 3 4
Material
Density (kg/m3)
cL (m/s)
cT (m/s)
Thickness (mm)
Number of elements
Coating-AR Coating Steel Steel-AR
1300
1500
675
7870
5770
3190
3.48 1.74 8.85 8.85
26 14 18 18
From Fig. 3(a), it is also clear that there is a similar relationship between the phase velocity and the relative material properties. When the two materials become more dissimilar, the velocity tends toward the Rayleigh wave speed for the dense material. Likewise, the velocity increases as the materials become more similar in physical properties. These two observations relating to attenuation and velocity suggest two potential physically based features that may be used to assess the bond condition of coatings and substrates in this geometry: Amplitude and travel time. Other studies have shown that experimental results match theoretical calculations for Stoneley and interfacetype waves (Lee and Corbly, 1977; Hsieh and Rosen, 1993; Mattei et al., 1997). [The theory has also been developed to describe the existence of interfacial waves for anisotropic materials (Barnett et al., 1985; Destrade and Fu, 2006).] These experiments typically look at metal materials and suggest that these types of interface waves could be used to evaluate bonded joints. In this paper, we expand upon this previous work by exploring the leaky Rayleigh-like wave regime and specifically consider relatively soft and viscoelastic coatings on a stiff steel substrate.
C. Semi-analytical finite element method with absorbing regions
The semi-analytical finite element (SAFE) method was first described by Lagasse (1973). This method uses an analytical propagating wave solution combined with a finite element mesh of a waveguide cross-section to calculate the solutions for guided wave modes that exist in a waveguide. With the advent of modern computational power, this method has gained in popularity over analytical solutions. There are a variety of reasons for this including the ability to model waveguides of almost arbitrary cross-section and the ease with which viscoelastic and anisotropic materials may be modeled. See Hayashi et al. (2003) or Bartoli et al. (2006) for the details of this method and several example problems. We choose to apply this tool for use in describing the propagation of interface waves for two main reasons. First, the handling of viscoelastic materials in the SAFE method is well understood, and the method is reliable because it does not rely on root-searching algorithms (where roots may be missed) to find solutions in viscoelastic waveguides. Second, we can change the waveguide with relative ease if we wish to consider modes in other related geometries, for example, those including an epoxy layer. Additionally, we can consider geometries where either the coating or the substrate is a J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
plate as opposed to a half space. This allows us to check our assumption of an interface wave for finite material thickness. The main alteration from the typical SAFE method formulation in this work is the addition of absorbing regions. These regions absorb outgoing waves to simulate a half space. An absorbing region is made of elements that have a gradual increase in the amount of damping as distance from the waveguide increases. The use of these regions is well understood, and guidelines have been suggested for proper use to ensure that outgoing waves are fully absorbed (see, e.g., Castaings and Lowe, 2008). These regions need to be long enough to absorb the waves at the frequencies of interest but need not be unnecessarily long such that they waste computation time. We verify that our SAFE method calculation with absorbing regions is working properly by comparing the result to the analytical solution. Table I displays the material properties, layer thicknesses, and number of elements used in each layer in the model. For an interface wave propagating at 1 MHz, we find the phase velocity and attenuation to be 2949 m/s and 277 dB/m, respectively. This agrees with the analytical solution to within a tenth of a percent, giving us confidence in our method. Proper use of our method can also be verified by examining the wave structure of the mode. Additionally, the wave structure should be analyzed to determine if the mode will interact with certain defect types. Figure 4 shows the displacement wave structure for a leaky Rayleigh-like wave mode at 1 MHz when a viscoelastic coating (with similar properties to those shown in Table I) is considered. Note that the wave structure in the steel (positive depth) is similar to that of a true Rayleigh wave. Additionally, the coating thickness used in the calculation for Fig. 4 was greater than that shown in Table I so that the leaked waves can be viewed
FIG. 4. (Color online) In plane (dashed) and out of plane (solid) displacement wave structure at 1 MHz for a leaky Rayleigh-like wave at the interface of steel (positive depth) and a viscoelastic coating. Bostron et al.: Interface waves at a soft-stiff boundary
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FIG. 5. (Color online) Sketch showing the coating, steel, and Plexiglas material regions of the FEM. Dark regions at the edge of the model are infinite element regions that are used to reduce end reflections and simulate a half space.
clearly. For this mode, there is a relatively large amount of in-plane displacement (and shear stress) at the interface, which confirms that it should be sensitive to the bonding condition (see, e.g., Pilarski and Rose, 1992). When the coating half space is modeled as elastic or viscoelastic, similar velocity and attenuation values are calculated. The interface wave velocity and attenuation values vary by up to 1%, since the modulus values are a function of the assumed attenuation values. However, when the viscoelastic model is applied to such problems as a thin coating layer on a half space or a weak interface, the results will be significant. Work is under way on these problems. D. Simulation of wave propagation
Wave propagation was simulated using a twodimensional (2-D) finite element model (FEM) in ABAQUS. The purpose of this model is to study wave interaction and identify potentially useful wave features correlated to bond length. Figure 5 shows a sketch of the model, which contained between 150 000 and 580 000 elements, depending on the material properties used. Four-node bilinear plane strain quadrilateral elements were used such that the largest element dimension was not more than 1/8 of the shortest wavelength of the propagating waves in each material. For this reason, models with lower sounds speed coatings had more elements. Four-node linear plane strain one-way infinite elements were used to simulate a half space and reduce end reflections. The excitation source is a surface pressure with a 1 MHz center frequency, six-cycle Hanning-windowed sine pulse applied to an angled wedge block. The angle is designed to excite Rayleigh waves on the surface of the steel. The waves propagate along the top of the steel surface and convert to leaky Rayleigh-like interface waves when the coating is present. The coating is viscoelastic, so a wave traveling into a thick coating layer is sufficiently absorbed and reflections
FIG. 6. (Color online) FEM displacement during simulated wave propagation. The interface wave interacts with the structure differently during wave propagation through (a) poor and (b) well bonded regions. As time progresses, the wave traveling through the well bonded region is highly attenuated. Light colored regions indicate high displacement (linear scale).
off the top surface do not noticeably affect the propagating interface wave. In the model, the steel and coating layers are 2.5 and 1.3 cm thick, respectively, and the coating length is 9 cm. The bondline in the model is 0.5 mm and six elements thick. The bondline may have epoxy material properties or have the same properties as the coating (no epoxy case). A bondline defect is simulated by dramatically decreasing the stiffness of this region. Changes in bond and defect length are used to develop an understanding of how the interface wave is affected by the bond length. Figure 6 shows a typical FEM wave propagation result. Figure 6 shows wave displacement at several time steps for propagation through poor and good bond regions. At a model time of 22.5 ls, the Rayleigh wave on the steel just reaches the edge of the coating. At 37.5 ls, the interface wave has traveled part way under the coating. There is very little interaction in the debond case, so the wave undergoes little attenuation or other changes. However, for the perfect bond case, the wave interacts strongly with the coating and is clearly attenuated during propagation. The attenuation is due to the wave energy leaking into the coating layer. Note that the leaked wave has relatively low amplitude because the coating is viscoelastic. We will examine attenuation and other waveform features to demonstrate how the FEM data can be used to suggest which physically based features may be useful in detecting bond condition in an experiment. Various models were run with different bond defect lengths, coating stiffnesses, and with/without epoxy bondlines. These materials are described in Table II. Viscoelastic
TABLE II. Material properties used in the finite element model simulation of wave propagation. Material Low-stiffness coating/epoxy Mid-stiffness coating High-stiffness coating/epoxy Steel (HY-100)
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Density (kg/m3)
cL (m/s)
cT (m/s)
aL(x)/x (1/mm)
aT(x)/x (1/mm)
1250 1250 1250 7870
1230 1700 2550 5770
660 900 1350 3190
0.05 0.05 0.05 0
0.25 0.25 0.25 0
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FIG. 7. (Color online) FEM interface wave characteristics: (a) Out-of-plane displacement, (b) amplitude envelope, and (c) frequency content from the low-stiffness coating FEM for bond lengths of 0 (solid), 3 (dashed), 6 (dashed-dotted), and 9 cm (dotted).
material properties were used for the coatings and implemented in ABAQUS using frequency data. Our FEM is conducted in the time domain, so the properties are converted from the frequency to the time domain by ABAQUS using a Prony series approximation. Details for using this method for representing viscoelastic materials in ABAQUS are given by Mu (2008), Chap. 6. For the viscoelastic material properties, we assume an attenuation coefficient, a, which is linear with respect to frequency, (a(x)/x is a constant) and is defined as part of the complex phase velocity cp ðxÞ
¼
1 aðxÞ i cp ðxÞ x
!1 ;
(1)
where cp is the real part of the phase velocity and these variables are dependent on the radial frequency, x. The assumption of a linear attenuation coefficient with frequency has been found to be true for polymer-based materials in the 0.3–5 MHz frequency range by several authors (Barshinger and Rose, 2004; Chan and Cawley, 1998; Baudouin and Hosten, 1996). Figure 7 shows wave characteristics from models with the low-stiffness coating. These data are representative for all of the models run. Figure 7(a) shows the out-of-plane displacement from an interface node from models with different bond lengths. Figure 7(b) shows the amplitude envelope of that displacement signal. Figure 7(c) shows the frequency J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
FIG. 8. FEM interface wave features: (a) Amplitude (solid) and energy (dotted) ratio, (b) pulse width, and (c) frequency ratio calculated from the data shown in Fig. 7.
content of the wave pulse. Figures 7(a)–7(c) provide a foundation from which to extract various features that correlate to bond length. Figure 8 shows several physically based wave features that correlate well to bond length. First, and most clearly, there is attenuation of the wave packet when there is a good bond. This feature is shown in Fig. 8(a) and is discussed in more detail in the following text. The amplitude ratio is calculated using the maximum amplitude from the wave envelope and normalizing by the zero bond length case. The “energy” ratio is calculated in a similar manner, but the area under the envelope is used instead. Second, Fig. 8(b) shows the pulse width calculated from the amplitude envelope of the wave packet. We find that the pulse width, defined by the time between 6 dB down points of the wave envelope from the maximum, increases as bond length increases. Third, we can identify two frequency-related features. The frequency of maximum amplitude from the FFT decreases as bond length increases. A more robust feature may be the frequency amplitude ratio shown in Fig. 8(c). We calculate this feature by taking the ratio of the sum of the frequency content below and above the excitation frequency (1 MHz). An increase in frequency ratio with bond length indicates that high frequencies are preferentially leaked/absorbed in good bond regions. Because attenuation is such a strong feature for this guided wave, we examine it in more detail. We create curves Bostron et al.: Interface waves at a soft-stiff boundary
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TABLE III. Sample characteristics and material properties. Coating material Sorbothane Polyurethane Polycarbonate Epoxy
Color
Density (kg/m3)
cL (m/s)
cT (m/s)
Black Amber Translucent Gray
1300 (62%) 1240 (62%) 1190 (62%) 1300 (62%)
1500 (62%) 1660 (62%) 2080 (61%) 2320 (61%)
700 (64%) 750 (64%) 940 (64%) 1120 (62%)
III. EXPERIMENT A. Sample fabrication and test setup
FIG. 9. (Color online) Amplitude vs bond length for (a) cast coatings (no epoxy layer) and (b) coatings with an epoxy layer. Line type indicates material property at bondline (solid, low; dotted, mid; and dashed, high stiffness), and symbol indicates material property for coating (䉫, low; 䊊, mid; and ⵧ, high stiffness). The material at the bondline plays a large role in determining the attenuation properties of the wave.
similar to Fig. 8(a) for models with different material properties. By normalizing the amplitude by the debond case, we can see how the wave packet is attenuated through interaction with different coatings as it travels through good bond regions. We compare the attenuation of the wave as it travels in each of the following cases: (1) Low-stiffness coating (no epoxy), (2) mid-stiffness coating (no epoxy), (3) highstiffness coating (no epoxy), (4) mid-stiffness coating with low-stiffness epoxy, (5) high-stiffness coating with lowstiffness epoxy, (6) mid-stiffness coating with high-stiffness epoxy, and (7) low-stiffness coating with high-stiffness epoxy. The result of this analysis is shown in Fig. 9. As bond length increases, the amplitude-related feature clearly decreases in all cases. This decrease is relatively constant with distance (dB/m). Moreover, the results shown in Fig. 9(a) support what we would expect from the SAFEM and analytical analysis, where the highest stiffness coating (most similar to steel) attenuates at a higher rate, while the least stiff coating (most dissimilar to steel) attenuates at a much lower rate. However, when the epoxy layer is added [Fig. 9(b)], we find that the attenuation feature is dominated by the stiffness of the epoxy as opposed to the coating material. This is because the wave traveling in the steel leaks energy based primarily on the material in direct contact with the surface. Even though the epoxy layer is relatively thin, it will dominate because it is in direct contact with the steel. (It appears that the result for the high stiffness material flattens out near 35 dB. However, additional models were run with over-dimensioned boundary conditions to confirm that this effect is due to the reflections generated from non-quiet “infinite element” boundaries in the FEM.) 4356
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Three different coating materials, each 2.5 cm thick, were studied for this paper (see Table III). The polyurethane and polycarbonate samples were bonded to the steel plate using a two part “SHT Material” epoxy from United Resin Corporation. The epoxy was a moderately viscous liquid when heated and took about a week to cure at room temperature. After the cure, the epoxy thickness was measured at the edge of the coating. In most places, the final bond thickness was between about 0.3 and 0.5 mm except near a couple corners where the coating lifted-off from the steel. Before bonding the materials, the steel surface was grit blasted and primed using Formula 150 or 153 Polyamide Epoxy primer; the polyurethane was roughed and primed as well. Both the polyurethane and polycarbonate materials were bonded to the primed steel surface using the epoxy. Sorbothane is a very soft polyurethane and is quite tacky (e.g., when cut, it will “self-heal”). No epoxy was used to bond the Sorbothane coating to the metal, but the Sorbothane was pressed onto a clean surface to simulate a bond. Additionally, due to this tacky property, a 3 mm (1/8in.) thick piece of Sorbothane was used to simulate a lowstiffness bondline with the polyurethane and polycarbonate coating materials. A stair-step shape was chosen for the samples to gain a variety of bond lengths in a small part size. The strategy we employ is to first understand the relevant wave features that correlate with bond length before searching for hidden defects. Pictures of several of the samples are shown in Fig. 10. There was an issue bonding the polycarbonate sample because the surface of the polycarbonate was not prepared properly. This caused large, visible (because the polycarbonate is transparent) defect regions at the epoxy-polycarbonate interface. In experimental tests, polystyrene wedge blocks were used to excite Rayleigh waves on the steel surface. An angle of 53 was chosen to excite guided waves according to Snell’s law sinhwedge sinhGW 2355m=s ¼53 ; ¼ ) hwedge ¼ sin1 2948m=s cL;wedge cp (2) where hGW ¼ 90 for guided waves, cL;wedge ¼ 2355 m/s for polystyrene, and cp is the phase velocity of the guided wave mode we wish to excite. This phase velocity is the Rayleigh wave velocity in HY-100 steel, 2948 m/s. Note that this angle corresponds to the center velocity of the range of Bostron et al.: Interface waves at a soft-stiff boundary
and receive electronic signals. GE Krautkramer Benchmark Series SWS Style 1.0 MHz/1.0 in. (2.5 cm) diameter transducers were excited with a 100 V, four-cycle tone burst. The wave speed of the propagating wave packet on the primed steel surface was measured to be within 0.5% of the Rayleigh velocity, giving us confidence that we were exciting the intended guided wave mode. B. Experimental results
FIG. 10. (Color online) (a) Epoxied polyurethane sample, (b) polycarbonate sample with sorbothane “bond,” and (c) experimental setup. Angled wedge blocks were used to excite and receive Rayleigh waves on the steel surface in T/T mode.
velocities excited due to the finite transducer size. The range of phase velocities excited is larger than the change in velocity due to the minor amount of dispersion that the wave contains. These waves travel along the coating-steel interface and are received in a through-transmission (T/T) mode, as shown in Fig. 10(c). GUIDED WAVE WORKSTATION (FBS, Inc.) generalpurpose lab measurement software and a 300 V peak-to-peak tone burst pulser and A/D converter were used to generate
FIG. 11. (Color online) Experimental interface wave characteristics: (a) Voltage signal, (b) amplitude envelope, and (c) frequency content for waveforms from the polycarbonate-epoxy-steel sample for bond lengths 0 (solid), 3 (dashed), and 5.5 cm (dashed-dotted). J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
Data were collected on epoxied polyurethane and polycarbonate samples and sorbothane bondline polyurethane, polycarbonate, and sorbothane samples. In this section, the same calculations are performed for the experimental data as were calculated for the FEM data in Figs. 7–9. Similar trends are shown, validating our model and describing a set of useful features correlated with bond length that can be used for bond inspection. Figure 11 displays data from interface wave propagation in the polycarbonate-epoxy-steel sample. Data from this sample were chosen because they are representative of data with clean signals and feature trends with little scatter. Figures 11(a)–11(c) show the voltage signal, waveform envelope, and frequency content of the received wave. Figures 12(a)–12(c) show several physically based wave features which correlate well to bond length. We notice that attenuation is again a dominant feature affecting the wave packet. This is expected because the epoxy used has similar properties to the high-stiffness material used in the model. The
FIG. 12. (Color online) Experimental interface wave features: (a) Amplitude ratio, (b) pulse width, and (c) frequency ratio calculated from the data shown in Fig. 11. Bostron et al.: Interface waves at a soft-stiff boundary
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cast coating, will allow for a longer inspection distances because the wave will undergo less attenuation per distance. However, in that case, the attenuation-related features vary more slowly with change in bond length, suggesting that the minimum detectable defect size may be larger. It is suggested to always take measurements at a short enough distance that detectable signal amplitudes should be received to avoid the risk of confusion between a good bond and a testing device which is not functioning properly. FIG. 13. (Color online) Amplitude vs bond length for epoxy-bonded coatings (dashed trendline) and coatings with sorbothane bondline (solid trendline). Symbols indicate the coating material (䉭, sorbothane; 䊊, polyurethane, and ⵧ, polycarbonate).
pulse width and frequency ratio features both increase with bond length, as shown in the model. Figure 13 shows attenuation-related feature data from all of the samples. Trend lines for the epoxy (dashed) and sorbothane (solid) bondline samples are shown. It is clear that the epoxied samples undergo very strong attenuation with distance when compared to the sorbothane bondline samples. The epoxied samples have an attenuation feature of about 6 dB/cm, which is similar to the 4.5–6 dB/cm shown in the model for the high-stiffness coating [see Fig. 9(b), dashed lines]. The sorbothane bondline samples show an attenuation feature of about 0.7 dB/cm, which is a bit less than the 1–2.5 dB/cm shown in the model [see Fig. 9(b), solid lines]. The difference could be due to the non-perfect bond condition created by the sorbothane on the primer, which would lower the bond strength and cause a smaller attenuation. We believe the flattening of the epoxied sample data near 45 dB is due to “coherent noise” from wave reflections off of the bottom of the finite sized steel plate. This effect was confirmed by FE models without absorbing boundaries. In Fig. 13, there are several data points located at zero bond length and between 0 and 3 dB normalized amplitude. These data points are the measurements where the wave traveled along a defect region of the epoxy bond in the polycarbonate sample. In the previous section, we mentioned that the polycarbonate sample had a large visible defect. This defect region is clearly detected using the amplitude ratio feature of the wave. This defect region would have been visually hidden had the coating material (polycarbonate) not been transparent. This bonding “mistake” during fabrication turned out to be useful in that it demonstrates the ability of the guided ultrasonic interface wave to locate and identify hidden defects. Additionally, the boundary between wellbonded and not bonded epoxy regions may be detected in a pulse-echo mode when the transducer is aligned nearly perpendicular to the boundary. This method shows promise for “mapping” the boundary of a well-bonded region but must be examined further in future work. The general attenuation effect shown in Fig. 13 suggests that a workable inspection distance could be defined based on the epoxy/bondline properties and measurement configuration/system. In general, a less-stiff epoxy, or low stiffness 4358
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IV. CONCLUDING REMARKS
In this paper, guided ultrasonic interface waves at a softstiff boundary were described. The wave velocity and attenuation characteristics for different material property combinations were calculated using the Stoneley wave equation. Finite element wave propagation studies have been used to simulate wave propagation and demonstrate the effect of different coating and epoxy property combinations. Experimental tests were conducted with polymer coatings epoxied to 2.5 cm thick steel to demonstrate the feasibility of using these waves to evaluate the bond between coatings and metal structures. These tests validated the model results and show several physically based wave features that are correlated to bond length, including amplitude ratio, pulse width, and frequency ratio. These features show great promise for bond evaluation and the identification of hidden defects using interface waves in a nondestructive evaluation approach. ACKNOWLEDGEMENTS
The authors would like to acknowledge Barry Musser for his assistance in sample preparation, FBS, Inc. for use of their facilities, and funding support from the ARL Walker Graduate Assistantship from the Applied Research Laboratory at the Pennsylvania State University. Barnett, D. M., Lothe, J., Gavazza, S. D., and Musgrave, M. J. P. (1985). “Considerations of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces,” Proc. R. Soc. London 402, 153–166. Barshinger, J., and Rose, J. (2004). “Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1547–1556. Bartoli, I., Marzani, A., di Scalea, F. L., and Viola, E. (2006). “Modeling wave propagation in damped waveguides of arbitrary cross-section,” J. Sound Vib. 295, 685–707. Baudouin, S., and Hosten, B. (1996). “Immersion ultrasonic method to measure elastic constants and anisotropic attenuation in polymer-matrix and fiber-reinforced composite materials,” Ultrasonics 34, 379–382. Castaings, M., and Lowe, M. (2008). “Finite element model for waves guided along solid systems of arbitrary section coupled to infinite solid media,” J. Acoust. Soc. Am. 123(2), 696–708. Chan, C. W., and Cawley, P. (1998). “Lamb waves in highly attenuative plastic plates,” J. Acoust. Soc. Am. 104(2), 874–881. Destrade, M., and Fu, Y. B. (2006). “The speed of interfacial waves polarized in a symmetry plane,” Int. J. Eng. Sci. 44, 26–36. Ewing, W., W. Jardetzky, and F. Press (1957). Elastic Waves in Layered Media (McGraw-Hill, New York), Chap. 3, pp. 74–123. Gilbert, F., and Laster, S. (1962). “Excitation and propagation of pulses on an interface,” Bull. Seismol. Soc. Am. 52, 299–319. Ginzbarg, A. S., and Strick, E. (1958). “Stoneley-wave velocities for a solid-solid interface,” Bull. Seismol. Soc. Am., 48, 51–63. Gusev, V., Desmet, C., Lauriks, W., Glorieux, C., and Thoen, J. (1996). “Theory of Scholte, leaky Rayleigh, and lateral wave excitation via the Bostron et al.: Interface waves at a soft-stiff boundary
laser-induced thermoelastic effect,” J. Acoust. Soc. Am. 100(3), 1514–1528. Hayashi, T., Song, W.-J., and Rose, J. L. (2003). “Guided wave dispersion curves for a bar with an arbitrary cross-section, a rod and rail example,” Ultrasonics 41, 175–183. Hsieh, T. M., and Rosen, M. (1993). “Ultrasonic leaky waves for nondestructive interface characterization,” Ultrasonics 31(1), 45–51. Lagasse, P. E. (1973). “Higher-order finite-element analysis of topographic guides supporting elastic surface waves,” J. Acoust. Soc. Am. 53(4), 1116–1124. Lee, D., and Corbly, D. (1977). “Use of interface waves for nondestructive inspection,” IEEE Trans. Sonics Ultrason. 24, 206–212. Mattei, C., Jia, X., and Quentin, G. (1997). “Direct experimental investigations of acoustic modes guided by a solid-solid interface using optical interferometry,” J. Acoust. Soc. Am. 102(3), 1532–1539. Mu, J. (2008). “Guided wave propagation and focusing in viscoelastic multilayered hollow cylinders,” Ph.D thesis, The Pennsylvania State University. Phinney, R. A. (1961). “Propagation of leaking interface waves,” Bull. Seismol. Soc. Am. 51(4), 527–555. Pilant, W. L. (1972). “Complex roots of the Stoneley-wave equation,” Bull. Seismol. Soc. Am. 62(1), 285–299.
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Pilarski, A., and Rose, J. L. (1992). “Lamb wave mode selection concepts for interfacial weakness analysis,” J. Nondestruct. Eval. 11(3/4), 237–249. Puthillath, P., and Rose, J. L. (2010). “Ultrasonic guided wave inspection of a titanium repair patch bonded to an aluminum aircraft skin,” Int. J. Adhes. Adhes. 30(7), 566–573. Roever, W. L., Vinine, T. F., and Strick, E. (1959). “Propagation of elastic wave motion from an impulsive source along a liquid/solid interface,” Philos. Trans. Roy. Soc. London 251, 455–523. Scholte, J. G. (1947). “The range and existence of Rayleigh and Stoneley waves,” Geophys. J. Int. 5, 120–126. Stoneley, R. (1924). “Elastic waves at the surface of separation of two solids,” Proc. R. Soc. 106, 416–428. Strick, E., and Ginzbarg, A. (1956). “Stoneley-wave velocities for a fluidsolid interface,” Bull. Seismol. Soc. Am. 46, 281–292. Van Velsor, J. V. (2009). “Circumferential guided waves in elastic and viscoelastic multilayered annuli,” Ph.D. thesis, The Pennsylvania State University, University Park, PA. Yamaguchi, R., and Sato, Y. (1956). “Stoneley wave-its velocity, orbit and distribution of amplitude,” Bull. Earthquake Res. Inst., Univ. Tokyo 33, 549–559.
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Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
Joseph L. Rose Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802
Clark A. Moose Composite Materials Division, Applied Research Laboratory, P.O. Box 30, State College, Pennsylvania 16804
(Received 18 April 2013; revised 26 August 2013; accepted 3 October 2013) Interface waves traveling along the boundary between two solids have been studied for nearly a century. However, little attention has been given to the case where interface waves travel at the boundary between a soft and stiff solid and when the soft material is relatively light and viscoelastic. In this paper, the characteristics of interface waves that propagate along a soft-stiff boundary are described. These waves are similar to a leaky Rayleigh-like wave on the stiff solid in terms of the wave velocity and displacement wave structure. Analytical and finite element models are used to model and simulate wave propagation. An example problem of bond evaluation for coatings on metal structures is considered. Experiments on 2.5 cm thick steel plate with 2.5 cm viscoelastic coatings show good agreement to models. Additionally, the results of models and experiments show several promising features that may be used to evaluate bonds in a non-destructive evaluation approach. C 2013 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4826177] V PACS number(s): 43.35.Pt, 43.35.Cg, 43.35.Zc [BEA]
I. INTRODUCTION
The general solution for waves that travel along the interface between two solid materials is well known. The solution was first described by Stoneley (1924). This is a good approximation for waves that travel at the interface of two plate-like materials, assuming the frequency is relatively high and/or the structure is relatively thick compared to a wavelength. The range of existence of non-attenuative Stoneley waves is known to be limited to materials with certain material property combinations (Scholte, 1947; Ewing et al., 1957). Outside of this limited range complex solutions are described that imply attenuation of the wave as it propagates along the interface. A variety of papers discuss liquid-solid interfaces (Roever et al., 1959; Strick and Ginzbarg, 1956; Phinney, 1961; Gilbert and Laster, 1962; Gusev et al., 1996) and solidsolid interfaces (Gilbert and Laster, 1962; Phinney, 1961; Yamaguchi and Sato, 1956; Ginzbarg and Strick, 1958; Lee and Corbly, 1977; Barnett et al., 1985; Gusev et al., 1996; Destrade and Fu, 2006). Of these, only two have experiments that consider materials with properties that approximate a relatively soft-stiff boundary. Hsieh and Rosen (1993) consider an aluminum and silicon carbide interface and Mattei et al. (1997) consider a Plexiglas and fused quartz interface. None of these studies consider much softer, less dense, and viscoelastic materials similar to those materials used as coatings for the protection of metal structures.
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
J. Acoust. Soc. Am. 134 (6), December 2013
Pages: 4351–4359
An example problem of nondestructive evaluation (NDE) of bonds for several viscoelastic coatings on steel is considered to demonstrate the use and characteristics of interface waves at a soft-stiff boundary. Previously, Pilarski and Rose (1992) studied the use of guided wave ultrasound to assess bond integrity. They show that increased sensitivity to bond defects may be achieved by choosing guide wave modes that contain shear-type vibration at the interface. Guided interface waves such as Rayleigh and Stoneley waves can fulfill this requirement. For relatively thick structures and/or relatively high frequencies, we can excite these ultrasonic guided interface waves to evaluate the bond at a coating-metal interface. Additionally, the use of interface waves allows us to generalize the technique for any structures where the metal substrate has low curvature and is above a certain thickness, regardless of internal ribs/structure, condition, and fill level (for tanks, etc.). For this reason, we consider the use of guided interface waves instead of plate waves in this paper. Recently, several authors used guided waves to study bond evaluation. Puthillath et al. (2010) used guided waves to identify adhesive and cohesive defects found in titanium repair patches bonded onto aircraft skin. Van Velsor (2009) used circumferential guided waves to study coating bond integrity on pipe. This paper extends the previous NDE-related work by considering interface waves for bond evaluation in thick structures. The objective of the research reported in this paper is to describe guided ultrasonic interface waves at a soft-stiff boundary and to demonstrate the feasibility of using these waves to evaluate the bond between coatings and metal structures. The research approach is divided into several
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C 2013 Acoustical Society of America V
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FIG. 1. Sketch of an interface wave propagating in a two-layer structure.
steps. First, we discuss the analytical solution for interface waves and the properties of waves at a soft-stiff boundary. Second, we describe the use of the semi-analytical finite element method with absorbing regions as a tool to assess mode properties. Third, we simulate wave propagation using a finite element model and search for potentially useful physically based wave features. Fourth, we discuss experimental tests with several coatings bonded to steel plate. Results indicate several physically based wave features that are correlated with bond length.
II. BASIS OF MODELS AND SIMULATIONS A. Stoneley wave solution
Consider waves that propagate along the interface of two solid materials as shown schematically in Fig. 1. The solution for waves that travel at an interface between two solids was first described by Stoneley (1924). One of the most detailed analyses of the results when considering different material properties is given by Pilant (1972). One interesting result given by Pilant is the description of the range of existence for Stoneley, attenuative interface, and Rayleigh-like wave regimes based on the relative material properties of the two materials. The range of existence for these wave types is broken into four general regions, illustrated in Fig. 2. Most previous research has focused in the Stoneley and interface wave regimes, in the lower half of Fig. 2. Hsieh and Rosen (1993) and Mattei et al. (1997) considered materials with a shear speed ratio above 4 and a density ratio of about 0.85. These
FIG. 2. Stoneley, interface, and Rayleigh-like wave regimes for materials with a Poisson’s ratio of 0.25 (after Pilant, 1972, Fig. 1). Lines indicate the boundary between wave types. Hidden indicates that there are no propagating solutions. 4352
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studies worked in the upper right region of Fig. 2, where Rayleigh-like and Interface wave types exist. Bulk shear wave speeds in coatings and epoxies are typically two to three or more times less than in steel (giving a squared velocity ratio of at least 5); this puts the waves considered in this paper firmly in the Rayleigh regime and, in the upper left corner of Fig. 2 since these materials are relatively light. In this regime, there is a Rayleigh-like wave propagating on the surface of material 2, leaking energy into the coating (attenuating) at a rate dependent on the relative material properties. The wave is non-dispersive, unless frequency-dependent viscoelasticity is considered. In that case, the wave can have a minor amount of dispersion, which contributes to an increase in pulse width in models and experiments. B. Leaky Rayleigh-like wave solution
True Rayleigh waves, which exist on the surface of an elastic half space in a vacuum, are non-attenuative, so intuitively, as the coating density and wave velocities tend toward zero, we expect the leaky Rayleigh-like wave to have less attenuation (leak less). In contrast, as the density and wave velocities in the coating material increase, we expect the leaky Rayleigh-like wave to couple better to the coating so more energy will leak away, attenuating the interface wave. This is the case in the Rayleigh region at the top of Fig. 2. Alternatively, we may plot the attenuation (in dB/m) for the leaky Rayleigh-like wave by considering the imaginary component of the solution to the Stoneley wave equation. This is plotted in Fig. 3. When the two materials become more dissimilar in either density or wave velocity [move left or up in Fig. 3(b)], the attenuation decreases. Likewise, the attenuation increases as the materials become more similar in material properties.
FIG. 3. (Color online) (a) Normalized velocity, c/cR, and (b) attenuation (dB/m) of leaky Rayleigh-like waves at 1 MHz for materials with a Poisson’s ratio of 0.25. Bostron et al.: Interface waves at a soft-stiff boundary
TABLE I. Parameters for the SAFE method with absorbing regions (AR) used to calculate the solution for a leaky Rayleigh-like wave at 1 MHz. Layer 1 2 3 4
Material
Density (kg/m3)
cL (m/s)
cT (m/s)
Thickness (mm)
Number of elements
Coating-AR Coating Steel Steel-AR
1300
1500
675
7870
5770
3190
3.48 1.74 8.85 8.85
26 14 18 18
From Fig. 3(a), it is also clear that there is a similar relationship between the phase velocity and the relative material properties. When the two materials become more dissimilar, the velocity tends toward the Rayleigh wave speed for the dense material. Likewise, the velocity increases as the materials become more similar in physical properties. These two observations relating to attenuation and velocity suggest two potential physically based features that may be used to assess the bond condition of coatings and substrates in this geometry: Amplitude and travel time. Other studies have shown that experimental results match theoretical calculations for Stoneley and interfacetype waves (Lee and Corbly, 1977; Hsieh and Rosen, 1993; Mattei et al., 1997). [The theory has also been developed to describe the existence of interfacial waves for anisotropic materials (Barnett et al., 1985; Destrade and Fu, 2006).] These experiments typically look at metal materials and suggest that these types of interface waves could be used to evaluate bonded joints. In this paper, we expand upon this previous work by exploring the leaky Rayleigh-like wave regime and specifically consider relatively soft and viscoelastic coatings on a stiff steel substrate.
C. Semi-analytical finite element method with absorbing regions
The semi-analytical finite element (SAFE) method was first described by Lagasse (1973). This method uses an analytical propagating wave solution combined with a finite element mesh of a waveguide cross-section to calculate the solutions for guided wave modes that exist in a waveguide. With the advent of modern computational power, this method has gained in popularity over analytical solutions. There are a variety of reasons for this including the ability to model waveguides of almost arbitrary cross-section and the ease with which viscoelastic and anisotropic materials may be modeled. See Hayashi et al. (2003) or Bartoli et al. (2006) for the details of this method and several example problems. We choose to apply this tool for use in describing the propagation of interface waves for two main reasons. First, the handling of viscoelastic materials in the SAFE method is well understood, and the method is reliable because it does not rely on root-searching algorithms (where roots may be missed) to find solutions in viscoelastic waveguides. Second, we can change the waveguide with relative ease if we wish to consider modes in other related geometries, for example, those including an epoxy layer. Additionally, we can consider geometries where either the coating or the substrate is a J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
plate as opposed to a half space. This allows us to check our assumption of an interface wave for finite material thickness. The main alteration from the typical SAFE method formulation in this work is the addition of absorbing regions. These regions absorb outgoing waves to simulate a half space. An absorbing region is made of elements that have a gradual increase in the amount of damping as distance from the waveguide increases. The use of these regions is well understood, and guidelines have been suggested for proper use to ensure that outgoing waves are fully absorbed (see, e.g., Castaings and Lowe, 2008). These regions need to be long enough to absorb the waves at the frequencies of interest but need not be unnecessarily long such that they waste computation time. We verify that our SAFE method calculation with absorbing regions is working properly by comparing the result to the analytical solution. Table I displays the material properties, layer thicknesses, and number of elements used in each layer in the model. For an interface wave propagating at 1 MHz, we find the phase velocity and attenuation to be 2949 m/s and 277 dB/m, respectively. This agrees with the analytical solution to within a tenth of a percent, giving us confidence in our method. Proper use of our method can also be verified by examining the wave structure of the mode. Additionally, the wave structure should be analyzed to determine if the mode will interact with certain defect types. Figure 4 shows the displacement wave structure for a leaky Rayleigh-like wave mode at 1 MHz when a viscoelastic coating (with similar properties to those shown in Table I) is considered. Note that the wave structure in the steel (positive depth) is similar to that of a true Rayleigh wave. Additionally, the coating thickness used in the calculation for Fig. 4 was greater than that shown in Table I so that the leaked waves can be viewed
FIG. 4. (Color online) In plane (dashed) and out of plane (solid) displacement wave structure at 1 MHz for a leaky Rayleigh-like wave at the interface of steel (positive depth) and a viscoelastic coating. Bostron et al.: Interface waves at a soft-stiff boundary
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FIG. 5. (Color online) Sketch showing the coating, steel, and Plexiglas material regions of the FEM. Dark regions at the edge of the model are infinite element regions that are used to reduce end reflections and simulate a half space.
clearly. For this mode, there is a relatively large amount of in-plane displacement (and shear stress) at the interface, which confirms that it should be sensitive to the bonding condition (see, e.g., Pilarski and Rose, 1992). When the coating half space is modeled as elastic or viscoelastic, similar velocity and attenuation values are calculated. The interface wave velocity and attenuation values vary by up to 1%, since the modulus values are a function of the assumed attenuation values. However, when the viscoelastic model is applied to such problems as a thin coating layer on a half space or a weak interface, the results will be significant. Work is under way on these problems. D. Simulation of wave propagation
Wave propagation was simulated using a twodimensional (2-D) finite element model (FEM) in ABAQUS. The purpose of this model is to study wave interaction and identify potentially useful wave features correlated to bond length. Figure 5 shows a sketch of the model, which contained between 150 000 and 580 000 elements, depending on the material properties used. Four-node bilinear plane strain quadrilateral elements were used such that the largest element dimension was not more than 1/8 of the shortest wavelength of the propagating waves in each material. For this reason, models with lower sounds speed coatings had more elements. Four-node linear plane strain one-way infinite elements were used to simulate a half space and reduce end reflections. The excitation source is a surface pressure with a 1 MHz center frequency, six-cycle Hanning-windowed sine pulse applied to an angled wedge block. The angle is designed to excite Rayleigh waves on the surface of the steel. The waves propagate along the top of the steel surface and convert to leaky Rayleigh-like interface waves when the coating is present. The coating is viscoelastic, so a wave traveling into a thick coating layer is sufficiently absorbed and reflections
FIG. 6. (Color online) FEM displacement during simulated wave propagation. The interface wave interacts with the structure differently during wave propagation through (a) poor and (b) well bonded regions. As time progresses, the wave traveling through the well bonded region is highly attenuated. Light colored regions indicate high displacement (linear scale).
off the top surface do not noticeably affect the propagating interface wave. In the model, the steel and coating layers are 2.5 and 1.3 cm thick, respectively, and the coating length is 9 cm. The bondline in the model is 0.5 mm and six elements thick. The bondline may have epoxy material properties or have the same properties as the coating (no epoxy case). A bondline defect is simulated by dramatically decreasing the stiffness of this region. Changes in bond and defect length are used to develop an understanding of how the interface wave is affected by the bond length. Figure 6 shows a typical FEM wave propagation result. Figure 6 shows wave displacement at several time steps for propagation through poor and good bond regions. At a model time of 22.5 ls, the Rayleigh wave on the steel just reaches the edge of the coating. At 37.5 ls, the interface wave has traveled part way under the coating. There is very little interaction in the debond case, so the wave undergoes little attenuation or other changes. However, for the perfect bond case, the wave interacts strongly with the coating and is clearly attenuated during propagation. The attenuation is due to the wave energy leaking into the coating layer. Note that the leaked wave has relatively low amplitude because the coating is viscoelastic. We will examine attenuation and other waveform features to demonstrate how the FEM data can be used to suggest which physically based features may be useful in detecting bond condition in an experiment. Various models were run with different bond defect lengths, coating stiffnesses, and with/without epoxy bondlines. These materials are described in Table II. Viscoelastic
TABLE II. Material properties used in the finite element model simulation of wave propagation. Material Low-stiffness coating/epoxy Mid-stiffness coating High-stiffness coating/epoxy Steel (HY-100)
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Density (kg/m3)
cL (m/s)
cT (m/s)
aL(x)/x (1/mm)
aT(x)/x (1/mm)
1250 1250 1250 7870
1230 1700 2550 5770
660 900 1350 3190
0.05 0.05 0.05 0
0.25 0.25 0.25 0
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FIG. 7. (Color online) FEM interface wave characteristics: (a) Out-of-plane displacement, (b) amplitude envelope, and (c) frequency content from the low-stiffness coating FEM for bond lengths of 0 (solid), 3 (dashed), 6 (dashed-dotted), and 9 cm (dotted).
material properties were used for the coatings and implemented in ABAQUS using frequency data. Our FEM is conducted in the time domain, so the properties are converted from the frequency to the time domain by ABAQUS using a Prony series approximation. Details for using this method for representing viscoelastic materials in ABAQUS are given by Mu (2008), Chap. 6. For the viscoelastic material properties, we assume an attenuation coefficient, a, which is linear with respect to frequency, (a(x)/x is a constant) and is defined as part of the complex phase velocity cp ðxÞ
¼
1 aðxÞ i cp ðxÞ x
!1 ;
(1)
where cp is the real part of the phase velocity and these variables are dependent on the radial frequency, x. The assumption of a linear attenuation coefficient with frequency has been found to be true for polymer-based materials in the 0.3–5 MHz frequency range by several authors (Barshinger and Rose, 2004; Chan and Cawley, 1998; Baudouin and Hosten, 1996). Figure 7 shows wave characteristics from models with the low-stiffness coating. These data are representative for all of the models run. Figure 7(a) shows the out-of-plane displacement from an interface node from models with different bond lengths. Figure 7(b) shows the amplitude envelope of that displacement signal. Figure 7(c) shows the frequency J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
FIG. 8. FEM interface wave features: (a) Amplitude (solid) and energy (dotted) ratio, (b) pulse width, and (c) frequency ratio calculated from the data shown in Fig. 7.
content of the wave pulse. Figures 7(a)–7(c) provide a foundation from which to extract various features that correlate to bond length. Figure 8 shows several physically based wave features that correlate well to bond length. First, and most clearly, there is attenuation of the wave packet when there is a good bond. This feature is shown in Fig. 8(a) and is discussed in more detail in the following text. The amplitude ratio is calculated using the maximum amplitude from the wave envelope and normalizing by the zero bond length case. The “energy” ratio is calculated in a similar manner, but the area under the envelope is used instead. Second, Fig. 8(b) shows the pulse width calculated from the amplitude envelope of the wave packet. We find that the pulse width, defined by the time between 6 dB down points of the wave envelope from the maximum, increases as bond length increases. Third, we can identify two frequency-related features. The frequency of maximum amplitude from the FFT decreases as bond length increases. A more robust feature may be the frequency amplitude ratio shown in Fig. 8(c). We calculate this feature by taking the ratio of the sum of the frequency content below and above the excitation frequency (1 MHz). An increase in frequency ratio with bond length indicates that high frequencies are preferentially leaked/absorbed in good bond regions. Because attenuation is such a strong feature for this guided wave, we examine it in more detail. We create curves Bostron et al.: Interface waves at a soft-stiff boundary
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TABLE III. Sample characteristics and material properties. Coating material Sorbothane Polyurethane Polycarbonate Epoxy
Color
Density (kg/m3)
cL (m/s)
cT (m/s)
Black Amber Translucent Gray
1300 (62%) 1240 (62%) 1190 (62%) 1300 (62%)
1500 (62%) 1660 (62%) 2080 (61%) 2320 (61%)
700 (64%) 750 (64%) 940 (64%) 1120 (62%)
III. EXPERIMENT A. Sample fabrication and test setup
FIG. 9. (Color online) Amplitude vs bond length for (a) cast coatings (no epoxy layer) and (b) coatings with an epoxy layer. Line type indicates material property at bondline (solid, low; dotted, mid; and dashed, high stiffness), and symbol indicates material property for coating (䉫, low; 䊊, mid; and ⵧ, high stiffness). The material at the bondline plays a large role in determining the attenuation properties of the wave.
similar to Fig. 8(a) for models with different material properties. By normalizing the amplitude by the debond case, we can see how the wave packet is attenuated through interaction with different coatings as it travels through good bond regions. We compare the attenuation of the wave as it travels in each of the following cases: (1) Low-stiffness coating (no epoxy), (2) mid-stiffness coating (no epoxy), (3) highstiffness coating (no epoxy), (4) mid-stiffness coating with low-stiffness epoxy, (5) high-stiffness coating with lowstiffness epoxy, (6) mid-stiffness coating with high-stiffness epoxy, and (7) low-stiffness coating with high-stiffness epoxy. The result of this analysis is shown in Fig. 9. As bond length increases, the amplitude-related feature clearly decreases in all cases. This decrease is relatively constant with distance (dB/m). Moreover, the results shown in Fig. 9(a) support what we would expect from the SAFEM and analytical analysis, where the highest stiffness coating (most similar to steel) attenuates at a higher rate, while the least stiff coating (most dissimilar to steel) attenuates at a much lower rate. However, when the epoxy layer is added [Fig. 9(b)], we find that the attenuation feature is dominated by the stiffness of the epoxy as opposed to the coating material. This is because the wave traveling in the steel leaks energy based primarily on the material in direct contact with the surface. Even though the epoxy layer is relatively thin, it will dominate because it is in direct contact with the steel. (It appears that the result for the high stiffness material flattens out near 35 dB. However, additional models were run with over-dimensioned boundary conditions to confirm that this effect is due to the reflections generated from non-quiet “infinite element” boundaries in the FEM.) 4356
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Three different coating materials, each 2.5 cm thick, were studied for this paper (see Table III). The polyurethane and polycarbonate samples were bonded to the steel plate using a two part “SHT Material” epoxy from United Resin Corporation. The epoxy was a moderately viscous liquid when heated and took about a week to cure at room temperature. After the cure, the epoxy thickness was measured at the edge of the coating. In most places, the final bond thickness was between about 0.3 and 0.5 mm except near a couple corners where the coating lifted-off from the steel. Before bonding the materials, the steel surface was grit blasted and primed using Formula 150 or 153 Polyamide Epoxy primer; the polyurethane was roughed and primed as well. Both the polyurethane and polycarbonate materials were bonded to the primed steel surface using the epoxy. Sorbothane is a very soft polyurethane and is quite tacky (e.g., when cut, it will “self-heal”). No epoxy was used to bond the Sorbothane coating to the metal, but the Sorbothane was pressed onto a clean surface to simulate a bond. Additionally, due to this tacky property, a 3 mm (1/8in.) thick piece of Sorbothane was used to simulate a lowstiffness bondline with the polyurethane and polycarbonate coating materials. A stair-step shape was chosen for the samples to gain a variety of bond lengths in a small part size. The strategy we employ is to first understand the relevant wave features that correlate with bond length before searching for hidden defects. Pictures of several of the samples are shown in Fig. 10. There was an issue bonding the polycarbonate sample because the surface of the polycarbonate was not prepared properly. This caused large, visible (because the polycarbonate is transparent) defect regions at the epoxy-polycarbonate interface. In experimental tests, polystyrene wedge blocks were used to excite Rayleigh waves on the steel surface. An angle of 53 was chosen to excite guided waves according to Snell’s law sinhwedge sinhGW 2355m=s ¼53 ; ¼ ) hwedge ¼ sin1 2948m=s cL;wedge cp (2) where hGW ¼ 90 for guided waves, cL;wedge ¼ 2355 m/s for polystyrene, and cp is the phase velocity of the guided wave mode we wish to excite. This phase velocity is the Rayleigh wave velocity in HY-100 steel, 2948 m/s. Note that this angle corresponds to the center velocity of the range of Bostron et al.: Interface waves at a soft-stiff boundary
and receive electronic signals. GE Krautkramer Benchmark Series SWS Style 1.0 MHz/1.0 in. (2.5 cm) diameter transducers were excited with a 100 V, four-cycle tone burst. The wave speed of the propagating wave packet on the primed steel surface was measured to be within 0.5% of the Rayleigh velocity, giving us confidence that we were exciting the intended guided wave mode. B. Experimental results
FIG. 10. (Color online) (a) Epoxied polyurethane sample, (b) polycarbonate sample with sorbothane “bond,” and (c) experimental setup. Angled wedge blocks were used to excite and receive Rayleigh waves on the steel surface in T/T mode.
velocities excited due to the finite transducer size. The range of phase velocities excited is larger than the change in velocity due to the minor amount of dispersion that the wave contains. These waves travel along the coating-steel interface and are received in a through-transmission (T/T) mode, as shown in Fig. 10(c). GUIDED WAVE WORKSTATION (FBS, Inc.) generalpurpose lab measurement software and a 300 V peak-to-peak tone burst pulser and A/D converter were used to generate
FIG. 11. (Color online) Experimental interface wave characteristics: (a) Voltage signal, (b) amplitude envelope, and (c) frequency content for waveforms from the polycarbonate-epoxy-steel sample for bond lengths 0 (solid), 3 (dashed), and 5.5 cm (dashed-dotted). J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013
Data were collected on epoxied polyurethane and polycarbonate samples and sorbothane bondline polyurethane, polycarbonate, and sorbothane samples. In this section, the same calculations are performed for the experimental data as were calculated for the FEM data in Figs. 7–9. Similar trends are shown, validating our model and describing a set of useful features correlated with bond length that can be used for bond inspection. Figure 11 displays data from interface wave propagation in the polycarbonate-epoxy-steel sample. Data from this sample were chosen because they are representative of data with clean signals and feature trends with little scatter. Figures 11(a)–11(c) show the voltage signal, waveform envelope, and frequency content of the received wave. Figures 12(a)–12(c) show several physically based wave features which correlate well to bond length. We notice that attenuation is again a dominant feature affecting the wave packet. This is expected because the epoxy used has similar properties to the high-stiffness material used in the model. The
FIG. 12. (Color online) Experimental interface wave features: (a) Amplitude ratio, (b) pulse width, and (c) frequency ratio calculated from the data shown in Fig. 11. Bostron et al.: Interface waves at a soft-stiff boundary
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cast coating, will allow for a longer inspection distances because the wave will undergo less attenuation per distance. However, in that case, the attenuation-related features vary more slowly with change in bond length, suggesting that the minimum detectable defect size may be larger. It is suggested to always take measurements at a short enough distance that detectable signal amplitudes should be received to avoid the risk of confusion between a good bond and a testing device which is not functioning properly. FIG. 13. (Color online) Amplitude vs bond length for epoxy-bonded coatings (dashed trendline) and coatings with sorbothane bondline (solid trendline). Symbols indicate the coating material (䉭, sorbothane; 䊊, polyurethane, and ⵧ, polycarbonate).
pulse width and frequency ratio features both increase with bond length, as shown in the model. Figure 13 shows attenuation-related feature data from all of the samples. Trend lines for the epoxy (dashed) and sorbothane (solid) bondline samples are shown. It is clear that the epoxied samples undergo very strong attenuation with distance when compared to the sorbothane bondline samples. The epoxied samples have an attenuation feature of about 6 dB/cm, which is similar to the 4.5–6 dB/cm shown in the model for the high-stiffness coating [see Fig. 9(b), dashed lines]. The sorbothane bondline samples show an attenuation feature of about 0.7 dB/cm, which is a bit less than the 1–2.5 dB/cm shown in the model [see Fig. 9(b), solid lines]. The difference could be due to the non-perfect bond condition created by the sorbothane on the primer, which would lower the bond strength and cause a smaller attenuation. We believe the flattening of the epoxied sample data near 45 dB is due to “coherent noise” from wave reflections off of the bottom of the finite sized steel plate. This effect was confirmed by FE models without absorbing boundaries. In Fig. 13, there are several data points located at zero bond length and between 0 and 3 dB normalized amplitude. These data points are the measurements where the wave traveled along a defect region of the epoxy bond in the polycarbonate sample. In the previous section, we mentioned that the polycarbonate sample had a large visible defect. This defect region is clearly detected using the amplitude ratio feature of the wave. This defect region would have been visually hidden had the coating material (polycarbonate) not been transparent. This bonding “mistake” during fabrication turned out to be useful in that it demonstrates the ability of the guided ultrasonic interface wave to locate and identify hidden defects. Additionally, the boundary between wellbonded and not bonded epoxy regions may be detected in a pulse-echo mode when the transducer is aligned nearly perpendicular to the boundary. This method shows promise for “mapping” the boundary of a well-bonded region but must be examined further in future work. The general attenuation effect shown in Fig. 13 suggests that a workable inspection distance could be defined based on the epoxy/bondline properties and measurement configuration/system. In general, a less-stiff epoxy, or low stiffness 4358
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IV. CONCLUDING REMARKS
In this paper, guided ultrasonic interface waves at a softstiff boundary were described. The wave velocity and attenuation characteristics for different material property combinations were calculated using the Stoneley wave equation. Finite element wave propagation studies have been used to simulate wave propagation and demonstrate the effect of different coating and epoxy property combinations. Experimental tests were conducted with polymer coatings epoxied to 2.5 cm thick steel to demonstrate the feasibility of using these waves to evaluate the bond between coatings and metal structures. These tests validated the model results and show several physically based wave features that are correlated to bond length, including amplitude ratio, pulse width, and frequency ratio. These features show great promise for bond evaluation and the identification of hidden defects using interface waves in a nondestructive evaluation approach. ACKNOWLEDGEMENTS
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