ABSTRACT

The Acoustics of wood is either a part of Wood science and a part of Physical Acoustics for materials characterization. The elastic characterization of wood with acoustic methods is based on the assumption that its properties can be represented by an equivalent homogeneous anisotropic continuum, namely an orthotropic one. Its elastic behavior can be expressed by nine stiffness coefficients. The stiffnesses can be measured with ultrasonic techniques. The principal advantage of ultrasonic technique is the flexibility in measuring velocity and attenuation of ultrasonic waves on a large variety of samples (trees, small clear specimens of solid wood or wood composites, bars, plates, cylinders, spheres, etc). Global and the local characterization of the material is possible. Defect detection can be performed based on the exact estimation of elastic constants and on velocity and attenuation measurements on trees, small clear specimens, lumber, logs and wood composites.

Keywords : nondestructive testing, ultrasound, elastic constants, defect detection

INTRODUCTION

Acoustics of wood as a part of Physical Acoustics for material characterization is related to the development of acoustic methods as an effective means for examining the physical properties of wood. In this article the discussion is concerned particularly with studies of short duration pulse methods. Material characterization is a possible response to practical considerations about the use of wood, because of the increasing interest in the development of nondestructive techniques that predict the mechanical characterization of wood. The challenges in the development of acoustic nondestructive techniques are: to know what information is needed to fully characterize each wood product and to develop new or improved properties of wood and to reduce costs.

BASIC ASPECTS RELATED TO THE THEORY OF WAVES PROPAGATION AND MECHANICAL CHARACTERIZATION OF WOOD

Wave propagation in anisotropic media was discussed in basic reference books (AULD 1973, GREEN 1973, MUSGRAVE 1970). The elastic properties of solids can be defined by generalizing Hooke's law, which relates the volume average of stress [s_ij] to the volume average of the strains [e_ij] by the elastic constants[C_ijkl] :
Eq(1):     [s_ij] = [e_ij] [C_ijkl] , or in more condensed form, [s] = [e] [C]. The relationships between the elastic constants and the velocity of wave propagation in anisotropic solids are given by Chrisoffel's equations :
Eq(2) :     [G_ij - d_ij rV^² ] = 0
where G_ij is the Christoffel's tensor, d_ij is the Kronecker delta tensor of rank two, r is the density and V is the velocity of bulk, longitudinal or shear waves.

The elastic constants of wood of several species are given in Table 1.

Table 1 : Elastic constants on wood measured with broad band transducers (1 Mhz) on 2 cm beech cubic specimens (BUCUR ; ARCHER 1984)
Parameters	Units	Values
Stiffnesses	108 N/m2	CLL 179.52	CRR 34.24	CTT 14.52
Shear moduli	108 N/m2	CTR 3.56	CLT 9.78	CLR 13.96
Young's moduli	108 N/m2	EL 9160	ER 18.51	ET 10.37
Poissons Ratios	-	nTR 0.146	nLT 0.90	nLR 1.244
Poissons Ratios	-	nRT 0.261	nTL 0.10	nRL 0.251

The scattering of an ultrasonic wave in solid medium results in frequency-dependent wave velocity and attenuation (CHRISTENSEN 19971; CHEVALIER 1988; HOSTEN 1991). The dispersion equation relating all the parameters of propagation phenomena in anisotropic solids is:


Eq(3):     [Gij*(w) - L*dij] = 0
Where Gij*(w) is the complex Christoffel tensor depending on frequency w
The eigenvalue L* of the dispersion equation is
Eq (4):     L* = r V²_ij (1- i a_ij V_ij /w)^²
r V_ij^² is the real part of stiffnesses and ia_ijV_ij/w is the ratio of the imaginary to real part of stiffnesses .

The attenuation of ultrasonic waves in wood is related to three main factors: the geometry of the radiation field, the scattering and the absorption. The first factor is concerned with both the properties of the radiation field of the transducer used for measurements (beam divergence and diffraction) and the wave reflection and refraction occurring at macroscopic boundaries of the medium. These factors are related to the geometry of the specimen. Scattering and absorption are phenomena related to the characteristics of the material under test. Table 2 gives some values of velocity attenuation and length of the near field of radiation for ultrasonic waves of different frequencies.

Table 2 : Velocity and attenuation measurements on beech specimens of different shape and size (cylinders and cubes) (BÖHNKE 1992)
Ultrasonic parameters
Anisotropic Direction	Velocity (m/s)	Attenuation (dB)	Frequency (kHz)	Wave length (mm)	Radiation field (mm)
Specimen : Cylinder 20 mm length, transduce 1Mhz, f = 14 mm
L R T	4887 2492 1735	17 12 14	151 79 75	32 32 23	1. 5 1.5 2.0
Specimen : Cube 20 mm, transducer 1 Mhz, f = 14 mm
L R T	4609 2648 1772	24 35 48	705 635 584	9 4 3	5.5 11.0 16.3

The exact knowledge on stiffness coefficients of the material and on impedance contrasts related to the scattering of elastic waves provide information on wood inhomogeneity. Ultrasonic imaging utilizing multiple sound paths and advanced signal processing will provide new inside of wood structure at macroscopic and microscopic scale. Focussing in depth of the material is a dominant feature of the ultrasonic imaging technique. Interface of bonding between layers and volumetric quality control (BERND et al. 1999) can be performed. Acoustic microscopy is part of this development and has the challenge to find a means of visualizing the anatomic feature of wood with high resolution. The very fact that an acoustic microscope visualizes directly the acoustic and elastic properties of wood may be a chief attribute in the development of a new nondestructive procedure for a very fine quantitative anatomical studies.

EXPERIMENTAL, MATERIAL, EQUIPMENT AND PROCEDURES

Ultrasonic velocity measurements can be made with broadband pulses or with narrow band bursts, and related to the time of flight and length of specimen. Either the immersion technique or the direct transmission technique can be used for wood material. The principal advantage of ultrasonic technique is the flexibility in measuring velocity and attenuation of ultrasonic waves.

Figure 1 : Block diagram of an ultrasonic devise (BUCUR 1995) 1 - ultrasonic generator ; 2 - transducer ; 3 - specimen ; 4 - mechanical devise ; 5 - oscilloscope ; 6 - spectrum analyzer ; 7 - computer

The most common block diagram for ultrasonic measurements is composed from an ultrasonic generator, piezoelectric transducers, a mechanical device to hold the specimen, an oscilloscope, a spectrum analyzer and a computer (Figure 1). Most frequently the transducers used for wood mechanical characterization are broadband with a central frequency of 1MHz (Figure 2a). The basic requirements of an ultrasonic transducer are good sensitivity and resolution, controlled beam pattern and reproducible performance under various testing conditions. Experimental limitation is introduced by the coupling medium. The ultrasonic signal can be disturbed and interference phenomena, phase shift and attenuation of the signal are associated with the propagation in the coupling layer. To avoid the difficulties introduced by the coupling media, recently Fraunhofer - Institute for Nondestructive Testing, in Saarbrücken, Germany, developed air coupled transducers (GERHARDT and KRÖNING 1999) with frequency above 100kHz (Figure 2b).

Figure 2a : Ultrasonic piezoelectric transducers a) contact measurements (PANAMETRICS, 1985) 1 - active element ; 2 - backing ; 3 - inner sleeve ; 4 - connector ; 5 - electrical leads ; 6 - electrical network ; 7 - external housing ; 8 - electrodes ; 9 - wear plate.	Figure 2b: air coupled transducers (GEBHARDT ; KÖNING, 1999) 1 - transducer ; 2 - compressed air ; 3 - air cushion ; 4 - connector

It is appropriate to observe that measurements of ultrasonic velocity is influenced by the requirements related to sample preparation, coupling of the transducers to the sample and to signal processing. The specimens could be trees, small clear specimens, planks, plates, etc. The purpose of the research determines the choice of shape and the size of the specimens.

Ultrasonic measurements of trees may be performed on the periphery of the trunk, without bark. Measurements of logs can be done on the transverse sections at both ends In this case no specific care is needed. The potential of ultrasonic velocity method was demonstrated in nondestructive measurement of the slope of grain of living tress and in log grading.

The range of ultrasonic velocities measured in wood 12% moisture content at 1MHz is between 6000 m/s for longitudinal waves in the fiber direction and 400m/s for shear waves in the transversal plane. The values of the attenuation coefficients are roughly 2dB/cm for longitudinal waves in the direction of the fiber and 15dB/cm for shear waves in the transverse anisotropic plane.

The conditions for satisfactory specimen preparation depend essentially on the magnitude of attenuation of ultrasonic waves in the wood species under test. Generally, the higher the attenuation, the greater the requirements concerning the flatness and parallelism of the specimen surfaces. In addition, the specimen must be accurately perpendicular to the direction of measurement. If all elastic stiffnesses are required, the sample size and shape constraints are more severe. For laboratory measurements it is necessary to manipulate rather small specimens in order to limit the effect of any spatial inhomogeneity of wood induced by its anatomical structure and to allow neglect of the annual ring curvatures related to the T direction. However, the specimen proposed for measuring the non-diagonal terms of the stiffness matrix does allow the propagation of quasi-longitudinal and quasi-shear waves out of the principal symmetry axes.

The influence of the natural variability of specimens, due to the biologic nature of wood, on velocity and attenuation may be studied by choosing the frequency of the source so that the acoustic wavelength in the material lie in a range roughly between the maximum dimension of the anatomical elements and the minimum specimen dimension. Parameters such as the probe diameter, the maximum pulse width, the attenuation of ultrasonic waves in wood in the three principal anisotropic planes, or the separation time of quasi-longitudinal and quasi-transverse waves must be considered when determining sampling strategy. Deviation off the energy flux vector of the quasi-longitudinal and quasi-transverse waves should not be ignored when determining the size of the specimen to be tested. In anisotropic and inhomogeneous materials such as wood, a mechanical transducer will simultaneously generate multiple modes. This phenomenon has special consequences for ultrasonic investigation of thin specimens in transverse plane, because the repetition rate of the pulse is too great to allow the various modes to be separated in time. Thus, misinterpretation of travel time or attenuation can occur.

A lower limit to the size of the specimen is also imposed by the requirement that waves should possess the character of plane waves in an infinite medium. The minimum size of the specimen ( <2l) must be established experimentally because no good theoretical criterion exists for this purpose. Finally, is worth remembering that the main advantage of using ultrasonic waves on wood specimens to measure velocity and attenuation is that the material under test is not affected by the propagation phenomena. The sample can be re-tested because no deformation or destruction occurs.

WOOD QUALITY ASSESSMENT WITH ULTRASONIC TECHNIQUES

The success of ultrasonic nondestructive techniques is related primarily to understanding the phenomenon of waves propagation in wood or wood based composites and ultimately too defining how to use the results of the basic research to improve the technology. The various stages that are usually taken into consideration during ultrasonic inspection are : detection, localization, characterization and decision to act on it, if the defect is important enough. The ultrasonic techniques are based on scattering phenomena, that use travel time, frequency, amplitude ratio, waveform shape, etc., or, images produced with both velocity and attenuation data. Most of these methods are performed using waves in frequency range between 50kHz and 2MHz. For high resolution ultrasonic imaging of wood at macroscopic scale transducers of 1 to 5 MHz were used (BERND et al. 1999). For acoustic microscopy a lens focused at 200MHz produced micrographs with a resolution of 6µm (BUCUR 1995).

Ultrasonic tests on trees were mainly related to the detection of the slope of the grain, of knots, of the juvenile wood and of the reaction wood, of the pruning zones and of the curly figures, decay, etc. (BUCUR 1995). Because of space limitation only several aspects will be analyzed in the following pages.

Precise determination of the slope of the grain was possible through understanding the mechanism of ultrasonic wave propagation in wood. The development of the transmission technique for precise measurement of the grain angle was based on the assessment that the propagation is governed by Christoffel's equation for orthotropic solids. The characteristic acoustic anisotropy of wood determines the parameters of the ellipsoidal propagation pattern. Moreover, three velocities can very precisely define the grain angle on this pattern, bearing in mind that along fibers the velocity value is maximum. An accurate prediction of the grain angle depends on the accuracy of the velocity measurements (<1%). For practical purposes an array of transducers could be set on the tested tree. The measurements can be performed in green or dry conditions. For local variation of the slope of grain around knots the same theoretical considerations are valid and we can refer CHAZELAS and al (1988). Stiffness mapping shows the changes in the elastic behavior of wood induced by the presence of tight or loose knots. As for visual pattern of grain, the stiffness variations reveal the nature of knots: tight or loose.

The presence of juvenile zone on Sitka spruce (Table 3) was revealed by five ultrasonic velocities (V_LL ; V_TT ; V_LR ; V_LT ; V_TR ). The presence of pruned zones on pruned trees on Douglas fir (Table 4) was detected on logs with V_LL and with the velocity of surface wave as well as with stiffnesses and X ray density components.

Table 3 : Ultrasonic velocities on juvenile and adult wood of Sitka spruce (BUCUR 1995)
Tree	Ultrasonic velocities (m/s)
	VLL	VTT	VLR	VLT	VTR
Adult tree Juvenile tree	4928 4894	1677 1758	1605 1535	1450 1448	592 521

Table 4 : Characteristics of Douglas-tir pruned tree compared with control tree (BUCUR 1995)
Tree	Ultrasonic stiffnesses (108N/m2)
	CLL	CTT	CLR	CLT	CTR
Pruned tree Control tree	121.8 112.8	16.4 1.4	11.6 12.2	10.6 10.9	1.5 1.3

Ultrasonic technique for lumber, timber and round wood grading and for nondestructive control of wood based composites was discussed by several authors in last ten years. The validity of this technique for solid wood products is based on the strong relationship established between ultrasonic velocity and modulus of rupture . More recently ultrasonic tomography was developed for the inspection of poles (TOMIKAWA et al. 1990) and small specimens (BIAGI et al 1994).

It is well known that wood based composites were designed and fabricated with the aim of obtaining boards having specific mechanical properties for particular uses. The estimation of the anisotropy of these composites is one of the pertinent question to be answered. The anisotropy and the interlaminar heterogeneity of commercial-sized boards can be expressed as the ratios of velocities or acoustic invariants. With the recent advances in transducers, the production and inspection configuration for any type of product requires a good fundamental understanding of wave propagation phenomena into the member under test. The influence of frequency range, geometric beam spreading, pulse receiver contact pressure, acoustic coupling, etc., can be controlled in practice and simultaneous measurements of several transient waveform parameters and velocity can be performed. Multiparameter techniques such as mode conversion of high resolution ultrasonic imaging can provide a convenient means for inspection of large areas using ultrasonic probes. This subject is obviously worthy of detailed investigation and great deal of work remains to be done to provide a reliable indication of defect location in specimens under test.

REFERENCES

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