Y Z Li

N Mangelinck-Noël

G Zimmermann

L Sturz

H Nguyen-Thi

Effect of solidification conditions and surface pores on the microstructure and columnar-to-equiaxed transition in solidification under microgravity

Keywords: Aluminum alloys, Solidification, Microgravity, Crystal structure, Columnar-to-Equiaxed Transition, Pore

Microgravity solidification experiments were carried out in the Material Science Laboratory on board the International Space Station. The influence of grain refinement, rotating magnetic field (RMF) and surface pores on the microstructure and columnar-to-equiaxed transition (CET) were investigated in two selected Albased samples solidified under microgravity conditions. The increase of the furnace pulling velocity leads to a finer dendrite structure, a smaller eutectic percentage and a more uniform eutectic distribution in the interdendritic regions. On the one hand, grain refinement ensures the occurrence of CET, which is progressive in the studied experiment because of the high temperature gradient. On the other hand, in the nonrefined alloy a RMF applied during solidification fails to trigger the CET, because the forced liquid flow is too weak compared to the solidification front velocity to transport fragments from the mushy zone above the solidification front. The presence of the pores at the sample surface leads to a peculiarity in the eutectic percentage and weakens the decrease of the dendrite arm spacing for both samples. These effects are ascribed to a forced extra liquid flow into the mushy zone due to the pore that *Manuscript Click here to view linked References promotes the growth of the dendrites along the liquid flow direction, resulting in elongated grains and postponing the CET in the refined alloy.

Answer: Our objective is to characterize the effect of the grain structure on the eutectic percentage distribution with the measurements we perform, using a box size 0.5 mm along the solidification direction and 0.4 mm in width. The eutectic fraction measured at higher velocity in stage II is lower compared to the case at low velocity in stage I because the solidification proceeds by coarse columnar competitive growth at low velocity. Indeed, on the one hand, at low velocity, the competition with neighboring large dendrites with random orientation leads to the formation of quite large solute-enriched liquid pockets which are transformed into the eutectic phase at the end of solidification. On the other hand, in stage II, the microstructure at higher velocity, either columnar or equiaxed, is much finer due to the higher growth velocity, leading to a more uniform intergranular E% distribution. This phenomenon was discussed in more details for other experiments in our previous study [Liu et al. Acta Materialia, 64 (2014) 253]. As our focus was on the pore formation for the present article, we did not develop the discussion on this important aspect. We now mention in the text that eutectic percentage in relation to the grain structure is characterized and briefly explain the difference observed between stages I and II. Moreover, we added a reference to previous work in the text. We thank the reviewer again for this comment.

Introduction

Morphological development during solidification remains of tremendous interest for both academic research and industrial applications, due to the tight relationship between the microstructures and the final properties [START_REF] Dantzig | Solidification[END_REF] . Indeed, growth in a high temperature gradient may result in elongated columnar structures, whereas a more uniform temperature favors isotropic equiaxed grains. Accordingly, a change from columnar to equiaxed grain structure is often observed during industrial processes such as ingot casting or welding by a simultaneous decrease of the temperature gradient and an increase of the growth velocity. CET is an important morphological transition in metallic alloys, which is mainly controlled by the liquid undercooling ahead of the dendritic front [2]. CET occurs when the number of equiaxed grains and the volume they occupy become sufficient to block the columnar front [START_REF] Hunt | Steady state columnar and equiaxed growth of dendrites and eutectic[END_REF][START_REF] Jung | CET by fragmentation during the solidification under natural and forced convection of non-refined Al-based alloys[END_REF][START_REF] Martorano | Predicting the columnar-to-equiaxed transition for a distribution of nucleation undercoolings[END_REF].

Equiaxed grains have two main origins: purposely added nucleating particles and dendrite fragmentation. Industrially, the main approach to favor the equiaxed microstructure is to add grain refiners, which act as preferential sites for nucleation with a low nucleation undercooling [START_REF] Greer | Modelling of inoculation of metallic melts: application to grain refinement of aluminium by Al-Ti-B[END_REF][START_REF] Quested | Understanding mechanisms of grain refinement of aluminium alloys by inoculation[END_REF]. For non-refined alloys, the most potent mechanism for the origin of the equiaxed grains ahead of the columnar front is the dendrite fragmentation [START_REF] Flood | Columnar and equiaxed growth: II. Equiaxed growth ahead of a columnar front[END_REF][START_REF] Jackson | On the origin of the equiaxed zone in castings[END_REF], which is believed to be at the origin of the central equiaxed core region in casting processes. Fragmentation occurs when dendrite branches are detached from the main primary trunks, as well as from the secondary or higher order arms. Fragmentation is favoured by the dendrite coarsening process but also by the initiation of local remelting due to the pile-up of solute within the partially solid-liquid sample region (mushy zone) [START_REF] Ruvalcaba | In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy[END_REF][START_REF] Liotti | A synchrotron X-ray radiography study of dendrite fragmentation induced by a pulsed electromagnetic field in an Al-15Cu alloy[END_REF]. The additional effect of gravity force (buoyancy force or natural convection) [START_REF] Salloum-Abou-Jaoude | Characterization of Motion of Dendrite Fragment by X-Ray Radiography on Earth and under Microgravity Environment[END_REF] or the impact of thermoelectro-magnetic force [START_REF] Wang | Thermoelectric magnetic force acting on the solid during directional solidification under a static magnetic field[END_REF] cannot be excluded in fragmentation phenomena. If these fragments are transported ahead of the columnar front by buoyancy forces or convection and if they can continue to grow, an equiaxed grains microstructure is formed that can stop the advancing columnar front. The competition of equiaxed grains with the advancing solidification front is a complex topic, which involves mechanical blocking as well as thermal and solutal interaction. J.D. Hunt proposed a geometrical criterion to explain this transition in terms of mechanical blocking [START_REF] Hunt | Steady state columnar and equiaxed growth of dendrites and eutectic[END_REF], but it is now recognized that the dominant mechanism for the CET is the solutal blocking , due to solute rejection from growing equiaxed and columnar dendrites [START_REF] Martorano | Predicting the columnar-to-equiaxed transition for a distribution of nucleation undercoolings[END_REF].

CET as well as the final microstructure features are strongly affected by gravity induced phenomena namely, sedimentation effect and coupling between flow and the solid-liquid interface. On Earth (1g), the melt flow plays a critical role in mass and heat transfer, and consequently affects the final microstructure, as well as the CET and the eutectic formation [START_REF] Zhong | Effect of interdendritic thermoelectric magnetic convection on evolution of tertiary dendrite during directional solidification[END_REF][START_REF] Tewari | Effect of magnetic field on the microstructure and macrosegregation in directionally solidified Pb-Sn alloys[END_REF][START_REF] Bogno | Analysis by synchrotron X-ray radiography of convection effects on the dynamic evolution of the solid-liquid interface and on solute distribution during the initial transient of solidification[END_REF][START_REF] Abou-Khalil | Influence of gravity level on Columnar-to-Equiaxed Transition during directional solidification of Al-20 wt.% Cu alloys[END_REF]. Microgravity experimentation is a perfect tool to deepen the study of CET, as it provides unique benchmark data by suppressing most of the gravity-driven phenomena during solidification, such as natural convection, as well as sedimentation or buoyancy. In microgravity environment, we can expect to achieve nearly diffusive conditions for transport [START_REF] Jansen | Solidification under microgravity[END_REF][START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Akamatsu | In situ observation of solidification patterns in diffusive conditions[END_REF]. Nevertheless, even in gravity-free conditions, fluid flow, generated by the sample shrinkage induced by the difference of solid and liquid densities, still exists [START_REF] Conti | Advection flow effects in the growth of a free dendrite[END_REF][START_REF] Murphy | Direct observation of spatially isothermal equiaxed solidification of an Al-Cu alloy in microgravity on board the MASER 13 sounding rocket[END_REF]. Another cause of fluid flow in gravity-free conditions is Marangoni convection [START_REF] Langbein | Fluid statics and dynamics in microgravity[END_REF][START_REF] Young | The motion of bubbles in a vertical temperature gradient[END_REF], due to the presence of free interfaces like liquid-gas surfaces. This contribution to convection is often negligible in directional solidification for which the only gas-liquid surface is at the top of the sample.

Porosities are considered as serious and common defects formed during solidification [START_REF] Blair | Predicting the occurrence and effects of defects in castings[END_REF], which result in a significant degradation of the mechanical properties and act as the origin of crack initiation because of stress concentration [START_REF] Campbell | Chapter 9 -Structure, defects and properties of the finished casting[END_REF][START_REF] Ludwig | Influence of Oxide Additions on the Porosity Development and Mechanical Properties of A356 Aluminium Alloy Castings[END_REF][START_REF] Pequet | Modeling of microporosity, macroporosity, and pipe-shrinkage formation during the solidification of alloys using a mushyzone refinement method: Applications to aluminum alloys[END_REF]. Up to now, the formation of porosity has been considered by numerous investigations, but, as a matter of fact, mostly focusing solely on the pore formation mechanism [START_REF] Wei | Nucleation of bubbles on a solidification front-experiment and analysis[END_REF][START_REF] Ha | Analysis and prevention of dent defects formed during strip casting of twin-induced plasticity steels[END_REF][START_REF] Bianchi | Gas segregation during solidification processes[END_REF][START_REF] Ramirez | Effect of welding variables and solidification substructure on weld metal porosity[END_REF][START_REF] Wang | Influence of Directionally Solidified Process on Porosity in the Cross-Section Transitions of Ni-Based Superalloy DZ417G[END_REF][START_REF] Elmquist | Shrinkage porosity and its relation to solidification structure of grey cast iron parts[END_REF][START_REF] Sigworth | Mechanisms of porosity formation during solidification: A theoretical analysis[END_REF]. It is generally accepted that the residual gases, which are mainly hydrogen, dissolve and accumulate at the solidification front, since gas solubility is often much less in the solid than in the liquid. As a result, bubbles readily nucleate to form porosities, not only at the crystal or dendrite interface, but also on the sample surface [START_REF] Bianchi | Gas segregation during solidification processes[END_REF][START_REF] Ramirez | Effect of welding variables and solidification substructure on weld metal porosity[END_REF][START_REF] Wilcox | Gas bubble nucleation during crystallization[END_REF]. Also reactions between the melt and the crucible walls at elevated temperatures may play a role.

Except their impact on crack initiation, the porosities also affect the solidified microstructure by triggering the deformation of the dendritic network [START_REF] Meidani | Multiphase-Field Modeling of Micropore Formation in Metallic Alloys[END_REF][START_REF] Murphy | In situ X-ray observations of gas porosity interactions with dendritic microstructures during solidification of Al-based alloys[END_REF] and creating Marangoni liquid flow around the pore region during the solidification [START_REF] O'shaughnessy | Numerical Investigation of Bubble-induced Marangoni Convection[END_REF][START_REF] Arlabosse | Numerical investigation of thermocapillary flow around a bubble[END_REF][START_REF] O'shaughnessy | Numerical Investigation of Bubble Induced Marangoni Convection: Some Aspects of Bubble Geometry[END_REF][START_REF] Miniewicz | Marangoni effect visualized in two-dimensions Optical tweezers for gas bubbles[END_REF]. Indeed, it has been reported that the mushy alloy could deform under external loads [START_REF] Meylan | Dilatancy and rheology at 0-60% solid during equiaxed solidification[END_REF][START_REF] Gourlay | Granular deformation mechanisms in semi-solid alloys[END_REF][START_REF] Veldman | Dendrite coherency of Al-Si-Cu alloys[END_REF]. The deformation mechanism changes with the increase of the solid fraction [START_REF] Meylan | Dilatancy and rheology at 0-60% solid during equiaxed solidification[END_REF]. The spongy deformation of the mushy zone during the solidification is also reported by Lesoult et al., together with the effect on segregation [START_REF] Lesoult | Segregation during solidification with spongy deformation of the mushy zone[END_REF]. Additionally, primary crystal deformation and flow of solute-enriched liquid towards the shear deformation plane have also been observed [START_REF] Sumitomo | The shear behaviour of partially solidified Al-Si-Cu alloys[END_REF][START_REF] Gourlay | Shear mechanisms at 0-50% solid during equiaxed dendritic solidification of an AZ91 magnesium alloy[END_REF]. Therefore, combined with the Marangoni effect, the liquid flow triggered by porosity formation should also be considered for the microstructure transformation. However, these porosity impacts on the microstructure features and CET have rarely been mentioned in experimental or numerical investigations before, to the best of our knowledge.

Our investigations are conducted by means of directional solidification in microgravity conditions. The quantitative analyses of the eutectic fraction and the dendritic structure, as well as the CET are provided and correlated with the solidification parameters. In addition, the influence of a pore at the surface of a sample on the microstructure formation has been analyzed in detail.

Experimental

Experiments

The Material Science Laboratory (MSL) was made available by the European Space Agency (ESA) on board the International Space Station (ISS), providing a platform for microgravity solidification investigations. In the framework of the CETSOL (Columnar to Equiaxed Transition in SOLidification processes) ESA MAP (Microgravity Applications Promotion programme) project [START_REF] Zimmermann | Investigation of columnar-to-equiaxed transition in solidification processing of AlSi alloys in microgravity -The CETSOL project[END_REF][START_REF] Gandin | Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL): a project of the European Space Agency (ESA) -Microgravity Applications Promotion (MAP) programme[END_REF][START_REF] Billia | Columnar-Equiaxed Transition in Solidification Processing: The ESA-MAP CETSOL Project[END_REF], thirteen microgravity experiments have been conducted in two batches named Batch 1 and Batch 2a. The six samples in Batch 1 were carried out using the Low Gradient Furnace (LGF), which have presented and discussed in detail in a previous study [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The samples in Batch 2a, which are the objects in this paper, were carried out using the Solidification and Quenching Furnace (SQF), which is also a directional solidification furnace but allows higher temperature gradient and cooling rate compared to the LGF.

The full SQF and the sample cartridge assembly (SCA) are schematized in Fig. 1. It consists of a hot and a cold zone separated by a so-called adiabatic zone. The cold zone is realized by a Liquid Metal Ring (LMR) to achieve a high temperature gradient (up to 8 K/mm in this SCA) and to allow for quenching. The hot zone is equipped with four heaters H1-H4, which can be adjusted independently to achieve the required temperature gradient along the sample axis. Solidification of the alloy is performed by the controlled displacement of the SQF along the fixed SCA at a chosen velocity, which can be varied during the experiment. The metallic alloy sample (8 mm in diameter and 245 mm in length) is mounted inside a protective Al 2 O 3 tube crucible together with Shapal plugs at both bottom and top ends. Twelve N-type (Nicrosil-Nisil) thermocouples (TC1-TC12), spaced by 20 mm, are located in four machined external axial grooves at the outer surface of the crucible to measure the temperature profile (purple dots in Fig. 1).

In the present work, a comparative study of two samples, labelled B2F1 and B2F2, from Batch 2a is conducted. The solidification conditions of the two selected experiments are the same in terms of temperature gradient and furnace pulling velocity profiles to allow direct comparison (see Table 1). The two major differences between the two samples are: (i) B2F1 is a grain refined alloy sample (Al -7wt% Si + 0.5 wt% of master alloy AlTi5B) whereas B2F2 is a non-refined Al -7 wt.% Si alloy and (ii) a rotating magnetic field (RMF) is applied during the second stage of the experiment B2F2 to analyze the impact of moderate forced fluid flow on CET in µg environment. The Al -7 wt.% Si alloys were provided by Hydro Aluminum Rolled Products GmbH, 0.5 wt% of master alloy AlTi5B was added to the sample for refinement. The rotating magnetic field (RMF) applied during stage II for B2F2 has a frequency f = 57 Hz and a magnetic field strength of B = 0.5 mT. The solidification profile consists of three successive stages:

-Stage I: The initial applied temperature gradient (G) is 4 K/mm. Solidification is initiated by the furnace motion for 20 mm at a low pulling rate (0.02 mm/s) in order to form a columnar microstructure in stationary conditions.

-Stage II: The second stage is triggered by a sudden pulling rate jump from 0.02 mm/s to 0.2 mm/s. This new pulling rate is applied for a movement of 50 mm together with a cooling down of the hot zone with 0.133 K/s. The simultaneous increase of the growth velocity and decrease of the temperature gradient are expected to induce the CET. Additionally for B2F2, a rotating magnetic field (RMF)

with frequency f = 57 Hz and magnetic field strength of B = 0.5 mT was applied to induce a moderate forced melt flow in the sample.

-Stage III: The quenching of the sample induced by a fast furnace pulling is applied to complete the solidification. During this final quenching stage, the temperature gradient and cooling rates are no longer controlled, but the temperature profile is still recorded.

Microstructure characterization

The characterization methods in the present study are similar with our previous study [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. For metallographic analysis, the solidified samples are cut into parts of 30 mm in lengths. The sketches of the cutting positions of the two samples are shown in Fig. 2 together with images of the processed samples. Then, longitudinal sections cut close to the centerline are mechanically polished with diamond suspension to reveal the dendritic structures by optical microscopy (OM).

First, the optical microscopy images of longitudinal sections L2 and L3 for B2F1 and sections L1 and L2 for B2F2 are segmented into binary images using a threshold to separate the two phases: the dendrite phase appears in white, while the eutectic is black. Based on those binary images, the eutectic percentage (E%) maps and the profiles of E% along the solidification direction, i.e. along the main cylindrical sample axis are determined using a box-averaging method, as well as dendrite arm spacing (DAS) using the linear-intercept method [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The box size for E% maps is 0.5 mm in length, in the direction of the sample central line axis, and 0.4 mm in width. The box size for both E% and DAS profiles is 0.5 mm in length and equal to the sample diameter in width. For one data point of DAS, 1000 lines are generated in random orientation in each box for accurate results. It is worth mentioning here that the DAS measured with this method is not equal to the primary or secondary dendrite arm spacing but a measurement of the average characteristic scale of the dendritic network [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Han | Microstructure Prediction in A356 Alloy Castings[END_REF].

In a second phase of analysis, Electron backscattered diffraction (EBSD) of sections L2 and L3 for B2F1 was performed to analyze the grain structure more accurately.

The EBSD measurement was carried out only for B2F1 sample, because it appears clearly that there is no CET during B2F2 experiment. The EBSD measurement was performed for the entire longitudinal sections with a scanning step of 8 μm. Based on EBSD data, the grain contours were reconstructed by separating neighboring grains with their misorientation being larger than 5°. The grain equivalent diameter (ED, defined as the diameter of a circle of equivalent grain area) and elongation factor (EF, defined as the ratio of the length of the major axis to the minor axis of a grain), are calculated from the EBSD measurements. The grains cut by the section boundaries were excluded in the calculation.

Results

Analysis of the processing parameters

The recorded cooling curves for both B2F1 and B2F2 are shown in Fig. 3a andb, with identification of the three stages delimited by the starting time points of the furnace movement of every stage. From Fig. 3a andb, it can be seen that the thermal histories recorded are very similar for B2F1 and B2F2, indicating that the addition of grain refiner (GR) and the application of RMF in stage II have negligible influence on the recorded temperatures and thus on the heat flow for the present experiments.

The negligible impact of GR on thermal distribution in the sample is expected, due to the very small amount of GR. On the contrary, the absence of RMF effect is more surprising, taken into account that a liquid flow is likely driven by the RMF [START_REF] Hainke | Numerical study on directional solidification of AlSi alloys with rotating magnetic fields under microgravity conditions[END_REF]. This issue is discussed later in the paper.

To evaluate the relationship between the microstructure and the actual thermal conditions, the temperature gradient G (Fig. 3c) and the velocity of the liquidus isotherm v (Fig. 3d) are calculated based on the temperature profiles of the thermocouples. The procedure to produce these data is similar to the method described by Ch-A. Gandin [START_REF] Gandin | Experimental Study of the Transition from Constrained to Unconstrained Growth during Directional Solidification[END_REF] and in our previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The temperature gradient ahead of the liquidus isotherm is calculated at the time when the liquidus isotherm (T L = 891 K for Al -7 wt.%) reaches a thermocouple. Moreover, by following the liquidus isotherm position in time, the velocity of the liquidus isotherm can be deduced. Using linear interpolation, the average temperature gradient and velocity of the liquidus isotherm are calculated every 10 mm. Additionally, the average values of the calculated temperature gradient and velocity of the liquidus isotherm for each stage, as well as the corresponding standard deviation are shown in Table 2. The curves in Fig. 3c andd show that the processing conditions of the two samples are very similar during the whole experiment and confirm the negligible influence of the GR and RMF on the thermal growth conditions during the solidification process. The eutectic is formed due to the solute rejection and accumulation in the interdendritic regions. For both samples, some quite large eutectic regions due to competition between randomly oriented columnar grains, up to 3 mm in length, are found in stage I and as a consequence, inhomogeneous distribution of the eutectic percentage is observed. At the transition from stage I to stage II, a similar change is found for both experiments. First, the size of the eutectic zones significantly decreases just after the pulling rate jump and the eutectic distribution is much more uniform, with a lower average eutectic percentage. This is a consequence of the finer dendritic microstructure during the stage II and has been discussed in more details in our previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF].

To better understand the evolution of the microstructure during the solidification, the analysis of the average eutectic percentage (E%) and dendrite arm spacing (DAS) along the sample axis has been done for both samples. In this calculation, the regions affected by the surface pores are excluded in a first step. The averaged longitudinal profiles of the E% and DAS along the solidification direction are shown in Fig. 5. Furthermore, the corresponding stage-averaged E% and DAS in each stage are also gathered in Table 2. As shown in the profiles in Fig. 5, both the E% and DAS continuously decrease from stage I to stage II in both B2F1 and B2F2 as well as in average according to the increase of the liquidus isotherm v (Table 2). The differences of the average E% and DAS values between B2F1 and B2F2 are minor in both stages I and II.

Analysis of the columnar to equiaxed transition (CET)

Considering the grain structure observed by OM, sample B2F1 presents a CET from stage I to stage II. The CET is progressive and not sharp and its limits are defined according to previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The highest position of the columnar grains issued from the initial dendrites zone defines the CET inception [START_REF] Gandin | From constrained to unconstrained growth during directional solidification[END_REF], and is noted CET min in Fig. 4a1 (about 134 mm for B2F1). The uncertainty on this position is due to the cut of a transverse section between sections L2 and L3. As concerns B2F2, no CET is observed along the entire sample.

In our previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF], it has been shown that CET min is not sufficient to define CET, especially when very elongated equiaxed grains are observed above this position. A second limit for complete CET, CET max , is defined using grain morphological characterisation. Indeed, according to Hunt and Biscuola [START_REF] Hunt | Steady state columnar and equiaxed growth of dendrites and eutectic[END_REF][START_REF] Biscuola | Mechanical Blocking Mechanism for the Columnar to Equiaxed Transition[END_REF], the complete transition from columnar to equiaxed grain growth can be characterized by the change of grain size and morphology. A critical value of the elongation factor (EF) of the grains was deduced from the mechanical-blocking fraction of the equiaxed grains to quantitatively define the CET. Grains are considered to be fully equiaxed when the EF value is below 2 and this gives the criterion to determine CET max position here. The grain structure is quantitatively analyzed using EBSD measurement data of sections L2 and L3. The constructed grain contour maps are displayed in Fig. 6a. Such a region with elongated equiaxed grains defines a progressive CET in B2F1 [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Steinbach | Deterministic nucleation model for equiaxed solidification[END_REF].

Analysis of the microstructure and CET at the level of surface pores

It can be seen from Fig. 5, that irregular E% is clearly detected at the position around 147 mm in stage II for both B2F1 and B2F2, which is exactly the location of the surface pores as shown in Fig. 4 (a1 and b1). Concerning the DAS profiles, a moderate slow-down of the DAS decrease is observed at the same position. In order to focus on the effect of the pore, the microstructure and the longitudinal profiles of the E% and DAS around this position are compared in Fig. 7.

It can be seen in Fig. 7 (a andb) that the lengths of the pore regions, about 6 mm for B2F1 and 10 mm for B2F2, are comparable to the sample diameter and to the length of the mushy zone calculated in section 3.1. Additionally, no obvious distortions of the primary dendrites are observed around the pore region for both samples.

It can be seen in Fig. 7c that the value of the E% is stable in the region far below the pore for B2F1 (below z = 143 mm). Then, it starts to decrease at about 1 mm below the pore start position. The E% stabilizes again until it starts to increase below the pore end, up to about 1 mm behind the pore end. After that, the E% returns to a constant value. The variation of the E% for B2F2 is significantly different from B2F1.

The E% firstly decreases with a low slope in the region far from the pore and then starts to decrease with a higher slope at a position close to the start of the pore.

When the pore is about to end, the E% increases until the end of the pore and then starts again to decrease, extending to the region far from the pore.

The variation of the DAS shows a continuously decreasing trend but with different decrease slopes around the surface pore region for both B2F1 and B2F2. The decrease slope of DAS around the pore region is slightly lower than in the region far from the pore, both before or after the pore region. Especially, the DAS value is almost stable around the pore region for B2F1.

Furthermore, on top of the effect on E% and DAS profiles around the pores, an irregular increase of EF is observed for B2F1 at this position (Fig. 6b). This indicates that the presence of the pore enhances the elongated growth of the grains in this region, indicated by the red circle shown in Fig. 6a.

Discussion

Effect of the grain refinement and RMF on the microstructure

As shown in Fig. 3 and Table 2, the GR and RMF have no significant effects on the detected thermal field. According to the simulation results within the CETSOL project [START_REF] Zimmermann | Estimation of the influence of RMF on the melt flow and segregation in CETSOL2#2 Flight experiment[END_REF], when a RMF is applied, a forced melt flow is created during stage II. The maximum value of the flow velocity along the sample axis direction is 0.003 mm/s in the center of the sample. The maximum flow velocity is approaching zero at the sample periphery. This forced liquid flow is the main flow during the solidification under the microgravity condition in this experiment. The maximum velocity of liquid flow along the direction along the sample axis is much smaller than the pulling velocity at the level of the solid-liquid interface, which is about 0.20 mm/s in stage II.

Accordingly, we can expect that the measured thermal field is not affected by the RMF induced forced flow.

The grain refinement of Al -7 wt.% alloy in B2F1 leads to a CET after the velocity jump, whereas only the development of a finer columnar dendritic microstructure is observed in the non-refined alloy (B2F2) with the same pulling velocity jump and other parameters comparable. As already mentioned above, the higher pulling velocity enhances the constitutional undercooling ahead of the dendrite tips. When the nucleation undercooling of the particles is attained, large amount of equiaxed grains randomly nucleate ahead of the columnar front and start to grow. This definitely blocks the growth of the columnar grains, leading to the inception of the CET, at CET min . Subsequent grain nucleation efficiently stops the growth of alreadynucleated neighboring equiaxed grains to continue the CET. In B2F1, progressive CET characterized by elongated equiaxed grains is observed. This is mostly attributed to the relatively high temperature gradient in this experiment. Indeed, nucleation only takes place in a shorter undercooled region due to the high temperature gradient, preventing the copious and simultaneous nucleation which is necessary to impede the growth of the new nucleated grains. Only a few layers of newly-nucleated grains may form in this case and grains get elongated during the growth.

There is no CET in the non-refined alloy B2F2. Indeed, there are no refining particles in such alloy to achieve the nucleation. Actually, CET in non-refined alloys was reported by many authors and ascribed to the dendrite fragmentation [START_REF] Abou-Khalil | Influence of gravity level on Columnar-to-Equiaxed Transition during directional solidification of Al-20 wt.% Cu alloys[END_REF][START_REF] Sturz | Investigations on columnar-to-equiaxed transition in binary al alloys with and without grain refiners[END_REF][START_REF] Jung | Columnar to equiaxed transition in nonrefined Al-based alloys during directional solidification in microgravity and on earth[END_REF] with the requirement that the dendrite fragments are transported in front of the columnar dendrites [START_REF] Abou-Khalil | Influence of gravity level on Columnar-to-Equiaxed Transition during directional solidification of Al-20 wt.% Cu alloys[END_REF][START_REF] Akamatsu | In situ observation of solidification patterns in diffusive conditions[END_REF][START_REF] Hellawell | Dendrite fragmentation and the effects of fluid flow in castings[END_REF]. The application of RMF in B2F2 is expected to enhance the dendrite fragmentation and to transport the fragments to the columnar front to trigger CET. A quite large liquid flow velocity along the sample axis, i.e. along the solidification direction, is necessary. However, according to the simulation results, even though the maximum azimuthal flow velocity is about 0.2 mm/s in the melt, it is reduced when approaching the solid-liquid interface or mushy zone.

Therefore, it might not be sufficient to produce enough fragments. Moreover, the maximum value of the flow velocity induced by the RMF along the sample axis direction is much lower than the growth velocity of the dendrites. Even if the liquid flow velocity would be higher than expected, the maximum flow velocity region would only be confined in the center of the sample, which implies that not enough fragments could be transported to the columnar front. Taking into account these two restrictions, it seems reasonable to assume that CET cannot be triggered by the RMF in stage II for B2F2.

Effect of the surface pore on the microstructure and CET

As described above, the irregular decrease of E% and change of decrease slope of DAS are observed in the vicinity of the surface pore regions for both samples (Fig. 7).

These effects are more apparent in B2F1 sample, concomitantly with the highly elongated grain growth and a sharp increase of EF for B2F1 (Fig. 6). These observations suggest that the surface pores affect the solidification process and consequently the microstructure and the CET.

From the post-mortem analysis of the samples, it is difficult to determine the nucleation position. However, if the surface pore forms in or close to the mushy zone (MZ), a deformation of the dendritic network would be expected. As reported by Lesoult et al. [START_REF] Lesoult | Segregation during solidification with spongy deformation of the mushy zone[END_REF], the MZ can deform as spongy, with squeezing out of the liquid from the interdendritic region. This MZ deformation becomes more difficult with the increase of the solid fraction up to the coherency value [START_REF] Meylan | Dilatancy and rheology at 0-60% solid during equiaxed solidification[END_REF][START_REF] Gourlay | Granular deformation mechanisms in semi-solid alloys[END_REF]. The solid fraction of the dendrite coherency point is very low, about 10% for large, highly branched dendrite arrays [START_REF] Veldman | Dendrite coherency of Al-Si-Cu alloys[END_REF][START_REF] Arnberg | Determination of dendritic coherency in solidifying melts by rheological measurements[END_REF]. For this reason, and considering the large size of the pores and no observation of the dendrite distortion around the pores, the pore most likely forms in the region at temperatures higher than the eutectic isotherm (T E ). In addition, assuming that the porosities form due to the dissolved residual gases, or gases from reactions with the crucible walls, accumulating at the solidification front, it is most likely that the nucleation position of the surface pore is close to the dendrite front, as illustrated in Fig. 8, which was also supported by the study of Atwood et al. [START_REF] Atwood | A three-phase model of hydrogen pore formation during the equiaxed dendritic solidification of aluminum-silicon alloys[END_REF].

During the formation and expansion of the surface pore, the liquid in the vicinity of the pore region can be pushed toward the center of the sample, due to the movement of the pore/liquid interface, as shown in Fig. 8a in the 2D longitudinal section. Liquid is pushed away from the pore and streamlines radiate from the pore as indicated by the black arrows outside the solid circle line.

At the left side of the pore, the liquid flows toward the eutectic front, oppositely to the solidification direction. At the far side of the pore (bottom of Fig. 8a), the flow has the same direction as the solidification direction. In the region close to the pore centerline, the liquid flow is initially perpendicular to the solidification direction, and then gradually turns parallel to the solidification direction (middle of Fig. 8a). At the right part of the pore, the liquid flows along the solidification direction.

For B2F1, in the region between the eutectic isotherm and the pore center line, a hotter and Si-poorer liquid is most likely squeezed in, replacing the original liquid and resulting in an increase of the temperature and a decrease of the Si content of the liquid in this region. In this case, the growth of the as-existing dendrites is promoted, yielding the decrease of the E% and reducing the DAS decrease rate in this region as shown in Fig. 7c. In the region close to the pore center, the squeezed liquid generates a constant but much lower E% value. In the region at the right of the pore center, the fluid flow coming from the mushy zone can induce a decrease of the temperature and an increase of the Si content of the liquid, leading to the increase of the E% and rising of the DAS decrease rate in this region, i.e. range of 1 mm before and after the pore end as shown in Fig. 7c.

This liquid flow influences not only the E% and DAS of the sample, but also the Elongated Factor (EF) of the grain structures. The liquid flow influence on the EF is mainly concentrated in opposite region of the pore in the sample diameter direction (bottom region in Fig. 8a). As discussed, the liquid flow in this region is parallel to the growth direction (from left to right in this figure), with the direction close to the sample axis. During the solidification, the solute rejection at the advancing solid-liquid interface leads to the build-up of a solute boundary layer [START_REF] Bogno | Analysis by synchrotron X-ray radiography of convection effects on the dynamic evolution of the solid-liquid interface and on solute distribution during the initial transient of solidification[END_REF]. The liquid flow resulting from the pore carries away the Si released by the dendritic network and lowers the Si concentration ahead of the tip. Concomitantly, the new nucleated grains are also carried away from the tip. Therefore, the dendrites grow faster and they do not face competition with new nucleated grains. So, the dendrites are prone to grow along the liquid flow direction and to be more elongated, leading to the grain structures observed at the far side of the pore as indicated by the red circle in Fig. 6a.

In B2F2 sample, similar liquid flow as shown in Fig. 8a is triggered, but with less effect because of the mixing effect of the rotating magnetic field [START_REF] Zimmermann | Estimation of the influence of RMF on the melt flow and segregation in CETSOL2#2 Flight experiment[END_REF] and the lower pore curvature compared with B2F1 sample. For the left part of the pore region, the simultaneous increase of the temperature and decrease of solute composition due to the squeeze-in of the liquid lead to the decrease of the E% and slowdown of the DAS decrease rate similarly to the case of B2F1. As concerns the region close to the pore center, the liquid squeeze-out results in the continuous decrease of the E% and generates the gradually decreasing E% pattern. However, all these effects are weaker when farther away from the pore.

For the sake of completeness, we have also estimated the strength of the Marangoni flow, which could play a role in this experiment. Indeed, a temperature gradient along the gas/liquid interface may lead to a melt flow from the hot region toward the cold region of the bubble [START_REF] O'shaughnessy | Numerical Investigation of Bubble-induced Marangoni Convection[END_REF][START_REF] Arlabosse | Numerical investigation of thermocapillary flow around a bubble[END_REF][START_REF] Napolitano | Marangoni convection in one-liquid and 2liquid floating zones[END_REF]. Although it is difficult to get the exact characteristic of this flow, the maximum value of the Marangoni velocity can be estimated to be much larger than the growth velocity [START_REF] Arlabosse | Numerical investigation of thermocapillary flow around a bubble[END_REF][START_REF] Napolitano | Marangoni convection in one-liquid and 2liquid floating zones[END_REF][START_REF] Avduyevsky | Some physical aspects of unidirectional crystallization in microgravity[END_REF], in a very thin layer clinging close to the pore/liquid interface. However, to obtain quantitative values, some specific simulations should be performed. The Marangoni liquid flow pattern in the region of the surface pore can be speculated as shown in Fig. 8b, from the hot to the cold liquid region [START_REF] Arlabosse | Numerical investigation of thermocapillary flow around a bubble[END_REF][START_REF] Barsi | Effects of void-induced convection on interface morphology and segregation during low-g solidification[END_REF]. Due to Marangoni effect, hotter and less Si concentration liquid is pushed towards the mushy zone as in the case of flow due to pore expansion, as shown in Fig. 8 so that these two kinds of liquid flow in the region around the pore contribute in a same way.

The discussion in section 4.4 indicates that the extra liquid flow, both induced by the pore formation and expansion and also by the Marangoni flow, may change the solidification conditions and consequently affect the microstructure significantly in the pore region. But the dominant factor cannot be determined in this study, based on metallurgical analysis. Some more quantitative analyses, especially for the formation and expansion of the pore, and also simulation about the impact of the pore are needed in the future.

Conclusion

Two microgravity experiments were carried out in the Material Science Laboratory on board the International Space Station using the Solidification and Quenching

Furnace. The influence of the GR, RMF and in particular, of surface pores on the microstructure and CET were studied.

(1) The increase of the furnace pulling velocity from stage I to stage II leads to finer dendrite structure in both refined and non-refined samples. Consequently, a smaller average eutectic percentage and more homogeneous eutectic phase distribution are obtained in stage II. The addition of the GR or RMF show very minor influence on the thermal conditions, and accordingly on the eutectic phase percentage and dendrite arm spacing.

(2) The CET is obtained only for refined alloys but with a progressive mode. Indeed, the rather high temperature gradient decreases the amount of continuous nucleation of grains ahead of the solidification front, leading to an elongated equiaxed grain zone and postponing the complete CET. The application of the RMF fails to trigger the CET in B2F2, because the moderate liquid flow velocity resulting from the RMF is not enough to enhance the fragmentation and to take the fragments away from the deep mushy zone to the solidification front.

(3) The formation of the surface pore influences the microstructure by inducing a liquid flow by the pore expansion and Marangoni effect. The E% decreases and the decrease of DAS induced by the increasing growth velocity in stage II is slowed down at the level of the pore in both samples. Moreover, the extra liquid flow due to the pore strengthens the growth of the dendrite grains along the liquid flow direction, especially on the far side of the defect and, as a result, postpones the CET in B2F1.

For 1 K 3 . 2 .

 132 the stage I, only one value can be obtained from the TCs for the temperature gradient (G = 4.4 K/mm for B2F1 and G = 4.5 K/mm for B2F2) and the isotherm velocity (0.02 mm/s for both samples). These values correspond to the applied nominal values. After the application of new solidification conditions (during stage II), the temperature gradient increases up to G = 5.2 K/mm for B2F1 (resp. G = 5./mm for B2F2), while the growth velocity increases to a maximum value of v = 0.14 mm/s for B2F1 (resp. v = 0.15 mm/s for B2F2). The discrepancy between those values and the applied nominal ones might be attributed to a change of the solidliquid interface position relatively to the LMR (Fig.1) when increasing the furnace pulling rate. Finally, the quenching of the sample induces a sharp increase of both the growth velocity and the temperature gradient.Additionally, the average values of G and v during stage I and stage II are given in Table2together with the corresponding standard deviations. As shown in Table2, the mean values of the calculated G and v are about 4.4/4.5 K/mm and 0.02 mm/s in stage I, and then increase to about 4.8 K/mm and 0.11 mm/s in stage II for both samples. The length of the mushy zone (L MZ ) during the solidification process, defined as the distance between the liquidus and eutectic isotherms was also calculated. The average values of the L MZ , for both B2F1 and B2F2 samples, are estimated at about 9.5 mm and 8.0 mm in stage I and II, respectively. Analysis of the microstructure Microstructures in longitudinal sections are shown in Fig.4 (a1 and b1). The bottom position in both figures corresponds to the start of the solidification process. The blank region between stage I and stage II is due to the material loss during the sample cut and the transverse section preparation. The furnace pulling velocities corresponding to the different solidification stages are marked out at the left side, based on the transition positions between successive stages determined in Fig.3c and d. The eutectic percentage (E%) distribution maps of the same regions are also shown in Fig.4(a2 and b2).In stage I of both samples, a columnar structure is obtained growing from the initial partially melted mushy region. From stage I to stage II, the microstructure significantly changes for B2F1 and B2F2. In B2F1, large columnar dendrites are observed in stage I, whereas equiaxed grains and much finer dendrite grains are obtained in stage II. The starting position of the equiaxed grains microstructure is about 134 mm, as shown by the red dash line in Fig.4a1. For B2F2, the dendrite structure remains columnar in both stages I and II, but with a transition from a coarse to a finer dendrite microstructure. Nevertheless, surface pores are visible around 147 mm in stage II in both samples, which can also be seen from the images of the two samples as shown in Fig.2.

  Fig.6b shows the average equivalent diameter (ED) and elongation factor (EF) along longitudinal sections. Each data point is obtained by the average value of 15 grains sharing closest gravity centre position. The average position of these grains is taken as the representative position of the corresponding average ED and EF.The results show that, both the ED and the EF of B2F1 sharply decrease from stage I to stage II. When excluding (not shown here) the region around the surface pore position (147 mm), the ED of all the grains and the EF of most of the grains remain at a low value after the transition from stage I to stage II. The EF mainly stays close but slightly above 2 after CET min up to 156 mm, which is close to the transition position from stage II to stage III. Based on the characterization of the ED and the criterion on the EF, the grain structure after CET min is equiaxed but elongated between 134 mm and 156 mm, and is fully equiaxed after 156 mm, which is the transition position from stage II to stage III, referred to as CET max , as shown in Fig.6b.

Fig. 1 .

 1 Fig. 1. Sketch of a CETSOL Batch 2a cartridge MSL-SCA integrated in the MSL-SQF

Figure 1 Fig. 2 .

 12 Figure 1

Figure 2 Fig. 3 .

 23 Figure 2

Figure 3 Fig. 4 .

 34 Figure 3

Figure 4 Fig. 5 .

 45 Figure 4

Figure 5 Fig. 6 .

 56 Figure 5

Figure 6 Fig. 7 .

 67 Figure 6

Figure 7 Fig. 8 .

 78 Figure 7

Figure 8

 8 Figure 8

Table 1 :

 1 Control parameters for the two selected samples solidified under microgravity: v n is the furnace pulling velocity and z n the furnace movement with v n in phase n. Sample with notation grain refiner contains 0.5 wt% of master alloy AlTi5B for grain refinement.

				Stage I		Stage II		Stage III
	Sample	Alloy	Initial G, K/mm	v 1 , mm/s	z 1 , mm	v 2 , mm/s	z 2 , mm	R, K/s	RMF
	B2F1	Al -7wt% Si + grain refiner	4	0.02	20	0.2	50 0.133 No Quenching
	B2F2	Al -7wt% Si	4	0.02	20	0.2	50 0.133 Yes Quenching

Table 2 :

 2

	I	4.4	0.1	0.02	0.003	57.5	55
	B2F1
	II	4.8	0.3	0.11	0.043	46.2	33
	I	4.5	0.1	0.02	0.003	55.2	57
	B2F2
	II	4.8	0.3	0.11	0.047	47.6	35

The calculated average temperature gradient G and the corresponding standard deviation  <G>, the calculated average velocity v at the liquidus isotherm and the corresponding standard deviation  <V> , the averaged eutectic percentage (E%) and dendrite arm spacing (DAS). Sample Stage <G>, K/mm  <G> , K/mm <v>, mm/s  <V> , mm/s E, % DAS, µm

Acknowledgement

This research work is supported by the European Space Agency under the CETSOL (Columnar to Equiaxed SOLidification processes) ESA MAP project, the French National Space Agency (CNES) and the German BMWi/DLR under FKZ 50WM1443.

The authors acknowledge Hydro Aluminium Rolled Products GmbH for providing the alloys used in this paper. We would like to thank F. Băltărețu, O. Budenkova and Y.

Fautrelle from SIMAP/EPM Laboratory in Grenoble for numerical modelling of melt flow induced by the rotating magnetic field.


Romain Lehnebach
email: lehnebach.romain@hotmail.fr

Stephane Corn
email: stephane.corn@mines-ales.fr

Arnaud Regazzi
email: arnaud.regazzi@mines-ales.fr

Jacques Beauchêne
email: jacques.beauchene@cirad.fr

Bruno Clair
email: bruno.clair@cnrs.fr

Julie Bossu
email: juliebossu@hotmail.fr

Interlocked grain and density patterns in Bagassa guianensis: changes with ontogeny and mechanical consequences for trees

Keywords: Interlocked grain, Basic density, Wood radial patterns, Tree architecture, Growth strategy, Biomechanics

Key message

Interlocked grain and basic density increase from pith to bark in Bagassa guianensis and greatly improve trunk torsional stiffness and wood tenacity in the radial plane.

Introduction

In the context of dense tropical forest, trees species develop a large diversity of growth strategies to reach a dominant position within the canopy while guaranteeing trunk load For this purpose, wood traits involved in tree biomechanics are continuously adjusted throughout plant development to meet the specific needs created by their growth strategy and environmental conditions [START_REF] Lachenbruch | Radial variation in wood structure and function in woody plants, and hypotheses for its occurrence[END_REF]. Wood tissues keep the memory of tree life history and inte-grate the overall successive modifications that occurred from seedling to mature stages. Such variations result in a specific radial gradient of wood properties within the trunk [START_REF] Lachenbruch | Radial variation in wood structure and function in woody plants, and hypotheses for its occurrence[END_REF]) which enables post interpretation of tree development and highlights the species' overall growth strategies.

Among the wood properties giving access to comprehensive elements to investigate tree growth, different authors reported the interest of studying the basic density (BD) radial patterns in trees. Indeed, several studies have demonstrated that BD can vary considerably within the tree [START_REF] Yao | Influence of growth rate on specific gravity and other selected properties of loblolly pine[END_REF][START_REF] Whitmore | Wood density variation in Costa Rican balsa[END_REF][START_REF] Fimbel | Wood specific gravity variability in Ceiba pentandra[END_REF][START_REF] Woodcock | Wood specific gravity and its radial variations: the many ways to make a tree[END_REF][START_REF] Williamson | Radial wood allocation in Schizolobium parahyba[END_REF][START_REF] Morel | Basic wood density variations of Parkia velutina Benoist, a long-lived heliophilic tree of Neotropical rainforest[END_REF])-especially under the tropics [START_REF] Wiemann | Radial gradients in the specific gravity of wood in some tropical and temperate trees[END_REF][START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF] where such gradients are even more pronounced-and depends to a great extent on growth conditions [START_REF] Mclean | The decreasing radial wood stiffness pattern of some tropical trees growing in the primary forest is reversed and increases when they are grown in a plantation[END_REF]. At the inter-specific level, several studies evidenced a negative relationship between growth rate and BD [START_REF] Arets | Responses of tree populations and forest composition to selective logging in Guyana[END_REF][START_REF] Muller-Landau | Interspecific and inter-site variation in wood specific gravity of tropical trees[END_REF][START_REF] Falster | Tradeoffs between height growth rate, stem persistence and maximum height among plant species in a post-fire succession[END_REF][START_REF] King | Tree growth is related to light interception and wood density in two mixed dipterocarp forests of Malaysia[END_REF]. At the intra-individual level, this relation is also relevant: the production of low-density wood (i.e. low construction cost) during early development stages enables rapid height growth. When a tree reaches the canopy, height growth levels off and the production of higher density wood starts (i.e. high construction cost). The later production of high-density wood is seen as a biomechanical adaptation to resist wind-induced stresses [START_REF] Woodcock | Wood specific gravity and its radial variations: the many ways to make a tree[END_REF]. High BD is hypothesised to be responsible for the balance between mechanics and metabolic cost by achieving high mechanical strength with a reduced volume of wood, which, in turn limits respiration cost compared to low-density wood [START_REF] Larjavaara | Rethinking the value of high wood density[END_REF]. Finally, BD is also considered as a critical parameter in tree buckling [START_REF] Mclean | The decreasing radial wood stiffness pattern of some tropical trees growing in the primary forest is reversed and increases when they are grown in a plantation[END_REF][START_REF] Fournier | Integrative biomechanics for tree ecology: beyond wood density and strength[END_REF]. For the reasons here mentioned, BD radial gradient is considered to be a key parameter in controlling tree growth throughout its development and have also been shown to have biomechanical advantages.

An alternative way to optimise tree mechanical design at constant construction costs is modifying the organisation of the fibre network. For example, the angle of the cellulose microfibrils inside the wood fibre cell wall can vary through ontogeny from high value in juvenile wood (enabling compliant fibres), to low value in mature wood (associated with stiffer fibres) [START_REF] Li | Transcriptome profiling of Pinus Radiata juvenile wood with contrasting stiffness identifies putative candidate genes involved in microfibril orientation and cell wall mechanics[END_REF]. Such modifications may modify trunk flexibility to adapt to environmental conditions [START_REF] Barnett | Cellulose microfibril angle in the cell wall of wood fibres[END_REF]. Another mechanism produces a similar effect in the tree at a larger scale: the orientation of wood fibres can be aligned along the trunk axis or inclined. In the second case, there may be small variations in the grain angle in the radial plane (wavy grain), increasing grain angle in the tangential plane from pith to bark (spiral grain), or periodic changes in the orientation of the fibres from the Z to S helix in the tangential plane (interlocked grain) (IG) [START_REF] Hejnowicz | The common basis of wood grain figures is the systematically changing orientation of cambial fusiform cells[END_REF][START_REF] Krawczyszyn | Cyclical cell length changes in wood in relation to storied structure and interlocked grain[END_REF][START_REF] Włoch | Does intrusive growth of fusiform initials really contribute to circumferential growth of vascular cambium?[END_REF][START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF]. The latter conformation is observable in numerous temperate and tropical tree species [START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF][START_REF] Thinley | Spiral and interlocking grain in Eucalyptus dunnii[END_REF][START_REF] Slater | Interlocking wood grain patterns provide improved wood strength properties in forks of hazel (Corylus avellana L.)[END_REF][START_REF] Özden | Fracture properties of green wood formed within the forks of hazel (Corylus avellana L.)[END_REF]. According to Kribs (1950, cited by Hernandez and[START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF]), 75% of the 258 tropical trees they analysed showed IG. [START_REF] Arostegui | Recopilacion y analisis de studios tecnologicos de maderas peruanas[END_REF] also found that 33 out of 60 Peruvian tropical hardwoods they tested had this feature. Nevertheless, only a few studies suggested a potential functional benefit of IG. [START_REF] Webb | Variation of interlocked grain in sweetgum (Liquidambar styracifula)[END_REF], supported by [START_REF] Détienne | Contrefil à rythme annuel dans les faro Daniellia sp[END_REF], proposed that IG could improve water distribution from the roots to the crown. However, as the inclination of fibres is known to reduce wood stiffness at local scale [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF][START_REF] Brémaud | Identification of anisotropic vibrational properties of padauk wood with interlocked grain[END_REF]), a possible role in mechanics was not taken into consideration.

The objective of the present study is to explore the mechanical role of IG in the whole stem in relation with variations in BD in Bagassa guianensis Aubl., a high growth rate and long life Amazonian species, known to develop both pronounced IG and large BD radial gradients [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF][START_REF] Bossu | New Insights on wood dimensional stability influenced by secondary metabolites: the case of a fast-growing tropical species Bagassa guianensis Aubl[END_REF]). This species is a suitable model to investigate the simultaneous effects of variations in IG and BD on trunk biomechanics. Moreover, its specific development ensuring both competitive growth and trunk longevity is an unusual and effective strategy that merits investigation.

The specific aims of the present work are (1) to characterise the changes in BD and IG in relation with the tree development stages in B. guianensis, [START_REF] Morel | Basic wood density variations of Parkia velutina Benoist, a long-lived heliophilic tree of Neotropical rainforest[END_REF] to measure the effects of such variations on local mechanical properties, and (3) to incorporate the results in a biomechanical model including both changes in fibre orientation and density to determine their combined effect on the elastic properties of the living trunk. Finally, the contribution of BD and IG variations to the species growth strategy and trunk biomechanics are discussed.

Materials and methods

Tree description

Eleven Bagassa guianensis Aubl. (commercially known as Tatajuba) trees were sampled near the Paracou experimental station (5°19′N; 52°56′W) in French Guiana, on the edge of a secondary forest along a trail opened almost 30 years ago. Specimens were chosen to cover a homogeneous distribution of diameters at breast height (DBH), ranging from 13 to 55 cm. Tree volumes were estimated by measuring successive stem segments, where one segment comprises the bole and the other the crown. Each segment was characterised by its length and both initial and final diameter. Volumes of the trunk and crown axis were calculated by adding the volumes of each segment considering them as successive cones. Like in most tree species, the crown of B. guianensis develops through a reiterative process duplicating the architectural unit (i.e. the fundamental set of axis categories inherent to the species) [START_REF] Barthelemy | Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny[END_REF]. Thus, the architectural stage of development (ASD) indicator [START_REF] Nicolini | Dating branch growth units in a tropical tree using morphological and anatomical markers: the case of Parkia velutina Benoist (Mimosoïdeae)[END_REF]) was used, allowing the characterisation of the ontogenetic stage through structural features.

ASD 1 is defined by the presence of sequential branches born by the trunk and the absence of a fork; ASD 2 by the presence of both a young fork and sequential branches; ASD 3 represents a mature stage in which the fork is well established with ramified branches and the bole is pruned.

Sampling

Radial planks around 30 cm in length were sampled at breast height on each tree, taking care to avoid defects and singularities. Planks were first planed to a thickness of 3 cm, marked to respect the same orientation during cutting and then sawed into three parts, respectively, 2, 15 and 3 cm in length. The top 2 cm part was planed to a thickness of 2 cm and split with a knife every 0.5 cm along the radial axis. The split samples were used to measure BD and grain angle. The 15 cm middle part was planned to a thickness of 1 cm, air dried and sawed every 0.2 cm along the radial axis to produce the elongated samples for modulus of elasticity (MOE) and microfibril angle measurements. Finally, the 3 cm bottom part was sawed at 4 cm intervals along the radial axis and air dried to produce samples for the measurement of tenacity and interlocked grain.

Wood properties

Basic density (BD)

Basic density was measured on small samples (R × T × L = 0.5 × 2 × 2 cm 3 ). BD was defined as the ratio between dry mass (M0%) and saturated volume (VSat): BD = M0%/VSat [START_REF] Kollmann | Principles of wood science and technology[END_REF]. Sample volume (VSat) was calculated using the Archimedes principle on a Sartorius CP224S balance (precision: 0.2 mg) as described in [START_REF] Bossu | New Insights on wood dimensional stability influenced by secondary metabolites: the case of a fast-growing tropical species Bagassa guianensis Aubl[END_REF]. Dry mass was measured on the same balance after 3 days of stabilisation at 103 °C.

Interlocked grain (IG)

Interlocked grain was assessed using two different methods. Each of these methods performed the measurements on the same samples as those scaled to fit to BD and tenacity analysis. On the BD samples, grain angle deviation in relation to the trunk was evaluated with a goniometer by visual assessment on the tangential-longitudinal plane of each sample. From the photographs of split tenacity samples, an interlocked grain index (IGIndex) was calculated with ImageJ software [START_REF] Schneider | Nih image to imagej: 25 years of image analysis[END_REF] to characterise each sample, given by the ratio of the surface deviation due to inclined grain to the radial dimension (respectively, S and R) (Fig. 1c,d). For more clarity, when referring to the variations in the grain angle from pith to bark and maximum amplitudes from negative to positive angles in IG samples, the terms "IG variations" and "IG amplitudes" respectively, are used hereafter.

Microfibril angle

Microfibril angles were measured using X-ray diffraction (XRD) on a 4-circle diffractometer (Gemini, Agilent Technologies, Santa Clara, USA) following the procedure described in [START_REF] Montero | Relationship between wood elastic strain under bending and cellulose crystal strain[END_REF]. The average microfibril angle of each sample was estimated using the ''improved Cave's method'' [START_REF] Yamamoto | A model of anisotropic swelling and shrinking process of wood[END_REF] which is more accurate when the angle is below 25°, which is the case for B. guianensis.

Wood mechanical properties

Modulus of elasticity (MOE)

MOE was measured on the elongated air-dry samples (R × T × L = 0.2 × 1 × 15 cm 3 ) after stabilisation in controlled conditions (23 ± 1 °C and 60 ± 2% RH). Tests were performed using non-contact forced vibrations of free-free bars. Specimens were supported by loose thin silk threads located at the nodes of the 1st mode of flexural vibrations. Vibrations were applied with an electro-magnet facing a thin iron plate glued to one end of the specimen and the displacement was measured at a vibration anti-node by a non-contact laser sensor. A frequency scan allowed detection of the first resonant frequency (in bending) from which the modulus of elasticity (MOE) was deduced according to the Euler-Bernouilli equation [START_REF] Brémaud | Characterisation and categorisation of the diversity in viscoelastic vibrational properties between 98 wood types[END_REF].

Tenacity

The purpose of this test is to reproduce cracks that might occur at the place of the fork when the two main axes of the crown undergo opposite charge loadings. To this end, the following experimental setup was designed in order to study if interlocked grain can limit the risk of trunk splitting at the place of the fork. In the 3 cm bottom part of radial planks, successive samples were produced from bark to bark along the radial direction (R × T × L = 4 × 3 × 3 cm 3 ), as illustrated in Fig. 1a. The specific length of 4 cm in the R direction has been chosen in order to include a complete period of interlocked grain (the pattern being reproducible every 4 cm). Tenacity was measured on each of the samples, characterized by varying IG amplitudes, following the method described in [START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF]. The cubic samples were first glued on their RL faces to wood handles (Peltogyne sp., density = 0.87) (R × T × L = 10 × 4 × 3 cm 3 ) using polyurethane glue and under press loading during 24 h. Then, a 1.6 cm pre-slit was sawn in the middle of the sample, as illustrated in Fig. 1b. The fracture energy, i.e. the energy necessary to split the sample in the TL fracture plan (Ashby et al. 1985) 1 , was measured using a strength piloted 3-points flexion test. On a sub-sample, tenacity tests were performed in both saturated and air-dry conditions and revealed that moisture content had a minor impact on tenacity measurement (mean difference of -2.04% from green to air-dry conditions; non-significant according to Kruskal-Wallis test: pv = 0.954).

Modelling of trunk biomechanical behavior

Description of the model trunks

The influences of BD variations, IG variations and their combined effects on tree biomechanical behaviour were evaluated through finite element analysis. Six different trunks were modelled as cylinders with a radius R = 20 cm and a unitary length l = 1 m. Each trunk was characterised by three different radial patterns of fibre orientation (axial grain, spiral grain or IG) and two radial patterns of BD (constant BD or BD = f(r)). BD = constant A constant value BDeq was chosen to correspond to an equivalent construction cost like in the variable BD model. BDeq was thus calculated by integrating the BD variation along the radius in order to have an identical mass of the trunk model, leading to the following formula:

BDeq = 2 R 2 ∫ R 0 r ⋅ BD(r)
dr , where r is the current radial coordinate in the cylindrical coordinates system of the trunk model.

Axial grain the grain angle was considered as null. Spiral grain the grain angle (GA) (in degrees) was set as proportional to the radial coordinate r (in cm) such that GA = r (with GA = 0-20° when r = 0 to 20 cm).

Interlocked grain GA = f(r) is a sinusoidal function adjusted based on the average radial variations obtained from the analysis of the wood traits (see "Results").

Mechanical simulations

Finite element simulations were performed using Comsol Multiphysics ® software to compare the axial compressive, transverse flexural and axial torsional stiffness of each model. The material behaviour was assumed to be elastic and transversely isotropic along the fibre direction. The modulus of elasticity (MOE) in the fibres direction was set according to the experimental results discussed below. The other elastic coefficients such as transverse modulus, shear modulus and Poisson's ratios were adjusted according to the experimental relations proposed by [START_REF] Guitard | Mécanique du matériau bois et composites[END_REF]. The variations of grain angle within the trunk led to an orthotropic finite element model. Three load cases were simulated for each model: compression, flexion and torsion. A unitary displacement or rotation was applied in the corresponding direction. The reaction force was evaluated for each load case, thus making it possible to estimate the apparent stiffnesses of the structure. All the calculations involved static analyses and small strain assumption. A mesh convergence study was carried out, which led to a 200,300 elements model.

Results

Radial variations in wood properties in the trunk

Basic density (BD)

In all individuals, BD was characterised by a major increase from pith to bark, ranging from 0.27 to 0.89 g cm -3 . Figure 2a shows the BD radial profiles at breast height of the 11 trunks showing a radial increase in BD in all the trees. A rupture point in the average BD increasing curve is graphically observable in all individuals with a diameter greater than 20 cm (Fig. 2b). Thus, BD was better predicted by a model accommodating a changing slope at a radial position of 9.48 cm (AICc = -1325.9, R 2 = 0.83) than by a simple linear model (AICc = -1109.23, R 2 = 0.73, pv < 0.001).

During the first phase, BD increased with a slope of 4.03 g cm -3 m -1 , whereas in the second phase (passing the rupture point), the slope was reduced to 0.92 g cm -3 m -1 . The change in BD is then accurately described as two linear functions of radial position (r), as follows:

Interlocked grain (IG)

Each of the 11 trees had interlocked grain (IG), i.e. fibre orientation periodically changed from Z to S helix with diameter, with a similar radial pattern: from pith to bark, grain angle variations followed a sinusoidal trend (Fig. 3a). Samples showed very low IG amplitudes near the pith, increasing toward the bark. Figure 3b shows the IG variations observed in the biggest tree in the sample, ranging from -31° to 23°. Smaller trees showed a narrower range but with a similar trend. For all trees, the parameters of the sinusoidal variations varied identically from pith to bark. The half-period did not vary significantly along the radial profile, i.e. it remained constant irrespective to the number of the halfperiod (pv = 0.251) (See Supplementary Material 1A), despite observable higher variability near the pith. For all individuals, grain angle periods were characterised by an average half period of 1.75 cm. Maximum IG amplitudes (absolute successive peak amplitudes, where each peak corresponds to a half period) increased linearly with radial (1) 1. for r ≤ 9.48 cm∶ BD = 0.34 + 0.04 × |r| 2. for r ≥ 9.48 cm∶ BD = 0.64 + 0.01 × |r| position (R 2 = 0.54; pv < 2.2e-16) (cf. Supplementary Material 1B). Therefore, grain angle (GA) can be approximated by a sinusoidal law of linearly increasing magnitude according to radial position r , which can be expressed as: GA= r × sin(Half period × r) , with Half period = 1.75 cm.

Microfibril angle

In contrast to IG, microfibril angle remained constant in mature wood, with little variation around 11.6° as mean value (variance of 3.6° obtained with 548 measured samples). Microfibril angle was higher (20°) in the first 5 cm around the pith.

Effect of BD and GA on wood mechanical properties

Modulus of elasticity (MOE)

The relationship between MOE and BD is not linear over the radial profile because of the influence of grain angle deviation on longitudinal MOE values. In Fig. 4a, it can be observed that when samples have only straight fibres (-5° ≤ GA ≤ 5°) (filled circles in Fig. 4a), MOE is maximum and increases linearly with BD. For this subsampling, the relationship between MOE and BD can be expressed as following:

Further from the pith, for BD higher than 0.65 g cm -3 , fibres are more and more out of the axis of the sample (largest circles in Fig. 4a) and MOE decreases drastically. Here, MOE variability is high, ranging from 6 to 27 GPa. The effect of high grain angle on MOE is illustrated on Fig. 4b: this representation highlights the negative relationship existing between MOE and GA in samples with BD > 0.65 g cm -3 (MOE = 19.9 -0.44 × |GA| , R 2 = 0.46, pv < 0.001) (Fig. 4b).

Tenacity

When evaluating the effect of density on fracture energy, a significant relationship (pv < 0.001) was detected. However, this relation was mainly due to a leverage effect caused by two outlier values with BD lower than 0.55 g cm -3 . After removal of these observations, the relationship was no longer significant (R 2 = 0.06, pv = 0.043). On the contrary, fracture energy measurements in tenacity tests revealed a positive relationship with IGindex (R 2 = 0.42, pv < 0.001) (Fig. 5). IG amplitudes increase with distance from the pith and the number of periods is equal on each side of the pith. The half-period is defined as the time lapse between two successive peaks

Modelling of the influence of BD and IG radial variations on trunk mechanical properties

Despite some disparities between individuals, reproducible patterns of BD, MOE and IG were observed. Such observations enable the construction of reliable trunk models to study the mechanical properties of the B. guianensis tree.

The radial patterns measured for BD and IG were implemented in the settings of the different model trunks and compared to the "axial grain and constant BD" model as a reference. The value used for the equivalent constant basic density for identical tree construction costs (BDeq) according to Eq. 1 was computed as 0.736. The equivalent MOE (MOEeq), calculated from BDeq according to Eq. 2, was computed as 19.17 GPa. The different parameters used for numerical modelling are summarised in Table 1. Figure 6 illustrates the geometry of the simulated trunk corresponding to the IG model.

Table 2 summarises the results of numerical simulations performed to assess the effect on trunk stiffness of variations in BD, grain angle (axial grain, spiral grain and IG) and their combination.

In the case of axial grain, as expected, BD variations had no effect on compressive stiffness but increased flexural stiffness by 3% and torsional stiffness by 5%.

For constant BD, compared to the axial model, spiral grain caused a strong increase in torsional stiffness (+ 25%) but a decrease in compressive and flexural stiffnesses (-34 and -24%, respectively). IG led to an even more significant improvement of torsional stiffness (+ 33%). But, unlike spiral grain, IG only slightly decreased compressive and flexural stiffnesses (-6 and -2%, respectively). For both constant and variable BD, IG always led to greater torsional stiffness than spiral grain. Grain angle influenced trunk stiffnesses more significantly than variations in BD. Indeed, the results of the combination of variable BD and variable grain angle were quite similar to those obtained by combining constant BD and variable grain angle. The models implemented show that a trunk with variable BD and IG ensures the highest torsional stiffness (140%) while maintaining most of the compressive and flexural stiffnesses.

Tree development and ontogenetic changes in BD and GA

Figure 7 illustrates the development of B. guianensis with regard to the above-mentioned variations in wood properties, through the example of the different radial patterns observed in the biggest individual tree in our sample. The description of tree structure according to ASDs indicates that crown development has not yet started in trees with DBH lower than 20 cm. At this stage, the tree structure is characterised by an orthotropic trunk bearing several sequential branches (Fig. 7a,ASD1) and tree height growth results from the elongation of the trunk (Fig. 7b). The wood produced by trees in the ASD1 stage is of relatively high microfibril angle (around 20°) and low BD, which respectively, decreases and Relative values are presented (where "constant BD and axial grain" model is the reference, i.e. stands as the 100% value) increases dramatically with an increase in radial distance (Fig. 7c,d), whereas variations in the grain angle remain low (Fig. 7e).

Conspicuous forks, i.e. the morphological marker of crown development, were observed in trees with DBH higher than 20 cm. At this stage, tree height growth results from the height growth of the first reiterated branches departing from the fork (Fig. 7b), whereas a few sequential branches remain present along the trunk (Fig. 7a,ASD2). Interestingly, the lowest value of DBH at breast height recorded in ASD2 trees (20 cm) corresponded approximately to the radial distance value (9.48 cm) after which the rate of increase of BD slowed down (Fig. 7c). In parallel, the decrease in microfibril angle also slowed down and stabilised around a radial position of 15 cm (Fig. 7d). During ASD2 development, we also observed the onset of the increase in IG amplitude (Fig. 7e).

The final stage (ASD3) is reached when the DBH increases until around 30 cm (Fig. 7b). In ASD3, the sequential branches have been shed, tree height continues to increase but the crown also expands laterally due to the development of new forks and new reiterated branches (Caraglio, unpublished) and measurements made in this study. b Tree height (circles) and crown stem volume (triangles) as a function of stem radius, regression were fitted over DBH, and graphed over the stem radius (i.e. DBH/2) for convenience with the other graphs. c-e represent, respectively, the radial variations of basic density (BD), microfibril angle (MFA) and Grain angle within the largest tree sampled. f Illustration of the typical "Y"-like crown shape of Bagassa guianensis trees, built around two long opposite axes (Fig. 7a). Crown expansion is highlighted by a drastic increase in crown stem volume after 15 cm of stem radius (Fig. 7b). Both the number of reiterated branches and crown stem volume are highly correlated (Pearson correlation, ρ = 0.99, pv < 0.001) and can be considered as indicators of crown expansion. At this stage, the mature crown of B. guianensis organized around two main opposite axes and funnel shaped, i.e. the crown is widest at the top, and the fork is approximately located at mid-height of the tree, as illustrated in Fig. 7f. During this final stage of development, microfibril angle shows almost no variation and remains constant at a low value (around 12°). Finally, in ASD3 trees, IG amplitude continues to increase (Fig. 7e) as well as BD, which increases at the same rate as trees in ASD2 stage (Fig. 7c).

Discussion

Variations in basic density (BD) within the tree

Strong radial variations in BD were observed in all the trees. Ontogenetical variations in BD have already been reported in numerous tropical tree species [START_REF] Wiemann | Radial gradients in the specific gravity of wood in some tropical and temperate trees[END_REF][START_REF] Omolodun | Wood quality in Hildegardia barteri (Mast.) Kossern-an African tropical pioneer species[END_REF][START_REF] Hernandez | Natural variation in wood properties of Alnus acuminata H.B.K. grown in Colombia[END_REF][START_REF] Parolin | Radial gradients in wood specific gravity in trees of central Amazonian floodplains[END_REF][START_REF] Woodcock | Wood specific gravity and its radial variations: the many ways to make a tree[END_REF][START_REF] Hietz | Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests[END_REF][START_REF] Morel | Qualité et usages du bois de cinq espèces forestières adaptées à la plantation à vocation de bois d'oeuvre et testées en Guyane française[END_REF]). An interspecific survey of radial changes in BD in the neotropics highlighted a negative relationship between radial in BD and BD at the centre of the stem [START_REF] Hietz | Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests[END_REF], in other words, species producing low density wood in the juvenile phase exhibit high radial variations. This result agrees with [START_REF] Wiemann | Extreme radial changes in wood specific gravity in some tropical pioneers[END_REF] who reported an extreme increase in radial BD in tropical pioneers, ranging between 0.7 and 1.0 g cm -3 m -1 and very low BD at the stem centre (0.09-0.17 g cm -3 ). More recently, [START_REF] Morel | Basic wood density variations of Parkia velutina Benoist, a long-lived heliophilic tree of Neotropical rainforest[END_REF] documented a radial increase of 1.1 g cm -3 m -1 in BD, with a BD of 0.3 g cm -3 at the stem centre of Parkia velutina, an emergent heliophilic species in French Guiana. These generally acknowledged extreme radial changes of BD are however lower than the change observed in B. guianensis. Indeed, here we report an overall gradient of 1.8 g cm -3 m -1 in B. guianensis, a very high gradient for a species producing a BD of 0.35 g cm -3 in the juvenile phase.

Such a strong positive gradient of BD from pith to bark is commonly considered as a distinctive feature of fast-growing species (i.e. heliophilic species) [START_REF] Woodcock | Wood specific gravity and its radial variations: the many ways to make a tree[END_REF][START_REF] Hietz | Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests[END_REF][START_REF] Osazuwa-Peters | Radial variation in wood specific gravity of tropical tree species differing in growthmortality strategies[END_REF].

Indeed, the low-density wood observed near the pith (i.e. low construction cost) might enable a rapid increase in diameter at a given construction cost, thereby enabling rapid height growth in the juvenile stage. Later, when the tree reaches the canopy and the crown develops, tree self-weight and crown surface exposed to wind increase the mechanical stresses applied to the stem. This change in the mechanical environment is accompanied by a decreasing microfibril angle and an increasing BD. As reported by [START_REF] Williamson | Age-dependent radial increases in wood specific gravity of tropical pioneers in Costa Rica[END_REF], the radial increase in BD concentrates denser wood at greater distance from the neutral axis of the stem, resulting in a stronger stem made of a limited amount of material.

Indeed, our numerical simulations implying radial BD variation suggest a slight improvement in trunk stiffness in flexion and torsion compared to constant BD. Despite these observations, considering mechanical performance only, it is more efficient to build a large low-density stem than a denser smaller stem with the same investment cost [START_REF] Larjavaara | Rethinking the value of high wood density[END_REF]. The occurrence of high BD can also be interpreted in terms of trunk maintenance. [START_REF] Larjavaara | Rethinking the value of high wood density[END_REF] proposed that the main advantage of high BD is the reduction in the surface area of the trunk, thereby reducing trunk maintenance and bark construction costs. For a given construction cost, BD radial increases represent an efficient strategy which enables a trade-off between height growth and radial growth during early stages of development, while limiting maintenance costs and guaranteeing trunk stiffness at the mature stage.

Variations in interlocked grain (IG) within the tree

We observed IG formation in all B. guianensis individuals. This characteristic is observed in numerous other tropical trees [START_REF] Kribs | Commercial foreign woods on the American market, a manual to their structure, identification, uses and distribution[END_REF] and has already been reported for several Amazonian tree species including Goupia glabra, Dipteryx odorata, Tabebuia sp. or Aspidosperma sp. [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF]. Like BD, in Bagassa guinanensis, IG is outstanding in its amplitude and is reproducible from tree to tree. [START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF] and [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF], respectively, reported maximum angle deviations of 16.4° in Amburana cearensis and 15.8° in Goupia glabra, whereas we measured almost the double in B. guianensis, with a maximum angle deviation of 31°. It should also be noted that extreme values depend on the size of the sampled trees and could be even larger in older trees. Another remarkable characteristic of the radial pattern of IG in B. guianensis is that variations in fibre orientation from pith to bark fit a sinusoidal model of constant parameters, despite the fact that the trees differed in their age and in the site where they were sampled. It is interesting to note that, in an eccentric disk sampled below the fork of one tree, we observed the same number of IG periods on each side of the pith despite different distances from pith to bark. This observation suggests that the control of the grain angle in IG in the cambium is more or less synchronous all around the disk.

IG has been mainly studied as it affects technological properties of wood products [START_REF] Weddell | Influence of interlocked grain on the bending strength of timber, with particular reference to utile and greenheart[END_REF][START_REF] Marsoem | The effect of interlocked grain on the mechanical properties of white meranti[END_REF][START_REF] Hernandez | Effects of wood density and interlocked grain on the shear strength of three Amazonian tropical hardwoods[END_REF]. Regarding the effect of IG on properties at sample scale, we observed an average loss of 0.44 GPa of MOE (2.2% decrease per degree) for an increase of 1° in GA. This result is consistent with the values reported by [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF] and [START_REF] Brémaud | Identification of anisotropic vibrational properties of padauk wood with interlocked grain[END_REF] respectively). It is important here to remind that consequences of IG at the tree scale are difficultly accessible. Indeed, large grain angle variations are only observable in mature tree having dimensions not adapted for experiments. Therefore, we observed properties at sample scale but these ex situ measurements must be analysed with caution, since they do not fully figure the behaviour at higher scale.

We used a numerical approach to simulate the impact of IG variation on tree biomechanics. The results of our model revealed that IG greatly improves torsional stiffness (increase of + 35% compared to axial grain, in the case of variable BD). In the literature, much concern has been given to analyse bending forces by wind on trees, using different shape models, but little attention has been to another type of mechanical loading like torsion. In the case of B. guianensis, its specific fibre network is an adaptive solution that intends to withstand the torsion induced by its particular architecture. Indeed, while symmetric trees are most likely subjected to bending loads when exposed to wind, asymmetric crowns induce different wind sail areas between the two sides of the stem. The latter result in strong twisting forces at the place of the fork that have been shown to be positively correlated to the degree of asymmetry and slenderness of the crown, subjecting the stem to a significant torque [START_REF] Skatter | Spiral grain-an adaptation of trees to withstand stem breakage caused by wind-induced torsion[END_REF][START_REF] Skatter | The cause of the prevalent directions of the spiral grain patterns in conifers[END_REF][START_REF] Skatter | Tree breakage from torsional wind loading due to crown asymmetry[END_REF]. In B. guianensis, the crown is particularly slender and asymmetric. When reaching its mature form, it is characterised by a particular funnel morphology, exhibiting two main parts ("Y"-like shape, see Fig. 7f). This form stands out among the usual hemispheric crown shape observed in most tropical trees, like Dicorynia guianensis [START_REF] Lehnebach | Heartwood/sapwood profile and the tradeoff between trunk and crown increment in a natural forest: the case study of a tropical tree (Dicorynia guianensis Amsh., Fabaceae)[END_REF] and Parkia velutina [START_REF] Morel | Basic wood density variations of Parkia velutina Benoist, a long-lived heliophilic tree of Neotropical rainforest[END_REF]). This final shape is even more asymmetric than the models proposed by [START_REF] Skatter | Spiral grain-an adaptation of trees to withstand stem breakage caused by wind-induced torsion[END_REF] and over exposes the crown to wind, transferring strong torsional loading from the fork to the trunk. This loading situation requires a strong torsional stiffness in addition to a sufficient bending stiffness.

As an answer to the torsion loading, Skatter and Kucera (1998) proposed that grain angle variations could be a growth strategy to ensure survival of the trees. The authors suggest that spiral grain in the outermost layers of mature pine trees could be a strategy to withstand torque. Here, our results show that IG is also an efficient adaptive mechanism improving trees´ torsional stiffness but, contrary to spiral grain, it also enable maintaining most of the compressive and flexural stiffness.

Our results also highlight an improvement in wood tenacity with an increase in IG. The positive correlation between IGindex and the fracture energy shows that IG improves resistance to stem opening in the TL fracture plane. This specific orientation of fibres limits the risks of cracks at the place of the fork (in this study, we did not measure higher IG below the fork, but IG was very high all along the trunk; data not shown). This hypothesis was also proposed by [START_REF] Cabrolier | Is interlocked grain an adaptive trait for tropical tree species in rainforest[END_REF], who suggested that IG would be a good way for adult trees to prevent the risk of stem splitting. This risk is particularly high at the fork, as both main branches exert a bending moment on opposite sides of the stem. Recent work on Corylus avellana L. showed that there was more interlocked wood grain formation close to branch insertions than in other sampling locations, leading to a higher specific fracture energy in the central apex zone (Özden et al. 2017). [START_REF] Slater | Interlocking wood grain patterns provide improved wood strength properties in forks of hazel (Corylus avellana L.)[END_REF] also reported that tortuous wood grain patterns as interlocked grain can supply additional strength to junctions in hazel trees. The authors even suggested that "this mechanical arrangement should inform anatomical studies of junctions and may inform the design of manufactured Y-shaped components made from fibrous composite materials". It is likely that a similar mechanism is at work in B. guianensis.

These elements support the hypothesis that in B. guianensis, IG may represent an optimal organisation of fibres to limit splitting risks at the central axis of the fork on the one hand, and stem torsional failure risks on the other hand. Such a strategy is even more optimal since, theoretically, the establishment of IG does not generate additional construction cost for the tree. Our results showed that IG could provide structural support, resistance to torsion and prevent the occurrence of cracks without producing more wood, i.e. is a good strategy with low carbon cost to offset the risks taken by the species to quickly reach the canopy and to resist wind forces when the crown is developed. Many other tropical species present combined variations of BD and IG within the tree. Comparing such patterns with the species growth strategies could provide interesting new information. Based on the example of B. guianensis, we look forward to more studies to evaluate if IG can be proposed as a functional trait for future studies in biomechanics and ecology.

Author contribution statement JB: sampling, measurements, analysis, discussion of the results and writing of the manuscript. RL: part of the sampling, analysis, discussion of the results and writing of the manuscript. SC: analysis and discussion of the results. AR: analysis and discussion of the results. JB: design of the research project and discussion of the results. BC: design of the research project, discussion of the results and writing of the manuscript.

Fig. 1

 1 Fig. 1 Tenacity test and measurement of the interlocked grain index (IGIndex) on split samples. a cutting of the radial bar; b experimental set up for fracture energy testing; c observation of the crack propaga-

Fig. 2 a

 2 Fig. 2 a Variations in basic density (BD) with distance from the pith. Each individual is represented by one colour. b Variations in basic density (BD) with absolute distance from the pith. The solid line cor-

( 2 )BFig. 3 a

 23 Fig. 3 a Observation of IG variations in a radial disk sampled at breast height in mature tree of Bagassa guianensis. b Corresponding IG variations over the radial profile measured with goniometer.IG amplitudes increase with distance from the pith and the number of periods is equal on each side of the pith. The half-period is defined as the time lapse between two successive peaks

Fig. 4 aFig. 5

 45 Fig. 4 a Variations of the modulus of elasticity (MOE) with basic density (BD). The diameter of the points or circles corresponds to a specific range of GA accordingly to the chart in the top-left corner. The filled circles correspond to samples characterised by the lowest

Fig. 6 Table 2

 62 Fig. 6 Example of a finite element model trunk in the case of an interlocked grain pattern. Colour levels indicate grain angles ranging from -20° (green) to + 20° (red)

Fig. 7

 7 Fig. 7 Tree development and radial changes in wood properties along the different Architectural Stages of Development (ASD). a Schematic drawings of Bagassa guianensis development based on previous observations of tree architecture (Caraglio, unpublished) and measurements made in this study. b Tree height (circles) and crown stem volume (triangles) as a function of stem radius, regression were

Table 1

 1 Details of the models of IG and BD variations within the radial profile used for finite element modelling

	Radial patterns	Corresponding model used for
		numerical analysis
	Axial grain	Grain angle = 0°S
	piral grain	Grain angle = r
	Interlocked grain	Grain angle = r ⋅ sin(1.75 × r)
	Variable BD	If r ≤ 9.48, BD = 0.34 + 0.04 ×r If r ≥ 9.48, BD = 0.64 + 0.01 ×r
		MOE = 2.86 + 22.158 × BD
	Constant BD	BDeq = 0.736
		MOEeq = 19.17 GPa

In this work, the fracture system will always be characterised by two letters accordingly toAshby et al. (1985): here for example the first letter "tangential" indicating the direction normal to the crack plane and the second letter "longitudinal" referring to the direction of crack propagation.

Acknowledgements

The authors thank Eric Nicolini (CIRAD-AMAP) and Onoefé NGwete (CIRAD-ECOFOG) for their help in tree identification and field work and Yves Caraglio (CIRAD-AMAP) to share his knowledge on Bagassa guianensis architecture. This research project was financially supported by the Labex CEBA (ANR-10-LABX-25-01), CNRS-INSIS and European Social Fund awards.

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflict of interest.