Measuring Poisson’s ratio: mechanical characterization of spruce wood by means of noncontact optical gauging techniques
 503 Downloads
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.
References
 An W, Carlsson TE (2003) Speckle interferometry for measurement of continuous deformations. Opt Lasers Eng 40:529–541. https://doi.org/10.1016/S01438166(02)000854 CrossRefGoogle Scholar
 Anwander M, Zagar BG, Weiss B, Weiss H (2000) Noncontacting strain measurements at high temperatures by the digital laser speckle technique. Exp Mech 40:98–105. https://doi.org/10.1007/BF02327556 CrossRefGoogle Scholar
 Bachtiar EV, Sanabria SJ, Mittig JP, Niemz P (2017) Moisturedependent elastic characteristics of walnut and cherry wood by means of mechanical and ultrasonic test incorporating three different ultrasound data evaluation techniques. Wood Sci Technol 51:47–67. https://doi.org/10.1007/s002260160851z CrossRefGoogle Scholar
 Bader TK, Eberhardsteiner J, de Borst K (2015) Shear stiffness and its relation to the microstructure of 10 European and tropical hardwood species. Wood Mater Sci Eng 12:82–91. https://doi.org/10.1080/17480272.2015.1030773 CrossRefGoogle Scholar
 Bodig J, Jayne BA (1982) Mechanics of wood and wood composites. Van Nostrad Reinhold Company, New YorkGoogle Scholar
 Bovik AC (2010) Handbook of image and video processing. Academic press, CambridgeGoogle Scholar
 Carrington H (1921) XVII. The determination of values of Young’s modulus and Poisson’s ratio by the method of flexures. Lond Edinb Dublin Philos Mag J Sci 41:206–210. https://doi.org/10.1080/14786442108636212 CrossRefGoogle Scholar
 Carrington H (1922a) The elastic constants of spruce as influenced by moisture. Aeronaut J (Lond Engl 1897) 26:462–471. https://doi.org/10.1017/S2398187300139465 CrossRefGoogle Scholar
 Carrington H (1922b) XCV. Young’s modulus and Poisson’s ratio for spruce. Lond Edinb Dublin Philos Mag J Sci 43:871–878. https://doi.org/10.1080/14786442208633943 CrossRefGoogle Scholar
 Choi D, Thorpe JL, Hanna RB (1991) Image analysis to measure strain in wood and paper. Wood Sci Technol 25:251–262. https://doi.org/10.1007/BF00225465 CrossRefGoogle Scholar
 Chu TC, Ranson WF, Sutton MA (1985) Applications of digitalimagecorrelation techniques to experimental mechanics. Exp Mech 25:232–244. https://doi.org/10.1007/BF02325092 CrossRefGoogle Scholar
 Crespo J, Aira JR, Vázquez C, Guaita M (2017) Comparative analysis of the elastic constants measured via conventional, ultrasound, and 3D digital image correlation methods in Eucalyptus globulus labill. BioResources 12:3728–3743CrossRefGoogle Scholar
 Dahl KB, Malo KA (2009) Planar strain measurements on wood specimens. Exp Mech 49:575–586. https://doi.org/10.1007/s1134000891620 CrossRefGoogle Scholar
 Dantec Dynamics A/S (2017) 3D ESPI system (Q300). https://www.dantecdynamics.com/3despisystemq300. Accessed 27 Aug 2017
 Davis JR (2004) Tensile testing. ASM international, Materials ParkGoogle Scholar
 DIN 52188:1979–05 (1979) Prüfung von Holz—Bestimmung der Zugfestigkeit parallel zur Faser (Testing of wood; determination of ultimate tensile stress parallel to grain). Deutsches Institut für Normung, Berlin (in German) Google Scholar
 DIN EN ISO 9513:201305 (2013) Metallische Werkstoffe—Kalibrierung von LängenänderungsMesseinrichtungen für die Prüfung mit einachsiger Beanspruchung (Metallic materials—calibration of extensometer systems used in uniaxial testing). Deutsches Institut für Normung, Berlin (in German) Google Scholar
 Eberhardsteiner J (1995) Biaxial testing of orthotropic materials using electronic speckle pattern interferometry. Measurement 16:139–148. https://doi.org/10.1016/02632241(95)000194 CrossRefGoogle Scholar
 Eberhardsteiner J (2002) Mechanisches Verhalten von Fichtenholz: Experimentelle Bestimmung der biaxialen Festigkeitseigenschaften (Mechanical behaviour of spruce wood: experimental determination of biaxial strength properties). Springer, Wien (in German) Google Scholar
 Figliola RS, Beasley DE (2001) Theory and design for mechanical measurements, 3rd edn. Wiley, New YorkGoogle Scholar
 Forsberg F, Sjödahl M, Mooser R et al (2010) Full threedimensional strain measurements on wood exposed to threepoint bending: analysis by use of digital volume correlation applied to synchrotron radiation microcomputed tomography image data. Strain 46:47–60. https://doi.org/10.1111/j.14751305.2009.00687.x CrossRefGoogle Scholar
 Garab J, Keunecke D, Hering S et al (2010) Measurement of standard and offaxis elastic moduli and Poisson’s ratios of spruce and yew wood in the transverse plane. Wood Sci Technol 44:451–464. https://doi.org/10.1007/s0022601003622 CrossRefGoogle Scholar
 Gindl W, Müller U (2006) Shear strain distribution in PRF and PUR bonded 3–ply wood sheets by means of electronic laser speckle interferometry. Wood Sci Technol 40:351–357. https://doi.org/10.1007/s0022600500518 CrossRefGoogle Scholar
 Gindl W, Sretenovic A, Vincenti A, Müller U (2005) Direct measurement of strain distribution along a wood bond line. Part 2: Effects of adhesive penetration on strain distribution. Holzforschung 59:307–310. https://doi.org/10.1515/HF.2005.051 CrossRefGoogle Scholar
 Gingerl M (1998) Realisierung eines optischen Deformationsmeßsystems zur experimentellen Untersuchung des orthotropen Materialverhaltens von Holz bei biaxialer Beanspruchung (Realization of an optical deformation measuring system for the experimental investigation of the orthotropic material behaviour under biaxial stress). Dissertation, Technische Universität Wien (in German)Google Scholar
 Hearmon RFS (1948) The elasticity of wood and plywood. For Prod Res 7:1–87Google Scholar
 Hering S, Keunecke D, Niemz P (2012) Moisturedependent orthotropic elasticity of beech wood. Wood Sci Technol 46:927–938. https://doi.org/10.1007/s0022601104494 CrossRefGoogle Scholar
 Hörig H (1931) Zur Elastizität des Fichtenholzes. I. Folgerungen aus Messungen von H. Carrington an Spruce (To the elasticity of spruce wood. I. Consequences of the measurements conducted by H. Carrington on Spruce). Zeitschr f techno Phys 12:369 (in German) Google Scholar
 Hörig H (1935) Anwendung der Elastizitätstheorie anisotroper Körper auf Messungen an Holz (Application of the elasticity theory of anisotropic bodies to wood measurements). Arch Appl Mech 6:8–14 (in German) Google Scholar
 Jin H, Sciammarella C, Yoshida S, Lamberti L (2013) Advancement of optical methods in experimental mechanics, volume 3: conference proceedings of the society for experimental mechanics series. SpringerGoogle Scholar
 Jones R, Wykes C (1989) Holographic and speckle interferometry. Cambridge University Press, CambridgeCrossRefGoogle Scholar
 Kamegawa MN (1999) Strain measuring instrument, European Patent No. EP 0 629 835 B1. European Patent OfficeGoogle Scholar
 Keunecke D, Hering S, Niemz P (2008) Threedimensional elastic behaviour of common yew and Norway spruce. Wood Sci Technol 42:633–647. https://doi.org/10.1007/s0022600801927 CrossRefGoogle Scholar
 Kollmann FFP, Côté WA Jr (1968) Principles of wood science and technology—solid wood. Springer, MünchenCrossRefGoogle Scholar
 Konnerth J, Valla A, Gindl W, Müller U (2006) Measurement of strain distribution in timber finger joints. Wood Sci Technol 40:631–636. https://doi.org/10.1007/s0022600600909 CrossRefGoogle Scholar
 Lekhnitskii SG, Fern P, Brandstatter JJ, Dill EH (1964) Theory of elasticity of an anisotropic elastic body. Phys Today 17:84CrossRefGoogle Scholar
 Longo R, Laux D, Pagano S et al (2018) Elastic characterization of wood by resonant ultrasound spectroscopy (RUS): a comprehensive study. Wood Sci Technol 52:383–402. https://doi.org/10.1007/s002260170980z CrossRefGoogle Scholar
 MajanoMajano A, FernandezCabo JL, Hoheisel S, Klein M (2012) A test method for characterizing clear wood using a single specimen. Exp Mech 52:1079–1096. https://doi.org/10.1007/s1134001195606 CrossRefGoogle Scholar
 Meschede D (2015) Gerthsen Physik. SpringerVerlag Berlin Heidelberg (in German) CrossRefGoogle Scholar
 Messphysik—Materials Testing (2017) Laser Speckle Extensometer ME53. http://www.messphysik.com/fileadmin/messphysikdaten/Download/Laser_speckle_extensometer_en.pdf#page=16&zoom=auto,205,558. Accessed 30 Aug 2017
 Milch J, Brabec M, Sebera V, Tippner J (2017) Verification of the elastic material characteristics of Norway spruce and European beech in the field of shear behaviour by means of digital image correlation (DiC) for finite element analysis (FEA). Holzforschung 71:405–414. https://doi.org/10.1515/hf20160170 CrossRefGoogle Scholar
 Müller U, Sretenovic A, Vincenti A, Gindl W (2005) Direct measurement of strain distribution along a wood bond line. Part 1: shear strain concentration in a lap joint specimen by means of electronic speckle pattern interferometry. Holzforschung 59:300–306. https://doi.org/10.1515/HF.2005.050 CrossRefGoogle Scholar
 Müller U, Ringhofer A, Brandner R, Schickhofer G (2015) Homogeneous shear stress field of wood in an Arcan shear test configuration measured by means of electronic speckle pattern interferometry: description of the test setup. Wood Sci Technol 49:1123–1136. https://doi.org/10.1007/s0022601507553 CrossRefGoogle Scholar
 Neuhaus FH (1981) Elastizitätszahlen von Fichtenholz in Abhängigkeit von der Holzfeuchtigkeit (Elasticity constants of spruce wood in relation to the wood moisture content). Dissertation, RuhrUniversität Bochum (in German)Google Scholar
 Niemz P, Caduff D (2008) Untersuchungen zur Bestimmung der Poissonschen Konstanten an Fichtenholz (Investigations to determine the Poisson’s ratio of spruce wood). Holz Roh Werkst 66:1–4. https://doi.org/10.1007/s0010700701882 (in German) CrossRefGoogle Scholar
 Niemz P, Sonderegger W (2017) Holzphysik: Physik des Holzes und der Holzwerkstoffe (Wood physics: physics of wood and woodbased materials). Carl Hanser Verlag GmbH Co KG, Munich (in German) CrossRefGoogle Scholar
 Pan B, Wang B (2016) Digital image correlation with enhanced accuracy and efficiency: a comparison of two subpixel registration algorithms. Exp Mech 56:1395–1409. https://doi.org/10.1007/s113400160180z CrossRefGoogle Scholar
 Pan B, Qian K, Xie H, Asundi A (2009) Twodimensional digital image correlation for inplane displacement and strain measurement: a review. Meas Sci Technol 20:062001. https://doi.org/10.1088/09570233/20/6/062001 CrossRefGoogle Scholar
 Perkins RW (1967) Concerning the mechanics of wood deformation. For Prod J 17:55–67Google Scholar
 Qing H, Mishnaevsky L (2010) 3D multiscale micromechanical model of wood: from annual rings to microfibrils. Int J Solids Struct 47:1253–1267. https://doi.org/10.1016/j.ijsolstr.2010.01.014 CrossRefGoogle Scholar
 Rastogi PK, Huntley JM, Jones JDC et al (2001) Digital speckle pattern interferometry and related techniques. Wiley, ChichesterGoogle Scholar
 Samarasinghe S, Kulasiri D (2004) Stress intensity factor of wood from cracktip displacement fields obtained from digital image processing. Silva Fenn 38:267–278. https://doi.org/10.14214/sf.415 CrossRefGoogle Scholar
 Toussaint E, Fournely E, Moutou Pitti R, Grédiac M (2016) Studying the mechanical behavior of notched wood beams using fullfield measurements. Eng Struct 113:277–286. https://doi.org/10.1016/j.engstruct.2016.01.052 CrossRefGoogle Scholar
 Valla A, Konnerth J, Keunecke D et al (2011) Comparison of two optical methods for contactless, full field and highly sensitive inplane deformation measurements using the example of plywood. Wood Sci Technol 45:755–765. https://doi.org/10.1007/s0022601003947 CrossRefGoogle Scholar
 Vial G (2004) Tech spotlight—video extensometers. In: Adv. Mater. Process. https://www.asminternational.org/documents/10192/1908540/amp16204p033.pdf/612298f5c2584490ab3e3ebc3f6e4daf. Accessed 5 July 2017
 Voigt W (1882) Allgemeine Formeln für die Bestimmung der Elastizitätskonstanten von Kristallen durch Beobachtung der Biegung und Drillung von Prismen (General formulas to determine the elastic constants of crystals by observing the bending and twisting of prisms). Ann Phys 252:273–321 (in German) CrossRefGoogle Scholar
 Voigt W (1887) Theoretische Studien über die Elastizitätsverhältnisse der Kristalle (Theoretical studies on the elasticity of crystals). Königliche Gesellschaft der Wissenschaften zu Göttingen (in German)Google Scholar
 Voigt W (1966) Lehrbuch der Kristallphysik (Textbook of crystal physics). Vieweg + Teubner Verlag, Wiesbaden (in German) CrossRefGoogle Scholar
 Vorobyev A, Arnould O, Laux D et al (2016) Characterisation of cubic oak specimens from the Vasa ship and recent wood by means of quasistatic loading and resonance ultrasound spectroscopy (RUS). Holzforschung 70:457–465. https://doi.org/10.1515/hf20150073 CrossRefGoogle Scholar
 Wolverton M, Bhattacharyya A, Kannarpady GK (2009) Efficient, flexible, noncontact deformation measurements using video multiextensometry. Exp Tech 33:24–33. https://doi.org/10.1111/j.17471567.2008.00370.x CrossRefGoogle Scholar
 Wommelsdorff O (1966) Dehnungsund Querdehnungszahlen von Hölzern (Elongation and transverse strain constants of wood). Dissertation, Leibniz Universität Hannover (in German)Google Scholar
 Xavier J, Avril S, Pierron F, Morais J (2007) Novel experimental approach for longitudinalradial stiffness characterisation of clear wood by a single test. Holzforschung 61:573–581. https://doi.org/10.1515/HF.2007.083 CrossRefGoogle Scholar
 Xavier J, Belini U, Pierron F et al (2013) Characterisation of the bending stiffness components of MDF panels from fullfield slope measurements. Wood Sci Technol 47:423–441. https://doi.org/10.1007/s0022601205076 CrossRefGoogle Scholar
 Zink AG, Davidson RW, Hanna RB (1995) Strainmeasurement in wood using a digital image correlation technique. Wood Fiber Sci 27:346–359Google Scholar
 Zwick/Roell (2001) Betriebsanleitung für MaterialPrüfmaschine Z100/SW5A (Operating manual of the universal testing machine Z100/SW5A). Tech Dokumentation.v17 (in German)Google Scholar
 Zwick/Roell (2017a) LaserExtensometer: laserXtens (Zwick/Roell). http://www.zwickusa.com/en/products/extensometers/noncontactextensometers/laserxtensr.html. Accessed 30 Aug 2017
 Zwick/Roell (2017b) Videoextensometer: videoXtens (Zwick/Roell). http://www.zwickusa.com/en/products/extensometers/noncontactextensometers/videoxtensr.html. Accessed 30 Aug 2017
 Zwick/Roell (2017c) Mechanicalextensometer: makroXtens (Zwick/Roell). https://www.zwick.com/extensometers/makroxtens. Accessed 3 Oct 2017
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.