Strength and stiffness predictions with focus on different acoustic measurement methods

Strength grading is an important step for the production of homogenous and high-quality solid wood material. In particular, for hardwoods, the use of non-visible characteristics is indispensable. Dynamic MOE (Edyn) is an important parameter widely used for grading of softwoods and applicable to hardwoods as well. There are two common ways to measure Edyn—ultrasound (US) wave propagation and longitudinal vibration (LV) method. Both methods are used in practice, however, due to the different inherent measurement techniques, the results differ. The current paper analyses the stiffness and strength coefficients of determination for several temperate European hardwood species and emphasizes the differences between the two measurement systems. The performance was analysed with regard to grading techniques, testing modes for the mechanical properties (tension and bending) and wood qualities. For more than 2861 pieces of European ash (Fraxinus excelsior), European beech (Fagus sylvatica), European oak (Quercus spp.) and maple (Acer spp.), the Edyn was measured using both techniques, and destructive tests (tension and edgewise bending) were applied. The results show that LV has higher coefficient of determination compared to the US Edyn. The coefficient of determination for both methods and tensile application can be increased by calculating Edyn with average density. Furthermore, the results support species-independent strength grading of hardwoods. Further research on the effect of different wood qualities and sawing patterns is required.


Introduction
Temperate hardwoods are very well known for their excellent mechanical properties, which make them favourable for structural purposes. As a naturally grown material, wood shows high variation in mechanical properties. Strength grading is a crucial step for the production of homogenous and high-quality solid wood material with defined material properties. Whereas the research on softwoods has led to the high acceptance of the machine strength grading methods, the application of those methods to hardwoods is less frequent. The research activities in recent years in the field of strength grading and engineered wood products aimed to bridge knowledge gaps with regard to hardwoods.
Recent research activities have been focused on novel methods of non-destructive testing, as well as applying the established methods of machine strength grading to hardwoods. In focus of the mechanical strength grading, the dynamic MOE (E dyn ) can be highlighted as a major criterion of interest. E dyn is a mechanical property of the material and describes the elastic behaviour of wood under dynamic cyclic stress and has been used to characterize wood material for decades (Kollmann and Côté 1968). The E dyn application for the strength grading of structural timber dates back to Görlacher (1990) and is currently one of the most frequent methods for the machine strength grading of wood. Generally, there are two possibilities to determine E dyn , which are: ultrasound (US) wave propagation and longitudinal vibration (LV) method. Both methods are related to the acoustic properties of wood. In the first case, an ultrasound wave signal is generated and the propagation in wood is measured, whereas in the other case, a stress wave is induced using a hammer and the eigenfrequency of wood is determined. Nowadays, the eigenfrequency method has established itself as very robust and is the most frequently used method. The characteristic vibrations in the board can be detected contact-free using a laser vibrometer (Giudiceandrea 2005).
As a grading parameter, E dyn shows a high correlation to static MOE, for both softwoods (Bacher 2008) and hardwoods (Frühwald und Schickhofer 2005). Although for softwoods the correlation is higher, for hardwoods, the coefficient of determination of both US and LV measurement methods seems to be lower. The R 2 values reported for the strength prediction range from 0.18 to 0.36 for temperate hardwoods (Nocetti et al. 2016;Ravenshorst 2015) and are lower for the tensile strength prediction of temperate hardwoods shown for a variety of species (R 2 < 0.25) (Ehrhart et al. 2016;Glos and Lederer 2000;Green and McDonald 1993). For tensile strength, the coefficient of determination depends on the quality of the material. Westermayr et al. (2018) report a high R 2 value of 0.48 for low-quality beech lamella, compared to the value achieved for high-quality ones with 0.22 (Ehrhart et al. 2016). The quality difference refers to visual grading criteria such as growth inhomogenities, visible slope of grain as well as knots. This might imply that for timber of rejectable quality, higher grading accuracy could be achieved. In most publications, the E dyn is determined using the LV. Therefore, questions arise regarding the performance of both methods and the differences between tensile and bending strength coefficient of determination. Frühwald and Hasenstab (2010) mention that the accuracy of the method is higher for LV.
The detection of the local inhomogeneities is crucial for hardwoods. LV and UV methods allow to determine the average wood quality. However, the local wood inhomogenities (such as knots and local slope of grain) are not detected using those methods. Both of them lead to a massive strength reduction (e.g., Kovryga et al. 2019). Therefore, the knot detection and measurement of the slope of grain using a variety of methods, such as laser scattering (Olsson et al. 2018), thermal conduction (Daval et al. 2015), automated image analysis (Ehrhart et al. 2018) and transversal ultrasound (Kovryga et al. 2020) are studied for the strength grading. However, due to their nature, those measurements have lower correlation to the elastic properties.
The present study aims to investigate the differences in the coefficient of determination between US and LV method on a large data pool of hardwood specimens tested at TU Munich in recent years. Both methods are compared regarding the correlation between E dyn and tensile strength and stiffness. Special focus is given to the differences between the species, the ability to apply species-independent strength grading, and the ability for bending and tensile strength prediction. The species ash, beech, maple and oak representing hardwood species with different anatomical structure (ringporous and diffuse porous) are investigated.

Materials
For the current study, in total 2681 specimens of European hardwoods-European ash (Fraxinus excelsior), European beech (Fagus sylvatica), oak (Quercus spp.) and maple (Acer spp.) were used. Table 1 gives an overview of the specimens and dimensions used. The length of the specimens varied between 3 and 5.5 m. The specimens originated from different projects run at TU Munich over two decades. Beech and oak were tested by Glos and Lederer (2000) within the hardwood strength grading project. Ash and maple tested in bending originate from the project on the assignment of those species to the bending strength classes (D-Classes) by Torno (2008a, 2008b). Tension test data of ash and maple were obtained by Kovryga et al. (2019) within the project on hardwood strength grading. Details are described in the mentioned publications. Table 2 summarizes the mechanical properties of the tested hardwoods. The tested specimens are representative of the tested wood species and, particularly, for the growth region in Central Europe. The mechanical property values are comparable to the values given in other publications. Thus, for ash, the mean tensile strength values

Non-destructive measurements
For all the specimens, the grading characteristics were determined. The E dyn was measured in two ways-using the ultrasound wave propagation and the longitudinal vibration (LV) method. The longitudinal US measurement was taken using Sylvatest device (Sandoz 1996) with a frequency of 20 kHz. During the non-destructive measurement, the runtime of the wave is measured longitudinal to the grain direction between the transmitting and receiving transducer.
The E dyn is calculated as a product of density ρ and ultrasound wave v using Eq. 1: For the LV method, a hammer is used to generate stress waves. The signal is recorded by means of a microphone or an accelerometer. Both measurements are taken at the laboratory of the TU Munich for repeatability check, as they provide similar results. In industrial facilities, a laser vibrometer can be used to record vibrations contact-free. By applying the FFT-transformation, the eigenfrequency is calculated. The E dyn,freq is calculated by combining the first eigenfrequency (f) with length (l) of the specimen and density (ρ) measurement using the following equation: The density is measured by weighing the specimen. For temperate hardwoods, density usually shows no correlation to the tensile and bending strength (Ehrhart et al. 2016;Westermayr et al. 2018;Frühwald and Schickhofer 2005). Therefore, E dyn was calculated using a constant density value to study the effect of eigenfrequency and ultrasound velocity on the strength properties. For each wood species, the average density from Table 2 was taken into account. The difference between the E dyn calculated with individual density readings and E dyn with an average density of the wood species is discussed in the paper.
To separate low-and high-quality specimens, the knottiness parameter tKAR (total knottiness area ratio) is used. tKAR is a parameter frequently used in scientific publications and in national visual grading standards, such as BS 4978. It is calculated as the area of knots appearing in a 150 mm long part of the specimen, projected on the crosssectional area. The overlapping areas are counted once.

Destructive tests
The hardwood specimens were tested in tension and in bending according to the test specification of EN 408 (2010)

Moisture content adjustment
The mechanical properties were adjusted to the reference conditions 20 °C and 65% relative humidity. For all species, the equation derived by Nocetti et al. (2015) on chestnut was used to adjust dynamic and static MOE. The procedure in EN 384 does not specify any adjustment factors for MC above 18%. For MOE below fiber saturation point (FSP), Eq. 3 was used.
where E u is the MOE measured at a certain moisture content level and u is the moisture content. For changes in MC above FSP, Eq. 4 was used: (3) The equation assumes a constant MOE value above FSP also shown by Unterwieser and Schickhofer (2011).
The bending strength (f m ) values are adjusted to the reference conditions by assuming a 1.4% increase in strength per 1% MC decrease up to fiber saturation point (Hernández et al. 2014). The selected factor is supported by the findings of Glos and Lederer (2000) for the tested sample who found the difference in bending strength between green and dry specimens of about 21%. The selected factor is designated on the safe side, as in some publications higher change rate is reported. Wang and Wang (1999) report a change rate of 3.9% in bending strength per 1% MC change for red oak.

Statistical analysis
For the statistical analysis, the linear regression and correlation analyses were used. To analyse the performance of LV and US for the strength and stiffness prediction, the samples were grouped by the destructive testing mode (bending, tension) after the grading and by the wood species. For each group, the correlation analysis was applied by calculating the Pearson correlation coefficient. Figure 1 shows the relationship between E dyn from the US and LV measurements. Generally, high consistency between (4) E 12 = E u 0.9 Fig. 1 Relationship between E dyn from US measurement and E dyn measured using LV method with E dyn calculated a with individual density reading and b calculated with constant density value, grouped by the hardwood species both measurements across the wood species can be observed. The coefficient of determination between ultrasound E dyn and eigenfrequency E dyn ranges between 0.7 for beech and 0.87 for ash. If the E dyn is calculated using average density (Fig. 1b), the overall R 2 value drops and the scatter shows significantly higher variation. Therefore, individual density values provide a homogenizing effect on the relationship between the E dyn from the US and LV measurements. Major differences in the prediction of grade determining properties, like strength and stiffness, are, therefore, expected for the E dyn without considering the density.

Stiffness prediction
The coefficient of determination for the tensile and bending MOE is shown in Table 3. E dyn from LV measurement shows higher R 2 values compared to the US measurement. Whereas for oak the difference is less pronounced, the difference for beech and maple increases up to max. 0.3. The prediction strength of static MOE drops for both E dyn ( E dyn,freq,dens,12 and E dyn,us,dens,12 ) calculated with average density. The coefficient of determination between US E dyn and LV E dyn is compared for a combined hardwood species data set in Fig. 2 dependent on the testing mode. The LV E dyn scatters less compared to the US measurement. For both measurements, the regression equation seems to predict tensile and bending MOE similarly well. The scatter has a similar shape. However, the variation around the regression line is higher for the correlation to the bending stiffness. For the specimens tested in tension, E t shows larger scatter with values up to 22 GPa.
The possibility of combining the wood species for the species-independent strength grading is visualized in Fig. 3. For both testing modes (bending and tension), the population of temperate European hardwoods shows homogenous scatter. The values scatter approximately within the same range. For ash in tension, the stiffness is slightly higher compared to beech and maple. Furthermore, specimens show,  (2015) regarding the applicability of the species-independent strength grading to the example of tension data.

Strength prediction
The bending and tensile strengths are predicted with US (E dyn,us,12 ) less accurately compared to the LV (E dyn,freq,12 ). The accuracy ranges between 0.007 and 0.312 for the US and 0.142 and 0.407 for the LV. The R 2 values between E dyn,freq,12 and strength (f t and f m ) are approximately two times higher compared to the values between E dyn,us,12 and strength. These findings support the results of Frühwald and Hasenstab (2010), who came to the conclusion that E dyn from LV is a better predictor for the tensile strength.
The scatter between E dyn calculated with average density and tensile strength is visualized for the frequency measurement in Fig. 4. The scatter for the US shows a similar pattern but higher variation (not shown here). The values for all the species fall within the same range and support the idea of species-independent scatter. In particular, for the tensile strength, the scatter is very similar. The slopes of the regression lines are almost equal, allowing for a speciesindependent strength grading.
The use of ultrasound and eigenfrequency E dyn depends on the density value used for the calculation of the E dyn . If the average density value of the wood species is used for the calculation of E dyn and not the individual density value, Fig. 2 Scatterplot between a E dyn measured using US device and static MOE and b E dyn measured using LV method and static MOE for all investigated hardwood species, split by the testing mode (bending, tension)

Fig. 3
Relationship between a E dyn measured using LV method and tension MOE and b E dyn measured using LV method and bending MOE, grouped by the hardwood species the strength coefficient of determination increases for some samples. For specimens tested in tension, a clear increase in coefficient of determination is observable, while for the specimens tested in bending, the exclusion of density value leads to a slight drop in R 2 values (0.015 on average). The same results have been shown by Nocetti et al. (2016) on chestnut timber tested in bending. The coefficient of determination for LV bending strength prediction decreased from 0.24 to 0.15. This behaviour is most likely attributed not only to the testing mode but rather to specimen dimensions and sawing pattern used. Figure 5 exemplarily visualizes the difference in coefficient of determination of the tensile strength using E dyn calculated with average density and individual density for European ash. For the relationship between E dyn calculated with average density and tensile strength, a scatter with less variation and steeper regression line can be observed. As a consequence of lower variation around the regression line, higher R 2 value can be achieved. By calculating with an average density, the variation in E dyn is reduced. The density is a part of E dyn calculation that shows either low correlation or no correlation to the timber strength. In the case of maple, the correlation is even negative (r = − 0.120).
The observable differences in strength prediction are most likely attributed to the cross-section size and the sawing pattern used. This can be observed on the ash tested in tension which comprises two sub-samples. The first subsample includes timber of thicker cross-section (50 × 100 and 50 × 150) and cut with "cutting all around" (without pith) pattern and the second sub-sample includes smaller Fig. 4 Relationship between a E dyn measured using LV and tensile strength and b E dyn measured using LV and bending strength, grouped by hardwood species  Table 1) cut with a sawing pattern that included the pith. For the larger samples, no significant difference in coefficient of determination using E dyn,freq,12 and E dyn,freq,dens,12 was observable. In contrast, for smaller ash dimensions, the coefficient of determination increased from 0.265 to 0.334 by using average density instead of individual reading. The juvenile wood present in the sawing pattern with pith is known for temperate hardwoods to have slightly higher density compared to the mature wood (e.g., Woodcock and Shier 2002; Gryc et al. 2008). Therefore, a higher share of pith specimens could negatively affect the applicability of the density to E dyn calculation for strength prediction. For those specimens, higher density of juvenile wood increases the numeric value of the E dyn , which would also indicate/evidence higher strength, which is obvioulsy not the case for juvenile wood. To make general conclusions and study the causes, a special testing program is required.
Additionally, the effect of the wood quality on the relationship between E dyn and strength can be observed in Fig. 6. The wood quality was defined as knot-free specimens and specimens with tKAR > 0.05. For the tensile and bending strength predictions, the greater slope of the regression line is visible on the knotfree specimens. In the case of tensile strength, the difference is even more pronounced. Although the R 2 value does not differ significantly between knot-free (tKAR < 0.05) and specimens with knots, the variation of measured values around the regression line in the case of knot-free specimens is greater. For bending strength, the coefficient of determination is slightly higher.

Conclusion
In this paper, the differences between the coefficient of determination of the dynamic MOE measured by using US and LV methods were studied. The E dyn measured by using LV results in higher coefficient of determination for the strength and stiffness. Nevertheless, the accuracy of the ultrasound E dyn is high as well, especially for the MOE prediction. The results also support the findings of Ravenhorst (2015) for the species-independent strength grading for both bending strength and tensile strength. The same regression equation can be used to predict both tensile MOE and bending MOE with E dyn . Furthermore, the effect of wood quality or knottiness of the wood on the grading accuracy was observed. Whereas for tension specimens the coefficient of determination did not differ much, the slope of the regression line and the scatter differ significantly. For tension test specimens, the use of average density in E dyn calculation increases the coefficient of determination for strength prediction. This could be caused by smaller cross-sections of the tested specimens, as well as by the different sawing patterns. Further research is required to better understand the wave propagation in such specimens.
Acknowledgements Open Access funding provided by Projekt DEAL.
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