Microscopic computed tomography aided finite element modelling as a methodology to estimate hygroexpansion coefficients of wood: a case study on opposite and compression wood in softwood branches

1.1 XµCT aided FE modelling of wood

A state-of-the-art method to determine parameters for modelling comes from the field of bone and composite research and is called X-ray computed tomography (XµCT) aided finite element (FE) modelling (Auenhammer et al. 2022; Keyak et al. 1998). This method has only recently been applied to wood (Badel and Perre 2001; Florisson 2022; Fortino et al. 2017; Hachem et al. 2018; Huber et al. 2022; Kamke et al. 2014) and is complex and involves several steps. Most research on XµCT aided FE modelling focusses on certain steps that make up this process, which minimises the compatibility between image quality and model development (Auenhammer et al. 2021). An automatic transfer of information between different steps in this process is typically lacking. Non-automated, i.e. manual procedures, create labour intensive processes, as well as errors within and between each step of such a process that are larger than with an automated process (Florisson and Gamstedt unpublished data; Keyak et al. 1990). Recently, a methodology for XµCT aided FE modelling of wood was developed to promote a more efficient design and execution of this method (Florisson and Gamstedt unpublished data). The methodology focusses on wood with a moisture and temperature dependent material behaviour, but can also be used on other materials or material levels (µm – m). The methodology is presented in Figure 1 and consists of five different steps labelled source, experiment, image processing, model development, and output. The general principle of the methodology is that tomograms should be of quality that benefits the material characterisation, segmentation, fibre reconstruction, digital volume correlation (DVC), meshing and material model, where tomograms refer to the 3D reconstructed images (Withers et al. 2021). It is therefore important to clearly state the aim and objective at the beginning of the XµCT aided FE process (Auenhammer et al. 2021). A detailed description of the methodology and its bottlenecks can be found in Florisson and Gamstedt (unpublished data).

Figure 1:

Methodology for the microscopic lab-based computed tomography (XµCT) aided finite element modelling of wood, where DIC indicates digital image correlation (2D) and DVC denotes digital volume correlation (3D) (Florisson and Gamstedt unpublished data).

1.2 Hygroexpansion in opposite wood and compression wood

In conifers, reaction wood is formed as compression wood (CW) in response to gravistimulus or external factors (Groover 2016). For instance, within the cross section of Norway spruce branches, the upper side consists of opposite wood (OW), what is known as normal wood (NW) in the stem, whereas the underside consists largely of CW (Timell 1986a,b,c). Compared to OW formed in branches of Radiata pine, CW differs in appearance, structure and properties. CW is recognised by its darker colour, and structurally by thicker tracheid walls, higher coarseness, larger microfibril angle (MFA), and higher wood density (Li et al. 2014). CW formed in the stem is also known to have a different chemical composition, having a higher lignification which is distributed over the entire tracheid wall, instead of being concentrated in the middle lamellae, as with OW (Nanayakkara et al. 2009; Timell 1986a; Zhang et al. 2016). CW found in branches and leaning stems show quite a difference in mechanical properties compared with the complementary OW or NW, respectively (Burgert et al. 2004; da Silva Moreira et al. 2023; Gonçalves et al. 2019; Guo et al. 2023; Marasigan et al. 2022; Müller et al. 2006; Stanzl-Tschegg et al. 2011), such as lower longitudinal stiffness. Research suggest that this is caused by the larger MFA of the cellulose strands in CW (Färber et al. 2001), however, its high lignification leads to comparable compression strength as in OW despite the MFA differences (Gindl 2002). The heterogeneity of wood, manifested by the presence of reaction wood, induces engineering challenges on the occasion of differential swelling and shrinkage due to moisture changes. CW found in branches of Scots pine shows a significant difference in longitudinal shrinkage compared to OW (Włoch 1975). Research suggests that this is due to the difference in chemical composition. In addition to the mentioned higher lignin content and different lignin distribution, a small proportion of highly swellable (1→3)-β-D-glucans is present in CW (Włoch 1975; Zhang et al. 2016). Both these components show significant shrinkage and swelling in isolated state. The chemical difference between CW in the stem, branch and seedlings is said to be similar (Nanayakkara et al. 2009). While reaction wood formed in trunks has been extensively investigated, relatively little has been reported on softwood branches. However, from a zero-waist perspective and an optimal use of material, the timber industry is looking for ways to use the entire tree in the production of engineered wood products rather than only stem wood (Hartwig and Gamstedt 2020; Olarescu et al. 2022). Therefore, a proper identification of the hygroexpansion properties of branch wood is needed. For a more general overview of reaction wood, please consider Groover (2016).

1.3 Digital volume correlation

The calibration of an XµCT aided FE model is often supported by techniques such as DVC (Buljac et al. 2018; Forsberg et al. 2010; Hartig et al. 2021; Hild et al. 2016; Keunecke et al. 2012). Here, a calibration is the iterative fit between FE results and XµCT data in order to obtain material properties for modelling. DVC is an image-processing technique that can be used to estimate the 3D displacement field of an object using a fixed image (reference tomogram) and a moving image (tomogram of the deformed object) (Bay et al. 1999). The technique knows a local and a global approach, where in the local approach, the tomograms get subdivided into small volumes, which are independently registered, and in the global approach, the entire moving image is mapped onto the fixed image, creating a continuous displacement field (Bay et al. 1999; Buljac et al. 2018; Madi et al. 2013). The mapping performed in the global approach is called image registration. Suitable registration methods for wood are affine and non-rigid (or elastic) registration, where affine registration is based on translation, rotation and scaling and non-rigid registration locally warps the image (Patera et al. 2018). To the authors knowledge, global DVC has not yet been used to analyse wood and its hygroexpansion coefficients.

1.4 Putting the methodology to test

The aim of the current paper is to test the recently developed XµCT aided FE methodology using a case study. The study focuses on the estimation of hygroexpansion properties of both OW and CW found in branches of Norway spruce. The FE model is developed using information from ex-situ hygroexpansion experiments performed with a XµCT scanner. Global DVC was adopted to obtain the displacement fields during testing, which were used to calibrate the numerical model.

2.1 Experiments

2.1.1 Specimen preparation

Branches of Norway spruce were retrieved from Tranås in Småland county in Sweden. The branches were labelled A1, A2, B1, B2, B3 and B4, where A and B indicated a different fan of branches. After felling, the branches were labelled, wrapped in plastic and kept under frozen conditions before being cut into specimens as seen in Figure 3 by a professional carpenter. During the cutting process, the specimens had the possibility to dry. In total 18 specimens of OW and 18 specimens of CW were obtained for testing. The selection procedure resulted in three OW specimens and three CW specimens per branch, which were numbered according to Figure 3a and were located as close to the stem as possible. The nominal cross-sectional dimensions of the specimens were 5 × 5 × 5 mm³. All 36 specimens were tested as part of the experiment. One randomly chosen OW specimen (B4-OW-1) and one matching CW specimen (B4-CW-1) were used in the DVC analysis and FE simulations.

Figure 3:

Location of the opposite wood (OW) and compression wood (CW) specimens within the tree branch: (a) the location within the branch and (b) the location within the cross section of the branch. Also, an indication of the local (l, r and t) and global (x, y, z) coordinate systems is given.

2.1.2 Test setup

2.1.2.1 Computed tomography

A SkyScan 1172 XµCT scanner (Bruker, Belgium) (see Figure 4a and b) was used to obtain tomograms of the 36 OW and CW specimens. The scanner was equipped with a filament, electromagnetic lens, target, scintillator, specimen stand and an image detector. The X-ray source, which produced a cone beam, and the detector were positioned on opposite sides of specimen stand, see Figure 4b and c. The stand rotated during scanning and has the possibility to change its position between the source and the detector. This allows scanning of different specimen sizes. The SkyScan NRecon reconstruction software was used to reconstruct the cross-sectional slices obtained from angular projections during XµCT scanning (SkyScan 2011). The software used a modified Feldkamp algorithm with automatic adaption for the reconstruction.

Figure 4:

Computed tomography scanner: (a) SkyScan 1172 XµCT scanner, (b) inside of scanner showing the detector, X-ray source, and specimen stand, and (c) graphical illustration of the 2D detector, cone beam X-ray, and specimen on holder.

2.1.2.2 Compression tests

A Shimadzu Autograph AGS-X universal testing machine (UTM: Shimadzu, Tokyo, Japan) was used to perform compression tests. The UTM was equipped with a 500 N load cell. The force-displacement curve was obtained with a TRViewX Shimadzu Digital Video Extensometer (Shimadzu, Tokyo, Japan), which is a non-contact extensometer. The compression test setup prevented sideways lateral contact slipping caused by Poisson effects. This causes shear stress to develop close to the loading plates. The loading plates are in a fixed position and not allowed to rotate, which can result in uneven compression of specimens with non-parallel contact surfaces. In addition, the non-contact extensometer measured the displacement of the loading plates instead of the displacement of the specimen. This was done due to the small dimensions of specimens and leads to average values of displacement rather than local measurements. These design choices can lead to small errors when it comes to the determined elastic moduli. It was assumed that any machine compliance did not influence the deformation measurements of the wood specimens.

2.2 Finite element model

A 3D numerical model was created in commercial software Abaqus FEA^® (SIMULIA 2017b). The model was used to simulate the hygroexpansion of specimens B4-OW-1 and B4-CW-1. The material model was implemented in user-subroutine UMAT (SIMULIA 2017a). The orthotropic material orientation was defined in user-subroutine ORIENT as a local material orientation. The FE model was kept relatively simple, since the aim of the case study is to test the proposed methodology rather than giving a detailed analysis of wood. This means that the material is assumed homogeneous, and no distinction is made in density differences due to latewood, transition wood and earlywood. Also, no moisture gradients are assumed in the wood’s volume, eliminating mechanosorption from the analysis.

2.2.2 Specifications FE model

The meshed geometry of the numerical model is presented in Figure 5a. The dimensions are based on the mean height, width and length of each OW and CW sample set measured inside the tomograms obtained at 44 % RH as part of the experiment. The values can be found in the SI section “Parameters for modelling”. A structured linear hexahedral mesh was used. A mesh refinement was performed based on the displacement results, where computational time was the limiting factor. The chosen mesh size was 0.2 mm. The cube is supported by four pinned supports as visualised in Figure 5a, where the circle in the centre of the cube shows the fourth support fixed in x, y and z direction and located at the bottom of the cube in the far back. The support on the left is fixed in x and y direction, whereas the other two supports are fixed in only y direction. The cube will be subjected to a RH change from 44 to 98 %. The model assumes this change as a linear change in the MC pf the cube in time, which occurs uniformly over the entire volume. This means that no moisture gradients will occur during wetting. The MCs are a mean value of each OW and CW sample set measured as part of the experiment. The values are presented in Section 3.3.

Figure 5:

Specifications model. (a) Geometry and boundary conditions model, (b) visualisation method for pith detection, and (c) visualisation of the orthotropic material orientation constructed by the numerical model.

The location of the pith in the global coordinate system (x, y, z) both at the front (p_2,x, p_2,y) and the back (p_1,x, p_1,y) of the B4-OW-1 and B4-CW-1 specimen at 44 % RH is needed to define the local coordinate system that describes the annual ring curvature for each specimen. The information is used in user-subroutine ORIENT to establish a local coordinate system (l, r, t). The method to determine the pith location in the x–y plane is visualised in Figure 5b. The locations were retrieved from the tomograms by manually drawing circles along the annual rings using commercial software Avizo™ 3D 2021.2. The centres of these circles were assumed to coincide with the pith. The subroutine draws a line between points p_1,x and p_2,x. The values obtained for the pith location are collected in the SI section. The locations were used to establish the local material orientation with user-subroutine ORIENT (SIMULIA 2017a).

The elastic moduli related to the l, r and t material direction will be described using

(7) E l = E l 0 + E l w ( w f − w a )

(8) E r = E r 0 + E r w ( w f − w a )

(9) E t = E t 0 + E t w ( w f − w a )

(10) w f = 0.3 ( 1 + 0.003 ( 20 − T ) )

where, E_l0 is a reference value, E _lw indicates the linear dependency of the elastic modulus on MC, w _f is fibre saturation point and can be determined with Equation (10), w _a indicates the MC below fibre saturation point, and T is temperature in degrees Celsius (Florisson et al. 2021). The values of E_l0 and E _lw will be determined with the results from the compression tests and a linear regression analysis performed in the Curve Fitter application provided by MATLAB^® using Custom Equation. The results are collected both in Section 3.3. The Poisson ratios and the MC and temperature dependent shear moduli are taken from Florisson et al. (2021). The values for each cube and RH level are collected in Table 3. The hygroexpansion coefficients related to the l, r, and t material direction are obtained with a calibration of the FE model based on DVC results. More details on this procedure can be found in Section 2.4.

Table 3:

Material properties at 44 % and 98 % relative humidity for modelling specimens B4-OW and B4-CW, where G is the shear modulus at 21 °C and v is the Poisson ratio, and l, r, and t indicate the local material directions.

	B4-OW-44	B4-OW-98	B4-CW-44	B4-CW-98
G lr (MPa)	666	516	666	516
G lt (MPa)	632	482	632	482
G rt (MPa)	52	48	52	48
v lr (−)	0.35	0.35	0.35	0.35
v lt (−)	0.60	0.60	0.60	0.60
v rt (−)	0.55	0.55	0.55	0.55

2.3 Digital volume correlation

A global DVC analysis was performed to obtain the 3D displacement fields caused by swelling directly from tomograms. The DVC analysis was performed in commercial software Avizo™ 3D 2021.2 (AVIZO 2021). The solution technique behind global DVC can be described as

where, f refers – in the current study – to the reference tomogram (fixed image) at 44 % RH and g refers to the deformed tomogram (moving image) at 98 % RH. The position vectors are indicated by x and the sought displacement field by u. Solving Equation (11) is equivalent to minimising the correlation residual η = f − g, which should be close to the imaging noise level (AVIZO 2021). The problem can be linearized and expressed as a matrix inversion problem

where M is the problem matrix, δu is the sought increment of displacement at the considered increment, b depends on the image gradient of f and residual η. Since M is constant, the solution consists of successive updates of b after each iteration. The algorithm converges when the displacement increment norm |δu| is smaller than the tolerance set by the user, and indicates that a desired solution for the displacement field u(x) is found. The algorithm stops when it has converged or if the maximum number of iterations is reached. The algorithm implemented in global DVC uses affine registration to align the fixed image and moving image for analysis. An affine transformation captures translation, rotation, scaling and shear. It uses global transformation, which indicates that a single equation is used to register the entire image. Affine registration is suitable to capture the heterogeneous deformations of wood (Patera et al. 2018). A detailed description of the global DVC algorithm can be found in Madi et al. (2013).

The initial displacement field needed for the global DVC analysis came from a local DVC analysis. The settings used to perform both calculations are collected in Table 4. The sub-volume size and mesh size, as well as the convergence criterion of the global analysis, were chosen based on a refinement study. The correlation threshold, which discards bad measurements, was also chosen with a refinement study. Manual measurements of displacement were used to validate the global DVC analyses. The measurements were also made in commercial software Avizo™ 3D 2021. For each primary direction (x, y and z), 10 manual measurements were made along the chosen direction using a spacing of 0.5 mm for every selected tomogram slice with also a spacing of 0.5 mm. The results of this validation can be found in the SI section.

2.4 Calibration

The hygroexpansion coefficients in the l, r, and t material direction for specimens B4-OW and B4-CW were determined with an iterative fit between numerical and DVC displacement data related to the x, y, and z direction. The fit was evaluated by computing the mean squared error (MSE) between the FE and DVC dataset. This was done in MATLAB^® using statement ‘immse’. The best fit was determined by the smallest MSE for all three orthotropic material directions.

3.1 Evaluation methodology

The XµCT aided FE process used in this study considered the following steps: specimen preparation, XµCT scanning, reconstruction, orthotropic material orientation, DVC, material model and prediction of material properties. In this section the bottlenecks observed within each step are discussed. The process is optimal when the experimental step is designed and executed to benefit the image processing and model development step. In the specimen preparation step, the specimens were brought to a constant MC with desiccators and covered in plastic to maintain this MC thorough scanning. The plastic coverage prevented motion artefacts from occurring in the tomograms, but resulted in a tedious DVC pre-processing. The specimens were tested in the XµCT scanning step using an ex-situ scanning approach. This approach led to rotational and translational misalignment between tomograms, which had to be manually undone. To automate the process and obtain higher quality tomograms, an in-situ scanning approach is recommended using a built-in climate chamber to the scanner. A visible artefact that was present inside the tomograms was ring artefacts. The dead pixels in the detectors resulted in ring artefacts during reconstruction, of which some could be removed through image processing. Such artefact negatively influences DVC (Limodin et al. 2011). In the material orientation step the pith detection was estimated manually using the structure of the annual rings. This detection can also be done automatically by using a Hough transformation (Huber et al. 2022). This method can be combined with an estimation of the local material orientation (l, r, t) using a gradient structure tensor. In the DVC step it was noticed that an appropriate spatial and contrast resolution is essential for DVC, since the tomograms need a recognisable random pattern for the analysis to converge. Both DVC analyses were successful, but it could be seen that the CW tomograms, with a higher level of contrast, led to an easier convergence (less iterations, smaller tolerance) and a smaller difference between manual and DVC measurements. Since the scanner does not run a warm up scan, the DVC measurements might be affected by thermal drift of the X-ray emission point (Wang et al. 2017). In the model development step, the assumption was made that the material is homogeneous, in the sense that no distinction between early, late and transition wood exists. Also, a linear change in MC was assumed, leading to an absence of moisture gradients within the volume during drying. This simplifies the displacements computed by the FE model. In general, it can be said that the estimation of hygroelastic properties is possible with the proposed methodology. However, the results showed that the accuracy of the properties is largely dependent on the level of detail of the model. Comparison with estimates using a more detailed numerical model is therefore warranted.

3.2 Hygroexpansion coefficient

In this study, we have tested the presented methodology on one specimen of OW and one of CW as a proof of concept to precisely determine hygroexpansion coefficients of OW and CW in their principal material directions – longitudinal, radial and tangential. The sample size is not large (number specimens) and differs (number branches, trees) enough to represent the variability of material. Therefore, more tests are required in the future to be able to draw statistically significant conclusions. The obtained hygroexpansion coefficients are collected in Table 5. It should be noted that these coefficients were all obtained from FE models built from tomographic data. The table also presents the error (MSE) at which the calibration of the FE model was accepted. Figure 6 shows the displacement data at which the error was smallest, together with colour plots from FE and DVC analyses.

Figure 6:

Displacement data from finite element (FE) and digital volume correlation (DVC) analyses for opposite and compression wood in principal material directions x, y, and z, with corresponding colour plots. Also, an indication of the global coordinate system is given, together with an indication of analysed surface (black). Displacement in principal material directions x, y, and z from finite element (FE) simulation and DVC analysis for opposite and compression wood.

The longitudinal hygroexpansion coefficient of OW is considerably smaller than the coefficient for CW. This observation was also made by Włoch (1975) for specimens of branch wood from Spruce pine. The hygroexpansion coefficient for OW found in this study is negative. This indicates a decrease in length during moisture uptake. Such a decrease was also reported by Burgert et al. (2007) for specimens of Norway spruce NW analysed at the micro level. Perstorper et al. (2001) found an average value of 0.00773 (−) for Norway spruce NW and 0.021 (−) for Norway spruce CW from stem. The hygroexpansion coefficient for CW found in this study is much larger than reported by Perstorper et al. (2001) for stem wood.

The transverse hygroexpansion coefficients found in this study only show small differences between OW and CW, with slightly higher values for OW. Perstorper et al. (2001) reported an average radial hygroexpansion coefficient for Norway spruce NW of 0.151 (–) and for CW from stem a value of 0.105 (–). For the tangential hygroexpansion coefficient, an average value of 0.334 (–) was found for NW and 0.242 (–) for CW from stem. Our results are also in agreement with the bulk results published by Lanvermann et al. (2014). However, the tangential values found in this study are unexpectedly higher than the radial values. The most likely explanation for this difference is the simple nature of the FE model. The model assumes the material as homogeneous in the sense that is makes no distinction between early, late and transition wood. It also neglects moisture gradients within the volume during drying. This simplifies the interpretation of material behaviour. In reality, a moisture gradient will arise during adsorption, which will create an internal constraint due to differential swelling over the cross section of the specimen. This differential swelling will create a stress pattern consisting of a tension and a compression zone that will induce mechanosorption. This is something that is currently neglected by the FE model and will simplify the calculated displacement field.

3.3 Elastic modulus

The elastic moduli E _x , E _y and E _z obtained with compression tests on 36 specimens are visualised in Figure 7 for both relative humidity levels. See Figure 7f for an indication of the x, y and z direction in relation to the annual ring and fibre orientation. The size of the branches did not allow for a precise alignment with the local coordinate system. It should be noted that the principal z direction maintained in the current study aligns with the predominant local direction. The values of both the CW and OW sample sets are plotted against the measured MC and dry density. The mean value and standard deviation of the set’s elastic moduli, dry density and MC are collected in Table 6.

Figure 7:

Relationship between elastic moduli, E, and moisture content, w, or dry density, ρ₀. CW indicates compression wood, OW indicates opposite wood, RH is relative humidity and w_a refers to the unitless moisture content below fibre saturation point.

At 44 % and 98 % RH, the mean E _z was 0.77 GPa and 0.71 GPa for CW, respectively, compared to 1.39 GPa and 0.92 GPa for OW. The mean E _z for CW is lower than that of OW, irrespective of the MC. For CW, a 23 % decrease in E _z was seen between 44 and 98 % RH, whereas for OW 44 %. The ratio between the E _z of CW and OW was 0.56 for 44 % RH and 0.77 for 98 % RH. The more prominent effect of MC on E _z of OW is reflected in this ratio. The lower E _z found for CW of stem is due to the larger microfibril angle of CW (Gindl 2002; Joffre et al. 2014; Kollmann and Côté 1968; Timell 1986a). For CW from stem, Timell (1986a) reported a longitudinal elastic modulus between 4.45 and 6.73 GPa and for NW between 10.56 and 12.56 GPa obtained for Picea abies tested in compression parallel to the grain, with ratios varying between 0.42 and 0.86. The values reported for E _z in the current study are smaller than those collected by Timell (1986a) for Norway spruce NW and CW from stem. This can be explained by the mechanical differences seen between stem and branch wood (Färber et al. 2001). For example, Timell (1986a) (page 576) reported an 11 % difference in longitudinal elastic modulus between stem (6.99 GPa) and branches (6.29 GPa) of American conifers. In addition, Gurau et al. (2008) reported a 428 % difference in modulus of elasticity between stem (11.20 GPa) and branches (2.12 GPa) of Scots pine. The research assigned the difference to the presence of juvenile wood, lower density then found in the stem, and compression wood. In addition, Färber et al. (2001) reported that the MFA for branches is generally larger than for stem wood of Norway spruce.

A mean value of 0.39 GPa is reported for E _x for OW at 44 % RH and 0.27 GPa at 98 % RH. For CW, these values are 0.42 and 0.33 GPa, respectively. The mean value of E _y is 0.26 GPa at 44 % RH and 0.20 GPa at 98 % RH for OW, and 0.38 and 0.34 GPa for CW, respectively. Since the principal global axes x and y do not align with the local cylindrical coordinate directions r and t, the elastic moduli, E _x and E _y , are both a combination of E _r and E _t . For Norway spruce NW, E _r tends to be larger than E _t (Keunecke et al. 2007). The elastic moduli related to the x direction presented in the current study are larger than those for the y direction, except for 98 % RH. This comes as a surprise, since the y direction is dominated by E _r . However, it should be noted that the standard deviation of E _x and E _y are relatively high. Keunecke et al. (2007) reported a mean value for E _r of 1.80 ± 0.01 GPa and a mean value for E _t of 1.18 ± 0.02 GPa. As seen for E _z , the values for E _y and E _x are much lower for branch wood then for stem wood. However, no values were found in literature to substantiate these finding. Both E _x and E _y for CW seem to be less affected by MC then OW. For E _x , a decrease of 32 % for OW was seen compared to 22 % for CW. For E _y , this decrease was 21 % for OW and 10 % for CW.

A linear relationship was established between elastic moduli and MC using Equations (7)–(10) for both OW and CW. These relations were established in the local coordinate system and incorporated into the FE model to simulate elastic behaviour. The results are visualised in Figure 7a–c and the constants needed to describe the relationship can be found in Table 7. The table also provides the goodness-of-fit (R²) for each regression analysis. The R² values are quite low, which indicates that the results do not follow a linear trend. This can be due to – for example – a high quality variation of wood, a general scatter and the small size of the sample set. Similar relationships between elastic modulus and MC were given in Ormarsson et al. (1998) for Norway spruce NW, and show much higher values for E _l , E _r and E _t , than given in the present study. Other modelling parameters obtained from experimental data, such as MC, dimensions and pith location can be found in the SI section.

3.4 Dry density

The second column of Figure 7 shows that the measurements seem to follow the trend between elastic modulus and density predicted by Gibson and Ashby, that is linearly and cubically increasing stiffness with respect to density in the longitudinal and transverse directions, respectively (Gibson 2004). The average value and standard deviation of the dry-density sets can be found in Table 6. An average dry density of 871 kg m⁻³ is found for CW and 796 kg m⁻³ for OW, with a CW to OW ratio of 1.09. The values are higher than generally expected for NW. For example, Niemz and Sonderegger (2017) reported values between 370 and 540 kg m⁻³ for Norway spruce NW, where Boutelje and Rydell (1995) (page 27) mentioned values between 370 and 440 kg m⁻³. The values reported in the current study also show higher values for CW than for OW, as would also be expected (Gardiner et al. 2014; Kollmann and Côté 1968; Timell 1986a). The cell walls of CW are significantly thicker than those of NW, dominating over the fact that the fraction of highly dense cellulose is lower in CW. Although values of dry density for branches is hard to find in literature, Timell (1986a) does mention CW to NW ratios between 1.1 and 1.8, which are almost in line with the value of 1.09 found in the current study. In addition, Li et al. (2014) reported an average dry density of 638 kg m⁻³ for CW found in a branch of Scots pine and 542 kg m⁻³ for the corresponding OW.

3.5 Moisture content

The MC determined for all specimens in the OW and CW sample sets are presented in the first column of Figure 7. The mean value and standard deviation of each set can be found in Table 6. The mean MC of OW was 9.33 % for a RH of 44 %. For the same RH, a mean MC of 10.56 % was found for CW. At 98 % RH, these values were 26.33 % and 24.12 %, respectively. These values lie around the ideal MC of 10 % (44 % RH) and 25 % (98 % RH) presented in previous section. No clear trends could be seen between CW and OW and no clear differences between NW, CW and OW are reported in literature. The differences in swelling is therefore not like to be due to more water in one type of wood, but rather a question of different structural reorganisation at molecular scale. Gardiner et al. (2014) do mention that the MC of green reaction wood is generally lower than that of NW and that the drying rate of CW is lower than that of NW.