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## A Method to Determine the Debonding Zones in Multilayers Wood Materials

R. Grimberg, A. Savin, A. Lupu, C. Rotundu
National Institute of R&D for Technical Physics, 47 Mangeron Blvd., 6600, Iasi, ROMANIA
L. Iancu
National Institute for Wood, 7 Fabrica de glucoza St., Sector 2, Bucharest, ROMANIA

Contact

### Introduction

The timber utilized in the furniture industry can be upgraded by sticking veneer foils of noble essence on the basic material. In this case, the basic material can be board or agglomerated wood chips stuck together in plates, a multi-layer structure being obtained. This is also the way to make multi-layer plywood. In these cases, a special problem the quality control is confronted with is represented by the control of the adhesion between the veneer and basic material.
This work is dedicated to a new method for determining the debondings in multi-layer wood materials, that makes use of Lamb waves excited by Hertzian contact.

### Theory

The Lamb waves are elastic wave modes propagating in solid plates with free boundaries [1] and representing a combination of both compression waves (P-waves) and shear waves (S-waves).
The wave number of the P and S waves are given by
 (1)

where w is the angular frequency of the ultrasound beam, r0 is the plate density, and l and m are the Lamé constants that can be expressed in terms of the Young modulus and Poisson coefficient n.
 (2)

If two solid bodies are superposed and pressed with relatively low forces, they get elastically deformed, giving rise to a Hertzian contact between each other. If one of the bodies is spherical of radius R, and the other one is an isotropic flat material, the contact area is circular of radius a, which can be determined from the relation [2].
 (3) where F is the pressure force and D is given by (4)

n 1, n 2, E1 and E2 standing for the Poisson coefficients and the Young moduli of the two bodies respectively.

Thus, by means of the Hertzian contact ultrasonic waves can be excited in a wood material without the necessity of a coupling liquid that could alter the quality of the controlled material.
Figure 1 schematically presents a ultrasonic transducer with Hertzian contact at the buffer rod-plate interface, which converts the P waves from the buffer rod to Lamb's wave from the plate.

 Fig 1: a. Transducer with Hertzian contact b. The detail of the control

For a P wave that propagates in the buffer rod reaching the interface at an incidence angle qP1 with the amplitude Ainc, both P and S waves will be generated in the plate, having the amplitudes [1]

 (5)

where r 1 is the density of he buffer rod material, r 2 the density of the wood material, cP1 and cS1 are the propagation speeds of the P and S waves respectively in the buffer rod and cP2, cS2 are their speeds in the wood material.
The combination of the P and S waves in the wood material results in a Lamb wave. For a low frequency ultrasonic beam, only the fundamental flexural mode will propagate in the plate, as the only non-dispersive mode.
The potentials describing the wave displacement can be written as

 (6)

where a2=k2 - k2p , b2=k2 - k2s , k is the wave number of the fundamental flexural mode, and c is the propagation speed.
The propagation speed along the Oy direction can be written as [3]

 (7) where c is given by (8) with (9)

h is the plate thickness, and r2, l2, m2 are the density and the Lamé constants respectively, for the wood plate.
When a debonding of the veneer layer, occurs the Lamb waves are split in two beams, one of them propagating in the veneer layer of thickness h1 with the sped c1, and the other in the layer h2=h-h1 with the speed c2. Therefore, the speed cy will be smaller, resulting in an increase of the propagation time between the transmitter with Hertzian contact placed on one face of the multi-layer plate, and the receiver of the same type placed on the opposite face.

### Experimental set-up

Figure 2 presents a sketch of the measuring equipment. The frequency of the ultrasound beam was 60kHz.

 Fig 2: The basic diagram of the equipment

The two buffer rods used at the emission and reception are both identical, being made of the 7075-T6 aluminum-magnesium alloy, with the density 2.7x103 kg/m3, the Young modulus 7x1010N/m2, the Poisson coefficient 0.34 and a point curvature radius of 3mm.
The plywood consists of two layers of 1mm thick beech veneer, glued on the two faces of a 2mm thick plate made of agglomerated poplar chips urelite was used for gluing according to the usual procedure. The debonding was simulated by inserting rectangular frames mades of a 80mm thin raylon foil, the frame width being 0.5mm and no adhesive being applied inside the frame.
The diagram of the etalon is presented in Figure 3.

 Fig 3: Diagram of the etalon

In a first approximation [4], one can consider that, given the small thickness, the density, the Young modulus and the Poisson coefficient for each layer apart coincide with the values for the whole multi-layer structure, namely the density 780kg/m3, the Young modulus 1.4x1010N/m2 and the Poisson coefficient 0.14 [5].

### Results

The dependence of the radius a of the contact between the buffer rod and the wood material for pressure forces of up to 100N, using the relations (3) and (4), was plotted in Figure 4.

 Fig 4: Dependence of the radius on pressure forces

The visual inspection established that a pressure force of 10N does not induce any remanent strain, this force value being relatively constant for both the emission and reception transducers.
According to the diagram in Figure 4 a contact radius of 0.13mm results. In this case, the efficiency of the utilized transducer with Hertzian contact can be defined by the values: AP/Ainc=1.1378 and AS/Ainc=0.0266.
Figure 5 presents the dependence of the speed of the fundamental flexural mode on the material thickness, calculated according to Rels.(8) and (9), the points in the diagram representing the experimentally measured values. A decrease of the speed with decreasing material thickness can be noticed.

 Fig 5: Dependence of the speed on the material thickness

For the inspected plywood without debondings, the speed cy is (4301±90)m/s. In the presence of a debonding, the speed cy in the veneer layer will be 2128m/s, and in the other region it will be 1103m/s, the values being calculated from Rel.(7). As the result, in the regions with debonding present an increase of the ultrasound propagation time will be noticed along the Oy direction, between the transmitter and the receiver.
Since the basic material is a conglomerate of chips stuck together, and the adhesive layer thickness can be locally different in the regions without debondings, a time of flight of 0.93 ± 0.02ms will be obtained.
In the material in which the time of flight is measured on a debonding area, a calculated value of 3.19ms and a measured value of 3.15±0.08ms will be obtained.
We present in Figure 6 a map of the time of flight measured on a plywood plate with artificially created debondings. The image can be improved by using a 2D digital conduction filter and choosing a Gaussian Kernel.

 Fig 6a: Fig 6b: Fig 6: Debonding zones map obtained by the above mentioned procedure

The examination of Figure 6 shows that the artificially created delamination have been rendered evident rather precisely.

### Conclusions

The examination of the Lamb waves generated in the multi-layer wood materials by means of the low frequency ultrasound transducers with Hertzian contact, has proved to be a fast and efficient metod for delamination detection. The filtration by means of a Gaussian convolution filter, of the obtained maps of the times of flight leads to a clearer image that correlates better with the delamination zone.

### References

1. L.W.Schmerr Jr.,Fundamentals of Ultrasonic Nondestructive Evaluation, Plenum Press, N.Y., 1998
2. L.Landau, E.M.Lifshitz,Theory of Elasticity, Pergamon, N.Y., 1959
3. F.Levent Degertekin, Butrus T. Khuri-Yakub, Single Mode Lamb Wave Excitation in Thin Plates by Hertzian Contacts, J.Appl.Phys. Lett., 69, 2, (1996), 146-148
4. R.James, S.M.Woodley, C.M.Dyer, V.F.Humphrey, Sonic Bands, Bandgaps and Defect States in Layered Structures-Theory and Experiment, J.Acoust. Soc.Am., 97, 4, (1995), 2041-2047
5. V.Bucur, An Ultrasonic Method for Measuring the Elastic Constants of Increment Cores Bored from Living Trees, Ultrasonics, 5, (1983), 116-126

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