The effect of the growth ring orientation on spring-back and set-recovery in surface-densified wood

2.1 Growth ring orientation

The GRO in the cross-section of the specimens was used as a parameter for a detailed analysis of how spring-back and set-recovery varied along the width of the specimens due to changing GRO. Additionally, it also allowed the effect of a variable GRO within the cross-section of the specimens to be studied. The GRO at an arbitrary point in the cross-section is described as the angle between the compressed surface and the tangent to the growth ring at the location of the arbitrary point (Figure 3).

Figure 3:

Determination of the growth ring orientation (GRO). For an arbitrary position (red dot) in the cross-section the local GRO is described by α, i.e., the angle between the compressed surface and the tangent to the growth ring at that position. The local GRO was averaged for the left, middle and right regions of the cross section for further analysis.

To quantify the local GRO, a digital image of one of the cross-sections for each specimen was taken with a camera (CANON EOS M3, Canon, Japan), and the local GRO was determined at every pixel on an enhanced digital image using a structure tensor algorithm (Jeppesen et al. 2021) using the Python programming language (van Rossum and Drake 2009). An increasing woGRO along the width of a specimen (if existing) was oriented in the same direction (to the right in the image). The images were saved in a 24 bit jpg-format and enhanced in ImageJ software (Abramoff et al. 2004). Growth ring-unrelated information in the images such as patterns from a rough surface related to the sawing were filtered with a Fast Fourier Transform (FFT) programme, allowing the retention of larger scale features such as the growth rings, whilst smoothing the low frequency texture of the wood surface. The contrast of the filtered images was increased by histogram equalisation prior to the application of the structure tensor algorithm. The local GROs did not differ much in the thickness direction of each specimen, and hence the average local GRO of the left, middle and right regions was calculated for further analysis, each region comprised a third of the specimens’ width (Figure 3).

To acquire a potential guide for the future grading of wood for densification due to GRO, the mean GRO at the three regions was used to sort the specimens into three groups: “Flat”, “Inclined” and “Hybrid” (Figure 4), which were defined as:

1. Flat: mean GRO in the left, middle and right regions, all below 15°.

2. Inclined: mean GRO in the left, middle and right regions, all above 15°.

3. Hybrid: mean GRO in the left region below 15° and at the right region above 15°. In the middle region the mean GRO can either be above or below 15°.

Figure 4:

Mean local growth ring orientation (GRO) determined at three different regions: left, middle and right. Number of specimens per group (Flat, Inclined and Hybrid) = 60.

This grouping was expected to give an indication how different patterns of GRO in the cross-section may affect the strain developed during densification and in turn the spring-back and set-recovery which are among the most important properties for the quality and the yield of surface-densified wood. The group Flat exhibits a low variation of the GRO over the width of the specimen, and the strains are therefore expected also to have a small variation, resulting in a uniform spring-back and shape-recovery. In comparison, the stronger increase (left to right) in GRO in the group Hybrid is expected to result in un-even spring-back and shape-recovery of the densified surface. In the groups Inclined and Hybrid, it was expected that shear deformation occurs along the growth rings of the wood in regions where the angle of the local GRO is relatively high. The low local GRO in the left position of the group Hybrid might restrict the shear deformation, resulting in a less even strain-distribution.

2.2 Thermo-mechanical surface densification

Prior to densification the specimens were conditioned at 20 °C and 65 % relative humidity (RH) until equilibrium moisture content (EMC) 12 % was reached. The specimens were uniaxially compressed in the thickness direction in a hydraulic laboratory press (HLOP15, Höfer Presstechnik GmbH, Taiskirchen, Germany) with one platen heated to a temperature as shown in Table 1. The specimens were pre-heated in the press by closing the press until the heated platen was in contact with the specimen and a contact pressure of 1 MPa was established, enabling compression of the wood at a temperature above the glass-transition temperature. The pre-heating time is shown in Table 1. The press was then further closed with a speed of 0.1 mm s⁻¹ until the target thickness of 16.8 mm was reached, and the press was kept closed and temperature kept constant for a specific holding time (Table 1) until the top-platen was cooled to a temperature of 60 °C, which allowed the material to solidify and the level of spring-back of the compressed wood was reduced. The maximum force applied during pressing was recorded and the required peak pressure for densification was calculated to determine the stress required to reach the target thickness. The surface of the specimens which was in contact with the heated platen was defined as the compressed surface.

The process parameters shown in Table 1 were chosen based on pre-tests with the goal to create a different degree of surface densification in the specimens. Three different combinations of pressing parameters were used. Specimens were compressed to a through-thickness compression ratio (CR) of approx. 26 % (see Laine et al. 2013). This aims to limits the plasticisation of the entire specimen, and hence concentrate the compression to the heated side of the specimen.

2.3 Measurement of density, dimension and shape

After densification, the density profile (DP) of each specimen was obtained by X-ray densitometry with a laboratory DP analyser (DENSE-LAB X, Electronic Wood System GmbH, Hameln, Germany) with a 50 μm spatial resolution of the X-ray beam. Measurements were undertaken with an increment of 44 μm in the thickness direction of the specimens. The peak density and the peak distance from the densified surface were extracted from each DP (Scharf et al. 2022b).

The maximum width of the specimens was measured with a calliper to determine lateral expansion. To determine spring-back, thickness was measured at three different locations; left, middle and right in line with the local GRO positions (cf. Figure 3). To initiate set-recovery of the densified region in the specimens the specimens were fully submerged in water at 21 °C room temperature for 72 h, and then dried to 0 % MC in an oven at 103 °C, and to exclude the swelling component in the measurements, followed by conditioning at 20 °C and 65 % RH until equilibrium was reached. The measurement of the thickness was repeated as before to determine set-recovery.

The material loss when shaping the densified and water-soaked specimens to a perfect rectangular cross-section was determined on binary images displaying the cross-sectional shape of the specimens after spring-back. This study was performed to estimate the volume yield due to cross-section distortion of large-dimension sawn timber due to compression in an industrial densification process. The images were created by intensity-thresholding of the digital images, followed by morphological closing to reduce the effect of fuzzy edges. The binary images were used to determine the cross-section area and compare it to a best-fit rectangle of the cross section.

2.4 Digital image correlation

Digital image correlation (DIC) was applied for a qualitative analysis of the strains that occur after densification, the spring-back and set-recovery. DIC allows the correlation of patterns between digital images for spatial studies of displacement and deformation. The cross-sections of 5 specimens of each treatment group (cf. Table 1) were covered with a combination of white and black spray paint to create a speckle-pattern. During the densification process, a digital image of the speckled cross-section was taken when the target thickness was reached, and the holding time passed. To acquire strain fields of spring-back and set-recovery two additional images were taken. The image for spring-back was captured after release of the pressure and was referenced to the image taken when the specimen was under pressure at its target thickness. The image for set-recovery was captured after conditioning the densified sample at 20 °C and 95 % RH and was referenced to the image taken after release of the pressure. Inducing set-recovery for the DIC-analysis by conditioning at high RH instead of water-soaking was done to avoid damages to the speckle-pattern.

A digital camera (CANON EOS M3 as earlier) with a CMOS 22.3 mm × 14.9 mm image sensor was used to capture images in the CR2 format with a resolution of 24.2 effective megapixel. A macro lens (0.25 m) set to its maximal focal length of 55 mm was used. An exposure of ISO 100 was used, a shutter speed of 1/30 s and an aperture of f/10. The standoff distance from the camera sensor to the speckled surface of the specimens was 250 mm, resulting in a pixel size of 0.158 mm. To apply the DIC algorithm, the images were transformed into TIFF format and cropped to a resolution of 3240 × 1506 pixels.

The DIC was computed with the open source 2D DIC image correlation software Ncorr v1.2 (Blaber et al. 2015) in the MATLAB environment. A circular subset of 63 pixels in radius with a step size of 5 pixels was used for the subset matching. The strain-rate tensor was smoothed using a circular neighbourhood, 5 pixels in radius. The result of the DIC are full strain fields displaying the local strains in the densification direction (ε _y) and orthogonally to the densification direction (ε _x).

Spring-back and set-recovery are describing the accumulated recovery (sum of all movements below the densified surface) in the thickness direction of the material and are determined by thickness measurements. The strain fields allow an investigation of these recoveries at a local level and hence the study of local spring-back (ε _{y,spring-back}) and local set-recovery (ε _{y,set-recovery}).

3.1 Thermo-mechanical surface densification

Table 2 shows the pressure measurements during densification and key parameters for the resulting density profile (DP) in the specimens. Specimens in the group Inclined required the lowest pressure to achieve target densification while exhibiting the largest increase in width, i.e., lateral expansion in relation to the compression force. This means that the “reinforcement” of the earlywood by the latewood that occur in e.g. “pure” tangential compression does not occur in specimens with a GRO below 45° and the deformation mechanism is suggested to be rolling shear between earlywood and latewood bands. Peak density and density-peak distance were mainly affected by the pressing temperature and holding time while the GRO showed no or very marginal influence. The GRO has an influence on the ratio of peak pressure to peak density, where relatively less pressure is needed to increase the density of specimens where rolling shear occurred unrestricted as shown in the inclined specimens. The rolling-shear strength of wood is low, and a large degree of displacement is therefore possible (Li et al. 2021).

If and how much a wood cell deforms under a transverse compressive stress depends on its mechanical resistance to the load. In thermo-mechanical densification, cell-wall deformation occurs in cells showing the lowest mechanical resistance to the compression load. This depends on a complex combination of the degree of plasticisation, load orientation, cell morphology and current state of deformation. These parameters are constantly changing during densification and determine where in the wood the induced stress results in further deformation. The temperature and moisture profile during densification result in different degree of plasticisation in the wood, which in turn influence where in the specimen cells deform first and how this deformation is propagated. The difference in thermal conductivity in the tangential and radial direction of Scots pine is small (Kollmann and Malmquist 1956). The bound-water diffusion coefficient of wood is 17–25 % higher in the radial direction than in the tangential direction (Stamm 1960) and is often assumed negligible (Konopka and Kaliske 2018; Siau 1971). The degree and depth of plasticisation is hence assumed to be nearly independent of the GRO. During thermo-mechanical surface densification, the through-thickness direction can be generally divided into a fully plasticised region, a transition region from fully plasticised to un-plasticised and an un-plasticised region. The exact expanses of these regions depend on the process parameters and the material properties. In general, the compression deformation occurs mostly in the earlywood of the strongest plasticised region, but due to other factors influencing the mechanical resistance of a wood cells, it is also possible that partially plasticised regions of the wood deform before other regions are fully plasticised, influencing how (elastically, elasto-plastically, plastically) the induced stress will be stored in the densified wood. The strain occurring at spring-back and set-recovery reflects the partial release of these stored stresses in the wood. In the present study, the variation in GRO allowed to investigate mainly the effect of the load orientation.

Figure 5 shows the mean DPs of the treatment groups pressed at 150 °C and an approximation of how the plasticisation looks in the end of the densification process (just before cooling). All groups exhibit an increased density in the plasticised and transition regions of the wood, which is typical in surface-densified wood. The DPs of the three treatment groups are similar in the fully plasticised region (approx. 0.5–2 mm) with the distance of the peak density (maximum density) to the densified surface being similar, indicating the low influence of the GRO on the degree of plasticisation. The difference in the peak density value is attributed to the different initial densities. The thickness of the region with an increased density, i.e., over the initial density, is larger in the groups Inclined and Hybrid (approx. 10 mm) than in the group Flat (approx. 8 mm) and might be a result of rolling shear deformation along the growth rings. The region assumed to be un-plasticised during compression (approx. 10–17 mm) shows an increased density compared to the mean density before densification. This indicates that wood cells in this region got plastically deformed because, at a given point during densification, these cells had a lower mechanical resistance to the compression force than the partially deformed wood cells in the plasticised surface region. This was observed in all treatment groups, where an increased pressing temperature (180°) and pre-heating time reduced this effect due to plasticisation penetrating further through the specimens. The effect seems to be strongest in the Inclined groups. However, the DPs represent the average density over the whole width of the specimens and thus a more detailed analysis is possible by examining the strain-fields of DIC and the thickness measurements at the different regions.

Figure 5:

Mean density profiles (continuous lines) of the groups pressed at 150 °C after the densification process and after spring-back. The dashed lines show the mean density of the groups before densification. The regions of the specimens were plasticised to a different degree during densification which is schematically presented by the colour-gradient.

3.2 Spring-back

The spring-back represents the release of the elastically stored energy when removing the compression load at the end of the densification process. The stress level in the wood material depends on the degree of plasticisation during deformation and when the compression load is removed. Ideally, cell deformation takes place in a fully plasticised cell, where the amorphous components of the wood are soft and movement between and within the wood cells is less restricted, permitting large displacements in the elastic domain (Heger 2004). The cell will be solidified (be un-plasticised) when the temperature is decreased, which means that the amorphous components return to their glassy state and movement between and within the wood cells is restricted. The elastic strain in the crystalline cellulose is interlocked by the solidified lignin-hemicelluloses matrix, as described in the introduction. If solidification occurs before the compression load is released, the spring-back will be low.

Figure 6 shows the degree of spring-back determined on a local scale by DIC on the cross-section, and on a global scale by thickness measurements at the left, middle and right regions of the specimens. Figure 6A shows the local strain ε _{y,spring-back} in the densification (y−) direction, which occurs due to elastic spring-back after release of the compression force. The strain-fields could only be acquired for specimens densified at 150 °C due to failure of the speckle-pattern at the higher temperature (cf. Figure 8).

Figure 6:

Spring-back of specimens: (A) full cross-sectional strain-fields (ε _{y,spring-back}) in the densification direction of one representative specimen per growth ring orientation (GRO) group compressed at 150 °C. t = distance to the densified surface. (B) Average thickness after release of the densification load at the left, middle and right regions for all GRO groups and pressing parameters.

For all GRO groups, the strain-fields showed that the region of the specimen, which was nearest the heated platen had a very low local spring-back (0.5–2 mm). This indicated that the wood cells were deformed at full plastisication. In the transition region, the local strains increased, which was attributed to the insufficient plasticisation of the lignin below temperatures of 150 °C at the used MC of 12 % (Salmén et al. 1986). In the un-plasticised region where all wood components are in their glassy state, the GRO groups exhibited differences in their local strain. This meant that the overall spring-back after release of the compression force mainly originated from local strain release in the transition region, where the wood cells were partially plasticised and re-solidified under the densification process.

Along the width, specimens in the group Flat exhibited a low and even spring-back as a result of small variations in the GRO at radial compression. In specimens of the groups Inclined and Hybrid, concentrated regions with a high degree of local spring-back occurred where the local GRO deviated significantly from radial compression, i.e., in the bottom right corner of the cross-section in Figure 6A. Additionally, the local spring-back was concentrated along the growth rings. This indicates that during densification, stresses were distributed by rolling shear in the earlywood in sections of steep GRO, which was also supported by the strain ε_x orthogonal to the densification direction and the increased lateral expansion. The elastic share of this deformation was exhibited as spring-back. The increased density in the un-plasticised region seen in the DPs of mainly the groups Inclined and Hybrid (cf. Figure 5) showed that this deformation also had a plastic component, because the DPs showed the state of the wood after the occurrence of spring-back.

Figure 6B shows the average thickness of the specimens at three different locations along its width after release of the densification load, representing spring-back on a global scale. The results for specimens densified at 150 °C were in line with the behaviour observed of local spring-back in the strain-fields acquired by DIC (Figure 6A), but similar behaviour could be expected at 180 °C. Radial densification when the GRO had a small variation over the width of the specimen (group Flat) resulted in a small variation in thickness after densification due to an even spring-back. The groups Inclined and Hybrid showed very uneven thicknesses between the different locations and showed the highest thickness in the right-hand position especially at higher pressing temperatures. The GRO was steepest and the rolling-shear deformation strongest in the un-plasticised regions according to the DIC analysis.

A comparison between the different processing parameters showed that the thickness and hence spring-back was highest in groups densified at 150 °C which might be due to insufficiently plasticised lignin. A pressing temperature of 180 °C reduced the spring-back in all GRO groups, due to the stronger plasticisation of lignin, while the pre-heating time had only a small influence on the spring-back.

3.3 Set-recovery

The high MC (20 %) in the specimens after conditioning led to a reduction of inter- and intra-molecular interactions between the hemicelluloses, the lignin and the amorphous part of the cellulose, thereby softening the wood material. The elastic energy stored in the crystalline cellulose which was locked-in by the solidified lignin-hemicelluloses matrix could be released and the wood could in theory recover almost to its original state, i.e., set-recovery takes place (Norimoto et al. 1993). The remaining permanent deformation is attributed to either structural damage of the cells in deformation below the glass-transition temperature of lignin, or thermal degradation of the wood components in deformation above the glass-transition temperature of lignin (Navi and Sandberg 2012).

Figure 7A shows the local strain ε _{y,set-recovery} in the densification (y−) direction induced after conditioning of the densified specimens at 20 °C and 95 % RH and determined by DIC. The local strain does not only include set-recovery but also the moisture-induced swelling of the wood. The region close to the heated platen dried more than other regions of the specimen. Additionally, in the Hybrid and Inclined specimen small regions of no strain and maximum strain were exhibited in the region close to the heated platen during densification. These extremes could be attributed to cracks in the speckle-pattern (cf. Figure 8D).

Figure 7:

Set-recovery of specimens: (A) full cross-sectional strain-fields (ε _{y,set-recovery}) in the densification direction of one representative specimen per growth ring orientation (GRO) group compressed at 150 °C. Note that the strain is one order of magnitude higher than in Figure 6. In the “grey regions”, no digital image correlation could be applied due to the distorted speckle-pattern. t = distance to the densified surface. (B) Average thickness after inducing set-recovery at the left, middle and right regions for all GRO groups and pressing parameters.

Figure 8:

Cross-section views of the densified specimens after set-recovery test: (A) a typical cross-section shape of a specimen with a low resin content (sapwood) where the densified surface has a small unevenness; (B) an extreme case of unevenness which was commonly accompanied in specimens with a high extractive content (red rectangle); (C) close-up of the speckle-pattern distortion in the densified region close to the heated platen during densification (red rectangle); and (D) delamination of the speckle-pattern from the wood surface and cracking of the speckle-pattern and cracking of the speckle-pattern after set-recovery (red rectangle).

For all GRO groups, the strain-fields showed that the local set-recovery was largest in the highly plasticised region closest to the heated platen (0–2 mm). Here the locked-in stresses could not release under un-loading and the spring-back was therefore low, but under remoistening a release occurred, which resulted in a high set-recovery. In the transition region (2–6 mm), the set-recovery was considerably lower. The cells in this region experienced on average less deformation during compression and the lock-in effect was less due to the lower degree of plasticisation; consequently the elastically-stored energy was lower. Most of the energy release occurred as spring-back, and less as set-recovery. Beneath the transition region, the local set-recovery was very low as deformation was induced in the glassy state of all components. The thickness of the highly-densified and the transition regions were similar in all three GRO groups.

In specimens from the group Flat the variation of the set-recovery along the width was low and there were distinct regions with different degrees of local set-recovery. The local set-recovery decreased gradually with increasing distance from the densified surface and a clear border to regions with very low local set-recovery was visible (5–6 mm from the surface in Figure 7A). Below this border, all wood components were believed to be in a complete unplasticised state during deformation, meaning no elastic energy was locked-in by the (lignin-)hemicelluloses matrix. In the specimens of the groups Inclined and Hybrid, the variation of the local set-recovery along the width was more uneven than in the group Flat. The border from set-recovery to no set-recovery followed the growth rings and was therefore less clearly related to the distance to the densified surface. Additionally, set-recovery was lower in the Inclined and Hybrid group than in the Flat group.

The differences in local set-recovery are believed to be due to the displacement-controlled process, where the compression load which stressed cells in the radial direction (group Flat) was sufficient to deform plasticised wood cells but insufficient to deform unplasticised wood cells. Completely plasticised wood cells were deformed before partially plasticised wood cells. As a result, the density increased depending on the distance to the heated platen, as seen by the depth-dependency of the local set-recovery (the reverse effect of densification) in the group Flat. However, if the load direction was not radial, i.e., specimens from the groups Inclined and Hybrid were densified, more shear stresses occurred. The lower resistance of the wood cells may lead to rolling shear stress resulting in the applied compression load being sufficient to deform non-plasticised or partially plasticised wood cells before they were plasticised to a higher degree. This would result in cell deformation where more of the wood components were in their glassy state and structural damage of the cells was induced, which was not recoverable. Even though rolling shear deformation might have occurred, the DPs after spring-back (cf. Figure 5) were similar between the three GRO groups. This can be explained by the reduced threshold for plastic deformation and increased possibility of strain influenced by temperature and moisture content (Uhmeier et al. 1998), which allowed slightly warmed-up cells to deform before cells at room temperature. The low rolling-shear strength and additional factors such as cell-wall thickness and the current state of deformation determined the region of cell deformation and might have led to the more patch-wise concentrations of local set-recovery in the transition region. The regions where deformation took place (based on the DP analysis and local spring-back), but no local set-recovery is exhibited, indicated shear deformation of un-plasticised wood cells.

Figure 7B shows the average thickness of the specimens (except the specimens used for DIC analysis) at three different locations along its width after inducing the set-recovery by water-soaking and subsequent conditioning. The set-recovery on a global scale was approx. between 75 % and 86 %, i.e., the thickness changed from 16.8 mm to 21.2–22.0 mm. The influence of pressing parameters and GRO on the spring-back were clearer than their influence on the set-recovery.

The variation in thickness between the different regions did not change significantly from spring-back to set-recovery in the group Flat. In the groups Inclined and Hybrid, the spring-back was highest at the right position (cf. Figure 6B), but this was not the case for the set-recovery. This indicated that more wood cells in this region got deformed in a partially or un-plasticised state, as already indicated by the higher spring-back (cf. Figure 6B) and density increase in the un-plasticised region seen in the DPs (cf. Figure 5). The set-recovery was lowest in the specimens from the group Inclined because of the plastic component of the rolling shear deformation in insufficiently-plasticised regions, which might have been restricted in the Hybrid groups due to the lower GRO in the left region of the specimens.

The influence of pressing temperature and holding time showed no clear trend. A reduced modulus of elasticity of the wood at elevated temperatures and drying out of the surface in contact with the heated platen might also have resulted in plastic deformation in the first 0–2 mm. These conditions can be found close to the heated platen but could not be tested by the DIC due to the speckle-pattern distortion. Several means of detrimental effects such as thermal degradation, plastic deformation of un-plasticised regions and the fixation by minor resin accumulations cannot be distinguished in this study.

3.4 The effect of resinous wood on shape-memory effects

The combination of compressing extractive-rich wood at elevated temperature and inducing high strains posed several constraints for the DIC and thickness measurements in this study. In 23 out of 180 specimens a large degree of unevenness was observed after inducing set-recovery (Figure 8B), which was independent of the pressing parameters and GRO. This was accompanied by an accumulation of extractives in the densified section of the cross-section, indicating a resin-based fixation of the compression set similar to methods using resin-impregnation (Gabrielli and Kamke 2010; Schwarzkopf 2021). Due to the inhomogeneous set-recovery, wood with a very high extractive content should be avoided in wood densification. To reduce the overlapping influence from resin-fixation on the GRO-related effects on set-recovery, specimens exhibiting these resin accumulations were excluded from all shape-memory-related analyses in the present study.

The use of DIC to investigate the strain development due to spring-back and set-recovery provided high resolution insights for a qualitative analysis. However, several issues occurred during the study. The application of heat and pressure led to liquids/extractives in the wood migrating longitudinally towards the cross-sectional surface, disturbing or covering the speckle-pattern (Figure 8C). In this study, a pressing temperature of 180 °C led to an excessive amount of speckle-pattern distortion, limiting the DIC analysis to specimens pressed at 150 °C. The high strains and the raised temperature and moisture conditions stressed the applied speckle-pattern layer which led to local delamination of the layer from the cross-section (Figure 8D). In that case, the strain in the wood was no longer transferred to the speckle-pattern and no DIC measurements were possible. The DIC algorithm could not match the subset in the image of the deformed image to a subset in the reference image and strain was not calculated in these regions. In other regions the speckle-pattern cracked and deformed independent of the cross-section of the underlying wood. Subset matching was possible, but it does not reflect the strain in the wood, but in the paint layer. A highly flexible and heat-resistant paint layer adapted to the surface roughness of the wood might be able to correctly follow the high strain occurring in the wood.

3.5 Estimation of volume losses due to shape-memory effects

Depending on the intended application, partial damage of the wood cells might be acceptable, but the deformation during densification and uneven spring-back might lower the material yield. To estimate the volume loss due to uneven spring-back, the shapes of the cross-section of the specimens were studied, i.e., the maximal rectangle possible to fit into the cross-section of the specimens were determined (Figure 9). In a production situation, the use of a standard board-size based on a kth percentile of the production output might be used. For a 5th-percentile the material yield due to spring-back and lateral expansion is 95.6 % for the group Flat and the yield decreased with increased deviation from a parallel GRO down to 91.0 % in the group Inclined, where large deviations in area yield were observed. As seen in Table 2, the lateral expansion of the specimens differed with the GRO and may be related to the area yield. Thus, the larger the measured expansion, the lower the overall yield.

Figure 9:

Area-yield after spring-back describing the volume loss due to uneven spring-back and lateral expansion. GRO, growth ring orientation.