D Mohr

G Gary

High strain rate tensile testing using a split Hopkinson pressure bar apparatus

A specially-designed specimen is proposed to investigate the tensile response of metals at high strain rates. This specimen may be directly used in a conventional split Hopkinson pressure bar system, thereby overcoming difficulties related to the gripping of traditional tensile specimens in dynamic testing. The specimen geometry has been optimized using finite element analysis. The dominant stress state in the specimen gage section is transverse plane strain. Explicit expressions are given to obtain the equivalent uniaxial stress-strain curve from the force and displacement measurements at the specimen boundaries. Quasi-static experiments have been carried and compared with standard uniaxial tensile tests to evaluate the accuracy of the force-stress and displacementstrain relationships. Using this new specimen, dynamic experiments have been performed on aluminum 2024-T351 showing that strain rates in the range of 1000/s may be obtained without oscillations.

INTRODUCTION

The virtual design of engineering structures subject to impact loading requires reliable experimental data for the development and calibration of computational material models. It is common practice to make use of the split Hopkinson pressure bar (SHBP) technique to determine the dynamic behavior of materials under uniaxial compressive loading. In addition to compression testing, the split Hopkinson bar technique has been developed for the torsion testing of cylindrical specimens. Dynamic tensile tests may also be performed by the means of a split Hopkinson bar apparatus. However, due to experimental difficulties, dynamic tensile tests are not very often used to characterize the high strain rate response of engineering materials. Consequently, most existing strain-rate dependent plasticity models have been developed on the basis of experimental data for uniaxial compression and shear.

While the high strain rate deformation response of metals under tension may be estimated within reasonable accuracy based on compression or shear data, dynamic tensile tests are indispensable in characterizing the crack initiation in metals. Most challenges in designing dynamic tensile experiments are related to the gripping of the specimen. When measuring the forces and displacements by the means of bars, the tensile specimen needs to be attached to the respective ends of the so-called incident and transmitter bars. For this, specimens with threaded specimen shoulders are usually directly screwed into the bar ends. As pointed out by Nicholas [START_REF] Nicholas | Tensile testing of materials at high rates of strain[END_REF], reliable testing of threaded specimens requires the elimination of all play out of the joints; in addition, perfect alignment of a considerably short tensile specimen is needed (Harding, Wood and Campbell [START_REF] Harding | Tensile testing of materials at impact rates of strain[END_REF]). The threads inside the bar ends generate spurious wave reflections in the vicinity of the bar-specimen interface. Failure to eliminate all gaps will amplify these reflections further, ultimately making it impossible to determine the forces and displacements at the specimen boundaries.

In this paper, we propose a specimen especially designed for the tensile testing in a split Hopkinson pressure bar apparatus. In close conceptual analogy with Luong's tensile specimen for geological materials [START_REF] Luong | Tensile and shear strength of concrete and rock[END_REF], the specimen converts an incoming pressure pulse into a tensile pulse acting on the specimen gage section. One key advantage of this technique is that those tests may be performed without attaching the specimen to the bar ends. Instead, the specimen is freely positioned between the flat ends of the incident and transmitter bars. Further, a conventional split Hopkinson pressure bar apparatus may be used to generate the incoming wave, thereby avoiding difficulties related to the generation of a tensile pulse in the incident bar.

SPECIMEN

Figure 1(a) shows the front view of the proposed specimen. It is called 'M-specimen' because its shape resembles the letter 'M'. The M-specimen is designed to convert an incoming compression wave into tension within its characteristic gage sections. The section between the points F and E is predominantly under compression. Similarly, the section A-B is subject to compressive loading while the sections B-C and D-E are subject to shear and bending loading. The specimen gage sections C-D on the other hand are predominantly stretched. The key design considerations in choosing the specimen dimensions are:

(i) Limit plastic deformation to the gage section. The geometric dimensions of the specimen must be chosen such that the gage section deforms plastically throughout the experiment while the surrounding specimen structure responds in a purely elastic manner. This must hold true for large deformations and strain hardening within the gage section. (ii) Minimize bending deformation. In the context of geometrically linear elasticity theory, the bending of sections D-E and B-C would not affect the stress and strain uniformity within the specimen gage section. However, in the case of finite deformations, the bending-induced rotation of points C and D will disturb the otherwise uniform fields within the gage section.

To minimize the bending loads, the length of the sections B-C and D-E should be as small as possible. Another efficient technique is the insertion of spacer blocks in the slot between C and F, thereby preventing the bending-induced lateral (inward) motion of point C. (iii) Prevent buckling. The section A-B is subject to compressive loading and therefore prone to buckling. Its minimal length is determined by the length of the gage section, the height of the bent-sections D-E and B-C, and the displacement to fracture of the gage sections. Here, we make use of an exterior frame that prohibits the lateral (outward) motion of point A. As a result, the effective buckling length of section A-B is significantly reduced, thereby increasing its structural stability. (iv) Minimize the distance of wave travel. The maximum acceptable loading velocity is limited by the time it takes for an incoming stress wave to travel from the top to the bottom boundary of the specimen. Clearly, this duration is directly related to the distance of wave travel. It is important that the specimen is in equilibrium throughout the dynamic experiment, i.e. the duration of wave travel must be small as compared to the duration of the loading pulse. Consequently, the total distance of wave travel along the path F-E-D-C-B-A must be short. (v) Achieve transverse plane strain conditions. The stress and strain fields also depend on the specimen width (the dimension in z-direction, Fig. 1b). The stress state within the gage section is uniaxial when the specimen width is of the order of the gage section thickness. However, in view of problems related to the specimen alignment (with respect to the loading platens) and the force measurement accuracy, the chosen specimen width should be large as compared to the gage section thickness and gage length which ultimately results in transverse plane strain conditions within the gage section. In other words, the strains along the z-direction are approximately zero.

Based on these considerations, we conclude that the gage section should be as thin as possible for optimal specimen performance in terms of maximum strain rate and field uniformity within the gage section. For the present specimen, we chose a gage section thickness of 0.5mm which results in overall specimen dimensions that can still be manufactured within reasonable accuracy using a computercontrolled wire EDM. A fully three-dimensional finite element model of the specimen (Fig. 1b) has been used to assess the stress and strain field uniformity within the specimen gage section.

DETERMINATION OF THE STRESS-STRAIN CURVE

Throughout the experiment, the forces and displacements are measured at the specimen boundaries, i.e. at the top and bottom surfaces of the M-specimen. Assuming that the specimen is in equilibrium (F top = F bot ), the resulting experimental output is a single force-displacement curve F (u)w h e r e u = u top -u bot . In the following, we determine the stress-strain curve for specimens made from Levy-Mises materials. For small to moderate deformations, we assume the additive decomposition of elastic and plastic deformation at the displacement level,

u = u e + u p (1)
Moreover, it is assumed that that the elastic displacements u e depend linearly on the applied force F ,

F = Ku e (2)
where the stiffness K accounts for the elastic stiffness of the specimen and the testing device. We have the nominal stress along the gage length, yy ,

yy (t) = F (t) A 0 ( 3
)
where A 0 denotes the total initial cross-sectional area of the gage sections. Assuming a constant effective gage section length l 0 , the corresponding nominal plastic strain, E p yy , reads: Assuming transverse plane strain conditions, we have the corresponding equivalent plastic strain:

E p yy (t) = u p l 0 = u(t) l 0 - F (
¯ p (t) = 2 √ 3 p yy (t)( 7 )
and the equivalent Von Mises stress

¯ (t) = √ 3 2 yy (t)( 8 )
Thus, using Eqs. ( 7) and ( 8), the stress-strain curve ¯ = ¯ (¯ p ) can be determined based on the experimental measurements F (t)andu(t). Static experiments on specimens machined from aluminum 2024-T351 have been performed to validate the proposed relationships for the stress-stain curve. For this, the M-specimen is placed between the flat loading platens of a screw-driven universal tensile testing machine (Model G45, MTS). The measured force-displacement history follows closely that obtained from numerical simulations. Subsequently, the Mises stress versus equivalent plastic strain curve has been calculated using the equations above. It was found that the calculated stress level is about 2% too low due to perturbations in the plane-strain stress field near the boundaries of the cross-section. Furthermore, the measured stressstrain curve needed to be corrected by a very small offset of about ¯ p = 0.0025 in order to match with that obtained from uniaxial tensile testing. This effect could be attributed to some initial bending-induced deformation which precedes the plastic deformation due to uniform stretching of the gage section. The resulting stress-strain curves as obtained from static testing are shown in Fig. 2.

DYNAMIC EXPERIMENTS

A SHPB apparatus consisting of two straight aluminum bars and an aluminum striker bar is used to subject the specimen to dynamic loading conditions. All bars are of cylindrical cross-section of 40mm diameter. The lengths are 1203mm for the striker bar, 2991mm for the incident bar, and 1850mm for the transmitter bar. Strain gages are positioned near the center of the incident bar (at a distance of 1493mm from the specimen/bar interface) and on the transmitter bar (at a distance of 335mm from the corresponding specimen/bar interface). The amplified signals of the strain gages are recorded at a sampling frequency of 1MHz.

After testing, the recorded incident, reflected and transmitted waves are 'transported' to the respective bar/specimen interfaces while correcting for geometrical dispersion (using the DAVID software). Consequently, the force and velocity histories are determined at both the top (incoming) and bottom (outcoming) specimen boundaries. The incoming and outcoming force histories for a selected experiment performed at a striker impact velocity of 4.33m/s are shown in Fig. 3a. The small deviation of the two curves indicates that the specimen is still under quasi-static equilibrium during the present experiment. The corresponding stressstrain curve is plotted in Fig. 3b. The same curve is shown for another experiment which has been performed at a similar velocity. Both curves are very close, which demonstrates the repeatability of the present experiment. Throughout the experiment, the equivalent plastic strain versus time curve (not shown) increases in a considerably linear manner at an average strain rate of about 1075/s.

Nonlinear finite element simulations of the split Hopkinson pressure bar experiment (FEA model including specimen and bars) have been performed to assess the quasi-static equilibrium at higher strain rates. Preliminary results have indicated that for impact velocities of up to 10m/s, the hypothesis of quasi-static equilibrium still holds approximately true. However, for very high loading velocities, the duration of the real experiment is only little longer than the rise time of the incoming wave (about 50 s). Therefore, perturbing transient effects related to the Pochhammer-Chree oscillations following the initial rise are likely to limit the strain rate range of reliable material characterization for the present experimental technique.

CONCLUSION

A new specimen has been proposed to characterize the high strain rate response of bulk metals under tensile loading. The specimen converts compression at its boundaries into tension within its gage section. Consequently, it can be used in conjunction with a split Hopkinson pressure bar apparatus, thereby circumventing difficulties associated with the gripping of specimens in conventional dynamic tensile testing devices. It is shown experimentally that this M-shaped specimen provides reliable results for strain rates of up to 1000/s.

Figure 1 .

 1 Figure 1. (a) Photograph of the EDM machined specimen, (b) 3D finite element model representing one quarter of the M-specimen (symmetry planes x-y and y-z); the contour plot indicates the intensity of the equivalent plastic strain.

  calculate the true stress yy = (1 + E p yy ) yy (5) and the logarithmic plastic strain p yy = ln(1 + E p yy )( 6 )

Figure 2 .

 2 Figure 2. Stress-strain curve for static loading as obtained from the testing of a flat dogbone specimen and the M-specimen.

Figure 3 .

 3 Figure 3. Experiments at an equivalent plastic strain rate of about ˙ p = 1075/s: (a) Plot of the measured force histories F in (t)andF out (t) at the top and bottom boundary, respectively; (b) Stress-strain curves for two dynamic experiments (striker velocities v I = 4.10m/s and v II = 4.33m/s).

Acknowledgments

The authors are grateful to Mr. R. Barre and Mr. R. Herbez for their assistance in performing the dynamic experiments. Thanks are due to Professor T. Wierzbicki from MIT for valuable discussions. Altair Engineering is thanked for providing a license of the pre-processing software Hypermesh.


C P Gameiro

J Cirne

G Gary

Dynamic crushing behaviour of aluminium tubes filled with cork

Cork is a natural cellular material with unique remarkable properties such as low density, great elasticity, chemical stability and resilience, no permeability to liquid and gases and resistance to wear and fire. Besides, it is ecological, hygienic, easy to maintain and a very durable material. Unfortunately, there are still application fields that have not been explored yet for the use of cork, possibly due to the fact that it is a complex cellular material, characterized by very variable mechanical properties which clearly depend on its microstructure. The fundamental aspects of the static and dynamic mechanical behaviour of natural and agglomerate cork, used alone and as filler inside a tube with small dimensions, under axial compressive loading, have already been studied by the authors. Aluminium cork-filled tubes and their empty counterparts were tested experimentally and numerically at quasi-static and dynamic strain rates from 10 -3 s -1 to 600 s -1 . Data from the Split-Hopkinson Pressure Bar and "deconvolution" techniques were used to generate stress-strain curves for the structures composed of natural and agglomerate cork. The numerical simulations of the dynamic compression of the specimens were carried out using the finite element method software LS-DYNA TM and showed quite good agreement with the experimental results. Hence, in this work, in order to extend the study started previously and investigate the possible advantages of cork-filling in longer tubes with a different section, the authors simulate, using the same software, the influence of the introduction of agglomerate cork in square and circular aluminium tubes with a diameter/width of 80 mm, a length of 300mm and a variable thickness. The mechanical properties of the structures composed of cork may constitute a potential for this material to be used in innovative applications related to diverse fields such as automotive, transport, ships and military applications.

INTRODUCTION

Energy-absorbing systems of various kinds are being extensively used in many engineering applications such as automotive and transport vehicles. Indeed, during an impact event, the energy of the crash and the manner in which the loads are transmitted through the system, are very important points. As a consequence, the axial crushing behaviour of thin-walled structures, which are efficient energy absorbers, has been a topic of great interest for many researchers.

Steel has been extensively used in energy absorption systems, due to low prices combined with excellent ductility. But the importance of the reduction of structural components mass has increased in the recent years. That's why the use of aluminium tubes with different shapes and geometries, and thus energy-absorbing efficiencies, has been frequently promoted [1,2]. Furthermore, computational mechanics has been an important tool in the assessment of the crash behaviour of various structures since numerical simulations enable new design and materials to be evaluated without extensive testing [3]. Many authors examined the parameters which could influence the crushing pattern of square and cylindrical tubes under quasi-static and dynamic axial loading since collapse mode transitions of thin tubes strongly influence the energy absorption [4][5][6][7][8]. Furthermore, the question of whether the performance of axially crushed tubes could be improved by introducing a filler material has also been asked several times during the past two decades [9][10][11][12][13][14].

Cork is a complex natural cellular material, with quite unknown or not well understood properties. The fundamental aspects of the mechanical behaviour of cork under static compressive loading have already been discussed in several studies [START_REF] Fortes | A Cortiça[END_REF]. However, the mechanical behaviour of cork when subjected to axial impact has been investigated very recently, when quasi-static and dynamic uniaxial compressive tests performed on natural and agglomerate cork were compared by the authors [START_REF] Gameiro | Design and Use of Light-Weight Materials[END_REF][START_REF] Gameiro | [END_REF].

Hence, the purpose of this study is to analyse the energy-absorption improvements caused by the use of cork as filler inside aluminium tubes subjected to uniaxial impact loading. Thus, circular cork-filled aluminium tubes of 50mm length were impacted using an experimental device in nylon called block-bar, inspired in Hopkinson pressure bars. Numerical simulations were carried out using the finite element code LS-DYNA TM , and globally showed good agreement with the experimental results. The validated numerical model was then used to study the energy absorption capacity of cork-filled square and circular aluminium tubes with a diameter/width of 80mm, a length of 300mm and a variable thickness, impacted at 10 and 15m/s. The aim of this systematic study was to analyse if the mechanical properties of the structures composed of cork may constitute a potential for this material to be used in innovative industrial applications.

DYNAMIC TESTING

Material

The dynamic tests were performed on circular tubes with and without micro-agglomerate cork-filler. Actually, the advantage of agglomerate cork is that it is produced industrially and available in many shapes and sizes, making possible to use it in diverse applications. The micro-agglomerate cork filled in the tubes contained 0.5 to 2mm cork particles joined with an adhesive. The circular tubes had an outer diameter of 25mm, a thickness of 1.5mm and were cut for a length of 50mm. The aluminium alloy was in accordance with the standard AW 6060/6063 and was submitted to a T5 heat treatment.

Experimental tests

An experimental technique that has been used often to obtain constitutive relations at high strain rates is the classic Split Hopkinson Pressure Bar. The first use of a long thin bar to measure stresses under impact conditions has been reported in [18]. The experimental setting with two long bars widely used today is pioneered by Kolsky [19]. However, one of its limitations consists in the fact that the strain for which one can obtain values for the stress in the tubes is limited. Actually, the time of loading applied to the sample is related to the striker length and the wave speed in the bars and determines the maximum strain considered in the sample for a given strain rate. That is the reason why the authors used an equipment device, called "block-bar" which is being developed in the Laboratoire de Mécanique des Solides (Palaiseau, France). This equipment allows carrying out force-displacement curves for higher strains. Basically, it consists of a nylon bar (diameter 81.7mm, length 8.923m), equipped with three strain gages and two zimmers. A steel striker (diameter 78.5mm, length 2m) impacts directly the sample which is placed strictly before the nylon bar. The analysis of the transmitted and reflected waves by deconvolution methods [20], associated to the equilibrium hypothesis of the sample, gives the forces and velocities for each face of the sample. The shifting of waves to specimen ends takes account of the dispersion (which means that the speed of the waves depends slightly on their frequency) and for damping. The authors use a dispersion relation that is the first mode solution of Pochhammer [21] and Chree [22] equation, generalised to the case of viscoelastic bars by Zhao and Gary [23].

The speed of the striker was fixed to 5.5m/s, corresponding to a strain rate of approximately 100s -1 .

Modelling studies

The numerical simulations were performed using the finite element method software LS-DYNA TM .The material model used for cork was 26.1.*MAT_HONEYCOMB, which is adequate to honeycomb and foam materials with real anisotropic behaviour. Some of the parameters used in the model were the result of experimental conclusions whereas others were found in the literature [START_REF] Fortes | A Cortiça[END_REF]. The stress-strain curve imported was the average dynamic curve obtained as a result of the dynamic tests performed on cork in nylon Hopkinson Pressure Bars and referenced in [START_REF] Gameiro | [END_REF].

The tubes tested experimentally with and without cork were modelled with the material 24.1.*MAT_PIECEWISE_LINEAR_PLASTICITY. This material models an elastic-plastic material with an arbitrary stress-strain curve and an arbitrary strain rate dependency can be defined. For the circular tubes (EN AW 6060/6063-T5), the data from the aluminium tensile curve were used and strain rate was accounted for, using the Cowper-Symonds model.

For the micro-agglomerate cork, the meshing consisted of 8-nodes hexahedral solid elements with 8 nodes and 3 degrees of freedom per node, for 8 points of integration (complete integration, with no problems of hourglass). Cork was meshed with 1mm elements along the volume. The circular aluminium tubes were drawn by their middle surface. The elements used were Belytshko-Tsay shell elements, with 7 integration points along the thickness and 1.5mm thickness at each node. No gap was introduced between the cork and the tube. Two rigid walls (modelled as rigid bodies) were placed next to the base and upper section of the samples. One of the rigid walls was fixed whereas the other impacts the material while associated to a mass and a velocity. The friction coefficient adopted was 0.25. The velocity introduced was the impact velocity experimentally tested (5.5m/s), and the mass was chosen so that the final deformation of the tube was at least equal to the maximum deformation observed experimentally. For each tubular structure, the Automatic_Single_Surface contact was used to prevent self-penetration of the lobes during deformation and the Automatic_Surface_to_Surface contact permitted to avoid the mutual penetration of the two coupled materials. For the tubes, the displacements of the nodes in contact with the compression rigid walls were not allowed, except the displacement of the upper nodes along the impact axis.

Results and numerical validation

The experimental and numerical force-displacement curves of 50mm empty and filled tubes are shown in figure 1. As seen, the agreement between experimental and numerical average load values is quite satisfactory. The numerical mean force is slightly superior since the model does not take into account the possible defects of the tube materialBesides, the model deformed shapes (concertina mode) and number of lobes exactly matched to the experimental deformed shapes, which again confirmed the agreement between model and experiments (figure 2). Of course, the numerical model did not capture the dimensions recovery of the filled cork but the overall behaviour is well described (figure 3). It is also noted that, for this type of tube geometry, the introduction of cork brought little benefits of energyabsorption, since the loads supported by the filled tubes are quite similar to the forces supported by the empty ones.

SQUARE AND CIRCULAR TUBES FILLED WITH CORK

The validated numerical model was then used to study the energy absorption capacity of longer square and circular thin-walled sections with varying thickness from 1mm to 3mm. In fact, the energy absorption performance of thin-walled tubes is very dependent on the section shape and on the slenderness ratios (diameter/thickness or width/thickness and length/thickness) [24]. Thus, numerical simulations were performed using the same software, in order to describe and better understand the influence of the impact velocity, the section shape and the thickness values on the energy absorption of 300mm length aluminium tubes with and without cork filler (figure 4). The external diameter or width considered was 80mm, independently of the thickness focused. The modelling parameters imported to the software were identical to the ones used for the 50mm length tubes. And the dimension of the elements used to mesh the tubes and the cork were fixed at approximately 3mm. The tubes considered were impacted at 10m/s and 15m/s and the mass of the rigid wall was always chosen so that the tube suffered at least 75% deformation. The study mainly focused on the mean collapse load, on the energy absorption and on the specific energy absorption of the tubes considered. For the thicknesses considered, the filled and non-filled circular and square tubes did not show significant mean collapse load differences, and thus relevant energy absorption differences, when the impact speed increased from 10m/s to 15m/s. This result was expected since the aluminium alloy chosen is known to be almost strain rate insensitive and the micro-agglomerate cork shows similar force-displacement behaviour in the range of strain rates focused in this study [START_REF] Gameiro | Design and Use of Light-Weight Materials[END_REF][START_REF] Gameiro | [END_REF].

Circular tubes

As seen in figure 5, the mean collapse load increases with increasing thickness and the load supported by the cork-filled tubes is always higher than the force supported by the empty ones, for a same thickness. This fact did not occur for the smaller circular tubes tested experimentally. It is also obvious that there is a critical value of the displacement for which a filled structure supports higher forces than the corresponding empty tube of thickness immediately superior, ie 0.5mm higher (see dashed line on figure 5). The displacement for which this transition occurs also increases with increasing thickness. However, the critical displacement value is never inferior to approximately 125mm. The peak loads may vary from 30KN (for 1mm thickness) to approximately 140KN (for 3mm thickness). As expected, the energy absorption of the non-filled and filled tubes increases with thickness. It appears that the structures filled with cork absorb more energy than the empty ones, for each thickness studied. Concerning specific energy absorption (SEA) values, the contrary occurs: the empty tubes are more efficient for the same thickness. Indeed, the introduction of micro-agglomerate cork considerably increases the mass of the whole structure. This can be a problem if weight-saving is an important goal. Apparently, only filled tubes with a thickness inferior to 1mm (thus very instable tubes with respect to global bending) could show a higher SEA than the corresponding empty tube (figure 6). In figure 8, one can see that the difference of energy absorbed (in %) between an empty tube and the same tube filled with cork, decreases with the increase of thickness. Thus, the thicker the tube is, the less the use of cork as a filler is positive in terms of energy absorption performance. For the tubes considered, the increase of energy due to the introduction of cork can vary from 50% to approximately 170%. Of course, this fact is strongly related to the possible collapse mode transitions, or deformation pattern transitions which can occur after the introduction of cork, as shown in figure 7.

Square tubes

The same parameters were observed: mean collapse load, energy and specific energy (SEA). As for circular tubes, the figure 9 highlights the fact that the mean collapse load increases with increasing thickness. The dashed lines represent the evolution of the displacement values for which using a corkfilled tube of lower thickness (0.5mm and 1mm lower) would be preferable to the use of an empty tube, in terms of mean collapse load. The peak loads may vary from 50KN (for 1mm thickness) to approximately 170KN (for 3mm thickness). In the range of thicknesses considered, the energy absorbed by the structures tested increases with increasing thickness. However, the difference of energy absorbed by a filled tube and the same empty tube at 75% strain tends to stabilise for thicknesses higher than 2.5mm (figure 11). Note that the increase of energy due to the introduction of cork in the square tubes studied can vary from 50% to approximately 360%.

Concerning the SEA values, it seems that filling aluminium tubes with cork is very positive above 3mm thickness. Indeed, in that range, the specific energy absorbed by the cork-filled tubes is well above the SEA absorbed by the empty tubes (the % difference can be up to 50%, see figure 12). This result may constitute a potential for this material to be used in innovative applications that focus on energyabsorbers performance. Obviously, all the square tubes studied show a change of the deformation pattern (from diamond to concertina), after the introduction of cork (figure 10). This could explain why corkfilled aluminium square tubes could be good energy absorbers when compared to the same empty tubes.

Comparison

The numerical results obtained for the circular and square aluminium tubes filled, or not, with cork allow to make a few interesting comparisons. First of all, the introduction of cork increases the energy absorption performance, and for some of the square tubes, the SEA performance of the tubes studied. Additionally, the benefits of square tubes over circular tubes of similar dimension are obvious and consist of:

• the decrease of the critical displacement for which using a tube with lower thickness is positive in terms of collapse load. For some displacements, decreasing the thickness of a square tube of 0.5 or 1mm, and filling it with cork can be very efficient in terms of mean collapse load. • the increase of the mean collapse load and peak load supported, for the same thickness.

• the increase of the difference of energy absorbed (empty vs cork-filled tube) values for the same thickness at 75% strain. • the increase of the maximum thickness above which filling a tube with cork is a positive point in terms of energy-absorption capacities and specific energy absorption performance.

CONCLUSION

This work studied some aspects of the use of micro-agglomerate cork as filler inside aluminium tubes with different thicknesses and section shapes, impacted at 10 and 15m/s. After testing experimentally 50mm length aluminium tubes, with and without cork-filler, the numerical results obtained with the finite element method software LS-DYNA TM were validated since they showed a good agreement with the dynamic tests performed. However, such tubes showed a bad performance as energy absorbers.

As a consequence, more simulations were performed in longer tubes, with square and circular crosssections and variable thicknesses, in order to assess if they may have good energy-absorbing properties.

The numerical results showed that, considering applications for which the use of tubes with a diameter/width of 80mm is indispensable, the square tubes present better energy-absorbing properties. This study also enhanced the fact that, depending on the application, on the mean collapse load values, SEA values, absorbed energy values and thickness required, filling aluminium tubes with agglomerate cork may be very beneficial. Concerning the increase of impact speed, it seems that it had no visible influence on the behaviour of the different structures tested.

Figure 1 .

 1 Figure 1. Experimental and numerical force-displacement curves for empty and cork-filled (CF) tubes.

Figure 2 .

 2 Figure 2. Shape histories of the tubes tested experimentally.

Figure 3 .

 3 Figure 3. Shape histories of the tubes simulated (empty tubes on the left, cork-filled [CF] on the right).

Figure 4 .

 4 Figure 4. Geometry of the tubes numerically studied.

Figure 5 .

 5 Figure 5. Mean collapse load vs displacement for the circular tubes impacted (

Figure 6 .

 6 Figure 6. Energy (a) and specific energy absorption (b) at 75% strain vs thickness ( filled, not filled). 10 and 15m/s impacts.

Figure 7 .

 7 Figure 7. Deformation patterns of the circular tubes tested for 1mm thickness (a) and 3mm thickness (b).

Figure 8 .

 8 Figure 8. Absorbed energy difference (empty vs CF tubes) at 75% strain, for 10 and 15m/s impacts.

Figure 9 .

 9 Figure 9. Mean collapse load vs displacement for the square tubes impacted.

Figure 10 .

 10 Figure 10. Deformation patterns of the square tubes tested for 1mm thickness (a) and 3mm thickness (b).

Figure 11 .

 11 Figure 11. Energy (a) and energy difference empty/cork-filled (b) at 75% strain vs thickness.

Figure 12 .

 12 Figure 12. SEA (a) and SEA difference empty/cork-filled (b) at 75% strain vs thickness ( filled, not filled). 10 and 15m/s impacts.

Acknowledgements

The authors are grateful to the Portuguese Foundation for Science and Technology (FCT) who financially supported this work, through the Program POCTI/35907/EME/2000 (Portuguese Government and FEDER) and SFRH / BD / 18964 / 2004, and to ROCAP for providing the cork samples.


Y Corre
email: yann.corre@cea.fr

A Grosjean

J P Gunn

K Krieger

S Ratynskaia

O Skalli-Fettachi

C Bourdelle

S Brezinsek

V Bruno

N Chanet

J Coenen

X Courtois

R Dejarnac

E Delmas

L Delpech

C Desgranges

M Diez

L Dubus

A Durif

A Ekedahl

N Fedorczak

M Firdaouss

J-L Gardarein

J Gaspar

J Gerardin

C Guillemaut

M Houry

T Loarer

P Maget

P Mandelbaum

R Mitteau

M Missirlian

P Moreau

R Nouailletas

E Nardon

C Pocheau

A Podolnik

P Reilhac

X Regal-Mezin

C Reux

M Richou

F Rigollet

J-L Schwob

E Thorén

P Tolias

E Tsitrone

Sustained W-melting experiments on actively cooled ITER-like Plasma Facing Unit in WEST

Keywords: Tungsten melting, Plasma Facing Unit, Heat flux calculation, IR thermography

The consequences of tungsten (W) melting on divertor lifetime and plasma operation are high priority issues for ITER. Sustained and controlled W-melting experiment has been achieved for the first time in WEST on a poloidal sharp leading edge of an actively cooled ITER-like plasma facing unit (PFU). A series of dedicated high power steady state plasma discharges were performed to reach the melting point of tungsten. The leading edge was exposed to a parallel heat flux of about 100 MW.m -2 for up to 5 s providing a melt phase of about 2 s without noticeable impact of melting on plasma operation (radiated power and tungsten impurity content remained stable at constant input power) and no melt ejection were observed. The surface temperature of the MB was monitored by a high spatial resolution (0.1 mm/pixel) infrared camera viewing the melt zone from the top of the machine. The melting discharge was repeated three times resulting in about 6 s accumulated melting duration leading to material displacement from three similar pools. Cumulated on the overall sustained melting periods, this leads to excavation depth of about 230 m followed by a re-solidified tungsten bump of 200 m in the JxB direction.

Introduction

Due to the introduction of poloidal and toroidal gaps (0.5mm width) associated to the monoblock (MB) technology [START_REF] Hirai | Design optimization of the ITER tungsten divertor vertical targets Fusion Engineering and Design[END_REF], magnetic field lines can penetrate into the gaps and intercept the poloidal leading edges (LEs) with near normal incidence [START_REF] Gunn | A study of planar toroidal-poloidal beveling of monoblocks on the ITER divertor outer vertical target[END_REF]. In ITER, this leads to very high heat load especially during ELMs (several GW.m -2 ) but also during steady state or inter-ELM periods (hundreds of MW.m -2 ) [START_REF] Pitts | Physics basis for the first ITER tungsten divertor[END_REF]. Because of potential misalignment between plasma facing units [START_REF] Pitts | Physics conclusions in support of ITER W divertor monoblock shaping[END_REF] or in case of failure of the components in the machine, like armor-to-heat sink bounding defect affecting the heat removal capability of the component [START_REF] Missirlian | The heat removal capability of actively cooled plasma-facing components for the ITER divertor[END_REF][START_REF] Ramaniraka | Data cross-checking from ultrasound testing, IR thermography and high heat flux tests for the qualification of WEST PFU divertor[END_REF], the risk of transient or sustained melting becomes a major concern for ITER and next step fusion devices Several experiments have been successfully carried out in both, limiter and divertor geometries, to investigate sustained (TEXTOR experiment using roof-like test-limiter [START_REF] Sergienko | Experience with bulk tungsten test-limiters under high heat loads: melting and melt layer propagation[END_REF]) or transient repetitive melting of tungsten (W) by ELM on special geometries, overexposed LEs as well as sloped lamella in AUG [START_REF] Krieger | Experiments on transient melting of tungsten by ELMs in ASDEX Upgrade[END_REF] and JET [START_REF] Coenen | ELM induced tungsten melting and its impact on tokamak operation[END_REF][START_REF] J W Coenen | Transient induced tungsten melting at the Joint European Torus (JET)[END_REF] tokamaks. These experiments have been performed with bulk tungsten but without active cooling such as ITER-like PFU, therefore with a strong dependence on surface temperature and pulse history compared to actively cooled component once stationary surface temperature is established. Prolonged steady-state exposures resulting in large material displacement could offer an opportunity to enlarge the energy fraction expended on solid/liquid phase transition and to reduce the sensitivity of molten mass to input heat flux [START_REF] Ratynskaia | Resolidification-controlled melt dynamics under fast transient tokamak plasma loads[END_REF].

To achieve melting in WEST, a 2mm deep groove was machined in one of the actively cooled MBs and a series of dedicated high power steady state plasma discharges were performed to reach the melting point of tungsten (≈ 3420°C). The experimental set-up is presented in section 2. The sustained Wmelting experiment (P inj = 5.5 MW, Ip = 500 kA, B = 3.7 T) is presented in section 3. The experimental results including IR thermography analysis and post-mortem confocal microscopy to evaluate the melt displacement are presented in section 4.

Experimental set-up

One of the aims of the WEST tokamak is to test actively cooled ITER-like PFUs [START_REF] Bucalossi | The WEST project: Testing ITER divertor high heat flux component technology in a steady state tokamak environment[END_REF][START_REF] Missirlian | The WEST project: PFC shaping solutions investigated for the ITER-like W divertor[END_REF]. During the C5 experimental campaign, the WEST divertor was equipped with 76 PFUs on two different sectors, each composed of 35 tungsten ITER grade MBs. To achieve melting, a groove (30 mm long toroidally, 9 mm wide poloidally, and 2 mm deep) was machined in one of the MBs in order to expose the sharp LE of the adjacent downstream MB directly to the full incident parallel heat flux at the outer region of the target module (figure 1). The groove was machined on the maximum heat flux area regarding the toroidal ripple effect (PFU#7), in a remote location accessible with far outer strike point (OSP) magnetic configuration only (MB28, while usual OSP position lies between MB24 and 27). To gain in power load and get easier access to the melting point, the PFU chosen to melt (PFU#8) has been misaligned in the vertical direction ( = +0.3 mm) compared to the upstream one (PFU#7). The total length fully exposed to the parallel heat flux is therefore 2.3 mm (see figure 2.b). The far OSP equilibrium also enables to minimize the magnetic flux expansion and thus to maximize the heat flux intensity at the target. The surface temperature of the MB was monitored by a very high spatial (VHR) resolution (0.1 mm/pixel) IR thermography system equipped with a medium-wavelength IR filter (3.9 µm) viewing the melt zone from the top of the machine [START_REF] Houry | The very high spatial resolution infrared thermography on ITER-like tungsten monoblocks in WEST Tokamak[END_REF]. The VHR system has a field of view (FoV) covering ~ 2x4 MBs (64 x 51 mm). The system is equipped with two orientable mirrors enabling to cover a wide surface of the divertor (~ 13° in the toroidal direction, corresponding to the area where ITER like PFU are installed, from PFU #6 to PFU #19) and the 2 strike point areas along the PFU in the poloidal direction (from MB #6 to #32). The IR system measured IR radiation and is calibrated using a black-body (BB) with surface emissivity =1. The spectral radiance of the surface MB (L w ) is given by the following equation [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF]:

𝐿 𝑊 = 𝐿 𝐵𝐵 × 𝜀 𝑊 + (1 -𝜀 𝑊 ) × 𝐿 𝑎𝑚𝑏 (1
) where L BB is the spectral radiance of the BB (Planck radiation), w is the surface emissivity of tungsten MBs and L amb is the spectral radiance of the actively cooled ambient environment (T amb = 70 °C). True temperature are computed afterward using equation as function of temperature based on emissivity measurement [START_REF] Gaspar | Emissivity measurement of tungsten plasma facing components of the WEST tokamak[END_REF]. The melting experiment and groove size have been designed to reach melting with heat flux intensity obtained in WEST during the LE experiments performed in the previous experimental campaign (C4) [START_REF] Grosjean | Very high-resolution infrared imagery of misaligned tungsten monoblock edge heating in the WEST tokamak[END_REF]. Numerical modelling of the temperature was performed with a 3D finite element method (FEM) including ITER-like MB prototypes with 28 mm width (ITER standard width for thermal calculation) and 6 mm tungsten thickness [START_REF] Hirai | Design optimization of the ITER tungsten divertor vertical targets Fusion Engineering and Design[END_REF] between the top surface and the CuCrZr cooling tube in steady state (figure 2). The heat load is computed with the optical projection of the parallel heat flux on the MB surfaces:

𝑞 𝑛 = 𝑞 // • sin 𝛼 (2)
where  is the angle between the magnetic field line and the MB surfaces. The heat flux distribution on the MB surfaces is computed using convolution of a Gaussian spreading with a truncated decaying exponential in the scrape off layer (SOL) as depicted in [START_REF] Eich | Empiricial scaling of inter-ELM power widths in ASDEX Upgrade and JET[END_REF] and already validated in WEST [START_REF] Fedorczak | Cross diagnostics measurements of heat load profiles on the lower tungsten divertor of WEST in L-mode experiments[END_REF]:

𝑞 // (𝑦) ∝ 𝑒𝑥𝑝 [( 𝑆 2• 𝑞 ) 2 - 𝑦-𝑦 0  𝑞 ] × 𝑒𝑟𝑓𝑐( 𝑆 2• 𝑞 - 𝑦-𝑦 0  𝑞 ) ( 3
)
Where y is the target position in the poloidal direction, y0 is the OSP location, λq is the local heat flux decay length on the target (i.e. not mapped to the outboard midplane), S is the heat flux spreading factor in the private flux region. The thermal modelling gives the spatial distribution of the surface temperature (TFEM) that is used afterward to compute the synthetic temperature (Tsynth) as seen by the IR camera as depicted in [START_REF] Corre | Methodology for heat flux investigation on leading edges using infrared thermography[END_REF]. To simulate the pixel size, optical blurring and deformation, the numerical radiance profile (calculated from TFEM using Planck equation) is convoluted with the transfer function of the instrument which is modelled by a Gaussian shape with a standard deviation σ = 0.175 mm for the VHR system as mentioned in [START_REF] Grosjean | Interpretation of temperature distribution observed on W-ITER-like PFUs in WEST monitored with a very-high-resolution IR system[END_REF]. The parallel heat flux was adjusted to reach the melting point on the leading edge assuming heat flux decay length q = 10 mm on target (value obtain during C4 experiment with similar heating power) and position of the OSP y0 = 4.2 mm to get the maximum heat flux in the centre of the groove (yqmax = 6 mm). A very high temperature gradient is observed near the LE, almost 700°C temperature decrease over 1 mm. Because of the spatial filtering effect of the IR camera far small objects (smoothing of the sharp temperature variation), the real temperature (Ttrue = 3420°C expected at the melting point) falls down to Tsynt = 3076°C as would have been measured by the instrument assuming BB emission, a decrease of ~345 °C compared to the true temperature (see figure 5-b). The maximum temperature measured on the synthetic profile is also located 0.4 mm away from the leading edge. The thermal modelling doesn't include the latent heat during melting as well as surface cooling effects due to vaporization and thermionic emission processes [START_REF] Thorén | The MEMOS-U code description of macroscopic melt dynamics in fusion devices Plasma[END_REF]. The calculation shows that we need at least 107 MW.m -2 parallel heat flux projected on the target to reach melting.

WEST experiment

The aim of the experiment was to achieve high and stationary heat flux for at least 5 s to reach thermal equilibrium in the MB (the theoretical time constant to reach 95% of the stabilized temperature is 2.4 s) and to get sustained melting for about two seconds. A far X-point magnetic equilibrium was developed to get the maximum heat flux location in the toroidally running groove located in MB28 keeping good RF coupling condition in front of the LHCD launchers. The magnetic strike point position is currently controlled with feedforward adjustment with accuracy of about 1 mm. As a consequence, increasing the input power, and so the Shafranov shift of the global magnetic equilibrium, led to an inward displacement of the peak heat flux toward MB 27. The X-point height was therefore adjusted pulse to pulse to keep the maximum heat flux in the center of the groove. The X-point height was moved from 102 mm at low power up to 112 mm during the melting experiment. The pulse scenario used during the melting experiment is displayed in figure 3. The plasma current is set to Ip = 500 kA during more than 10s with magnetic field BT = 3.7 T. The heating power is injected from 5s up to 10s with the two LHCD launchers (a). Figure (b) displays the BB temperature as measured by the IR system during the melting experiment. 95% of the stabilized temperature is reached after about 2.5s which is consistent with numerical expectation. The melting phase lasts for about 2s, then the IR safety system was activated due to a hot spot on one of the two LHCD launchers and the melt was expected to re-solidify 0.6s second before the power cut-off. During melting phase, total radiated power (P rad ~ 2.3 MW) and tungsten impurity content evaluated with ultra-violet (UV) spectrometer (W 43+ emission line) remained stable at constant input power (figure 3-a). No melt ejection was observed with the VHR IR system which is consistent with the sample post-exposure surface analysis results reported in figure (4). During the power increase, few pulses before reaching the melting point (with LE temperature clearly above the ductile-to-brittle temperature threshold), premature cracking has been detected with the VHR IR system thanks to local emissivity enhancement due to local cavity effect (figure 4 #56538). The melting was detected with the VHR IR thermography during the cooling phase: one can observe clear rounding of the LE, with a small hollow followed by a bump about 2 mm away from the melt point (figure 4 #56543), which is the consequence of material displacement as expected with the JxB volumetric forces [START_REF] Thorén | The MEMOS-U code description of macroscopic melt dynamics in fusion devices Plasma[END_REF]. The pulse with melting conditions was repeated three times with similar injected energy to check the consequence of melting for plasma operation. The melt displacement results therefore in melting of three similar and consecutive pools (2s each, 6s of cumulated melt duration in total). In-situ visual inspection of the leading edge of the MB performed with the Articulated Inspection Arm (AIA) [START_REF] Bruno | WEST regular in-vessel Inspections with the Articulated Inspection Arm robot[END_REF] confirm the melting of the LE in middle of the MB (figure 4).

Experimental results

During the C5 experimental campaign, only two divertor sectors were equipped with actively cooled ITER-like PFUs (16% of the total surface covered). The other divertor sectors were equipped with Wcoated graphite PFUs. The heat load was derived from standard IR thermography system looking at the W-coated graphite PFUs [START_REF] Fedorczak | Cross diagnostics measurements of heat load profiles on the lower tungsten divertor of WEST in L-mode experiments[END_REF] and embedded thermocouples (TCs) [START_REF] Gaspar | First heat flux estimation in the lower divertor of WEST with embedded thermal measurements[END_REF]. During the W melting experiment, we found a parallel heat flux of about 95 MW.m -2 (IR data) and 75 MW.m -2 (TC data) and target heat flux decay length of 7 mm (IR data) and 10 mm (TC data) respectively, which represent slightly lower power load compared to the exposed LE. An image delivered by the VHR IR system during the melting phase (at 8s) is displayed in figure 5-a. The temperature profile extracted from the IR image along the toroidal direction is displayed in figure 5-b for comparison with FEM modelling. On the melting location, the BB temperature is found to be TBB=1580°C (black crosses) while synthetic data would predict 3076°C (blue crosses) due to the spatial filtering effect of the IR system assuming melting point is reached. The guarantee to reach melting is used afterward as reference point to evaluate the emissivity of tungsten from equation ( 1). Here we found  = 0.32 at IR =3.9 m assuming Ttrue = 3420°C and Tsynt = 3076°C. The emissivity is then extrapolated at lower temperature using laboratory emissivity measurements [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF]. The full temperature profile is corrected using the extrapolated emissivity with square root reduction scheme to derive the true temperature (green crosses). The experimental toroidal temperature profile is found to be consistent with synthetic data over almost 10 mm away from the LE, confirming the steep temperature gradient near the LE 700°C/mm. Significant discrepancy is found further away, in the middle of the MB, due to local surface effect generated by plasma wall interaction (erosion and deposition processes) and leading to potential increase of the emissivity [START_REF] Gaspar | Emissivity measurement of tungsten plasma facing components of the WEST tokamak[END_REF]. The final surface deformation profile, measured with confocal microscopy after removal of the molten PFU from the machine, is presented in figure 4-d. A crater, 230 μm deep and extending 2 mm along the poloidal direction, is found in the vicinity of the maximum heat flux location. The melt, moving from the location of initially induced pool, has re-solidified on the adjacent surface, forming a 200 μm high bump. The displacement is consistent with flow in the JxB direction as predicted by MEMOS-U modelling [START_REF] Thorén | The MEMOS-U code description of macroscopic melt dynamics in fusion devices Plasma[END_REF]. The total melt displacement volume was evaluated to be 0.28 mm -3 . Such surface morphology explains the fact that no melt ejection was observed: the modest deformation and displacement signify that the melt pool was rather shallow and did not reached the PFU edge.

Conclusion

Sustained melting was achieved for the first time in WEST on ITER-like PFU under well controlled conditions. Radiated power and tungsten impurity content remained stable at constant input power, without noticeable impact of melting phases and no melt ejection was observed. The qualitative observation of the material displacement with the VHR IR camera, rounding the initially straight leading edge, was the first evidence of melting. In-situ visual inspection performed afterward with the AIA confirms the melting and its extension over two millimetres in the poloidal direction. VHR IR camera has been used to monitor the temperature distribution around the melted LE and compared to the thermal simulation. The melting point is used afterward to derive the emissivity of the tungsten which is used as a reference for extrapolation at lower temperature. Emissivity correction was performed to get true temperature along the MB. The modelled and experimental temperature gradients in the toroidal direction agree well with a value of about 700°C/mm near the melting zone. The heat load derived from the IR data analysis will be used as input to MEMOS-U code to model the melt dynamics at the actively cooled components under steady state plasma heat load. After removal of the melted component from the tokamak device, a melt displacement volume of 0.28 mm -3 has been determined by confocal microscopy. The observed bump of resolidified melt located next to the excavated melt crater is consistent with a flow in the JxB direction as predicted by MEMOS-U. Additional surface analysis, based on Scanning Electron Microscopy (SEM) and Electron BackScattering Diffraction (EBSD) measurements is ongoing to investigate the microstructure of the melted volume, the characteristic crack size and the tungsten grain size in both areas, crater and bump. The measurements collected during this experiment serve to further validate the underlying physics models of the MEMOS-U code in order to improve its predictive capability for the assessment of potential surface damage by accidental melt events in ITER in case of excessive heat loads.

Figure 1 :

 1 Figure 1: picture of the groove machined on PFU#7 to expose the sharp leading edge on the PFU#8.

Figure 2 :

 2 Figure 2: Thermal modelling assuming q//= 107 MW.m -2 , y0 = 4.2 mm; q = 10 mm, S = 1 mm as depicted in equation (3). (a) full view showing the groove and the overexposed LE to be melt, (b) zoom on the overexposed sharp LE showing the vertical misalignment between PFU#7 and PFU#8.

Figure 3 :

 3 Figure 3: Injected power (Low Hybrid), radiated power measured with bolometry and UV emission measured in the core plasma at  = 270.7 Å, a line identified to be a second order from 4s 2 4p 2 P 3/2 -4s4p 2 2 D 5/2 transition for W 43+ at 135.34 Å (a) and BB temperature (b) measured during the melting experiment (maximum value in the region of interest located in front of the groove in the centre of the MB) as function of time.

Figure 4 :

 4 Figure 4: picture of the MB taken before the C5 experimental campaign (a), IR images taken during the cooling phase of the MB (b) few seconds after the power switch-off, before (#56538) and after melting (#56543), picture taken after the melting experiment with the AIA robot (c), and confocal microscopy (d).

Figure 5 :

 5 Figure 5: (a) VHR IR image during the melting experiment #56541 at t=8s when the thermal equilibrium is reached. (b) Temperature distribution along the toroidal direction: experimental IR data (black crosses), corrected (green crosses), synthetic (blue crosses) and FEM data (red line).

Acknowledgement

Work performed under EUROfusion WP PFC. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.