·Table of Contents ·Materials Characterization and testing | A Method to Determine the Debonding Zones in Multilayers Wood MaterialsR. Grimberg, A. Savin, A. Lupu, C. RotunduNational 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 |
(1) |
(2) |
(3) | |
where F is the pressure force and D is given by | |
(4) |
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 q_{P1} with the amplitude A_{inc}, 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, c_{P1 }and c_{S1} are the propagation speeds of the P and S waves respectively in the buffer rod and c_{P2}, c_{S2} 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) |
(7) | |
where c is given by | |
(8) | |
with | |
(9) |
h is the plate thickness, and r_{2}, l_{2}, m_{2} 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 h_{1} with the sped c_{1}, and the other in the layer h_{2}=h-h_{1} with the speed c_{2}. Therefore, the speed c_{y} 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.
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 2.7x10^{3} kg/m^{3}, the Young modulus 7x10^{10}N/m^{2}, 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/m^{3}, the Young modulus 1.4x10^{10}N/m^{2} and the Poisson coefficient 0.14 [5].
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: A_{P}/A_{inc}=1.1378 and A_{S}/A_{inc}=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 c_{y} is (4301±90)m/s. In the presence of a debonding, the speed c_{y} 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 |
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