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Aydın, M., and Aydın, T. Y. (2023). “Influence of growth ring number and width on elastic constants of poplar,” BioResources 18(4), 8484-8502.


The objective of this work was to evaluate the effect of growth ring number (specimens including 2, 4, and 6 rings from the bark) and growth ring width on elastic constants in the radial direction of Populus x canadensis, which has not been revealed before. The longitudinal (2.25 MHz) and transverse (1 MHz) ultrasonic waves were propagated to calculate the longitudinal (VRR) and shear (VRL, VLR, VTR, and VRT) wave velocities and used to determine the elasticity modulus (ER), and shear moduli (GRL and GRT). The average growth ring widths of specimens including 2, 4, and 6 rings were 17.0 mm, 17.8 mm, and 18.2 mm, respectively. According to the results, only VRL steadily increased with increased ring number, while other velocities fluctuated. The same fluctuations were observed for moduli except for GLR, which constantly increased with ring number. The influence of ring number on velocity was statistically significant only for VRL and VRT. However, all moduli were significantly affected by ring number. Linear regression statistics revealed that there were significant relations between the ring width and density, VRL, VLR, VRT, GRL, and GRT.

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Influence of Growth Ring Number and Width on Elastic Constants of Poplar

Murat Aydın,a,* and Tuğba Yılmaz Aydın b

The objective of this work was to evaluate the effect of growth ring number (specimens including 2, 4, and 6 rings from the bark) and growth ring width on elastic constants in the radial direction of Populus x canadensis, which has not been revealed before. The longitudinal (2.25 MHz) and transverse (1 MHz) ultrasonic waves were propagated to calculate the longitudinal (VRR) and shear (VRL, VLR, VTR, and VRT) wave velocities and used to determine the elasticity modulus (ER), and shear moduli (GRL and GRT). The average growth ring widths of specimens including 2, 4, and 6 rings were 17.0 mm, 17.8 mm, and 18.2 mm, respectively. According to the results, only VRL steadily increased with increased ring number, while other velocities fluctuated. The same fluctuations were observed for moduli except for GLR, which constantly increased with ring number. The influence of ring number on velocity was statistically significant only for VRL and VRT. However, all moduli were significantly affected by ring number. Linear regression statistics revealed that there were significant relations between the ring width and density, VRL, VLR, VRT, GRL, and GRT.

DOI: 10.15376/biores.18.4.8484-8502

Keywords: Annual ring number; Annual ring width; Ultrasonic wave velocity; Elasticity modulus; Shear modulus

Contact information: a: Department of Machinery and Metal Technologies, Isparta University of Applied Sciences, Isparta, Türkiye; b: Department of Wood Products Engineering, Isparta University of Applied Sciences, Isparta, Türkiye; *Corresponding author:


Poplar is an important hardwood species. Its outstanding traits are low density and diffuse-porous and short fibers with small-celled structures. Because of its good machining, bonding, and finishing properties (Balatinecz and Kretschmann 2001), various industrial fields, such as veneer (veneering, package, plywood, and matches), packing (pallet, chest, package), furniture (sawn-timber, generally utilized elements or goods for interior applications, etc.), timber chipping (pulping, wood-based engineered products, etc.), and construction (timber from log sawing, generally utilized to build roofs) use poplar wood (Birler 2014). Such a wide range of utilization brings poplar wood to the forefront either for commercial or scientific applications. One of the notable commercial applications involves plantation forestry because of the fast-growing ability, which makes the logs shortly available in the market with cheaper prices compared to other hardwood species. Providing logs in a short time provides sustainable consumption of resources. It is important because the demand for timber sources remarkably increases daily. Additionally, a considerable amount of the new inventory will be supplied by the plantations of fast-growing trees, including poplars (Balatinecz et al. 2001). However, the quality and mechanical properties of wood obtained from fast-growing trees generally are lower and weaker when compared to natural trees (Liu et al. 2019). However, some modification applications can be easily employed to overcome such disadvantages.

When compared to many other fast-growing species, one of the notable distinct qualities of poplar wood is the growth rings (GRs), where the growth-ring width (GRW) is bigger, and the latewood (LW) section of a GR is smaller (Birler 2014). Furthermore, earlywood (EW) and LW sections in a ring can be easily definable. This is because there is a distinctness in surface pattern between the LW (cells and cell walls are commonly small and thick, respectively) and the EW of the following period (cells and cell walls are commonly big and slim, respectively) (Wheeler 2001). Structural properties have significant influences on the wood properties. Thus, Dackermann et al. (2016) reported that ultrasonic wave velocity (UWV) decreases due to GR, which functions as a barrier against the propagated wave. For a homogeneous and highly porous structure, such as wood, there are many factors that affect wave propagation. Reflection, refraction, absorption, scattering, and attenuation are some of the phenomena ultrasound encounters while propagating through the wood. Because of the orthotropic nature of wood, such phenomena can be remarkably influenced by the propagation direction and polarization. In this manner, Aydın (2022) evaluated the barrier function of GR on pine (Scots, red, and black) and cedar woods using 1 MHz transverse and 2.25 MHz longitudinal ultrasonic waves. It was stated that UWV tends to decrease while the growth-ring number (GRN) increases. However, except in some cases, neither GRN nor GRW had statistically significant influences on UWV. Even if this is the case for UWV, no study revealed the influence of AR properties on the elastic properties of poplar wood. However, the following are studies that dealt with different aspects of GR-related property evaluation. Roig et al. (2008) determined the density of the 12- to 19-year-old poplar clones using X-ray densitometry and correlated it with GRW properties. The influence of climate circumstances on the GRW for Populus ussuriensis Kom (Gou and Chen 2011), Canadian poplar (Populus x canadensis Moench) (Ziemiańska and Kalbarczyk 2018), and Populus hybrids in Latvia (Šēnhofa et al. 2016), and length and temperature of the day on the ring properties of Populus alba L. (Baba et al. 2022) were evaluated relative to the interaction with mechanical properties.

Lang et al. (2002, 2003), Roohnia et al. (2010), Casado et al. (2010), Ettelaei et al. (2019), Virgen-Cobos et al. (2022), Papandrea et al. (2022), Zhang and Lu (2014), Rescalvo et al. (2020), Hajihassani et al. (2018), Özkan et al. (2020), Narasimhamurthy et al. (2017), Aydın et al. (2007), Monteior et al. (2019), Guo et al. (2011), and Sözbir et al. (2019) dynamically and/or statically determined the EL of different poplar species as solid wood (unmodified or modified), standing trees, or engineered products prepared from Populus x canadensis. A few studies considered the shear modulus or full (twelve) elastic constants. Roohnia et al. (2010) dynamically calculated the GLR and GLT of Populus deltoides. Longo et al. (2018) determined the elasticity (ER, ET, EL) and shear (GTL, GRL, GRT) moduli of Populus deltoides using Resonant Ultrasound Spectroscopy (RUS) and Ultrasonic (US) testing (2.25 MHz) methods. Full (twelve) elastic constants for poplar were predicted only by Zahed et al. (2020) for OSB made from Populus deltoides and Zahedi et al. (2022) for Populus deltoides.

As seen in the abovementioned studies, even though there are six moduli (three elasticity and three shear) for wood, the EL is a commonly determined elastic constant. It is meaningful when the preparation direction of wooden elements in construction is taken into consideration. Furthermore, determining the pure shear modulus is a difficult task that requires special tools. However, both elastic constants are required to perform non-linear real-like numerical analyses to design safe structures using computer-aided engineering applications. Furthermore, the influence of radial variations on elastic constants needs to be clarified for numerical applications. Moreover, providing not only GR-related elasticity and shear moduli in the radial direction but reliable input parameters for three-dimensional finite element analysis are crucial issues that should also be clarified. Therefore, this study aimed to elucidate the influence of GRW and GRN on the longitudinal UWV through radial direction (VRR) and transverse UWV through radial direction and longitudinal and tangential polarizations (VRL, VLR, VRT, and VTR), and ER, GRL, and GRT modulus that have not been presented before for Populus x canadensis.


Populus x canadensis was used for specimen preparation. Two poplar logs were obtained from the plantation located in the Atabey, Isparta, Türkiye. The elevation and the coordinates of the plantation site are 1150 m and 37°57’03’’N 30°38’19’’E, respectively. Logs (from the breast height) were plain-sawn. Radially cut laths (Fig. 1) were divided into two from the pith, and heartwood (HW) sections were removed. Laths were planed to obtain smooth surfaces of approximately 20 mm thickness. As can be seen in the figure, ring borders were marked on the sapwood (SW) section to obtain samples (20 for each property and 10 per log) with 2, 4, and 6 GRs. Rings were counted and marked from the bark side to the pith side to prevent variations in ring properties. Therefore, the radial lengths of the specimens differed from each other, while the longitudinal and tangential dimension was around 2 × 2 cm. The radial to tangential angle was almost 90° to eliminate the effect of ring inclination.

Specimens were acclimatized at 20 ± 1 °C and 65% relative humidity (RH) using a chamber (Memmert Gmbh+Co. KG, Schwabach, Germany) until their weight became constant. At the end of the acclimatization, the density of the samples was determined according to the TS 2472 (2005) standard. To minimize or eliminate the density variations, all samples were matched in terms of the section and height of the pieces seen in Fig. 1. Furthermore, samples that had lower and upper bound density values were not taken into consideration.

The L, R, and T lengths of the specimens were measured using a digital caliper. Three measurements for each direction (nearby the endpoints and midpoint) were taken and the average length was calculated using arithmetic means of the measurements. The GRWs were calculated by dividing the average length of the R direction by GRN. To ensure the exact start and finish border of GR, the surface of the specimens was also sanded using sandpapers.

Ultrasound propagation was performed using an Olympus EPOCH 650 (Olympus, Waltham, MA, USA) digital ultrasonic flaw detector. The contact type A133S-RM and V153-RM (Panametrics-NDT, Waltham, MA, USA) transducers with 2.25 MHz (Pressure-P or longitudinal) and 1 MHz (Shear-S or transverse) central frequencies were used for wave propagation in direct mode to measure transmission time in µs. To reduce the noise and ensure the proper contact between transducers and the specimen, Olympus B2 Glycerin and SWC2 gel (Chemtrec, Waltham, MA, USA) were used. The longitudinal wave propagated through the R direction without polarization to calculate the VRR. The transverse wave propagated through the R direction with L and T polarizations to calculate the VRL and VRT, respectively. For shear moduli determination, VLR and VTR were also measured.

Fig. 1. Radially cut laths and sample preparation details

Because of the different and longer sizes in the R direction, three different (nearby the endpoints and midpoint) measurements were taken and then averaged, particularly for VLR and VTR. Consequently, dynamic elasticity modulus in the R direction (ER) and shear moduli in RL and RT planes (GLR and GRT) were calculated using Eq. 1 and Eq. 2, respectively,


where ER is the elasticity modulus (MPa) in the R direction, ρ is density (kg/m3), and VRR is the longitudinal UWV (m/s) in the R direction without polarization,


where Gij is the shear modulus (MPa) in IJ planes, ρ is density (kg/m3), and Vij is the transverse UWV (m s-1) in I direction and J polarization (LR, RL, RT, and TR).

For the transverse wave, the VİJ is not equal to V, and the average of these two velocities was taken into consideration while calculating the shear modulus in the IJ plane. The objective was to discover the influence of GRN and GRW on the velocity and moduli predicted using velocities. Therefore, shear moduli were also calculated by assuming VİJ is equal to V to comprehend the diffraction not only between the VİJ and V but also the moduli values.

The One-Way ANOVA test was conducted to interpret the influence of GRN on physical and mechanical properties and UWV. Significant differences between the means were found using Duncan’s multiple range test (DMRT). Linear regression statistics were presented to evaluate the influence of GRW on the properties and to express how the properties were successfully predicted by GRW.


Physical Properties

The means for the physical properties are presented in Table 1. The means of GRW ranged from 17 to 18.2 mm, and the average GRW of all the groups was 17.7 mm. Ziemiańska and Kalbarczyk (2018) reported 5.37 mm GRW for SW of the Populus x canadensis Moench, which is around 3.3 times lower than the average GRW of this study. Remarkably lower averages (6.63 mm and 8.3 mm) were also reported by Ziemiańska et al. (2020), including both SW and HW. In contrast, higher means, 19.8 mm (Erten and Önal 1995), 27.8 mm (LeBlanc et al. 2020), 28.6 and 28.8 mm (Šēnhofa et al. 2016), and 45 to 55 mm (DeBell et al. 2002), were also reported for different poplar species. There are many reasons for such high diffraction within the same species. The most important factor that influences the GRW is the climate, and precipitation and temperature have effects on width (Bozkurt and Erdin 1989a). Conversely, such remarkable differences can be meaningfully explained by sampling because the width of the growth ring can be dramatically changed. For example, Zhang et al. (2022) reported around 1.2 cm GRW for the first ring from the pith of hybrid clone of I-69 (P. deltoides) and I-45 (P. euramericana) clones. It increased to around 1.75 cm at the 4th ring and decreased to 0.3 cm at the 12th ring. Therefore, it is not easy to exactly compare or weigh the means because the parameters are not identical.

Density is one of the essential determinants for classifying wood. According to the means, P. canadensis met the requirement for European strength classes C24 (350 kg/m³), and it can be used for structural purposes. The density of the samples ranged from 335 to 373 kg/m3, and the average of all the samples was 348 kg/m3. Flórez et al. (2014) observed a 310 to 450 kg/m3 basic density range for P. canadensis. Further, 365 kg/m3 (Zhang et al. 2017), 405.6 kg/m3 (Hodoušek et al. 2017), 464 kg/m3 (Villasante et al. 2021), and 529 kg/m3 (Niklas and Spatz 2010) density means were reported for P. canadensis. Either averaged or the separate means of the 2, 4, and 6 ring groups are comparable to that of the literature. However, Birler (2014) reported 400 to 450 kg/m³ air-dry density for exotic poplar wood cultivated in Türkiye, which is at least 13% higher than the maximum average density of this study. In contrast, the lower bound for the means of this study was around 3.3% higher than those of Aydın et al. (2007) reported for poplar. Because the P. canadensis is a naturally occurring hybrid of P. deltoides and P. nigra, the following densities of 390 kg/m3 (Zahedi et al. 2020), 460 kg/m3 (Hajihassani et al. 2018), 375 and 387 kg/m3 (Altınok et al. 2009), 410 kg/m3 (Bozkurt and Erdin 1989b), 420 kg/m3 (Keleş 2021), 425 kg/m3 (varied from 346 to 523) (Monteiro et al. 2019), and 450 kg/m3 (Suleman 2015) should be taken into consideration.

In this study, the UWV ranged from 1607 to 1850 m/s and 504 to 1588 m/s for P and S waves, respectively. In the literature, only Zahedi et al. (2022) reported VRR, VLR, VRL, VRT, and VTR values for poplar wood. As shown in Table 2, these values are comparable with the results of this study. Furthermore, when UWVs were averaged within the GRN groups, these values and differences from the reported data become 1746, 1486, 1548, 544, and 513 m/s, and -5.6%, 8.5%, 23.9%, -18.8%, and 21.1%, respectively. In this regard, diffractions are at reasonable levels.

Table 1. Descriptive and Statistics for Physical Properties

Table 2. Reported UWV for Poplar Related to Radial Direction Only

Influence of AR properties on physical properties

As can be seen in Table 1, GRW means presented insignificant differences, which was essential for its influence evaluation on the physical and mechanical properties. Lars et al. (2005) stated that when the GRW is widening, the density of wood decreases. However, DeBell et al. (2002) reported that there is no significant correlation between GRW and density. Furthermore, the width of the rings is not identical every year and causes variations in density. For example, the density of Scots pine (with 2 to 7 rings) increased when the GRN increased to 23 but sequentially decreased when the GRN increased to 49 (Krauss and Kudela 2011). Ištok et al. (2016) reported 0.65 and 0.549 R² values between density and GRN (3 to 18 from pith) for I-214 and S1-8 poplar clones, respectively. The authors also stated that there is a negative correlation between density and GRW. As shown in Table 1, the mean density of 2 GRN presented significant differences and according to linear regression statistics (Table 3), there is a weak (0.309 R²) but significant adverse relationship between GRW and density. This may influence the wave velocities which is one of the basic determinants for mechanical property calculation (Eqs. 1 and 2). This is because UWV is directly related to the elastic moduli and density of a solid material (Stegemann et al. 2016). However, Krauss and Kudela (2011) revealed that the velocity of a longitudinal ultrasonic wave propagated through the L direction of wood (VLL) does not linearly increase or decrease with the increase in GRN. Furthermore, Hasegawa et al. (2011) reported that there is no change in VRR when the distance from the pith increases. In this study, except for VRL, neither longitudinal nor transverse ultrasonic waves presented stable increase or decrease tendencies against GRN. Therefore, the barrier effect of GRN on UWV was not proved because as shown in Table 1, VRL did not drop with the increase in GRN. In contrast, 5.1% and 6.5% increases were observed when GRN increased from 2 to 4 and 6, respectively. Furthermore, VLR, VRT, and VTR for 6 GRN were higher than those of 2 GRN.

According to the ANOVA results seen in Table 1, significant differences in the UWV means were only observed for VRL and VRT. However, the homogeneity groups between the velocities were not the same. Therefore, it is not possible to say that increase in GRN influences the UWV in the same manner, but the VRR was the most negatively affected UWV by the GRN while VRL was positive.

According to linear regression statistics (Table 3) and models (Fig. 2), there were positive and negative relationships between GRW vs. UWVs. As illustrated in Fig. 2, considering the coefficients, when GRW tended to increase, density and VRT increased while others decrease. But, except for VRR and VTR, the relationships were found to be significant. The R² values ranged from 0.012 (VTR) to 0.644 (VRL). Therefore, models can explain a maximum of 64.4% variability of the response data around its average.

Table 3. Linear Regression Statistics for GRW

Density vs. UWVs

Even if it is not prominent as in the T direction due to ray cells being aligned in the R direction, wave refraction occurs for ultrasonic waves while passing a GR. This is because of the sequential but nonhomogeneous formation of the EW and LW that causes density diffraction. As a result, the wave attenuates by losing its energy, and attenuation causes velocity alterations. However, the influence of density on UWV in wood is controversial because there are opposite conclusions.

Fig. 2. Linear regression models and coefficients of determination for physical properties

For example, positive values have been reported for VLL of different softwood and hardwood species (de Oliveira and Sales 2006; Baar et al. 2012), negative for VLL of 11 Australian hardwoods (R:0.647) (Bucur and Chivers 1991), significant negative for VLL, while insignificant positive for VRR and VTT for Japanese cedar (Hasegawa et al. 2011). On the other hand, Hasegawa et al. (2011) also reported statistically significant negative for VLL and insignificant negative VRR and VTT for Japanese cypress. Furthermore, neutral conclusions for VLL vs. density were expressed by Mishiro (1996) and Ilic (2003). De Oliveira and Sales (2006) reported 0.8 to 0.88 R² between VLL and density for Caribbean pine, lemon-scented gum, rose gum, goupie, and courbaril species. A positive relation and 0.84 to 0.89 R² between VLL vs. density were also reported by Yılmaz Aydın and Aydın (2018a) for cedar. However, a weak (0.146 and 0.29 R²) and negative relationship between VLL vs. density was also reported by Krauss and Kudela (2011) for Scots pine and Liu et al. (2019). In this study, R² values between UWV vs. density (Fig. 3) ranged from 0.000 (VTR) to 0.331 (VRL).

Indeed, there can be several factors (such as microfibril angle-MFA, the slope of grain, etc.) that cause variations in UWVs other than density. The proper positioning of the transducer for measuring can reduce or eliminate the influence of anatomical alterations such as tracheid length or MFA (Hasegawa et al. 2011). However, quantification of such issues requires both orthotropic material knowledge and expertise in technological equipment usage. For instance, there is a positive strong relationship (R 0.85 and 0.91) between VLL and tracheid length, while there is a negative strong relationship (R 0.82 and 0.9) between VLL and MFA (Hasegawa et al. 2011). Furthermore, VLL varies from pith to bark (Bucur 2006). Conversely, VRR has no correlations with tracheid length, MFA, and density (Hasegawa et al. 2011). Therefore, as Baar et al. (2012) expressed, it is not easy to find a direct effect of density on velocity that reflects the opposite conclusions.

Fig. 3. Linear regression models and coefficients of determination for density vs UWVs

Mechanical Properties

The means for the mechanical properties are presented in Table 4. The ER ranged from 705 to 1696 MPa. As shown in Table 5, reported ER values range from 700 to 1900 MPa. The upper bound reaches 5 GPa for the OSB produced using P. deltoides. However, the ER of P. deltoides solid wood without any modification is 900 MPa, which was predicted using the US. It is the same with the literature data reported by Longo et al. (2018). As shown in Table 4, the ER means of this study are in the range of the reported values. When considering the unavailable dynamic ER values in the literature for Populus x canadensis, this study can contribute to the literature by providing comparable data.

Table 4. Descriptives and Statistics for Mechanical Properties

Table 5. Reported Moduli for Poplar Species Related to Radial Direction Only

The shear modulus values in LR and RT planes ranged from 693.8 to 912.2 MPa (705 to 940.1 MPa for VRL = VLR) and 83 to 124.5 MPa (80.7 to 123.6 MPa for VRT = VTR), respectively. The shear modulus means (Table 4) were in harmony with the reported averages seen in Table 5. When all GRN groups were averaged, the GRL and GRT values were 802.8 and 97.5 MPa (VİJV) and 836.3 and 103.5 MPa (VİJ = V), respectively. The GRL (VİJV) of this study was 33.8% higher and 39.4% lower than the lower and upper bounds of reported data (Table 5), while GRT was 2.5% and 55.7% lower, respectively. The GRT is included in the reported range when GRN groups were averaged. However, it is around 53% lower than the reported upper bound. Essentially, even if the species is same, such diffraction is not abnormal for wood materials that present different properties not only between species by species but also due to test methods, growing conditions (climate, elevation, etc.), sampling, etc.

Influence of AR properties on mechanical properties

As in UWV, ER did not present linear behavior. Indeed, it increased and then significantly decreased with the increase in GRN. Among the evaluated properties, ER was the most adversely affected property by GRN increment. The maximum range (-22% to 5%) for the diffraction was observed for ER. The ANOVA results demonstrated that 6 GRN caused significant diffraction on ER. The model for GRW vs. ER (Fig. 4) was able to predict only 1.4% of the variables, and according to linear regression results (Table 6) the relationship between ER vs. GRW was found to be insignificant. Dinulică et al. (2021) reported a 0.21 R² value (p = 0.03) for the relationship between ER vs. GRW of Norway spruce. The authors stated that ER increases with the increase in SW ring width but decreases with LW width irregularity. Vega et al. (2020) reported that the dynamic MOE of Eucalyptus nitens increased with the increase in rings from the pith and tends to be constant following the outerwood section. It was reported that the density and MFA increased, decreased, and became constant following the outerwood section. Therefore, samples should not include transition sections as in this study.

The GLR constantly increased with the increase in GRN. In contrast, GRT decreased and then surpassed the initial value when GRN increased. The same was true when moduli were calculated using the VİJ = Vassumption. The GLR was the most positively influenced property by the GRN increment. This advancement was more pronounced when moduli were calculated with the equal velocity assumption. According to ANOVA results (Table 4), GRN had significant influences on the shear moduli calculated using either VİJ = V or VİJV assumptions. However, the velocity assumption caused diffraction in the homogeneity grouping of GRT. According to linear regression results seen in Table 6 and Fig. 4, there was a positive and significant relationship between GRW vs. GLR and around 55 to 58% of variables can be predicted using GRW. In contrast, a negative weak but significant relationship was observed for GRW vs. GRT. As illustrated in Fig. 4, considering the coefficients, when GRW tended to increase, ER and GLR increased while GRT decreased.

Table 6. Linear Regression Statistics for GRW