Measuring Poisson’s ratio: mechanical characterization of spruce wood by means of noncontact optical gauging techniques
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Abstract
In contemporary wood science, computeraided engineering (CAE) systems are commonly used for designing and engineering of highvalue products. In diverse CAE systems, highfidelity models with a full material description, including elastic constants such as Poisson’s ratios, are needed. Only few studies have dealt so far with the investigation of the Poisson’s ratio of spruce wood (Picea abies (L.) Karst.) or wood in general. Therefore, in the present study all six main Poisson’s ratios of spruce wood were determined in uniaxial tensile experiments by employing optical gauging techniques like electronic speckle pattern interferometry and a combination of laser and video extensometry. Consistent results for the Poisson’s ratios were found by applying these different optical gauging techniques. However, values found in the literature are sometimes considerably different from values established in this study. For that reason, the optical gauging techniques were evaluated with a conventional mechanical extensometer, which proved that there were no significant differences between the established measurements. Finally, in this study the feasibility of different noncontact optical gauging techniques was evaluated and compared through the comparison of the Poisson’s ratios, which showed that noncontact optical gauging techniques are suitable for establishing the Poisson’s ratio of (spruce) wood.
Introduction
Nowadays, computeraided engineering (CAE) methods such as finiteelement modeling (FEM) are used for designing and engineering of highvalue products. Reliable FEM is based on a sound data basis of material properties, such as elastic constants, including the Poisson’s ratio (ν). For anisotropic materials like wood, the Poisson’s ratio for one orthogonal direction is the ratio of the transverse contraction (transverse strain (ε_{q})), to the axial extension (axial strain (ε_{l})). These parameters have mainly been investigated in the last 4–5 decades by mechanical or electrical measurement systems (e.g., strain gauges, mechanical extensometer systems, inductive strain measurement devices), because of the lack of availability and the high price of optical measurement systems (Davis 2004).
The first examinations of the Poisson’s ratio of spruce wood were conducted by Carrington (1921, 1922a, b). He deduced the Poisson’s ratio from flexure experiments by measuring the curvature in lateral direction (transverse strain (ε_{q})) and longitudinal direction (axial strain (ε_{l})) with a telescope. Hörig (1931) reevaluated the data and adopted the ideas of Voigt (1882, 1887, 1966), about the orthotropic behavior of materials on wood. The model by Hörig (1935) is the basis for the orthotropic description of wood that is used nowadays. Further substantial studies on spruce wood were carried out by Wommelsdorff (1966) and Neuhaus (1981). They determined the six orthotropic Poisson’s ratios using inductive strain measurement devices and also strain gauges by means of tensile and flexure experiments. Furthermore, Niemz and Caduff (2008) and also Keunecke et al. (2008) investigated the Poisson’s ratio of spruce wood. Keunecke et al. (2008) have chosen digital image correlation (DIC) to measure the strain distribution. DIC is a noncontact optical surface deformation gauging technique (Chu et al. 1985; Zink et al. 1995; Pan et al. 2009; Valla et al. 2011).
In more recent studies, threedimensional optical digital measurements (3D ODM) and also resonant ultrasound spectroscopy (RUS) methods were used to establish all elastic constants by using only one type of specimen (Forsberg et al. 2010; MajanoMajano et al. 2012; Vorobyev et al. 2016). A clear advantage is that all components of the stiffness tensor are established with the same specimen by employing a consistent method. Currently, though, not all elastic constants can be derived robustly (e.g., Poisson’s ratio)—as for example the viscoelastic damping of wood may cause an overlapping of resonant peaks (Longo et al. 2018) which eventually may lead to a wrong iterative deduction of the elastic constants in the inverse identification. This applies in particular to wood with low density. Further, Longo et al. (2018) pointed out that the free resonance frequencies are very insensitive to ν_{RT} and not sensitive at all to v_{LR} and ν_{LT}. Threedimensional ODM requires highresolution cameras and a high level of expertise in material characterization, due to the need of the mathematical implementation of the procedure to establish consistent measurements (MajanoMajano et al. 2012). Moreover, the setup may bias the measurement results, which needs to be clarified before this technique can be considered as standard method for future wood material characterization. In summary, RUS and 3D ODM for establishing Poisson’s ratio are uncertain and may only be indicated when nondestructive testing is required (Bachtiar et al. 2017).
Optical gauging techniques that provide independent mechanical material properties in micro or even nanoscale were found to be suitable for wood characterization (Xavier et al. 2007, 2013; Valla et al. 2011; Toussaint et al. 2016). Furthermore, these methods have the advantage to be contactless, which means avoiding any mechanical influences on the specimen. Therefore, in this study the optical gauging techniques “Electronic Speckle Pattern Interferometry (ESPI), laser extensometry and video extensometry” are compared headtohead for establishing the Poisson’s ratio of (spruce) wood. Former studies prove that these methods are suitable for the mechanical characterization of the elastic properties of wood (Gingerl 1998; Eberhardsteiner 2002; Samarasinghe and Kulasiri 2004; Gindl et al. 2005; Müller et al. 2005; Konnerth et al. 2006; Gindl and Müller 2006; Dahl and Malo 2009; Valla et al. 2011; Bader et al. 2015; Crespo et al. 2017; Milch et al. 2017).
ESPI is a noncontact gauging technique based on the Michelson interferometer (Meschede 2015), which is used for planar strain measurement in the present study. The technique uses laser light (coherent light wave) together with a CCD camera to record displacements of the specimen surface. The surface is illuminated with a laser beam from two different planar directions, and the reflected light is registered by a CCD sensor. The ESPI system converts the light information into a speckled image, which describes the surface of the object. Deformation of the specimen results in a new speckle pattern. By subtracting the new speckle pattern from the reference pattern, an illustration with typical fringe pattern is obtained (Jones and Wykes 1989). In the next step, a phaseshift method is used to transform the fringe picture into a socalled 2πmodulo image, which is used to create a map of displacement (Eberhardsteiner 1995; An and Carlsson 2003; Müller et al. 2015). Additional material data (for example strain distribution) can be gained from the deformation map through postprocessing. More comprehensive information about the ESPI technique is available in other studies (Gingerl 1998; Rastogi et al. 2001; Eberhardsteiner 2002; Müller et al. 2005).
The basic principles of the laser extensometry method are similar to the ESPI technique. A laser source radiates a beam, which is projected on the surface of the specimen. The reflected light beams are recorded on a camera sensor, which generates a speckle pattern on the basis of the intensity distribution (Messphysik—Materials Testing 2017). The mechanical load induces movements on the object surface. Those movements indicate displacements of the speckle pattern as well. The core of the technique is to identify pattern areas of the initial picture in the upcoming images (Zwick/Roell 2017a). Due to the unique gray value distribution of any defined pattern area, it is possible to find these speckle zones in any upcoming deformation image. After that, a complex algorithm runs to find the motion of the defined speckle zone between the initial picture and the following images. For the estimation of the strain in one direction, it is necessary to perform this procedure on two selfcontained pattern zones at least. More comprehensive information about the laser extensometry technique can be found elsewhere (Choi et al. 1991; Kamegawa 1999; Anwander et al. 2000; Jin et al. 2013; Messphysik—Materials Testing 2017; Zwick/Roell 2017a).
The video extensometry method is based on capturing ongoing images of the specimen, for example, during a tensile test by using a digital video camera. To capture the lateral movements, the specimens need to be marked somehow (e.g., sticker and pen marker) at least on two different positions. By using this method, it is important to have high contrast between the object surface and the measurement points (markers) to ensure unaltered results. While the specimen is stressed, the pixel distance between these markers is tracked continuously. Image processing algorithms are used to track these motions in real time. Automatically, a direct strain measurement value can be obtained by mapping these motion measurements against the initial specimen image. For recording the transverse deformations of the specimens, no extra marking is required. In this case, special edge detection algorithms are applied (Zwick/Roell 2017b). The video extensometry technique provides noncontact realtime strain measurement in lateral and transverse direction independently from each direction. More specific information about the fundamentals of the technique can be found in Vial (2004), Wolverton et al. (2009), Bovik (2010) and Zwick/Roell (2017b).

ESPI, laser extensometry and video extensometry are suitable for the detection of the Poisson’s ratio of wood.

Poisson’s ratio gained by means of ESPI, laser extensometry and video extensometry will show no statistically significant differences.
Materials and methods
Material
Solid wood made of Norway spruce (Picea abies (L.) Karst.) specimens was used in the experiments. Sawn timber without noticeable defects like knots or cracks was meticulously selected. Semifinished elements in the different anatomical directions were cut out of the boards by means of a circular saw. For producing the samples out of these elements, a CNC and a conventional planning and a milling machine were used. After manufacturing the raw material to the desired shape, samples were conditioned at a temperature of 20 ± 2 °C and a relative humidity of 65 ± 5% (after ISO 554) to an average moisture content of ω = 12%. Under this condition, the average sample density (ρ) was 465 ± 30 kg/m^{3}.
Designation of Poisson’s ratio
Calculation of Poisson’s ratio as compliance coefficient
It means that the linear elastic mechanical behavior can be described by three moduli of elasticity, three shear moduli and three Poisson’s ratios, whereas only three of the six main orthogonal Poisson’s ratios are independent material constants. Other bounds on the moduli of orthotropic materials are caused by the requirement that the compliance matrix must be positive definite. More fundamentals about the calculation and estimation of the Poisson’s ratio of wood and woodbased materials can be found in Kollmann and Côté (1968), Bodig and Jayne (1982) and Niemz and Sonderegger (2017).
Experiments
Summarized comparison of the characteristics of the gauging techniques ESPI, laser extensometry and video extensometry with respect to the conducted measurements
Characteristics  ESPI  Laser extensometry  Video extensometry 

Experimental setup of the device  Experience required, due to the high sensitivity  Easy, since the devices are part of the universal testing machine  
Measurement method  Fullfield measurement  Speckle tracking  Punctual measurement 
Data acquisition  Slow, measurements has to be interrupted  Fast, continuous while the experiments are performed  
Postprocessing  Fast; programming of macros is possible  Not necessary, data are gained automatically  
Measurement resolution  ≥ 0.03 µm  ≥ 0.11 µm  ≥ 0.2 µm 
FoV  26 × 13 mm^{2}  40 × 20 mm^{2} (RL, RT, TR and TL) and 70 × 20 mm^{2} (LR and LT)  
Recorded pixel  1020 × 1020 px  1280 × 1025 px  
Spatial resolution  40 µm/px  60 µm/px  
Flexibility  Good  Intermediate  
General investment  Considerable  Moderate 
ESPI measurement
The ESPI Q300 DantecEttemeyer devices were mounted on the testing machine in such a way that the optical axis of both devices coincided and the specimen was clamped exactly in the center point in between both devices (Fig. 2a). Any vibrations of the devices were minimized by additional supporting frames. A free clamping length of 350 mm (for the dogboneshaped specimen Fig. 1a) and 70 mm (for the stripshaped specimen Fig. 1b, c) was chosen. In both cases, a field of view (FoV) of 26 × 13 mm^{2} was used, to observe deformation on the specimen. To prevent biasing of the data due to vibration artifacts, a preforce was applied prior to starting the test procedure to stabilize specimens. For longitudinal dogboneshaped samples (Fig. 1a), a preforce of 100 N was applied, and for stripshaped samples, a preforce of 20 N (Fig. 1b) and 10 N (Fig. 1c) was applied. The total deformation had to be established by accumulating the deformation determined in several load steps, because of the high sensitivity of the ESPI technique. It was assumed that two to three fringes in the yaxis picture would give reliable results per load step. The load step had to be adjusted to the stiffness of the material. Stiff material would lead to large load steps, which could be selected. A load step of 100 N and 10 N was found to be appropriate for testing wood in longitudinal (Fig. 1a) and transverse (Fig. 1b, c) direction, respectively. At every load step, the crosshead of the testing machine was stopped for 5 s to capture the generated speckle images in x and ydirection. For all samples, total deformation was divided into six load steps, which resulted in a maximum load of 700 N tested in longitudinal, 80 N (Fig. 1b) and 70 N (Fig. 1c) in transverse direction. Therefore, samples were stressed to σ = 5.83 MPa, σ = 0.67 MPa and σ = 0.58 MPa in longitudinal, radial and tangential direction, which corresponded to less than 20% of the breaking strength in the different directions. All ESPI images were recorded and analyzed with the postprocessing software ISTRA 2001 DantecEttemeyer (Ulm, Germany) to determine the Poisson’s ratio, afterward. For this, the mean values of axial and transverse strains were measured within the FoV and Poisson’s ratio was calculated corresponding to Eq. (1).
Laser and video extensometry measurement
The laser and video extensometry measurements were carried out on a universal testing machine Zwick/Roell Z020 (Ulm, Germany), equipped with an optical extensometer system including both gauging techniques. Therefore, the extensometer system contains a gauging sensor, a digital camera and a laser light source. An absolute measurement accuracy of 0.11 µm of the laser extensometry system, laserXtens (Zwick/Roell, Ulm, Germany), is specified by the manufacturer. With the laser extensometry system used, axial and transverse strain measurements can be performed simultaneously (Zwick/Roell 2017a). The video extensometry device, videoXtens (Zwick/Roell, Ulm, Germany), is a camera which is enclosed in a metal housing, with a measurement accuracy dependent on the field of view (FoV) (Zwick/Roell 2017b), for FoVs smaller than 200 mm with a measurement accuracy meeting the requirements specified in DIN EN ISO 9513:201305 (2013). In this study, the FoV was selected such as to ensure an accuracy of 0.2 µm. As illustrated in Fig. 2b, the video extensometry device was positioned in the center, which was flanked by two laser sources of the laser extensometry device. The measuring points of the laser extensometry device were positioned on the upper and lower side of the specimen. For the dogbone shaped samples, the distance of the measuring points was 70 mm, whereas for the stripshaped samples a distance of 40 mm was chosen. Contraction of the samples was measured in the center of the specimens. For this, the video extensometry device used the contrast of the edges of the specimen. Increased contrast of the edges was achieved by illuminating the specimen from the back. This setup was chosen because it is not possible to measure the axial strain (ε_{l}) and the transverse strain (ε_{q}) with videoXtens simultaneously.
First, laser extensometry was applied to measure strain in axial and transverse direction. In transverse direction, results showed a high variability. Hence, a hybrid approach was selected, using laser extensometry for measuring axial extension (ε_{l}) and video extensometry for transverse contraction (ε_{q}). Thereafter, the Poisson’s ratio was calculated by means of the software testXpert 2 V3.5 (Ulm, Germany) automatically. The clamping and measurement length for the dogbone shaped samples (LR and LT) amounted to 350 mm and 80 mm, respectively. For the stripshaped samples (RL, RT, TL and TR), the distances amounted to 70 mm and 40 mm, respectively. The specimens LR and LT (Fig. 1a) were stressed at maximum with a force of 4000 N and a preforce of 100 N, and the specimens RL, RT, TL and TR (Fig. 1b, c) with a preforce of 10 N and a maximum load of 200 N. Accordingly, the maximum tensile stress ε amounted to 34.17 MPa (specimens LR and LT) and 1.75 MPa (specimens RL, RT, TL and TR), which is far lower than the yield stress of spruce wood.
Mechanical extensometer measurement
MakroXtens is a conventional clipon mechanical extensometer with a measurement resolution of 0.5 µm, which meets the requirements specified in DIN EN ISO 9513:2012 class 0.5 (Zwick/Roell 2017c). More comprehensive information about mechanical extensometers can be found elsewhere in the literature (Figliola and Beasley 2001; Zwick/Roell 2001, 2017c; Davis 2004; Pan and Wang 2016).
Statistical evaluation
All statistical tests were carried out using the software package IBM SPSS Statistics 21. Initially, the Shapiro–Wilk test was applied to verify whether the measured data follow a normal distribution. Because the null hypothesis was rejected, which meant that the data did not follow a normal distribution, the Wilcoxonmatched pair test was used to determine the statistical equivalence of two data sets. To perform a statistical comparison with more than two data sets, the Friedman’s test was employed.
Results and discussion
Experimentally determined material data of spruce wood in comparison with the literature references: moisture content (ω), mean values (x̅) and coefficient of variation (COV) of the density: ρ_{L}, ρ_{R}, ρ_{T}, Poisson’s ratio: ν_{LR}, ν_{LT}, ν_{RL}, ν_{RT}, ν_{TL} and ν_{TR}, and the modulus of elasticity: E_{L}, E_{R} and E_{T}
Own measurements  Literature references  

ESPI  Laser extensometry (ε_{l}) in combination with video extensometry (ε_{q})  Hörig (1935)  Wommelsdorff (1966)^{a}  Neuhaus (1981)  Niemz and Caduff (2008)  Keunecke et al. (2008)  
Moisture content (ω)  (%)  12  12  9.8  13.7  12  12.1  12 
x̅[ρ_{L}]  (kg/m^{3})  473  473  465  –  417  435  470 
x̅[E_{L}]  (MPa)  –  14,635  16,324  11,287  11,877  11,496  12,800 
CoV[E_{L}]  (%)  –  18.2  –  –  –  20  9.2 
x̅[ν_{LR}]  (–)  –  0.706  0.43  0.447  0.409  0.376  0.36 
CoV [ν_{LR}]  (%)  –  36.6  –  –  –  26  13.2 
x̅[ν_{LT}]  (–)  –  0.690  0.53  0.561  0.549  0.420  0.45 
CoV[ν_{LT}]  (%)  –  19.7  –  –  –  18  8.2 
x̅[ρ_{R}]  (kg/m^{3})  478  478  423  –  417  486  480 
x̅[E_{R}]  (MPa)  970  1038  699  980  817  1099  625 
CoV[E_{R}]  (%)  16.7  17.1  –  –  –  12  20.4 
x̅[ν_{RL}]  (–)  0.110  0.120  0.019  0.049  0.055  0.022  0.018 
CoV[ν_{RL}]  (%)  60.1  58.7  –  –  –  62  – 
x̅[ν_{RT}]  (–)  0.656  0.681  0.42  0.586  0.599  0.640  0.48 
CoV[ν_{RT}]  (%)  8.2  12.2  –  –  –  17  19.2 
x̅[ρ_{T}]  (kg/m^{3})  442  442  458  –  417  415  460 
x̅[E_{T}]  (MPa)  293  281  400  429  420  452  397 
CoV[E_{T}]  (%)  27.5  23.6  –  –  –  13  10.3 
x̅[ν_{TL}]  (–)  0.041  0.033  0.013  0.028  0.035  0.015  0.014 
CoV[ν_{TL}]  (%)  78.1  87.9  –  –  –  42  – 
x̅[ν_{TR}]  (–)  0.739  0.690  0.24  0.26  0.311  0.335  0.21 
CoV[ν_{TR}]  (%)  7.6  18.1  –  –  –  33  16.8 
Almost all Poisson’s ratios established in this study violate the symmetry condition of the linear elastic and orthotropic compliance matrix [S]. This phenomenon has also been mentioned in previous studies (Neuhaus 1981; Bodig and Jayne 1982; Garab et al. 2010; Hering et al. 2012; Bachtiar et al. 2017). The stiffness or compliance matrix is symmetric due to Betti’s reciprocity theorem [the deflection d (in direction A) due to a unit force p (in direction B) is equal to the deflection d (in direction B) due to a unit force p (in direction A)]. It becomes asymmetric as soon as this theorem is violated, i.e., when deformation is dissipative (friction, damage) or the deformation is nonlocal. In order to still obtain a symmetric compliance matrix [S], as required for timeefficient FEM (and for parameterizing orthotropic material models), the calculation of the average value from each corresponding offdiagonal term, i.e., Eqs. (4–6), followed by a backward calculation to reobtain the elastic material parameters was pursued as proposed by Bachtiar et al. (2017).
Lekhnitskii et al. (1964) showed that all bodies can be divided into homogenous (physical properties remain invariant in all directions and all points) and nonhomogenous bodies, as well as in isotropic and anisotropic. Perkins (1967) noted that wood is inhomogeneous at macro and microscopic scale. Qing and Mishnaevsky (2010) investigated the effect of annual ring structure, microfibril angle and cell shape angle on the elastic constants in a numerical study employing a 3D micromechanical computational model of softwood, considering the wood’s structure at four scales from microfibrils to annual rings. They showed that v_{LR} increases with increasing microfibril angle and decreases with wood density. The v_{LT} increases with the increasing microfibril angle and cell shape angle. Hearmon (1948) showed that Poisson’s ratios can even gain negative values at certain microfibril angles. Consequently, it means that in future experimental testing, more parameters must be recorded (annual ring radius, content of early and latewood, microfibril angle, etc.).
In general, the Poisson’s ratios determined in this study have a higher mean value compared to the literature references. Particularly, the mean value x̅[ν_{RL}] is about 6.7 times higher than the lowest value found in the literature (Table 2). Even the values found in the literature are not consistent with each other and show wide dispersions. The differences to the literature references are open to speculation, because on the one hand, the scattering of the literature data could suggest similar median values compared to the own measurements. On the other hand, diverse gauging techniques and apparatuses with different measurement resolutions were used by each researcher. Nevertheless, in this study different gauging techniques were directly compared to each other with the same sample set.
Summarized results of the test of normality distribution (Shapiro–Wilk test) applied to the Poisson’s ratio: ν_{LR}, ν_{LT}, ν_{RL}, ν_{RT}, ν_{TL} and ν_{TR}, and to the modulus of elasticity: E_{L}, E_{R} and E_{T}
Shapiro–Wilk test  

Gauging technique  Parameter  Statistic  df  Sig. 
ESPI  E _{L} ^{a}  –  –  – 
ν _{LR} ^{a}  –  –  –  
ν _{LT} ^{a}  –  –  –  
E _{R}  .947  24  .238  
ν _{RT}  .958  12  .760  
ν _{RL}  .811  12  .013  
E _{T}  .881  23  .010  
ν _{TR}  .827  13  .014  
ν _{TL}  .805  10  .017  
Laser extensometry (for ε_{l}) in combination with video extensometry (for ε_{q})  E _{L}  .938  20  .222 
ν _{LR}  .884  8  .204  
ν _{LT}  .948  12  .608  
E _{R}  .890  21  .023  
ν _{RT}  .969  10  .886  
ν _{RL}  .949  11  .626  
E _{T}  .932  20  .167  
ν _{TR}  .950  11  .647  
ν _{TL}  .895  9  .227 
Summarized results of the test on statistical equivalence (Wilcoxon test) of the data gained by means of ESPI compared to laser extensometry (for ε_{l}) in combination with video extensometry (for ε_{q})
Wilcoxon test^{a}  

Parameter  Mean rank  Sum of ranks  Z  Asymp. Sig. (2tailed) 
E _{L} ^{b}  –  –  –  – 
–  –  
ν _{LR} ^{b}  –  –  –  – 
–  –  
ν _{LT} ^{b}  –  –  –  – 
–  –  
E_{R}  12.83  77.00  − 1.607  .108 
11.00  176.00  
ν_{RT}  4.40  22.00  − .561  .575 
6.60  33.00  
ν_{RL}  6.75  27.00  − .533  .594 
5.57  39.00  
E_{T}  10.09  111.00  − .224  .823 
11.00  99.00  
ν_{TR}  6.00  42.00  − .800  .424 
6.00  24.00  
ν_{TL}  5.25  21.00  − .178  .859 
4.80  24.00 
Summarized results of the test on statistical equivalence (Friedman test and Wilcoxon test) for the axial strain (ε_{L}) measurement by means of ESPI versus laser extensometry versus video extensometry versus mechanical extensometer
Friedman test  

Mean rank  N  χ ^{2}  df  Asymp. Sig. 
2.68 (ESPI)  19  1.421  3  .701 
2.53 (laser extensometry)  
2.21 (video extensometry)  
2.58 (mechanical extensometer) 
Wilcoxon test  

Gauging technique  Mean rank  Sum of ranks  Z  Asymp. Sig. (2tailed) 
Laser extensometry—ESPI  8.50  102.00  − .282  .778 
12.57  88.00  
Video extensometry—ESPI  10.8  108.00  − .523  .601 
9.11  82  
Mechanical extensometer—ESPI  10.58  127.00  − .400  .689 
11.56  104.00  
Video extensometry—laser extensometry  8.85  115.00  − .805  .421 
12.5  75.00  
Mechanical extensometer—laser extensometry  10.22  92.00  − .121  .904 
9.80  98.00  
Mechanical extensometer—video extensometry  8.75  70.00  − 1.006  .314 
10.91  120.00 
However, as the specimens and the testing conditions were identical for the own measurements, it is possible to say that there are no statistical differences between the measurement techniques ESPI, laser extensometry and video extensometry. Moreover, the results obtained confirm the first hypothesis of this study, i.e., the noncontact optical gauging techniques ESPI, laser extensometry and video extensometry are suitable for the detection of the Poisson’s ratio of wood.
Conclusion
In this study, three optical gauging techniques (electronic speckle pattern interferometry (ESPI), laser and video extensometry) and one mechanical gauging technique were used to establish the six Poisson’s ratio of spruce wood (Picea abies (L.) Karst.) in uniaxial tensile experiments.
All techniques were found to be suitable for establishing the Poisson’s ratios and returned statistically equivalent results. However, there are limitations in terms of the setup and specimen type. For example, with the “dogboneshaped specimen” it was not possible to establish ESPI measurements, because at a certain load level the specimens started to creep while capturing the image. Furthermore, the measurement of the transverse strain of any specimens via laser extensometry was not possible to establish due to the very small transverse contractions of the specimens that led to very small displacements of the measurement zones, which were not exceeding the measurement resolution of the device.
In engineering, wood is usually assumed to behave orthotropic. This model implies that the material behaves loadsymmetric elastic (tension/compression), is homogenous and features three mutually orthogonal elastic symmetry planes. Due to Betti’s theorem, the compliance tensor is generally assumed symmetric (about its diagonal), which is also advantageous for the time and resource (memory)efficient FEM calculations. The Poisson’s ratios established in this study, though, are violating the symmetry conditions of elastic orthotropic materials, which might be caused by, for example, nonlocal deformations. The authors recommend to follow the procedure outlined by Bachtiar et al. (2017) (calculating the average value from each corresponding offdiagonal term, followed by a backward calculation to reobtain the elastic material parameters), to warrant efficient FEM calculation and the use of preimplemented material models.
While the Poisson’s ratios established are consistent within the study, they were found considerably different to some of the values found in the literature. Various researches have shown that the elastic constants, including the Poisson’s ratios, are sensitive to the annual ring structure, microfibril angle and cell shape angle as well as density. The wide spread of values published in the literature clearly shows that in experimental testing of wood specimens more parameters (other than the density and moisture content) must be recorded: annual ring radius, content of early and latewood, and microfibril angle. Future testing may also distinguish between Poisson’s ratios in each lamina (early/latewood) of the wood specimen—something which might only be possible with fullfield optical gauging techniques.
In summary, the study shows that optical gauging techniques are suitable for determining the Poisson’s ratios of (spruce) wood. The discrepancies with the values found in other studies, though, clearly show the need to characterize and record the morphology of each specimen. Optical gauging techniques may further offer the possibility to establish the Poisson’s ratio laminawise.
Notes
Acknowledgements
Open access funding provided by University of Natural Resources and Life Sciences Vienna, Austria (BOKU). The results presented in this study are part of the research project “WoodC.A.R.” (Project No.: 861.421). Financial support by the Austrian Research Promotion Agency (FFG), Styrian Business Promotion Agency (SFG), Standortagentur Tirol and the companies DOKA GmbH, DYNAmore GmbH, EJOT Austria GmbH, ForstHolzPapier, Holzcluster Steiermark GmbH, IB STEINER, Lean Management Consulting GmbH, Magna Steyr Engineering GmbH & Co KG, MAN Truck & Bus AG, Mattro Mobility Revolutions GmbH and Weitzer Parkett GmbH & CO KG is gratefully acknowledged.
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