© The Author(s), Published by EDP Sciences, 2023

1 Introduction

Laminated glasses are used in many fields like architecture, automotive, solar panels, and other applications requiring additional features and properties such as aesthetic or safety enhancement. Essentially, a laminated glass consists of two or more glass plates bonded by a thin adhesive interlayer, mostly of polymers like polyvinyl butyral (PVB) and ethylene vinyl acetate (EVA) [1]. In a laminated glass, the primary purpose of the interlayer is to bond multiple glass plates into a single pane. However, the layer also serves other design objectives, such as improving structural strength, retaining fragments upon breakage, and adding colors or textures. Adhesion strength depends on many factors, such as the materials, curing pressure and temperature, cleaning process, and moisture content.

An inspection procedure becomes necessary to ensure that the laminated glass meets and maintains consistency with the stipulated specifications, including the bonding quality of the laminates. In evaluating the adhesion strength, the challenge is that the standard inspection procedures involve destructive testing by tensioning, peeling, and most commonly by pulverizing into fragments, known as Pummel test [1–3]. Investigators have been working on developing non-destructive techniques to overcome the challenge. One is an acoustic method that utilizes ultrasonic guided waves [4–6]. Guided waves has already been known as an efficient method to detect debonding of multilayered structure through several approaches such as analysis of reflected waves [7], nonlinearity behavior [8], and the occurrence of mode conversion [9]. Consequently, engineers and researchers have already been familiar with the technique and apparatus for this kind of investigation. However, adhesion strength evaluation is a distinct case since all the bonded components remain intact without the presence of discontinuity due to layer separation, thus researchers need to tackle this problem differently. More specifically, an approach through the analysis of velocity and attenuation of Lamb waves has also been developed for evaluating the adhesion in laminated glass [10, 11]. Investigations such as those described in the aforementioned references are done through pitch-catch experiments. The damage indicators are extracted by processing the received signal to analyze the time and frequency domain parameters including, but not limited to, the speed of sound, attenuation, and harmonics.

Because of the ubiquitous availability of phased array transducers in facilities applying ultrasonic NDT in production, the use of bounded beam effects for certain investigations is inviting. One of such effects is Schoch effect. As a proof of concept, in this work we use acousto-optic Schlieren imaging to study the Schoch effect, or reflected beam displacement, on the glass plates of interest, because it allows clear visualization of the effect interesting for such a study. In practical situations however, the use of a phased array transducers would be more convenient, more compact and could be done by engineers experienced with the devices, rather than a requirement to incorporate acousto-optics and corresponding expertise in the production chain.

This proposed technique based on Schoch effect observation does not require signal processing and analysis since the discrepancy in adhesion strength is indicated directly by the appearance, the extent, or the absence, of a non-specular reflection lobe read by the phased array receiver. Thus, it allows a straightforward interpretation and demands less computational power, aside from the phased array controller. Another advantage of this technique is that the affected area is a point rather than a line, as in the conventional pitch-catch Lamb waves experiments, which, nevertheless, have proven their worthiness [12]. Therefore, it is possible to make a high-resolution point-by-point scanning, for instance, to evaluate the uniformity of adhesion level over the whole plate of laminated glass. The technique, therefore, harvests the best of point-by-point scanning as would be undertaken in C-scans, and the Lamb wave sensitivity to the adhesion layer as exploited in references [4–6, 10, 11].

In the present work, we describe a Lamb waves technique for evaluating the laminated glass adhesion strength. Instead of implementing a conventional pitch-catch experiment, we exploit the Schoch effect to detect the propagating Lamb waves by calculating the velocity based on the incident angle. A Schlieren imaging setup is utilized to facilitate the measurements in this work. With this method, one may characterize the adhesion level of a point in a laminated glass through visual inspection of the Schlieren image and measuring the angle of incidence.

2 Schoch effect for observing Lamb waves characteristics associated with interlayer adhesion

The displacement effect of ultrasonic bounded beams, as described by Schoch [13], is a lateral shift of a reflected acoustic beam upon total internal reflection, such that the reflected beam departs at an offset, on the interface plane, from the point where the incident beam hits the interface. It, therefore, differentiates this particular circumstance from the typical specular reflection in which the reflected beam leaves the interface from the exact point where the incident beam arrives. Schoch attributed this displacement to the condition when the trace velocity of the incident waves is equal to the velocity of Rayleigh waves on the surface; hence it takes place at the Rayleigh angle. A similar effect, however, also occurs for plates, when Lamb waves are generated, which is exploited in the current paper. The analysis for the effect caused by Rayleigh waves or Lamb waves is, nevertheless, the same. Brekhovskikh [14] discusses Schoch’s work with extensive explanation of the displacement, Δ_s, and is given by Equation (1):

$${\Delta }_s=-\left(\frac{\mathrm{\partial }\varphi }{\mathrm{\partial }{k}_p}\right),$$(1)

where the phase, ϕ, is obtained through Equation (2),

$$\varphi =2h\sqrt{(k^2-k_p^2)},$$(2)

where h is the distance from a point on a beam to the plane of the interface, k is the wave vector, and k_p is the projection of the wave vector on the plane of the interface. Note that k_p is essentially a vector component along the surface that will match the wave vector of the Rayleigh wave, through Snell’s law. In his book, Brekhovskikh goes on to show how the displacement effect is carried over into the mathematical analysis of the beam’s energy flux, concluding that as the beam displacement increases, so does the energy flux of the reflected beam.

Nevertheless, Bertoni and Tamir [15] later rectified Schoch’s concept by pointing out that his model only took into account the interferences of plane waves involved in specular reflection and did not explicitly include the contribution of leaky Rayleigh waves (or, in our case, leaky Lamb waves). On the other hand, their theory attributed the phenomenon to the superposition of specular and leaky waves. Hence, they could explain not only the beam displacement but also the existence of a null field in the reflected beam that causes the appearance of multiple lobes. In addition, they also revealed that Schoch’s displacement, in Equation (1) holds only if the beam width is more than 5 times the displacement itself. Although, as already indicated, those theories are developed for Rayleigh waves, they are also pertinent to other leaky waves that travel along the plane of the reflecting interface, which in the case of this paper, are Lamb waves.

Since the beam displacement effect is linked to leaky waves propagating in the solid on which the beam is reflecting, it can be used to characterize the waves in question. In this work, a bounded ultrasonic beam excites Lamb waves in laminated glass plate specimens with a different adhesion strength of their interlayer. As Lamb waves’ behaviors depend strongly on the structure’s material properties, our samples are made so that all layup materials and thicknesses are identical across specimens. Thus, the adhesion strength of the interlayer becomes the parameter that determines the waves’ characteristics. In other words, the adhesion level of the interlayer will, in turn, affect the displacement of the reflecting bounded beam.

In the investigation on the interlayer adhesion strength of laminated glass, Huo and Reis [10] have demonstrated that the adhesion level affects the velocity of a Lamb mode at a given frequency. They found out that a higher phase velocity of a Lamb mode indicates a more robust adhesion level, which they benchmarked against an industrial-standard measure of laminated glass adhesion strength, namely the Pummel test. Huo and Reis also approached their analysis from the wave attenuation aspect [11], where they found that the attenuation of the propagating Lamb waves increases with the adhesion level. In their works, they utilized a numerical simulation program, Disperse™, to study the mode shape and power flow in the structure to explain how interlayer properties influence the velocity and attenuation of the propagating waves. Still, Huo and Reis depend their measurements on a pitch-catch setup, therefore causing average adhesion values over a given distance, which is what our work avoids by applying a local acousto-optic measurement.

Here, we built our technique upon those concepts. The adhesion strength of the interlayer will determine the velocity of a Lamb mode. That velocity dictates the angle of incidence at which beam displacement phenomena occur because the said Lamb mode is excited at such an angle where the component of incident beam velocity parallel to the interface plane matches the velocity of the mode. Eventually, one can deduce the relative adhesion strength between similar laminated glasses by emitting a bounded beam onto the laminated glass at a known angle that excites a particular Lamb mode and observing the variation around that angle. If the variation is towards the smaller value of the angle, i.e., the mode velocity is higher, then the adhesion is more substantial, and vice versa.

3 Experiment

Three samples of laminated glasses are investigated. According to the manufacturer’s product datasheet, they are made up of identical glass panes but with different adhesion strengths. Those three laminated glasses are from the same product line with identical glass plates and PVB (polyvinyl butyral) interlayer materials and thicknesses. Nevertheless, the manufacturer marketed this product line in various variants based on the interlayer adhesion strength to offer the users choices depending on their requirements. For instance, safety-concerned automotive windshield glasses require a higher adhesion level than decorative ones for architectural installations. The strength of adhesion is a function of several variables in the manufacturing process, including temperature, pressure, bonding time, surfaces’ cleanliness, and the polymer’s quality [16]. In this investigation, the examined glass samples are designated with numbers 1–3 in the increasing order of adhesion strength. Hence Sample 1 is the lowest, Sample 2 is higher than 1, and Sample 3 is the highest. However, the datasheet does not disclose any quantitative measure of the adhesion strengths.

During the experiment, a specimen is immersed in water and irradiated with an ultrasonic beam of 10 mm width at a fixed angle. An ultrasonic Schlieren apparatus, as illustrated in the schematic in Figure 1, resembling the one described in references [17, 18], is employed to visualize the beam. The same setup has also been used in other works for investigating single-layer aluminum and glass plate and yielded satisfactory results in creating and visualizing the Schoch effect [19]. In the setup, a parallel laser beam is passed across the incident and reflected ultrasound paths, where it underwent acoustic–optical interaction due to diffraction by the ultrasonic waves. The Schlieren technique removed the undiffracted light from the beam, so only the diffracted light is projected onto the screen. The resulting image is a Schlieren image, in which the light intensity represented the sound intensity. A transducer is attached to a mechanism that allowed adjustment of the angle of incidence of the ultrasonic beam. As the angle is being adjusted in small steps during the experiment, any phenomenon that occurred to the ultrasound beam could be continuously monitored on the screen.

Figure 1 Schematic of the Schlieren setup employed in this work.

As performed in our experiments, acousto-optic Schlieren imaging with a HeNe laser of sound in water works best in the frequency range of 2–20 MHz, with optimal frequencies around 9 MHz. However, using a lower than 9 MHz frequency for Lamb waves investigation is more suitable to avoid exorbitant attenuation. Therefore, we opted for a 3 MHz transducer as a trade-off between the desired ultrasound frequency for the NDT purpose and that which will deliver the best visualization in the acoustic–optics Schlieren imaging. In addition, frequencies of around 3 MHz are also standard in the industry and phased array transducers that work within that range are widely available in the market.

We mainly focus on the Schoch effect, where non-specular reflected sound emerges from Lamb waves generation in the plate. Upon the occurrence of the Schoch effect, the reflected beam, as shown in the Schlieren image in subsequent figures, consists of lobes shifted parallel to the glass plate.

4 Numerical simulation of propagating Lamb waves

To estimate the Lamb modes that propagate at the occurrence of the Schoch effect, theoretical dispersion curves of the corresponding structure are calculated using Disperse™, a guided waves simulation software [20]. The software employs a global matrix method representing the layered system as a single matrix. The matrix contains the relation of stresses and displacements in each layer through Hooke’s law, Euler’s, and Navier’s equations of motion. The dispersion curves are assembled from points determined by finding the root of characteristic equations, i.e., the points that create zero value of the matrix determinants. To simulate mode shape and energy flow, the program calculates amplitude, stresses, and displacement with finite element procedures [21].

Our laminated glass specimen is modeled as a three-layer structure consisting of two soda lime glass plates bonded by a PVB interlayer between the glasses, as illustrated in Figure 2. The thickness and mechanical properties of constituent layers in the model are taken from the product datasheet that came with the glass plates purchased from the manufacturer.

Figure 2 Illustration of the laminated glass structure.

Since the glass and the PVB polymer are isotropic mediums, Disperse™ two-dimensional infinite plate model is sufficient to represent the problem. In addition, the multilayered plate is a symmetric structure, which improves computational efficiency. The mechanical properties of materials as input parameters for the simulations are listed in Table 1. Recall that the properties are the same across the samples, only the process-dependent adhesion strengths are different. Thus, the simulation provides the result in an ideal bonding condition.

5 Results and discussions

In the experiments, the Schoch shift is observed on the Schlieren imaging screen at several angles of incidence, exhibited in Figures 3–5 for each tested sample. The images in Figures 3–5 are obtained as follows: the angle of incidence is adjusted manually until the Schlieren image shows a beam displacement or multiple lobes. Consequently, the angle is fine-tuned to see the best visible result with the best optical contrast. Each time such an angle is found, the image is captured with a camera for further analysis. The respective angles of incidence are extracted geometrically from the obtained images.

Figure 3 Schlieren photographs of Schoch effect on sample 1.

Figure 4 Schlieren photographs of Schoch effect on sample 2.

Figure 5 Schlieren photographs of Schoch effect on sample 3.

The angle when the non-specular lobe appears defines the velocity of the excited Lamb waves mode, calculated through Snell’s law:

$$v_{\mathrm{mode}}=\frac{v_{\mathrm{water}}}{\sin \theta },$$(3)

where v_mode is the velocity of the excited Lamb mode and θ is the angle of incidence of the ultrasonic beam. In this experiment, the velocity of sound in water (v_water) is 1479 m/s. Measurement uncertainties of v_water and θ are 1 m/s and 0.1°, respectively. From Equation (3), we can estimate the errors in calculated v_mode based on those uncertainties by computing its partial derivatives as given by Equation (4) below:

$$\Delta v_{\mathrm{mode}}=\left|-\frac{v_{\mathrm{water}}}{(\sin \theta {)}^2}\right|\Delta \theta +\left|\frac{1}{\sin \theta }\right|\Delta v_{\mathrm{water}}.$$(4)

To determine which mode is excited at the angle where the Schoch effect appears, the calculated velocity is compared with the dispersion curves generated by Disperse™. The estimated modes have velocities close to the calculated values obtained from Equation (3). Since the ultrasound emission is at 3 MHz, the velocity matching to find the modes in question is made at frequency f = 3 MHz, as depicted in Figure 6 and tabulated in Table 2.

Figure 6 (a) The points along f = 3 MHz indicate the velocities at the angle of incidence where the Schoch effect appears. The error bars represent the estimated errors by measurement uncertainties (0.1° for the angle and 1 m/s for the sound velocity in water). (b) The enlarged area around A6, A5, and S3, for the clarity of points’ locations. (c) to (g) Further magnification shows snapshots of groups of points predicted to correspond to each mode. Note that in figures (c) to (g), the plots are not to scale in terms of velocity (vertical) axis from one snapshot to the other since the primary purposes are to show the relative positions of points and the variance of the angle of incidence at which the Schoch effect appears.

In Table 2, there are some instances where two different angles are assigned to the same mode. We associate this occurrence with the experimental practice carried out to obtain the angles, as explained at the beginning of this section. In most cases, a distinctive beam displacement is visible. Still, the experimental procedure is undertaken meticulously to include every angle where the effect is observable, even when unclear. In some cases, however, we observe that the onset of a displacement is visible at a particular angle. Then the effect is not observable for increasing angle until it is again visible at a slightly larger angle. Therefore, two angles are extracted in this case as if they are two distinct phenomena. As can be seen, compared to the dispersion curves, they must have been the onset and the end of the same phenomenon while increasing the angle of incidence. Meanwhile, the actual angle of occurrence does not deliver a visible effect on the projection screen of the Schlieren set-up. This situation is apparent in Sample 1 for modes S8 and A6, Sample 2 for modes A6 and A7, and Sample 3 for mode S8. We can see two data points at a slight angular distance apart for the same mode. Assuming that the effect appears perfectly in the middle of the two observations, then that average angle perfectly matches the dispersion curve.

The data points at the higher phase velocity regime in Figure 6a do not present a particular pattern. Near mode S8, in Table 2 and Figure 6c, the Schoch effect appears at two angles for Sample 1 (4.9° and 5.0°) and Sample 3 (4.8° and 5.1°). Following the angle averaging rationale described in the previous paragraph, the expected angles are 4.95° for both samples. For the other specimen, Sample 2, the angle corresponding to S8 is 4.9°. That 0.05° difference is smaller than the prescribed angle measurement uncertainties of 0.1°, Therefore, no noticeable tendency can be deduced from those points around S8. Likewise, mode S7 is not helpful for comparison because only one sample (Sample 2) responded to that mode. Nevertheless, the locations of data points of Sample 2 for S7 support the angle averaging argument since the average of both points is close to the calculated curves, as shown in Figure 6d.

More visible tendencies are exhibited in the lower phase velocity regime, which portion is enlarged in Figure 6b. In that region, a particular order of the phase velocity of each sample is readily noticeable. At the same predicted mode, Sample 3 has the highest velocity, followed by Sample 2 and 1, respectively. In Figure 6e, which snapshots the area around A6, Samples 1 and 2 share the same point at 13.6°. Nevertheless, there are other points for each sample that, if averaged with that shared angle value, the stated order from highest to lowest holds: Sample 3, Sample 2, and Sample 1.

Considering that all the dimensional and material parameters are identical across the samples, the only differentiating factor is the adhesion strength level. Based on Huo and Reis’s investigation in [10], the relative magnitude of phase velocity describes the interlayer adhesion strength of a laminated glass of the same kind. Accordingly, we conclude, based on the present local acousto-optic method, that the order of adhesion strength level for our samples, from high to low, is Sample 3, Sample 2, and Sample 1, which also agrees with the expectation we had when we purchased the samples. In addition, we have also found that the modes sensitive to interlayer adhesion strength in our specimens are modes A6, A5, and S3.

Upon inspection of the Schlieren photographs in Figures 3–6 and correlating to the order of adhesion level of each sample as discussed in the preceding paragraph, we observe two significant phenomena related to the beams’ appearance. One phenomenon is that the width and intensity of the second lobe tend to decrease with the level of adhesion. To quantify the beam width and intensity from the image, we employ a software named ImageJ [22, 23]. It is an open-source scientific image-analysis software supported by the US National Institutes of Health (NIH). The beam profile is measured along the line parallel to the glass surface at a distance of 50 mm, as shown in Figure 7a. The software returns the profile along that drawn line as a gray value, i.e., a measure of pixel brightness we take as beam intensity. From the profile, the intensity of each beam extracted is normalized against the intensity of the incident beam in the same image. Hence the value is always unity for the incident beam, as seen in Figure 7b.

Figure 7 Illustrations: (a) Obtaining beam intensity profile on a line parallel to the glass surface at an offset of 50 mm. (b) Extracting beams’ relative intensities and widths, where the gray value in the vertical axis signifies the intensity of a pixel in the image. The width is taken at half of the corresponding beam’s maximum intensity (full width at half maximum, FWHM).

The lobes’ relative intensity, i.e., the intensity of lobes relative to that of the incident beam, for each mode and sample are presented in Figure 8. Note that we only take modes A6, A5, and S3 for the analysis because we have already concluded that the other modes (S8 and A7) are not sensitive to adhesion properties. By recalling the previous finding that the order of adhesion strength from low to high is Sample 1, Sample 2, and Sample 3, respectively, one can see that for mode A6, it is evident that the intensity of Lobe 2 decreases with the increased of adhesion strength. Meanwhile, in mode S3, the intensity rank of Lobe 2 for Sample 1 and 2 are not exactly like that in A6, Sample 3, as the specimen with the most robust adhesion stays at the lowest intensity. A zero intensity for Lobe 2 in Sample 1 for mode A5 is because only one reflection lobe is detectable at the specified measurement distance. The possibility is that the null field between the first and second lobes is so narrow that both are merged and shown as one lobe. It is also possible that there is no null field in that region since the superposition of the specular reflection beam and leaky waves, as described in ref. [15], does not result in zero intensity in that spatial range. A small lobe appearing in the image (Fig. 3 at 17.2°) does not extend to 50 mm at a detectable intensity. That small lobe may also be the weaker subsequent (third) lobe, as it appears faintly in other cases. Overall, the sample with the most robust adhesion, Sample 3, returns a lower-intensity reflection.

Figure 8 Relative intensities (ratio of the intensity of a lobe to that of the incident beam) for modes A6, A5, and S3.

The width of the beam is calculated based on the full width at its half-maximum intensity (FWHM). The FWHM approach is taken because it could resolve all the beams at the specified distance, except for Sample 1 at 17.2° where the second lobe is not detected. Measuring the beam width at a higher intensity level is not convenient because there are ripples near some peaks. Measuring it at the lower part of the beam would cause difficulties in resolving adjacent beams since some are merged just below the 50% intensity of one of the beams. To allow comparison of the beams from different images, the relative width value is expressed as the lobe-to-incident beam width ratio in the same image. The magnitudes of lobes widths are plotted in charts in Figure 9, from which one can infer that the width of Lobe 2 is generally shrinking for the samples with higher adhesion strength. Again, the presence of a zero value in Sample 1 at 17.2° for mode A5, plotted in Figure 9b, is because the first two significant lobes are not resolvable at the observation line, as previously explained for the same phenomena in terms of intensity. This hypothesis is also supported by the evidence that, in that case, the width of Lobe 1 is more than 20% larger than the incident beam, at the amount still reasonable for being the sum of Lobe 1 and Lobe 2 widths.

Figure 9 Relative width (ratio of the width of a lobe to that of the incident beam) for modes A6, A5, and S3.

An analysis of the physical characteristics of waves propagating in the structure is required to understand the drop in intensity and beam width of the non-specular lobes above. As also described by Huo and Reis in [11], the adhesion level is a laminated glass’ property that affects wave attenuation. The attenuation is associated with power flow distribution and displacement at the interlayer interface region. To further describe it, we select modes A6 and S3 for analysis because they have no data point with zero value in both lobe width and intensity as mode A7 does; see Figures 8b and 9b. The physical characteristics of those modes, simulated in Disperse™, are presented in Figure 10. In the interface region, there is a gradient of particle displacement and wave energy flow, creating shear stress on the glass-PVB interfaces. Higher adhesion strength induces more resistance within the shearing interface, producing higher attenuation to the propagating waves.

Figure 10 Power flow, particle displacement distribution and mode shape of (a) S3 and (b) A6.

From the theoretical point of view pertaining to the appearance of the beams, we correlate the impact of attenuation through the superposition theory established in ref. [15], stating that the reflection field (v_refl) is the sum of specular field (v₀) and leaky waves field (v₁), as expressed in Equation (5). There, the x-axis is parallel to the surface and the z-axis is normal to it.

$$v_{\mathrm{refl}}\left(x,z\right)=v_0\left(x,z\right)+v_1\left(x,z\right).$$(5)

The specular field is the product of the incident wave field (v_inc) and the reflection coefficient (R₀):

$$v_0\left(x,z\right)=R_0{v}_{\mathrm{inc}}\left(x,z\right),$$(6)

and the leaky wave field is given by:

$$v_1\left(x,z\right)\simeq -\frac{4}{{\Delta }_s}\sec \theta \cdot \exp \left[{\left(\frac{w_0}{{\Delta }_s}\right)}^2\right]\cdot \exp \left[i\left(k_x\sin \theta +\mathrm{i\alpha }\right)x\right],$$(7)

with θ the angle of incident and leaked waves, Δ_s is the Schoch displacement as described in Equation (1), w₀ is one-half of the incident beam width, k_xsinθ is the leaky wave component, and α is the attenuation parameter. Although in the analysis a lossless structure is assumed, in which the decay is caused only by the guided waves’ energy radiation (leakage), the appearing attenuation, α, is due to inherent elastic properties and defects embedded in the structures on top of the radiation loss.

Besides, in ref. [15], a reflection coefficient, R₀, diminishes with the increase of medium’s loss parameter at the angle of incidence around which the leaky wave is excited, in their case, the Rayleigh angle. Since attenuation reduces both specular and leaky wave fields, their superposition will also decrease, particularly in the far field. Note that the decrease in intensity does not always lead to a smaller beam width because the width is calculated based on the span measured at half of a beam’s maximum intensity, regardless of the intensity level. Meanwhile, the superposition resulting from Equation (5) may produce a beam profile with lower intensity but spans over an extended length. It is particularly true in the near field where the intensity is still sufficiently strong. Nevertheless, the measured beam width shrinks accordingly in the far field on the plane of the surface (or x-axis), where the intensity has considerably weakened. It explains the decline in intensities and Lobe 2 widths in the sample with stronger adhesion, which means higher medium attenuation.

Another critical notion in Figure 6 is that the data points around A6 have broader gaps between each other, using the averaging approach, compared to those near A5 and S3. Thus, it is easier to detect the variation in adhesion level by using the A6 mode. In other words, that mode is the most sensitive to adhesion strength among all propagating modes observed in our investigation. The higher sensitivity of one mode over the other has, in a particular case, also been reported by Huo and Reis [10]. Their observation focuses on the fundamental modes at low frequencies close to 350 kHz, where within that band, the S0 is found to be more sensitive than the A0. The current work, however, observes the high-frequency regime at 3 MHz where the higher order asymmetric mode A6 provides superior sensitivity to adhesion level compared to other excited modes. Analogous to the previous discussion about the attenuation of modes, the sensitivity is attributed to the distribution of power flow and displacement at the interface. As one can readily notice from Figure 10, the gradient of particle displacement and power flow at the region where the interlayer is located, particularly at the interface areas, are more abrupt in mode A6 than in S3. Consequently, any alteration to the interface condition will render a more significant impact on mode A6.

As a practical example of implementing the technique for evaluating laminated glass adhesion strength, the angle of incidence at which the most sensitive mode is excited on a standard reference product must be known first. The excitation of that mode is indicated by the occurrence of the Schoch effect, captured by, for instance, a phased array transducer. Measurement is to be conducted around that specified angle. Suppose the Schoch effect is detected at an angle more significant than the reference for other arbitrary products. In that case, the interlayer adhesion level of that tested product is higher than the reference glass and vice versa.

6 Conclusion

This paper describes the Schoch effect phenomena in laminated glasses through experiments and numerical simulation. The obtained results exhibit the capability of the Schoch effect analysis to examine the adhesion level of the interlayer in laminated glass.

It has been shown that the angle of incidence at the Schoch effect’s occurrence correlates to the level of adhesion in laminated glass. The observed phenomena agree with those that occur in conventional pitch-catch methods, thus confirming the validity. The main difference is that the proposed method is local, in contrast, to pitch-catch methods, and may be better suitable for scanning surfaces to detect adhesive layer variations caused by production or use. We demonstrated the potential of using the Schoch effect for nondestructive evaluations as a valid assessment technique based on the well-established Lamb waves inspection methods. Concerning the beam phenomena, our findings show that the intensity and width of the reflection’s second lobe decrease with the increase of adhesion strength due to a larger attenuation in the interlayer region. In terms of physical behavior of the propagating Lamb waves, the velocity of damage-sensitive modes tends to be greater in samples with higher level of adhesion. That difference in velocities leads to the deviation of angle of incidence at which a particular mode is excited, and consequently, the angle where Schoch effect emerges.

Therefore, based on phased array technology, a nondestructive evaluation system can be envisioned to inspect the quality or uniformity of adhesive bonds by, for instance, measuring the angle of incidence at which the most adhesion-sensitive Lamb mode is excited.

Conflict of interest

The authors declare that they have no conflict of interest in relation to this article.

References

All Tables

All Figures

	Figure 1 Schematic of the Schlieren setup employed in this work.
In the text

	Figure 2 Illustration of the laminated glass structure.
In the text

	Figure 3 Schlieren photographs of Schoch effect on sample 1.
In the text

	Figure 4 Schlieren photographs of Schoch effect on sample 2.
In the text

	Figure 5 Schlieren photographs of Schoch effect on sample 3.
In the text

Figure 6 (a) The points along f = 3 MHz indicate the velocities at the angle of incidence where the Schoch effect appears. The error bars represent the estimated errors by measurement uncertainties (0.1° for the angle and 1 m/s for the sound velocity in water). (b) The enlarged area around A6, A5, and S3, for the clarity of points’ locations. (c) to (g) Further magnification shows snapshots of groups of points predicted to correspond to each mode. Note that in figures (c) to (g), the plots are not to scale in terms of velocity (vertical) axis from one snapshot to the other since the primary purposes are to show the relative positions of points and the variance of the angle of incidence at which the Schoch effect appears.

In the text

	Figure 7 Illustrations: (a) Obtaining beam intensity profile on a line parallel to the glass surface at an offset of 50 mm. (b) Extracting beams’ relative intensities and widths, where the gray value in the vertical axis signifies the intensity of a pixel in the image. The width is taken at half of the corresponding beam’s maximum intensity (full width at half maximum, FWHM).
In the text

	Figure 8 Relative intensities (ratio of the intensity of a lobe to that of the incident beam) for modes A6, A5, and S3.
In the text

	Figure 9 Relative width (ratio of the width of a lobe to that of the incident beam) for modes A6, A5, and S3.
In the text

	Figure 10 Power flow, particle displacement distribution and mode shape of (a) S3 and (b) A6.
In the text