| NDT.net - March 2001, Vol. 6 No. 03 |
 12th International Symposium on Nondestructive Testing of Wood | Ultrasonic Measurement of Applied Stresses in Wood by Acoustoelastic Birefringent MethodSasaki, YasutoshiAssoc.Professor Hasegawa, Masumi Graduate Student Graduate School of Bioagricultural Sciences Nagoya University, Nagoya 464-8601, Japan Corresponding Author Contact: Email: gasteig@agr.nagoya-u.ac.jp |
The velocity changes of ultrasonic shear waves propagating transverse to the direction of the applied stress in wood were investigated experimentally. Their direction of oscillation was parallel and normal to the direction of uniaxially applied stress. Additionally, bending stress distributions in wood beam specimen were estimated by measuring ultrasonic shear wave velocities, that is, by the acoustoelastic birefringent method. The investigation showed that the ultrasonic waves changed speed a little due to the applied stress and the velocity of the shear waves propagating transverse to the direction of the stress was dependent on whether its direction of oscillation was parallel or normal to the direction of the stress. The relative differences of the ultrasonic velocities were given as functions of applied stress and the acoustoelastic constants for texture- and stress-induced birefringences were obtained. By using these constants and ultrasonic velocities of shear waves polarized parallel and normal to the direction of principal stresses, the difference of the principal stresses can be obtained and this is called the acoustoelastic birefringent method for the determination of the stress states. According to this acoustoelastic technique, bending stress distributions in wood beam specimen were tried to determine, and the stress states estimated agreed well with the stress values obtained by strain gauge method and mechanical calculation. The acoustoelastic birefringent phenomena can be applied to determine stress conditions of wood.
An elastic material under stress, either internally generated or externally applied, becomes double refracting, meaning that the velocity of shear waves propagating transverse to the direction of the stress is dependent on whether its direction of oscillation is parallel or normal to the direction of the stress. This phenomenon is called the acoustoelastic birefringence, and the acoustoelastic technique can be applied to stress analyses of materials (Benson and Raelson 1959, Bergman and Shahbender 1958, Crecraft 1967, Fukuoka 1993, Tokuoka and Iwashimizu 1975).
In our previous reports (Hasegawa et al. 2000, Sasaki et al. 1995, 1997, 1998), the results of an experimental investigation of the velocity changes of ultrasonic waves propagating in wood parallel or normal to the direction of applied stress were given. The ultrasonic modes were longitudinal and shear waves polarized parallel to the direction of the stress. 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. Moreover, the stress conditions of wood under bending were estimated by using these acoustoelastic phenomena (Sasaki et al. 2000). According to the method shown in the previous paper (Sasaki et al. 2000), however, the stress states (compression or tension) in wood could not be determined. Only stress values could be estimated. This was a disadvantageous point for applying the ultrasonic technique to determine stress conditions in wood.
The final object of this study is to develop a new method for evaluating stress condition in wood by using ultrasonic technique. This paper reports two items. Firstly, the experimental results of acoustoelastic birefringent effect of ultrasonic shear waves in a stressed wood specimen were shown. That is, the changes in the velocities of ultrasonic shear waves propagating transverse to the direction of applied stress in wood were measured. The ultrasonic modes considered were shear waves polarized parallel and normal to the direction of the applied stress. Compressive and tensile stresses were applied in the longitudinal direction of small clear wood specimen, and ultrasonic shear waves were propagated through the radial direction of the wood specimen. Stress-induced velocity changes of the ultrasonic shear waves were measured, and acoustoelastic constants for texture- and stress-induced birefringences were determined. Secondly, based on the acoustoelastic birefringent effect, the measurement method and estimated results of the bending stress distributions in wood beam specimen were shown to better apply the technique.
2.1. Materials and methods
Materials used in this experiment were from Japanese magnolia (Magnolia obovata Thunb.). Small clear specimens of solid wood were processed from air-dried lumber sample of the selected timber species. At least 10 specimens 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 3 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 shear wave was propagated transverse to the direction of loading, that is, in the radial direction of the wood. Its direction of oscillation was parallel and normal to the direction of loading. Figure 1(a) illustrates the oscillation directions of shear wave and loading direction. The ultrasonic velocity propagating through wood under loading was measured by the sing-around method (Krautkrämer 1990, Negishi and Takagi 1984, Sasaki et al. 1997, 1998, Toda 1993a, 1993b), using a model UVM-2 (commercially available sing-around unit by Ultrasonic Engineering Co., Ltd., Tokyo, Japan) (Sasaki et al 1997, 1998, Toda 1993b).
Fig 1: (a): Relation between loading direction, and propagation and
oscillation directions of ultrasonic shear wave, (b): Block diagram of acoustoelastic experiment in compressive loading. 1, Electric displacement meter; 2,ultrasonic transducer; 3, rubber band; 4, wood specimen; 5, load cell; 6, cross-head of universal testing machine; 7, commercially available sing-around unit “UVM-2”; 8, data-logger “7V-14”; 9, personal computer; 10, periodic time of sing-around; 11, displacement of specimen; 12, strain of the specimen; 13, applied load. |
The sing-around method is a method for measuring the transit time with very high accuracy and the principle of the method is explained as follows: The electric signal is transmitted from the generator to the emitter, and transformed to an ultrasonic pulse. The ultrasonic-pulse travels through the specimen, is received by the receiver, and is transformed to an electric signal, which is visualized on an oscilloscope. Triggering by this received pulse, the next pulse transmission waits for a fixed delay time until reverberation of the ultrasonic vanishes. After waiting for a fixed delay time, the next pulse is transmitted. This operation is repeated many times, and this repeated operation is the so-called "sing-around". A periodic time of the sing-around is counted by a counter, and then the elapsed time between the emission and reception is measured. The sing-around unit UVM-2 makes these procedures automatically. In this experimental procedure, the repeating time of sing-around was adjusted to 1000.
The transducers used were a commercially available piezoelectric type of shear wave, 0.5-MHz in center frequency, and 1-inch in diameter (model CR-0016-SA by Harisonic Labs., CT, USA). Frequency also affects ultrasonic velocities. High-frequency is better for measurement accuracy. However, transceiver can not receive high-frequency signals traveling through specimens because of the great attenuation of wood (Bucur 1995, Negishi and Takagi 1984). The frequency of 0.5-MHz was selected for this experiment. Rubber band was used to hold the transducers during loading against a wood specimen. Coupling medium - epoxy resin - was used to ensure bonding of the transducers to the wood specimen (Bucur 1995, Toda 1993b).
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. Figure 1(b) shows block diagram of acoustoelastic experiment. The above procedures were done in an air-conditioned chamber at 24oC and 55% relative humidity.
2.2. Results and discussion
2.2.1. Changes in velocities under uniaxial stress for wood
Figure 2 shows typical experimental results indicating the relationships between the stress, strain, and the changes in the velocity of a shear wave under compressive stress in an elastic region of less than 10 MPa for Japanese magnolia. The oscillation directions of shear waves in Figs. 2(a) and 2(b) were parallel and normal to the stress direction, respectively.
Fig 2a: Relations between compressive stress, strain, and ultrasonic velocity of shear wave polarized parallel to the direction of applied stress.
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Fig 2b: Relations between compressive stress, strain, and ultrasonic velocity of shear wave polarized normal to the direction of applied stress. |
The stress-strain and stress-velocity relationships were represented by linear lines. The mean ± SD of the initial velocities for the natural state (zero stress and zero strain) obtained were 1524.5 ± 13.6 m/s and 743.1 ± 13.8 m/s, in which the shear wave motions were parallel and normal to the loading direction, respectively. The former values were large owing to the oscillation direction of the wave. As shown in both figures, the ultrasonic velocities decreased with increasing stress immediately after the natural state. The range of the change in velocity in Fig. 2(a) was large compared with it in Fig. 2(b). Whether the direction of the oscillation of shear wave was parallel or normal to the loading direction affected much the changes in the wave velocity. The shear wave velocity polarized parallel to the loading direction changed much with the loading.
Figure 3 shows typical experimental results under tensile stress in an elastic region. It shows the relationships between stress, strain and changes in the velocity of a shear wave. The oscillation direction of shear waves in Figs. 3(a) and 3(b) were parallel and normal to the direction of applied stress, respectively. The initial mean ± SD of velocity obtained was 1564.6 ± 11.5 m/s in parallel oscillation to the direction of applied stress, and 671.8 ± 11.5 m/s in normal oscillation. The stress-strain and stress-velocity relationships were also represented by linear lines. However, on the contrary to Fig. 2 in compression, the shear wave velocity increased with increasing tensile stress immediately after the natural state in both Figs. 3(a) and 3(b). In addition, in the case of tension, the range of the change in velocity shown in Fig. 3(a), in which the oscillation of the wave was parallel to the loading direction, was larger.
Fig 3a: Relations between tensile stress, strain, and ultrasonic velocity of shear wave polarized parallel to the direction of applied stress.
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Fig 3b: Relations between tensile stress, strain, and ultrasonic velocity of shear wave polarized normal to the direction of applied stress. |
Changes in velocity 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 the above figures are also generally observed in metallic materials, 99.5% pure aluminum, 99.9% pure copper, and 0.01% carbon iron, for example. For these materials, velocities of the shear and longitudinal waves under uniaxial stresses change slightly with increasing stresses (Pao et al. 1984, Toda 1993). 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 (Bergman and Shahbender 1958, Iwashimizu 1994). 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 in previous reports (Sasaki et al. 1997, 1998). This suggests the existence of a relationship between the acoustoelastic phenomena and the anatomical structure of wood.
2.2.2. Relative differences of ultrasonic velocities and acoustoelastic birefringent constants
From the results of the acoustoelastic birefringent experiments, the relationships between the relative differences of the shear wave velocities and the applied stresses were obtained. The relative differences of the wave velocity were calculated by (V1 – V2) / VT, where V1 and V2 were the velocities of shear waves polarized parallel and normal to the direction of the stress respectively and VT was the average of V1 and V2. This is also called the acoustic anisotropy.
Fig 4: Relative changes of acoustic anisotropy for a deformed wood specimen in uniaxial compression.
| 
Fig 5: Relative changes of acoustic anisotropy for a deformed wood specimen in uniaxial
tension. |
Figure 4 shows examples of the relative differences of the shear wave velocities due to applied compressive stresses. One of these lines of the figure was obtained from Figs. 2(a) and 2(b). The relative differences of the shear wave velocities decreased with increasing application of compressive stress, and they revealed clearly inverse proportional relationships. The average proportional constant of the lines in Fig. 4 was about 6.68 x 10-4 MPa-1. Figure 5 also shows examples of the relative differences of the velocities due to the applied tensile stress, and one of them was obtained from Figs. 3(a) and 3(b). The relationships between them were also expressed by straight lines, but in contrast to the changes seen in Fig. 4, they clearly showed proportional relationships. In Fig. 5, the average proportional constant of these lines was 1.80 x 10-4 MPa-1.
From these figures, acoustoelastic birefringent constants were obtained. One is the acoustoelastic constant for the texture-induced birefringence, a, also called the initial birefringence (at unstressed condition) or texture acoustic anisotropy. The other is the acoustoelastic constant for the stress-induced birefringence, Ca, (at stressed condition). The former, the acoustoelastic constant for the texture-induced birefringence, was obtained as the intercept of the asymptote, and the latter, the acoustoelastic constant for the stress-induced birefringence, was obtained as the slope of the asymptote (proportional constant of the line) in these figures. The relationships between them were expressed as follows: (V1 – V2) / VT = a + Ca (t1 – t2), where t1 and t2 were principal stresses. The average values of these constants, a and Ca, for each experimental conditions, were shown in Table 1. The initial birefringence a means the anisotropy induced by the texture. The larger the value of the initial birefringence a is, the severer the anisotropy becomes. The values of the initial birefringence a of wood in Table 1 were larger than those of aluminum, isotropic material (Murakami et al. 1989). The magnitudes and signs of velocity changes were much different depending on the materials, ultrasonic wave modes, direction of
| Materials | Applied stress | Texture acoustic anisotropy a | Stress-induced birefringence Ca [ MPa-1 ] |
| Japanese magnolia | Compressive | 0.686 (0.014) | 6.68 x 10-4 (3.94 x 10-4) |
| Tensile | 0.807 (0.031) | 1.80 x 10-4 (1.09 x 10-4) | |
| Aluminum (Murakami et al. 1989) | Compressive | 0.770 x 10-2 | -3.97 x 10-5 |
| Tensile | 0.750 x 10-2 | -4.14 x 10-5 | |
| Table 1: Acoustoelastic birefringent constants of wood obtained in this study. | |||
propagation, and so on. The sign of the constants Ca were the same regardless of the directions of the applied stresses as shown in Table 1. This means that different phenomena were observed due to the applied (compressive and tensile) stresses as shown in Figs. 4 and 5. This is important for the determination of the stress states, compression or tension. Knowing the sign of the difference between the texture- and stress-induced birefringences ((V1 – V2) / VT – a) enables one to determine the stress states. It is considered an advantageous point for the acoustoelastic birefringent method.
3.1. Materials and methods
Material used was Japanese magnolia. Beam specimens were processed from an air-dried
lumber, which was the same material as used in the acoustoelastic birefringent
experiment conducted in Chapter 2. Dimensions (length x height x breadth) of the specimens were 1300 mm x 105 mm x 15 mm. The directions of the length, height, and breadth of the specimen coincided with the longitudinal, tangential, and the radial directions of wood respectively. Bending moment was centrally applied by using an Instron-type testing machine, over a loading span of 350 mm, under four-point loading over a 1100 mm span. Under loading, the velocities of shear waves polarized parallel and normal to the direction of bending stress (V1 and V2 respectively) were measured at 7 points along the center of the span of the specimen by using the sing-around method. Ultrasonic waves were propagated transverse to the direction of applied bending stresses, that is, in the radial direction of the wood. A special holder was used to attach the ultrasonic transducers to the beam specimen with constant pressure at all measuring positions. Methods and equipment for the bending load, strain, and velocity measurements were the same as described in Chapter 2. Figure 6 illustrates a setup for the applied load, strain, and ultrasonic wave velocity measurements in the specimen under bending.
Fig 6: Setup for ultrasonic wave velocity measurement in wood beam specimen
under bending. 1, Wood beam specimen; 2, ultrasonic shear wave sensors (the direction of oscillation is polarized parallel or normal to the direction of the bending stress); 3, strain gauges 10 mm long; 4, load 350 mm span; 5, support 1100 mm span; 6, commercially available ultrasonic velocity measurement unit “UVM-2”; 7, data logger “7V-14”; 8, personal computer; 9, periodic time of sing-around; 10, applied load; 11, strain |
According to the acoustoelastic birefringent effect, the difference of the principal stresses is obtained with the relative difference of the wave velocities, and the acoustoelastic birefringent constants (a, Ca) as follows: t1 – t2 = ((V1 – V2)/ VT – a) / Ca. These constants (a, Ca) were obtained by the acoustoelastic birefringent experiment conducted separately in Chapter 2 using small clear specimens, which was the same material as used in the beam specimen. Additionally in this experimental mode, only bending moment was produced and no shear force was produced over a loading span of the beam specimen. The difference of the principal stresses becomes the bending stress around the center of the span.
For the comparison of the acoustoelastic birefringent stress measurements, strain gauges 10 mm long were attached at 7 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℃ and 55% relative humidity.
3.2. Results and discussion
Table 2 shows examples of the experimental results of ultrasonic shear wave velocities (V1, V2)
under bending tests. These values in the table were obtained with the ultrasonic mode of the shear waves under 2 kN-bending load for Japanese magnolia. The velocities of ultrasonic shear waves were different due to the different measuring positions. In addition, the values of the velocities V1 were larger than those of V2 at each measuring position. The measuring position 0.0-mm means on the neutral axis of the beam specimen. Their values of V1 and V2 in the table ranged from 1593.2 to 1669.9 m/s and 667.5 to 809.9 m/s respectively and they had no tendencies due to the measuring position. However, the velocity near the neutral axis (at 7.5 mm from the neutral axis) was the highest. This may be connected with the relationship between the propagation direction of ultrasonics and the orientation of annual rings.
| Measuring Position [mm] | Shear wave velocity | Acoustic anisotropy | | Predicted stress | ||
| V1 [m/s] | V2 [m/s] | (V1-V2)/VT | a | (V1–V2)/VT–a | ||
| 37.5 | 1665.177439 | 807.200439 | 0.694050 | 0.705222 | -0.011172 | Compressive |
| 22.5 | 1593.169440 | 770.930770 | 0.695604 | 0.701760 | -0.006156 | Compressive |
| 7.5 | 1669.930124 | 809.920628 | 0.693598 | 0.696047 | -0.002449 | Compressive |
| 0.0 | 1650.939579 | 798.516950 | 0.696010 | 0.696047 | -0.000037 | Compressive |
| -7.5 | 1622.229745 | 724.327590 | 0.765293 | 0.764115 | 0.001178 | Tensile |
| -22.5 | 1631.149193 | 709.883245 | 0.787060 | 0.786074 | 0.000986 | Tensile |
| -37.5 | 1613.009345 | 667.486260 | 0.829226 | 0.826521 | 0.002705 | Tensile |
| Table 2: Results of shear wave velocities, acoustic anisotropy, and predicted stress states under 2 kN loading. | ||||||
The relative differences of the shear waves ((V1 – V2) / VT) in the table, acoustic anisotropy, showed smaller values at the upper positions (7.5, 22.5, and 37.5 mm from the neutral axis) and larger at the lower positions (–7.5, –22.5, and –37.5 mm). The differences between the texture- and stress-induced birefringences ((V1 – V2) / VT – a) were negative values at the upper positions and positive values at the lower positions.
The results from the above and the acoustoelastic birefringent experiments suggested that the compressive bending stresses were distributed in the upper side of the beam specimen and the tensile in the lower side. The bending stress values were calculated as follows: ((V1 – V2) / VT – a) / Ca, where Ca was the acoustoelastic birefringent constant.
The bending stresses obtained by the velocity measurements of shear waves were indicated as
| Measuring Position [mm] | Stress-induced birefringence | Estimated bending stress | ||
| Ca [x 10-4MPa-1] | sa [MPa] | sc [MPa] | sg [MPa] | |
| 37.5 | 11.456020 | -9.75 | -9.40 | -9.80 |
| 22.5 | 1.456020 | -5.37 | -5.64 | -6.19 |
| 7.5 | 11.456020 | -2.14 | -1.87 | -1.38 |
| 0.0 | 11.456020 | -0.03 | 0.00 | -0.11 |
| -7.5 | 4.415881 | 2.67 | 1.87 | 2.23 |
| -22.5 | 1.458840 | 6.76 | 5.64 | 5.76 |
| -37.5 | 2.878196 | 9.40 | 9.40 | 9.32 |
| Table 3: Acoustoelastic birefringent constants and estimated stress values. | ||||
In the table, the stress values obtained by the strain gauge method and mechanical calculations were also given ass g ands c 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 be estimated adequately by the acoustoelastic birefringent method. This finding suggests that the acoustoelastic birefringent phenomena of wood can be applied to determine the stress conditions of wood.
The effect of stresses on ultrasonic shear wave velocity propagating transverse to the direction of applied stress in wood was investigated experimentally. The ultrasonic modes considered were shear waves polarized parallel and normal to the direction of the applied stress. The experimental results indicated the existence of acoustoelastic birefringent phenomena. The velocities of shear waves polarized parallel and normal to the direction of the applied stress were different each other. The relative differences of the shear wave velocities were given as functions of the applied stress. The acoustoelastic birefringent constants were obtained from the relationships between the relative differences of the shear wave velocities and the applied stresses. The absolute values of the constants of wood were larger than those of metallic materials.
The acoustoelastic birefringent phenomena showed a difference in character under compressive and tensile stresses. This was considered an advantageous point when applying the acoustoelastic birefringent effect for stress determination of wood.
The bending stress values by the acoustoelastic birefringent method seemed to have been adequately estimated and agreed well with those obtained by the strain gauge method and mechanical calculation.
The above results indicated that ultrasonic shear wave velocities propagating through wood changed with great sensitivity to the applied stress, and suggested the possible application of acoustoelastic birefringent technique for the determination of the stress conditions of wood. To make it possible, systematic research on the acoustoelasticity of wood should be made according to the ultrasonic mode, propagating direction, and stress direction. In addition, development in ultrasonic technique, a new ultrasonic sensor of non-contact type for example, should be desired for the simple and accurate measurement.
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