Ce ´dric Barrey
email: cedric.barrey@chu-lyon.fr

Marc-Antoine Rousseau

Sylvain Persohn

Sophie Campana

Gilles Perrin

Wafa Skalli

Relevance of using a compressive preload in the cervical spine: an experimental and numerical simulating investigation

Keywords: Biomechanics, Biomechanical testing, Cervical spine, Preload, Spinal implants, Follower load

of background data Simulating compressive action of muscles, a follower load attends to reproduce a more physiological biomechanical behaviour of the cervical spine. Only few experimental studies reported its influence on kinematics and intradiscal pressure in the cervical spine. Study design In vitro human cadaveric and numerical simulating evaluation of a compressive preload in the cervical spine. Objectives To analyse the influence of a compressive follower preload on the biomechanical behaviour of the cervical spine. Methods The present study was divided into two parts: part 1: in vitro investigation; part 2: numerical simulating analysis. Part 1: Twelve human cadaveric spines from C2 to T2 were evaluated intact and after application of a 50-N follower load. All tests were performed under load control by applying pure moments loading of 2 Nm in flexion/ extension (FE), axial rotation (AR) and lateral bending (LB). Three-dimensional displacements were measured using an optoelectronic system, and intradiscal pressures were measured at two levels. Part 2: Using a 3D finite element model, we evaluated the influence of a 50-and 100-N compressive preload on intradiscal loads, facets forces and ranges of motion. Different positions of the follower load along the anteroposterior axis (±5 mm) were also simulated. Results Part 1: Mean variation of cervical lordosis was 5°± 3°. The ROM slightly increased in FE, whereas it consistently decreased in AR and LB. Coupled lateral bending during AR was also reduced. Increase in hysteresis was observed on load-displacement curves only for AR and LB. Intradiscal pressures increased, but the aspect of load-pressure curves was altered in AR and LB. Part 2: Using the FE model, only minimal changes in ROM were noted following the simulation of a 50-N compressive load for the three loading conditions. Compared to intact condition, \10 % variation was observed with regard to the different magnitude and positioning simulated. Intradiscal loads and facets forces were systematically increased by applying compressive preload. Conclusions Although the follower load represents an attractive option to apply compressive preload during experimental tests, we found that this method could affect the native biomechanical behaviour of spine specimen depending on which movement was considered. Only minimal effects were observed in FE, whereas significant changes in kinematics and intradiscal pressures were observed for AR and LB.

Introduction

In vitro investigations of cervical spine implants represent an important preclinical step prior to their implantation in humans [START_REF] Barrey | In vitro evaluation of a ball-and-socket cervical disc prosthesis with cranial geometric center[END_REF][START_REF] Goel | Test protocols for evaluation of spinal implants[END_REF][START_REF] Macafee | Cervical disc replacementporous coated motion prosthesis: a comparative biomechanical analysis showing the key role of the posterior longitudinal ligament[END_REF][START_REF] Puttlitz | Intervertebral disc replacement maintains cervical spine kinematics[END_REF]. However, this in vitro evaluation

Materials and methods

Part 1 in vitro tests

Spinal specimen preparation

Twelve adult cervical spines were harvested from fresh human cadavers coming from the department of anatomy of the University. Each spinal segment included C2 to T2 vertebrae. There were six male and six female with a mean age at death of 62 ± 6.4 years (55-77).

Radiographs were performed to exclude pathologic spines. Once harvested, each spine was immediately conserved in plastic bags at -20 °C. The day before biomechanical testings, all spines were thawed at ?4 °C for 12 h. On the day of testing, all soft tissues including paravertebral muscles were removed while preserving spinal ligaments, joint capsules, discs and bony elements.

The cranial vertebra (C2) was fixed in a container using a low-fusion point alloy (MCP 70, MCP Metalspecialities Inc, Fairfield, CT), whereas the caudal vertebra (T2) was firmly mounted in a specific device designed with metallic rods and screws.

Compressive preload

A 50-N compressive preload was applied symmetrically each side by two waxed and flexible cables fixed at the top container and passing through brass-drilled-head screws that were inserted between the anterior and posterior ridges of the transverse processes from C3 to C7 (Fig. 1). These guiding screws were approximately positioned at the posterior third of the vertebral body, close to the theoretical location of the mean axis of rotation in flexion-extension [START_REF] Amevo | Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers[END_REF][START_REF] Dvorak | In vivo flexion/extension of the normal cervical spine[END_REF][START_REF] Van Mameren | Cervical spine motion in the sagittal plane II. Position of segmental averaged instantaneous centers of rotation-a cineradiographic study[END_REF].

Biomechanical tests protocol

Tests were performed at room temperature; in order to avoid tissue dehydration, specimens were kept moistened with physiological saline serum spray during the tests.

Loads were applied to the upper vertebra (C2), which was allowed to move unconstrained in all degrees of freedom. Pure moments loading was successively applied in flexion/extension, lateral bending and axial rotation to a 2-Nm maximum moment loading with 0.2-Nm steps. Flexion and extension were completed in the same sequence (loading-unloading complete cycle); the same was performed for left and right lateral bending, and for left and right torsion. Three loading cycles were applied for preconditioning the specimen. implies to reproduce closely as possible in vivo conditions during experimental tests. Although in vitro investigations permit to analyse the biomechanical behaviour of spinal segments under precise control of applied forces with accurate measurement of intersegmental range of motion [START_REF] Panjabi | Mechanical properties of the human cervical spine as shown by three-dimensional load-displacement curves[END_REF][START_REF] Wen | Three-dimensional biomechanical properties of the human cervical spine in vitro. I. Analysis of normal motion[END_REF][START_REF] Wilke | Testing criteria for spinal implants: recommendations for the standardization of in vitro stability testing of spinal implants[END_REF], one limitation is that the effect of the musculature is only partially reproduced [START_REF] Panjabi | Mechanical properties of the human cervical spine as shown by three-dimensional load-displacement curves[END_REF][START_REF] Goel | Controversy: biomechanical testing of the spine. Load-controlled versus displacement-controlled analysis[END_REF].

Predominant action of paraspinal muscles is considered to mainly result in axial compressive forces [START_REF] Gardner-Morse | Physiological axial compressive preloads increase motion segment stiffness, linearity and hysteresis in all six degrees of freedom for small deplacements about the neutral posture[END_REF][START_REF] Panjabi | Effects of preload on load displacements curves of the lumbar spine[END_REF][START_REF] Panjabi | Criticial load of the human cervical spine: an in vitro experimental study[END_REF][START_REF] Patwardhan | A follower load increases the load-carrying capacity of the lumbar spine in compression[END_REF]. To simulate physiological compressive loads, some authors evaluated different testing protocols by applying compressive preload [START_REF] Gardner-Morse | Physiological axial compressive preloads increase motion segment stiffness, linearity and hysteresis in all six degrees of freedom for small deplacements about the neutral posture[END_REF][START_REF] Panjabi | Criticial load of the human cervical spine: an in vitro experimental study[END_REF][START_REF] Patwardhan | A follower load increases the load-carrying capacity of the lumbar spine in compression[END_REF][START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF][START_REF] Patwardhan | Effect of compressive follower preload on the flexion-extension response of the human lumbar spine[END_REF][START_REF] Rohlmann | Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine[END_REF]. However, most experimental studies were reported in the lumbar spine [START_REF] Patwardhan | Effect of compressive follower preload on the flexion-extension response of the human lumbar spine[END_REF][START_REF] Rohlmann | Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine[END_REF][START_REF] Patwardhan | Compressive preload improves the stability of anterior lumbar interbody fusion cage constructs[END_REF][START_REF] Renner | Novel model to analyze the effect of a large compressive follower preload on range of motions in a lumbar spine[END_REF]. Only few experimental studies investigated the effects of a compressive preload in the cervical spine [START_REF] Panjabi | Criticial load of the human cervical spine: an in vitro experimental study[END_REF][START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF][START_REF] Miura | A method to simulate in vivo cervical spine kinematics using in vitro compressive preload[END_REF]. In addition, Panjabi et al. [START_REF] Panjabi | Criticial load of the human cervical spine: an in vitro experimental study[END_REF] demonstrated that application of a pure vertical compressive load on the cervical spine resulted in collapse of spinal specimen at very low loads far below physiological loads. Similar findings were reported by Patwardhan et al. [START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF].

Therefore, Patwardhan proposed a method to apply compressive preload consisting of a follower preload applied along the spinal segment, remaining tangent to the spinal curve and allowing for reduction in bending moments [START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF]. Using this follower load protocol, these authors reported that the cervical spine specimens could support a 120-N compressive load versus only 20 N in case of vertical load [START_REF] Patwardhan | A follower load increases the load-carrying capacity of the lumbar spine in compression[END_REF][START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF].

Although using follower load to apply compressive load could be an attractive option to simulate physiological muscles action, the way that a follower load may precisely affect spine posture, spine kinematics and loads transfer in the cervical spine has only been partly reported. In addition, Miura et al. [START_REF] Miura | A method to simulate in vivo cervical spine kinematics using in vitro compressive preload[END_REF] reported that compressive preload affected spinal motion differentially depending on which direction was considered. True impact of follower load positioning in relation with the centre of rotation has not been clearly investigated for the cervical spine. For these reasons, no standardisation has been established with regard to the conditions in which compressive preload should be applied and there are still controversies to use systematically axial preload during in vitro cadaveric testing [START_REF] Goel | Test protocols for evaluation of spinal implants[END_REF][START_REF] Wilke | Testing criteria for spinal implants: recommendations for the standardization of in vitro stability testing of spinal implants[END_REF].

The objective of the present study was then to fully investigate the biomechanical influence of a follower load in the cervical spine in terms of spine posture, spinal kinematics and intradiscal pressure (IDP) using both in vitro human cadaveric and numerical simulating evaluations.

Each spinal specimen was evaluated sequentially in two conditions: intact and loaded after application of the compressive load.

Displacements measurement

Biomechanical tests were performed under load control using a three-dimensional optoelectronic measurement system (POLARIS TM VICRA system, Northern Digital Inc, Waterloo, ON) connected to an acquisition and data processing system. All measurements were performed during the third cycle for each load case reducing the influence of the viscoelastic behaviour of spinal specimens. Angular and linear displacements were measured using reflective markers rigidly fixed on each vertebra from C3 to C7.

To determine the displacements of a vertebra with regard to the lower adjacent one, the anatomical frame of each vertebra and the local frame of its associated reflective markers were determined from 3D reconstructions that were obtained from EOS TM biplanar X-ray system [START_REF] Dubousset | A new 2D and 3D imaging approach to musculoskeletal physiology and pathology with low-dose radiation and the standing position: the EOS system[END_REF][START_REF] Rousseau | Reproducibility of measuring the shape and three-dimensional position of cervical vertebrae in upright position using the EOS stereoradiography system[END_REF], (Fig. 2). Accuracy in linear and angular measurements was previously calculated to 0.5 mm and 0.5°, respectively. Typical load-displacement curves were obtained for each different testing condition.

Intradiscal pressure measurement

Special pressure sensors (EPL-B02-100P; Entran, Fairfield, NJ) were placed into the C3-C4 and C4-C5 intervertebral discs allowing measurement of intradiscal pressure at these levels during experimental tests. They were inserted so that the pressure sensitive area was located at the anterior third of the intervertebral space in the AP plane, at the midheight of the disc and aligned with the midline in the frontal plane. Load sensors position was checked on frontal AP and lateral radiographs acquired with the stereoradiographic EOS TM X-ray system (Fig. 2).

Statistical analysis

Statistical comparison of spine posture, ROM, NZ and maximal IDP between intact and loaded spines was carried out using paired Wilcoxon test. All p values were considered statistically significant for a p value \0.05.

Part 2 finite element modelling

Construct of FE Model

A nonlinear three-dimensional FE model of the lower cervical spine was generated in our institution and recently published [START_REF] Laville | Parametric and subjectspecific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns[END_REF][START_REF] Maurel | A three-dimensional parameterized finite element model of the lower cervical spine. Study of the influence of the posterior articular facets[END_REF][START_REF] Rousseau | Influence of the geometry of a ball-and-Socket intervertebral prosthesis at the cervical spine. A finite element study[END_REF]. It consists of a parametric and subjectspecific model, in which mesh was based on hexahedral elements and built from 3D reconstructions using EOS TM biplanar imaging system. It is composed of cervical vertebra from C3 to C7 and soft tissues including intervertebral discs, endplates, facets cartilage and the main ligament structures (Fig. 3).

All mechanical properties of materials have already been described in detail in the literature [START_REF] Laville | Parametric and subjectspecific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns[END_REF]. Cortical and cancellous bones have been differentiated, and tensiononly springs elements have been used to model peripheral annulus and ligament structures. Contact interfaces have The model was then tested in the same conditions for in vitro study by applying pure moments loading to the superior aspect of C3 in FE, LB and AR to a 2-Nm maximum moment loading with 0.2-Nm steps. For each loading condition, the model was tested with 0-, 50-and 100-N follower magnitude and with the follower placed 5 mm behind, 5 mm in front of and at the theoretical emplacement (0 mm).

Three-dimensional ranges of motion, intradiscal loads (anterior part of the nucleus) and facets forces were measured for each configuration.

Results

Part 1 in vitro tests

Cervical spine curve

The effect of the follower load on the spinal curve is presented in Fig. 4. Compared to intact spines, the mean change in C3-C7 sagittal angle was 5°± 3°(0.5-12) following the placement of the compressive load. The change was in flexion for 6/12 specimens (that is reduction in lordosis) and in extension for 6/12 specimens (that is increase in lordosis). The variation was \5°in 6/12 cases and \10°in all cases but one (specimen R2: 11.9°decreased).

Ranges of motion

Main motions in FE, LB and AR The six moments were grouped into three pairs: flexion/extension, left/right axial Fig. 2 Prior to biomechanical tests, precise location of reflective markers (fixed on each vertebra from C3 to C7 to allow for measurement of 3D displacements), guiding screws and intradiscal load sensors was determined using AP (a) and Lateral (b) views of cervical spine specimen Fig. 3 Oblique view of the nonlinear three-dimensional FE model of the lower cervical spine composed by four functional spinal units from C3 to C7 [START_REF] Laville | Parametric and subjectspecific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns[END_REF] been established for facets joints and between spinal processes. Finally, the C3-C7 FE model comprised a total of 5873 nodes, 4142 solid elements, 256 shell elements and 952 tension-only spring elements.

Numerical simulation

A follower load was simulated by using thermo-isotropic truss elements between each vertebra approximately located at the posterior third of the vertebral body close to the rotation and left/right lateral bending. Average load-displacement curves are illustrated in Fig. 5 for intact and loaded spines showing increase in hysteresis in axial rotation and lateral bending. Compared to intact spines, the mean C3-C7 ROM slightly increased from 54.6°± 9°( 37-71) to 56.1°± 9°(38-72) in flexion-extension, p = 0.01; decreased from 45.4°± 8°(27-57) to 38.0°± 7°(21-48) in axial rotation, p = 0.002; and decreased from 43.3°± 6°(32-51) to 37.3°± 7°(24-47) in lateral bending, p = 0.002, Fig. 6a.

Intersegmental angular ROMs (C3/C4, C4/C5, C5/C6 and C6/C7) are summarised in Table 1 for intact and loaded spines.

Coupled motions in AR and LB Following the application of the follower load, the mean coupled axial rotation during lateral bending reduced from 24.6°± 13°(4-54) to 20.7°± 11° . It represented 54.7 ± 26 % (12-105) and 53 ± 22 % (14-95) of the main motion, respectively, without significant difference, Fig. 6b.

The mean coupled lateral bending during axial rotation reduced from 33.5°± 6°(26-43) to 24.6°± 5.9° [START_REF] Rohlmann | Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine[END_REF][START_REF] Patwardhan | Compressive preload improves the stability of anterior lumbar interbody fusion cage constructs[END_REF][START_REF] Renner | Novel model to analyze the effect of a large compressive follower preload on range of motions in a lumbar spine[END_REF][START_REF] Miura | A method to simulate in vivo cervical spine kinematics using in vitro compressive preload[END_REF][START_REF] Amevo | Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers[END_REF][START_REF] Dvorak | In vivo flexion/extension of the normal cervical spine[END_REF][START_REF] Van Mameren | Cervical spine motion in the sagittal plane II. Position of segmental averaged instantaneous centers of rotation-a cineradiographic study[END_REF][START_REF] Dubousset | A new 2D and 3D imaging approach to musculoskeletal physiology and pathology with low-dose radiation and the standing position: the EOS system[END_REF][START_REF] Rousseau | Reproducibility of measuring the shape and three-dimensional position of cervical vertebrae in upright position using the EOS stereoradiography system[END_REF][START_REF] Laville | Parametric and subjectspecific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns[END_REF][START_REF] Maurel | A three-dimensional parameterized finite element model of the lower cervical spine. Study of the influence of the posterior articular facets[END_REF][START_REF] Rousseau | Influence of the geometry of a ball-and-Socket intervertebral prosthesis at the cervical spine. A finite element study[END_REF][START_REF] Bogduk | Biomechanics of the cervical spine. I: normal kinematics[END_REF][START_REF] Watier | Etude expe ´rimentale du rachis cervical: comportement me ´canique in vitro et cine ´matique in vivo[END_REF](29)[START_REF] Rohlmann | Applying a follower load deliver realistic results for simulating standing[END_REF][START_REF] Pospiech | Intradiscal pressure recordings in the cervical spine[END_REF][START_REF] Veron | Helicoidal axes to characterize cervical spine kinematics. A finite element study[END_REF](33)[START_REF] Barrey | Cervical disc prosthesis versus arthrodesis using one-level, hybrid and two-level constructs. An in vitro investigation[END_REF], which represented 75.5 ± 15.9 % (51-105) and 65.7 ± 14.3 % (37-85) of the main motion, respectively, p \ 0.005, Fig. 6b.

Intradiscal pressure

Load-pressure curves were obtained for intact and loaded spines in flexion-extension, axial rotation and lateral bending (Fig. 7). At C3-C4 and C4-C5, intradiscal pressures were systematically higher for loaded spines than for intact spines for the three loading conditions. In contrast to flexion-extension, the shape of the load-pressure curves was significantly affected by the application of the follower load in axial rotation and lateral bending. Typical V-shape was replaced by a flat curve.

In flexion, the maximal IDP at 2 Nm slightly increased from 7.35 ± 2.8 bar (2.6-11) to 8.68 ± 3.5 bar (2.8-13.8) for C3-C4 (?18.1 %), p = 0.016, and from 7.58 ± 3.8 bar (2.3-12) to 8.11 ± 4 bar (3.5-13.9) for C4-C5 (?7 %), without significant difference (p = 0.182).

Part 2 finite element modelling

FE model validation

Validation of the FEM was performed by comparing loaddisplacement curves of intact condition (0-N follower load) provided by the model in flexion-extension, axial rotation and lateral bending with the corresponding curves from the in vitro experiments. The FEM was considered validated whether the load-displacement curve from the model was located inside the corridor observed from the in vitro study (Fig. 8).

Effects of follower load

Mean changes in ROM observed following the simulation of a 50-N compressive load are presented in Fig. 9 for the three loading conditions. ROM increased from 61°to 62°i n FE, and decreased from 31.5°to 30.5°in AR and from 31°to 30.5°in LB. Compared to intact condition, no more than 10 % variation was observed with regard to the different magnitude and positioning simulated. Maximal variation of ROM in FE was observed with 100-N follower preload (?3.5 %), and the greatest difference between intact and loaded condition was observed for 50 N at -5 mm in AR (ROM decreased from 31.4°to 28.3°, that is -9.9 %).

Concerning intradiscal loads, aspect of load-pressure curves is presented in Fig. 10 for intact and 50-N loaded spines. Compared to intact spines, intradiscal loads were systematically increased following simulation of compressive load. In flexion, at 2 Nm, IDP increased by approximately 22 and 26 % at C3-C4 and C4-C5, respectively.

Finally, facets forces were systematically increased by applying compressive preload by approximately 5-10 % at 2 Nm in extension, 7-12 % in axial rotation and 7-9 % in lateral bending, Fig. 11.

Discussion

The objective of this study was to evaluate the influence of applying a follower preload on the biomechanical behaviour of the cervical spine using both in vitro human cadaveric and numerical simulating methods.

In vitro protocol

Our protocol allowed for measurement of 3D angular and linear displacement for each load case and determination of main and coupled motions. The use of the EOS TM stereographic system gave us the opportunity to precisely determine the relative position of markers-dependent frame with reference to the anatomical frame of each vertebra. The values of the intact model in our study were comparable to those previously reported in the literature, suggesting the reliability of our in vitro protocol [START_REF] Wen | Three-dimensional biomechanical properties of the human cervical spine in vitro. I. Analysis of normal motion[END_REF][START_REF] Bogduk | Biomechanics of the cervical spine. I: normal kinematics[END_REF][START_REF] Watier | Etude expe ´rimentale du rachis cervical: comportement me ´canique in vitro et cine ´matique in vivo[END_REF][29].

Application of compressive follower preload

Comparing the follower load to a simple vertical load, Patwardhan et al. [START_REF] Patwardhan | Load-carrying capacity of the human cervical spine in compression is increased under a follower load[END_REF] demonstrated that cervical spine segments could support a compressive load of 250 N without instability whereas pure vertical compressive load resulted in great changes in lordosis angle at only 20-to 40-N loading. Putting each spinal segment in nearly pure compression, a follower load increased the load-carrying capacity of the spine specimens. Thus, we did not investigate a simple vertical load to simulate the physiological compressive muscles action during experimental tests. The follower load consists of a compressive load applied along the spine, perpendicular to the transversal plane of the disc space and tangent to the spinal curve, in order to put the spine in compression with minimal changes in spinal curvature [START_REF] Patwardhan | A follower load increases the load-carrying capacity of the lumbar spine in compression[END_REF][START_REF] Rohlmann | Applying a follower load deliver realistic results for simulating standing[END_REF]. The position of guiding screws by which the follower load is applied may affect the type of sagittal bending moment induced and thus the effect of Fig. 7 Average intradiscal pressures at C3-C4 and C4-C5 (n = 12 spines) in flexionextension, axial rotation and lateral bending follower load on spinal curve. With regard to the balance point, posterior position may result in extension moment and induce increase in cervical spine lordosis whereas anterior positioning may result in a more flexed spine, affecting potentially the biomechanical behaviour of the spinal segment. Our study demonstrated that positioning the follower load between anterior and posterior ridges of the transverse process resulted in only minor changes in spinal curve (only 5°on average), suggesting that this anatomical landmark was close to the natural centre of rotation and was a reliable landmark in terms of reproducibility.

Influence on kinematics, intradiscal pressures and facet loads

Under a follower load, we found that the biomechanical behaviour of cervical spine specimens was significantly more affected in axial rotation and lateral bending than in flexion-extension.

Flexion-extension

In flexion-extension, variations in terms of total ROM, NZ and profile of load-displacement curves were negligible. Only significant effects observed were increase in intradiscal pressures (around 10 %) slightly inferior to the results suggested by the model. Considering that, by applying follower load, the objective was to put each intervertebral segment in compression, close to in vivo conditions, without affecting the native biomechanical behaviour of spines, our study suggests that this method is quite adequate for flexion-extension.

In addition, regarding the results from our numerical simulation study concerning the impact of follower positioning, we observed that the follower could be placed in an area of 10 mm around the theoretical CMR without major changes in spine kinematics.

Axial rotation and lateral bending

In our study, not only the extent of main motion was significantly reduced in axial rotation and lateral bending but also coupled motion was affected following application of follower load. Shape of load-displacement curves was characterised by a significant increase in the hysteresis with significant changes in the magnitude of NZ, suggesting that the quality of motion could also be affected. These findings have already been reported in the lumbar spine through human experimental study [START_REF] Rohlmann | Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine[END_REF] and through a porcine model [START_REF] Gardner-Morse | Physiological axial compressive preloads increase motion segment stiffness, linearity and hysteresis in all six degrees of freedom for small deplacements about the neutral posture[END_REF]. In addition, significant alterations were observed for load-pressure curves in axial rotation and lateral bending, suggesting that application of follower load induces a less physiological load transfer trough the disc space, potentially due to shear forces mentioned above. Similar changes in profile of load-pressure curves after simulation of muscles forces have also been reported by Pospiech et al. [START_REF] Pospiech | Intradiscal pressure recordings in the cervical spine[END_REF]. Considering that these findings were not confirmed through our numerical simulation, we hypothesised that these changes in spinal kinematics may be the consequence of the set-up used in vitro to apply the compressive preload.

In fact, nearly pure compression of spinal segment is probably obtained during FE whereas during AR and LB, the application of follower load may result in a combination of compression and shear forces inducing significant changes in spine kinematics. The presence of sliding frictions along the follower load path during axial rotation and lateral bending is highly suggested by the increase in hysterisis on load-displacement curves. As described by Patwardhan et al. [START_REF] Patwardhan | Effect of compressive follower preload on the flexion-extension response of the human lumbar spine[END_REF], these frictions may induce at each contact between screw heads and flexible cables a double-component force consisting of a tangential one perpendicular to the transversal plane of the disc space (compressive force) and a transversal one parallel to the disc space (shear force).

However, it is difficult to determine precisely the relative value of these two forces during in vitro tests. By waxing flexing cables and smoothly drilling the screw heads, the frictions can only be limited considering that contact between screws and flexible cables is unavoidable.

These results are concordant with those mentioned by Miura and Cripton [START_REF] Miura | A method to simulate in vivo cervical spine kinematics using in vitro compressive preload[END_REF] which reported that the application of preload resulted in reduction in spinal motion differentially depending on loading condition. The authors consequently proposed to apply different moments in different directions. Comparing two different protocols, they found that pure moments of 2 Nm in FE and LB and 4 Nm in AR (2:4:2 protocol) reproduced more closely in vivo values than equal moments of 1 Nm in each direction.

Finally, coupled motions in the lower cervical spine have been reported to be secondary to the orientation of facets joints [START_REF] Maurel | A three-dimensional parameterized finite element model of the lower cervical spine. Study of the influence of the posterior articular facets[END_REF][START_REF] Veron | Helicoidal axes to characterize cervical spine kinematics. A finite element study[END_REF]. By compressing the facet joints as demonstrated through our numerical simulation investigation (approximately 10 % increase in facets forces), the follower load could affect more specifically coupled motions during axial rotation and lateral bending than flexionextension, which is a relatively pure motion in the sagittal plane.

Relevance of follower load for in vitro tests

Theoretically, the follower load represents an attractive option permitting to simulate more closely in vivo conditions by reproducing head weight and cervical muscles action. However, our results suggested that the placement of such compressive preload may significantly affect the biomechanical behaviour of spine specimen especially during AR and LB and thus leads to some degree of variability from a specimen to an other.

Considering our results and that follower load is relatively time-consuming and technically demanding, we assume that the application of follower load should be considered according to the goal of experimentation and especially the type of instrumentation tested. When intend to investigate classical rigid spinal implants and rigid constructs, follower load may not be beneficial during in vitro tests.

On the contrary, when there is a risk of separation between implant and bone surfaces or between implant parts, as observed for disc prostheses or cages alone [START_REF] Patwardhan | Compressive preload improves the stability of anterior lumbar interbody fusion cage constructs[END_REF]33,[START_REF] Barrey | Cervical disc prosthesis versus arthrodesis using one-level, hybrid and two-level constructs. An in vitro investigation[END_REF], segmental compressive force should be useful, thus limiting the separation of bearing surfaces or separation

Fig. 1

 1 Fig. 1 AP (a), oblique (b) and lateral (c) view of cervical spine specimen after insertion of guiding screws (black star) between anterior and posterior ridges of the transverse process

Fig. 4 Fig. 5

 45 Fig. 4 Changes in cervical spine curve following the placement of the follower preload

Fig. 6

 6 Fig. 6 ROM in FE, AR and LB for intact and loaded spines (a) and coupled motions during AR and LB for intact and loaded spines (b)

Fig. 8

 8 Fig. 8 Load-displacement curves provided by the model were compared to those measured from experimental tests for the 12 specimen in FE, AR and LB

Fig. 10

 10 Fig. 10 Load-pressure curves provided by the FE model for intact and 50-N loaded condition in FE, AR and LB

Fig. 11

 11 Fig. 11 Facets forces in extension, right AR and right LB

Table 1

 1 Intersegmental ROMs for intact and loaded spines (n = 12) in the three loading conditions

		C3-C4	C4-C5	C5-C6	C6-C7
	Flexion-extension
	Intact	12.7 ± 3.6	14.4 ± 3.7	13.9 ± 4.1 13.6 ± 3.2
	Follower 12.9 ± 3.5	14.8 ± 3.5	14.5 ± 4.1	14 ± 3.1
		ns	p \ 0.05	p \ 0.01	p \ 0.01
	Axial rotation
	Intact	15.7 ± 3.8	12.5 ± 2.8	9.1 ± 2.8	7.8 ± 1.9
	Follower 12.8 ± 3.2	11.9 ± 3.1	7.9 ± 2.5	6.7 ± 2.6
		p \ 0.005	ns	p \ 0.01	p \ 0.05
	Lateral bending
	Intact	11 ± 2.3	10.2 ± 2.3	10.2 ± 3.4 9.1 ± 2.1
	Follower 9.5 ± 2.7	9.1 ± 2.6	8.7 ± 3.4	7.5 ± 2.3
		p \ 0.005	p \ 0.01	p \ 0.005	p \ 0.005

Conflict of interest None.


Adriana Neag
email: adriana.neag@ipm.utcluj.ro

Véronique Favier

Régis Bigot

Mariana S Pop

Microstructure and flow behaviour during backward extrusion of semi-solid 7075 aluminium alloy

Keywords:

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Introduction

Semi-solid processing by thixoextrusion (one of the thixoforming processes) refers to the shaping of metals by extrusion at a temperature between solidus and liquidus as mentioned in Kirkwood et al.'s (1992) patent. [START_REF] Kapranos | Semi-solid processing of tool steel[END_REF] analysed thixoextrusion and found that this technology can be applicable to most engineering alloy families, including aluminium, magnesium, copper and ferrous alloys. [START_REF] Suery | Mise en forme des alliages métalliques à l'état semi-solide[END_REF] and [START_REF] Atkinson | Modelling the semisolid processing of metallic alloys[END_REF] compared the conventional hot-extrusion processes to thixoextrusion processes of aluminium alloy. They illustrated the most important advantages, such as reduction of the extrusion force and of friction forces between material and tools, higher fluidity of material, longer tool life, high productivity, etc., of the thixoextrusion process. This process required a non-dendritic microstructure made of solid spheroids surrounded by a liquid matrix in order to obtain thixotropic flow behaviour. Several methods can be used to produce this target microstructure. Amongst them, there are the RAP (recrystallisation and partial melting) method patented by [START_REF] Kirkwood | Thixotropic materials[END_REF] and the SIMA (strain-induced melt activation) method patented by [START_REF] Young | Fine grained metal composition[END_REF]. The main difference between these two methods regards the working temperature of the material before reheating. The SIMA route involves hot working at temperatures above the recrystallisation temperature. The RAP route involves working at temperatures below the recrystallisation temperature. In both cases, the billet is reheated into the semi-solid state using either electrical resistance furnace or induction system. In their recent review, Hirt et al. (2009a) mentioned that the heating using classical electric resistance furnace based on radiation/convection heating is cheap but involves long heating time and is a robust process control structure. Induction heating is shorter and provides the possibility of flexible process control. Induction heating systems are mostly used in industrial environments because of their shorter heating time, though [START_REF] Moschini | Manufacture of automotive components by semi-liquid forming processes[END_REF] reported the use of a classical furnace. Many materials were tested using both techniques. Bolouri et al. (2010) and [START_REF] Shang | Deformation mechanism and forming property of Al6061 alloys during compression in semi-solid state[END_REF] both used an electrical resistance furnace to reheat aluminium 7075 and 6061 alloys, respectively. Induction systems were used to reheat aluminium-silicon casting alloys [START_REF] Kapranos | Near net shaping by semi-solid metal processing[END_REF], 7075 aluminium alloy (Vaneetveld et al., 2008a) and steels such as 100Cr6 and X210CrWl2 [START_REF] Hirt | Semisolid forging of 100Cr6 and X210CrW12 steel[END_REF]. When the billet is reheated in an induction furnace, heat losses caused by convection and radiation at the lateral surface of the slug and by heat conduction at the surface bottom occur. Consequently, there is a large difference between the core and the edge temperature. Heating 7075 aluminium alloy, Vaneetveld et al. (2008b) observed that the position of the slug in the inductor did not have any influence on recrystallisation. Using a protective gas leads to large grains on the side of the slug revealing a lack of recrystallisation because it raises the heat losses. In order to reduce heat losses, Hirt et al. (2009b) optimised the coil geometry to increase the energy at the edges. In any case, most of thixoforming experiments are carried out with dies at much lower temperatures than the initial slug. They are interesting because they reproduce non-isothermal conditions that can be found in industrial applications. However, they involve solidification phenomena near the die-billet interface because of heat losses. [START_REF] Forn | Thixoextrusion of A357 aluminium alloy[END_REF] found that the external quality of an A357 aluminium alloy thixoextruded component is better using colder die temperature (room temperature) because the higher solidification rate raises the pressure applied on the material. Conversely, Vaneetveld et al. (2008a) demonstrated that the optimal external quality for 7075 aluminium alloy component is reached for tool temperatures ranging from 75 • C to 100 • C. Better understanding of microstructure changes during the forming process is thus required. Clarifying the role of agglomeration-disagglomeration processes from solidification phenomena on the flow behaviour is not possible for non-isothermal processes. Few quasi-isothermal thixoforming trials of steels [START_REF] Bobzin | Microstructural evolution during semisolid state strain induced melt activation process of aluminium 7075 alloy[END_REF] and aluminium alloys [START_REF] Kapranos | Thixo-extrusion of 5182 aluminium alloy[END_REF] exist in literature. They involved ceramic dies but remain a challenging task mainly because of die corrosion and mechanical resistance issues. Compression tests on semi-solid aluminium alloys are more often carried out under quasi-isothermal conditions. Observations of quenched microstructure obtained after deformation help the understanding of the material flow. Kang et al. (1999), who worked on A356 alloy having solid fraction ranging from 50% to 90%, showed that macro separation appeared between the liquid and the solid but that more homogeneous structure phenomena can be observed with greater compressive velocity. For semi-solid 6061 Al alloys also with high solid fraction, [START_REF] Shang | Deformation mechanism and forming property of Al6061 alloys during compression in semi-solid state[END_REF] found that plastic deformation of solid particles and also sliding among the solid particles were dominant deformation mechanisms.

The aim of this paper is to provide such information in the case of quasi-isothermal backward extrusion test of 7075 aluminium alloy in the semi-solid state. The billet was heated inside the extrusion die to avoid the convective and radiation heat losses obtained when the billet is directly heated by induction. The evolution of the formation of the semi-solid microstructure when the billet is placed in a resistance heating furnace or inside a die heated by induction is investigated. It is found that reheating the steel die and the aluminium billet placed into the die at the same time using an induction furnace provides rapidly a very homogeneous microstructure suitable for thixoforming. During thixoextrusion, despite the high solid fraction, the solid globules are weakly connected and slide over each other without any plastic deformation. The flow remains quasi homogeneous resulting in homogeneous induced microstructure so that uniform mechanical properties of the component are expected.

Experimental procedures

Material

The material used for thixoextrusion was a commercially 7075 aluminium alloy having the following chemical composition Zn (5.1-6.1)-Mg (2.1-2.9)-Cu (1.2-2)-Cr (0.18-0.28)-Fe (max0.5)-Si (max0.4)-Ti (max0.2) (numbers indicate wt.%). The material supplier was Euro Alliages/Locatelli, Florange, France. The 7075 wrought aluminium alloy is typically used in aircraft, automotive structural parts and other highly stressed applications where very high strength and good resistance to corrosion are required. The as-received alloy was extruded with an extrusion ratio of 16:1. After extrusion the material was T6 heat treated. The typical microstructure of this material is shown in Fig. 1. Specimens used to analyse the microstructure were ground with P80-P1200 grit paper, polished using 6-1 micron diamond paste and etched using Keller etch. Optical micrographs revealed microstructures consisting of unrecrystallised primary ␣(Al) elongated grains, aligned in the extrusion direction, with the grain boundaries well delineated.

Semi-solid billet preparation

A DSC analysis was obtained by courtesy of Mr. Vaneetveld from Liege University [START_REF] Vaneetveld | Conception of tooling adapted to thixoforging high solid fraction hot-crack-sensitive aluminium alloys[END_REF]. Fig. 2 shows the evolution of the solid fraction vs. temperature obtained by calorimetric experiments (heating at 15 • C/min). It reveals low temperature sensitivity for temperatures ranging from 470 • C to 610 • C and much higher temperature sensitivity for temperatures ranging from 610 • C to 650 • C. The working temperature window was chosen equal to 580-610 • C in order to get a not too high solid fraction (ranging from 0.9 up to 0.7) required to get thixotropic behaviour but also a not too low solid fraction to get a reliable process, namely to avoid strong changes of solid fraction due to variation in temperature.

Since the as-received material was cold deformed, the RAP process to get the semi-solid microstructure was investigated. Two different reheating processes are applied: electrical resistance furnace and inductive system. In both cases, the billets are cylindrical specimens with 40 mm in diameter and 27 mm height, machined from the extruded bar. These dimensions were chosen to obtain a complete filling of the die after thixoextrusion test. Various heating times to the semi-solid temperature ranging from 5 min to 280 min were investigated. After heating, the billet, alone in the case of resistance heating and inside the dies in the case of inductive heating, was quenched into cold water to "freeze" the microstructure in the semi-solid state. Cross sections of the cylindrical billets were prepared for metallographic observations. They were polished and then etched using the same procedure as for the as-received material. In each case, the whole section was observed but the quantitative analyses were achieved in the centre of the section, unless otherwise stated. The quantitative results were obtained by the image analysis software ImageJ. The mean grain size was measured using a mean linear intercept method. The shape factor was calculated using the equation F = 4 × × A/P 2 where A and P are the area and the perimeter of the globule, respectively.

Reheating in electrical resistance furnace

Billets were heated at 580 • C in an electrical resistance furnace and quenched after holding for 5, 15, 20, 30, 60, 120, 180 and 240 min. In these cases, thermal radiation generated by the electric resistance heat the billet surface. Heat transfer across the billet occurs by thermal conduction.

Reheating by induction

The reheating was performed using an induction system used in the LCFC laboratory from the "Arts et Métiers ParisTech" Metz (Fig. 3a). In this case, the billet is put inside the die used for thixoforming which has the gauge dimensions of ∅100 mm × 115 mm and a cup shape (Fig. 3b). The dies are made of tool steel X38CrMoV5. The inductor was designed to perform the reheating of the die containing the slug and to allow the backward extrusion test through the induction coil in order to avoid the transfer of the slug (Fig. 4). The thixoextrusion die containing the initial extruded billet was positioned in the centre of the inductor coil and was placed on a special ceramic support in order to be thermally insulated. The frequency of the electrical generator ranged between 10 and 30 kHz. The electrical power was 25 kW. This heating system is controlled by an electronic device which programs the reheating cycles (Fig. 3d). Two "K" type thermocouples were inserted to monitor the temperature evolution: the first one into the centre of the slug (a hole of 2.5 mm (Fig. 3c) was drilled into the centre of the billet) and the second one was into the die at less than 5 mm from the slug surface (Fig. 3b). The heating route consisted in 4 successive power stages to ensure a homogeneous temperature in the slug (Fig. 3d). It was obtained by trial and error procedure. Typically, the complete heating cycle lasted 13 min so that the average heating speed was about 45 • C/min. Note that in this case, the heat sources are generated by Foucault currents induced by the electromagnetic field within the metal. The induction frequency is about 10-30 kHz, so that the penetration depth of the Foucault currents is about 1 mm from the die surface.

Then, heat transfers by thermal conduction across the die up to the centre of the billet (assuming perfect thermal interface between the die and the billet). Placing the billet into the die avoids the convective and radiation heat losses obtained when the billet is directly heated by induction as Hirt et al. (2009b) had shown.

Thixoextrusion tests

Thixoextrusion tests were carried out on the hydraulic 200 kN press located at the "Arts et Métieres ParisTech" Metz. As mentioned above, the billet was placed into the die. Both were reheated using the induction system (Fig. 4a). They were placed on an Inconel support. A Nefacier 1500 © board was placed between the Inconel support and the table press to reduce heat losses. A tool protector coating (Acheson Pulvegraph D31A) is sprayed after each extrusion test to protect tool surface against wear and chemical attack of aluminium on steel. Upon reaching the desired temperature and holding time, the electric power of the induction system was shut down and the thermocouple which was in the centre of the slug (Fig. 3b) was extracted [START_REF] Neag | Study on thixo-extrusion of semi-solid aluminium[END_REF]. The backward extrusion test was then immediately carried out through the induction coil in order to avoid the transfer of the slug (Fig. 4b andc). Hence, quasiisothermal conditions are obtained. The expected ram speed during the forming was about 6 mm/s and the displacement of superior die is limited on the inferior die. After heating and forming, the set was water quenched.

Results and discussion

3.1. Semi-solid microstructure before thixoextrusion

Reheating by electric resistance furnace

The microstructure of the material quenched after 5 min from 580 • C at the centre part of the billet cross section is shown in Fig. 5a. The grains are elongated and display winding boundaries. After 15-20 min, the grains evolved to a much more equiaxed shape (Fig. 5b andc) but grain boundaries were still winding. After 30 min (Fig. 5d), the microstructure changed to an irregular polygonal structure: grain boundaries are much smoother and are faceted. Some solid particles are surrounded by liquid film (dark phase). The starting microstructure was thus strongly removed. The grain boundaries were gradually penetrated by liquid due to the dissolution of the last solidified phase of low melting temperature like the literature shows [START_REF] Atkinson | Microstructural coarsening of semi-solid aluminium alloys[END_REF]. Atkinson et al. (2008) indicated that the formation of liquid stimulates the recrystallisation in extruded T6 7075 aluminium alloys. Thanks to the prior deformation and the storage of elastic energy, new more equiaxed grains but having irregular shape replaced the initial elongated grains. The size of the recrystallised grains is highly dispersed ranging from few micrometers to hundred micrometers. Prolonging the holding time (Fig. 5e-h) leads to lubricating more and more grain boundaries, spheroidising solid grains, increasing the number and the size of the intragranular liquid droplets and increasing the mean grain size while reducing the grain size dispersion. These observations are confirmed by more quantitative results. The liquid fraction was found to reach its steady state at 30 min (Fig. 6a). The value obtained (∼8%) is in good agreement with DSC analysis results (Fig. 2) and close to the value reported by Atkinson et al. (2008). Prolonging holding times does not change the liquid fraction but changes the microstructure: the number of solid grains decreases while the mean grain size rises up to steady state reached at 120 min (Fig. 6b). The degree of spheroidisation is found equal to 0.85. The mean grain size is about 75 m.

Clearly, grain growth occurred during electrical resistance reheating. As mentioned by [START_REF] Luo | An investigation of microstructure evolution of RAP processed ZK60 magnesium alloy[END_REF] who analysed the impact of the compression ratio on the microstructure after RAP process on Mg alloys, grain growth involved two mechanisms:

(1) coalescence of solid grains and (2) Ostwald ripening. Concerning (1), low angle/low energy grain boundaries (for which gb < sl where is surface energy and subscripts gb and sl stand for solid/solid and solid/liquid interface, respectively) are not wetted [START_REF] De Freitas | Rheological behaviour and deformation characteristics of a commercial and a laboratory-cast Al-4%Cu alloy in the semi-solid state[END_REF][START_REF] Luo | An investigation of microstructure evolution of RAP processed ZK60 magnesium alloy[END_REF]. These solid/solid contacts favoring re-welding and coalescence of the grains. As [START_REF] Luo | An investigation of microstructure evolution of RAP processed ZK60 magnesium alloy[END_REF] demonstrated, this mechanism explains why some solid particles (indicated by arrows in Fig. 5g) keep irregular and are faceted despite prolonged holding time. The arrows show migration of some of the grain boundary films. Concerning (2), the finest solid particles melted because of their high curvatures in favor to the larger ones, like in [START_REF] Koke | Flow behaviour of semi-solid metal alloys[END_REF], Atkinson and Liu (2008) and [START_REF] Luo | An investigation of microstructure evolution of RAP processed ZK60 magnesium alloy[END_REF]. Our observations are in good agreement to [START_REF] Tzimas | Evolution of near-equiaxed microstructure in the semisolid state[END_REF], [START_REF] Koke | Flow behaviour of semi-solid metal alloys[END_REF], [START_REF] Atkinson | Microstructural coarsening of semi-solid aluminium alloys[END_REF] that clearly shows that this last mechanism is not dominant for the first 240 min as expected at low liquid fraction. Some liquid droplets are present in the primary phase (Fig. 5). These intragranular liquid droplets possibly originate from the internal inhomogeneity of the primary solid, which is caused by chemical segregation.

With increasing holding time, the number of intergranular droplets decreases and their mean size increases. According to Bolouri et al. ( 2010), on the one hand, some contiguous intragranular liquid droplets gradually merge into some bigger intragranular droplets by coalescence. On the other hand, Ostwald ripening occurs: small droplets disappear in favor of bigger droplets by diffusion through the solid phase.

As far as microstructure homogeneity is concerned, the solid particles are not uniformly distributed in the slug cross section. The solid grains continue to grow after the first 120 min at the specimen edge. In addition, Fig. 7 shows evidence of grain coalescence. As a result, interconnected grains form a layer of 300-400 m thickness at the slug surface.

The presence of large grains was also observed by [START_REF] Wang | Improvement of grain coarsening on the surface of extra-low carbon wire rods[END_REF], Manson-Whitton et al. (2002) and Vaneetveld et al. (2008b). In order to explain this phenomenon, [START_REF] Wang | Improvement of grain coarsening on the surface of extra-low carbon wire rods[END_REF] and Manson-Whitton et al. (2002) mentioned strong coarsening while Vaneetveld et al. (2008b) suggested that the stored energy within the grains at the surface of the extruded cylinder was not sufficient for recrystallisation. Indeed, friction during extrusion at the solid state induced heat that could decrease the stored energy. The evidence of coalescence (Fig. 7) and the fact that this phenomenon does not exist when the billet is reheated using the induction system, suggest that the large grains observed here result from a prolonged isothermal heating. Further investigations are needed to assess this hypothesis. This large grain layer may impact the flow of the semi-solid during the forming process.

Reheating of the billet within the die by induction furnace

Fig. 8 shows the microstructure of 7075 aluminium alloy quenched after 13 min induction reheating. The temperature at the slug centre during the reheating is given in Fig. 3d. The target temperature was 580 • C. The light primary solid phase and the dark eutectic phase, corresponding to the solid phase and to the liquid phase which are supposed to be present in the semi-solid state, can be clearly seen in the cross and longitudinal section (Fig. 8).

The microstructure contains almost perfectly globular recrystallised grains. The intragranular liquid droplets are homogeneously distributed in the grains and are smaller than in the case of resistance reheating. The microstructure presented in Fig. 9 shows clearly that some small liquid pockets (indicated by A) are entrapped within the spherical solid particles. The particles are surrounded by solid bonds "B" and the not entrapped liquid (indicated by arrow C), at 580 • C. The solid fraction is 0.87 in the cross section and 0.81 in the longitudinal section. The average grain size does not exceed 70 m. These values are of the same order as in the case of resistance reheating. After induction reheating, it was also observed that the solid particles are much more uniformly distributed on the cross section surface (Fig. 8c). The variation of the shape factor with isothermal holding times is shown in Fig. 10. The shape factor is strongly dependent on holding time and processes of reheating. It increases up to a steady state value of 0.85 at 60 min when using the resistance furnace while it increases up to 0.95 after only 13 min when using the induction system. In other words, spheroids are more fully rounded when using the induction system.

Since the low liquid fraction and the quite short holding time involved here, coalescence is the dominant grain coarsening mechanisms as found for resistance reheating. Fig. 9 area B supports this hypothesis. Induction reheating produces quite similar semi-solid microstructure more rapidly than resistance heating. However, we can notice two major differences. Firstly, the grains are more spherical in shape: they are still faceted but do not display sharp corners. Secondly, the microstructure is more homogeneous in the slug cross section. Induction heating produces very much higher power densities than thermal radiation. This allows short interaction time to reach the required temperature while preventing from grain growth. Recrystallisation occurred entirely and homogeneous microstructure with spherical grains is obtained. This microstructure is suitable for thixoforming and short heating time is obviously very interesting for industrial application. Microstructure changes during thixoforming were investigated and results are presented in the next section. The load ranged from 0 to 30 kN. The load-displacement curve can be divided into four stages. The first stage associated with zero force corresponds to the motion of the upper ram until it touches the upper part of the die. Then, the slug is compressed and fills the lower part of the component (stage II). The stages III and IV are related to the backward extrusion and the filling of the cup. During this filling, the contact area between the slug and the die increases. As a result, the load rises due to the increasing friction. Note that complete die filling was obtained.

Thixoextrusion test: load and induced microstructure

The load clearly decreased with decreasing solid fraction. This result is expected and consistent with literature data for any semi-solids such as Sn-Pb alloys shown by [START_REF] Fan | Modeling of rheological behavior of semisolid metal slurries. Part 2. Steady state behavior[END_REF], aluminium alloys by Kang et al. (1999) and [START_REF] Liu | Rapid compression of aluminum alloys and its relationship to thixoformability[END_REF], or steels by [START_REF] Shimahara | Investigation of flow behaviour and microstructure on X210CrW12 steel in semi-solid state[END_REF]. At f s = 0.69, the material does not display sufficient resistance to be measured by the load cell until the stage IV. It was difficult to remove the cup from the upper part of the die due to a strong adherence. The cup was found with a very bad surface quality while the cup displayed a much better surface quality for 0.77 and 0.82 solid fraction. As f s = 0.77 appears as a good compromise to get lower load and a good surface quality, we analysed the microstructure of the component obtained after forming and quenching.

The extruded cup was sectioned along the vertical axis for metallographic observations. No appreciable difference is observed between the seven microstructures (Fig. 12). A globular structure of the primary Al phase, similar to that found in Fig. 8 obtained after reheating, is observed in the whole section of the cup. More quantitative results show that the solid fraction is about 0.8 at the bottom of the cup and slowly decreases up to 0.74 at the upper part of the cup. These results reveal the presence of (1) a slight segregation of the liquid during the forming process and (2) sliding among solid particles without any plastic deformation.

In these experiments, despite the high solid fraction (0.75-0.8), the solid grains are very weakly connected and most of grain boundaries are wetted by a thin liquid film. As a result, the flow is mainly driven by the liquid and remains quasi homogeneous. Under these quasi isothermal conditions, the slight segregation phenomenon is attributed to the geometry of the cup. In the course of the filling, the flow front surface area increases with increasing diameter of the cup. Such an increase is easily accommodated by the liquid phase which is much more fluid whereas the solid particles could interfere with each other and slow down in their movement (Hirt et al., 2009b). This segregation phenomenon remains small because of the small amount of liquid. As mentioned in Kang et al. (1999) and [START_REF] Becker | Impact of experimental conditions on material response during forming of steel in semi-solid state[END_REF] for steels and aluminium alloys, the solid/liquid phase macro separation seems to require a high enough amount of liquid, or more precisely, a high enough amount of free liquid. Then, a preferred flow path develops dominated by the free liquid. As a result, a critical temperature above which the flow is heterogeneous seems to exist. [START_REF] Suery | Effect of strain rate on deformation behaviour of semi-solid dendritic alloys[END_REF], [START_REF] Valette-Brives | Mise en forme d'aciers à l'état semi-solide: étude expérimentale et modélisation[END_REF] and [START_REF] Rouff | Contribution à la caractérisation et à la modélisation du comportement d'un acier à l'état semi-solide[END_REF] suggested the existence of a critical strain rate above which homogeneous flow was observed. [START_REF] Li | Microstructural evolution and flow stress of semi-solid type 304 stainless steel[END_REF], who worked on stainless steel, mentioned that the critical temperature does not depend on strain and strain rate. Our experiments displaying very slight segregation phenomena involved small strain rates -about 1 s -1 -and low semi-solid slug temperature [START_REF] Neag | Study on thixo-extrusion of semi-solid aluminium[END_REF]. These results are arguments to claim that the slug temperature plays a key role on liquid phase segregation phenomena. Geometry and temperature of the dies also affects macro segregation as [START_REF] Kopp | Characterization of steel thixoforming tool materials by high temperature compression tests[END_REF], [START_REF] Li | Microstructural evolution and flow stress of semi-solid type 304 stainless steel[END_REF] and [START_REF] Becker | Impact of experimental conditions on material response during forming of steel in semi-solid state[END_REF] found, but probably to a lower extent.

Conclusions

The present paper reported for 7075 aluminium alloy (1) the semi-solid microstructure obtained by two reheating systems and (2) the microstructure and flow behaviour during thixoextrusion tests. Results show that:

1. Reheating an extruded aluminium billet inside the steel die by an induction furnace avoids heat losses and too strong coarsening of grains. It rapidly provides a homogenous microstructure made of globular solid grains surrounded by thin liquid film, which is suitable for thixoforming. 2. During the quasi isothermal thixo backward extrusion tests, the flow remains quasi homogeneous. Deformation takes place by rearrangement of the globules with respect to each other without any plastic deformation. Despite the high solid fraction (>0.75), the solid particles are weakly connected. 3. The slight liquid phase macro segregation phenomenon observed for quasi-isothermal thixo backward extrusion test at temperature lower than 609 • C is attributed to the geometry of the die. Increasing the slug temperature (and so the thixoextrusion test) at temperatures higher than 609 • C promotes much stronger macro segregation resulting in bad component in shape and in surface state.

Fig. 1 .

 1 Fig. 1. Typical microstructure of 7075 (T6) extruded aluminium alloy (etched Keller 10s).

Fig. 2 .

 2 Fig. 2. Solid fraction vs. temperature curves of the 7075 alloy obtained by DSC analysis (heating rate 15 • C/min; Vaneetveld et al., 2010).

Fig. 3 .

 3 Fig. 3. a) Induction heating process scheme; b) thermocouples positioning scheme; c) dimensions of the billet; d) heating cycle of 7075 aluminium alloy in a die.

Fig. 4 .

 4 Fig. 4. a) Extrusion device on the press; schematic representation of the thixoextrusion device: b) heating step before thixoextrusion; c) end of thixoextrusion process.

Fig. 5 .

 5 Fig. 5. Microstructure evolution of 7075 aluminium alloy after different period of isothermal reheating at 580 • C: a) 5 min; b) 15 min; c) 20 min; d) 30 min; e) 60 min; f) 120 min; g) 180 min; h) 240 min.

Fig. 6 .

 6 Fig. 6. a) Variations of liquid fraction; b) globular grain size and number of grains in the semisolid microstructure as a function of different isothermal holding time at 580 • C.

Fig. 7 .

 7 Fig. 7. Microstructure evolution of 7075 aluminium alloy on the slug surface after heating in electrical furnace for 240 min.

Fig. 8 .

 8 Fig. 8. Microstructure evolution of 7075 aluminium alloy after induction reheating at 580 • C and maintained for 13 min: a) transversal section; b) longitudinal section; c) transversal section close to the slug surface.

Fig. 9 .

 9 Fig. 9. Microstructure of 7075 alloy after induction reheating at 580 • C and maintained for 13 min.

Fig. 11

 11 Fig.11shows the load-displacement responses for three temperatures: 602 • C, 609 • C and 617 • C. These temperatures correspond to solid fraction of 0.82, 0.77 and 0.69, respectively (Fig.2).

Fig. 10 .

 10 Fig. 10. Shape factor vs. time.

Fig. 11 .

 11 Fig. 11. Load-displacement responses during thixoextrusion at three temperatures.

Fig. 12 .

 12 Fig. 12. Quenched microstructure of the thixoextruded cup (T = 609 • C, f l DSC = 25%).

Acknowledgements

This paper was supported by the project "Develop and support multidisciplinary postdoctoral programs in primordial technical areas of national strategy of the research-developmentinnovation" 4D-POSTDOC, contract nr. POSDRU/89/1.5/S/52603, project co-funded from European Social Fund through Sectorial Operational Program Human Resources 2007-2013 and by the PAI Brâncus ¸i Program.