Acoustoelastic Phenomena of Wood

NDT.net - November 1999, Vol. 4 No. 11

Acoustoelastic Phenomena of Wood

Yasutoshi Sasaki and Kosei Ando
Faculty of Agricultural Sciences, Nagoya University
Nagoya 464-8601, Japan

5th World Conference on Timber Engineering
1998 August 17-20, Montreaux, Switzerland.
Reproduced with the publisher's autorization.
©1998, Presses polytechniques et universitaires romandes, Lausanne, Suisse.

TABLE OF CONTENTS

ABSTRACT
INTRODUCTION
ACOUSTOELASTIC EXPERIMENT
ACOUSTOELASTIC STRESS MEASUREMENT OF WOOD
CONCLUSIONS
REFERENCES

ABSTRACT

The velocity changes of ultrasonic waves propagating transverse to the direction of applied stress in wood were investigated experimentally. Additionally, bending stress distributions in wood beam specimen were estimated by measuring ultrasonic velocity, that is, by the acoustoelastic method. The investigation showed that the ultrasonic waves change speed a little due to the applied stress. The percentage change in the ultrasonic velocity was given as a function of the applied stress, and the acoustoelastic constants were obtained. The velocity change depended on the species, ultrasonic modes, and the applied stresses. Bending stress distribution estimated by the acoustoelastic technique agreed well with the stress values obtained by strain gauge method and mechanical calculation. The acoustoelastic phenomena can be applied to determine stress conditions of wood.

1. INTRODUCTION

In our previous reports [7-9], the results of an experimental investigation of the velocity changes of ultrasonic longitudinal waves propagating parallel to the direction of applied compressive stress in wood were given. The results indicated the existence of an acoustoelastic phenomenon in wood, and the percentage changes in the ultrasonic velocities were given as functions of the applied stresses.

The first objective of this study is to investigate experimentally the changes in the velocities of ultrasonic waves propagating transverse to the direction of applied stress in wood, and the second objective is to estimate the bending stress distribution by the acoustoelastic method. The ultrasonic modes considered are longitudinal waves, and shear waves with particle motion along the direction of the applied stress. Compressive and tensile stresses are applied in the longitudinal direction of small clear wood specimen, and ultrasonic waves are propagated through the radial direction of the wood specimen. Stress-induced Velocity changes of the ultrasonic waves are measured, and acoustoelastic constants are also determined. Additionally, stress distributions in bending of wood beam specimen are estimated by measuring ultrasonic velocity.

2. ACOUSTOELASTIC EXPERIMENT

2. 1 Materials and methods
Materials used in this experiment were from two timber species - Japanese beech (Fagus crenata Blume) and white spruce (Picea glauca (Moench) Voss). Small clear specimens were processed from air-dried lumber samples of the selected timber species. At least 10 specimens of each species were prepared for the tests. Their dimensions were 6 cm (longitudinal) by 3 cm (tangential) by 2 cm (radial) for compressive loading, and 29 cm (longitudinal) by 5 cm (tangential) by 1.5 cm (radial) for tensile loading specimen. The longitudinal axis of each specimen coincided with the longitudinal direction of the wood. The test specimens were kept under air-dried condition.

Both the compressive and the tensile loads were applied parallel to the longitudinal axis of the wood test specimens using an Instron-type testing machine. The ultrasonic wave was propagated transverse to the direction of loading, that is, in the radial direction of the wood. The ultrasonic velocity under loading of the wood was measured by the sing-around method [8-12], using a model UVM-2 (commercially available sing-around unit by Ultrasonic Engineering Co., Ltd., Tokyo, Japan) [8,9,12]. Transducers used were commercially available piezoelectric type of longitudinal and shear waves, 0.5-MHz in center frequency, and 1-inch in diameter (model CR-0016-S (longitudinal wave) and CR-0016-SA (shear wave) by Harisonic Labs., CT, USA). Coupling medium - silicone grease and epoxy resin - were used to ensure bonding of the transducers to the wood specimen [12,13]. For the stress-strain measurements, load-cell and strain gauges were used. Two strain gauges were attached to the center of the symmetrical surfaces of the radial section of the specimen, and oriented parallel to the directions of wave propagation and applied stress. Dimensional changes in the specimen in the loading and ultrasonic propagation directions during the test were measured by these strain gauges. For the calculation of the ultrasonic velocity, the distance between the ultrasonic transducers was corrected by this measurement. The equipment for the stress, strain, and velocity measurements was connected to a personal computer, and the data were automatically recorded. The above procedures were done in an air-conditioned chamber at 24°C and 55% relative humidity.

2. 2 Results and discussion

2. 2. 1 Changes in velocities under uniaxial stress for wood
Fig. 1 shows a typical experimental results indicating the relationships between the stress, strain, and the changes in the velocity of a shear wave under compressive stress for white spruce. The stress-strain relationships are represented by generally recognized curves for longitudinal compression of softwood species. The mean ą SD of the initial velocity for the natural state (zero stress and zero strain) obtained was 1692.0 ą 19.8 m/s. The values of the initial velocity were small because the ultrasonic waves were propagated through the radial direction of wood. The ultrasonic velocity decreased with increasing stress and strain immediately after the natural state. With severe deformation of more than 0.5 % strain, the ultrasonic velocity decreased more steeply. However, the range of the changes in velocity in this experiment was small compared with the previously reported results in which the ultrasonic waves were propagated parallel to the direction of applied stress [16-18]. Similar results were also obtained for Japanese beech (not discussed here).

In the combination mode of ultrasonic longitudinal wave and compressive stress, however, a different phenomenon was observed for Japanese beech. The ultrasonic velocity of longitudinal wave increased with increasing compressive stress at an initial stress level, and then gradually decreased with increasing stress. In the case of white spruce, the longitudinal wave velocity decreased with increasing compressive stress immediately after the natural state, as in fig. 1.


Fig. 1. Relationships between compressive stress, strain, and shear wave velocity of white spruce.	Fig. 2. Relationships between tensile stress, strain, and shear wave velocity of white spruce.

Fig. 2 shows a typical experimental results under tensile stress for white spruce. It shows the relationships between stress, strain and changes in the velocity of a shear wave. The initial mean ą SD of velocity obtained was 2571.9 ą 39.0 m/s. At an initial stress level of less than 20 MPa, the strain and ultrasonic velocity increased with increasing tensile stress. The velocity then gradually decreased with increasing stress and strain from a stress level of more than 30 MPa. This phenomenon which was also obtained for Japanese beech (not discussed here) differed from the result in fig. 1. Changing velocity gradually from increase to decrease, at a low stress level, is considered a unique phenomenon in wood. A similar phenomena was common and characteristic when ultrasonic longitudinal waves were propagated parallel to the direction of applied compressive stresses in longitudinal direction of wood as reported in previous papers [7,8].

But, in the combination mode of ultrasonic longitudinal wave and tensile stress, the longitudinal wave velocity decreased with increasing stress and strain immediately after the natural state in both species.

Variations in velocity change with stress were due to difference in material, ultrasonic wave mode, direction of propagation, and so on. Magnitudes and signs of velocity changes also varied. The phenomena observed in fig. 1 are also generally observed in metallic materials. For 99.5% pure aluminum, 99.9% pure copper, and 0.01% carbon iron, velocities of the longitudinal waves under uniaxial compressive stresses decrease slightly with increasing stresses [2,12]. There exist obvious linear relationships between them and changes in the velocities of these materials are smaller than those of wood.

The origins of the changes in the propagation velocities of ultrasonic waves

have been accounted for by the changes in the densities and elastic moduli of the materials. As a result of the application of stress to an elastic material, the density and elastic modulus of the material change [1,14]. This change is considered to lead to a change in the propagation velocity. Such phenomena that density or elastic moduli change due to applied stresses or deformations are, however, not confirmed yet for wood. In addition to this, the phenomenon obtained for wood is considered to relate to its cellular structure complexity as described in the above and also in previous reports [8,9]. This suggests the existence of a relationship between the acoustoelastic phenomena and the anatomical structure of wood.

2. 2. 2 Relative changes of ultrasonic-wave speeds and acoustoelastic constants
From the results of acoustoelastic experiments, the relationships between the relative changes of ultrasonic velocities and stresses were obtained at a low stress level of less than 20 MPa. Following our previous reports [8,9], the percentage changes in velocity were calculated by ( V - V0 ) x 100 / V0 (%), where V is the velocity at an arbitrary stress, and V0 is the initial velocity for the natural state.

Fig. 3 shows examples of the percentage changes in shear wave velocities due to applied compressive stresses for white spruce. The figure was obtained from fig. 1. The velocity changes of shear waves decreased with increasing application of compressive stress, and they revealed clearly an inverse proportional relationships. The average proportional constant of the lines in fig. 3 was about 1.93 x 10^-4 MPa^-1.


Fig. 3. Relationships between percentage changes in velocity of shear wave and compressive stress of white spruce.	Fig. 4. Relationships between percentage changes in velocity of shear wave and tensile stress of white spruce.

Fig. 4 also shows examples of the percentage changes in shear wave velocity due to the applied tensile stress for white spruce, and was obtained from fig. 2. The relationships between the velocity changes and the applied tensile stress were straight lines, but in contrast to the changes seen in fig. 3, they clearly showed proportional relationships. In fig. 4, the average proportional constant of these lines was 0.66 x 10^-4 MPa^-1.

The acoustoelastic constants were obtained from the proportional constants of the relationships between the velocity changes and stresses shown in figs. 3 and 4. The relationships between them were expressed as follows: ( V - V0) / V0 = K , where K is the acoustoelastic constant and the applied stress. The average values of K for each experimental conditions are shown in table 1.

The magnitudes and signs of velocity changes were much different depending on the materials, ultrasonic wave mode, direction of propagation, and so on. The signs of the constants in longitudinal waves for compressive stress, shown in table 1, seemed to depend on the species and the structural directions of wood, suggesting a relationship between the acoustoelastic phenomena and the anatomical structure of wood.

Table 1: Acoustoelastic constants of wood obtained in this experiment.

Specimens	Ave.acoustoelastic (MPa^-1)	constants (SD:MPa^-1)	Stress	Wave
White spruce	5.43x10^-4	(5.28x10^-4)	Compressive	Longitudinal
	-1.69X10^-4	(1.06x10^-4)	Tensile	Longitudinal
	1.93x10^-4	(1.09x10^-4)	Compressive	Shear
	0.66x10^-4	(0.35x10^-4)	Tensile	Shear
Japanese beech	-0.50x10^-4	(0.18x10^-4)	Compressive	Longitudinal
	-0.80x10^-4	(0.35x10^-4)	Tensile	Longitudinal
	0.78x10^-4	(0.98x10^-4)	Compressive	Shear
	0.65x10^-4	(0.54x10^-4)	Tensile	Shear

The signs of the constants for white spruce for the longitudinal wave were different due to the applied stresses as shown in table 1. This means that the same phenomena are observed for longitudinal waves under both (compressive and tensile) applied stresses. In this case, the longitudinal velocities for white spruce decreased with increases in applied stresses. This is important for white spruce and it seems difficult to apply longitudinal waves to measure stress conditions.

The absolute values in table 1 were somewhat smaller than those for longitudinal waves along the direction of applied compressive stress, as reported previously [8,9]. But these were still larger than those of metallic materials.

As shown in the table, the acoustoelastic constants obtained in this experiment showed large variations. Large variations in the constants were also obtained for longitudinal waves along the direction of applied compressive stress, as reported previously [8,9]. The reason the constants were so variable is still not clear. The origins of the large variations may be attributed to an unexpected problem of acoustoelastic experiment, or a natural property of wood.

3. ACOUSTOELASTIC STRESS MEASUREMENT OF WOOD

3. 1 Materials and methods
Materials used in this experiment were Japanese beech and white spruce. Beam specimens were processed from air-dried lumber, which was the same material as used in the acoustoelastic experiment (Chapter 2), Dimensions (length x height x breadth) of the specimens were about 210 cm x 12 cm x 1.5 cm. The, directions of the length, height, and breadth of each specimen coincided with the longitudinal, tangential, and the radial directions of wood respectively.

Bending moment was centrally applied, over a loading span of 30 cm of the specimen, by hanging weights at both ends of the specimen.

Before loading, the initial velocity (V0) distribution was measured at 7 points along the center of the span of each specimen by using the same method and instruments as in the acoustoelastic experiment. After loading, the velocity (V) distribution was measured at the same position and the changes in the propagation velocity of ultrasonic waves were determined as ( V - V0) 1 V0. Ultrasonic waves were propagated transverse to the direction of applied bending stresses, that is, in the radial direction of the wood. This is the same ultrasonic mode as in the acoustoelastic experiment. A special holder made from wood was used to hold the transducers to the specimens with constant pressure at all measuring points. By using this holder, the measurements were efficiently performed. The ultrasonic modes considered were longitudinal waves and shear waves with particle motion along the direction of the applied bending stress. The mode of shear waves with particle motion transverse to the direction of the applied bending stress was not considered in this experiment.

According to the acoustoelastic method, the stress ( a) is obtained as follows: a = (( V - V0 ) / V0 ) / K, where V is the ultrasonic wave velocity at stressed condition, V0 is the ultrasonic wave velocity at unstressed condition, and K is the acoustoelastic constant determined by the acoustoelastic experiment.

For the comparison of the acoustoelastic stress measurements, strain gauges 10 mm long were attached at 9 points along the ultrasonic measuring positions. The longitudinal axis of the gauges coincided with the direction of the bending stress. The experimental procedures were followed in an air-conditioned chamber at 24°C and 55% relative humidity.

3. 2 Results and discussion
Table 2 shows examples of the experimental results of ultrasonic velocities under bending tests. These values in the table were obtained with the ultrasonic mode of the shear waves under 60 kgf-bending load for white spruce. The initial velocities of ultrasonic shear waves were different due to the different measuring positions. Their values ranged from 1847.8 to 1933.2 m/s and had no tendencies due to the measuring position. However, the initial velocity near the neutral axis (at 52.5 mm from the lower edge of the specimen) was the highest. This may be connected with the relationship between the propagation direction of ultrasonics and the orientation of annual rings.

The ultrasonic velocity at each position changed due to the loading, and the absolute values of the changes in ultrasonic velocities increased with increasing loading. At the upper positions (52.5, 70, 80, and 90 mm from the lower edge) of the beam specimen, the shear wave velocities increased due to the loading and resulted in positive changes. In contrast, the velocities at the lower positions (35, 25, and 15 mm) decreased due to the loading and resulted in negative changes.

The results from the above and the acoustoelastic experiments show that the tensile bending stresses were distributed in the upper side of the beam specimen and the compressive in the lower side. Their magnitudes were greater in the outer sides of the beam than in the inner sides near the neutral axis.

The bending stresses obtained by the velocity measurements of shear waves were indicated as a in table 2. In the table, the K values were the acoustoelastic constants obtained in the acoustoelastic experiments. They were the experimental values of the individual specimens which were obtained from the measuring positions of ultrasonic waves in the beam specimen.

Table 2: Test results by using shear wave under 60 kgf-loading (white spruce).

Position (mm)	V0 (m/s)	V (m/s)	DV/V0	K (MPa^-1)	ra (MPa)	rg (MPa)	rb (MPa)
90	1865.20	1865.58	0.0002015	0.66 x l0^-4	3.05	4.70	5.34
80	1847.82	1848.33	0.0002772	0.81 x 10^-4	3.42	3.50	3.91
70	1854.05	1854.36	0.0001644	0.66 x l0^-4	2.49	2.15	2.49
52.5	1933.19	1933.24	0.0000284	0.31 x 10^-4	0.91	0.20	0.00
35	1911.05	1909.45	-0.0008376	3.34 x 10^-4	-2.51	-2.56	-2.49
25	1903.72	1901.39	-0.0012270	3.34 x 10^-4	-3.67	-3.90	-3.91
15	1882.98	188l.81	-0.0006260	0.96 x10^-4	-6.52	-5.42	-5.34

In the table, the stress values obtained by the strain method and mechanical calculations were also given as rg and rb respectively. There were only little differences in the stress values obtained by the three methods and they almost agreed with each other. It was suggested that the bending stress distribution of wood was estimated adequately by the acoustoelastic method. This finding suggests that the acoustoelastic phenomena of wood can be used to determine the stress conditions of wood.

4. CONCLUSIONS

The patterns of the changes in the ultrasonic velocities depended on species of wood and ultrasonic modes. The acoustoelastic phenomena by using shear waves showed a difference in character under compressive and tensile stresses. On the contrary, the phenomena by using longitudinal waves for white spruce showed the same character under both stresses. This point should be considered when applying the acoustoelastic technique by using longitudinal waves for stress determination of wood.

The bending stress values from the acoustoelastic stress measurements seem to have been adequately estimated and agree well with those obtained by the strain gauge method and mechanical calculation.

The above results indicate that ultrasonic velocity propagating through wood changes with great sensitivity to the applied stress, and suggest the possible application of acoustoelastic technique for the determination of the stress conditions of wood. The origins or the mechanism of the changes in the ultrasonic velocities are, however, not explained for wood. The results of the present and previous studies [7-9], suggest the existence of a relationship between the acoustoelastic phenomena and the anatomical structure of wood. This may also explain the difference in the mechanism of acoustoelastic phenomena of wood and metallic materials.

Further experimental and theoretical investigations should be made to find explanation for the mechanism and the application of the technique.

REFERENCES

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