1 Introduction

Composite materials are nowadays widely used in many applications: aero-space, cars, wind turbines and others. The reliability of composite materials is based on the quality of the connection. The realization of good adhesion between metal and polymer can cause problems due to the difference of their surface energy. Most synthetic polymers used commercially have a low surface energy; by contrast metallic coatings have a high surface energy. This leads to low adhesion between the two materials. The key to achieve a strong polymer-metal adhesive connection is to choose materials depending on the type of function groups presented in the polymer and properly prepare its surface [1,2,3,4].

Most testing methods providing information about the strength of the connection between the components in composites cause irreparable damage to the samples tested. Such examinations make it impossible to use those samples for further analysis or (re)utilization and are called destructive testing. It is therefore desirable-or even necessary-to detect hidden defects in layered structures using Non-Destructive Testing (NDT) [5,6,7]. During the production of polymer objects defects can occur inside the polymer, not visible from the outside when the polymer is not transparent. Another problem can arise when different parts are glued together and both parts are not sticking together in all places. A typical example is a polymer strip reinforced by a metal plate, with a local failure of the glue. It is important to check components before, during or after use for defects in such a way that they can be used or reused. A well-established method to study defects in laminates are shearographic and ultrasonic measurements [8,9,10,11,12]. Also Laser scanning Doppler Vibrometry [LDV] is used [9, 13,14,15,16,17]. We studied this type of defects with a digital holographic vibrometer, which can also be applied in a production line. The vibration and phase patterns of metal-polymer samples were analyzed with high spatial resolution and low energy excitation. Digital holographic vibrometry allows to measure amplitude and phase of many points synchronously, in our case more than 250 000, much more than with LDV, which uses typical less than 100 points [9, 16].

2 Experimental

The goal of our research is to detect unknown and invisible defects in polymer-metal laminates. The fact that the defect is unknown makes simulation very difficult and also the clamping of object and piezo transducer has to be taken into account. Simulating nm vibrations on objects with dimensions of cm is, if possible at all, also very difficult, even when the defect is known. We choose therefore to investigate such laminate defects experimentally, using the technique of holographic vibrometry. An advantage of holography is that we can observe the whole surface of a sample simultaneously and synchronously at a large number of surface points. This applies even when observing the upper and the lower sides of a sample and allows e.g. to discriminate between flexural and extensional vibration modes.

2.1 Holographic Vibrometer

An Optonor Vibromap 1000 digital holographic vibrometer [13] was used to test the samples. This instrument uses a frequency-doubled 150 mW Nd:YAG laser with a wavelength of 532 nm as light source.

The instrument is basically a Michelson [18, 19] interferometer set-up. A light beam emitted from this instrument illuminates the object under study. This object is imaged onto a CCD-camera with 640 × 480 pixels. A second beam of the laser is internally send to the camera. The two light beams interfere on the camera and produce a hologram. The use of holography [20,21,22,23] implies that a large number of points (up to 640 × 480 in the case of the Vibromap 1000) can be observed simultaneously and synchronously. The object can be vibrationally excited with a sinusoidally signal transferred by a piezo transducer, PI P-010.00P with a high resonant frequency (129 kHz) [24]. The frequency used by the Vibromap 1000 can be varied from 100 Hz to 25 MHz. The camera is recording at 60 Hz and can therefore only record a time-averaged hologram, averaged over many periods. In such a situation the intensity is a function of the amplitude, described by the Bessel function of the first kind J0 [22, 23].

The excitation conditions (frequency and amplitude) of the sample are provided by a function generator under control of the program "Vibromap" by Optonor. This program also controls the recording of the hologram and is running on a dedicated PC. This control program also allows different recording modes. One of this is "real time", which was used to select appropriate frequencies. The "numerical mode" allows storing the average of several holograms in a Matlab.mat file, containing the amplitude and the phase of the hologram in matrices Ax,y, resp. φx,y for further evaluation. The deflection in each point x, y is given by \({\Delta }_{xy}={A}_{xy}cos\left(\omega t+{\varphi }_{xy}\right)\). The amplitude resolution of the vibrometer is better than one nm. Objects from a few cm2 to one m2 can be studied with this instrument. A scheme of the measurement set-up is given in Fig. 1. In the standard holographic vibrometric set-up (see Fig. 1a) only one side of the sample can be seen during a measurement. For the purpose of this study the set-up was improved to enable observing both sides of a sample simultaneously (see Fig. 1b).

Fig. 1
figure 1

Holographic vibrometric measurement set-up: a top view of a set-up to investigate one side of a sample; b side view of the improved set-up to look at two sides of a sample simultaneously

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2.2 Sample Preparation

In our experiments polyamide 6, injection molding grade, Tarnamid T-27 (supplied by Grupa Azoty, Tarnów, Poland), characterized by a melt volume flow index (MVI) of 120 cm3/10 min at 275 °C, was used. The metal plates were made of non-alloy quality steel 1.0338 (grade DC 04) En 10,130 plates, 1 mm thick.

The polymer strips were produced using an ENGEL 20/80 HLS injection moulding machine with a screw diameter of 22 mm. The temperature profile along the injection barrel was 225–230–240–260 °C and the machine injection pressure was 7 MPa. The injection speed was 90 mm/s.

The steel sheets, with dimensions of 150 × 10 mm (length × width), were first cleaned with ethylene alcohol to remove surface contaminations. The metal and polymer strips were than glued together at ambient temperature with epoxy Araldite 2011.

At the location of the defect the metal and polymer strips can to some extent, dependent on the frequency, vibrate independently; when glued together they influence each other. This results in different vibration patterns at defect locations.

Three different defects were created in the middle of the samples (see Fig. 2):

  • an 18 mm long connection defect across the full width in the middle of the samples

  • one with a 12 mm wide defect and

  • one with a 6 mm wide defect (see Fig. 2).

Fig. 2
figure 2

Two samples with an epoxy glue layer between metal and polymer with a glue defect in the middle of the sample and a detailed picture of part of the lower one

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2.3 Sample Mounting and Excitation

The sample holder constructed allowed observation of both sides of the sample simultaneously (see Figs. 1b and 3). The piezo transducer could be mounted below (polymer side) or on top (metal side) of the sample (see Fig. 4).

Fig. 3
figure 3

Sample mounting system and mirror placement

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Fig. 4
figure 4

Piezo transducer and sample mounting system

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The samples were mounted with two clamps (one on each side of the sample) (see Figs. 1, 3, 4). The excitation was induced by a piezoelectric transducer in direct contact with the surface of the sample mounted in a clamp along with the sample (see Fig. 4). The whole sample holder was mounted on a damped pillar to avoid excitation by external sources as well as avoiding exciting vibrations in the mirrors. The piezo transducer was always outside the part imaged. We registered the amplitude and phase patterns of the vibration of the sample’s surfaces.

2.4 Data Evaluation Software

Several programs were written to extract information about the vibration patterns of the images of our samples from the time-averaged holograms. The programming language used was "R" [25], which is open source and has excellent statistical and visualization facilities and executes much faster then e.g. Octave/Matlab.

These programs were running on a GNU/Linux desktop computer, which allows a more efficient handling of the large amount of data obtained. In R it is easy to extract the matrices describing the amplitude resp. the phase from the.mat files mentioned in Sect. 2.1. The R-packages "EBImage" and "plot3D" were very useful in visualizing features of the vibration patterns, while “pracma” offered some useful mathematics routines. The resulting pictures varied from simple two-dimensional plots of the amplitude and the phase patterns on our samples (see e.g. Fig. 5) to three-dimensional animations. Stills from these animations are also very helpful to study properties of our samples (see e.g. Fig. 6). From the latter we also constructed deflection patterns, averaged over one dimension of our sample (see Fig. 7). All programs offer the possibility to view upper (tv) and under-side (bv) of the sample in one picture or animation, which is useful in comparing both sides.

Fig. 5
figure 5

Amplitude patterns for two samples: left—without a glue defect, right—with a glue defect; excitation frequency 8300 Hz; x and y axes in units of pixels, tv: top view, bv: bottom view (see Fig. 2). The size of the visible part of the sample is 84 × 10 mm2

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Fig. 6
figure 6

3D plot of the vibration pattern at one moment in the vibration cycle; tv: rear part top view; bv: front part bottom view; left—without a glue defect, right—with a glue defect; excitation frequency 8300 Hz; z axis—amplitude in nanometers, x and y axes in units of pixels

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Fig. 7
figure 7

Amplitude [nm], averaged over the y-direction, of two samples for an excitation frequency of 8300 Hz: left—without a glue defect, right—with a glue defect; blue—polymer side (bv); red—metal side (tv); green—difference between metal and polymer amplitude (Color figure online)

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3 Results

3.1 Detection of a Defect

The repeatability of the resonant frequencies and spatial distributions of vibrations with amplitudes in the range of nanometers were examined. All samples were tested in the same frequency range (200–125 000 Hz, limited by the available piezo-transducer) to determine resonant frequencies. The resonant frequencies and spatial distributions of vibrations were highly repeatable.

The quality of the connection between metal and polymer (see Sect. 2.2) was tested. A clear difference in the amplitude pattern was found between samples without and with a glue defect (see Figs. 5, 6, 7). Samples without a glue defect had a regular pattern similar for both sides of the sample for both amplitude and phase (see Fig. 5). Samples with a glue defect showed a large amplitude maximum in the localization of the defect (the rest of the sample had a very low amplitude) and an often less regular phase distribution (see Figs. 5, 6, 7, 8, 9).

Fig. 8
figure 8

The defect can be located using a wide frequency range; here 350 Hz for the sample with an 18 mm wide defect

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Fig. 9
figure 9

Three samples with different defect sizes: from left to right 18 mm, 12 mm resp. 6 mm wide, running from rear to front edge. The sample in the rightmost picture had a second small defect to the right side of the main one, only at the rear edge

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3.2 Frequency Range of Response to a Defect

Our method can be considered as a kind of LDR (Local Defect Resonance) [26,27,28,29] but with a wider frequency response (see Fig. 8). This makes it possible to scan the whole frequency range we use (200–130 000 Hz) with large steps and then investigate the relevant frequency region in more detail. To model the defect is therefore not necessary and in a practical case, when location, size and shape are not known, in fact impossible.

3.3 Three Samples with Different Defect Size

Three samples with defects of different size were tested to see if they gave different results (see Fig. 9). Not only the different sizes could be observed but the resonant frequencies were also clearly different. In all cases no defects could be localized using subharmonic or higher harmonic excitation.

From Fig. 9 it is also clear that at the defect location the phase pattern changes too. In the leftmost picture the phase of the upper and the lower view differ by about π, except at the location of the defect. This means that when one side moves towards the observer, the other side moves away. Outside the defect both sides move therefore in the same direction, as in Fig. 6 left and we have a flexural mode. On the location of the defect the phases are more equal, especially in the rightmost picture: they move in opposite direction as in Fig. 6 right (extensional mode). The center picture shows another advantage of using the phase pattern: on the lower (polymer) side the phase on the front edge (blue-green) is opposite to the phase on the rear edge (purple); the sample exhibits torsion: one edge moves upwards when the other moves downwards. This is confirmed by the animations produced by our evaluation software (see paragraph 2.4). The metal side is almost not affected. Using the phase makes it possible, although more difficult, to locate defects, even when the amplitude is very small.

4 Summary

With NDT digital holographic vibrometry we could detect defects in metal-polymer laminates with high spatial resolution and low energy excitation. The vibration amplitudes observed had a magnitude of only up to 40 nm, which helps to avoid damage to the sample. Also the phase patterns can be very helpful. A glue layer defect between metal and polymer can be seen even when hidden from view. The resonant frequency depends strongly on the size of the defect. The programs developed allow to investigate clearly and in detail metal-polymer laminates.

Our non-destructive method makes it possible to determine location, size and shape of defects in metal-polymer laminates, allowing the objects tested to be (re)used after testing; important in a production line. They can also be studied with other (eventually destructive) test methods.