Comparison between static modulus of elasticity, non-destructive testing moduli of elasticity and stress-wave speed in white spruce and lodgepole pine wood

ABSTRACT

Static bending tests to measure modulus of elasticity (MOE_ST) or wood stiffness provide an indicator of the structural performance of a finished product. These tests are however, slow and expensive. Tests to measure MOE using non-destructive testing (NDT) provide alternatives to MOE_ST tests; however, relationships between the different modes of measurement need to be established. Non-destructive testing MOE measured by two methods (SilviScan [MOE_SS] and time of flight [MOE_TOF]) have been compared with MOE_ST for lodgepole pine and white spruce. The relationships between stress wave speed (SWS) and MOE_ST have also been evaluated. Simple linear regressions of MOE_SS, MOE_TOF, and SWS had greater explanatory power (higher coefficients of determination (R²)) than did multiple linear regressions including growth rate or other wood fibre attributes. Simple linear regression from MOE_TOF and MOE_SS on MOE_ST had lower R² for lodgepole pine than for white spruce; however, the converse was true for SWS. SWS had the highest R² (89%) and MOE_SS the lowest R² (47%) when regressed on MOE_ST in lodgepole pine. The results were tool and species specific, suggesting that R² between MOE_ST and non-destructive testing MOE values must be validated separately for each commercial tree species and for each measurement technique.

KEYWORDS:

• Mechanical properties of wood
• juvenile wood
• mature wood
• linear regressions
• ASTM-D-143

1. Introduction

The mechanical properties of wood are among the most important wood and fibre attributes (WFA) for many end products. With the emergence of multistory timber-building systems (Cecobois 2013) for which precise knowledge of the performance of wood products is required, it has become essential to have up-to-date information on the variation of wood products mechanical properties in general, and their stiffness or modulus of elasticity (MOE) in particular. This information should take into account the differences between juvenile wood (JW) and mature wood (MW) (Zobel and Sprague 1998) and the impact of growth rate (Vincent et al. 2011). This assessment is necessary because to date, quality control of structural sawn timber has hardly considered the differences between JW and MW, and growth rate has only been considered in extreme cases of fast-grown plantations. The 3-point static bending test and the 4-point static bending test are the traditional means for measuring static modulus of elasticity (MOE_ST) in woody material (Brancheriau et al. 2002, Ross 2015). The main differences between these two methods are the location of the maximum bending moment and maximum axial fiber stresses which occurs directly at the specimen mid-point (i.e. below the loading nose) in three-point loading, but is spread out over the area between the loading noses in the four-point method (Chitchumnong et al. 1989, Ross 2015). For this reason, one has to apply conversion factors before comparing results from one method to another (Brancheriau et al. 2002, Hein and Brancheriau 2018). The 3-point static bending test involves submitting a wood sample of normalized length (L), width (e), and height (h) and known moisture content (MC) to a known load (P) at its mid-span (l/2). The resultant deflection (f) is measured and MOE_ST is computed from the linear portion of the load-deflection curve, far from the elastic limit, as described in equation 1 (Brancheriau et al. 2002). Measuring MOE_ST for wood pieces with static bending tests is an expensive, time-consuming, and destructive process, which limits the use of these tests in research and forestry operations. Therefore, many studies have focussed on developing tools and techniques for rapid, non-destructive, and cost-effective measurement of mechanical properties that could be used as substitutes for static bending tests; the speed of sound transmission and attenuation (Ross and Pellerin 1994; Wang et al. 2004) and the SilviScan technology (Evans 1999; Evans et al. 1999) are among the most promising. However, these technologies still need to be validated for many commercial tree species, including white spruce and lodgepole pine. (1) $\begin{array}{rl}& MO{E}_{ST}=\left({\displaystyle \frac{L^3}{4e{h}^3}}\right)\times k\\ & \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}k={\displaystyle \frac{\left|\mathrm{\Delta }\mathrm{P}\right|}{\left|\mathrm{\Delta }\mathrm{f}\right|}}\end{array}$(1) Where L is sample length (span), e is sample width, h is sample height, k is indentation coefficient, P is applied load and f is deflection at midspan.

The measurement of the longitudinal modulus of elasticity in wood, sometimes called dynamic modulus of elasticity was carried out for the first time at the United States Department of Agriculture’s Forest Products Laboratory in Madison, Wisconsin, before World War II (Bell et al. 1954) and has greatly evolved since then. Acoustic resonance and acoustic time of flight (TOF) are the two methods used to measure acoustic velocity (Legg and Bradley 2016, Schimleck et al. 2019). In both cases, the longitudinal stress wave travels in a direction parallel to the grain of wood from a transmitting probe to a receiving probe. Acoustic resonance signal is reflected from each end of the sample many times and standing waves are generated and measured (Legg and Bradley 2016). In acoustic TOF, the stress wave is induced by a transmitting probe, travels through the wood, and is detected by a receiving probe located at a known distance (d) from the transmitter. The time taken by the stress wave to first reach the receiving probe, known as TOF (Brashaw et al. 2009), is then used to compute the stress wave speed (SWS), as described in equation 2. SWS is an economically feasible alternative way to estimate the mechanical properties of wood in standing trees or logs (Baillères et al. 1998; Jacques et al. 2004, Wang et al. 2007). It is particularly appealing because it allows users to estimate the mechanical properties of wood more quickly and at less cost than if they also measured wood density (WD). Some SWS equipment may be used in adverse environmental conditions and do not require highly qualified personnel for their operation. It has been successfully used for mechanical classification of structural hardwood (Baillères et al. 1998) and for genetic selection of softwood with superior mechanical properties (Jacques et al. 2004). SWS is also used in the one-dimensional wave equation (equation 3), which establishes the relationships among TOF modulus of elasticity (MOE_TOF), SWS, and WD (Wang et al. 2004, Mahon et al. 2009; Ross 2015). (2) $SWS={\displaystyle \frac{\mathrm{d}}{\mathrm{T}\mathrm{O}\mathrm{F}}}$(2) (3) $\mathrm{M}\mathrm{O}{\mathrm{E}}_{\mathrm{T}\mathrm{O}\mathrm{F}}=\mathrm{S}\mathrm{W}{\mathrm{S}}^2\times WD$(3) Where d is sample length (distance), TOF is time of flight, and WD id wood density.

SilviScan is a tool composed of several proven technologies, which allows assessment of a range of WFA in an automated, rapid, cost-effective, and non-destructive way (Evans 1999; Defo et al. 2010, Knowles et al. 2004). An advantage of SilviScan over other techniques being used to measure MOE is the determination of the pith to bark radial pattern, which can be compared with other WFA (Raymond et al. 2007). Physical WFA (e.g. wood density) and morphological WFA (e.g. growth ring width) are measured by means of X-ray densitometry, a well-established and widely used technology (Koubaa et al. 2005). Anatomical WFA (e.g. microfibril angle) are measured by means of X-ray diffraction, another well established and widely used technology (Brändström 2001). SilviScan MOE (MOE_SS) is obtained through a combination of these two technologies and image analysis (equation 4). The main disadvantage with SilviScan is that it is available in only few laboratories around the world. Therefore, samples often need to be sent away for testing (Knowles et al. 2004, Schimleck et al. 2019). (4) $\mathrm{M}\mathrm{O}{\mathrm{E}}_{\mathrm{S}\mathrm{S}}=A\times \left(I_{CV}\times \rho \right){}^B$(4) Where I_cv is the coefficient of variation of the intensity of the X-ray diffraction profile, ρ is the wood density obtained from X-ray densitometry, A is a scaling factor and B is an exponent to allow for curvature (Evans 1999, 2006; Evans et al. 1999).

Unlike acoustic TOF, acoustic resonance requires two cut ends, and cannot be used on standing trees (Legg and Bradley 2016). Acoustic resonance MOE and acoustic TOF MOE are not directly comparable but have a good correlation once the bias is corrected (Schimleck et al. 2019). Studies have found that the MOE_TOF is higher than both the resonance MOE and the MOE_ST, but strong correlation were found between resonance MOE and MOE_ST (Legg and Bradley 2016). There is also a good correlation between MOE_TOF and MOE_ST (Ide 1935; Wang et al. 2004; Liang and Fu 2007; Mora et al. 2009). MOE_TOF generally exceeds MOE_ST by 8% to 15% in many species (Wang et al. 2004; Jacques et al. 2004; Liang and Fu 2007). Ide (1935) suggested that MOE_TOF exceeds MOE_ST because it is obtained for minute alternating stresses, far below the elastic limit, which do not give rise to complex creep effects or elastic hysteresis. Haines et al. (1996) and Ouis (2002) suggested that viscoelasticity is the most likely source of the differences noted between MOE_TOF and both MOE_ST and resonance MOE. However, it is not uncommon for the measurement of MOE using non-destructive testing [MOE_NDT] to be lower than the measurement of MOE_ST. A 30.6% decrease from static to MOE_TOF was found by Lindström et al. (2004), when they compared MOE_TOF with axial compression MOE on 3-year-old radiata pine clones. Haines et al. (1996) found an average decrease of 6%, with some samples having a 20% decrease, when they compared resonance MOE and static MOE of Norway spruce construction lumber. Due to the anisotropic nature of wood, MOE_TOF is highest in the longitudinal direction, followed by the radial radiation and lowest in the tangential direction (Bucur 2006, Wessels et al. 2011, Schimleck et al. 2019). The longitudinal MOE_TOF is negatively influence by knots, MC, tree height (Hsu 2003), branches and bark (Lasserre et al. 2007).

There is a good correlation between MOE_SS and MOE_ST (Defo et al. 2010; Raymond et al. 2007). Defo et al. (2010) found high correlations for both small clear battens (r = 0.80–0.82) and lumber (r = 0.79) of balsam fir and black spruce. In small clear battens, MOE_SS exceeded MOE_ST by 10% in radiata pine (Raymond et al. 2007), by 32.8% in balsam fir, and by 47% in black spruce (Defo et al. 2010). In lumber sampled from the same trees, MOE_SS exceeded MOE_ST by 6.9% and 15.8% for balsam fir and black spruce, respectively (Defo et al. 2010). However, the results were species specific, indicating the need to validate the suitability of SilviScan for use in each species of interest (Defo et al. 2010).

While SilviScan (Evans 1999) and the 3-point static bending test (Brancheriau et al. 2002) are clearly designed for laboratory use, the Picus 3 TOF Tomograph was developed for field use (Brashaw et al. 2009, Argus Electronic GmbH 2017). In practice, many TOF tools are used interchangeably for field and laboratory tests. Although this is an accepted practice, the best relationships are obtained when the appropriate technique is used.¹ Although a close relationship exists between MOE_NDT values computed using different technologies, MOE_NDT values do vary according to the technology used (Liang and Fu 2007; Raymond et al. 2007). Few studies have compared MOE_ST and MOE_NDT values measured from the same small clear battens (Bell et al. 1954; Gerhards 1982; Wang et al. 2004; Raymond et al. 2007). In addition, few studies have examined the variation in MOE_NDT values measured using different technologies on the same trees (Liang and Fu 2007; Bell et al. 1954; Raymond et al. 2007). White spruce (Picea Glauca (Moench) Voss) and lodgepole pine (Pinus contorta Dougl. ex. Loud.) are prominent components of the commercial forest land base in western Canada; they are principally used for lumber production and are of vital economic importance to the Canadian forestry industry (Nienstaedt and Zasada 1990; Lotan and Critchfield 1990; MFFP 2015). Cost-effective and validated tools for measuring the mechanical properties of wood are essential for optimizing the use of this important resource. The objective of this study was to compare MOE_SS and MOE_TOF to MOE_ST for both lodgepole pine and white spruce, and to compare SWS to MOE_ST.

2. Material and methods

2.1. Material

Ten lodgepole pine trees and 10 white spruce trees were used in this study (Table 1). The stand age, plot size, and desired codominant crown class of free of visible defects trees limited the number of trees that could be removed for testing. However, a sampling size of 10–15 trees/site resulted in marginally smaller standard errors for the mean estimate of wood density for a site (Raymond 2006, Jordan et al. 2007). The lodgepole pine trees were harvested from the MacKay thinning trial, Alberta (Stewart et al. 2006) in 2016. These trees were part of a fire-origin stand that was thinned at 22 years to 1680 stems/ha. White spruce trees were harvested from several long-term monitoring (buffer areas) plots in natural untreated forest stands near Calling Lake, Alberta in 2016. All trees were of the codominant social class.

Table 1. Tree-level average values of modulus of elasticity (MOE) obtained from SilviScan, time of flight (TOF), and static bending tests for lodgepole pine and white spruce, presented in decreasing order using SilviScan MOE values.

TreeID	Tree age (years)	Transition age (years)	JWP (%)	DBH (cm)	Tree height (m)	MOESS (GPa)	MOEST (GPa)	MOETOF (GPa)	MFA (°)	RD (kg/m^3)	WD (kg/m^3)	RW (mm)	SWS (m/s)
Lodgepole pine
Pl 1	70	21	10.8	15.7	18.5	18.38	13.84	9.52	10.3	519.9	628.8	1.1	3892
Pl 2	71	13	11.6	15.3	19.5	17.79	12.04	7.04	7.5	461.7	521.9	0.9	3671
Pl 3	72	20	17.1	16.7	20.6	17.62	12.39	7.58	7.3	467.9	547.3	0.9	3721
Pl 4	72	44	54.2	18	20.8	17.39	14.38	8.47	6.4	426.6	543.4	0.9	3948
Pl 5	74	34	38.8	17	21.9	16.57	12.74	7.87	10.1	470.8	542.8	1.1	3807
Pl 6	70	12	14.8	13.2	16.2	16.44	10.70	7.11	9.0	451.6	572.5	0.8	3525
Pl 7	73	29	36.1	17.8	21	16.30	10.60	6.68	8.2	424.2	514.1	0.9	3606
Pl 8	70	29	31.7	14.2	17	15.86	13.42	8.1	8.0	436.5	575.5	0.8	3766
Pl 9	71	38	50.1	15.3	17.	14.45	9.21	5.63	9.1	402.4	453.2	0.8	3524
Pl 10	69	13	10.4	14.5	19.7	13.26	10.56	7.11	12.8	430.0	543.3	0.9	3619
Average	71.2	25.4	27.6	15.8	19.2	16.40	12.04	7.51	8.9	449.2	543.8	0.9	3706
White spruce
Sw 1	107	36	23.2	34.9	29	15.23	9.89	6.71	9.0	390.0	430.2	1.4	3948
Sw 2	153	18	2.0	41.8	28.7	14.02	9.84	6.48	8.4	368.5	427.5	1.1	3890
Sw 3	107	23	6.5	34.8	24.7	13.90	9.18	6.01	10.7	382.8	492.7	1.4	3498
Sw 4	107	15	5.1	35.5	25.6	13.81	8.69	5.86	8.7	351.6	411.3	1.4	3773
Sw 5	78	18	6.8	24.3	27.6	13.19	9.74	6.56	10.4	362.6	434.1	1.6	3884
Sw 6	55	13	3.0	30.5	24.9	12.67	9.39	5.99	11.9	368.9	407.2	2.4	3835
Sw 7	148	28	15.0	32	26.8	12.39	10.15	7.64	19.4	452.6	508.3	1.0	3869
Sw 8	75	40	33.7	26.9	24.1	12.15	7.36	5.06	12.5	362.0	413.6	1.5	3496
Sw 9	55	15	6.8	32.7	21.9	8.93	7.61	4.61	15.2	301.5	352.2	2.6	3619
Sw 10	51	8	0.7	39.5	24.5	8.92	5.97	4.26	14.6	297.7	341.6	3.3	3535
Average	93.6	21	10.3	33.3	25.8	12.52	8.78	5.92	12.1	363.8	421.9	1.8	3735

Note: Pl, lodgepole pine; Sw, white spruce; JWP, juvenile wood proportion computed from SilviScan ring width at breast height, assuming a circular shape for all trees; DBH, diameter at breast height; MOE_SS, SilviScan modulus of elasticity; MOE_ST, static modulus of elasticity; MOE_TOF, TOF modulus of elasticity; MFA, microfibrils angle; RD, wood density measured with X-ray densitometry using SilviScan3; WD, wood density measured gravimetrically from battens; RW, ring width measured with X-ray densitometry using SilviScan3; SWS, stress wave speed measured with the Picus instrument.

2.2. Testing methods

A 5-cm-thick disk was collected at breast height from every felled tree, air dried in the laboratory at the Northern Forestry Centre, Edmonton, Alberta, and sent to the EvaluTree laboratory of FPInnovations, Vancouver, British Columbia, for Silviscan analysis. A 12 by 12 mm (tangential by longitudinal) radial block was taken from pith to bark of each disk. These blocks were extracted with acetone to remove resins and then conditioned to 8% equilibrium moisture content. A 2 by 7 mm (tangential by longitudinal) strip was sawn from each block and used to measure WFA with SilviScan. All standard measurements available with SilviScan were performed, including wood density (RD) measured at 25 µm resolution and microfibril angle (MFA) measured at 5 mm resolution (Evans and Ilic 2001). MOE_SS was calculated from wood density and X-ray diffraction metrics as described in Eq. 4.

A 60-cm (longitudinal) bolt was cut just above the disk and used to prepare small clear battens for static bending measurement according to the guidance for secondary method specimens (25 by 25 by 410 mm) in ASTM-D-143 (ASTM 2014). Battens were sawn and air dried in the laboratory at the Northern Forestry Centre. One to 6 pith-free battens per bolt were collected, depending on the tree’s diameter and defects. The battens were taken from along the north and south line across the bolt, as closely as defects and branch traces would allow. These were shipped to the Université du Québec en Abitibi-Témiscamingue (UQAT) for further processing. Upon arrival in UQAT, battens were stored in a Labocon climate chamber (model LHC-103) at 20°C and 65% relative humidity for a target 12% equilibrium MC of all samples. Acoustic velocity was measured on the battens with a through transmission test method (Senalik et al. 2015) using the point-to-point measurement mode on a Picus 3 TOF Acoustic Tomograph developed by Argus Electronic Gmbh (Brashaw et al. 2009, Argus Electronic GmbH 2017), and mainly used to detect decay and cavities in standing trees non-invasively. The experimental setup consisted of 2 common (roofing) nails inserted (2–3 mm deep) into each end of the batten in the longitudinal direction. The tapping pin of an electronic radio hammer was bound to 1 nail, and the wave was induced by gently hitting the tapping pin with the electronic hammer. One receiving magnetic sensor was bound to the other nail. To avoid reproducibility and accuracy issues (Andrews 2000), the Picus TOF instrument was operated within a few days by a single user, who inserted all probes parallel to the small clear batten edges and tried to keep the same impact angle and impact strength of the hammer. The longitudinal SWS was computed automatically by the Picus and the average of 5 hits was recorded as the SWS for the batten in question. The battens were reconditioned after the speed of sound measurements to avoid MC variation before the static bending tests.

After the SWS measurement, a universal testing machine (Zwick/Roell, model Z020) with 20 kN capacity and equipped with an extensometer was used for the 3-point bending test measurement according to the guidance for secondary method specimens (25 by 25 by 410 mm) in ASTM-D-143 (ASTM 2014). After testing, a 25-mm cube was taken at 1 cm from the batten edge and weighed to 0.001 g precision with a Mettler Toledo scale (model XS204). These cubes were then oven dried at 103°C in a Quincy Lab drying oven (model 40 GC) to determine the batten’s MC (Reeb and Milota 1999). Another small sample (approximately 150 mm long) was cut from the batten and sanded. After sanding, these samples were conditioned in the Labocon at the same condition as the battens, weighed with an Ohaus Precision scale to 0.01 g precision and measured with an electronic caliper to 0.01 mm precision for gravimetric wood density (WD) determination. MOE_ST was computed with the Zwick equipment using Eq. 1, and MOE_TOF was calculated from SWS and WD as described in Eq. 3.

2.3. Statistical analyses

The first two rings from the pith represent a minor proportion of the stem volume but exhibit highly variable values for WFA. These were removed from the SilviScan database to avoid undue leverage by these values and to facilitate model fitting (Alteyrac et al. 2005, Chen et al. 2016). This process removed 2% of the whole SilviScan database. The lodgepole pine and the white spruce datasets were partitioned into JW and MW based on the MOE transition age calculated using a linear-linear segmented model (Wang and Stewart 2013). Linear regressions proved efficiency in converting MOE measurements from a testing method to another (Knowles et al. 2004, Hein and Brancheriau 2018), and were used to compare MOE_TOF, MOE_SS, and SWS to MOE_ST. Model fitting was completed with the R statistical software (R Core Team 2017). Analyses were performed separately for the JW and the MW zones, and by combining these two subsamples, for each wood species. Additionally, a database that included those tree rings that had MOE values obtained with all three technologies was created for each wood species. Comparisons across the different modalities of measurement were conducted at the whole disc level and at the level of the individual small clear batten. For the latter, only those SilviScan values observed for the rings that occurred in each given batten were used for comparison with the TOF and static measurements on the batten (matched-rings comparison). Whole-disc comparisons used all of the measurements made for each measurement modality.

3. Results and discussion

3.1. Tree characteristics, radial pattern and average values

Tree-level average values of diameter at breast height, trees height, MOE_SS transition age (TA) and corresponding juvenile wood proportion (JWP) are presented in Table 1 for both lodgepole pine and white spruce. The TA and JWP variation within species and between species in this study were consistent with earlier studies (Zobel and van Buijtenen 1989; Mvolo et al. 2015a; Wang and Stewart 2012, 2013).

MOE_SS increased to about 75 and 45 growth rings from the pith for white spruce and lodgepole pine, respectively, where it started decreasing with age (Figure 1). This pattern was also observed with MOE_TOF and MOE_ST (figures not shown). These MOE_SS radial patterns were consistent with previously described patterns in spruce (Alteyrac et al. 2006) and pine (Wang and Stewart 2013). The MOE_SS values were similar to those previously reported for lodgepole pine (Wang and Stewart 2013 [5–19 GPa]) and white spruce (Sattler and Stewart 2016 [4–18 GPa]). The MOE_TOF was lower than the previously reported value for lodgepole pine lumber (Liang and Fu 2007 [15 GPa]). The MOE_ST values were comparable to those previously reported for lodgepole pine (Jessome 2000 [11 GPa]; Liang and Fu 2007 [11.7 GPa]) and white spruce (Jessome 2000 [9.93 GPa]; Sattler et al. 2014 [4–14 GPa]). Static testing equipment usually relies on the same ASTM standard, and one can expect SilviScan equipment to be comparable across laboratories. Therefore, it is straightforward to compare MOE_SS and MOE_ST values among studies, making sure the same technique (3-points vs. 4-points) is used for MOE_ST, or proper conversion factors are applied (Brancheriau et al. 2002, Hein and Brancheriau 2018). It is less straightforward to compare MOE values calculated using acoustic tools (TOF or resonance) because there is no established standard used across studies (Liang and Fu 2007; Mahon et al. 2009).

Figure 1. Variation from pith to bark in modulus of elasticity (MOE) measured by SilviScan in lodgepole pine (Pl) and white spruce (Sw); standard errors are represented by the grey zones

The average MC of battens at the time of testing was 11.03%. Wood density is usually measured on samples stabilized at 12%MC. However, given the very low percent volumetric shrinkage observed from 11% to 12% MC (Glass and Zelinka 2010), we didn’t attempt to determine any correction factors for MC. Tree-level average values of wood density (WD) determined gravimetrically and wood density (RD) determined by SilviScan using X-ray densitometry are presented in Table 1 for both lodgepole pine and white spruce. As expected, RD values were different from WD values. However, these values are not strictly comparable, because SilviScan samples were extracted radial strips, while unextracted longitudinal battens were used to determine wood density gravimetrically. The RD values that we observed in this study were similar to those previously reported for lodgepole pine (Mansfield et al. 2009 [275–575 kg/m³]) and white spruce (Middleton et al. 2000 [275–413 kg/m³]). The WD values were higher than those previously reported for lodgepole pine (412 kg/m³) and white spruce (372 kg/m³) by Jessome (2000). This difference may be explained by sampling, as we used small samples collected avoiding defects and branch traces. Most of these samples were closer to the pith than to the bark. The radial pattern of pines and spruces wood density belongs to the type II as described by Panshin and de Zeuuw (1980), in which the closer to the pith, the higher the wood density. The average SWS values found in this study for lodgepole pine and white spruce, respectively (Table 1), were comparable to the 3292 and 3486 m/s values reported by Wang et al. (2004) for western hemlock and Sitka spruce, respectively. The faster stress wave transmission in spruce compared to pine, and the associated lower MOE_TOF agreed with values reviewed by Ross and Pellerin (2015).

3.2. Comparisons of MOE measurement methods

SilviScan showed the largest variability among the three technologies, followed by static equipment; the lowest variation was found with the TOF equipment (Figure 2, Table 2). The largest variability found with MOE_SS may be explained by the fact that the SilviScan measurement was done at a finer scale, allowing a better capture of MOE variation, as one can see in Figure 1. The lowest variation found with the acoustic TOF equipment may have been because the longitudinal wave in our samples travels preferentially through the earlywood, where both wood density and stiffness are lower, and SWS passes with lower velocity (Haines et al. 1996; Feeney et al. 1998; Xu et al. 2004). To avoid this issue, acoustic resonance tools are often preferred to acoustic TOF tools, since the wave reflects many times from the ends of the sample (Haines et al. 1996; Lindström et al. 2004, Legg and Bradley 2016). However, wood is known to be less attenuative in the longitudinal direction (Feeney et al. 1998), and the impact of the differences between earlywood and latewood on MOE_TOF was beyond the scope of this study.

Figure 2. Variability in modulus of elasticity (MOE) between lodgepole pine (Pl) and white spruce (Sw), and among measurement techniques

Table 2. SilviScan, acoustic time of flight (TOF), and static bending test modulus of elasticity (MOE) values obtained by wood zone for lodgepole pine and white spruce small clear battens and thin radial strip (minimum, average, and maximum MOE values in GPa).

Species	MOE type	Count	Minimum	Average	Maximum	S.D.	C.V.
Lodgepole pine	Whole section
	Static	18	8.69	12.00	14.53	1.709	14.2
	TOF	18	5.41	7.44	9.52	0.971	13.1
	SilviScan	691	4.60	16.41	22.20	3.526	21.5
	Juvenile wood
	Static	5	8.69	10.40	11.60	1.205	11.6
	TOF	5	5.41	6.54	7.40	0.895	13.7
	SilviScan	223	4.60	13.13	19.80	3.544	27.0
	Mature wood
	Static	13	10.38	12.61	14.53	1.479	11.7
	TOF	13	6.56	7.78	9.52	0.775	10
	SilviScan	468	12.00	17.97	22.20	2.196	12.2
	Matched-rings
	Static	18	8.69	12.00	14.53	1.709	14.2
	TOF	18	5.41	7.44	9.52	0.971	13.1
	SilviScan	18	9.68	15.78	20.70	3.051	19.3
White spruce	Whole section
	Static	41	5.15	8.65	11.97	1.805	20.9
	TOF	41	3.85	5.83	8.60	1.103	18.94
	SilviScan	916	4.10	13.00	17.70	2.774	21.3
	Juvenile wood
	Static	5	5.96	7.93	9.27	1.310	16.5
	TOF	5	4.79	5.72	6.84	0.947	16.6
	SilviScan	184	4.10	9.99	15.60	2.753	27.6
	Mature wood
	Static	36	5.15	8.75	11.97	1.856	21.22
	TOF	36	3.85	5.84	8.60	1.134	19.4
	SilviScan	732	6.60	13.75	17.70	2.208	16.1
	Matched-rings
	Static	41	5.15	8.65	11.97	1.805	20.9
	TOF	41	3.85	5.83	8.60	1.103	18.9
	SilviScan	41	7.52	12.84	16.56	2.594	20.2

Note: S.D., standard deviation; C.V., coefficient of variation.

For both lodgepole pine and white spruce, MOE values were largest with SilviScan, followed by static MOE, and the lowest MOE values were registered with the acoustic TOF equipment (Figure 2, Table 1). This higher MOE_SS value compared to MOE_ST value is consistent with findings from previous studies on black spruce and balsam fir (Defo et al. 2010) and on radiata pine (Raymond et al. 2007). The lowest MOE_TOF may have been because our samples were too short for the equipment used. The longitudinal acoustic velocity was found to diminish below a length/width ratio of 20 (Bucur 2006). The length/width ratio for secondary method specimens in ASTM-D-143 used in this study is 16.4. Acoustic TOF are usually designed for probes being inserted at about a meter of distance one from the other in field environment (Schimleck et al. 2019). Our probes were inserted at about 0.4 m one from the other. Even for samples having the same length/width ratio, the longitudinal acoustic velocity diminishes with shorter samples. This was explained by mode conversion phenomena in infinite solid vs. rod (Bucur et al. 2002, Bucur 2006). The shorter distance used in TOF equipment compared to resonance equipment has also been suggested as the reason for TOF measurements being more sensitive to errors resulting from local heterogeneity in the wood (Legg and Bradley 2016). Following this reasoning, despite the care taken in selecting our samples, one can expect branch traces and small knots to significantly reduce MOE_TOF (Hsu 2003, Bucur 2006, Lasserre et al. 2007) in these short battens than it would do in longer samples. A more appropriate setup for stress wave measurements using secondary method specimens designed for ASTM-D-143 may be using a digital oscilloscope.

Our finding that values were higher for MOE_ST than for MOE_TOF for both lodgepole pine and white spruce is consistent with findings from a previous study comparing MOE_TOF and axial compression MOE on 3-year-old radiata pine clones (Lindström et al. 2004). Despite the common observation that MOE_NDT exceeds MOE_ST (Legg and Bradley 2016), some studies have found a higher MOE_ST than MOE_NDT. For instance, Haines et al. (1996) found higher MOE_ST than acoustic resonance MOE in Norway spruce construction lumber. Given that acoustic resonance methods are known to have lower MOE value than acoustic TOF methods (Legg and Bradley 2016), an even larger decrease could be expected if the construction lumber were tested by TOF technology. However, in the same study, an increase from MOE_ST to acoustic TOF MOE and acoustic resonance MOE was also found for Norway spruce and silver fir small clear battens. Despite the discrepancies among MOE values, the results obtained with all three technologies followed the expected pattern produced with MOE_SS (Figure 1). Also, when one looks at our trees ranked according to their MOE_SS values (Table 1), all 3 technologies followed the same overall decreasing trend, in accordance with a previous report (Lindström et al. 2004). Finally, all 3 technologies produced the expected overall increasing relationships with wood density and SWS (Haines et al. 1996) and the expected overall decreasing relationship with MFA (Lindström et al. 2004).

MOE values were higher in lodgepole pine than in white spruce, independent of the measurement technique (Figure 2, Table 2) and wood zone considered (Table 2). These differences in MOE between species, and with all 3 technologies, are consistent with previous reports (Wang et al. 2004; Raymond et al. 2007; Defo et al. 2010). It confirms that any comparison between MOE values must take the tree species and the measurement technologies and operating conditions into account. On average, MOE_SS values from matched-rings subsamples were comparable to whole-disc MOE_SS values (Table 2). This similarity between matched-rings and mean-disc MOE values while using SilviScan suggests that one could sample only a few selected rings from pith to bark and have a representative value of mean pith-to-bark MOE, as is done with measurements of other WFA that are expensive to collect (Mvolo et al. 2015b, Mvolo et al. 2019). As expected, MOE_SS values were higher and less variable in MW than in JW.

3.3. Comparison between MOE values

Despite the differences in measurement modality and scale noted above, the estimations of static MOE from either of the NDT methods were linear and gave significant and useful predictions (Table 3, Figure 3). Overall, predicting MOE_ST from MOE_TOF and MOE_SS using linear regression produced lower coefficients of determination (R²) for lodgepole pine than for white spruce. Conversely, the linear regression from SWS had higher R² values for lodgepole pine than for white spruce. The lodgepole pine and white spruce R² values between the TOF and static methods presented in Table 3 were in the same range as correlations previously reported in other coniferous species (Lindström et al. 2004; Liang and Fu 2007). However, these values were slightly lower than the 0.98 found by Bell et al. (1954) and the 0.91 found by Wang et al. (2004) using a laboratory setup with an oscilloscope. This advocate for using purposely designed experimental technique for measuring TOF MOE in laboratory environment.

Figure 3. Predicted modulus of elasticity (MOE) from non-destructive testing (NDT) techniques, SilviScan, time of flight (TOF), and stress wave speed (SWS) versus observed static MOE for matched-rings of lodgepole pine (a), matched-rings of white spruce (b), disc mean of lodgepole pine (c), and disc mean of white spruce (d); the grey line is the 1:1 regression line and standard errors are represented by the grey zones

Table 3. Parameters and statistics from regression models estimating static modulus of elasticity from time of flight modulus of elasticity (MOE_TOF), SilviScan modulus of elasticity (MOE_SS) and stress wave speed (SWS).

Species/modality	Mean disc			Matched-rings
	Intercept	Slope	R^2%	Intercept	Slope	R^2%
Lodgepole pine
SWS	−26.80	0.010	89	−27.57	0.011	72
MOETOF	1.81	1.363	81	0.97	1.482	71
MOEss	0.31	0.715	47	4.75	0.459	67
White spruce
SWS	−13.61	0.006	61	−15.58	0.006	55
MOETOF	1.37	1.253	88	0.04	1.478	82
MOEss	2.34	0.515	62	0.89	0.604	75

Note: All parameter estimates were significant at p ≤ 0.01. SWS, stress wave speed; MOE_TOF, time of flight modulus of elasticity; MOEss, SilviScan modulus of elasticity.

The lodgepole pine and white spruce R² values between the SilviScan and static methods were lower than those between the TOF and static technologies (Table 3). This was expected, because the static and TOF technologies used the same longitudinal battens, while SilviScan samples were radial strips. Similarly, we expected the R² between MOE_SS and MOE_ST to be higher in the matched-rings database than in the mean-disc database, in part because, when we used the matched-rings, all values were the same age in comparing between the SilviScan technology and the static technology. All WFA measured with the SilviScan equipment were tested using simple linear regressions against MOE_ST for both mean-disc and matched-rings values. None of these variables presented a higher R² than the MOE_SS, nor did these WFA (including growth rate) improve the adjusted R² when included in multiple linear regression with MOE_SS (results not shown). Lodgepole pine juvenile wood MOE measured with the SilviScan equipment explained 57% (p value: 0.01) of mean tree MOE measured with the static equipment. White spruce SilviScan juvenile wood MOE failed to explain mean tree static MOE variation (R²: 29% and p value: 0.11). A dummy variable for wood zone (JW and MW) was used in multiple linear regression to test the combined effect of MOE_NDT and wood zone on MOE_ST, but these models did not improve R² with respect to simple linear regression, except for the model including SWS and wood zone for lodgepole pine.

The R² values between SWS and MOE_ST for lodgepole pine presented in Table 3 were higher than both the R² between MOE_TOF and MOE_ST and the R² between MOE_SS and MOE_ST. This finding was surprising, given that SWS is part of the MOE_TOF formula, and therefore one would expect MOE_TOF to have higher explanatory power than SWS. However, our attempts to model MOE_ST as a multiple linear function of WD and SWS were unsuccessful, with SWS explaining most of the variation and WD being non-significant. SWS has been presented as a valuable and flexible way to estimate MOE non-destructively, both in standing trees (Grabianowski et al. 2006; Wang et al. 2007; Eckard et al. 2010; Paradis et al. 2013) and in lumber (Wang et al. 2004; Liang and Fu 2007). It is particularly appealing because it allows users to estimate the mechanical properties of wood more quickly and cheaply than by also measuring wood density. However, a similarly high R² between SWS and MOE_ST was not found with white spruce samples. Therefore, one may conclude that the higher performance of SWS is species specific.

MOE values predicted from SilviScan and TOF equipment had a consistent pattern, and their confidence intervals largely overlapped across all databases (Figure 3), supporting the use of these technologies to estimate MOE_ST from MOE_NDT. Both MOE_SS and MOE_TOF overestimated MOE_ST for lower MOE value and underestimated MOE_ST for higher MOE values, in agreement with previous findings (Mora et al. 2009). However, we did not attempt to determine any correction factors for MC between SilviScan and TOF samples, because MC values among sampling modalities were comparable (8% vs. 11%) and all sampling was done at close locations in the trees. MOE predicted from SWS did not show a consistent pattern across databases. It overestimated (Figure 3(a)), underestimated (Figures 3(b and c)), and both overestimated MOE_ST for lower MOE values and underestimated MOE_ST for higher MOE values (Figure 3(d)). Except as shown in Figure 3(d), the confidence intervals of MOE predicted from SWS did not overlap with the MOE calculated using the other NDT measurement modalities. The lack of consistency among MOE values predicted from SWS across sampling strategies, together with the species-specific performance discussed earlier and its distinct confidence intervals, suggests that more testing is still required with SWS, using a laboratory designed setup, before sound conclusions can be drawn.

3.4. Practical implication and limitations

The main achievements of this study were in establishing coefficients of determination between MOE_ST and MOE_NDT (using SilviScan and Picus). SWS was also found to be a relevant variable in estimating lodgepole pine MOE_ST. Together, these results suggest that each NDT tool can be confidently used to estimate MOE_ST. SWS has the advantage of being easy to measure and interpret and involves relatively affordable and non-destructive testing equipment. These tools could be used to segregate trees in terms of MOE classes earlier in the supply chain. If this were done, trees with high MOE values could be used for high-value lumber production, and trees with low MOE values could be used for pulp and paper, bioenergy/bioproducts, or other non-structural products. The results of this study were in line with previous research. However, although we believe that this study adds a significant piece of knowledge in this field, we acknowledge that a larger sampling (compared to the 59 battens of this study), inclusion of resonance tools, measurement of standing trees before felling, measurement of longer samples (together with the secondary method specimens in ASTM-D-143), and a more appropriate setup for stress wave measurements in laboratory environment will add scientific value to subsequent work.

4 Conclusion

The objective of this study was to compare measurements of the modulus of elasticity (MOE) determined with SilviScan (MOE_SS) and acoustic time of flight (MOE_TOF) equipment with measurements of standard static MOE (MOE_ST) for lodgepole pine and white spruce. MOE_SS values were highest, followed by MOE_ST, and MOE_TOF was the lowest MOE values. The high explanatory power of the regression models relating MOE_ST and both MOE_TOF and MOE_SS are evidence that both non-destructive testing (NDT) tools can be confidently used as alternatives to standard static bending testing. The stronger relationship between the stress wave speed (SWS) and MOE_ST for lodgepole pine supports the use of SWS for estimation of MOE_ST. However, SWS relationship with MOE_ST was not strong in white spruce, suggesting that more testing is required with this technology before sound conclusions can be drawn. Overall, this study confirmed that coefficients of determination between static and NDT MOE are species and tool specific. Therefore, a similar validation process must be undertaken for each individual tree species and measurement technique combination.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Acknowledgements

The authors thank the Canadian Wood Fibre Centre (CWFC) for funding under the Forest Innovation Program (FIP). They also acknowledge the work of Jared Salvail (CWFC) in carrying out the field work and that of William Belhadef (Université du Québec en Abitibi-Témiscamingue) in the static and TOF measurement of modulus of elasticity. The support of Sharon Meredith (Foothills Growth and Yield Association) was instrumental in carrying out this research. Comments on earlier versions of the manuscript by Isabelle Duchesne and two anonymous reviewers are greatly appreciated.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Ross RJ, personal communication.