1 Introduction

Wood is a natural and renewable material with variations in properties of color, texture, density, rigidity, and strength [1,2,3]. It is the only major building material that grows naturally, it is widely used in the construction sector [4, 5]. Wood is an organic, heterogeneous, and anisotropic material characterized by its diversity in chemical, physical, and mechanical properties, and such differences may occur within the same species and among different species [6,7,8]. The mechanical properties of wood such as the modulus of rupture (MOR) and the elasticity modulus (MOE) are important factors to determine its suitability and its applications. These characteristics depend on: wood species, tree maturity, and density of the wood [9,10,11]. Additionally, moisture content and temperature have also significant effects on wood’s mechanical properties [12,13,14].

The mechanical properties of wood materials can be measured by destructive and/or non-destructive tests. Non-destructive tests are mainly based on the propagation velocity of acoustic waves or ultrasound through wood materials. Non-destructive tests are useful to measure the acoustic-mechanical properties of wood [15,16,17,18]. Through the ultrasonic wave technique, it is possible to obtain indirect information about wood.

Due to their rapid growth rate, various eucalyptus species are planted in large areas of the word to meet the increased demand for wood [19, 20]. Eucalyptus wood displays many flaws such as warping and cracking after harvest and during wood processing which reduce its fields of applications in industry. In many cases, these defects are caused by growth stress [21]. In Morocco, the eucalyptus species occupies about 12 % of tree plantation surface. It plays an important role in Moroccan forestry economics; it is used for firewood, log and pulp production, and the urgent need for environmental protection, for its high productivity in marginal areas and can produce a variety of useful forest products [22,23,24].

In Morocco, clonal eucalyptus was intended for the manufacture of pulp. After the Moroccan cellulose factory closed in 2013, it was mainly used as firewood. Therefore, better knowledge of the mechanical properties of clonal Eucalyptus wood is essential for any attempt to develop and valorize this wood type and will allow the identification of its conditions of use.

The objectives of this study are (i) to estimate the rupture stress and elasticity modulus using destructive tests: “axial compression, four-points bending and axial tension” for two clones of Eucalyptus wood; (ii) and to estimate the dynamic elasticity modulus using the non-destructive method based on the measurement of ultrasound wave propagation velocity in longitudinal wood direction.

2 Materials and Methods

Twelve 9-year-old trees of clonal Eucalyptus wood were used in this study from the plantation established in the Maâmora forest area (North-West of Morocco): six trees of E. grandis (clone No. 3758) and six others of E. camaldulensis (clone No. 579). The mean diameter of the selected trees ranges from 20 cm to 30 cm, with good straightness, they were also free from defects (parasitic attacks, fungi, etc.) and carried few branches.

2.1 Preparation of Wood Specimens

The mechanical tests to evaluate the modulus of rupture, the static elasticity modulus (in the axial compression, axial tension and four-points bending) and the dynamic modulus of elasticity using ultrasonic waves were carried out on standardized samples taken from boards 30 mm thick in diameter and free from natural growth defects (knots, cracks, twisted fibers, etc.) (Fig. 1). The boards were taken from the first and/or second log for each tree. Thirty samples were taken from each tree of each clone for each test at moisture content of 12 %.

Fig. 1
figure 1

Wood samples preparation for mechanical and acoustic tests

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2.2 Experimental

The mechanical properties are the characteristics of the material’s response to external forces applied to it. They include the elastic properties which describe resistance to deformation and distortion.

2.2.1 Axial Compression

The axial compression tests were carried out using a Universal hydraulic press of the “Testwell” brand (Fig. 2), its maximal load cell is 12 tons. The machine was set at an average displacement velocity of 6 mm·min−1 to obtain the values of displacements and suitable rupture loads. The tests were performed according to the French standard NF B 51-007 [25] on series of 30 specimens of each tree for each clone; their dimensions are (60 × 20 × 20) mm3 according to longitudinal (L), radial (R) and tangential (T) directions, which were measured by a Mitutoyo comparator.

Fig. 2
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Testwell hydraulic press for the axial compression test

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The rupture stress in axial compression (σc) is expressed by N·cm−2, and given by the following equation [25, 26]:

$$\sigma_{c} = \frac{F}{r \times t}$$
(1)

where F is the maximum applied force (N), t and r are the transversal dimensions of the wood sample (mm).

The elasticity modulus in axial compression (Ec) can be estimated from the slope of the linear part of the force–displacement curve (Fig. 3) according to the following equation:

$$E_{c} = k\frac{{L_{o} }}{{S_{o} }}$$
(2)

where Lo is the initial length of the sample, So is the initial area of the sample, k is the linear part slope of the force–displacement curve.

Fig. 3
figure 3

The force curve as a function of displacement for the wood samples

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2.2.2 Axial Tension

Tests of axial tensile were carried out according to the French standard NF B 51-017 [27, 28], on a series of 30 specimens from each tree for each Eucalyptus clone. The wood samples were cut into rectangular parallelepipeds, their section 20 × 5 mm2 in transverse directions (R, T) and 350 mm in longitudinal direction (L) (Fig. 4a). The apparatus used for this test is a Universal 3R machine (Fig. 4b); this device is controlled by a computer; its maximal capacity is 100 kN and its velocity was set to 0.5 mm·min−1.

Fig. 4
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Tensile test: (a) geometric characteristics of tensile test specimen; (b) machine of axial tensile

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The rupture modulus (σT) is calculated by dividing the maximum load (Fmax) by the section (S) of the test sample and given by the following equation [29]:

$$\sigma_{T} = \frac{{F_{\hbox{max} } }}{a \times b}$$
(3)

where Fmax is the maximum load (N), a and b are the rectangular part dimensions of the test sample.

The elasticity modulus in axial tensile (ET) can be estimated from the slope of the linear part of the force–displacement curve (Fig. 5).

Fig. 5
figure 5

The force–displacement curve for a sample of wood in axial tensile

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2.2.3 Dynamics Tests

Ultrasonic waves were used to determine the dynamic elasticity modulus of clonal Eucalyptus wood. The ultrasound generator device used in this study is from the TICO brand (Fig. 6a), it generates ultrasound with a frequency of 54 kHz [30]. Thirty samples of the following dimensions 360 × 20 × 20 mm3 in the longitudinal, radial and tangential directions (L, R, T) were used from each tree and for each eucalyptus clone. The ultrasounds were propagated in the longitudinal direction of wood sample (Fig. 6b). By knowing the waves propagation velocity V and the volumetric mass ρ of the wood sample, the dynamic elasticity modulus can be estimated using the following equation [31]:

Fig. 6
figure 6

Determination of the dynamic elasticity modulus: (a) ultrasonic device; (b) the direction of ultrasound propagation in the wood sample

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$$E_{dyn} = \rho \times V^{2}$$
(4)

2.2.4 Four-Point Bending Tests

The four-point bending tests were performed on the same wood samples that were used to determine the dynamic elasticity modulus. It was carried out according to the French standard NF B 51-008 [28, 32], using a 3R universal apparatus with a maximum load of 100 KN, equipped with a four-point bending bench (Fig. 7).

Fig. 7
figure 7

Four-points bending tests

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The wood sample placed on two cylindrical supports separated by a distance of 320 mm (Fig. 8), and the distance between the two loadings supports is 160 mm. They are brought into contact with the sample upper face under a pre-load of zero (0) Newton. The machine velocity was set to 4 mm·min−1. The LVDT comparator measures the specimen deflection in the central part which is subjected to pure bending, it consists of a cylindrical bar moving in the direction parallel to the forces. The comparator is placed on the part stressed by compression between the two central supports to be in contact with the test sample.

Fig. 8
figure 8

Illustration of the setup of the four-point bending test [33]

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To determine the elasticity modulus and rupture stress in four-point bending, the measurements were performed in two stages:

  • The first step is to set the LVDT comparator at a constant velocity (4 mm·min−1) from zero to 8 mm, then the apparatus is turned off and the LVDT comparator is reset to zero;

  • The second step consists of resuming the operation at the same velocity (4 mm·min−1) until the wood sample is ruptured, thus the maximum load (F) is determined (Fig. 9a).

    Fig. 9
    figure 9

    Typical curves to bending test: (a) force–displacement curve; (b) force–deflection curve measured by LVDT comparator (elastic part)

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To calculate the elasticity modulus according to the NF B 51-016 standard [28, 32], the force–deflection curve was drawn (Fig. 9b), then 3 values of force and corresponding deflection were taken on the curve’s linear part (force–deflection) which are 200, 600 and 1000 N. The statistical elasticity modulus (EF) is determined by the following equation [32]:

$$E_{F} = \frac{{\left( {l - a} \right) \times \left( {2l^{2} + 2la - a^{2} } \right)}}{{8bh^{3} }} \times \frac{\Delta F}{\Delta w}$$
(5)

The ultimate stress (σF) is determined according to the equation [34]:

$$\sigma_{f} = \frac{{3 \times F\left( {l - a} \right)}}{{2bh^{2} }}$$
(6)

where, l is the distance between the axes of the cylindrical supports (mm), a is the distance measured between the axes of the loading heads (mm), b is the measured width of the specimen (mm), h is the measured height of the specimen (mm), ΔP/Δw is the slope of the Force–deflection curves at LVDT.

2.3 Statistical Analysis

The mean values of the elasticity modulus, rupture stress, maximum loading and velocity of ultrasound propagation for the two clones Eucalyptus wood were compared using the T-test for independent samples at a 5 % significance level.

3 Results and Discussion

The Experimental results of the mechanical parameters measured in axial compression and axial tension are reported in Table 1. It demonstrates that E. camaldulensis wood exhibits higher maximal, minimal and average values for both ultimate force and rupture stress in axial compression and axial tension compared to E. grandis wood. Furthermore, E. camaldulensis wood exhibits higher values of elasticity modulus in axial tensile than E. grandis wood, but displays lower values of elasticity modulus in axial compression.

Table 1 Values of parameters measured in axial compression and tensile tests for clonal Eucalyptus wood
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The differences in rupture stress and elasticity modulus between the wood of two eucalyptus clones are due to growth conditions, naturel growth (knots, splits, grain straightness, etc.) and wood anisotropy, which contributes to the variation of the wood resistance.

Due to E. camaldulensis’s density being greater than of E. grandis’s, the mechanical properties of the latter are relatively lower than those of E. camaldulensis. Famiri and El Alami [25, 35] have shown that the basic mechanical properties (compression, flexion) of wild E. camaldulensis are higher than those corresponding wild E. grandis.

Table 2 presents the minimal, maximal and average values of the parameters measured in the four-points bending and dynamic tests. It shows that E. camaldulensis wood has a higher ultimate force, rupture stress, and elasticity modulus in both static and dynamic bindings compared to E. grandis wood. It also shows that the average value of elasticity modulus obtained by the ultrasound tests is higher than the one obtained by the bending tests for E. grandis wood and E. camaldulensis wood (Fig. 10). The differences between dynamic and static elasticity modulus are about 21 % and 12 % for E. grandis and E. camaldulensis, respectively.

Table 2 Measured parameters in 4-points bending and ultrasound tests for clonal Eucalyptus wood
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Fig. 10
figure 10

Comparison between modulus of elasticity static and dynamic for two clones of eucalyptus wood

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The difference between the values of static elasticity modulus and dynamic elasticity modulus can be explained by the nature of the tests and the complexity of the wood material. The MOE values calculated by the bending test are a measure of the average load and deformation relationship for the wood specimen. While the MOE value obtained by the ultrasound tests are based on the measured wave velocity and the density of the wood material being tested.

A T-test was performed to determine if there were differences in the mean values of the measured mechanical parameters between the two eucalyptus clones tested. The analysis results indicated that there were significant differences in the mean values for these two clones (P < 0.05) at 5 % significance level (Table 3).

Table 3 T-test analysis for the measured mechanical parameters of the two Eucalyptus clones
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3.1 Relationship Between Modulus of Elasticity and Density of Wood

Modulus of elasticity (MOE) varies significantly with wood density for the two Eucalyptus clones (Fig. 11), which implies density is a main parameter that influences the mechanical properties of wood. The results indicate a strong linear positive correlation between wood density and modulus of elasticity in axial compression, axial tension and four-points bending. According to the coefficients of determination (R2), it is clear that the correlation between the modulus of elasticity and wood density for E. camaldulensis wood is greater than for E. grandis.

Fig. 11
figure 11

Modulus of elasticity as a function in wood density of clonal Eucalyptus wood

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The density affects the modulus of elasticity dynamic of wood [36, 37]. A strong positive linear correlation is found between the dynamic elasticity modulus and wood density of the two eucalyptus clones (Fig. 12). The correlation is much greater for E. grandis wood according to its determination coefficient value (R2).

Fig. 12
figure 12

Relationship between dynamic elasticity modulus and wood density of the two Eucalyptus clones

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3.2 Relationship Between Rupture Stress and Modulus of Elasticity

The relationship between modulus of elasticity and rupture stress in axial tensile for 180 wood samples of each eucalyptus clone is shown in Fig. 13. This relationship is positive linear with a correlation coefficient R2 = 0.553 for E. grandis and 0.828 for E. camaldulensis.

Fig. 13
figure 13

Modulus of elasticity as a function of axial tensile stress for clonal Eucalyptus wood

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3.3 Relationship Between Dynamic and Static Elasticity Modulus

The comparison of the modulus of elasticity in 4-points bending and dynamic MOE shows that the dynamic modulus of elasticity is greater than the elasticity modulus in 4-points bending for the two Eucalyptus clones wood (Table 2). The relationship between the static elasticity modulus in 4-points bending and the dynamic modulus of elasticity measured by ultrasound in the longitudinal direction for 180 wood samples of each Eucalyptus clone is illustrated in Fig. 14. It is linear and strong; the coefficients of determination R2 is more important for E. Camaldulensis wood compared to E. grandis wood.

Fig. 14
figure 14

Modulus of elasticity in four-points bending as a function of dynamic elasticity modulus for clonal Eucalyptus wood

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4 Conclusions

This study investigated the mechanical properties for two Eucalyptus clones wood using axial compression, axial tensile, four-points bending, and ultrasonic waves. The achieved results point to the following:

  • According to the rupture stress, E. camaldulensis wood has a greater resistance compared to E. grandis wood;

  • E. camaldulensis wood has a greater rigidity in both axial tension and bending compared to E. grandis wood. whereas it is the opposite in axial compression;

  • The dynamic elasticity modulus of E. camaldulensis wood is higher due to its high density compared to E. grandis wood;

  • According to the mechanical properties determined in this study, clonal eucalyptus wood can be used in some construction applications.

The difference between the mechanical properties for these two Eucalyptus wood clones can be attributed to the combination of the anatomical structure of wood and silvicultural factors. The next study will be devoted to investigating the effect of moisture content and temperature on the mechanical properties of the clonal eucalyptus woods.