Mechanical Properties of Small Clear Specimens of Eucalyptus globulus Labill

Eucalyptus globulus Labill stands out as one of the hardwood species produced in Europe with prominent mechanical properties, which is undergoing a growing interest in extending added value. The development of engineered wood products with this species and its application in timber structures involving numerical finite element simulations requires knowledge of the mechanical properties for the different orthotropic material directions. The aim of the present study is to determine the main mechanical properties of E. globulus from small clear specimens, necessary for the development of finite element models. The work provides experimental results on the ultimate capacity and modulus of elasticity considering different stresses: tension parallel and perpendicular to the grain, compression parallel and perpendicular to the grain (in radial and tangential directions), shear and longitudinal static bending. The work is complemented with experimental data on timber-to-timber friction coefficients for 0°, 45°, and 90° orientation angles, which are useful in the modeling of traditional joints. Very high values of ultimate stress and modulus of elasticity for the different mechanical properties were obtained, highlighting the great potential of this species for structural applications.


Introduction
The increasing political and social demands regarding the use of eco-friendly building materials are leading in recent years to a strong rise in the use of wood due to its CO 2 absorption capacity and the quality of renewable natural resource.
There is growing interest in Europe towards glued laminated structural products made of hardwoods due to several reasons, such as the shortage of softwoods, large stocks of hardwoods, and policies of re-afforestation for several hardwood species due to better adaptation to soil and climate conditions. In most cases, these products reach greater bending strengths than those of the highest European softwood glulam strength classes [1], usually made of spruce or pine.
Eucalyptus globulus Labill is a temperate-climate hardwood with growth in Europe, Asia, Africa, Oceania, and America [2]. In Europe, it can be found mainly in Spain, Portugal, and Italy. Spanish E. globulus L. is structurally characterized [3] and can be assigned to D40 strength class, which is currently the highest strength class for European hardwood species [4]. In addition, E. globulus from Galicia region (Spain) shows a high natural durability against fungi, similar to that of chestnut and oak [5].  The specimens were clamped on either end, and the clear distance between the grips was at least 350 mm. The cross-sectional dimensions at the middle were 20 mm in radial direction and 10 mm in tangential direction.
In order to determine the modulus of elasticity in tension parallel to the grain, E t,0 , strains at a central area of the specimen of 50 mm length were measured during testing using a digital image correlation (DIC) technique, ARAMIS 3D of 12 MPixels (GOM mbH, Braunschweig, Germany) [23] ( Figure 1a). This is a non-contact and material-independent measuring system which provides full-field strain measurements, which is advantageous compared with other traditional techniques such as strain gauges.
Tension perpendicular to grain tests were performed in accordance with UNE 56538:1978 [24]. A total of 36 specimens were cut to the shape shown in Figure 1b with a minimum cross-section of 20 × 20 mm 2 and oriented in such a way that loading was produced in radial direction. The ends of the specimens were clamped with symmetrical grips. The tests were executed at a constant velocity of 400 kg/min.
Compression parallel and perpendicular to the grain tests ( Figure 1c) were carried out according to ISO 13061-17:2017 [25] and ISO 13061-5:2020 [26], respectively. For the cases of compression parallel to the grain, 20 prismatic specimens of 60 × 20 × 20 mm 3 were used, and 20 of the same dimensions were used for compression perpendicular to the grain with load applied in radial direction. In the case of compression perpendicular to the grain with load applied in tangential direction, 20 specimens of 20 × 20 × 20 mm 3 were used instead due to thickness limitation of the eucalyptus boards.
Strain gauges were located on the specimens' faces to measure strains and derive the modulus of elasticity for each direction (see Figure 1c). Further details on the compression setup can be found in a previous work by the authors [16] which had the objective of determining the orthotropic elastic constants of eucalyptus.
The ultimate value of the stresses in axial direction (ultimate tensile stress parallel to grain, σ t,0 ; ultimate tensile stress perpendicular to grain, σ t,90 ; and ultimate stress in compression parallel to grain, σ c,0 ) were calculated from the maximum load in each batch of tests, F max , and the cross-sectional dimension at the middle of the specimen, S, according to Equation (1): Regarding the compression perpendicular to grain, it is not possible to clearly determine a F max because the load is continuously increasing in this type of test. Therefore, the proportional limit stress, σ c,90,y , and the stress at a specific deformation level (2 mm), σ c,90,2 , were reported. σ c,90,y was calculated as the relationship between the load at the proportional limit and the specimen cross-section. σ c,90,2 was determined from the load at 2 mm deformation and the specimen cross-section. The 2 mm deformation was measured from the intersection of the straight line tangent to the elastic slope of the load-deformation curve and the horizontal axis.
Static bending tests were performed following a 4-point loading configuration as specified in EN 408:2011 [27] in order to have constant moment at the central beam area (Figure 1d). The cross-section of the specimens was 20 × 37 mm 2 . The span corresponded to 15 times the specimen depth. Loads were applied at a distance of 4.5 times the depth measured from every support. A total of 22 specimens were tested.
Deflections were measured by DIC technique (ARAMIS 3D). The modulus of elasticity in bending, E m , was calculated using the relationship between the applied force and measurements of mid-span deflection relative to the supports of the test piece in accordance with Equation (2): Materials 2020, 13, 906 where a is the distance between the load application point and the nearest support; l is the span; b and h are the width and height of the specimen, respectively; F 1 − F 2 indicates the load increase on the regression line comprised in the range between 0.1F max and 0.4F max which provides a minimum correlation coefficient of 0.99; and w 2 − w 1 is the increase of deflection corresponding to F 1 − F 2 . The ultimate static bending stress, σ m , was calculated from the maximum load F max following Equation (3): where b and h are the width and height of the specimen, respectively, and a the distance between the load application point and the nearest support. Relationships between stress and modulus of elasticity were determined for all the tests where strains could be measured. Linear trendline based on least squares methods and the corresponding R 2 value were obtained for these relationships.
Shear tests were performed following UNE 56543:1988 [28]. A total of 44 specimens were prepared to the shape and dimensions indicated in Figure 1e. The loading plate was placed on the specimen notch. Part of the underside of the specimen rested on the table being 3 mm separated from the shear failure plane. The test displacement control was kept at 0.6 mm/min. The ultimate shear stress was calculated from the maximum load, F max , and the shear cross-section, S v , according to Equation (4): The static friction coefficients were determined from pairs of eucalyptus pieces oriented at 0 • , 45 • , and 90 • with respect to the friction plane ( Figure 1f) according to the procedure detailed in [29].
The dimensions of each of the two prismatic pieces that formed every specimen were 80 × 20 × 20 mm 3 . During testing, a constant vertical dead load (N) of 2.435 kN was acting on the specimen while another horizontal force (equivalent to the friction force, F R ) was applied to the bottom piece ( Figure 2). where a is the distance between the load application point and the nearest support; l is the span; b and h are the width and height of the specimen, respectively; F1 − F2 indicates the load increase on the regression line comprised in the range between 0.1Fmax and 0.4Fmax which provides a minimum correlation coefficient of 0.99; and w2 − w1 is the increase of deflection corresponding to F1 − F2.
The ultimate static bending stress, σm, was calculated from the maximum load Fmax following Equation (3): where b and h are the width and height of the specimen, respectively, and a the distance between the load application point and the nearest support. Relationships between stress and modulus of elasticity were determined for all the tests where strains could be measured. Linear trendline based on least squares methods and the corresponding R 2 value were obtained for these relationships.
Shear tests were performed following UNE 56543:1988 [28]. A total of 44 specimens were prepared to the shape and dimensions indicated in Figure 1e. The loading plate was placed on the specimen notch. Part of the underside of the specimen rested on the table being 3 mm separated from the shear failure plane. The test displacement control was kept at 0.6 mm/min. The ultimate shear stress was calculated from the maximum load, Fmax, and the shear cross-section, Sv, according to Equation (4): The static friction coefficients were determined from pairs of eucalyptus pieces oriented at 0°, 45°, and 90° with respect to the friction plane ( Figure 1f) according to the procedure detailed in [29].
The dimensions of each of the two prismatic pieces that formed every specimen were 80 × 20 × 20 mm 3 . During testing, a constant vertical dead load (N) of 2.435 kN was acting on the specimen while another horizontal force (equivalent to the friction force, FR) was applied to the bottom piece ( Figure 2). The static friction coefficient between the eucalyptus pieces, μs,α, was calculated as the relationship between the two mentioned forces (Equation (5)). A total of 130 specimens were tested.  The static friction coefficient between the eucalyptus pieces, µ s,α , was calculated as the relationship between the two mentioned forces (Equation (5)). A total of 130 specimens were tested.

Results and Discussion
Load-displacement curves in tension parallel to the grain are shown in Figure 3a left. As can be seen, timber behaved linearly until failure in all of the tests, giving a mean ultimate stress value, σ t,0 , of Materials 2020, 13, 906 6 of 12 176.3 MPa. A mean modulus of elasticity, E t,0 , of 23.80 GPa was also attained. Both values are very high in comparison with those obtained from other softwoods. In particular, σ t,0 and E t,0 resulted to be around 2 and 2.5 times higher than the respective values attained for Scots pine in [30], which highlights the great mechanical performance of Eucalyptus globulus L.

Results and Discussion
Load-displacement curves in tension parallel to the grain are shown in Figure 3a left. As can be seen, timber behaved linearly until failure in all of the tests, giving a mean ultimate stress value, σt,0, of 176.3 MPa. A mean modulus of elasticity, Et,0, of 23.80 GPa was also attained. Both values are very high in comparison with those obtained from other softwoods. In particular, σt,0 and Et,0 resulted to be around 2 and 2.5 times higher than the respective values attained for Scots pine in [30], which highlights the great mechanical performance of Eucalyptus globulus L. A relatively good correlation coefficient (R 2 = 0.52) was found between ultimate stress and modulus of elasticity from tension tests parallel to grain (Figure 3a right). Therefore, the modulus of elasticity could be an adequate physical property to estimate the ultimate tension stress in this direction.
The main failure mode was identified as cross-grain tension failure in the center part of the specimen, with visible cracks extending along the direction of the grain (Figure 4 left). . Load-displacement curves (left column) and correlation between ultimate stress and modulus of elasticity (right column): (a) tension parallel to grain; (b) tension perpendicular to grain; (c) compression parallel to grain; (d) compression perpendicular to grain in radial direction; (e) compression perpendicular to grain in tangential direction.
A relatively good correlation coefficient (R 2 = 0.52) was found between ultimate stress and modulus of elasticity from tension tests parallel to grain (Figure 3a right). Therefore, the modulus of elasticity could be an adequate physical property to estimate the ultimate tension stress in this direction.
The main failure mode was identified as cross-grain tension failure in the center part of the specimen, with visible cracks extending along the direction of the grain (Figure 4 left). In the case of tension perpendicular to grain tests, also a linear behavior until failure was exhibited (see Figure 3b). As it is known, tension perpendicular to the grain is the most critical stress in timber. Particularly, the mean value of ultimate stress resulted in 7.5 MPa, which is 23 times lower than the ultimate stress obtained in tension parallel to grain. All of the specimens showed a clean failure at the central cross-section as evinced in Figure 4 (right).
Figure 3c (left) shows the load-displacement curves in compression parallel to the grain. These curves exhibited an initial elastic domain practically up to Fmax and a plastic behavior without hardening afterwards with a noticeably horizontal tangent. The mean value of the ultimate stress in compression parallel to grain, σc,0, resulted in 73.6 MPa, that is, 42% of σt,0. This value was much higher (in between 52% and 84%) than that obtained from analogous compression tests carried out on the four Spanish softwoods that are structurally classified (Pinus radiata, Pinus pinaster, Pinus sylvestris, and Pinus nigra) [31]. A mean value of 18.06 GPa resulted for the modulus of elasticity, Ec,0, meaning 76% of Et,0. For this stress, a not very high correlation between ultimate stress and modulus of elasticity was obtained (R 2 = 0.37, see Figure 3c right).
The typical failure mode exhibited by the specimens subjected to compression parallel to grain can be seen in Figure 5 (left). It is a crushing failure, typical of small specimens subjected to this type of stress. It is usually characterized by folding of the cellulose microfibrils that can begin at low stress levels [32]. Folding takes place also at the cell wall at high stress levels, and eventually leads to gross failure of the specimen. The load-displacement curves for compression perpendicular to the grain in radial and tangential direction are depicted in Figure 3d,e, left, respectively. In these cases, the curves did not show a decrease in loading during testing, so a clearly defined maximum load cannot usually be obtained. The stress at the proportional limit and stress at 2 mm deformation were reported (see Table 1). In the case of tension perpendicular to grain tests, also a linear behavior until failure was exhibited (see Figure 3b). As it is known, tension perpendicular to the grain is the most critical stress in timber. Particularly, the mean value of ultimate stress resulted in 7.5 MPa, which is 23 times lower than the ultimate stress obtained in tension parallel to grain. All of the specimens showed a clean failure at the central cross-section as evinced in Figure 4 (right). Figure 3c (left) shows the load-displacement curves in compression parallel to the grain. These curves exhibited an initial elastic domain practically up to F max and a plastic behavior without hardening afterwards with a noticeably horizontal tangent. The mean value of the ultimate stress in compression parallel to grain, σ c,0 , resulted in 73.6 MPa, that is, 42% of σ t,0 . This value was much higher (in between 52% and 84%) than that obtained from analogous compression tests carried out on the four Spanish softwoods that are structurally classified (Pinus radiata, Pinus pinaster, Pinus sylvestris, and Pinus nigra) [31]. A mean value of 18.06 GPa resulted for the modulus of elasticity, E c,0 , meaning 76% of E t,0 . For this stress, a not very high correlation between ultimate stress and modulus of elasticity was obtained (R 2 = 0.37, see Figure 3c right).
The typical failure mode exhibited by the specimens subjected to compression parallel to grain can be seen in Figure 5 (left). It is a crushing failure, typical of small specimens subjected to this type of stress. It is usually characterized by folding of the cellulose microfibrils that can begin at low stress levels [32]. Folding takes place also at the cell wall at high stress levels, and eventually leads to gross failure of the specimen. Figure 3. Load-displacement curves (left column) and correlation between ultimate stress and modulus of elasticity (right column): (a) tension parallel to grain; (b) tension perpendicular to grain; (c) compression parallel to grain; (d) compression perpendicular to grain in radial direction; (e) compression perpendicular to grain in tangential direction.
A relatively good correlation coefficient (R 2 = 0.52) was found between ultimate stress and modulus of elasticity from tension tests parallel to grain (Figure 3a right). Therefore, the modulus of elasticity could be an adequate physical property to estimate the ultimate tension stress in this direction.
The main failure mode was identified as cross-grain tension failure in the center part of the specimen, with visible cracks extending along the direction of the grain (Figure 4 left). In the case of tension perpendicular to grain tests, also a linear behavior until failure was exhibited (see Figure 3b). As it is known, tension perpendicular to the grain is the most critical stress in timber. Particularly, the mean value of ultimate stress resulted in 7.5 MPa, which is 23 times lower than the ultimate stress obtained in tension parallel to grain. All of the specimens showed a clean failure at the central cross-section as evinced in Figure 4 (right). Figure 3c (left) shows the load-displacement curves in compression parallel to the grain. These curves exhibited an initial elastic domain practically up to Fmax and a plastic behavior without hardening afterwards with a noticeably horizontal tangent. The mean value of the ultimate stress in compression parallel to grain, σc,0, resulted in 73.6 MPa, that is, 42% of σt,0. This value was much higher (in between 52% and 84%) than that obtained from analogous compression tests carried out on the four Spanish softwoods that are structurally classified (Pinus radiata, Pinus pinaster, Pinus sylvestris, and Pinus nigra) [31]. A mean value of 18.06 GPa resulted for the modulus of elasticity, Ec,0, meaning 76% of Et,0. For this stress, a not very high correlation between ultimate stress and modulus of elasticity was obtained (R 2 = 0.37, see Figure 3c right).
The typical failure mode exhibited by the specimens subjected to compression parallel to grain can be seen in Figure 5 (left). It is a crushing failure, typical of small specimens subjected to this type of stress. It is usually characterized by folding of the cellulose microfibrils that can begin at low stress levels [32]. Folding takes place also at the cell wall at high stress levels, and eventually leads to gross failure of the specimen. The load-displacement curves for compression perpendicular to the grain in radial and tangential direction are depicted in Figure 3d,e, left, respectively. In these cases, the curves did not show a decrease in loading during testing, so a clearly defined maximum load cannot usually be obtained. The stress at the proportional limit and stress at 2 mm deformation were reported (see Table 1). The load-displacement curves for compression perpendicular to the grain in radial and tangential direction are depicted in Figure 3d,e, left, respectively. In these cases, the curves did not show a decrease in loading during testing, so a clearly defined maximum load cannot usually be obtained. The stress at the proportional limit and stress at 2 mm deformation were reported (see Table 1). The mean values of proportional limit stress in compression perpendicular to the grain resulted similar for both directions (11.1 and 10.2 MPa), being approximately seven times smaller than the ultimate compression stress in parallel direction. However, notably different stiffness values were found for radial and tangential orientations (1.78 and 0.69 GPa, respectively).
In general, correlations between the respective modulus of elasticity and ultimate stress in compression resulted lower than correlations derived from tension tests (Figure 3d,e, right).
Load-deflection curves in static bending are shown in Figure 6 left. During testing of small clear beams, initial yielding usually occurs on the compression side, followed by compression failures. The ultimate stress is reached when brittle failure at the tensile side occurs. This is the typical bending behavior produced in small clear beams subjected to bending. The compression zone enlarges and the neutral surface shifts toward the tensile side of the beam as the tensile stress continues to increase [32]. This fact explains that mean ultimate stress and modulus of elasticity values in bending (124 MPa and 22.3 GPa, respectively) are in between tension and compression results. Even so, some of the beams presented brittle failure due to small grain deviations (cross-grain tension failure) without yielding at the compression side ( Figure 5, right). The mean values of proportional limit stress in compression perpendicular to the grain resulted similar for both directions (11.1 and 10.2 MPa), being approximately seven times smaller than the ultimate compression stress in parallel direction. However, notably different stiffness values were found for radial and tangential orientations (1.78 and 0.69 GPa, respectively).
In general, correlations between the respective modulus of elasticity and ultimate stress in compression resulted lower than correlations derived from tension tests (Figure 3d,e, right).
Load-deflection curves in static bending are shown in Figure 6 left. During testing of small clear beams, initial yielding usually occurs on the compression side, followed by compression failures. The ultimate stress is reached when brittle failure at the tensile side occurs. This is the typical bending behavior produced in small clear beams subjected to bending. The compression zone enlarges and the neutral surface shifts toward the tensile side of the beam as the tensile stress continues to increase [32]. This fact explains that mean ultimate stress and modulus of elasticity values in bending (124 MPa and 22.3 GPa, respectively) are in between tension and compression results. Even so, some of the beams presented brittle failure due to small grain deviations (cross-grain tension failure) without yielding at the compression side ( Figure 5, right).
The mean ultimate bending stress of E. globulus was around 1.7 times higher than that obtained also from 4-point bending tests on small clear specimens of Eucalyptus grandis x E. Urophylla hybrids in [33]. Similarly to tension parallel to grain, a relatively good correlation coefficient (R 2 = 0.57) between ultimate stress and modulus of elasticity was found in bending (Figure 6 right). The load-displacement curves obtained from shear tests are represented in Figure 7 (left). The ultimate stress values ranged from 8.5 to 22.5 MPa, with 16.2 MPa being the mean value, around 9% of the ultimate tension stress parallel to grain. This value resulted between 1.5 and 2 times higher than those reported in [31] for the four Spanish pines following the same standard. It was also higher The mean ultimate bending stress of E. globulus was around 1.7 times higher than that obtained also from 4-point bending tests on small clear specimens of Eucalyptus grandis x E. Urophylla hybrids in [33]. Similarly to tension parallel to grain, a relatively good correlation coefficient (R 2 = 0.57) between ultimate stress and modulus of elasticity was found in bending (Figure 6 right).
The load-displacement curves obtained from shear tests are represented in Figure 7 (left). The ultimate stress values ranged from 8.5 to 22.5 MPa, with 16.2 MPa being the mean value, around 9% of the ultimate tension stress parallel to grain. This value resulted between 1.5 and 2 times higher than those reported in [31] for the four Spanish pines following the same standard. It was also higher than most of the respective data obtained from shear block tests in a broad number of wood species compiled in [34]. A clear fracture by the shear plane was produced in all the specimens (Figure 7 right). The load-displacement curves obtained from shear tests are represented in Figure 7 (left). The ultimate stress values ranged from 8.5 to 22.5 MPa, with 16.2 MPa being the mean value, around 9% of the ultimate tension stress parallel to grain. This value resulted between 1.5 and 2 times higher than those reported in [31] for the four Spanish pines following the same standard. It was also higher than most of the respective data obtained from shear block tests in a broad number of wood species compiled in [34]. A clear fracture by the shear plane was produced in all the specimens (Figure 7 right).    Figure  8 (right), the mean values of static friction coefficient for the three analyzed angles are plotted. The mean friction coefficient between the eucalyptus pieces with the grain oriented parallel to the friction plane, μs,0, resulted in 0.08. This value increased 2.5 times (μs,45 = 0.20) when the grain formed 45° with that plane. However, the friction coefficient hardly increased for the specimens with the grain oriented at 90° in comparison with 45°, resulting in an average value of μs,90 = 0.24.
The variation of friction coefficients with respect to grain direction follows a nonlinear trend. In Figure 8 (right), two curves proposals (a bilinear and a quadratic approximation) are presented to estimate the friction coefficient for different orientation angles to those studied here. Of course, more tests would be necessary to fit these curves with greater accuracy. The μs,90 coefficient determined for eucalyptus resulted to be around half of the value obtained for Picea abies (L) Karst following the same test procedure in previous work by the authors [29]. The experimental results of all the mechanical properties are summarized in Table 1. Mean value, standard deviation (SD), and coefficient of variation (CoV) for each property are listed together with the number of tested specimens (n).  The variation of friction coefficients with respect to grain direction follows a nonlinear trend. In Figure 8 (right), two curves proposals (a bilinear and a quadratic approximation) are presented to estimate the friction coefficient for different orientation angles to those studied here. Of course, more tests would be necessary to fit these curves with greater accuracy. The µ s,90 coefficient determined for eucalyptus resulted to be around half of the value obtained for Picea abies (L) Karst following the same test procedure in previous work by the authors [29].
The experimental results of all the mechanical properties are summarized in Table 1. Mean value, standard deviation (SD), and coefficient of variation (CoV) for each property are listed together with the number of tested specimens (n).

Conclusions
Mechanical tests on small clear specimens of Eucalyptus globulus L. were performed. Very high values of ultimate stresses and modulus of elasticity were obtained in comparison with common softwoods, highlighting the great potential of eucalyptus for structural applications.
The best correlations between ultimate stress and modulus of elasticity were found in bending and tension parallel to the grain. Compression tests showed the lowest correlations between both properties.
The timber-to-timber friction coefficients resulted lower than those of other species. The values followed a nonlinear trend considering different grain orientations with respect to the friction plane.
The mean values of stiffness, ultimate stresses, and friction coefficients attained are of great interest to be used as input parameters in the development of local finite element models. Funding: The work has been developed within the framework of the research project BIA2015-64491-P Analysis of the stress relaxation in curved members and new joints solutions for timber Gridshells made out of Eucalyptus globulus, co-financed by the Ministry of Economy and Competitiveness of Spain Government and ERDF funds.

Conflicts of Interest:
The authors declare no conflict of interest