Benoît Wittmann
email: wittmannbenoit@gmail.com

Christian Gauthier

Alain Burr

Jean-François Agassant

Damien Favier

Pierre Montmitonnet

Alain Casoli

Jean- François Agassant

Study of scratch resistance of a hard-on-soft polymer bilayer: Combination of in situ vision, X-ray tomography and numerical simulations

Keywords: Scratch test, polymers, coating, tribology, X-Ray tomography, finite elements, damage

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

Introduction

Protective, anti-scratch coatings are often used on polymeric thin film, e.g. top-coat on paints, varnish on eyeglasses etc. Their anti-scratch performance is strongly connected with their mechanical properties, and their thickness must be optimized with respect to the kind of contact and loading they will be submitted to [START_REF] Bull | Failure mode maps in the thin film scratch adhesion test[END_REF] (2) (3). The scratch test, which has been developed to study resistance of material to tribological agressions, is very often used for coated materials, in particular coated polymers.

During the scratch test of a bulk polymer material, different scenarios can happen. Depending on the material properties and the experimental conditions, five scratch modes are known for uncoated surfaces: reversible (visco)elastic (4) (5) [START_REF] Pelletier | Viscoelastic and elastic-plastic behaviors of amorphous polymeric surfaces during scratch[END_REF], smooth or unstable ductile ploughing [START_REF] Briscoe | The hardness of poly(methylmethacrylate)[END_REF] [START_REF] Bucaille | The influence of strain hardening of polymers on the piling up phenomenon is scratch tests: Experiments and numerical modelling[END_REF], folds [START_REF] Schallamach | How does rubber slide ?[END_REF], brittle behavior with cracks in the groove of the scratch [START_REF] Jardet | Viscoelastic effects on the scratch resistance of polymers: relationship between mechanical properties and scratch properties at various temperatures[END_REF] [START_REF] Baietto | 3D crack network analysis during a scratch test for a polymer: A combines experimental and multirigid X-FEM based numerical approach[END_REF], machining [START_REF] Briscoe | The hardness of poly(methylmethacrylate)[END_REF] [START_REF] Briscoe | Scratching hardness and deformation maps for polycarbonate and polyethylene[END_REF] which corresponds to the degeneracy of a frontal bulge into a chip prone to detach as a wear particle.

Because of the wide variety of observed mechanisms, finding a universal way to increase the scratch resistance of a material is difficult, but a commonly used method in industry is the deposit of an antiscratch hard coating. This hard coating allows decreasing the plastic deformation of the substrate, hence the residual local slope of the furrow and its visibility. This method works for low to moderate normal loads but leads to complex rupture mechanisms at higher load, making the residual scratch more visible. Indeed, the scratch behavior of a multilayer material depends on the relative mechanical properties of the substrate and the coating. For example, a hard coating on a soft substrate leads to through thickness coating cracking, while a hard coating on a hard substrate leads to chipping [START_REF] Bull | Failure mode maps in the thin film scratch adhesion test[END_REF]. Moreover, the scratch behavior of a coated material depends on the adherence between the two layers. In the case of an elastic-brittle coating, when a crack appears in the coating and propagates until the interface, two scenarios can happen: if the adhesion is weak, the crack propagates along the interface and a delamination occurs. If the interface is strong, the crack propagates in the substrate, without delamination (1) [START_REF] Burnett | The relationship between hardness and scratch adhesion[END_REF]. In some very particular cases where the substrate and the coating are ductile and the adherence very weak, a stationary delamination regime with a crescent that moves forward ahead of the tip is observed [START_REF] Houerou | Mechanical analysis of blistering and chipping of a scratch-resistant coating[END_REF] [START_REF] Houerou | Mechanical analysis of the blistering of a thin film deposited on a glassy polymer[END_REF].

Because of the numerous parameters having an influence on the mechanical behavior of a material during a scratch test, the interpretation of the mechanisms observed experimentally remains difficult. Thus, numerical models have been developed to study the local mechanical conditions leading to the different mechanisms.

The first numerical simulation of a scratch test by a sharp indenter has been done by Bucaille et al. [START_REF] Bucaille | Simulation numérique de l'indentation et de la rayure de verres organiques[END_REF] in 2001 with a conical tip on a bulk material. An elastic -perfectly plastic behavior law [START_REF] Bucaille | Mechanical analysis of the scratch test on elastic and perfectly plastic materials with the three dimensional finite element modeling[END_REF] has been used. These computations in particular allowed studying the way the material elastically unloads after the passage of the tip, depending on the factor [START_REF] Johnson | The correlation of indentation experiments[END_REF]:

X = E σ 0 cot(ө) (1)
with E the Young's modulus of the material, σ0 its yield stress and ө the semi-apical angle of the cone. This X-factor represents the ratio of the average total strain around the indenter (cot(ө)) to the elastic strain the material may undergo (~σ0/E). For high X values, the behavior is mainly plastic while for low values, there is an important elastic recovery at the rear face of the tip. Moreover, these first simulations provided a better understanding of the relation between the apparent friction coefficient and the material mechanical properties: for high values of X (dominantly plastic deformation) they reach the theoretical Goddard and Wilman's value µ = tan(ө) [START_REF] Goddard | A theory of friction and wear during the abrasion of metals[END_REF] of the apparent friction. However, for lower X values (large elastic strain), the computed apparent friction coefficient is lower than the theoretical value because the sliding is more elastic and therefore the elastic recovery behind the tip is large, decreasing the dissymmetry of the contact shape. Indeed the Goddard and Wilman model has been developed for metals, for which the elastic recovery is negligible compared with their plastic deformation during a scratch test. Finally, an analytical model of friction has been developed, taking into account this elastic recovery [START_REF] Bucaille | Mechanical analysis of the scratch test on elastic and perfectly plastic materials with the three dimensional finite element modeling[END_REF]. Later, they have shown the insufficiency of the elasticperfectly plastic behavior law by showing that at high penetration depth, the strain hardening of the material has a first order influence on the geometry of the piling-up [START_REF] Bucaille | The influence of strain hardening of polymers on the piling up phenomenon is scratch tests: Experiments and numerical modelling[END_REF]. Another advantage of the numerical simulation is the possibility to study the stresses and strains fields in the material during the scratch. This approach is particularly useful on coated materials to understand the mechanical conditions leading to different complex rupture mechanisms (20 [START_REF] Hossain | Scratch behavior of multilayer polymeric coating systems[END_REF]. In the case of a thick hard coating on a soft substrate, the coating allows decreasing the plastic deformation of the substrate, which reduces the depth of the residual furrow [START_REF] Kermouche | Finite element modeling of the scratch response of a coated time-dependent solid[END_REF]. In the case of a thin coating, the mechanical properties of the coating cannot modify the stress and strain fields of the contact; the thickness of the coating must be adjusted to the roughness of the moving tip to prevent these roughnesses from generating plastic microscopic scratches in the macroscopic furrow left after the contact time [START_REF] Demirci | Mechanical analysis of the dammage of a thin polymeric coating during scratching: role of the coating thickness to the roughness of a scratching tip[END_REF]. Tensile stress behind the indenter causes perpendicular cohesive crack of the coating [START_REF] Li | Three dimensional finite element modelling of the scratch test for a TiN coated titanium alloy substrate[END_REF]. For scratch test on a soft polypropylene coated by hard polyurethane, H. Jiang et al. [START_REF] Jiang | Mechanical Modeling of scratch behavior of polymeric coatings on hard and soft substrates[END_REF] have observed that the maximal principal stress moves from ahead to behind the tip with increasing normal load. This is in good adequacy with the rupture mechanisms that they have observed experimentally: in front of the tip at low load, behind the tip at high load. In the same paper, they have compared the scratch resistance of: 1) a soft acrylic coating on a hard steel substrate and 2) a hard polyurethane coating on a soft polypropylene substrate. They observe that, in terms of normal force at which a fracture mechanism is initiated, the hard coating on soft substrate material is better. Demirci et al. [START_REF] Demirci | Mechanical analysis of the dammage of a thin polymeric coating during scratching: role of the coating thickness to the roughness of a scratching tip[END_REF] have shown for a polymeric hard coating on a softer polymeric substrate that cracking does not appear at the edge of the contact area but under the contact area. Cracking first appears in the rear half of the contact area, whatever the tip velocity and the normal load applied. They described a mechanism of initiation and growing of the cracking recorded in-situ (2). Hamdi et al. [START_REF] Hamdi | Fundamental understanding on scratch behavior of polymeric laminates[END_REF] studied the mechanical behavior of a bi-layered coating composed of polypropylene (E=1.65 GPa) + Polyamide (E=2.82 GPa) deposited on aluminium (E=70GPa). They compared the scratch resistance of the material depending on the order of the two polymeric layers (aluminum /polypropylene /polyamide and aluminum /polyamide /polypropylene). They concluded that the aluminium / Polyamide / polypropylene is much better because of a lower gradient between the mechanical properties, and a lower friction between the tip and the polypropylene. All these works show the difficulty to analyze the mechanical response and the fracture mechanisms of a layered material during a scratch test because of the high number of parameters and the coupling between some of them, and the difficulty to access experimentally to information on the location of the first damage to understand its mechanism.

) (3) (21) (22) (23) (24) (25)
Visual aspect is a key problem for the flooring industry. Indeed, the ambience of a room is directly linked to the design of the materials that compose the walls, the ceiling and the floor. In the past, floor covering were made of wood, stone, ceramics or linoleum. But since the second half of the XX th century, PVC based floor covering was developed for performance and economic reasons. Floor covering is daily submitted to various solicitations: walking, sliding chairs, furniture feet indentation, sliding objects, cleaning devices etc. All these solicitations are liable to cause wear of the product and degradation by scratches, which negatively impacts its visual aspect. Therefore, it is protected by a thin layer of a harder polymer.

In this article, the influence of a deposit of hard polyurethane coating on the scratch resistance of a soft plasticized PVC is studied. First, the scratch behavior of an uncoated and a coated PVC are compared.

Then, the three rupture mechanisms observed on the coated PVC are analysed in details. The in situ observations of the tip/material contact surface allow observing the place in the surface plane where cracks appear and propagate. The analysis of these mechanisms is completed by a X-Ray tomography observation of the scratch: this complements the 2D visual observations with a 3D view which discloses how cracks have propagated in the depth of the material, without cutting the material with the risk to create new cracks or deform those formed during scratching. Of course one limitation will be the comparison between geometrical information under loading (2D in situ) with those post mortem after unloading (X-Ray tomography). Therefore, a numerical model using the Finite Element Method (FEM) of the scratch test has been developed on Forge NxT to precise the local stress conditions leading to the different rupture mechanisms.

Materials and methods

Microvisio-Scratch

As described in (4), the apparatus is a homemade set-up based on a commercial servomechanism allowing the scratching action by moving the sample relative to the tip. The scratch test can be piloted in normal force (from 0.05N to 35N) and in scratching velocity (from 1 to 10 4 µm/s). Moreover, the sample is enclosed in an insulated box allowing a control of the temperature (from -50°C to 110°C) and moisture. A microscope coupled to a camera allows an in situ vision of the contact area provided transparent samples are used. A detailed diagram of the apparatus and an example of a scratch test performed on a perfectly transparent sample are in appendix A. Since the camera is located at the same abscissa as the indenter, its optical axis is normal to the interface; furthermore, the two materials have very close indices of refraction. Hence the interface does not degrade the transmission of light.

A first scratch is done on uncoated PVC, and a second one on coated PVC. Both are performed in the same conditions: T = 22°C, ambient humidity, with a spherical tip of radius R = 100 µm. In the following of this article, all lengths will be normalized by the tip radius R.

Samples studied

The first sample is a flexible plasticized PVC sheet (thickness = 6 R). The second sample is composed by the first sample covered by a hard filled polyurethane anti-scratch coating (thickness tcoating = 0.2 R).

The role of fillers is not to increase the scratch resistance of the material, but to control its gloss. The uncoated PVC has a roughness Sa = 180 nm and the coated one has a roughness Sa = 712 nm. Sa is the arithmetical mean height, defined as :

S a = 0 |z(x,y)| dxdy 0 (2)
With x, y and z the spatial coordinates of the topography of the sample. Altitude z is referred to the mean plane and L is the sampling length.

The mechanical properties of each material have been measured by tensile tests on an Instron 3344 (Instron, Norwood, USA) at 22°C and a deformation rate of 0.3 s -1 . Three tensile tests were performed on each material. In tension, the PVC has an elastic-plastic behavior and the PU has an elastic-brittle behavior. The mechanical properties of both materials are given in the table 1. They are rendered nondimensional using the Young's Modulus of the PVC.

PVC PU Non-dimensional E

1 (± 0.06) 6.7 (± 0.

Confocal microscopy

The roughness of the samples and the depth of the residual grooves has been measured by a STIL confocal microscope (STIL SAS, Aix-en-Provence, France), with a MG140 optical pen (-x,-y resolution = 2µm; -z resolution = 30 nm; maximum light cone angle = 27°). The samples are positioned on a x-y stage, measurements have been carried out with x and y steps of 5 µm.

Numerical model

The numerical model of the scratch test has been set up in the commercial implicit (quasi-static) FEM software Forge NxT (version 3.0) in view of its remeshing capacity and the large mesh distorsions observed. As shown figure 1, the tip is modelled by a spherical analytic rigid solid of radius R. The material is defined as a parallelepiped (20 R x 6.2 R x 5 R). This parallelepiped is defined as a multiple material object: Instead of defining one object for the PVC, another object for the PU, and defining a contact law between the two, only one domain is defined with a unique mesh in which two zones are defined: a first one below the plane z = 6 R, and a second above this plane. The behavior law associated to each finite element depends on its position compared to this plane: the PVC constitutive model is used for elements below and the PU model for elements above. As shown figure 1, there is no element crossing the interface, which would increase incertitude and numerical noise. This approach is less time consuming than the multi-domain approach because there is no contact to compute between the two materials. Note that the initial meshing as well as remeshing strategies allow a well-defined, plane, smooth interface (see fig 1). The main limitation of this single domain strategy is that it does not allow delamination and conclusions will be restrained to systems with high interface adhesion. This is not a detrimental limitation for the experimental material studied (PVC / PU), because it has been observed experimentally that the adherence between the PVC and the PU is sufficient to avoid delamination even under the most severe loadings applied in this work (see part 3.1.3).

The plane y = 0 is a symmetry plane. The planes x = 0, x = 20 R and y = 5 R are defined as symmetry planes too in order to prevent any perpendicular displacement. The stresses computed close to these borders are found negligible compared with the stress around the tip ; this allows concluding that the domain considered is large enough to avoid edge effects.

The software uses four node tetrahedra which allows automatic, unstructured remeshing, with a P1 + -P1 stabilized formulation. Here, remeshing is forced in the whole domain every 10 th time increments (time increment ≈ 3.8.10 -3 s). The nodes on the PVC/PU interface are fixed in order to keep a welldefined interface throughout the computation.

Far from the tip, the mesh is coarse (0.5 R). Just under the interface, in the PVC, the mesh in finer (0.1 R) on a width of 1.5 R along the Oy axe. In the PU zone, the mesh in very fine (0.03 R) on a width of 1.5 R along the Oy axe.

The PU is modeled by an isotropic linear elastic law with EPU = 6.7 (normalized by the young modulus of the PVC) and νPU = 0.4. The PVC follows an elasto-plastic law: EPVC = 1 (normalized by the young modulus of the PVC), νPVC = 0.3 and the stress -plastic strain curve is given by the power law:

σ = A (ε+ε 0 ) m (3)
with A = 0.054 (Unitless because normalized by the Young's modulus of the PVC), m = 1.80, and ε 0 = 0.68.

Friction is modeled by a Coulomb law with µ = 0.35. It is the value of the apparent friction that is measured experimentally at low load, when the obstacle component of the apparent friction coefficient is negligible compared with the local friction component [START_REF] Lafaye | A surface flow model of scratching tip: apparent and true local friction coefficients[END_REF].

The rupture of the material is not modeled because the objective of these computations is only to determine the stress fields leading to the different fracture mechanisms.

In sections 3.2.1 and 3.2.2, the test is piloted by normal force imposed to the tip. In section 3.2.3, a vertical displacement is imposed to the tip and the normal force is computed. The material moves in the -x direction on a length of 10 R which has been checked systematically to be sufficient to reach a steady state, as in the experiments.

About the computation done on uncoated PVC, the same model is used with only one difference: the material is not defined as a bi-material object and the PVC behavior law is used everywhere.

Experimental results

Deformation and rupture modes observed

Figure 2a is a photograph of the residual scratch performed on uncoated PVC. This scratch test has been performed two times, with exactly the same results : there is a ductile groove and no cracks: the material is deformed elastically and plastically during the whole test.

The corresponding photographs of the residual scratch on PVC coated by polyurethane (figures 2.b and 2.c) show five distinct areas at increasing normal force. Again, this scratch test has been performed twice and the different mechanisms appear at the same normal load for the two tests.

Thanks to a microscope coupled to a camera, the contact area between the tip and the material is observed in situ i.e. continuously during the test, showing the very moments and locations at which cracks appear. Figure 3 shows an in situ photograph for the main steps of the scratch shown on figure 2.c. Since it is difficult to determine precisely the contact area from only one photograph, its evaluation is helped by the video. Indeed, the movement given by the video offers a better vision of the contact. There is, in the supplementary material of this article, an animated figure showing a part of the video for each step, allowing a better visualization of the phenomena.

1: The material is deformed almost exclusively elastically. The contact area is circular and there is no residual groove after the contact time.

2:

The substrate is deformed plastically and the contact area is not circular anymore. The material does not totally recover behind the tip because of plastic yielding, so that a residual groove is observed on the post-test photograph.

3: Cracks appear on the rear edge of the contact, oriented at ~ 45° to the scratch direction Ox, pointing towards +x. The intercrack distance is rather regular (≈ 1 contact length).

4: In addition to the cracks at 45°, still visible, the coating tears under the tip. It first opens parallel to the scratch direction and propagates in the direction Ox, following the movement of the tip. After a propagation of few contact lengths, the crack deviates towards the side of the groove; then another one appears under the tip, generally deviating later towards the other side of the scratch in a rather regular manner. The intercrack distance is rather regular as well (≈ 2 contact length).

5: In addition to the cracks at 45° and the tearing under the tip, a circular crack appears beyond the front edge of the contact, perpendicularly to the tip, periodically also, every one or two contact lengths.

Depth of the residual grooves

The roughness has been measured along the scratches done on uncoated and coated PVC in order to compare the residual grooves. The measurements, performed by confocal profilometry, are shown in figure 4.

From x/R = 0 to 10, there is almost no influence of the coating on the mechanical response of the material: on coated as well as uncoated PVC, there is no residual depth meaning that the material deformed almost totally elastically; the coated sample is rougher due to the filler, the size of which is not small compared with the coating thickness. From x/R = 10 to 60, the residual depth on coated PVC is clearly lower than on uncoated PVC. This means that uncoated PVC deforms plastically whereas elasticity is more pregnant on coated PVC; whether this effect is mostly due to the depth under load being smaller (protection of the soft substrate by the hard coating) or to elastic recovery after unloading being larger, cannot be told at this stage. From x/R = 60 to 100, the residual depth is again lower on coated PVC, in average, but the profile is very rough along the groove, because of the fractures that happen at this load level.

It can be concluded that profilometry captures the cracks morphology to a certain extent. The highest points are measured well above the initial surface level, which means that rotation of fractured blocks of PU has occurred beyond x/R = 60. It is not possible at this stage to tell if the lowest points are on the interface. Tomography is therefore used to describe the cracks with more precision.

Tomography characterization

In situ observation gives a lot of information leading to a better understanding of the mechanisms involved. However, it only gives information in the (xy) plane, as illustrated in figure 3, it does not give any information in the plane (yz) perpendicular to the plane of the surface. One possibility could be to cut the material after the test in order to study the cracks propagation in the depth in the plane (yz). This method is risky because new cracks could be created by cutting and wrongly attributed to the scratch test. In order to avoid this problem, the scratch is analyzed nondestructively by X-Ray tomography. This tomography, reported figure 5, has been performed on part 5 of the scratch of figure 2, where all three types of cracks are present. The cross sections in the (yz) planes (figure 5.b) show that there is no delamination between the two layers, although it is evident that very severe deformation has taken place. This has been found systematically. Some cracks that initiated in the PU have propagated into the PVC. Cracks never propagate along the interface, but always in the PVC, which testifies for a good adhesion between the two layers. This legitimates for this particular system the hypothesis of ideal adhesion done in the numerical model.

Another tomography measurement was done on the whole residual scratch, in order to distinguish the different steps and analyse separately the different rupture modes. The results are in appendix B.

First, this tomography shows that the first mechanism only concerns the coating, it doesn't propagate in the substrate. Then, the second mechanism concerns the coating and the substrate. Indeed, this mechanism is visible until a depth of ≈ 0.35R. Finally, the last mechanism concerns the coating and the substrate, as it is observed until a depth of ≈ 0.4R.

Furthemore, the visualisations in the planes (xy) and (yz) well show that the 3 mechanisms superimpose to each other with increasing force, without disrupting each other.

Influence of the fillers on the mechanical response

A scratch test was perfomed on the PVC covered by 0.2R of PU without filler in order to observe the influence of the roughness on friction, and the influence of the fillers on crack initiations. This coating has a roughness Sa = 96 nm. The scratch test has been performed under exactly the same conditions as the one presented figure 2.c. This experiment has been done two times, the repeatability is fair and a representative photograph of a residual scratch is shown figure 6. The three same mechanisms appear with filled and unfilled coating. There is in the supplementary material of this article an animated figure showing in situ videos of the apparition of each mechanism. However, we note two main differences in the two tests :

1) The local friction is different : µ = 0.35 with filled PU and µ = 0.7 with unfilled PU (The local friction is measured in the beginning of the test, for Fn = 0.2N.

2) The occurrence of the 3 mechanisms is less regular. With filled PU, the mechanisms 1 and 2 appear regularly and periodically. With unfilled PU, the mechanisms appear irregularly, there is a general periodicity but some occurrences are missing. On figure 6, it is very clear for the mechanism 1. An explanation is proposed paragraph 4.7.

Numerical simulations results

Validation of the model

A numerical simulation of each scratch (on uncoated and coated PVC) has been carried out with a normal load of 0.5N, which corresponds to the second part of figure 2 (ductile deformation for uncoated and coated material). The first objective is to compare the numerical results to the experimental ones, in order to validate the model. Figure 7 shows the comparison of the modeled and the experimental contact areas between the tip and the material, on uncoated and coated PVC.

-Uncoated PVC: ac/R = 0.82 in the experiment and ac = 0.65 in the model. The order of magnitude are consistent, even if the PVC is a little bit more rigid in the model. Moreover, there is a large ductile groove behind the tip. This large groove is also present in the numerical model. -Coated PVC: ac/R = 0.49 in the model and ac = 0.4 in the experiment. Again, the order of magnitude are consistent, even if the material is a little bit more rigid in the model. Moreover, the ductile groove on the coated material is much smaller than on the uncoated one, for both numerical model and experiment.

Comparison between coated and uncoated material

From the same two computations than the ones presented in part 3.2.1, we are interested in the contact geometry between the tip and the material, in the plane (yz), during the contact and after elastic unloading. The results are shown figure 8 as cross sections of the grooves. -Uncoated PVC: The penetration depth is 0.22R. During the contact, the material fits the shape of the tip. Moreover, there is a pile up (lateral bulge) on the side of the contact with a well-defined ridge at the edge of the contact with the tip. Therefore the attack angle of the tip on the PVC is high and the contact radius between the tip and the material is high (ac/R = 0.65). The residual depth is 0.14R, meaning an elastic unload in the bottom of the groove of 36%

-Coated PVC: The penetration depth is 0.2R. During the contact, there is a large sink-in effect of the material under the load. Therefore, the attack angle is less than on uncoated PVC, and contact radius is lower (ac/R = 0.4). The residual depth is 0.09R, meaning an elastic unload in the bottom of the groove of 55% i.e. much more than for uncoated PVC.

From these two simulations, the plastic dissipation power is computed as a function of the displacement of the tip. It corresponds to the total power spent to deform the material plastically, as illustrated by eq.4. The curves are plotted figure 9.

σ V . ε (4)
With V the volume of the domain, σ the equivalent stress and ε the equivalent plastic strain rate.

In the stationary regime, the uncoated PVC dissipates 0.2 mW plastically while the coated PVC dissipates 0.05 mW. In other words, uncoated PVC plastifies much more than coated PVC during a scratch test, for a same normal load applied on the tip.

Analysis of the three rupture mechanisms

Two numerical simulations have been carried out:

1) The first simulation is done with a vertical tip displacement of d = 0.4 R (i.e. twice the thickness of the coating). This vertical displacement leads to a normal force of Fn = 1.14N. This corresponds to part 4 of figure 2. 2) The second simulation is done with a tip vertical displacement of d = 0.5 R (2.5 x coating thickness). This vertical displacement leads to a normal force of Fn = 1.7N. This corresponds to part 5 of figure 2.

The results of the two computations are presented in figure 10. The color code gives the intensity of the first (highest, most tensile) principal stress, whereas grey arrows indicate the corresponding principal direction.

d = 0.4 R: There are two different locations of stress concentration. The first one is at the top surface of the coating, at the rear side of the contact edge. The principal axis is oriented at ≈ 45° to the scratch direction.

The second stress concentration is under the tip, in the symmetry plane y = 0, at the coating/substrate interface. This stress is oriented along the axe (Oy). d = 0.5 R shows three stress concentration:

The previous two are still present, but their values have significantly increased. The main difference is the formation of a frontal bulge. Because of this bulge, the coating is solicited in bending in front of the tip so there is a large tensile stress on the top of the bulge (external surface of the coating), forming a circle ahead of the front of the contact. This stress is oriented in the radial direction with respect to the tip centre, i.e. for example the Ox direction on the (xz) symmetry plane. In the three zones, the 1 st principal stress is an increasing function of the normal load applied on the tip. For Fn =0.8N (the normal load at which the 1 st mechanism appears experimentally), σI = 0.6 EPVC behind the tip. For Fn =1.1N (the normal load at which the 2 nd mechanism appears), σI = 1 EPVC under the tip at the interface. For Fn = 1.7N (the normal load at which the 3 rd mechanism appears) σI = 1 EPVC in front of the tip. This gives us a first approach of the coating toughness in terms of critical stresses.

Discussions

Influence of the coating the geometry of the contact and on plastic strain

When the thickness of the coating is negligible in front of the size of the scratching asperity, the coating only modifies friction and/or envelops elastically the roughness of the asperity to avoid creating micro grooves inside the macro groove (2).

On the other hand, if the thickness is very large compared with the scratching asperity size and its penetration depth, the coating behaves like a bulk and the scratch behavior is governed by the mechanical properties of the harder coating rather than those of the softer substrate.

In the case studied in this article, the size and the penetration depth of the tip is of the same order of magnitude as the coating thickness: these two interpretations of how a coating may improve scratch resistance become insufficient.

The numerical simulations of figure 8 show that in this case, for a given normal force imposed to the tip, the coating does not have a big influence on the penetration depth (the difference between the uncoated and the coated material is 0.02R). However, the elastic unloading and the plastic power dissipation are completely different: the uncoated material undergoes much more plasticity than the coated one. This difference does not result from a smaller penetration depth but from the geometry of the contact. As shown figure 8, in the contact, due to the occurrence of pile-up in the uncoated case versus sink-in in the coated one, the slope of the furrow in the coated material is much lower.

It is admitted in the literature that the equivalent strain of a material during a scratch test can be computed for spherical tips as a function of the contact and tip radii (5) (28):

ε eq = 0.2 a c R (5)
In our case, a c,uncoated R = 0.65 and a c,coated R = 0.4, so ε eq,uncoated = 0.13 and ε eq,coated = 0.08, which explains the lower plasticity in the coated material (ε yield,PVC = 0.05), even if the penetration depth is almost the same in the two cases.

Qualitatively, the way a hard coating increases the scratch resistance of a soft substrate, when d ~ tcoating, can be explained by the modification of the contact geometry. By increasing the global elastic deflection of the material, the coating blunts the geometry of the scratching asperity, reducing the attack angle thus the equivalent deformation of the substrate.

To achieve this objective, the coating needs to be harder than the substrate, which generally implies a more brittle behavior. PVC is ductile on a large deformation range and even at high deformation, no cracks are observed during a scratch test. The PU coating decreases the plastification of PVC, leaving shallower grooves at low load, but its brittle behavior leads to cracks at higher loads.

Cracks at 45°, behind the tip (fracture mechanism 1)

Cracks at 45° are initiated on the rear edge of the tip as shown by the in situ vision, at a distance from the symmetry plane ; starting from the side of the contact, they propagate outward. However, in-situ optical observation cannot tell where, in the depth, these cracks are initiated. The numerical simulations show a localization of tension on the rear face of the tip, away from the symmetry plane, precisely at the location where these cracks are initiated experimentally. Moreover, at this place, the 1 st principal stress is oriented at ~ 45° (perpendicular to the crack propagation direction), which explains this fracture mode. This concentration of stress is localized on the top surface of the material, meaning that the crack is initiated on the extreme surface and then propagates along the direction -z down to the interface, together with the x+y direction.

Tearing under the tip (fracture mechanism 2)

Under the tip, the flexible and ductile PVC easily deforms. The PU that adheres on it follows its deformation and is therefore solicited in bending. Because of this bending, tensile stress appears in the PU at the interface PVC/PU. The elastic-brittle PU cracks under this tensile stress. The numerical simulation shows a stress concentration in the PU under the tip near the interface. The first principal direction is (Oy) which explains the initiation of the longitudinal tearing with a recognizable crack tip in the contact area (part 4 of figure 3). Unlike the cracks at 45° that are initiated at the surface and propagate downward (in the -z direction), this tearing is initiated at the interface and propagates upward through the PU (+z direction). It also propagates in the -z direction from the interface into PVC. Indeed two scenarios may occur: either the crack propagates at the interface PU/PVC, leading to delamination of the coating, or into the bulk PVC. The tomography shows that there is no delamination and a blunt crack propagates in the PVC instead of the interface (figure 5b), then stops at a certain depth. This observation confirms the strong adhesion between the two layers. Subsequently, the tangential displacement of the tip in the direction +x imposes that the crack spreads in the same direction. Then the crack deviates from the central axis, because of local defects (PU thickness variation, local friction coefficient variation …) that create an asymmetry in the stress field.

4.4 Cracks in front of the tip (fracture mechanism 3)

At higher deformation level, in situ observations show that the cracks at 45° and the tearing mechanism under the tip still occur. Moreover, there is a circular crack forming in front of the tip, the principal direction is radial (Ox on the symmetry plane). This crack is symmetrical with respect to the vertical plane containing the movement of the center of the tip. Again, the in situ observation does not show why, and where in the depth the crack is initiated. The answer is given by the numerical simulation which shows the formation of a frontal bulge (figure 10). On the top of this bulge, the coating is solicited in bending which leads to tensile stresses oriented in the (Ox) direction. These tensile stresses are responsible for the rupture of the coating in front of the tip. Moreover, this numerical simulation shows that the crack is initiated at the coating upper surface and propagates in the -z direction.

Since the rupture and the stress relaxation that follows is not taken into account, the numerical modelling developed does not allow ascertaining a scenario for the succession of cracking events, but a probable scenario can be proposed. After the formation of the frontal bulge, the tip climbs over this "wrinkling" and slides past it, resuming contact with uncracked coating, and the mechanism starts again after a motion of ca. two contact lengths (the length necessary to rearm the stress field). Then the three fracture mechanisms can be reset.

Again, the three mechanisms are triggered independently of each other, and it can be assumed that the stress relaxations linked to each one do not reduce the stress values far enough to prevent the apparition of the other mechanisms. This explains the coexistence of these three mechanisms.

Evaluation of a critical rupture stress of the PU

From figure 11, the stress in the PU coating that initiates each fracture mechanism may be evaluated. The second mechanism is initiated, experimentally, for a normal force of Fn = 1.1N which corresponds, in the simulation, to a stress of 1EPVC under the tip, at the interface. The third mechanism is initiated, experimentally, for a normal force of Fn = 1.7N which corresponds, in the simulation, to a stress of 1EPVC in front of the tip. So the mechanisms 2 and 3 (mode I) are triggered for the same value of stress σ , ≈ 1. E .

The first mechanism is initiated, experimentally, for a normal force of Fn = 0.8N, which corresponds, in the simulation, to a stress of 0.6.EPVC behind the tip, away from the symmetry plane. This stress is lower than the stress that triggers the 2 nd and the 3 rd mechanism. Two explanations can be proposed:

-either the first mechanism is not a mode I opening, meaning that the first principal stress is not the relevant criterion. It could be a mode II opening caused by shear stresses for exemple.

-or the value of the friction coefficient used in the numerical model is underestimated. Indeed, if the 1 st mechanism is effectively a mode I opening, the stress under the tip is an increasing function of the friction coefficient (the higher the friction coefficient, the higher the tensile forces behind the tip, the higher the stress).

Applicability of the results for different values of R

In this article, all the experiments and simulations were done with a R = 100µm tip. Are these results still valid if we change the radius of the tip ?

On uncoated materials, the average deformation is independent on the scale but only depends on the ratio ac/R (as long as all characteristic dimensions of the polymeric macromolecular structure are negligible in front of R). Therefore, the deformation regime (elastic, elastoplastic, ductile…) is independent of the scale.

On coated materials however, it is not the case. Indeed, the deformation regime depends on the ratio between R and the thickness of the coating tcoating, as explained in section 4.1: there is a structure effect. The deformation regime may be independent on R, as long as the ratio tcoating/R is constant (0.2 in our case).

It is more difficult to conclude on fracture: cracks are initiated from defects in the material (air bubbles, bad adhesion between the particles and the matrix…), and these defects have a given density and a given size δ, independent of tcoating. Therefore, the ac/R ratio at which the cracks are initiated probably depends on δ /R, so the cracks profile might be different depending on the scale, even for a same tcoating/R ratio.

Influence of the fillers on the rupture initiation

The local friction is very different for the test performed on filled coating (µ = 0.35) and on unfilled coating (µ = 0.7), probably because the smooth unfilled PU surface results in a large adhesive friction term, contrary to the rough filled PU surface where the indenter mostly contacts mineral filler particles. Moreover, it is well known in the litterature that the mechanical response of a material during a scratch test is very sensitive to friction [START_REF] Lafaye | A surface flow model of scratching tip: apparent and true local friction coefficients[END_REF]. Therefore, it is not surprising to observe some differences in the mechanical behavior with filled and unfilled coating since the friction is very different.

The three same mechanisms appear with filled and unfilled coating, which have very different local friction. Therefore, it can safely be said that these three mechanisms are the consequence of the structure of the material (rigid-brittle coating on soft elastoplastic substrate). So, the difference between the uncoated PVC and the coated one during the scratch tests comes from the structure difference, not from the difference in roughness and friction.

But the most interesting phenomenon is the difference of periodicity in the initiation of the ruptures in the two experiments (periodic for the filled coating, periodic with the same period but with missing occurrences for the unfilled one). Our interpretation is the following :

The periodicity comes from the stationary regime of the deformation. The tip deforms the material until it achieves a critical deformation which initiates a crack. The consequence of this crack is a stress relaxation which has an influence on a given length. Then, the tip keeps moving on and once it has crossed this certain distance, the material can reload and this mechanism starts again.

However, as mentioned section 4.6, a crack needs a defects to be initiated. With fillers in the coating, the volumic density of defect is high (each particle). Therefore, as soon as the stress is high enough to initiate a rupture, it is initiated directly from a particle because there is necessarily a sufficiently close one. Then, the material reloads and a new crack appears as soon as the critical stress is achieved, for the same reason : the apparition of cracks is periodic.

With unfilled coating, this reasoning does not work : as there are no fillers, the volumic density of defects is much lower. Therefore, when the critical stress is achieved, there is not necessarily a defect close enough to initiate a crack. : the apparition of cracks loses its periodicity.

Conclusion

In this paper, the mechanical behavior during a scratch test of soft polymer substrate coated by a harder, more brittle polymer is studied under loads such that the scratch depth is of the order of the coating thickness.

At low loads, the coating increases the scratch resistance by decreasing the plastic deformation of the substrate. However, in connection with its hardness, the coating is more brittle than the substrate and fractures at higher loads. Observations and simulations show three successive rupture mechanisms at growing load and penetration : cracks at 45° behind the tip, tearing under the tip and circular cracks in front of the tip on top of the frontal bulge. These 3 rupture mechanisms superimpose to each other rather than replacing each one, which is particularly interesting.

In situ vision shows where are initiated and how the different cracks propagate in the surface plane. Tomography, which is a real novelty in the analysis of a scratch test, gives information about the depth at which the cracks is finally present. Finally, FEM explains the mechanical conditions leading to each rupture mechanism, especially the depth at which they are initiated.

In summary, the three tools used (in situ vision + X-Ray tomography + numerical simulation) are very complementary and allow a good understanding of a complex coating damage mode involving three competing damage mechanisms observed on this bimaterial. Indeed, the successive apparition of three rupture mechanisms which don't influence each other is a particularily interesting phenomenon whose analysis would have not been possible without the combination of these three tools.

  The characterization of the scratched samples has been performed by a X-Ray Solution tomograph, model Easytom 150-160 (RX solution SAS, Chavanod, France). The X-Ray generator is an open tube Hamatsu Microfocus with a tungsten filament and a tungsten target. The detector is a matrix plane sensor ("Flat Panel") Varian PaxScan 2520DX 1920x1536 pixels ( pixel size = 127 µm x 127 µm ) -16 bits. The scan is done with the following parameters: Resolution = 1.2 µm, Source -sample distance = 3.29 mm, source -sensor = 347 mm, X-Ray energy = 80 kV, beam intensity = 65 µA. 1984 projections are done over 360°. Averaging = 15 images per position. The sensor has a cadence of 2 images per second. The whole scan lasts 4.5 hours. The reconstruction method used is the filtered back projection.

Figure 1 :

 1 Figure 1: Numerical model of the scratch test

Figure 2 :

 2 Figure 2: Photographs of the residual scratches. Scratch done on uncoated PVC (a). Scratch done on coated PVC, observed in reflection (b). The same scratch on coated PVC, observed in transmission (c). The reflection lightening allows a good visualization of the local slopes (lateral and frontal bulges are clearly visible, lighter grey) and the transmission lightening allows a better visualization of cracks. The combination of both allows a good visualization of the 5 types of behavior respectively: 1) elastic sliding, 2) elastic plastic scratching, 3) 1st fracture mechanism, 4) 1st and 2nd fracture mechanisms, 5) 3 kinds of fracture mechanism simultaneous.

Figure 3 :

 3 Figure 3: In situ photographs and schematic representation of the damage regimes. Photograph numbering corresponds with the text. An animated version of this figure is in the supplementary material of this article, allowing a better visualisation of the different mechanisms.

Figure 4 :

 4 Figure 4: Depth of the residual grooves: on uncoated PVC (a), on coated PVC (b). Comparaison of the profiles of the bottom of the groove in the (xz) vertical-longitudinal plane, uncoated and coated PVC (c)

Figure 5 :

 5 Figure 5: Tomography of the scratch of figure 2 (part 5). 3D Representation (a), 3 cross sections in (yz) planes for different x positions (b), 3 cross sections in (xz) planes for different x positions (c). The lines i) to vi) show the locations of the cross sections.

Figure 6 :

 6 Figure 6 : Photograph of the residual scratch done on PVC coated with unfilled PU

Figure 6 :Figure 7 :

 67 Figure 6: Comparison of the contact radius between the experiment and the numerical model for a normal load of 0.5N on uncoated PVC (above) and on coated PVC (in the middle). The graph (below) summarizes the four values of ac

Figure 8 :

 8 Figure 8: Plastic dissipation power in function of the tip displacement, for uncoated and coated PVC. Peaks are numerical artefacts corresponding to mechanical field transport after remeshing.

  Other simulations have been carried out for different vertical displacement of the tip, from d = 0.1 R to 0.6 R leading to normal forces from Fn = 0.2N to 2.1N. For each simulation The first principal stress values have been recorded at the three areas where stress concentrations are observed in figure 10: behind the tip out of the symmetry plane, under the tip at the interface, in front of the tip at the surface. The results are plotted figure 11.

Figure 9 :

 9 Figure 9: Numerical results: 1st principal stress normalized by the Young's modulus of the substrate. Computations done for a tip vertical displacement of d = 0.4 R (left) and d = 0.5 R (right). The grey arrows show the principal direction of the stress tensor corresponding to σI at the interesting areas.

Figure 10 :

 10 Figure 10: 1 st principal stress normalized by the Young's modulus of the substrate in function of the normal load applied to the tip, in the three areas of interest (tensile stress concentrations) . The appearance of fracture mechanisms 1, 2 and 3 is positioned according to experiments.

  The velocity is constant at 30 µm/s. The tests are done in 10 increasing normal force steps, from 0.2 N to 3 N.

	All the tests have been doubled to check repeatability. The latter has been found very good in all cases.
	Nomenclature
	PVC	Polyvinyl chloride
	PU	Polyurethane
	E	Young's modulus
	ν	Poisson's coefficient
	σy	Yield stress
	m	Strain hardenning coefficient
	T	Temperature
	µ	Coulomb's friction coefficient
	R	Radius of the tip
	ac	Contact radius
	d	Indentation depth
	εeq	Equivalent deformation
	Ppl	Plastic dissipation power
	σ eq	Equivalent stress
	ε̅ pl	Equivalente plastic strain rate
	tcoating	Coating thickness
	Sa	Roughness arithmetical mean height

Table 1 : Mechanical properties of the materials. The Young's modulus and the yield stress are normalized by the Young's modulus of the PVC. The PU has no yield stress because it has an elastic-brittle behavior. Poisson's coefficients have not been measured but taken from literature.

 1


D Cuesta

J Baudot

G Claus

M Goffe

K Jaaskelainen

L Santelj

M Specht

M Szelezniak

I Ripp-Baudot

Operation of a double-sided CMOS pixelated detector at a high intensity e + e -particle collider

Keywords: silicon pixel detector, CMOS sensor, vertex detector, charged 7 particle tracking 8

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

Introduction

Tracking detectors in high energy particle physics experiments at collid-10 ers must sustain very high detector occupancy, e.g. produced by pile-up or 11 beam-induced background particles. In the meantime, accurate particle track- The PLUME detector (Pixelated Ladder with Ultra-low Material Embed-16 ding) [START_REF] Nomerotski | PLUME collaboration: Ultra-light ladders for linear collider vertex detector[END_REF] is an ultra-light, double-sided ladder equipped with CMOS pixel sen-17 sors on both sides. This concept was developed originally in the perspective 18 *

Corresponding author

Email address: isabelle.ripp@iphc.cnrs.fr (I. Ripp-Baudot) 1 Present address: J. Stefan Institute, 1000 Ljubljana, Slovenia of a future ILD vertex detector [START_REF] Abramowicz | The ILD detector at the ILC[END_REF][START_REF] Winter | Present Status and New Perspectives of an ILC Vertex Detector[END_REF] within the collaboration of three institutes (DESY-Hamburg, IPHC-Strasbourg and the University of Bristol). It has already been characterized with various test beams, using pions at CERN and electrons at DESY [START_REF] Boitrelle | Development of a double-sided ladder for tracking in highenergy physics[END_REF][START_REF] Maria | Study of the time-dependent CP asymmetry in D 0 decays in the Belle II experiment[END_REF]. We report in this paper the first operation of a PLUME detector in the interaction region of a particle collider.

Based on the PLUME concept, we developed and installed temporarily into the Belle II detector [START_REF] Abe | [END_REF] a dedicated system, henceforth abbreviated as PLUME, with the ability to map hit rates in specific areas, while adding minimal material. As part of a wider ensemble of radiation monitors, that constituted the setup replacing the vertex detector during the Phase 2 run of the e + e -Su-perKEKB collider, PLUME contributed to monitoring the background induced by SuperKEKB in the inner tracker volume.

The first run of SuperKEKB is called Phase 1 and took place in 2016. Each beam was circulated individually, no collisions were performed, and single beam backgrounds were studied by a dedicated setup called BEAST II Phase 1 [START_REF] Lewis | First Measurements of Beam Backgrounds at SuperKEKB[END_REF], installed in the interaction region in place of the Belle II detector. First collisions were delivered during the second run of SuperKEKB, a.k.a. Phase 2 run, that occurred from March to July 2018. For the Phase 2 run, the Belle II detector was placed at the collision point and commissioned, and the final focus magnet was in place. However only one sector in the φ acceptance of the Belle II vertex detector was installed, the rest of the inner tracker volume being equipped with dedicated BEAST II Phase 2 detectors [START_REF] Schwenker | Operational experience and commissioning of the Belle II vertex detector[END_REF]. The main goal of the BEAST II effort was to study and minimise the parasitic particle rate produced by the collider during the machine parameter tuning, to validate the simulation of this background and to check whether it was safe to install the full inner tracker in Belle II. This paper details the design, integration, operation experience and data analysis procedure of the PLUME system in BEAST II during the Phase 2 run.

Results on the background induced by SuperKEKB beams are not the goal of this report and will be presented in a dedicated paper in preparation in the Belle II machine background group.

Sections are organised as follows. The PLUME device and its acquisition system are described in section 2. Data taking and detector stability during operations are discussed in section 3. Section 4 reviews the data analysis to extract hit rates and information related to double-sided measurement, before concluding in section 5.

System description

Detector design and geometry

The PLUME detector in the Phase 2 setup of BEAST II consists of two double-sided modules shaped as ladders, each one equipped with 12 MIMOSA-26 sensors [START_REF] Hu-Guo | First reticule size MAPS with digital output and integrated zero suppression for the EUDET-JRA1 beam telescope[END_REF]. One ladder is installed parallel to the beam axis, at a radius R = 5 cm and an azimuthal angle φ = 225 • in the transverse plane around the beam pipe. The second ladder, located at φ = 135 • , is inclined with a polar angle θ = 18 • with respect to the beam axis, and provides radial coverage from R = 5 cm to R = 9 cm, in order to scan the rate of background particles at roughly the same radii as the silicon strip vertex detector of Belle II before its installation for the Phase 3 run in 2019. The PLUME layout in the Phase 2 setup of the BEAST II inner tracker volume is shown in figures 1 and 2. In the following, the so-called outer or inner sides of a ladder means the ladder side facing respectively the Belle II outer part of the detector or the beam.

Both ladders are self-stiffened thanks to the sandwich-effect of silicon sensors glued on a low-mass kapton-copper flexible PCB assembled on both sides of a low density SiC foam of thickness 2 mm (see figures 3 and4). Each ladder is very light with a total weight of about 7 g, resulting in a material budget of 0.42 % of the radiation length X 0 . It is supported mechanically on one extremity in a cantilever way, with halogen-free support structures made of polyetheretherketone (PEEK) and aluminum, screwed to the Belle II inner tracker support structure.

Passive radiochromic films [START_REF] Campajola | Absolute dose calibration of EBT3 Gafchromic films[END_REF] are glued on both sides of the ladder aluminium supports, to estimate the total radiation dose that impacted PLUME during the full Phase 2 run. Both sides of the ladders are cooled down by blowing nitrogen

MIMOSA-26 CMOS sensors

MIMOSA-26 sensors [START_REF] Hu-Guo | First reticule size MAPS with digital output and integrated zero suppression for the EUDET-JRA1 beam telescope[END_REF] have been designed in on the AMS 0.35 µm OPTO process. They are thinned down to a thickness of 50 µm. They feature a sensitive surface of 1×2 cm 2 , segmented in 576×1,152 square monolithic active pixels of dimension 18.4×18.4 µm 2 . The pixel matrix is read out in a columnparallel rolling shutter mode. Analog signal of each pixel is converted to a binary digital output at the end of each of the 1152 columns of the pixel matrix, and passes through a 0-suppression stage with a discrimination threshold set as a multiple of the average measured pixel noise σ. This 0-suppression mechanism [START_REF] Himmi | A Zero Suppression Micro-Circuit for Binary Readout CMOS Monolithic Sensors[END_REF] reduces by a factor 10 to 100 (depending on the occupancy level) the data flow produced by the 8×10 6 pixels of each ladder, while maintaining a detection efficiency above 99.5 % and a pixel fake rate of about or below ×10 -6 per readout frame (for a discrimination threshold set to 8σ and as long as the sensor temperature remains below 70 • C) [START_REF] Baudot | JRA-1 Milestone: Validation of the Final Sensor Equipping the EUDET Beam Telescope[END_REF]. Each pixel line is read out successively in about 200 ns, resulting in a total read-out time, also the pixel integration time, of 115.2 µs for the full sensor matrix consisting of 576 pixel lines. This corresponds to a readout frequency of 8680 frames/s, and a capability to read out at least 10 6 hits/cm 2 /s (depending on the hit spatial distribution).

Data acquisition system

Beam background generated by SuperKEKB during Phase 2 was detected by BEAST II detectors and registered by each detector's standalone DAQ (data acquisition) system, independently of the Belle II global DAQ system including all Belle II detectors [START_REF] Yamada | Data Acquisition System for the Belle II Experiment[END_REF]. A synchronisation clock was provided by SuperKEKB and included in PLUME data. The PLUME detector during Phase 2 provided two kinds of outputs:

-EPICS output [START_REF]Web page of EPICS, The Experimental Physics and Industrial Control System[END_REF] used to monitor on-line the beam-induced background and This standalone DAQ system is based on the one commonly used to read out the EUDET beam telescope [START_REF]Web page of EUDET-type beam telescopes[END_REF][START_REF] Jansen | Performance of the EUDET-type beam telescopes[END_REF] equipped with MIMOSA-26 sensors, adapted here to particular integration constraints and also to read out 4 times more sensors. In particular, two acquisition paths were designed, each one handling one ladder, see figure 5. This design was developed to accommodate orthogonal constraints of electronic noise and radiation levels. The first DAQ path, referred to as AUX1-2 in figure 5, has active components in a possible high radiation environment but allows to limit the electronic noise because the signal is buffered close to the detector, at 2.5 m from it. The second acquisition path is used for the second ladder and referred to as AUX1-AUX2 in figure 5. In that case only radiation-tolerant power supply and slow control boards (AUX2) are placed 2.5 m away from the detector. The signal is buffered with AUX1 board, 13.5 m away from the PLUME detector on top of the Belle II detector, in an environment less exposed to radiations. To reduce electronic noise and dispersion of the propagation delay arising along the long transfer path (46 m between the detector and the electronic-hut), the 48 signal data are transmitted over differential LVDS pairs. Signal is buffered and re-amplified every 11 m (constrained by the cable length) and deskewed at the DAQ system level. In the end, the full system, including slow control of the detector, monitoring of the sensor temperature and power dissipation, fuse-box and protection against latch-up, consists of 13 custom-designed boards and is summarised in figure 5. was decreased from 8 to 3 mm (corresponding to a vertical beam size σ y of about 300 nm) and beam currents were increased up to nearly 800 mA in both LER and HER, to increase the instantaneous luminosity up to 0.54×10 34 cm -2 s -1 [START_REF] Funakoshi | Operation of SuperKEKB in Phase 2[END_REF]. A number of runs were also operated under stable beam conditions to accumulate statistics for physics analysis.

Data taking and detector stability

2 βy is the ratio between the variance of the vertical dimension of the beam, and the beam emittance. This quantity depends on the location along the beam trajectory, and β * y refers to its value at the interaction point. Besides these very few intentional down-times, few spontaneous switch-offs were triggered by the security system of PLUME against single event latch-up. Such over-current events occurred only a few times over 4 months of continuous running, at the level of the digital voltage, and were mainly generated during high beam injection noise as discussed in section 4.1.

As explained in section 2, PLUME was operated permanently as a continuous hit rate monitor sending hit rates on-line without saving the raw data, and sometimes also with full raw data storage for offline analysis allowing detailed studies of background rates as a function of beam parameters, as illustrated with figure 6. The analysis technique to extract hit rates is described in section 4.

Radiation tolerance

The SuperKEKB Phase 2 run was an important commissioning period that required tuning of multiple accelerator parameters and was exposing the detector systems to possible direct beam losses. A wide range of hit rates was expected in the detectors and no robust estimates of the expected total ionising dose and of the fluence of particles inducing non-ionising energy loss (NIEL) were available beforehand.

The pixel fake rate of individual PLUME sensors was carefully monitored over the entire Phase 2 period in order to detect potential performance degradation induced by radiations. Radiations may indeed impact CMOS sensors in two ways. On the one hand, NIEL may damage the silicon crystalline structure, creating charge traps which decrease the signal amplitude, and increasing the leakage current. On the other hand, cumulative ionising dose may lead to the accumulation of electric charges in oxide layers of CMOS circuits while they are powered up [START_REF] Deveaux | Radiation Tolerance of CMOS Monolithic Active Pixel Sensors with Self-Biased Pixels[END_REF][START_REF] Garcia-Sciveres | A review of advances in pixel detectors for experiments with high rate and radiation[END_REF], generating additional temporal noise. Both effects may increase the pixel fake rate of sensors like MIMOSA-26, that apply a signal threshold to discriminate between pixels registering an ionising particle crossing and those registering only electronic noise.

Radiation tolerance of MIMOSA-26 sensors equipping PLUME has been formerly studied with a 120 GeV π beam at the CERN-SPS after exposing these circuits to 10 keV X-rays and/or to neutrons produced by a nuclear reactor [START_REF] Deveaux | Radiation Tolerance of CMOS Monolithic Active Pixel Sensors with Self-Biased Pixels[END_REF][START_REF] Voutsinas | Studies for a 10 µs, thin, high resolution CMOS pixel sensor for future vertex detectors[END_REF]. Stable performances have been observed up to 1.5 kGy of total ionising dose combined with a fluence of 3 × 10 12 1 MeV neutron equivalent /cm 2 . However, after a total ionising dose of 3 kGy, the pixel fake rate significantly increased by a factor ×3 to ×5, depending on the discriminating threshold applied on sensors.

During Phase 2 operations, the non-ionising particle fluence was not expected to be an issue. Ionising radiation damage, on the other hand, could degrade the detector performance (depending on the level), but if not beyond the acceptable limits its effects can be mitigated either by increasing the discriminating threshold, or by masking the pixel using a programmable mask built into the sensor, or by masking the pixel off-line.

The average pixel fake rate over all PLUME sensors during the full Phase 2 run was measured to be 6×10 -8 per pixel and per read-out frame with a discriminating threshold of 10σ. It decreased to 5×10 -10 by masking off-line 0.06 % of the pixels, and to 2.5×10 -10 by masking 0.1 % of them. PLUME data without beam were registered at regular intervals to monitor the pixel fake rate. No significant impact was observed, as shown in figure 7, and the total integrated dose was estimated to be 200 Gy at maximum according to reference studies reported above in this section. This conclusion was cross-checked by radiochromic film measurements (see section 2), which reported observed radiation levels in the vicinity of PLUME ladders, decreasing with increasing radius from about less than 1 kGy to a few 100 Gy. These doses cannot be simply extrapolated to estimate what is expected after 50 ab -1 of Belle II data taking. The beam parameters will be further tuned, additional collimators will be added and the vacuum will be improved. These measures will mitigate the single beam induced background, while the luminosity-dependent beam-beam background will become dominant with increased instantaneous luminosity. At nominal instantaneous luminosity, a total ionising dose between 1 to 5 kGy/year is expected at the location of the PLUME detector.

Extracting detector hit rates

Event selection

As already mentioned, SuperKEKB beam parameters were optimized during the Phase 2 run, resulting in a wide variation of the hit rate observed in PLUME. Nevertheless, outside the beam injection periods, the detector occupancy remained below the MIMOSA-26 sensor limits. However when new bunches were injected in the beam, their initial non-optimal orbit led to a background rate increase by at least one order of magnitude. In such a situation, saturation was observed in the sensor due to the limited size of the embedded memory as explained in [START_REF] Hu-Guo | First reticule size MAPS with digital output and integrated zero suppression for the EUDET-JRA1 beam telescope[END_REF]. Figure 8 illustrates a real MIMOSA-26 frame with a saturated event. In this figure a pattern with many adjacent impacts along columns and rows can be seen in the lower left part of the sensor, while the rest of the sensor is empty. In comparison to such a saturated frame, usual frames feature only a number of isolated impacts.

The hit rate cannot be estimated robustly in case of a saturated frame.

Such frames can nevertheless be easily removed from further analysis, based on a simple cut considering the number of fired pixels within the frame. This cut does not impact the measured hit rate since the injection frequency during Phase 2 was generally negligible with respect to the 1 Hz hit rate update, corresponding to about 10 4 MIMOSA-26 frames. Additionally, this cut was not used for the specific study of the background conditions generated by newly injected bunches. From previous beam tests with 120 GeV π beam, the average cluster size for perpendicular crossing particles was observed to be 2 pixels with a standard deviation of 1 pixel, operating the sensor with a threshold of 10σ. The corresponding measured spatial resolution was measured to be 3.6 ± 0.1 µm [START_REF] Winter | Development of CMOS Pixel Sensors fully adapted to the ILD Vertex Detector Requirements[END_REF]. Of course, particles with much lower energies and a wide range of incoming angles were expected from beam induced background. The observed distribution of the number of pixels per cluster is displayed in figure 9, where the last bin contains all entries larger than 20. Though 2-pixel clusters dominate the distribution, the long tail indicates the presence of large incidence angles. The non-negligible amount of single-pixel clusters reflects the presence of both particles depositing a small ionizing charge in the sensor or generating ionization close to the collecting diode, and fake hits. The position of each hit is computed from a simple average of the positions of all pixels associated to the hit. This position can potentially be used to detect background hot spots but usually a simple, sensor-based segmentation map was used, like depicted in figure 10.

Double-sided measurement

The double-sided pixelated PLUME ladder provides two very close measured positions per crossing charged particle. As a first benefit, this feature brings redundancy in hit rate measurements between the two sides of the same ladder.

In addition, the two positions along each particle trajectory can be exploited for a helix fit to the track, assuming one additional constraint. This strategy can be applied for particles originating from the beam interaction point, which position is the needed third point. This is the case for background generated by beam-beam electromagnetic interactions, in contrast to background particles stemming from single beam effects that usually produce showers in surrounding material, which secondaries are detected by PLUME ladders.

We first tried the method with simulated beam-beam induced background. Unfortunately we could not apply this method on Phase 2 data because the luminosity was below the method sensitivity to beam-beam induced background. Such an analysis intended to discriminate background particles originating from beam-beam induced background, scaling with luminosity, against single-beam effects, using for instance the χ 2 yielded by the track fit. This strategy however holds when hits from both PLUME sides can be associated with good efficiency and purity, which occurs for low hit rates resulting in low random hit probability.

However during the Phase 2 runs at the highest instantaneous luminosities, corresponding to the highest expected beam-beam background contributions, hit rates induced by single-beam background particles exceeded 50×10 3 hits/cm 2 /s and were still 1,000 times higher than hit rates produced by beam-beam background particles. Such rates led to an overwhelming combinatorial hit association and did not allow for proper use of the momentum fit ability offered by PLUME.

Conclusion

We reported the first use of a detection system based on CMOS pixel sensors in the interaction region of an e + e -collider, and also the first operation of double-sided pixelated detectors in a collider environment. Two double-sided PLUME ladders, previously developed for a future linear collider to feature the very low material budget of 0.4 % X 0 , were inserted temporarily in the inner volume of the Belle II experiment. The read-out system was designed to match potential adverse radiation conditions and long data cable paths. Observed fake rates were equivalent to levels measured during beam tests under controlled conditions. No signs of radiation damaged were observed after the successful running period. Both detecting ladders operated smoothly during the Phase 2 run of SuperKEKB and allowed monitoring online the rate of background particles generated by the beams. Though simulation studies demonstrated the possibility to estimate the momentum of particles originating from the interaction point based on the double-sided feature of PLUME, the hit rate levels observed during the Phase 2 run was too high to allow a robust use of the method with these data.

12 ing

 12 requires granular and light detection layers. In this respect, one of the most 13 promising technologies for charged particle tracking in current experiments and 14 their future upgrades is based on pixelated CMOS silicon sensors.

15

 15

Figure 1 :

 1 Figure 1: CAD drawing of the two PLUME ladders around the SuperKEKB beam pipe in the interaction region.

Figure 2 :

 2 Figure 2: Picture of the two PLUME ladders around the SuperKEKB beam pipe in the interaction region, before insertion in the Belle II inner tracker volume.

Figure 3 :

 3 Figure 3: Schematic concept of a PLUME ladder. Note that the vertical and horizontal axes do not share the same scale.

Figure 4 :

 4 Figure 4: Picture of a self-stiffened PLUME ladder (courtesy of J. Goldstein, university of Bristol).

3. 1 .

 1 Data analysed SuperKEKB started circulating the first beam during Phase 2 on 19 March 2018. Very first SuperKEKB collisions were delivered on 26 April and the Phase 2 run was completed on 17 July 2018. SuperKEKB being an asymmetric machine, there are two storage rings, called the High Energy Ring (HER, in

Figure 5 :

 5 Figure 5: Layout of the acquisition system of the 2 double-sided PLUME ladders in the Phase 2 setup of BEAST II vertex detectors, with indication of the location of the different components. IR stands for Interaction Region.

which 7

 7 GeV electrons are circulated) and the Low Energy Ring (LER, in which 4 GeV positrons are circulated). HER and LER beam parameters can be varied independently. During the Phase 2 run, the beam-induced background was carefully studied for the two beams in the following conditions: HER and LER beam current scans (bunch charge and number of bunches), HER and LER beam size scans, luminosity scans, collimator settings, continuous injection, beam steering scans, vacuum scrubbing. During these studies, the β * y parameter 2

  PLUME was running smoothly and registering data during about 99 % of the Phase 2 period. It was only occasionally switched off manually, mainly during a few early vacuum scrubbing periods. Such conditions indeed generate possibly high radiation dose, which could have damaged PLUME sensors and compromised the quality of future data taking. Another reason to switch off PLUME was when the sensor temperature was increasing above 70 • C because the cooling system of the BEAST II vertex detector volume was switched off.

Figure 6 :

 6 Figure 6: Hit rate measured with the two PLUME ladders (inner and outer sides) as a function of time, for different LER and HER beam conditions.

Figure 7 :

 7 Figure 7: Pixel fake rate measured per CMOS sensors as a function of time during the whole Phase 2 run.

Figure 8 :

 8 Figure 8: A typical saturated MIMOSA-26 frame due to too high hit rate, showing a distinct pattern where only the first rows and columns can register fired pixels. The x and y axes correspond respectively to columns and lines of the sensor pixel matrix and each red point is a fired pixel.

4. 2 .

 2 Hit reconstructionClusters (or hits) are reconstructed off-line from the list of fired pixels, i.e. showing a signal above the discrimination threshold, provided by sensors. The clustering algorithm gathers fired pixels with adjacent sides (not corners) and allows single-pixel hit.

Figure 9 :

 9 Figure 9: Distributions of the number of pixels per cluster for the four PLUME modules, without relative normalization. The last bin contains all entries beyond 20 pixels.

Figure 10 :

 10 Figure 10: Typical hit rate (arbitrary units) maps obtained with PLUME ladders as a function of radius r and z coordinate along the beam axis. Both ladders are represented, this means 6 sensors per side of each ladder.

Figure 11

 11 Figure 11 displays the transverse momentum distribution obtained with such a constrained helix fit using two PLUME points and the interaction point. The distribution features a strong cut-off below 15 MeV/c, matching the minimal transverse momentum required to reach the PLUME ladder from the interaction point within the Belle II 1.5 T magnetic field. The transverse momentum residual distribution depicted in figure 12 indicates that momenta are estimated within ±1 MeV/c for 50 % of the tracks. The long tail for the lower part of the residual corresponds to momentum over-estimation occurring when the origin of the particle is not the interaction point.

Figure 11 :

 11 Figure 11: Distribution of the reconstructed momentum with PLUME hits for particles emitted by simulated beam-beam induced background.

Figure 12 :

 12 Figure 12: Distribution of the momentum residual (true -reconstructed values) for particles emitted by simulated beam-beam induced background.

Acknowledgement This work was supported by the Institut National de Physique Nucléaire et de Physique des Particules of CNRS (CNRS/IN2P3) and by Investissements d'Avenir and Université de Strasbourg (IdEx grants W15RPE12 and W17RPD30).

We thank Katsuro Nakamura (KEK laboratory, Tsukuba), for his help as our KEK liaison. We thank the SuperKEKB accelerator physicists. We are also grateful to Ingrid Gregor (DESY laboratory, Hamburg) and Joel Goldstein (university of Bristol) for helping manufactoring PLUME ladders for the Phase 2 setup of BEAST II vertex detectors.