Julien Avenet
email: julien.avenet@univ-nantes.fr

Arthur Levy
email: arthur.levy@univ-nantes.fr

Jean-Luc Bailleul
email: jean-luc.bailleul@univ-nantes.fr

Steven Le Corre
email: steven.le-corre@univ-nantes.fr

Jerôme Delmas
email: jerome.delmas@univ-nantes.fr

Adhesion of high performance thermoplastic composites: development of a bench and procedure for kinetics identification

Keywords: A. Thermoplastic resin, B. Adhesion, D. Mechanical testing, E. Assembly

Thermoplastic welding, tape placement, 3D printing, overmoulding or even thermostamping involve adhesion of thermoplastic polymer at high temperature. Build-up of the mechanical resistance between two substrates is usually assumed to be driven by the diffusion of macromolecules at the interface, called healing phenomenon. Moreover, in continuous processes, such as some used in manufacturing of composites for aerospace structures, cycles are very short. Thus, there is a need for quantifying the adhesion of such materials especially when processed for short durations. With this aim, a temperature and pressure controlled welding bench was designed to enable the welding of double cantilever beam samples for short time (down to 1s). Adhesion of a carbon/PEKK composite was characterized over a wide range of residence times ranging from 1 second to 1 hour. Three bonding regimes were observed, corresponding to different stages of the adhesion build-up at the interface. Finally, the healing kinetics was identified.

Introduction

Thermoplastic matrix composites have gained popularity over recent decades partly because they do not require lengthy curing cycles, thus speeding their processing. Moreover, the ability to melt the matrix has led to many new forming and assembling processes, including thermo-forming, automated tape placement, 3D-printing, pultrusion or welding processes such as ultrasonic or induction welding. In order to ensure good final quality, all these processes require heating and consolidation steps. Depending on authors, the word consolidation can refer to several different mechanisms: reduction of voids to fulfill allowable porosity levels [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF][START_REF] Sridhar Ranganathan | A Non-Isothermal Process Model for Consolidation and Void Reduction during In-Situ Tow Placement of Thermoplastic Composites[END_REF][START_REF] Tierney | Modeling of Heat Transfer and Void Dynamics for the Thermoplastic Composite Tow-Placement Process[END_REF], minimization of internal stresses [START_REF] Parlevliet | Residual stresses in thermoplastic composites -a study of the literature. Part I: Formation of residual stresses[END_REF] or maximization of the final crystallinity [START_REF] Ageorges | Fusion Bonding of Polymer Composites[END_REF]. In this paper, we focus on the adhesion between plies [START_REF] Fazil | Analysis of the on-line consolidation process in thermoplastic composite tape placement[END_REF][START_REF] Khan | Parametric study on processing parameters and resulting part quality through thermoplastic tape placement process[END_REF][START_REF] Grouve | Optimization of the tape placement process parameters for carbon-PPS composites[END_REF] or between two composite parts in welding processes [START_REF] Ageorges | Fusion Bonding of Polymer Composites[END_REF][START_REF] Levy | Inter-layer thermal contact resistance evolution with the degree of intimate contact in the processing of thermoplastic composite laminates[END_REF][START_REF] Sacchetti | Interlaminar toughness of fusion bonded thermoplastic composites[END_REF][START_REF] Shi | Modelling of Heat Transfer and Consolidation for Thermoplastic Composites Resistance Welding[END_REF]. The difference with the previously described consolidation phenomenon is that in our case we are interested in the interfacial consolidation between the coupons which we will refer to as adhesion. The autohesion phenomenon [START_REF] Wool | A theory of crack healing in polymers[END_REF][START_REF] Awaja | Adhesion of polymers[END_REF] of the thermoplastic matrix is indeed a crucial mechanism that needs to be controlled in order to ensure sufficient end-quality of the welds.

Adhesion of thermoplastics, and more specifically thermoplastic composites, has been investigated for years. To enable adhesion, the composite substrates are pressed together for a certain time above the processing temperature of the polymer matrix. Several phenomena then lead to a build-up of strength at the interface [START_REF] Ageorges | Fusion Bonding of Polymer Composites[END_REF][START_REF] Stokes | Strength and bonding mechanisms in vibration-welded polycarbonate to polyetherimide joints[END_REF][START_REF] David A Grewell | Plastics and Composites Welding Handbook[END_REF]. Wool and O'Connor [START_REF] Wool | A theory of crack healing in polymers[END_REF] described the adhesion process as a succession of five steps: (1) surface rearrangement, (2) surface approach, (3) wetting, (4) diffusion and ( 5) randomization. During the first two stages, the assembly has no mechanical strength as the initial interface still exists. First, deformation of the surface roughness, driven by the contact pressure and wetting, is required to ensure contact at the microscopic scale. This is the so-called intimate contact, which has been studied and modelled by several authors in various manufacturing processes. Once intimate contact is achieved, the interface gradually disappears through a healing process (steps (4) & ( 5)), and the mechanical strength at the interface develops to finally approach that of the bulk.

Contact between two substrates is not immediately perfect because of surface roughness. The concept of intimate contact was introduced to take into account the initial roughness of the surfaces and the evolution of physical contact between the substrates. Dara and Loos [START_REF] Dara | Thermoplastic Matrix Composite Processing Model[END_REF] first introduced the degree of intimate contact D ic , which increases to 1 for full contact. Dara and Loos' model was then simplified by Lee and Springer [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF] who modelled the surface as a succession of identical rectangles that spread under temperature and pressure loading. Some attempts were made to improve this geometrical description, e.g. Yang and Pitchumani [START_REF] Yang | A fractal Cantor set based description of interlaminar contact evolution during thermoplastic composites processing[END_REF]. All these models of the degree of intimate contact use a characteristic intimate contact time t ic [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF]:

t ic ∼ µ(T ) P ( 1
)
where P is the closing pressure applied between the adherends and µ(T ) is an effective temperature-dependent viscosity of either the polymer or the composite blend.

Once intimate contact is established, the macromolecules are free to move across the interface through the inter-diffusion process, which is also called autohesion in the case of two similar composite parts. This motion is usually described by de Gennes reptation theory [START_REF] De Gennes | Reptation of a polymer chain in the presence of fixed obstacles[END_REF] where a molecular chain is considered as though confined in a tube representing the topological constraints due to neighboring chains, which prohibits lateral motions along the tube. Since the chain can only relax along the tube direction, the chain ends are free to move in any direction away from the tube so that the memory of the initial conformation is gradually lost up to a time t rep , called the reptation time, when the chain has completely forgotten its initial configuration. The degree of healing D h is classically defined as the ratio of the interface strength σ to bulk strength σ ∞ and is thus written [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF][START_REF] Wool | A theory of crack healing in polymers[END_REF][START_REF] Dara | Thermoplastic Matrix Composite Processing Model[END_REF]:

D h = σ σ ∞ = G IC G IC,∞ 1/2 (2)
where G IC,∞ is the bulk fracture energy. Some authors [START_REF] Jud | Fracture Mechanics Studies of Crack Healing and Welding of Polymers[END_REF][START_REF] Prager | The healing process at polymerpolymer interfaces[END_REF][START_REF] Young | A theory of healing at a polymerpolymer interface[END_REF] have different theories to relate the microscopic scale macromolecule diffusion to the macroscopic mechanical properties. All agree that the fracture energy G IC of the interface increases with the square root of time. Wool and O'Connor [START_REF] Wool | A theory of crack healing in polymers[END_REF] showed that when the reptation time approaches, diffusion and randomization stages are completed and the maximum mechanical strength of the interface is reached. For long macromolecules, the full mechanical strength may be reached even for partial chain diffusion. Some authors [START_REF] Wool | A theory of crack healing in polymers[END_REF][START_REF] Young | A theory of healing at a polymerpolymer interface[END_REF][START_REF] Wool | Welding of Polymer Interfaces[END_REF][START_REF] Yang | Interlaminar contact development during thermoplastic fusion bonding[END_REF] therefore suggest to define the welding time t w,∞ required to reach the maximum mechanical strength of the interface. Thus this welding time t w,∞ is lower than the reptation time t rep and

D h = t t w,∞ 1/4 , (3)
can be adopted for isothermal conditions. Within the scope of composite manufacturing process modelling, the above law of evolution can classically be extended to anisothermal temperature cycles [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF][START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF][START_REF] Ageorges | Advances in fusion bonding techniques for joining thermoplastic matrix composites: A review[END_REF]. One then needs to integrate the degree of healing rate which is written:

d D 4 h dt = 1 t w,∞ (4)
This is a classical approach used in the modelling of several manufacturing processes, such as press forming or compression moulding [START_REF] Dara | Thermoplastic Matrix Composite Processing Model[END_REF][START_REF] Loos | Non-Isothermal Autohesion Model for Amorphous Thermoplastic Composites[END_REF], tape placement processes [START_REF] Fazil | Analysis of the on-line consolidation process in thermoplastic composite tape placement[END_REF][START_REF] Khan | Parametric study on processing parameters and resulting part quality through thermoplastic tape placement process[END_REF] or welding [START_REF] Levy | Modeling of the heating phenomena in ultrasonic welding of thermoplastic composites with flat energy directors[END_REF].

Welding processes and adhesion mechanisms are well understood for unreinforced thermoplastics, where the mechanical resistance of the welded parts approaches the bulk properties of the adherends. In the case of fibre reinforced thermoplastic composites, some issues may arise due to their manufacturing and to the simple presence of fibres, often at very high volume fractions:

• confinement effects due to the presence of fibres, especially the case at high fibre fractions where the mean distance between fibres is very low,

• low amount of matrix available to melt at the interface,

• high roughnesses, due to the fibrous structure, leading to very different intimate contact from neat polymers,

• internal stresses intrinsically present at different scales (fibres, fibre bundles or unidirectional plies) [START_REF] Parlevliet | Residual stresses in thermoplastic composites -a study of the literature. Part I: Formation of residual stresses[END_REF],

• thermal history, such as autoclave cycle, that can induce matrix changes, especially for high performance composites that are processed at high temperature [START_REF] Tanguy Choupin | Macromolecular Modifications of Poly (EtherKetoneKetone) (PEKK) Copolymer at the Melting State[END_REF][START_REF] Cender | Continuous Fusion Bonding of High Temperatures Thermoplastic Composite Structures with Volumetric Heating[END_REF]; it can also generate additional internal stresses likely to influence the adhesion values.

Overall, adhesion theories have been well experimentally validated for long residence times, ranging from a few minutes to a few days [START_REF] Woo | A Model of the Manufacturing Process of Thermoplastic Matrix Composites[END_REF][START_REF] Dara | Thermoplastic Matrix Composite Processing Model[END_REF][START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF][START_REF] Voyutskii | The Role of Diffusion Phenomena in Polymer-to-Polymer Adhesion[END_REF]. However, composite forming processes are becoming faster and faster (some are even continuous) and the adhesion step is expected to be as short as possible, with residence time around a few seconds as shown in Fig. 1. A proper characterization of the mechanical bond between adherends for such short residence times is, therefore, very relevant to understanding and controlling the rapid processes used in the industry.

The first section of this paper presents the materials and the experimental approach developed in this work, including the design of a new laboratory scale bench dedicated to the study of composite adhesion kinetics at short residence time by the means of a stopped welding experiment. The second section validates this novel procedure. In the last section, results for an industrial aeronautical grade thermoplastic composite are presented. The obtained bonding kinetics is identified and compared with existing results on longer residence times.

Experimental methods

This section describes the adhesion characterization procedure. Thermoplastic composite laminate coupons were welded together using the welding bench. The adhesion was then assessed using a double cantilever mechanical test following the ASTM standard [START_REF]D5528 -Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites[END_REF].

Material

The material used in this study was an aeronautical grade Arkema PEKK 7002 thermoplastic reinforced with carbon fibres. Laminates consisted of 12 plies of symmetric unidirectional fibre layup of [0 • /90 • ]. Samples were hand laid-up into a flat plate. On one of the surfaces, a 50 µm thick film of neat PEKK polymer, shown in Fig. 2, was applied to ease the welding process. The layup was then consolidated in an autoclave at 380 • C for 2 hours. The melting temperature of this material ranged from 300 • C to 350 • C, with a melting peak temperature of 330 • C. The crystallization kinetics of the PEKK 7002 matrix was investigated by Choupin et al. [START_REF] Choupin | Isothermal crystallization kinetic modeling of poly(etherketoneketone) (PEKK) copolymer[END_REF] and found to be rather slow compared to other high performance thermoplastics: the matrix is partially amorphized at a cooling rate of 20 • C/min and completely quenched at 50 • C/min.

The manufacturer recommends processing at a temperature above 350 • C. It has been shown degradation can occur at such temperatures, associated with chemical modification [START_REF] Tanguy Choupin | Macromolecular Modifications of Poly (EtherKetoneKetone) (PEKK) Copolymer at the Melting State[END_REF][START_REF] Cender | Continuous Fusion Bonding of High Temperatures Thermoplastic Composite Structures with Volumetric Heating[END_REF], which likely influences the welding time, as discussed below.

Before the welding experiments, the 2.3 mm thick composite plates were cut into 125 x 25 mm samples (Fig. 3) using a Protomax waterjet cutting machine. A countersunk hole was machined in each sample 10 mm from one end to insert a loading pin used for gripping the sample during the fracture test. The coupons were then manually cleaned using acetone solvent and dried in a vacuum chamber at 180 • C for 20 hours in order to remove residual water and limit the laminate deconsolidation phenomenon that would occur during the welding sequence.

The side of the composite that would be in contact with the mold was covered with polyimide tape to facilitate the removal of the welded coupons after the welding procedure. The initial crack between the two composite adherends was created by inserting a non-adhesive 20 µm thick aluminum foil between the two samples at 50 mm from the load application point such that the welded area was 65 mm long by 25 mm wide, matching the ASTM D5528 standard. Finally, the loading pins were inserted into the samples prior to the welding experiment. They were engaged in a cavity machined inside the mold as described in the next section.

Experimental welding bench

The welding bench was developed for welding composite substrates for a finite amount of time (down to a few seconds) and under constant isothermal conditions. The TACOMA (for Thermo-Adhesion by COnductive heating of composite MAterials) setup is shown in Fig. 4.

Design. The mold comprises two L-shaped copper symmetric platens. One is static and the other moving. Their dimension is the same as that of the samples, i.e. the width b is 25 mm and the length L 125 mm. Thus, the entire lengths of the samples are heated and pressed together. Additionally two lateral copper plates (one on each side of the mold) are fastened on the mold to separate the cavity from the ambient air and ensure a confined cavity. In order to avoid holding issues of the samples [START_REF] Harkous | Influence of the temperature on the composites' fusion bonding quality[END_REF], the setup was designed with the moving platen sliding horizontally. Thus, the samples are simply positioned vertically on each platen, facing each other and resting on their sides. Thanks to the lateral plates, the static platen acts as a die and the moving platen as a punch. Finally, a slider is attached to the insulating material of the sliding platen to control the shear edge gap and bear the weight of the platen.

Temperature control. Control thermocouples are embedded inside the copper platens near the sample surfaces (1 mm from the surface). The platens are heated with heating cartridges. Additionally, two internal channels were machined in each platen in order to allow fast and spatially homogeneous water cooling of the copper mold, thus making it possible to quench the samples and perform stopped experiments.

Pressure control. The moving platen is attached in series to a pneumatic piston, a load cell and an insulating material to protect the load cell from the high temperatures and to limit heat losses. The 80 mm diameter pneumatic piston uses compressed air with a maximum entry pressure of 6 bars, which results in a maximum force of 5 kN corresponding to a maximum effective pressure on the samples of about 10 bars. The force is recorded with a 10 kN load cell.

Synchronisation. The temperature PID controller, piston pressure application and water quenching are all controlled automatically via a homemade Labview interface. Temperatures and forces are also acquired in Labview every 0.5 s. The whole procedure is written in one integrated program, ensuring synchronisation.

Protocol. The experimental protocol to weld the two composite coupons is illustrated in Fig. 5. After positioning the two substrates in the mold with a platen open to ensure a separation gap, the procedure can be divided into five steps:

1. heating of the copper block from room temperature up to a temperature higher than the melting temperature of the material (at first the two samples are not in contact and the matrix-rich surfaces are facing each other), 2. homogenization of the temperature at the surface of the coupons for a dwell time t dwell , 3. once the setpoint temperature is reached and homogeneous inside the mold, pressure is applied with the pneumatic piston to weld the samples during a defined contact time t c , 4. fast cooling of the setup with water circulation to stop the welding process and 5. the pressure is released.

Double Cantilever Beam (DCB) fracture test

The mechanical strength of the welded interface was assessed using a double cantilever beam (DCB) fracture test following the ASTM D5528 standard [START_REF]D5528 -Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites[END_REF]. The welded samples were mounted on a 100 kN Zwick Roell tensile machine and homemade sample holders were used to fix the loading pins onto the machine grips. Tests were performed in displacement control mode with a constant displacement rate v of 1 mm.min -1 , which corresponds to a quasi-static condition. The pins were designed and machined to minimize unwanted torque in the load (see Fig. 6). The pins did not, in fact, conform to the ASTM standard which suggests bonded systems. Nevertheless their design prevented failure between the sample and the pins since they were directly inserted into the sample. Furthermore, they were well centred in the sample width, which prevented torsion phenomena.

The load and displacement were continuously recorded during the test. Intrinsically, due to the nature of DCB tests on composite plates, the lever arm between the application point and the welded area generates bending inside both composite plates, which results in some elastic energy storage.

The mode I strain energy release rate also called interlaminar fracture toughness is defined as the energy necessary to propagate a crack over a unit surface. For an elastic linear structure, the analysis of a double cantilever beam test is based on the change of compliance. The growth of a crack from a to a + ∆a induces a change in the compliance, resulting in a loss of the stored energy. In this method, the compliance is determined using standard Euler-Bernoulli beam theory, which considers that the adherents are cantilevered at the crack tip. It is then possible to determine the interlaminar fracture toughness from the Irwin-Kies equation [START_REF] Irwin | Critical Energy Rate Anaysis of Fracture Strength[END_REF]:

G I = P 2 2b ∂C ∂a ( 5
)
where b is the width of the samples, P is the applied force. The compliance C = δ/P and the displacement δ at the loading point, according to Euler-Bernoulli beam theory are respectively:

C = 8a 3 Ebh 3 δ = 2P a 3 3EI ( 6
)
where h is the thickness, E is the Young modulus and I = bh 3 /12 is the moment of inertia of the beam. The derivation of Eq. ( 6) and substitution in [START_REF] Ageorges | Fusion Bonding of Polymer Composites[END_REF] gives the most frequently used expressions of the mode I interlaminar fracture toughness [START_REF]D5528 -Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites[END_REF][START_REF] Tamuzs | Delamination properties of translaminar-reinforced composites[END_REF]:

G I = 3P δF 2ba ( 7
)
where F is a correction factor accounting for large displacement effects [START_REF]D5528 -Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites[END_REF], i.e. shortening of the moment arm and tilting of the loading pins. This factor is strongly dependent on the sample and pin geometry and clamping stiffness.

Test matrix

Welding tests were carried out for three different temperatures above the melting temperature of the polymer matrix: 355, 370 and 380 • C, and for various contact times from 1 second to 1 hour, as detailed in Table 1. At least three replicates were performed for each contact time at 355 • C and 380 • C. These two temperatures were thoroughly investigated whereas less data points were tested for 370 • C.

Procedure validation

The adhesion characterization procedure consisted of the stopped welding experiment in the TACOMA bench followed by a DCB test to assess bonding quality. In this section, temperature homogeneity and quenching quality in the TACOMA bench are first discussed. We then cover how the DCB test is then validated.

Thermal management

Temperature homogeneity inside the TACOMA setup was first characterized by placing a type K thermocouple at different locations between the two copper platens of the mold without any samples, such that the thermocouple did not touch the mold. These tests were performed with and without the two lateral copper plates described in section 2.2.

Samples instrumented with 80 µm type K thermocouples were also tested in the TACOMA setup. The thermocouples were embedded on the matrix-rich layer of samples, at locations given in Table . 2, in order to record the temperature at the interface between the two samples during the welding sequence. The sequence consisted in heating to 380 • C, followed by 100 seconds contact. Fig. 7 shows the evolution of the temperature at the interface between the two samples at different positions during the welding sequence. At first, the characteristic cooling rates in the mold and at the sample interface (at position T4) are 20 • C.s -1 and 12 • C.s -1 , respectively. This confirms that the sample was quenched. According to the crystallization kinetics identified by Choupin et al. [START_REF] Choupin | Isothermal crystallization kinetic modeling of poly(etherketoneketone) (PEKK) copolymer[END_REF], the sample is completely amorphous. This validates the rapid stopping of the healing process. This test, therefore, allows the determination of the time needed for the targeted temperature at the interface to be reached, which occurs during the heating phase. The lateral plates indeed prevent natural air convection in the cavity. In order to perform an isothermal welding cycle, the pressure must be applied once the interface has reached the targeted temperature. For a welding temperature of 380 • C, the dwell time is about 300 seconds.

The test also provided information on edge effect. Indeed, samples are positioned against the copper mold. All faces of the sample except the one that will be welded are in contact with the copper. Therefore, a 3D temperature gradient develops in the samples and leads to gradients in degree of adhesion. The instrumentation of the sample along its width validated that edge effects are present on the sides. For instance, in Fig. 7, heating and cooling rates are faster for thermocouple T3. The edge effects are crucial during the cooling phase since they might induce a healing degree profile along the width of the sample: the centre of the sample stays at a high temperature for longer before the cooling starts. The iso degree of adhesion along the sample width could therefore present a profile that is not straight. Nonetheless, as discussed in the following section, the adhesion gained during cooling was negligible compared with that gained during the contact phase under isothermal conditions.

DCB validation

The load-displacement curves obtained from the double cantilever beam fracture tests are presented in Fig. 8. They present a saw-tooth behaviour characterized by sudden drops in the recorded force that correspond to unstable fractures. This is known as stick-slip crack growth [START_REF] Webb | Crack Growth Resistance Curves and Stick-Slip Fracture Instabilities[END_REF] accompanied by highspeed propagation and arrest. In contrast, stable behaviour is characterized by continuous crack growth with increasing displacement. This phenomenon has been observed by different authors. Harkous et al. [START_REF] Harkous | Influence of the temperature on the composites' fusion bonding quality[END_REF] attributed it to very rapid failure of the welded area and explained that, for high resistance composite, the large amount of energy released causes a long propagation of the crack and, consequently, a complete breaking of the part. Sacchetti et al. [START_REF] Sacchetti | Effect of resin-rich bond line thickness and fibre migration on the toughness of unidirectional Carbon/PEEK joints[END_REF] also observed this unstable behaviour for unidirectional Carbon/PEEK laminates and explained that it was due to a non-uniformity of the matrix rich layer at the surface of their samples, resulting in a non-uniform interlaminar fracture toughness along the crack path.

Due to unstable crack propagation and difficulties in measuring crack length during the double cantilever beam test, interlaminar fracture toughness G IC can be calculated at the crack initiation point, corresponding to the first peak in the load-displacement curve. At this point, the crack length is known and corresponds to the length a 0 of the non-adhesive aluminum insert. These G IC,ini values are calculated using Eq. [START_REF] Khan | Parametric study on processing parameters and resulting part quality through thermoplastic tape placement process[END_REF].

In order to confirm the relevance of this G IC,ini value, incremental DCB tests were performed. This consisted in positioning a clamp at different positions along the sample length to stop crack propagation and performing a DCB test. Once the crack had propagated from its initial length to the one corresponding to the clamp position, the samples were unloaded at 25 mm.min -1 , the clamp was moved to a further position and the samples were reloaded at 1 mm.min -1 . This allowed the calculation of G IC at each position of the clamp, corresponding to different known crack lengths. The load-displacement curves corresponding to these tests are presented in Fig. 9. The propagation of the crack remained unstable between two locations of the clamp, characterized by a sudden force drop. G IC values were calculated as before using Eq. ( 7), with a being the location of the clamp from the loading application point, in this case successively 55, 60, 65 and 75 mm. The first value corresponds to the crack initiation G IC,ini while the other values are associated with crack propagation and can be written as G IC,prop . As visible from Fig. 9, incremental curves sometimes exhibit a slight non-linearity before the next propagation of the crack. This can be attributed to the fact that the clamp might not perfectly stop the crack propagation leading to a more disturbed crack front for the next clamp position. This leads in turn to this observed change of compliance. Evolution of G IC values versus crack length is plotted in Fig. 10 for three different welding times. This incremental test is particularly useful for samples welded for very short residence times, due to low fracture resistance and heterogeneity along the total welded length. In practice, it was only used for low adhesion situations.

The repeatability of the classical DCB tests shows a 15 % error on G IC,ini measurement. This 15 % error was applied to the first point of the incremental DCB test. In Fig. 10 the hatched area corresponds to this error measurement interval and the dotted line to G IC,ini value. Overall, the G IC,porp obtained from incremental DCB tests all fall within this interval. For our material, this validates that the energy release rate for crack propagation equates that for initiation. Thus, G IC,ini will be used in the following the initiation values.

Results and discussion

In this section, the characterization methodology described above is applied to the Carbon-PEKK material. The experimental campaign described in section 2.4 and Table 1 is followed.

Bonding regimes

Interlaminar fracture toughness of the samples welded at different temperatures are plotted against contact time in Fig. 11, where three adhesion regimes can be identified. Micropgraphs and SEM images of the interfaces corresponding to these respective regimes are visible in Figure 12.

The first regime corresponds to a short residence time during which intimate contact is not completed. Air gaps are visible at the welded interface in Fig. 12. Contact is probably achieved only at a few spots where healing has started. Healing is also probably incomplete at those contact points, which results in overall poor bonding energies as evidenced by the SEM images in Fig. 12. It should be remembered that for this TACOMA test, the closing pressure is fairly high (3.2 bars) and thus ensures rapid intimate contact compared with the healing phenomenon, as clearly seen in Fig. 11.

The second regime starts when intimate contact is fully achieved on the whole surface and the evolution of bonding energy is only due to healing. This regime will be discussed in the next section and used for healing kinetics identification. The micrograph in Fig. 12 reveals a residual matrix-rich layer at the interface. The SEM image shows matrix deformation indicating that the fracture is mostly cohesive. Adhesion is polymer autohesion.

Finally, in the terminal regime, the fracture energy is still increasing with time. The cross-section shows that the resin-rich layer has disappeared due to fibre motion and resin bleed. This stage is characterized by a competition between matrix cohesive bonding and other adhesion phenomena such as fibre bridging combined with differential flow and segregation of the polymer matrix, as seen sparsely in Fig. 12. Such phenomena lead to higher values of G IC and are thus not associated with autohesion healing process through macromolecule reptation. In addition, these values present a strong standard deviation due to the non-repeatability in the occurrence of these phenomena. Such observations of fibre bridging have been reported in the literature [START_REF] Pereira | Mode I interlaminar fracture of carbon epoxy laminates[END_REF][START_REF] Kaushik | Experimental and numerical characterization of Mode I fracture in unidirectional CFRP laminated composite using XIGA-CZM approach[END_REF] but, as mentioned by Sacchetti et al. [START_REF] Sacchetti | Effect of resin-rich bond line thickness and fibre migration on the toughness of unidirectional Carbon/PEEK joints[END_REF], these studies were based on typical consolidation techniques such as hot plate pressing or autoclave manufacturing, characterized by long residence time that allow the fibres to migrate at the interface. In the case of welding for a short residence time, fibre bridging is expected to be reduced, especially with the presence of a matrix-rich region at the interface. In our case, the observed fibre bridging can be related to these consolidation studies since it only occurs at long welding time. Thus, this validates that the corresponding bonding energies are part of a third regime where healing is already complete.

G IC values can be seen to reach a small plateau at the end of the second regime. G IC,∞ was calculated as the mean value of G IC measured on this plateau and is equal to 2.3 ± 0.1 kJ.m -2 . It corresponds to the maximum mode I interlaminar fracture toughness of fully healed samples, i.e. to D h = 1. Values of mode I interlaminar fracture toughness G IC might seem high compared with values for high performance polymers found in the literature. This is explained by the TACOMA welding process cycle. At such a high cooling rate, the matrix is completely amorphous [START_REF] Choupin | Isothermal crystallization kinetic modeling of poly(etherketoneketone) (PEKK) copolymer[END_REF], thus leading to a high ductility compared with semi-crystalline state. It results in a high plastic deformation of the matrix as demonstrated by Sacchetti et al. [START_REF] Sacchetti | Effect of cooling rate on the interlaminar fracture toughness of unidirectional Carbon/PPS laminates[END_REF] for carbon/PPS unidirectional laminates, thus increasing the interlaminar fracture toughness compared to crystallized parts. Similar high values were reported for unidirectional carbon/PEEK laminates by Sacchetti et al. [START_REF] Sacchetti | Effect of resin-rich bond line thickness and fibre migration on the toughness of unidirectional Carbon/PEEK joints[END_REF] who demonstrated that matrix plastic deformation indeed induces an increase of G IC values.

Healing identification

The raw data corresponding to regime II in the previous section were used to characterize the welding time for the healing mechanism. Degree of healing was calculated using the classical law in Eq. ( 2) where G IC,∞ is the one determined in the previous section and is plotted versus the fourth root of the contact time in Fig. 13. Since healing kinetics was identified on the second regime, the first data points, corresponding to the first coupled regime, are discarded from the linear fit, and the curves do not intersect the origin. The welding times are directly identified from the slope of the linear fit in Fig. 13, which is equal to 1/t 4 w,∞ according to Eq. ( 3). The welding times for the three isothermal temperatures are given in Table . 3.

The laminates used in this study were consolidated for 2 hours in an autoclave at 380 • C. At these temperatures it has been shown that degradation associated with chemical modification can occur [START_REF] Tanguy Choupin | Macromolecular Modifications of Poly (EtherKetoneKetone) (PEKK) Copolymer at the Melting State[END_REF][START_REF] Cender | Continuous Fusion Bonding of High Temperatures Thermoplastic Composite Structures with Volumetric Heating[END_REF], thus increasing the relaxation time. The identified welding time was consequently increased, explaining the large values -of a magnitude of one hundred seconds -that are obtained.

The welding time was fitted to a temperature dependant Arrhenius relationship:

t w,∞ (T ) = A exp E a RT (8)
where E a is the activation energy and A the pre-exponential factor. These parameters could be determined for our composite using the Arrhenius plot given in Fig. 14. The pre-exponential factor obtained was A = 3, 01.10 -3 s and the activation energy E a = 55, 5 kJ.mol -1 . The degree of healing could now be computed by integrating the degree of healing rate (4) substituting the identified healing kinetics Eq. ( 8) for any industrial temperature history.

Conclusion

In this work, adhesion of high performance thermoplastic composites was investigated. Besides the intimate contact phenomenon that may limit adhesion when rough surfaces are welded or limited pressure is used, healing is the main phenomenon controlling the bonding quality. The objective was to characterize adhesion for conditions close to the industrial process, especially short residence time.

A novel instrumented laboratory scale welding bench was developed to weld composite substrates for controlled contact times and under controlled constant pressure and isothermal conditions. The lower time limit of this bench is 1 second, due to inertia of the piston, and the upper pressure limit onto the samples is about 10 bars. Instrumented samples were used to validate the thermal homogeneity of the bench and the characteristic cooling rates it enabled at both the mold and the sample interfaces. Our device was shown to enable the quenching of our composite samples, thus proving the effectiveness of a stopped healing process.

The mechanical quality of the bonded substrates was assessed with a double cantilever beam test. Because composite samples systematically show unstable crack propagation, only the value of the interlaminar fracture toughness at the crack initiation was used in the analysis. Nevertheless, an original incremental DCB procedure was developed and was shown to give the same results as the initiation point method. By doing so, both procedures, which are therefore equivalent, were validated and the incremental DCB fracture test was proved to be of particular interest for the characterization of low adhesion energies, associated with short residence time.

Welding tests over a wide range of contact time were performed on a high performance thermoplastic composite. It was revealed that adhesion between two composite substrates develops following three successive regimes. The first regime is a coupled regime where intimate contact is not yet achieved. The second regime is purely associated with inter-diffusion of the chains, i.e. healing, where the healing degree evolves linearly with the fourth root of time. Finally, a third adhesion regime was found in our case. For longer welding times, other adhesion phenomena occurred such as fibre bridging and matrix segregation, leading to the bond strength to exceed the cohesive strength of the matrix. They are therefore not associated with pure healing. They imply motion of fibres that leads to a mechanical fastening, but probably also to unwanted microstructural changes. Healing kinetics were finally identified from a test campaign on three isothermal temperatures. For our carbon PEKK plates, the identified welding time to complete the healing process is of the order of one hundred seconds, which can be attributed to thermal aging during autoclave pre-manufacturing of the samples. This novel experimental welding bench can be used to characterize adhesion for residence time as short as a few seconds, under isothermal conditions. As a perspective for future research, investigations will be carried out at a shorter time scale to study the kinetics of intimate contact and then characterize and model the whole adhesion process. To do this, further investigations will be needed to account for the transient thermal regime induced by the quenching and to separate the intimate contact from the healing contributions in this socalled coupled regime.

Figure 1 :

 1 Figure1: Many thermoplastic forming processes consist in short residence times at processing temperature. To our knowledge, however, there are no existing characterization methods for such short times.

Figure 2 :

 2 Figure 2: Cross-sectional micrographs of autoclave consolidated samples. The resin-rich layer is shown in the zoomed picture.

Figure 3 :

 3 Figure 3: Dimensions of the composite coupons to be welded and tested with double cantilever beam tests. The grey circle represents the countersunk hole to insert the loading pin.

Figure 4 :Figure 5 :

 45 Figure 4: The experimental TACOMA setup, designed for welding under isothermal conditions followed by a fast cooling. (top): general view and (bottom): schematic view.

Figure 6 :Figure 7 :

 67 Figure 6: Double Cantilever Beam (DCB) setup. The initial crack length a 0 is known from the non-adhesive foil insert.

Figure 8 :

 8 Figure8: Load-displacement curves from the fracture double cantilever beam test corresponding to samples welded at 380 • C for different contact times. Crack propagation is unstable, as observed by previous authors[START_REF] Harkous | Influence of the temperature on the composites' fusion bonding quality[END_REF][START_REF] Sacchetti | Effect of resin-rich bond line thickness and fibre migration on the toughness of unidirectional Carbon/PEEK joints[END_REF].

Figure 9 :

 9 Figure 9: Load-Displacement curves using clamps positioned successively at different locations for 1 s contact time.

Figure 10 :Figure 11 :

 1011 Figure 10: Interlaminar fracture toughness G IC measured at different crack lengths from the incremental DCB fracture test. Samples were welded at 380 • C for three different contact times. The hatched area corresponds to the standard deviation taken from the classical DCB test. The values for crack propagation all fall within this interval.

Figure 12 :Figure 13 :

 1213 Figure 12: Cross-section optical micrographs (left) and SEM images of the fracture surfaces (right) of welded samples at 380 • C under 3.2 bars with various residence time tc. The arrow on the top left of the SEM images corresponds to the direction of crack propagation during the fracture test. Top: regime I with partial intimate contact, middle: regime II with a cohesive fracture of interfacial resin, and bottom: regime III with fibre bridging and pullout.

1 )Figure 14 :

 114 Figure14: The obtained welding time tw,∞ is plotted against the inverse of the isothermal temperature 1/T . This Arrhenius plot immediately identifies a temperature dependant law for welding time on temperature.

Acknowledgements

The authors would like to acknowledge the funding they received from the PERFORM project managed by IRT Jules Verne (French Institute for Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures), which made this work possible. The authors would like to associate the industrial partners of the PERFORM project: Airbus, Stelia Aerospace, Faurecia, Naval Group and Daher.

The authors would also like to thank Professor Erwan Verron for fruitful discussion about fracture mechanics. The bench design and manufacturing was initiated thanks to Thomas Cender to whom we are deeply grateful for his contribution. We thank Yannick Benoit from Ecole Centrale de Nantes for his help with the SEM images. Finally, the design and manufacturing would not have been possible without the help of Nicolas Lefevre.


Arthur Levy
email: arthur.levy@univ-nantes.fr

Pascal Hubert

Vacuum-Bagged Composite Laminate Forming Processes: Predicting Thickness Deviation in Complex Shapes

Keywords: A, Prepreg B, Defects C, Analytical modelling D, Out-of-autoclave processing

This paper focuses on the manufacturing of composite laminates using vacuum-bag processes. When forming complex shapes, such as corners, the laminate thickness may deviate from the nominal thickness obtained for flat plates. This is due to two phenomena that occur in corners: (i) because of the geometry, the available consolidation pressure differs from the expected pressure; and (ii) friction may prevent adequate conformation of the laminate to the mould. The thickness deviation is associated with defects (porosity, dry or resin-rich areas or fibre wrinkling). We propose an analytical model to describe these two phenomena, which relies only on two geometric ratio: radius *Manuscript Click here to view linked References 2 to flange length and thickness to radius, and two material properties: bulk factor and inter ply friction coefficient. The model estimation was compared to an extensive experimental database including a variety of configurations: male or female tools and various flange lengths, weavings and corner radii.

INTRODUCTION

Composite materials, which offer good specific properties, have superseded traditional metallic materials in a number of sectors, particularly transport. Load bearing structures are typically manufactured in the form of laminates, using a stack of continuous fibres in the form of unidirectional or woven plies. In vacuum-bag processes, which include autoclave and out-of-autoclave processes, the plies are stacked manually or automatically onto a rigid mould. The setup is then put under vacuum using a consumable vacuum system (i.e., breather, peel plies, vacuum bag) and other bagging elements like pressure intensifiers or caul plates. When the stack conforms correctly to potentially complex moulds, curved shape laminates are obtained. As described in [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF] for instance, these complex features can include stiffeners, ribs or corner features with a double curvature. The processing of flat or low curvature composite parts is generally not problematic with vacuum-bag-only prepregs.

The moulding of parts with sharp corners, however, often leads to significant thickness variations and voids concentrated at the corners (see Figure 1). When forming L-shape laminates, defects will typically occur in corner locations. These lead to corner thickness deviation [START_REF] Hubert | A Review of Flow and Compaction Modelling Relevant to Thermoset Matrix Laminate Processing[END_REF][START_REF] Fernlund | Experimental and numerical study of the effect of caul-sheets on corner thinning of composite laminates[END_REF][START_REF] Hassan | Effect of bagging configurations on vacuum bagging onlyoven cured to the thickness variations for the complexshaped laminate composite[END_REF], which is related to microstructural defects including porosity, resin-rich areas, delamination or wrinkling [START_REF] Ma | Vacuum Bag Only Processing of Complex Shapes: Effect of Corner Angle, Material Properties and Process Conditions[END_REF][START_REF] Ma | Defect Reduction Strategies for the Manufacture of Contoured Laminates Using Vacuum BAG-Only Prepregs[END_REF][START_REF] Krumenacker | Effect of Processing Deficiencies on Vacuum-Bag-Only Complex-Shape Prepreg Laminate Consolidation and Interlaminar Tensile Behaviour[END_REF][START_REF] Wang | Correlated Rules between Complex Structure of Composite Components and Manufacturing Defects in Autoclave Molding Technology[END_REF]. Corner thickness deviation quantifies the thickness difference between corner and nominal flange region thicknesses. This macroscopic magnitude reflects all the microstructural defects listed above. Corner thickness deviation, because it is easy to quantify, is a very common quality indicator for a complex shape laminate [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF][START_REF] Fernlund | Experimental and numerical study of the effect of caul-sheets on corner thinning of composite laminates[END_REF][START_REF] Hassan | Effect of bagging configurations on vacuum bagging onlyoven cured to the thickness variations for the complexshaped laminate composite[END_REF][START_REF] Ma | Vacuum Bag Only Processing of Complex Shapes: Effect of Corner Angle, Material Properties and Process Conditions[END_REF][START_REF] Ma | Defect Reduction Strategies for the Manufacture of Contoured Laminates Using Vacuum BAG-Only Prepregs[END_REF][START_REF] Krumenacker | Effect of Processing Deficiencies on Vacuum-Bag-Only Complex-Shape Prepreg Laminate Consolidation and Interlaminar Tensile Behaviour[END_REF][START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF][START_REF] Hubert | Towards a design guideline for corners in composite parts[END_REF][START_REF] Hubert | Aspects of the Compaction of Composite Angle Laminates: An Experimental Investigation[END_REF][START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF][START_REF] Hallander | Influence of the forming process on the shape distortion of a composite c-shaped aerospace spar[END_REF][START_REF] Gu | Pressure transfer behaviour of rubber mould and the effects on consolidation of L-shape composite laminates[END_REF]. Prediction of corner thickness deviation is thus very useful for process designers.

As initially proposed by Hubert & Poursartip [START_REF] Hubert | Aspects of the Compaction of Composite Angle Laminates: An Experimental Investigation[END_REF], an important mechanism behind thickness variations in complex shape laminates consists in the difference in reaction stress between the corner and the flange. This hypothesis was experimentally verified by placing a pressure sensor (XSENSOR Technology Corporation) at the corner of the laminate tool interface [START_REF] Hubert | Private communication[END_REF]. Figure 2 clearly shows a significant 40% compaction pressure drop in the corner region for a 10 mm thick laminate compacted on a 12 mm radius female mould.

Meanwhile, friction between plies prevents adequate conformations of the plies together, or the plies against the mould [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Cauberghs | Out-of-Autoclave Manufacturing of Aerospace Representative Parts[END_REF]. These two competing effects lead to corner thickness deviation. Prediction of corner thickness deviation is, however, a complex task since various different physical phenomena are involved. Hubert & Poursartip [START_REF] Hubert | A Review of Flow and Compaction Modelling Relevant to Thermoset Matrix Laminate Processing[END_REF] reviewed the existing modelling and simulation work on shear and percolation flow in composite processing, making a special focus on complex shapes such as L-shape corners. Such models usually require a spatial discretization (such as finite elements) [START_REF] Li | Numerical and Experimental Study on the Effect of Lay-Up Type and Structural Elements on Thickness Uniformity of L-Shaped Laminates[END_REF]. Models for porosity based on the equilibrium of a bubble still require fine tuning to be predictive [START_REF] Du Plessix | Improved simplified approach for the prediction of porosity growth during the curing of composites parts[END_REF]. Furthermore, they require prediction of the pressure field using a spatial description of the corner. For instance, Helmus et al. [START_REF] Helmus | Modelling void formation in corners during out-of-autoclave prepreg processing[END_REF] proposed to predict the void evolution in corner regions using a stochastic model coupled with a 2D finite element method for the pressure distribution description. Lightfoot et al. [START_REF] Lightfoot | A new mechanism for the formation of ply wrinkles due to shear between plies[END_REF] identified the coefficient of thermal expansion mismatch and tool/part friction as the main phenomena leading to fibre wrinkling in corner regions. Predicting such instabilities appears to be a difficult modelling task, as shown in the work of Dodwell et al. [START_REF] Dodwell | Out-of-plane ply wrinkling defects during consolidation over an external radius[END_REF] or, more recently, Belnoue et al. [START_REF] Belnoue | Consolidation-Driven Defect Generation in Thick Composite Parts[END_REF]. Besides these attempts to model the physical phenomena leading to corner thickness deviation, Wang et al. [START_REF] Wang | Correlated Rules between Complex Structure of Composite Components and Manufacturing Defects in Autoclave Molding Technology[END_REF] suggest following a statistical approach to obtain predictive correlation rules between the processing conditions and final thickness deviation. Empirical rules of thumb can be obtained this way based on practical knowhow of the process. Previous work by the same authors [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF] consisted in developing a semi-empirical analytical model for corner thickness deviation in the case of female L-shape corners. The model was validated on one material system.

In this paper, we investigate the mechanisms that govern the compaction of complex shape composite laminates using vacuum-bag processing of prepregs. The goal is to develop guidelines and tools for the satisfactory design and manufacture of parts with sharp corners, using only vacuum-bag processing methods. We aim to predict the thickness variation between the flanges and the corner of a laminate processed in a male or female Lshape tool, or in a U-shape tool. Understanding and controlling the consolidation of Lshape corners and U-shape corners provides preliminary insight before investigating the consolidation of these complex three-dimensional shapes. Section 2 proposes analytical models of the compaction in the corner. The models include pressure and friction effects. Section 3 makes a review of the experimental manufacturing of L-shape laminates using aerospace grade vacuum-bag-only prepreg composites, bringing together over 100 data points on a wide range of geometries or material systems. We compared the corner thickness deviations measured experimentally in these papers with the predictions of a semi-empirical unified model and thus validated it. In the final section, we provide step-bystep design guidelines to predict the corner thickness deviation for various material systems or manufacturing procedures.

MODEL DEVELOPMENT

While processing out-of-autoclave composite using vacuum bag only, one of the challenges is to extract the remaining air from the part during the vacuum hold prior to cure. To this end, out-of-autoclave prepreg composites have a dry area to ensure a connected flow path. This results in a very high bulk factor for such materials: during heating, impregnation will be completed and the nominal thickness of the part will be greatly reduced [START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF]. This high bulk factor results in a large geometry change between the final layup at room temperature and the final fully impregnated part. This dimension change is the inherent characteristic of out-of-autoclave prepreg that will result in large corner thickness deviation. During the compaction associated with impregnation, flat parts will have their thickness reduced from ! " , the initial nominal thickness after layup, to: the nominal final thickness after cure, where # is the bulk factor, a material property.

Nonetheless, in corner regions, because of the curvature, the material will undergo a different compaction:

• The interply friction might constrain the layers from conforming to the mould, thus preventing adequate compaction in the corner [START_REF] Dodwell | Out-of-plane ply wrinkling defects during consolidation over an external radius[END_REF]. This is the so-called friction dominated mechanism.

• Even if interply slippage occurs, as mentioned in a previous study by Hubert & Poursartip [START_REF] Hubert | Aspects of the Compaction of Composite Angle Laminates: An Experimental Investigation[END_REF], because of the curvature in the corner, the bagged surface may differ from the facing mould surface. The available consolidation pressure in the part is then different from the expected vacuum-bag pressure. This is the so-called pressure dominated phenomenon.

! $ = ! " # (1)
In the following sections we will examine and model the pressure and friction dominated phenomena.

Geometry

This paper considers all cases of corner laminates: from L-shape laminate manufactured in a concave (female) and convex (male) moulds to U-shapes. The corner angle is called & and is equal to:

• 0 for a U-shape laminate

• '/2 for a female tool

• ' for a flat plate (only useful for model validation)

• 3'/2 for a male tool
The initial geometry is given in Figure 3. This geometry is obtained after a layup and debulk that is supposedly defect free. Consumable materials effects, such as wrinkling or bridging, are ignored. This means that the part thickness is uniformly ! " in the corner and in the flange, such that for a concave mould or a U-shape and for a convex mould.

+ , -+ " = ! " (2)
+ " -+ , = ! " (3)
Plain strain is assumed along the length . of the corner. Compaction during manufacturing using a vacuum bag is considered nominal over a part / $ of the flange. The final thickness along this flange is therefore ! $ , as shown in Figure 3. Moreover, in the corner area, after compaction, the bag side surface of the part supposedly has a circular curvature of radius + $ leading to a corner thickness ! $ 0 , deviating from the nominal ! $ .

Conformation number

If no interply slippage occurs, because the first ply on the bag side is inextensible it does not conform to the corner region (Figure 4 where 5 is the outward normal vector along which the atmospheric pressure 6 is applied and 7 8 the unit horizontal vector along the 9 direction. The constant curvature of Γ 4 (1/+ $ )

gives

1 2 = 65 ⋅ 7 8 <= > ? (4)
1 2 = + $ 6. (5)
If the tension 1 2 is higher than the interply friction limit 1 2 ,A8 in the flange, it will initiate slippage. The friction limit can be defined using a Coulomb friction behaviour model with a coefficient B as where / $ 6 is the normal load applied on the flange section. The dimensionless conformation number Λ 2 naturally appears:

Λ 2 is an indicator of whether the compaction is friction or pressure dominated in the bag side ply:

• If Λ 2 < 1, the interply friction limit is not reached in the flange, and the outermost ply will not conform to the corner. This is a friction dominated compaction.

• If Λ 2 > 1, the friction limit is reached, and the first ply can slip, thus coming into contact with the second ply. The compaction is now pressure dominated in this ply.

If slippage occurs, the first ply will contact the second, and the same analysis should be carried successively to each interply interface. A series of conformation numbers Λ " then provide indicators of whether the ply F would slip over ply F + 1. The last element,

1 2 ,A8 = B/ $ 6. (6)
Λ 2 = 1 2 1 2 ,A8 = + $ B/ $ . (7)
Λ H = + , B/ , . (8)
indicates whether all the plies, up to the tool side ply, slipped or not.

Friction dominated model

This section considers the friction dominated case. The corner thickness ! $ 0 and its deviation I! = (! $ 0 -! $ )/! $ from the nominal final thickness ! $ are investigated. This analysis is simply geometric.

Female corner

First, let us consider the female tool where & = '/2 . The total height of the L-shape before and after compaction (Figure 3a) can be equated, giving

The length of the first diagonal (being at 45°) can also be equated before and after compaction, giving Finally, considering the outermost ply to be inextensible, its length can be equated before and after compaction:

Eq. ( 9), ( 10) and ( 11) along with the initial configuration in Eq. ( 2) and the bulk factor Eq. ( 1) give the corner thickness deviation for this case of the female tool as

+ , + / , = + $ + ! $ + / $ (9)
+ , + 2 / , = + $ + ! $ 0 + 2 / $ (10) 2/ , + ' 2 + " = 2/ $ + ' 2 + $ (11)
This is in agreement with previous work [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF].

Male Corner

For the male tool (Figure 3b) where & = 3'/2, the total height gives the length of the first diagonal:

and the outermost ply inextensibility:

The corner thickness deviation, for this case of male tool thus also gives

U-Shape

In the case of a U-Shape corner (where & = 0), the total U-shape height should be considered (Figure 3c):

I! = ! $ 0 -! $ ! $ = ' 4 2 -1 1 - ' 4 O P # -1 (12)
+ , + / , + ! $ = + $ + / $ (13)
+ , + 2/ , = + $ -! $ 0 + 2 / $ (14) 2/ , + ' 2 + " = 2/ $ + ' 2 + $ (15)
I! = ! $ 0 -! $ ! $ = ' 4 2 -1 1 - ' 4 O P # -1 (16)
as should the total length of the U-shape:

The outermost ply inextensibility can now be written

The corner thickness deviation, for this case of U-shape tool now gives

Flat Plate

For a flat plate, where & = ', the corner thickness deviation is 0,

Pressure dominated

For the pressure dominated mechanism, perfect slip is considered between the plies, and between the ply and the mould, thus allowing conformation to the mould. Previous work by Brillant & Hubert [START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF], Levy et al. [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF] or Hubert et al. [START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF] consisted in an

2+ , = 2+ $ + 2! $ (17)
+ , + / , = + $ + ! $ 0 + / $ (18)
/ , + ' 2 + " = / $ + ' 2 + $ (19)
I! = ! $ 0 -! $ ! $ = ' 2 O P # -1 (20)
I! = ! $ 0 -! $ ! $ = 0 O P × # -1 (21)
analytical model for female corners. We therefore extended this model for male and Ushaped moulds.

Female Corner

Considering the free-body diagram in Figure 4b), Eq. ( 4) is modified. Because the plies slipped and conformed to the mould, there exists a mould reaction stress =. Moreover, because the compaction is now pressure dominated, a full relaxation of the tensions in the plies 1 " is assumed such that 1 " = 0. This comes down to disregarding the interply friction relative to the pressure terms. The force equilibrium then reduces to

6+ $ - = ⋅ 7 8 <= > R = 0 (22)
The normal reacting stress = ⋅ 5 over the flat part of the mould side boundary Γ , is close to that of the flange, and thus assumed to equate 6. The average of the normal reacting force = ⋅ 5 over the curved part of the mould side boundary Γ , is considered equal to = AST . The projection of the integral term on 7 8 then consists of two terms:

The first of these terms is the integral over the curvature + , of the mould side boundary Γ , . The second term is integral over the flat part of the mould boundary Γ , of length / " -/ $ (as shown on Figure 4b). Eq. ( 22) can then be written

= ⋅ 7 8 <= > R = = AST + , + 6 / " -/ $ . (23)
Using the total corner height, Eq. ( 9) yields the following forces equilibrium relation:

Now, in order to close the relation, = AST needs to be determined.

Under low pressure conditions found in out-of-autoclave manufacturing (i.e., 100 kPa), a linear elastic compaction behaviour of the prepreg bed can be assumed. Also, from Figure 4b), the laminate compaction stress along the axis of symmetry (bisection) varies between 6 on the bag side and the extreme reaction pressure min = , at the center of the corner, on the tool side. Given that the average tool reaction pressure = AST is defined as the average over the same range min = , 6 , we assume that the average laminate compaction stress across thickness on the axis of symmetry is also = AST .

Given the above statements, the ratio between the compaction stresses and the normal strain at the flange (\ $ ) and on the axis of symmetry (\ 0 ) of the corner both equate the bed stiffness:

By definition, the strains at the flange and at the corner are given by 6+ $ -= AST + , -6 / " -/ $ = 0.

6 + , -! $ -= AST + , = 0 (25)

6 \ $ = = AST \ 0 (26)
\ $ = ! " -! $ ! " = # -1 # and \ 0 = ! " -! $ 0 ! " = # -! $ 0 /! $ # (27)
Eq. ( 26) and [START_REF] Krumenacker | Experimental study of variability and defects in vacum-bag-only corner laminates[END_REF] give Substituting = AST in Eq. ( 25) gives

Because atmospheric pressure 6 is positive, the bracket factor is zero. After rearrangement, it gives the corner thickness deviation:

Male corner

For male corners, the free body analysis (i.e., Eq. ( 22) to ( 24) ) is still valid (Figure 4d). The total height Eq. ( 13) then modifies the sign in the force equilibrium relation:

The compaction behaviour (Eq. ( 26) to [START_REF] Martin | Carbon fibre reinforced polymer inter-ply friction experimental characterization[END_REF]) is also unchanged. The corner thickness deviation is then written

U-shape

For U-shapes, the free body analysis (Eq. ( 22)) becomes

= AST = 6 # -! $ 0 /! $ # -1 . ( 28
) 6 ! $ 0 /! $ -1 # -1 + , -! $ = 0. ( 29
) δ! = ! $ 0 -! $ ! $ = # -1 ! $ + , (30)
6 + , + ! $ -= AST + , = 0 (31)

δ! = ! $ 0 -! $ ! $ = -# -1 ! $ + , (32)
6× 2+ $ - = ⋅ 7 8 <= > R = 0 (33)
where the second term is now written

The compaction behaviour (Eq. ( 26) to ( 28)) is unchanged and gives

Using the height of the U-shape (Eq. ( 17)), the corner thickness deviation is obtained as

Flat Plate

In the case of a flat plate (Corner angle & = '), the corner thickness deviation is written

= ⋅ 7 8 <= > R = = AST × 2+ , + 0. ( 34
)
+ $ = + , # -! $ 0 /! $ # -1 . ( 35
) δ! = ! $ 0 -! $ ! $ = # -1 ! $ + , (36)
δ! = 0 (37)

Summary

In all cases of a friction dominated mechanism, the corner thickness deviation can be written whereas in all cases of a pressure dominated mechanism, it is written where the compaction parameters ^$ and ^_ depend on the corner angle as given in Table 1.

RESULTS AND DISCUSSION

In this section we analyse an extensive experimental database built from the literature. It mostly comprises experimental data for thermoset continuous fibre laminates.

Thickness deviation is measured in the corner after curing and compared with the nominal thickness measured in the flange section.

Database

In order to validate the model, experimental data obtained with out-of-autoclave prepreg material (showing large bulk factors) and processed out-of-autoclave were analysed. Over 100 data points from the literature were analysed. The database is available

I! = ^$× # -1 (38)
I! = ^_× ! $ + , # -1 (39)
as an Excel spreadsheet in the supplementary materials of this article. The dataset includes results from five different works:

• The L-shapes by Brillant and Hubert [START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF] were manufactured on male and female 90° toolings with 8 harness satin (8HS) and plain weave (PW) Carbon/5320 epoxy resin. The friction coefficient for this material was measured by Levy et al. [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF] as 0.17. The bulk factor is adapted from the literature [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF][START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF][START_REF] Hubert | Towards a design guideline for corners in composite parts[END_REF][START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF] and taken as 1.23 for 8HS and 1.2 for PW.

• The L-shape by Levy et al. [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF] was similar but manufactured with 8HS only.

• The L-shape by Ma et al. [START_REF] Ma | Vacuum Bag Only Processing of Complex Shapes: Effect of Corner Angle, Material Properties and Process Conditions[END_REF][START_REF] Ma | Defect Reduction Strategies for the Manufacture of Contoured Laminates Using Vacuum BAG-Only Prepregs[END_REF] had angles over 90°. They were nevertheless compared with the model prediction for 90° angles. Concave and convex moulds were used. They were manufactured with the same 8HS material, thus using the same properties as above.

• The L-shapes by Krumenacker & Hubert [START_REF] Krumenacker | Effect of Processing Deficiencies on Vacuum-Bag-Only Complex-Shape Prepreg Laminate Consolidation and Interlaminar Tensile Behaviour[END_REF] were manufactured in the same material with unidirectional architecture (UD) and show a smaller bulk factor of 1.1.

The friction coefficient for UD is also smaller. It was adapted from Larberg & Akermo's [START_REF] Larberg | On the interply friction of different generations of carbon/epoxy prepreg systems[END_REF] measurement AS4/8552 and taken as 0.10. Concave and convex moulds were used.

• The L-shapes by Hughes and Hubert [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF] were manufactured on concave moulds only, using 8HS 5320 material (the above properties were thus also used in the model).

The material properties used with these data points are listed in Table 2. Four specific data points are discussed below. The conformation number Λ H = + , / B/ , appears to provide a good estimate of whether the pressure or friction mechanism dominates. To illustrate this capacity, four specific data points are presented in Figure 5. Two cases are for male corners and two for female corners. For each configuration, cases of low and high values of conformation number Λ ` were chosen. For each case, the experimental corner thickness deviation is bounded by the friction and pressure dominated models (Eq. ( 38) and ( 39)).

The pressure dominated model predicts a lower bound, which is even negative (corner thinning) for the male case. The friction dominated model predicts a higher bound. For high values of Λ a , which correspond to a good conformation, the measured deviation is closer to the pressure dominated model, whereas for low values of Λ a , the experimental values are closer to the friction dominated model.

The friction dominated model bound is never approached experimentally as the highest conformation number found in the database is not that high.

Unified semi-empirical model

The conformation number Λ H = + , / B/ , provides a good estimate of whether the pressure or the friction mechanism dominates. In order to provide a unified model, the following semi-empirical rule of mixture is proposed for the corner thickness deviation:

I! = b c `×^_× ! $ + , # -1 + 1 -b c `×^$× # -1 ( 40
)
where b is a smoothed step function that ensures both asymptotic behaviours, namely

The following step function, which ensures both conditions, is proposed:

where d is a smoothing parameter that will be identified experimentally. It quantifies the width of the transition zone between non-conformation (friction dominated compaction)

and free sliding of plies (pressure dominated compaction). The graph of g is given in Figure 6. It shows that both asymptotic behaviours of Eq. ( 41) are recovered with the empirical function as well as the experimental data.

Using this step function, the unified model gives the corner thickness deviation as where the compaction parameters ^_ and ^$ are given for various corner configurations in Table 1.

Finally, one single modelling scalar, the step function parameter d, was obtained by fitting the experimental data:

lim f g →i b = 0 and lim f g →kl b = 1 (41) b c ` = c ` d + c ` (42)
I! = ! $ 0 -! $ ! $ = ^_ ! $ B/ , + d^$ × # -1 d + + , B/ , (43)
d = 0.58 (44)
The effect of the material properties uncertainty can be evaluated using the variance formula where o pq is the standard deviation expected on the modelled corner thickness deviation. o r is the standard deviation associated with the uncertainty over the friction coefficient B and o s over the bulk factor #. o s = 0.03 can be assumed for the bulk factor, which is the typical standard deviation obtained for values of # ∼ 1.1. An o r = 0.05 can be considered for the friction coefficient, which is very variable. It corresponds to a ∼25% higher coefficient of variation since B ∼ 0.2 in our cases. The average standard deviation o pq obtained over all the out-of-autoclave cases, arising from these material properties uncertainty is

Additionally, the experimental error in measurement of corner thickness deviation can be roughly approximated as ±300 Bz, which gives an error of roughly 10% on the thicknesses investigated in the database.

o pq = { I! {B o r | + { I! {# o s | (45)
o pq = 0.043 (46)
the database is 0.05. Although this could seem high, the following facts should be considered:

1. The model is a very simple analytical formula based on strong assumptions (Coulomb friction, fibre bed elasticity, etc.).

2. It includes only two material properties (bulk factor and friction coefficient) and thus cannot accurately describe the complex behaviour of composite material.

3. The materials used in the database are highly variable in terms of morphology.

In particular, the friction and sliding behaviour is likely to be stochastic. This is reflected in the propagation of uncertainty discussed above. A fair estimate of the standard deviation arising from the material uncertainty appeared to be around 0.05, which is comparable to the experimental standard deviation.

4. Variability is also caused by the laminator (stacking, edge effect, bagging configuration, debulking, etc.). Indeed, besides the various configurations, the database includes five different laminators, with slight differences in bagging conditions (edge breathing, bag folds, etc.).

5. Variability in experimental thickness deviation may also arise from the experimental procedure, which differed slightly between the works referenced. This is also discussed with regard to the propagation of uncertainty above.

Yet, apart from a couple of outliers, the model successfully captured the correct trend between thinning and thickening (only lower left and upper right quadrants are populated in Figure 7).

GUIDELINES FOR USING THE UNIFIED MODEL

For a given material system, this section presents the step-by-step method for predicting corner thickness deviation using the above unified model. Ultimately, it would be possible to produce a design chart.

Parameter characterisation

First, the two material properties, namely the bulk factor # and the friction coefficient B should be characterised for the material system studied. For the 5320 system, these are given in Table 2.

Bulk factor

The bulk factor of the prepreg composite system is the ratio of between the thickness prior to processing (after debulk) and after processing; this is straightforward to obtain by direct thickness measurement as in [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF][START_REF] Cauberghs | Out-of-Autoclave Manufacturing of Aerospace Representative Parts[END_REF].

A typical value of the bulk factor would be around 1.2 for out-of-autoclave prepreg [START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF] and usually slightly lower for UD than for woven prepregs.

Friction coefficient

The ply-to-ply friction coefficient of the prepreg B is much harder to characterise as this requires a special technique. Various research teams developed in-house devices to try and characterise this friction behaviour [START_REF] Larberg | On the interply friction of different generations of carbon/epoxy prepreg systems[END_REF][START_REF] Sachs | A Friction-Test Benchmark with Twintex PP[END_REF][START_REF] Sun | Interply friction of carbon fiber/epoxy prepreg stacks under different processing conditions[END_REF], which includes dry and lubricated contributions and is usually quite complex. One can also refer to existing literature to estimate the Coulomb friction coefficient B [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Larberg | On the interply friction of different generations of carbon/epoxy prepreg systems[END_REF][START_REF] Sun | Interply friction of carbon fiber/epoxy prepreg stacks under different processing conditions[END_REF].

For woven materials, higher values of about 0.11-0.15 are usually obtained. This is the case for the Cycom 5320 system used in this study and characterised in a previous one [START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF]. For Cycom 5320-1 plain weave material, an average value of 0.11 was obtained for temperatures ranging from 50-120°C [START_REF] Martin | Carbon fibre reinforced polymer inter-ply friction experimental characterization[END_REF]. For UD systems, lower values around 0.05 are usually obtained. Additionally, all the cases in the database consider either 0°/90° stacking or quasi-iso stacking. Nesting, which may occur in highly aligned stacking (including 0°/0°) and may lead to a different friction coefficient, is thus ignored.

Design charts

Using the unified model Eq. ( 43), design charts can be constructed for a wide range of thickness to flange length ratio ! $ // , and tool radius to flange length ratio + , // , . Some typical such design graphs are presented in Figure 8. One is for a female mould with a bulk factor # = 1.23 and a friction coefficient B = 0.17, which corresponds to an 8 harness satin carbon / 5320 epoxy resin prepreg system. The second example in Figure 8 is for a male mould with a bulk factor # = 1.20 and a friction coefficient B = 0.17, which correspond to a plain weave carbon / 5320 epoxy resin prepreg system [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF][START_REF] Ma | Vacuum Bag Only Processing of Complex Shapes: Effect of Corner Angle, Material Properties and Process Conditions[END_REF][START_REF] Levy | Corner consolidation in vacuum bag only processing of out-of-autoclave composite prepregs laminates[END_REF][START_REF] Brillant | Out-of-Autoclave Processing of Complex Shape Laminates[END_REF]. These two charts, plotting the iso-values of corner thickness deviation, were produced with a MATLAB code available in the supplementary materials of this article.

The four cases discussed in section 3.1 and Figure 5 are illustrated by red lines on the chart.

Given an acceptable corner thickness deviation, such design charts can then predict the geometries that should be avoided. The designer may then either modify the geometry or suggest innovative solutions (such as pressure intensifiers [START_REF] Gu | Pressure transfer behaviour of rubber mould and the effects on consolidation of L-shape composite laminates[END_REF][START_REF] Cauberghs | Out-of-Autoclave Manufacturing of Aerospace Representative Parts[END_REF] or using ply cuts [START_REF] Hughes | Out-of-autoclave Prepreg Processing: Effect of Integrated Geometric Features on Part Quality[END_REF])

to ensure the allowable thickness deviation is respected.

CONCLUSION

This article investigates the thickness deviation occurring in complex shapes produced with vacuum-bag processing of prepreg composite materials. In corner locations, thickness may deviate from the nominal flange thickness due to two mechanisms: (i) the pressure difference between corner and flange, which results in different compaction of the fibre bed; and (ii) the friction between plies, which prevent adequate conformation of the laminate to the mould. We modelled these two mechanisms for the cases of simplified Lshape geometries (concave and convex). The two analytical models obtained could then be combined in a semi-empirical unified model Eq. (43) making it possible to predict the corner thickness deviation using only two material parameters and two geometric ratios. The charts correspond to: (top) the female case with a bulk factor # = 1.23 and friction coefficient B = 0.17, corresponding to a 5320 8 harness satin system; and (bottom) the male case with a bulk factor # = 1.2 and friction coefficient B = 0.17, corresponding to a 5320 plain weave system. The four cases discussed in section 3.1 and Figure 4 are predicted with the red lines.

  Figure 4 a) and c), one can equate the tension in that first ply 1 2 with the result of the

Figure 7

 7 Figure 7 compares the experimental and modelled corner thickness deviation. The

Figure 1 :

 1 Corner thickness deviation in composite L-shapes[START_REF] Krumenacker | Experimental study of variability and defects in vacum-bag-only corner laminates[END_REF]. Examples of corner thinning (a), and thickening with porosity in the corner area (b).

Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure 2: Pressure sensor profile at the 10 mm silicone rubber laminate tool interface compacted on a 12 mm radius female mould in a vacuum bag.

Figure 6 :Figure 7 :Figure 8 :

 678 Figure 6: Step function g used in the unified model as a function of the conformation number Λ `. The step function weights the friction to pressure effects. The higher the conformation number, the closer it should get to unity (pressure dominated bound), whereas it should tend to 0 (friction dominated bound) when the conformation number approaches 0. The experimental weights between pressure and friction bounds are also plotted for all the data points.

Table 2 :

 2 Material properties for the 5320 resin system.

		Friction coefficient B	Bulk factor #
	Plain weave	0.17	1.2
	Harness satin	0.17

For validation purposes, over 100 experimental data points were gathered from five different published sources. These experimental corner thickness deviations were compared with the predictions of the unified model. The standard deviation of the error was around 5% and validates, to some extent, the unified model. The unified model can therefore be used to produce design charts, such as those shown in Figure 8. These prove useful for the manufacturing designer to predict whether a process will be capable of producing parts in the allowable range of thickness deviation.

The method presented here could also be extended to other forming processes, such as those employing pressure intensifiers, such as rubber pads or high pressure autoclaves.

To be predictive, the semi-empirical unified model needs to be adjusted. With this objective, the use of correction factors was first suggested [START_REF] Hubert | Out-of Autoclave Prepreg Processing[END_REF][START_REF] Hubert | Towards a design guideline for corners in composite parts[END_REF], but further investigation of the friction, sliding and wrinkling effects also seem to be required.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial support from the National

TABLES

Table 1: Compaction parameters ^$ for the friction dominated models, and ^_ for the pressure dominated models. The parameters depend on the corner angle. The corner thickness deviation predictions are obtained using the unified model, Eq. ( 43


A Lenoble

J.-J Tiercelin

A Delagnes

Nadung'a 4 excavations are part of the West Turkana

2) Vertical size sorting: vertical displays of artifact density show a gaussian distribution where the greatest part of the assemblage is included in a 0,4 meter-thick layer. This indicates an origin from a single archaeological level. Size artifacts proportions compared to those produced by experiments point out no sorting for this richest layer and sorting for the debris scattered outside this layer.

5) Assemblage consistency:

the vertical distribution of artifacts from the same original block of raw material refutes the hypothesis of stratification inside the archaeological layer.

4) Field evidences:

the correspondence between sharp lower boundaries of the artifact layer and slickensides has been observed during excavations.

3) Artifacts distribution:

two main highly concentrated areas can be observed on the map of artifacts. The southernmost one is less concentrated and presents a polygonal network. On vertical backplots, the archaeological layer is thicker in the southern part of the site. Low density areas in the centers of the polygons appear as depressions with well-defined lower boundaries. These slanted outlines explain the undulating appearance of the archaeological layer. Their shape and distribution are similar to those of the slickensides associated with a bowl structure in the lower horizon of a vertisol.

All of these data support the interpretation that a single archaeological level was modified by argilliturbation. Sliding along slickensides was the main cause of this disturbance.

Vertisol pedogenesis is typical of wet/dry tropical climates with soil swelling upon wetting and shrinking when dried. If well expressed, the profile is constituted by a top organic-mineral horizon under which is the horizon characterized by wedge-shaped parallel aggregates (sphenoids) and cracks during dry conditions. Glossy striated surfaces (slickensides) occur in the underlying horizon. Micro-relief in such soils is known as gilgaï, i. e. microknolls and micro-depressions more or less regularly arranged with a diameter generally measuring a few meters. To the micro-lows on the landscape correspond a "bowl-shaped" arrangement of the slickensides and the sphenoids.

Under Tropics, floodplain deposits commonly support a vertisol pedogenesis. It is for this reason that argilliturbation is likely to disturb sites in this context. In East Africa, a significant number of archaeological sites are found in deposits with vertic properties: Lokalelei 1, Kokiselei 4, Gona -OGS7, etc.

The site

Nachukui formation deposits are located on the west side of lake Turkana and have a cumulative thickness of 712 m for the period 4-0,7 million years. Paleolithic sites are discovered along modern ephemeral stream eroding these deposits. In the Nadung'a stream area are retrieved the more recent sites of the formation (ca 0,7 Mya). Presently, a dozen sites are known from different lithofacies. A surface measuring 53 m2 has been excavated at the site 4 of the Nadung'a complex, and an assemblage of 6800 lithic artifacts recovered. The majority of the assemblage consists of flakes and cores produced by a discoid reduction method. Formal tools are represented by notches and denticulates. A few heavy duty tools (e. g. worked pebbles, and hammerstones) complete the assemblage. Faunal remains are equally present and consist in a partial carcass of an elephant.

Sedimentological data

The one meter thick archaeological level is contained in a unit of brown clays including lenses of ill-sorted sands and gravels. These deposits are interpreted as an Argiliturbation and Site Formation Processes in East Africa: the case of Nadung'a 4

East-African Plio-Pleistocene deposits contains archaeological sites from fluvio-lacustre environment. A number of works allow us to discuss the modifications of assemblages recovered from fluvial channel or banks. In contrast, sites retrieved from floodplain deposits are generally assumed to be well preserved and few studies have addressed site formation processes in such environments. The site of Nadung'a 4 has yielded detailed data concerning typical modifications in this environment.

  distributions are typically interpreted as the result of sinking into desiccation cracks. Distributions at Nadung'a 4 cannot be explained in this way. Thus, we propose a new model of perturbation by argilliturbation. Our model stresses the role of sliding along slickenside and their related bowl shaped structure. This model can explain the upward and downward movement of artifacts, as well as the polygonal pattern of artifact distribution. showing artifacts from the same original block. Each color represents a single block.

slickenside

  Plio-pleistocenes outcrops in the lake Turkana area and site situation Areas fromLenoble et Bertran (2004) Archaeological dataExcavations provide several lines of evidences for determining the role of natural site formation processes: 1) Orientation and dip: the orientation and dip measurements of mapped artifacts in Benn's diagram indicate that Nadung'a 4 is typical of archaeological sites disturbed by argilliturbation.

0

  Stratigraphic distribution of some Nadung'a complex archaeological sites.

  ancient mud flat crosscut by small streams and regularly swamped during the seasonal floods of the lake or tributaries. Noteworthy features of the clays are prismatic structure, slickensides and cracks filled with sands indicative of a vertisol type paleosol. In thin sections, crack infilling and cross-striated b-fabric support this interpretation. The thickness of the deposits and the superposition of features associated with initially distinct horizons indicate a cumulative soil. Present-day examples of this type of soil are encountered in low topographical positions, such as floodplains, in semi-arid regions with an alternation of long dry seasons and short pluvial events, which typically support woody savannah vegetation.

Archaeological Project led by H. Roche. Funds for the geoarchaeological study has been provided by the Fyssen project " L'évolution des comportements techno-économiques des Homo erectus aux environs de 700 000 ans en Afrique de l'Est " conducted by A. Delagnes and by the French Prehistoric Mission in Kenya run by H. Roche. I thank W. Banks for his help in improving the translation.