Arnauld Clauvy's Engonga Edzang

Claude Feldman

Pambou Nziengui

Serge Ekomy Ango

Samuel Ikogou

Rostand Moutou Pitti

Comparative studies of three tropical wood species under compressive cyclic loading and moisture content changes

Keywords: Tropical species, internal humidity impact, cyclic compressive loading Nomenclature

The objective of the present study is to perform an experimental comparative cyclic compressive loading test on three tropical species (Aucoumea Klaineana Pierre, Milicia Excelsa and Pterocarpus Soyauxii), at different internal moisture content stages. 150 samples of these three species, dimensioned according to standard NF EN 408 were tested. The specimens were loaded into the static compressive test until they collapsed in order to obtain the mechanical characteristics of each species in terms of: (i) the modulus of elasticity, (ii) the maximal strength and (iii) the stress at the yield point. The specimens are submitted five times to loading-unloading-reloading in cyclic compressive at different internal moisture contents. The applied force was taken at 10% of the maximum rupture force of Okoume species and kept constant at each cycle. The results show a stiffening of the three types of specimens with the loading cycles. The stiffening is faster from the densest species to the least dense species, respectively. In addition, the phenomenon of densification, that occurs during the five loading-unloading cycles, is done with constancy of compressive strength in the three species studied.

Introduction

Providing viable solutions to global warming is one of the major challenges of our century. As we know, one of the origins of climate change is the proliferation in the environment of non-ecological construction materials or tools such as steel and concrete. There is growing interest in the use of wood in the construction industry worldwide, particularly in European countries. This is valid both in so-called temperate regions, and so-called tropical regions. In Gabon, this involves the harvesting of new wood species. Indeed, Okoume or Aucoumea Klaineana Pierre has long been the only species harvested in Gabon. During the 20th century, its production continued to increase with the continuous improvement of machinery and the increased harvesting surface areas [START_REF] Medzegue | Radial growth and characterization of juvenile and adult wood in plantation grown okoumé (Aucoumea klaineana Pierre) from Gabon[END_REF][START_REF] Peyrot | Incidences écologiques, anthropiques et paléoécologiques sur l'évolution des forêts du Gabon. Essai de synthèse[END_REF]). However, from the 1960s, we saw harvesting of new species of so-called diverse woods. Among these species we have: the Iroko or Milicia Excelsa and Padouk or Pterocarpus Soyauxii [START_REF] Peyrot | Incidences écologiques, anthropiques et paléoécologiques sur l'évolution des forêts du Gabon. Essai de synthèse[END_REF][START_REF] Mertens | Atlas Forestier Interactif du Gabon[END_REF]). These species, at 12% moisture content, offer chemical and physical-mechanical properties superior to those of Okoume. Thus, for a better use of these species called diverse woods, it is necessary to study them under complex loading conditions.

Wood is a material whose mechanical properties (elastic, viscous, breakage...) are related to the conditions of variation of environmental parameters such as the relative moisture and temperature (Eurocode 1 2005, [START_REF] Moutee | Modélisation du comportement mécanique du bois au cours du séchage[END_REF][START_REF] Gerhards | Effect of moisture content and temperature on the mechanical properties of wood: an analysis of immediate effects[END_REF][START_REF] Ebrahimzadeh | Effects of humidity changes on damping and stress relaxation in wood[END_REF]. The mechanical properties of the wood material depend on the moisture content and dimensional changes induced by these moisture changes often result in significantly greater displacements than those caused by the mechanical loads [START_REF] Mårtensson | Effect of moisture and mechanical loading on wooden materials[END_REF][START_REF] Lenth | Moisture dependent softening behavior of wood[END_REF][START_REF] Moutee | Modeling the creep behavior of wood cantilever loaded at free end during drying[END_REF][START_REF] Mukudai | Modeling and simulation of viscoelastic behavior (tensile strain) of wood under moisture change[END_REF][START_REF] Navi | Effects of thermo-hydro-mechanical treatment on the structure and properties of wood[END_REF]. Also, the work of [START_REF] Gerhards | Effect of moisture content and temperature on the mechanical properties of wood: an analysis of immediate effects[END_REF] show that many of the mechanical properties of wood reduce when its moisture content varies between 12% and 20%, below the fibre saturation point (FSP). These results are also supported by Guitard et al. (1987), through its numerical model to calculate elastic properties, it shows the dependency of these parameters on moisture content variations. In addition, the interaction of moisture changes with mechanical loads can lead to excessive strains in wood structures [START_REF] Redman | Characterisation of wood-water relationships and transverse anatomy and their relationship to drying degrade[END_REF][START_REF] Manfoumbi Boussougou | Experimental and numerical aspects in diffusion process characterization in tropical species[END_REF]. By themselves, these two examples describe the influence of moisture on the behaviour of the wood material in structures sufficiently well.

The literature review shows that the stresses on wood materials and timber structures are mainly due to the combined impact of mechanical and environmental effects (Eurocode 1 2005, Moutee 2006, Eurocode 5 2005). In fact, there are very specific processes used to describe the laws of mechanical behaviour of materials in general and wood in particular in interaction with environmental factors. Among these processes, we have different tests such as creep, bending, traction, compression, torsion and shear tests. All these processes have the sole purpose of determining the relationships between the stresses and strains of the tested material. To these tests, we can add the cyclic tests, characterized by a mode of fatigue breakage which is just as important but rarely studied, especially on wood material (Pambou Nziengui et al. 2017, Nafa and[START_REF] Nafa | Applied data for modeling the behavior in cyclic torsion of beams in glued-laminated wood: influence of amplitude[END_REF], and even less so on tropical species. Also, Pambou and al (2017) through the study on the mechanical behaviour of Okoume under cyclic stress, have shown on the one hand that deterioration of Okoume is faster in cyclic compression than in static compression. On the other hand, they showed that the coupling of the number of loading cycles with the variation of the moisture content of Okoume amplifies the latter's loss of mechanical performance under a variable load. [START_REF] Nafa | Applied data for modeling the behavior in cyclic torsion of beams in glued-laminated wood: influence of amplitude[END_REF] worked on the damage to laminated timber beams submitted to cyclic torsional loading and showed the influence of the load level on the behaviour and durability of laminated timber beams. However, these studies alone are not enough to account for the behaviour of the wood material under cyclic stress, especially that of tropical woods in a variable environment.

Moreover, when loading cyclically with a fairly low stress to a limited number of cyclics, densification occurs on the loaded material [START_REF] Kutnar | The mechanical properties of densified VTC wood relevant for structural composites[END_REF]. During this densification, the cellular structure of the wood is permanently modified, giving a material with new properties [START_REF] Blomberg | Plastic deformation in small clear pieces of Scots pine (Pinus sylvestris) during densification with the CaLignum process[END_REF]Persson 2004, Kutnar and[START_REF] Kutnar | Densification of wood[END_REF]. One of the main factors influencing the mechanical and physical behaviour of densified wood is the amount and type of cell collapse. We are interested here in the environmental factors affecting the behaviour of densified wood, especially moisture. Our study therefore deals with the problem of the mechanical behaviour of tropical woods, subjected to the combined stress of cyclic mechanical loadings and changes in the internal moisture content of wood. The objective is to understand the behaviour in cyclic compressive testing of three tropical species, namely the Okoume, Iroko and Padouk. The first part of this article presents the experimental setup used, as well as the protocol adopted to conduct our study. The second part presents the results obtained during the experimental tests, namely: the results on the impact of the loading combined with moisture variations on the behaviour of our three species.

Material and methods

Wood specimens

Okoume, whose scientific name is Aucoumea klaineana Pierre, is a species in the Burseraceae family, which can be found in Gabon (from the coast to a line passing through Okondja in eastern Gabon and between Mitzic and Oyem in northern Gabon), Cameroon, Congo and over almost the whole Equatorial Guinea region [START_REF] Medzegue | Etude comparative des bois d'Okoumé (Aucoumea Klaineana P.) issus des plantations et de la forêt naturelle: anatomie, durabilité naturelle[END_REF]. Okoume is a fast-growing species that grows to a height of over 50 m and has a trunk diameter of up to 2 m. In Gabon, it is used mainly for the manufacture of plywood, but also for structures such as sliced veneer and multi-ply plates [START_REF] Martin | Guide d'utilisation des bois africains éco-certifiés en Europe[END_REF][START_REF] Gérard | Synthèse sur les caractéristiques technologiques de référence des principaux bois commerciaux africains[END_REF][START_REF] Gérard | TROPIX 5.0 : caractéristiques technologiques de 215 essences tropicales[END_REF]). The term "Iroko" refers to the two species of the genus Milicia in the Moraceae family: Milicia Excelsa and Milicia Regia, which are very similar in morphology. Milicia excelsa is generally found on the African continent, from Guinea Bissau to Ethiopia, to Angola and Zimbabwe in a southerly direction; it is found particularly in Gabon. This tree reaches a maximum height of 45 to 50 m with a diameter of about 2.5 m. It was first used in Gabon for the construction of canoes, then for structures such as glued laminated posts and carpentry [START_REF] Martin | Guide d'utilisation des bois africains éco-certifiés en Europe[END_REF][START_REF] Daïnou | Identité et écologie des espèces forestières commerciales d'Afrique centrale: le cas de Milicia spp.(synthèse bibliographique)[END_REF][START_REF] Gérard | Synthèse sur les caractéristiques technologiques de référence des principaux bois commerciaux africains[END_REF]. Padouk of Africa is the commercial name of Pterocarpus Soyauxii Taub of the Fabaceae family, a species found in Central and West Africa but whose optimal growing area is Gabon and Cameroun. It is suitable for carving, cabinet making but also for hydraulic work in immersed marine environments and shipbuilding. Moreover, with its very interesting resonance properties (very pure metallic resonance), it is also perfectly suitable for the manufacture of organs, pianos or other musical instruments. Padouk trees reach a height of nearly 50 m, with a diameter of about 60 to 100 cm and are free of branches up to about 30 m [START_REF] Gérard | Synthèse sur les caractéristiques technologiques de référence des principaux bois commerciaux africains[END_REF][START_REF] Martin | Guide d'utilisation des bois africains éco-certifiés en Europe[END_REF][START_REF] Gérard | TROPIX 5.0 : caractéristiques technologiques de 215 essences tropicales[END_REF]). The choice of these three species is explained by the fact that in this study one of the objectives is to highlight the impact of density on the mechanical behaviour of the wood. Hence the choice of a very light wood (Okoume), a medium-heavy wood (Iroko) and a heavy wood (Padouk) The Iroko and Padouk specimens used for our tests were taken in Libreville, from an open-air sawmill site, located between the Nkembo junction and the bus station interchange. On this site, a 3 m Padouk batten and a 2.5 m Iroko board were purchased for our work. As for the Okoume samples (Figure 2.4), they were taken from the sample stock of the Laboratoire de Recherche et Valorisation du Matériau Bois (LaReVa Bois) at the Ecole Nationale des Eaux et Forêts (ENEF).

Type of specimens used

The dimensions of the wood specimens for the three species used (Fig. 1) are those given by the French standard NF EN 408 for a compression test, i.e. 20 × 20 × 60 mm 3 . A total of 240 test pieces were obtained, with 80 specimens per species. However, we only had to use 174 specimens, i.e. 58 per wood species.

Sample preparation

The experimental device is a combination of a "United testing systems machine" press, with a maximum load capacity of 100 kN and a computer equipped with a data acquisition system managed by the Datum 5.0 software. To humidify the specimens, we used tanks filled with water, in which the specimens were immersed.

Determining the intermediate dried weight (M oi )

Firstly, an intermediate dried weight (M oi ) was determined for each group of species and for all the specimens. This M oi is considered as the own dried weight of the specimen. Five specimens of each group of species were selected, for a total of 15 specimens and put in an oven set to be dried at a temperature of 103 ° C [START_REF] Odounga | Mode I fracture of tropical woods using grid method[END_REF]. Before they were dried by the oven, the starting weight of each sample was determined at time t = 0.

Then, in order to monitor changes to their respective weights in the oven, their weights were measured on a weighing scales at 6 hour intervals until the weights stabilized. Figure 2 shows the changes during oven drying to the average weight of the species measured over time until the weights stabilized. There is a very rapid decrease in the weight of the specimens of all three species after 6 hours of drying. This decrease corresponds to a loss of moisture in the specimens (Moutee 2006, Moyne and[START_REF] Moyne | Etude experimentale du transfert simultane de chaleur et de masse au cours du sechage par contact sous vide d'un bois resineux[END_REF]. The dry weight is reached when a stabilization (linear part of the curves of Figure 2) of the sample weight is observed. Compared to Okume and Iroko, the dry weight of the Padouk is much higher due to its very high density. In addition, since Okoume and Iroko have rather similar densities, their dry weights seem similar. The weight value of the specimen, after it has stabilised in the oven, represents the own dried weight of the specimen. Finally, the intermediate dried weight (Moi) of each species, which will be used to determine the MC, was obtained by calculated the average dried weight of the five specimens using the following Equation:

The results obtained from this calculation are shown in table 1 below.

Determining the moisture content (MC) of the specimen

In this study eight different levels of Moisture Content (MC) for the specimens were chosen: 10%, 15%, 25%, 30%, 35%, 40%, 60% and 90%. To have these different levels of MC for each specimen, they were firstly put in tanks filled with water for saturation for six weeks for the Okoume and Iroko specimens and eight weeks for the Padouk specimens. Then, the results of the Moi (see table 1) calculated for each species were used to determine the moisture content (MC) of each specimen studied by combining the empirical method of MC determination and the Moi values for each species using the following equation:

Where: M H is the weight of the wet sample and M oi the intermediate dried weight for each species.

Results and discussions

Static compression loading

Static compression tests were first performed on 5 specimens for each species to mechanically characterise them. Thus, by using these tests, we were able to determine the maximum stress at the collapse point and the modulus of elasticity (MOE) of each species for the static compressive test.

Figure 3 shows the change in the relationships between the stresses and deformations of the Okoume (Figure 3a), Iroko (Figure 3b) and Padouk (Figure 3c) specimens in static compression at 12±2% MC.

According to the literature, two main sections can be identified on these stress-strain curves, i.e.: a linear part corresponding to the elastic zone and a parabolic shaped part corresponding to the plastic zone (Figure 3). The analysis of the different curves obtained during these static compression tests enabled us to determine the mechanical properties of our three species.

MC (%) = [ ] ×100 (2)
Tables 2, 3 and 4 show the main physical and mechanical parameters of our three species for the five tests performed As expected, we see in Table 1 that Padouk is the species that has the highest maximum stress at break point in static compression, followed respectively by Iroko and Okoume. This is easily explained by their respective densities. Padouk being the densest species with 0.728 ± 0.023 of density, its maximum stress at break point is therefore the highest, followed respectively by Iroko and Okoume (with respective densities of 0.474 ± 0.021 and 0.469 ± 0.007). This observation is also valid for the modulus of elasticity, Padouk still having the highest MOE value, followed by Iroko and Okoume.

The MOE values obtained experimentally differ from those obtained in the literature [START_REF] Gérard | TROPIX 5.0 : caractéristiques technologiques de 215 essences tropicales[END_REF][START_REF] Gérard | Synthèse sur les caractéristiques technologiques de référence des principaux bois commerciaux africains[END_REF]) by 23%, 2% and 7% respectively for the Okoume, Iroko and Padouk specimens. Likewise, the maximum stresses differs by 27%, 5% and 8% respectively for the Okoume, Iroko and Padouk specimens. These differences between our experimental values and those from the literature can be explained in part by the origin of the species from which the specimens were taken. Indeed, several studies have shown that depending on their biological origins, the characteristics of wood materials can vary between species, within the same species and within the same tree [START_REF] Medzegue | Radial growth and characterization of juvenile and adult wood in plantation grown okoumé (Aucoumea klaineana Pierre) from Gabon[END_REF][START_REF] Pâques | Variabilité naturelle du mélèze. I. Mélèze d'Europe : bilan de 34 ans de test comparatif de provenances[END_REF][START_REF] Guitard | Paramètres structuraux et/ou ultrastructuraux facteurs de la variabilité intra-arbre de l'anisotropie élastique du bois[END_REF][START_REF] Almeida | Influence de la structure du bois sur ses propriétés physico-mécaniques à des teneurs en humidité élevées[END_REF][START_REF] Charron | Etude comparative des caractéristiques physiques et mécaniques du bois des mélèzes d'Europe (Larix decidua Mill.), du Japon (Larix kaempferi (Lambert) Carr.) et de leur hybride (Larix x eurolepis Henry)[END_REF].

Cyclic compression loading

For each species studied, five compression loading cycles parallel to the fibres at a constant stress level (i.e. 10% of the maximum stress at the Okoume break point) were carried out. Figure 4 shows the general behaviour of the stress-strain curves of for the Okoume, Iroko and Padouk specimens obtained after the cyclic compression tests, at 10% of MC (Fig. 6a), 25% of MC (Figure 4b), 30% of MC (Figure 4c) and 60% of MC (Figure 4d). It appears at each MC level of the specimens, that for the three species, the loading path differs from the unloading path. In other words, Okoume, Iroko and Padouk present hysteresis at unloading during the different cycles. These hysteresis phenomena can be explained by the fact that our materials are not perfectly elastic [START_REF] Fozao | Modeling the stress-strain behavior of Bamboo under cyclic uniaxial loading[END_REF]. We also observe on these curves (Figure 4) that after the first loading cycle, the strain does not return to its initial position after the unloading path. This highlights the existence of the residual permanent strain that appeared in the first loading cycle, despite the low intensity of the force used [START_REF] Pambou Nziengui | Impact of cyclic compressive loading and moisture content on the mechanical behavior of Aucoumea Klaineana Pierre[END_REF]). However, the residual permanent strain observed during the first loading cycle remains constant in the following cycles. Everything happens as if the specimen had adapted to the stress exerted.

Impact of loading combined with variations in moisture content (MC) on strain amplitude

The histograms in Figure 5 show the change in deformation of the specimen after each cycle at different MC levels.

A closer observation of the stress-strain curves in Figure 4 shows a decrease in the strain amplitude (ε s ) with the number of loading cycles. Between the first and fifth loading cycles, a regression of ε s of 0.11%, 0.10% and 0.05% for the Okoume, Iroko and Padouk respectively at 10% moisture (Figure 5a). At 25% moisture (Figure 5b), the regression is 0.16%, 0.12% and 0.08% for the Okoume, Iroko and Padouk respectively. At 30% moisture (Figure 5c), it is 0.12%, 0.07% and 0.08% for the Okoume, Iroko and Padouk respectively. Finally, at 60% moisture (Figure 5d), the regression is 0.08% for the Okoume and Iroko, 0.06% for the Padouk. In other words, there is specimen strain during the loading cycle despite the low intensity of the load used. This explains the permanent strains that we observe on the curves in figure 5. This regression of ε s can be explained by the densification phenomenon that appears during the different loading cycles (Kutnar et al. 2015, Blomberg and[START_REF] Blomberg | Plastic deformation in small clear pieces of Scots pine (Pinus sylvestris) during densification with the CaLignum process[END_REF]. Indeed, just as in the drying process, the cell wall is compacted and the mass of the ligneous substance in a given volume increases during the different loading cycles [START_REF] Kutnar | Effects of different silvicultural measures on plant diversity -the case of the Illyrian Fagus sylvatica habitat type (Natura 2000)[END_REF][START_REF] Segovia | Mechanical behaviour of sugar maple in cantilever bending under constant and variable relative humidity conditions[END_REF]). This has the consequence of stiffening the specimens and thus reducing the strain in the following cycles. Also, the change in behaviour between the Iroko and Padouk specimens observed in the second loading cycle (Figures 4a,4b,4c,4d) suggests that the densification observed occurs earlier in the Padouk specimens compared to the Iroko specimens. This regression of the strain amplitude can also be explained by the accommodation effect [START_REF] Nguyen | Experimental characterization and thermo-mechanical modeling of cyclic behavior of polyethylene[END_REF]. Indeed, after the first loading cycle, we have the specimen adapts to the stress imposed which can cause the stabilization of the strain observed in the following cycles. The difference in behaviour between the Iroko and Padouk specimens from the second loading cycle suggests that the stabilisation of ε s is quicker among the Padouk specimens compared to the other two species. For each cycle, we have traced the changes to the strain amplitude with different moisture levels.

Figure 6 shows the change in ε s at each loading cycle as a function of each moisture level for the specimens tested.

Figure 6. Changes in strain amplitude (ε s ) for the Iroko, Okoume and Padouk specimens according to the moisture levels. The ellipses represent the hygroscopic domain of our three species.

In general, for the three species studied, we observed an increase in strain amplitude at each cycle up to a certain moisture level close to 30% (Figures 6a,6b,6c,6d,and 6e). This increase in ε s as moisture levels rose can be explained by the softening of the test pieces due to the increase in the moisture content. Indeed, the change in moisture content deeply affects the balance of the elastic constants of the wood, especially where the moisture content is in the hygroscopic domain [START_REF] Dinh | Linear elastic and non-linear behaviour of wood according to its structure[END_REF][START_REF] Gerhards | Effect of moisture content and temperature on the mechanical properties of wood: an analysis of immediate effects[END_REF][START_REF] Moutee | Modeling the creep behavior of wood cantilever loaded at free end during drying[END_REF]. Thus, the increase in humidity causes a decrease in the rigidity of the specimens. This decrease in the rigidity has the effect of increasing the specimen strains during loading. However, Figure 7 also shows that the increase in strain as with moisture levels rise is not continuous. There is a discontinuity due to the FSP, the point from which the MC level becomes too large to judge the effect of the stress. It is therefore more than likely that the area where this change of variation occurs matches the hygroscopic domain of our three species. The ellipse observed on each of the curves in Figure 7 thus shows the hygroscopic domain. Finally, it should be said that these results are fairly consistent with the data in the literature, which indicates PSF at around 30%, 25% and 21% moisture respectively for the Okoume, Iroko and Padouk specimens [START_REF] Gérard | TROPIX 5.0 : caractéristiques technologiques de 215 essences tropicales[END_REF][START_REF] Gérard | Synthèse sur les caractéristiques technologiques de référence des principaux bois commerciaux africains[END_REF], Medzegue et al. 2007).

Conclusion

The objective of this study was to perform a comparative study to highlight the impact of cyclic compressive loading combined with variations in moisture content, on the mechanical behaviour of 3 tropical species. Three wood species were chosen including a very soft wood (Okoume), a medium hardwood (Iroko) and a very hard wood (Padouk). The dimensions of the wood specimens for the three species used are those set down in French standard NF EN 408 for a compression test, i.e. 20 × 20 × 60 mm. The cyclic tests carried out (in the elastic domain) made it possible, firstly, to highlight the emergence of a constant residual permanent strain in the specimens of the three species during the different loading cycles. In other words, the strains generated during the loading are not fully absorbed when unloaded. Hysteresis is then observed during unloading. On the other hand, these cyclic tests carried out with a constant load level and at different moisture levels made it possible to show that there is a densification of the specimens which occurs with the loading cycles, thus causing the regression of the strain. In addition, they show that the densification observed is faster respectively from the densest species (Padouk) to the least dense species (Iroko and Okoume respectively) in the dry state (here at 10% of MC). This trend tends to change in the hygrometric domain where the impact of moisture content coupled with loading becomes less and less important.

For future work, in order to better evaluate the resistance of our three species subjected to cyclic stress in compression; it would be interesting to increase the number of loading cycles. In other words, it would be interesting to also perform fatigue tests in compression. It would also be interesting to perform cyclic bending tests to understand the behaviour of structures such as bridges.

Figure 1 .

 1 Figure 1. (a) Specimens of the species used, (b) general geometric configuration of test specimens; (c) specimens of the three topical species used.

Figure 2 .

 2 Figure 2. Changes to the average mass of the three species up to stabilisation

Figure 3 .

 3 Figure 3. Typical stress-strain curves of static compression tests for the specimens: (a) Okoume, (b) Iroko and (c) Padouk

Figure 4 .

 4 Figure 4. Typical stress-strain curves of cyclic compression specimens

Figure 5 .

 5 Figure 5. Comparison of the amplitudes of strain of the five loading cycles on the Okoume, Iroko and Padouk specimens

Table 1 .

 1 Intermediate anhydrous weight of the specimens

	Specimens	Okoume	Iroko	Padouk
	Spe 1	9.6829	9.5512	14.4766
	Spe 2	10.4028	9.5586	18.0570
	Spe 3	9.7914	10.2745	16.2674
	Spe 4	9.8849	9.1987	15.4956
	Spe 5	9.7829	9.6924	15.1801
	M oi	9.9090	9.6551	15.8953

Table 2 .

 2 Physical and mechanical parameters of Okoume

	Specimens	L	Size (mm) e moy	h moy	MC (%)	M (g)	ρ (kg/m 3 )	MOE (MPa)	MS (MPa)
	Oks 1	61.38	20.22	19.52	12.2	11.120 0.459 8464.56	38.35
	Oks 2	61.28	19.79	19.67	12.8	11.177 0.469 14105.43	63.81
	Oks 3	60.70	19.61	19.61	12.5	11.146 0.478 12881.18	44.01
	Oks 4	61.45	19.73	19.70	12.6	11.159 0.467 13734.36	49.28
	Oks 5	61.81	19.78	19.31	12.2	11.113 0.471 14685.61	51.31
	Table 2. Physical and mechanical parameters of Iroko
	Specimens	L	Size (mm) e moy	h moy	MC (%)	M (g)	ρ (kg/m 3 )	MOE (MPa)	MS (MPa)
	Irs 4	60.79	19.54	19.09	13.06 10.916 0.482 12968.65 63.17
	Irs 2	60.88	19.39	19.40	11.08 10.725 0.468 12553.06 64.90
	Irs 3	60.83	19.38	19.27	12.80 10.891 0.479 14772.57 36.13
	Irs 5	60.80	19.49	19.33	11.47 10.762 0.470 10815.78 57.07
	Irs 1	60.94	19.65	19.56	12.53 10.865 0.464 14352.90 64.22
	Table 4. Physical and mechanical parameters of Padouk
	Specimens	L	Size (mm) e moy	h moy	MC (%)	M (g)	ρ (kg/m 3 )	MOE (MPa)	MS (MPa)
	Pas 1	61.29	19.73	20.56	12.2	17.833 0.717 15321.28	56.46
	Pas 2	61.61	20.18	19.62	12.3	17.846 0.731 18841.60	47.68
	Pas 3	60.99	19.53	19.74	12.4	17.871 0.760 15020.71	66.35
	Pas 4	61.65	19.57	20.14	12.2	17.834 0.734 17930.03	61.51
	Pas 5	61.73	20.20	20.46	11.8	17.776 0.697 20327.38	68.37

Table 5 below

 5 , shows the average modulus of elasticity (MOE) values and the maximum stress (MS).

	Table 3. Average of the mechanical characteristics obtained for each species in static compression
	of Iroko, Okoume and Padouk
	Parameter	MOE (MPa)	MS (MPa)
	Okoume	12774 ± 2496.599	49.35 ± 9.519
	Iroko	13093 ± 1573.295	57.10 ± 12.126
	Padouk	17488 ± 2284.289	60.07 ± 8.321

Acknowledgments

The authors wish to thank the Network of Forestry and Environmental Training Institutions of Central Africa (RIFFEAC) for the implementation of the Wood Science Master of the Ecole Nationale des Eaux et Forêts (ENEF -GABON) as well as the PEPS project CNRS "RUMO" and the Auvergne Rhône-Alpes Region (AURA) for financial support under the SCUSI project.


J R Tsafack Nzifack

J S Mabekou Takam

Rostand Moutou Pitti

Medard Fogue

Pierre Kisito Talla

STUDY OF THE TEMPERATURE OF CEREBRAL ARTERIAL BLOOD FLOW, FOR THE CHARACTERIZATION OF THE DEGREE OF STENOSIS: APPLICATION TO STROKE

Keywords: Temperature, Penne's equation, Stenosis, Hematocrit

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

With the advancement of clinical medicine in thermal diagnosis of diseases, it is very important to understand thermal phenomena and the behavior of biological body temperature. One approach is to study the distribution of temperature in biological tissue. However, precise thermal analysis of biological tissue is difficult because they include conduction, convection, radiation, internal metabolism, evaporation, phase change and the regulation of the inherent temperature. Not only is the tissue heterogeneous and anisotropic, but the mechanisms also maintaining body temperature, such as blood flow and metabolic heat generation. Recently, the development of research shows that the problem of heat transfer in biological tissues becomes a complex problem. But there are several discussions without conclusion in this area. Thus in (HenneryPennes, 1948) proposed a simple linear mathematical model to describe the thermal interaction between human tissue and perfused blood, and the effect of metabolism. He measured the radial temperature in the forearm by drawing thin thermocouples through the arms of nine elongated subjects. This was based on experimental observation. Using this experimental concept, the model [START_REF] Mitchell | An analytical model of the countercurrent heat exchange phenomena[END_REF], the model (Keller and Seiler 1971), the model [START_REF] Wulff | The energy conservation equation for living tissue[END_REF], the model [START_REF] Chen | Micro-vascular contributions in tissue heat transfer[END_REF], the model [START_REF] Weinbaum | A new simplified bioheat equation for the effect of blood flow on local average tissue temperature[END_REF], the model [START_REF] Khaled | The role of porous media in modeling flow and heat transfer in biological tissues[END_REF], (Nakayama and Kuwaha Model 2008) have discussed thermal behavior in various constant parameters with human tissue layers. The distribution of temperature takes over in the blood and arterial tissues. [START_REF] Cooper | A Probe Technique for Determining the Thermal Conductivity of Tissue[END_REF] found an analytical solution of heat diffusion equation for brain tissue with negligible effect on blood flow and metabolic heat generation. (D. B. [START_REF] Gurung | Mathematical Study of Abnormal Thermoregulation in Human Dermal Parts[END_REF] studied the abnormal thermoregulation model in the human dermal part. He also studied the temperature distribution in the steady state and in the unstable state in three layers of the dermal part. He also used the numerical method for the finality of the techniques of solution which is the most precise for the analysis of the temperature in the human body. (Hen and Dil 2018) study the effect of the thermal parameters of the dermal part in living cylindrical tissues. For the different models which have been investigated in literature, none of them did not considered the effect of hematocrit and stenosis which strongly influences the flow regime. In the present work, we are going to use the model of [START_REF] Pennes | Analysis of Tissue and Arterial Blood Temperature in Resting Human Forearm[END_REF] use by (Hen and Dil 2018), by coupling with hematocrit and stenosis to better control the variation of the temperature. Furthermore, we shall analyze the partitioning effect of hematocrit and the evolution of atherosclerosis on variation temperature variation. Here, we neglected the axial and angular direction and considered only the stationary state model of radial direction. The numerical (finite difference method) and analytical result obtained are presented graphically and compared to the result of [START_REF] Zhang | An Analytic Solution of One-Dimensional Steady-State Pennes Bioheats Transfer Equation in Cylindrical Coordinates[END_REF] and (Hen and Dil 2018) by applying the appropriate values of the physical and physiological parameters. The solution obtained can be used for the measurement of thermal parameters, the reconstruction of the temperature field and thermal diagnosis and in the treatment which maximizes the therapeutic effect while minimizing undesirable side effects. It may also be useful to design medical devices to operate within a special range of heating and cooling temperature rates, such as [START_REF] Zhang | An Analytic Solution of One-Dimensional Steady-State Pennes Bioheats Transfer Equation in Cylindrical Coordinates[END_REF], thus for the prediction of cerebrovascular diseases.

II) MATRIELS AND METHODS

II-1) MODELISATION OF TEMPERATURE

Over the past years, many researchers have developed different models with different views.

The mathematical model used for the transfer of bio-heat is based on the Penne equation. [START_REF] Pennes | Analysis of Tissue and Arterial Blood Temperature in Resting Human Forearm[END_REF]) is preferable for studying the heat transfer between the blood and the tissues which also associates the metabolism effect and the blood perfusion. The modified Pennes equation is written as where are the density (k/ ), the specific heat (J/kg. ) and the thermal conductivity of tissue, respectively. is the blood perfusion rate per unit volume (kg/s. ). is the specific blood, is the metabolic heat generation pert unit volume (w/ ), represents the temperature of arterial blood ( and T is the tissue temperature ( ). Based on the Pennes equation, the one-dimensional mathematical model was used to describe the heat transfer from living cylindrical tissues, in the stationary state, is presented below (Kai and Xinxin;

Hen and Dil 2018).

The model is axial symmetric, so the boundary conditions are described as (Kai and Xinxin

;Hen and Dil 2018):

Where R is the radius of the concerned tissue, is the coefficient of heat transfer which accounts for the effects of both convection and radiation on the surface of the tissue, is the ambient temperature. the Reynolds number (Re). The Reynolds number is a dimensionless quantity which is useful for determining whether the flow is laminar or turbulent: if it is greater than a critical value, the flow is turbulent, if it is less, the flow is laminar. In general, the Reynolds number is defined by the flowing formulation Where is the blood density, d is the diameter of the vessel, is the mean blood velocity throughout the vessel and it can be expressed as the ratio between the mean incoming flow (Q) and the inlet area (A):

is the blood viscosity that is express using a simplified formulation of the Einstein relationship and is given by the following formula where represents plasma viscosity

For low value of shear rate, blood behave like pseudoplastic fluids and this behavior occurs for >12%.This is due to the presence of fibrinogen which determine the aggregation of the red blood cells into "rouleau",generally mode up by fewer tens of erythrocytes, increasing blood viscosity. Since these parameters were known, Reynolds number were calculated at rest condition both for the non-stenotic model and in correspondence of the 3 stenoses diameter, to see if these three degrees of stenosis may promote a laminar flow or cause a turbulent flow.

The value obtained by (Maurizio 2018) are reported in the following table (1) From equation ( 14), ( 15) and ( 16) we can find the following system of linear equations represented in matrix form:

AX=B ( 17
)
where ;

and B= a= -(2+ ; = ) and ) where i is the number of line .

The matrix (17) gives the nodal values in FDM which make it possible to calculate the temperature distribution profile.

II-7) ANALYTICAL RESOLUTION

To solve analytically, we first carry out the dimensioning of equation ( 9) and its boundary condition by introducing the characteristic quantities [START_REF] Ozisik | Heat Conduction[END_REF][START_REF] Wang | Study on the Basic Equations of Biomedical Heat Transfer[END_REF] Then, replace equation ( 16) in equation ( 9):

Here the dimensionless parameters and variables will be defined as Thus equations ( 9) and (3) can be rewritten in the form Also, in order to normalize the equation, we assume By thus substituting equation ( 21) in equation ( 19), we obtain:

It is clear that equation ( 22) is a modified zero order Bessel differential equation, the general solution of which can be expressed as follows:

Where and are respectively the modified Bessel function of the second type. In order to determine, if the analytical solution can be expressed by the Bessel function, equation ( 22)

was compared to the generalized Bessel equation as follows:

The corresponding solution of equation ( 24) is:

Where and are respectively the modified Bessel functions of the first type, and are arbitrary constants which can be obtained as a function of the given boundary conditions. The result of the comparison between equation ( 22) and equation ( 24) is shown below:

, m=0, ,p=1, Thus, the solution of equation ( 22) can be expressed as:

By replacing ( 26) with ( 21), the solution of ( 19) can be written as The next step is to determine the values of two arbitrary constants .

According to the characteristics of the Bessel equation, when z = 0, we have Taking into account the boundary conditions ( 20), simple derivations lead to: so we have :

Finally, the analytical solution of T is:

II-8) DETERMINATIONS OF PARAMETERS

III) RESULTS AND DISCUSSIONS

III-1) VALIDATION OF RESULTS

The results of the new model were validated by the reproduction of the results of the literature established for a simple pipe (without stenosis and Hematocrit). Figure ( 1) shows a decrease in temperature when the radial direction becomes important. This is due to the fact that when the body temperature is above the set value, the hypothalamus causes the phenomenon of sweating, evaporation, which causes a lowering of the skin temperature. At the same time, the skin arterioles dilate in order to promote heat exchanges with the outside. It shows that, as the obstacle increases, the temperature increases too. This increase in temperature is due to the friction of the fluid particles. This implies that, the stress becomes important at the cross of the stenosis section and it will therefore be important to control the temperature to avoid the evolution of stenosis. In the previous work of [START_REF] Tsafack | study of cerebral blood flow by the lumped parameter model to predict the rupture of the arterial wall: application to stroke[END_REF] it was observed that, when the stenosis increased radially, the amplitude of the oscillations decreased as the inertial blood flow decreased rapidly due to blockage of the lumen. This suggests that the loss of singular inertial blood flow occurs when there is disturbance of the normal flow.

In the same vein (Gou et al 1999) shows for a high temperature, more than 38 , the patient is victim of cardiovascular and cerebrovascular disease. This is in agreement with our result, since figure (2) shows that, at a higher temperature of 38 the stenosis is already more than 50% of reduction in the initial wall.

Furthermore, in the experience of (kin et al 1996), he observed a rat with a body temperature above 40 , plunging into a brain violation in a few hours. this is in agreement with our result, since figure (2) shows that, when the temperature is higher than 40 , the degree of stenosis is higher than 75% of reduction of the arterial wall, therefore this is normal that, this rat is exposes to the brain offense.

  II-2) STENOSIS MODELING Stenoses are characterized by a lesion of lipid infiltration, called an athermous plaque which develops on the internal surface of the arterial vessel (Figure II-1) and which blocks blood circulation and hematocrit (Figure II-2).

Figure

  Figure (II-1) https://www.doctissimo.fr/html/sante/encyclopedie/sa_1583_ischemie_cereb.htm

Figure ( 1

 1 Figure (1): Temperature as a function of the radial direction

Figure

  Figure (2): Influence of stenosis on temperature 0 0.005 0.01 0.015 0.02 0.025 0.03 34

Figure ( 3

 3 Figure (3): Influence of the heat transfer coefficient on temperature

Figure ( 5

 5 Figure (5): Influence of hematocrits (ht) on the temperature

Figure ( 6

 6 Figure (6): Influence of the generation of metabolic charger (qm) on temperature

Table (

 (

	with h=
	1): Different stages of artery conditions with correspondent of Reynolds values
	determine by (Maurizio 2018) at rest condition Now let us introduce equation (11) and (12) into equation (10), with have
	Different stage	Non-stenotic	30% stenosis	50% stenosis	75% stenosis
	of	artery	model
	condition
	where
	Re		334.04	482.27	675.15	1350.33
	II-6) DISCRETISATION OF BOUNDARY CONDITION
	from equation (3)
	II-4) FINAL MODEL FORMULATION
	In this section, we will couple the bio-heat model with the stenos model. Introducing equation
	6 into equation 4, we will have for i=1,2…,R-1
	Using equation (7), we have the new blood density
	and for i=R
	Now let us introduce equation (8) into equation (2) to have a final expression of our model
	with
	D=[(2+		) -	(1+ )]
	II-5) RESOLUTION BASED ON FINITE DIFFERENCE METHOD
	From equation (9), we have E= (1+ )
	Using the Finite Difference Method (FDM)

Table 2 :

 2 Values of parameters

	Symbol	Value	Unit	Description	Reference
		0.00003	Kg/s.	Blood perfusion
		3850	J/Kg.	Blood specific	Hen and Dil
				heat		2018
	K	0.48	W/m.	Tissue thermal	Hen and Dil
				conductivity	2018
		30.023	W/m.	Heat	transfer	Hen and Dil
				coefficient	2018
		1085	W/	Heat generation	Hen and Dil
				per unit volume	2018
		37		Artery		Hen and Dil
				temperature	2018


Claude Feldman
email: pclaudefeldman@gmail.com

Pambou Nziengui

Jonas Turesson

Mats Rostand Moutou Pitti

Mats Ekevad

Experimental Assessment of the Annual Growth Ring's Impact to the Mechanical Behavior of Temperate and Tropical Species

Keywords: Tropical species, Temperate species, Congo basin forest, Massif central forest, Bending test

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Predicting the behavior of wood under mechanical or environmental stress is essential to improve the design and durability of timber structures (Gérard et al. 2011). This refers to the understanding of the various physical and mechanical characteristics of wood. This understanding is affected by the multitude of climates encountered throughout the world, which attribute to each species endemic characteristics proper to the environment in which the species is found (Manfoumbi Boussougou 2012). One explanation of these intrinsic characteristics could be given by the anatomical structure for each species (Fig. 1). The microscale structure in wood globally affects its mechanical behavior. This can be investigated due to advancements in theoretical, numerical, and experimental approaches. [START_REF] Gershon | Multiscale mechanical and structural characterizations of Palmetto wood for bio-inspired hierarchically structured polymer composites[END_REF] have shown that it is necessary to know the microscale structure ofpalmetto wood to be able to optimize its fracture toughness. Another work on palmetto wood (Saavedra Flores 2016) explains that there are influences of several micro-structural features (such as cellulose content and its crystallinity, the microfibril angle, and the cell-wall thickness of micro-fibers) on the Young modulus and density. The growth of annual rings affects the mechanical behavior of wood [START_REF] Miksic | Effect of fatigue and annual rings' orientation on mechanical properties of wood under crossgrain uniaxial compression[END_REF]. Wood is a heterogeneous, anisotropic, and hygroscopic natural composite material, with high strength and stiffness relative to its weight [START_REF] Mishnaevsky | Micromechanical modelling of mechanical behaviour and strength of wood: State-of-the-art review[END_REF]Bahar 2019). By starting from these hypotheses, [START_REF] Stanzl-Tschegg | Microstructure and fracture mechanical response of wood[END_REF] noted that the structure of wood is highly optimized for the needs of living trees. This does not mean that wood is optimized for usage in constructions where this article is focusing. The study by Morales-Conde and Machado (2017) assesses the cross-section for variation of timber bending of modulus of elasticity and brings more information linked to our work. The authors show, despite the stress waves approach used, a great correlation between the cross-sectional variation and the modulus of elasticity of the wood studied, which roughly fits with the aims of this study. Based on previous studies (Jaskowska-Lemańska and Wałach 2016; [START_REF] Ramage | The wood from the trees: The use of timber in construction[END_REF][START_REF] Zeller | Tree ring wood density of Scots pine and European beech lower in mixed-species stands compared with monocultures[END_REF]Abdelmohsen et al. 2018), it is logical to say that the mechanical behavior of wood is based on its micro-structural features, for example content of cellulose, fibril angles, and the annual growth rings.

This work aims at performing an experimental comparative study on five species with different physico-mechanical characteristics. The study is made possible due to a specific experimental approach built by connecting annual growth rings with global mechanical behavior by determining their intrinsic mechanical characteristics. Five species were studied: two European temperate species from the Massif Central in France, Douglas fir (Pseudotsuga menziesii) and White fir (Abies alba Mill); and three tropical species from Gabon, Okume (Aucoumea klaineana Pierre), Iroko (Milicia excelsa) and Padouk (Pterocarpus soyauxii). The difference between the chosen species is the climate of their habitat. In Gabon, for example, the climate shows a mean annual rainfall of 1900 mm, a mean relative humidity of 85%, and mean annual temperature of 27 °C [START_REF] Medzegue | Radial growth and characterization of juvenile and adult wood in plantation grown okoumé (Aucoumea klaineana Pierre) from Gabon[END_REF]Pambou Nziengui et al. 2017;Engonga Edzang et al. 2020). This kind of region has two types of seasons: a six months' dry season and a six months' rainy season.

During the dry season, almost no rainfall occurs in comparison to the rainy season when most of the rainfall occurs. Thus, the quantity of water absorbed by the tree during the rainy season becomes very important for the growth of the tree.

To date, no study has compared tropical species (African tropical region) and temperate species regarding the link between the growth of annual rings and the mechanical properties. The reason for this concern is that the tropical species has a continuous growth of annual rings during the year (Manfoumbi Boussougou 2012; [START_REF] Ramage | The wood from the trees: The use of timber in construction[END_REF]) and this is not the case for the studied temperate species. Both the tropical and temperate species are commonly used in structure for heavy and light frameworks, glulam, paper pulp, fiber panels, in cooperage, packaging, maritime work, and luxury furniture (Adamopoulos 2009;[START_REF] Treml | Splinter formation of OSB strands during flat disc cutting of ring porous hardwoods[END_REF][START_REF] Sopushynskyy | Wood density and annual growth variability of Picea abies (L.) Karst. growing in the Ukrainian Carpathians[END_REF]. In France there were more than 170 Mm 3 of white fir and 93 Mm 3 of Douglas fir in 2009 (Pambou [START_REF] Pambou Nziengui | Notched-beam creep of Douglas fir and white fir in outdoor conditions: Experimental study[END_REF]. The chosen tropical species are the most widespread species in the tropical forest of Gabon and also among the most exported and used species in the field of timber structures [START_REF] Odounga | Mode I fracture of tropical woods using grid method[END_REF].

EXPERIMENTAL Wood specimens

The wood specimens were cuboid shaped with the approximately dimensions of 200×10×10 mm 3 (Fig. 2). These specimens were cut following the fiber direction (in the longest direction). A total of 125 clear wood specimens was obtained. The specimens of temperate species were taken from collapsed beams used in an earlier study of creep tests (Pambou [START_REF] Pambou Nziengui | Notched-beam creep of Douglas fir and white fir in outdoor conditions: Experimental study[END_REF][START_REF] Tran | Reliability assessment and updating of notched timber components subjected to environmental and mechanical loading[END_REF]. The specimens of tropical species were cut from butt logs at an approximate position of one meter above the roots of the standing tree [START_REF] Odounga | Mode I fracture of tropical woods using grid method[END_REF]. To equalize the moisture content (MC) of the specimens, the specimens were stored in a climate chamber for 48 h. The temperature and the relative humidity in the climate chamber were set to 20 °C and 64.7%, respectively. Table 1 shows the total number of specimens and the statistical mean of the principal physical characteristics for each group before the experimental campaign. To distinguish the earlywood and latewood, which make up the annual growth ring, the specimens were scanned in a computed tomography scanner (CT-scanner). The data from the CT-scanner was visualized and analyzed by the Image J software (https://imagej.nih.gov/ij/).

Four-points flexural test

All specimens were loaded in four-point flexural test until failure by an electrostatic press (Fig. 2). The four-point bending test set-up was performed according to the European requirement (EN 1995(EN -1-1 2004) and as presented by (Manfoumbi Boussougou 2012). The specimens were measured and weighed to determine their physical parameters (Table 1). The modulus of elasticity (MOE) was calculated for each specimen according to Eq. 1,

(1) where F2-F1 is an increase of force on the regression line and W2-W1 is the increase of the corresponding displacement as described in the European standard requirement (EN 1995(EN -1-1 2004)). L represents the distance between the two supports (Fig. 2), I z the moment of inertia, G is the shear modulus, b and h are the width and height of the specimen, respectively. Due to lack of data for the tropical species, the influence of G was neglected. The maximum flexural stress was defined to Eq. 2,

C max =M y /I z (2)
where M is the flexural moment at the maximum force, F max , during the four-point flexural test, y is the distance from the neutral axis to the area of highest flexural moment and I z the moment of inertia. For this four-point flexural test set-up, M was calculated as presented by Eq. 3,

M=(LF max )/3 (3)
To calculate C max , the length y in Eq. 2 can be set equal to h/2 [25]. A comparison between C max calculated in this study and the maximum flexural failure stress given by the CIRAD wood collection (Gérard et al. 2011), C mcir , was done.

RESULTS AND DISCUSSION Mechanical Characterization of the Specimens in Static Tests

The mean values of modulus of elasticity (MOE), maximum loading (F max ), and maximum flexural stress (C max ) obtained, for each species studied, are presented in Table 2. The C mcir value is the maximum flexural stress given by the CIRAD wood collection (Gérard et al. 2011). The highest MOE mean of 15.6 GPa was obtained for DF species. The lowest MOE mean of 9.2 GPa was calculated for O. The lowest and highest F max , mean was measured for WF and DF, respectively and the specimens with largest variation among the tropical and temperate species was P and DF, respectively. By taking into account the results of (Gérard et al. 2011) and its dry density (Table 1), P was expected to have the highest C max mean among all tested species, but according to Table 2, it had a lower C max mean but with the highest COV. In general, all tested species (except WF and P) had a higher C max , mean than C mcir . These results highlight the intra-extra trees variability, which exists for specimens taken from the same trees. 3 shows the evolutions of the C max versus MOE for all tested specimens. There was an increasing C max for a higher MOE. This behavior is observable for the both temperate and tropical specimens. The difference in COV, which exists for the groups of specimens presented in Table 2 is also visible in Fig. 3 by the highlighting of the dispersion, which seems large for DF (for the temperate specimens) and P (for tropical specimens). The groups of specimens with lower COV (O and WF) showed a nonscattering pattern in Fig. 3 compared to groups of specimens with higher COV. The R 2values for the trendlines were calculated as 0.41, 0.41, 0.53, 0.30, and 0.53 for DF, WF, I, O, and P, respectively. Figure 4 shows a comparison between the ρ dry and C max . Due to the low COV for the ρ dry of the DF, the DF specimens are non-scattered. The lower values of C max for some DF specimens occur due to material variations. The DF specimens with lower C max were kept in the analysis because they could not be classified as statistical outliers. The results for the temperate specimens were similar for the tropical specimens where the group of specimens with highest COV could illustrate a trendline with reasonable R 2 -values. The trendlines in Fig. 4 had an R 2 -value of 0.40 and 0.35 for WF and I, respectively. The other temperate and tropical specimens resulted in trendlines with low R 2 -values and are not presented. Iroko (I) was the only tropical group of specimens following a trendline. O and P did not illustrate a trendline due to the low COV of ρ dry , which were 4.1% and 3.0%, respectively. This variation in ρ dry was too low compared to the COV of ρ dry for I and WF, which were 13.8% and 8.1%, respectively. This statistical study done on the intrinsic mechanical characteristics of the specimens from temperate and tropical species, gives interesting information to build a database of the mechanical properties of the species studied. This database will be important for the next sections of this work.

Cross-section Characterization of the Specimens

The CT scans of specimens cross-sections are presented in Fig. 5. The earlywood and latewood, which make up the annual growth ring of tree, are illustrated with white and black color, respectively. The distinction between earlywood and latewood is easily observable for the temperate specimens (Fig. 5, DF and WF species), but on the cross sections of the tropical specimens, the distinction of annual growth ring is almost impossible to see (Fig. 5; O, I and P species). These observations are in accordance with the literature (EN 1995(EN -1-1 2004;;[START_REF] Sopushynskyy | Wood density and annual growth variability of Picea abies (L.) Karst. growing in the Ukrainian Carpathians[END_REF], which shows that the distinction between earlywood and latewood is therefore not obvious in tropical species. The main explanation of the non-perception of this difference, for the tropical specimens, could be given by the harsh climate met in the region of their growth and the fact that the tropical species has a continuous growth of the annual rings during the year (Manfoumbi Boussougou 2012; [START_REF] Ramage | The wood from the trees: The use of timber in construction[END_REF]. Specifically, for the P specimens the distinction between the lines of latewood and earlywood seems very difficult to observe, which is the same case for O and I. In the specimens O2, O12, I3, I5 (Fig. 6), there is little distinction observable between the latewood and earlywood of these tropical species. The density difference through the specimen could explain the difference. By taking into account this result, globally for the tropical species, the scanning of their cross-section does not make it possible to distinguish the line between earlywood and latewood. Starting from this map (Fig. 5), Image J software was used to examine the width of the earlywood for the temperate specimens. The results and the summary of the width mean values of earlywood rings ( mean ) and the number mean values of earlywood rings (NE mean ) are presented in Table 3. The tropical specimens had a lower NE mean than the temperate specimens. Lowest number of NE mean of 1.9 had P. For the tropical specimens, O had the highest NE mean and COV. The temperate specimens had the highest and lowest COV of 56.6% (WF) and 22.9% (DF), respectively, for the NE mean . No  mean could not be measured for the tropical specimens due to difficulty of define where earlywood starts and latewood ends (see Fig. 5 for specimens of species I, P, and O).

Assessment of the Annual Growth Ring in the Mechanical Properties of the Species Studied

To understand the effects of the annual growth ring on the mechanical behavior, comparisons were made between the ρ dry and NE (Fig. 6) and the ρ dry and Fig. 7). The temperate specimens show that there was a correlation between the ρ dry and NE. This conclusion was drawn only from the WF specimens and not the DF specimens due to the DF specimens low COV of 22.9%. For the tropical specimens, a correlation between ρ dry and NE is difficult to see due to the low spread of the specimens. The illustrated trendlines for the tropical specimens had lower R 2 -values of 0.30 and 0.32 for I and O, respectively, compared to the R 2 -value of 0.40 for WF. The tropical trendlines was showing a positive correlation between ρ dry and NE but due to the lower R 2 values, the trend is not as clear as for the temperate specimens. For the group of DF specimens and the group of P specimens trendlines were not presented due to the low R2-values.

The correlation between the ρ dry versus  for the temperate specimens is presented in Fig. 7. A negative correlation between ρ dry and  could be seen for the WF specimens. Due to the low COV of 22.9% and 31.4% for ρ dry and , respectively, for the DF specimens it was not possible to see any correlation between ρ dry and  The trendline for the group of WF specimens had an R 2 -value of 0.60. A trendline for the group of DF specimens was not presented due to the low R 2 -value. 1. An experimental study of the evaluation of the annual growth ring impact on the intrinsic physico-mechanical characteristics of wood has been done. The samples were dimensioned and tested in a four-point flexural test according to the European standard requirement. Two groups of specimens have been studied (temperate and tropical species). To be able to visualize the earlywood and latewood (annual growth ring), the specimens were scanned by a computed tomography scanner before the four-point flexural test.

2. The results show that, for temperate species, the distinction between earlywood and latewood make up the annual growth ring and is easily distinguishable. However, for a tropical species the distinction is less clear. The study shows trendlines for the temperate and tropical specimens connecting the modulus of elasticity to the maximum flexural stress. It was also possible to show a trendline between the dry density and the maximum flexural stress for the two groups of temperate and tropical specimens of White fir and Iroko, respectively. Another trendline was shown between the dry density and number of earlywood rings for the group of temperate specimens of White fir and the groups of tropical specimens of Iroko and Okume. A last trendline was shown between the dry density and the mean width of the earlywood rings for the group of temperate specimens of White fir. The mean width of the earlywood rings was not possible to measure for the groups of tropical specimens due to the difficulty of define exactly where earlywood starts and latewood ends.

3. The results showed a connection between the annual growth rings of the tree and their intrinsic physico-mechanical characteristics mainly based on the dry density of the wood for both the tropical and temperate specimens. It was possible to show that the dry density was affected by the number and width of the earlywood rings. Moreover, the dry density affected the maximum flexural stress and where the maximum flexural stress is strongly connected to the modulus of elasticity. This results in an increased number of earlywood rings which then results in an increased modulus of elasticity and increased maximum flexural stress. These results illustrate the need to have a fairly large number of specimens to avoid the large variation noted within the mechanical properties determined in this work. These results are interesting but are limited by the fact that it is a new experimental approach used for this type of study.

It could be necessary for the next experimental study to create a method to distinguish clearly the annual growth rings of tropical species by increasing, for example, the size of the samples to be studied.

Fig. 1 .

 1 Fig. 1. (a) Cross-section of a tree trunk and (b) annual growth ring of wood

Fig. 2 .

 2 Fig. 2. Four-point flexural test set-up with the fiber direction of the specimen loaded

Fig. 4 .

 4 Fig. 4. Modulus of elasticity (MOE) versus maximum flexural stress (C max ) for the groups of temperate and tropical specimens

Fig. 5 .

 5 Fig. 5. Dry density (ρ dry ) versus maximum flexural stress (C max ) for the groups of temperate and tropical specimens

Fig. 6 .

 6 Fig. 6. Result from the CT-scanner with specimens named and numbered after species

Fig. 7 .

 7 Fig. 7. Dry density (ρ dry ) versus the number of earlywood rings (NE) for the groups of temperate and tropical specimens

Fig. 8 .

 8 Fig. 8. Dry density (ρ dry ) versus the width of earlywood rings for the groups of temperate specimens

Table 1 .

 1 Number of Specimens and Physical Characteristics for Each Tested Species Group with Coefficient of Variation (COV) in Parentheses

		Species	Name	No.	MC mean [%]	ρ dry, mean [kg/m	3 ]
	Temperate	Douglas fir White fir	DF WF	30 48	9.8 (11.1%) 9.9 (13.6%)	563 (4.5%) 447 (8.1%)
		Iroko	I	17	9.0 (17.8%)	582 (13.8%)
	Tropical	Padouk	P	15	8.3 (13.4%)	733 (3.0%)
		Okume	O	15	10.3 (15.7%)	505 (4.1%)
	No.: number of specimens; MC

mean : mean moisture content;  dry, mean : mean dry density

Table 2 .

 2 Result from the Four-Point Flexural Test with COV in Parentheses

		Name	MOE mean (GPa)	F max, mean (N)	C max, mean (MPa)	C mcir (MPa)
	Temperate DF	15.6 (10.5%)	522 (20.7%)	102 (20.4%)	91
		WF	10.7 (16.4%)	383 (15.3%)	77 (16.0%)	80
	Tropical	I	12.8 (18.1%)	492 (13.7%)	94 (14.8%)	87
		P	14.1 (13.5%)	407 (21.6%)	83 (21.5%)	116
		O	9.2 (9.1%)	422 (12.7%)	82 (11.9%)	62
	Figure

Table 3 .

 3 Mean Width ( mean ) and Number of Earlywood Rings (NE mean ) for the Groups of Tropical and Temperate Specimens with COV in Parentheses

		Name	 mean [mm]	NE mean
	Temperate	DF	5.07 (31.4%)	2.8 (22.9%)
		WF	3.37 (69.6%)	5.5 (56.6%)
	Tropical	I	-	2.3 (29.9%)
		P	-	1.9 (30.7%)
		O	-	2.5 (45.6%)

PambouNziengui et al. (202#). "Annual growth rings," BioResources #(#), ###-###.