Mohamed A Imaddahen
email: mohamed-amine.imaddahen@ensam.eu

Mohammadali Shirinbayan

| Houssem Ayari

| Mathieu Foucard

Abbas Tcharkhtchi

| Joseph Fitoussi

Multi-scale analysis of short glass fiber-reinforced polypropylene under monotonic and fatigue loading

Keywords: fatigue analysis, fracture, mechanical properties, polypropylene, thermoplastics

Short fiber-reinforced polypropylene is largely used in the automotive industry. Fatigue failure is one of the most failure modes observed in this class of materials. In order to better understand the damage mechanisms and plasticity evolution, this article provides an overall experimental investigation of the mechanical properties of a PPGF40 composite (polypropylene matrix reinforced by a 40% weight content of short glass fibers) including monotonic and cyclic loading. The effect of various parameters such as the loading direction, the strain rate, the temperature, and the fatigue are analyzed. The evolutions of the loss of stiffness and plastic strain during monotonic and fatigue tests are analyzed. Self-heating during cyclic loading is also studied. Moreover, the coupling effect of damage and plasticity is analyzed by plotting the evolution of the relative loss of stiffness vs the plastic strain increment for monotonic and cyclic loadings. For quasi-static loading, the results emphasize an intrinsic curve independent of the loading direction. Moreover, a sharp increase in the damage and plasticity levels due to the local effect occurring during cyclic loading is observed and correlated to SEM fracture surface analysis.

| INTRODUCTION

Short fiber-reinforced thermoplastics (SFRT) are widely used in the automotive industry. Their high strength-toweight ratio, reprocessing quality, low-manufacturing price, and ability to be shaped using a conventional molding process such as injection make them great materials for automotive components with complex geometry and a high-volume production rate. [1,2] Among them, short fiber-reinforced polypropylene is largely used for the manufacturing of automotive exterior parts such as the bumpers and the hatch due to its low density, allowing high-fiber content filling and low-water absorption in comparison with polyamide. [START_REF] Karger-Kocsis | Polypropylene Structure, blends and Composites[END_REF] For such a use, glass fiber-reinforced polypropylene must exhibit great structural durability especially against mechanical and thermal fatigue loading. For example, tailgates (cars back doors), are stressed in fatigue with opening and closing cycles of up to 70 000 cycles.

It is commonly known that the damage evolution for SFRT during fatigue occurs in three stages [START_REF] Esmaeillou | [END_REF][5][6] : the first stage is described by a high reduction in stiffness due to damage mechanisms such as fiber/matrix debonding and matrix cracking. The second stage corresponds to the coalescence and propagation of microcracks. A gradual stiffness decrease is observed in this stage. The last stage is characterized by a drastic decline in stiffness due to rapid crack propagation leading to failure. The Analysis of the stiffness reduction during loading-unloading monotonic tests is used by several authors [7][8][9] to evaluate the macroscopic damage evolutions of SFRC. During the fatigue test, the dynamic modulus (slope of the stress-strain hysteresis) is commonly used as a damage indicator. [START_REF] Esmaeillou | [END_REF][10][11][12] Arif et al [13] applied the dynamic modulus to evaluate the damage evolution during fatigue loading. They concluded that the latter might overpredict the damage evolution for high amplitude due to the high-viscous effect of the composite.

Bellenger et al [14] studied the thermal and mechanical fatigue of a PA66/glass fiber composite material. They focused on analyzing the effect of the physical state of the matrix on the fatigue behavior and the failure surfaces. They showed that the fatigue behavior of thermoplastic composites could be obtained by inducing the thermal and mechanical fatigue. The induced temperature was not only caused by the damping induced by crack initiation but also by the change in the physical state of the matrix. There was a fast increase of the loss modulus E 00 at the glass transition temperature hence the increase in the dissipated energy at each loading cycle. They concluded that the damage is initiated at fiber ends close to sample edges where the stress concentration was the highest.

In another study, [15,16] the results showed that the thermal fatigue had a very significant role in rising temperature and decreasing fatigue lifetime. Consequently, it is necessary to know the conditions at which thermal fatigue happens.

Zuo et al [12] studied the multiscale analysis of the effect of loading conditions on the monotonic and fatigue behavior of a glass fiber-reinforced polyphenylene sulfide composite. They concluded that the increasing frequency would lead to lower fatigue lifetime and more generalized plasticity. They demonstrated that fiber orientation in the loading direction would improve both the monotonic and fatigue strength.

Shirinbayan et al [17,18] studied the coupled effect of the loading frequency and amplitude on the fatigue behavior of an advanced sheet molding compound (A-SMC). They also studied the isodamage evolution curves obtained from postfatigue dynamic tests to those which could be obtained in monotonic dynamic traction. The comparison was done on equivalent E damage states corresponding to different values of the lifetime fraction, N/Nr. They concluded that the elastic modulus remained insensitive to the strain rate for predamaged A-SMC composites. The fatigue predamaged samples showed a remaining monotonic mechanical potential always lower than the virgin samples.

Moreover, polymeric composites are known to exhibit strong time and temperature dependence. [19][20][START_REF] Achour | Microstructural and experimental analysis of strain rate effect for short glass fiber reinforced polypropylene[END_REF][START_REF] Kim | [END_REF][23][24][25] For polymers, it is known that Young's modulus and the maximum stress increase with the strain rate and decrease with the temperature. For a glass fibers reinforced polypropylene based copolymer, [26] Fitoussi et al emphasized a strong increase in all the mechanical properties (including ultimate strain) with the strain rate. These authors introduced the concept of visco-damage occurring at the local scale due to both plastic deformation of the matrix and the strain rate dependence of the fiber matrix interfacial strength. For moderate to high-strain rates, Jendli et al [20,27] also emphasized this effect for a short fiberreinforced thermoset.

The work of Horst and Spoormaker [28,29] on the damage mechanisms of short glass fiber polyamide 6.6 in quasi-static and fatigue allowed proposing a scenario of damage in fatigue similar to that of Sato, [30,31] mainly based on the creation of a vacuum at the matrix fiber interface. Since then, this scenario has been widely validated in the literature [32,33] and has affirmed its independence from many parameters, including the type of loading and the temperature. For both researchers, the difference between each loading would lead to the level of the kinetics of the damage propagation.

A good understanding of the damage phenomenon at the macroscopic and the microscopic scales is therefore necessary to better size this type of structure and to propose criteria and models capable of predicting their mechanical response. On the other hand, the bibliographic research has not provided many studies concerning the damage and plasticity evolution during the fatigue of these type of materials. The investigation of the monotonic and fatigue properties of these composites including damage and plasticity evolution as well as coupling, is the main objective of this study.

In this article, we propose an overall experimental characterization of the mechanical properties of short glass fibers reinforced polypropylene at different fiber orientations (0 , 45 , and 90 vs injection molding direction). Due to the different application conditions, monotonic tensile tests at different strain rates (0.0001, 0.04, and 0.25 s -1 ) and temperatures (-30 C, 23 C, and 80 C) are performed. Loading-unloading tests are performed at room temperature at a quasi-static strain rate (4.10 -4 s -1 ) to analyze the macroscopic damage evaluation.

The progressive loss of stiffness and the macroscopic residual strain increase are used to characterize damage and apparent plasticity evolution. Tensile-tensile fatigue tests are performed at frequencies of 1 and 10 Hz and a stress ratio of R = 0.1. Damage analysis during fatigue is proposed by mean of dynamic modulus, plastic strain, and self-heating evolution. Finally, the scanning electronic microscope (SEM) observation of fracture surfaces at quasi-static and fatigue loading is performed to understand the failure mode and the damage mechanisms occurring for both loading conditions.

| MATERIAL AND EXPERIMENTAL PROCEDURE

| Material description

The studied material is a 40% (weight content) short glass fibers reinforced polypropylene provided by FLEXNGATE (PPGF40). The material is obtained by the compounding polypropylene pellets and short glass fibers. The material is then injected to obtain 400 * 320 * 3 mm 3 rectangular plate.

| Microstructure characterization methods

| Microscopic observations

Microscopic observations and image analysis, using SEM (HITACHI 4800 SEM) are performed to qualitatively investigate the material microstructure, especially the fiber orientation. The SEM observation of the fracture surfaces of the specimen after tensile and fatigue tests are performed and a comparison of the damage mechanisms and the fracture mode is then proposed.

| Ultrasonic measurement

The ultrasonic wave propagation measurement is used to characterize the orientation and spatial distribution in a short glass reinforced composite plate. Indeed, several authors [34,35] used an innovative ultrasonic immersion method to characterize the fiber orientation of short fiber-reinforced polymers. Here, the same characterization method is used. The sample is placed between two probes to create an ultrasonic wave propagating in the material through the water. An angle of 45 is respected between the sample and the incident ultrasonic wave in order to create shear waves propagating in the plane defined by the incident ultrasonic direction and the normal vector to the sample. The latter is then rotated from 0 to 360 by a step of 30 around its normal vector. This rotation allows the shear wave to propagate through different material planes. Knowing the distance between the two probes, the sample thickness and the time taken by the wave to propagate, between the two probes, as well as the velocity of the ultrasonic shear wave in the material are then calculated. The variation in the ultrasonic velocity allows a direct quantification of the amount of fibers orientated in the different planes of propagation. Indeed, the presence of fibers in a specific propagation plane increases the ultrasonic velocity.

Experimental procedure

We start by immersing two identical probes in a tank filled with water: a first transmitter marked (E.) and a second receiver marked (R). The two probes are positioned opposite each other at a well-known distance (d). The first step is to measure the speed of wave propagation in the liquid alone, using an oscilloscope, we determine the flight time T o and knowing the distance we deduce the speed V 0 : Figure 1

V o = d t o : ð1Þ
In a second step, we have on the ultrasonic path, the element of our material by which we want to know the main fiber orientation (Figure 2). This element is arranged perpendicular to the ultrasonic wave. This generates longitudinal waves V OL (compression wave) in the material propagating in the thickness of the material.

Thickness "e" is usually determined using a micrometer. We then measure the new flight time t e (still using an oscilloscope).

The flight time t e is then equal to:

t e = d -e V o + e V e , ð2Þ
where V e is the velocity of the longitudinal waves in the sample. After doing the calculation, we get:

F I G U R E
V e = e t e -d -e V o = V OL : ð3Þ
A third step in the ultrasound analysis is to rotate the sample using the device illustrated in Figure 3-a by an angle of incidence (i). This configuration makes it possible to generate transverse waves which will in turn propagate at speed V OT through the thickness of the sample in a direction (r) governed by the Snell-Descartes law (Figure 3B)

sin i ð Þ V 0 = sin r ð Þ V 0T : ð4Þ
On the oscilloscope we read the new flight time t e . By taking into account the routes EA and BR, which are made at speed V o and the course AB which takes place at speed V OT , and considering the Snell-Descartes law, we get:

V OT = eV o ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi e 2 + 2eV o t e -t o ð Þcos i ð Þ + V 2 o t e -t o ð Þ 2 q : ð5Þ
The sample is then rotated from 0 to 360 by a step of 30 around its normal vector, the results are represented in Figure 7B.

| DMTA-analysis

To measure the main transition temperature, thermomechanical (DMTA) tests have been performed using DMA Q800 instrument, from TA Company. The tests are realized according to the following conditions: dual cantilever configuration; temperature range from -75 C to 125 C; frequency of 1 and 10 Hz; and temperature rate 2 C/min.

| Mechanical characterization methods

| Monotonic tension behavior

Monotonic tensile tests until failure are performed using a servo-hydraulic machine MTS 830 according to the ISO 527 standard at crosshead speed variating from 2 to 1200 mm/min, which correspond to strain rates ranging from 4.10 -4 to 0.25 s -1 . The temperature effect is also studied by performing tensile test at a controlled temperature of 85 C and -30 C at 4.10 -4 s -1 . In this case, specimens are conditioned inside an oven for 30 minutes to get a uniform temperature all over the specimen. A contactless image analysis technique using a CANON camera with a frame rate of 50 images per second allows the strain measurement by following the relative displacement of two marked points drawn on the surface of the specimen before testing. The video-obtained by the camera are treated with the software ImajeJ and the strain measurement is then synchronized with the data machine.

| Damage analysis in monotonic loading

To study the evolution of the macroscopic damage and apparent plasticity at the quasi-static regime, loadingunloading tests at different increasing maximum applied stresses are performed at a crosshead speed of 2 mm/min and at room temperature. For each test, the sample is submitted to a total of eight to ten loading-unloading cycles at a gradual increasing stress gap of about 10% of the ultimate tensile stress (σ u ), as shown in Figure 4. The residual strain at a zero stress gives an evaluation of the residual macroscopic apparent plastic strain. Young's modulus is evaluated by the slope of the curve at the beginning of each cycle.

| Fatigue tests

Fatigue tests are performed at different applied maximum stresses (σ max ) on the MTS 830 servo-hydraulic fatigue machine. A sinusoidal signal is applied under stress-controlled mode, the constant amplitude and the fixed loading ratio. To prevent the specimen from buckling, the chosen stress ratio R is 0,1. The main study frequency is 10 Hz; however, a second frequency of 1 Hz is used in order to study the effect of velocity and selfheating on the fatigue performance. The mechanical behavior during fatigue of the three types of samples tested (0 , 90 , and 45 ) is investigated by means of stiffness reduction, evolution of apparent plastic strain and self-heating. The temperature of the specimen is followed using a contactless infrared camera. The strain measurement during fatigue is done using the displacement data given by the machine coupled with a correction factor.

| Specimen for mechanical testing

To overcome the problems related to the machining process, tensile specimens are obtained by a water jet cutting technique from injected plates. Specimens are extracted from the center of the plates and a globally uniform microstructure. To study anisotropy, specimens were cut along three directions: 0 , 90 , and at 45 regarding the injection direction. Figure 5 shows the dumb-bell specimen geometry allowing uniform stress repartition along the working area.

| RESULTS AND DISCUSSIONS

| Microstructure analysis

The microstructure obtained from the injection molding process has been largely studied in the literature. [13,[36][37][38] In fact, the shear flow is maximum at the mold surface, making the fibers well oriented in the flow direction. However, at the core, the shear flow is negligible which makes them perpendicular to the flow direction. Arif et al [13] used the X-ray microcomputed tomography (μCT) technique on short fiber-reinforced polyamide and distinguished four types of microstructures. First, the skin layer was oriented with random fibers. Then the fibers in the shell layer were mainly oriented in the injection direction. After that, a shell-core transition layer was oriented with random fibers. Finally, core layer with fibers oriented perpendicularly to the injection direction. The SEM observations confirm the presence of this microstructure distribution for our material. Figure 6 is a reconstitution of multiple images taken with SEM along the thickness with a 200 times magnification. The typical skin-shell-core microstructure of the injected material clearly appears. The original ultrasonic method described in Section 2.2.2 is used to analyze the spatial distribution of the microstructure of the plate. Sixteen rectangular samples are cut from the rectangular injected plate (Figure 7). Figure 7A represents the locations of the samples in the plate and Figure 7B depicts the corresponding polar diagrams of the shear wave velocity. The latter clearly reveals a strongly orientated microstructure in the injection direction. Despite the simple geometry of the plate small variations can be distinguished from one location to another. Indeed, the main orientation of fibers is not always found in the mold flow direction especially at some edges of the studied area. For example, samples 5, 14, and 16 show a main orientation direction at 30 from the injection direction. Another observation is that the velocity of the shear ultrasonic wave drops by more than 70% when passing from the main fiber orientation to the transverse direction, this indicate a highanisotropic behavior of used material. Following these results, we have decided to extract the mechanical test specimens from the central zone of the plate in which the microstructure is homogeneous and well oriented in the mold flow direction. In the following, a 0 specimen means that it has been cut in the mold flow direction.

| Thermomechanical analysis

To study the effect of the temperature, DMTA tests are performed using dual cantilever at a strain of 0.01% and frequencies of 1 and 10 Hz. Figure 8 illustrates the evolution of the storage and loss modulus for the two frequencies vs temperature.

In this figure, three different zones can be identified corresponding to the glassy state, glass transition zone, and rubbery state. It is demonstrated also that raising the frequency leads to increasing E 0 and E 00 without changing the transition temperature. Indeed, it must be noted that evolution E 00 shows three peaks corresponding to the three transitions T β (at-30 C), T α (at 10 C) and T αc (at 70 C). T β corresponds to the movement of short molecular segments. For an amorphous polymer, T β corresponds to the ductile-brittle transition temperature. T α , which is generally related to the glass transition temperature, is not affected by the presence of fibers. For pure polypropylene (PP) T α is around 10 C. T αc , which corresponds to the mobility of chains near the surface of crystallites, [24] goes up from 50 C for pure PP to nearly 70 C when introducing fibers. This is probably due to the stiffening of the chain segments in this intermediate zone between the amorphous phase and the crystalline phase and

| Effect of fiber orientation on tensile properties

The tensile properties of PPGF40 composites are described in Figure 9. Five specimens are tested for all fiber directions, the main mechanical characteristics of the material are reported in Table 1 by the means of their averages and deviations. The strong anisotropy induced by the injection molding process of the material is well illustrated. Indeed, specimens loaded in the longitudinal direction show higher mechanical properties than those in transversal (almost 100% increase in Young's modulus and ultimate stress) and 45 direction. However, transverse and 45 specimens show more ductile properties characterized by higher elongation at fracture.

It is interesting to note that for the three sample orientations the stress-strain curves exhibit a nonlinear behavior caused by plasticity and damage. Note that an elastic behavior rises when the fibers are misoriented vs tensile direction. Indeed, in this case, matrix and fiber matrix interfaces are more solicitated than in the case of longitudinal-loading, for which a minimum nonlinear behavior is observed.

| Temperature effect on tensile properties

Tensile behavior of PPGF40 highly depends on temperature due to the relatively low-glass transition temperature of the PP (about 5 C, see Figure 8). [23] Figure 10 illustrates the effect of high (+85 C) and low temperature (-30 C) on the tensile properties; it shows that at 85 C, the material is still highly anisotropic, but Young's modulus and the maximum stress drop for more than 50% in comparison with the results at room temperature. However, ductility is improved by more than 350% even for the longitudinal direction. At -30 C there is an improvement of the maximum stress, but the change of Young's modulus remains neglectable. This effect is probably due to the β transition of the matrix in a glassy state, related to the molecular mobility of short chain segments.

| Strain rate effect on tensile properties

The materials under investigation show a strong strain rate-dependent behavior. [16,25,[39][40][41][42] The study made by Fitoussi et al [41] demonstrated that mechanical characteristics, in terms of damage and plastic strain threshold, ultimate properties, were highly sensitive to the strain rate. As the strain rate rose, Young's modulus would increase by 50%. The "visco-damage" effect that they introduced produce a delay of the first damage phenomenon, a slower damage rate at high-strain rate and a delay in the plastic strain threshold.

Even for a strain rate less than 1 s -1 , a slight improvement of Young's modulus and the maximum stress may be observed. Indeed, Figure 11 shows an improvement of 20% at strain rate of 0.25 s -1 for the three microstructures in comparison with quasi-static loading performed at 4.10 -4 s -1 . At a higher strain rate, the improvement should be much more important. [16] In fact, the viscoelastic behavior of the matrix impacts the composite response. [START_REF] Achour | Microstructural and experimental analysis of strain rate effect for short glass fiber reinforced polypropylene[END_REF]26,27,41]

| Macroscopic damage and apparent plasticity evolution during loading-unloading tests

Figure 12 illustrates both the loading-unloading response and the monotonic stress-strain curves for the three configurations 0 , 45 , and 90 . This figure demonstrates that there is no significant gap between the monotonic and the cyclic envelopes for all sample orientations. This confirms that there is no significant change in the behavior of PPGF40 by the loading-unloading test compared to tensile loading.

Damage and residual strain (apparent plastic strain) evolution during loading-unloading quasi-static tests is analyzed in Figure 13. Three specimens are tested for each configuration. For the three microstructures, the plasticity threshold is lower than the damage threshold. Therefore, the presence of two deformation stages can be noticed: the first one involving matrix an elasticity and the second one coupling damage to plasticity. Maximum damage and plasticity are observed for the transverse direction followed by the 45 direction and then the longitudinal direction, which exhibits the lower levels of damage and plasticity. From Figure 13, the value of the plastic stain reached at the threshold of damage: ε th P .can be extracted This value should be directly read in Figure 14 for each orientation. Therefore, the difference between the total plastic strain, ε P and ε th P , represents the increment of plastic strain during the second stage involving both damage and plasticity. Thus, the coupling effect of damage and plasticity should be emphasized by plotting the evolution of the loss of stiffness, E E 0 vs ε P -ε th P . Figure 15 shows that this evolution follows a unique curve for all the orientations. This means that there is an intrinsic relation between the macroscopic loss of stiffness and the increment of plastic strain during the second stage involving both damage and plasticity. As a consequence, it can be concluded that for a given microstructure, knowing the stiffness loss for applied loading leads directly to the corresponding plastic strain, independently of the orientation of fibers. This result should be useful for component design. F I G U R E 1 6 Evolution of normalized dynamical modulus, maximum plastic strain and temperature during fatigue twice higher than the transverse direction. It is interesting to note that the fatigue life is slightly improved when increasing the frequency from 1 to 10 Hz. The average strain rate undergone during a 10 Hz fatigue test is about 0.25 s -1 . As it was depicted in Figure 8, at this rate, the material exhibits higher mechanical properties due to matrix visco-plasticity and visco-damage. Therefore, the plasticity and coupled damage plasticity stages emphasized in Figure 10 may be influenced in terms of thresholds (delayed) and kinetics (lower). This can explain the improvement of the fatigue strength. Moreover, Figure 16 illustrates the evolution of the stiffness loss, apparent plastic strain and the temperature of the specimens during fatigue. These results show that the longitudinal direction presents the maximum temperature evolution with self-heating of 10 C. This temperature is reached for medium amplitudes. Indeed, lower and higher amplitudes exhibit lower self-heating. It can also be noted that a variation in the temperature from 22 C to 32 C due to self-heating corresponds to a variation of the storage modulus from 3725 to 3275 MPa (a variation of 12%), as represented in Figure 8. Therefore, the strain rate effect shown in Figure 11 together with possible higher deformation possibility due to self-heating lead to a slight improvement of the fatigue strength at 10 Hz.

| Macroscopic damage and plasticity evolution

Figure 16 illustrates the evolutions of the normalized dynamic modulus, the maximum plastic strain, and temperature for the three studied orientations. Considering continuum damage mechanics, the loss of dynamic stiffness can be used as a damage indicator during fatigue. For amplitudes higher than 0.85 S u (where S u is the ultimate stress), the dynamic modulus decreases rapidly in a linear logarithmic regime until fracture of the specimen. For amplitudes between 0.85 S u and 0.60 S u , the dynamic modulus exhibits three decreasing regimes: a rapid one during the first 1000 cycles, followed by a gradual one, and finally a drastic decrease just before fracture. It is noted that for amplitude below 0.6 S u , the specimen exhibit a higher fatigue life up to 10 6 cycles. It is interesting to notice that medium amplitudes exhibit the greatest values of stiffness loss and plastic strain. For high amplitudes, damage mechanisms and failure occur rapidly so that stiffness loss, plastic strain, and self-heating cannot evolve until reaching the maximum values.

As it is analyzed in Section 3.2.4 for quasi-static loading, the coupling effect of damage and plasticity during fatigue should be analyzed. First, it is obvious from Figure 16 that after a first increment due to the first cycle, plastic strain remains stable while stiffness decreases. Thus, contrary to quasi-static loading where the first stage is described by plasticity without damage, for fatigue loading, the first stage corresponds only to the damage phenomenon. However, generally after 1000 cycles, plastic strain and damage increase together rapidly during a second stage.

As in Figure 14, Figure 17 depicts the coupling effect of damage and plasticity during the second stage of the fatigue tests. Some general comments can be made:

• For the three orientations, it can be noticed that the stiffness reduction vs plastic strain curves in fatigue start like the monotonic curve, but they do not show the same kinetics. In fact, the maximum damage and plastic strain reached under fatigue are considerably greater than those reached during monotonic tests (up to × 2.5 for damage and × 2 for plastic strain). This is probably due to the local plastic strain cumulated around the fiber during cyclic loading, which behaves as a barrier that prevents fiber matrix interface microcracks from branching off into the matrix, so that damage and plasticity can diffuse more largely through the material. • However, this effect is limited when the fibers are oriented in the loading direction (0 ). Indeed, in this case,

F I G U R E 1 9
Fracture faces for tensile and fatigue tests matrix plasticity and fiber matrix interface damage are reduced. • Two stages are observed: The first stage is characterized by a strong damage kinetic, which means that to a given plastic strain increment corresponds a sharp loss of stiffness. The latter effect increases when increasing the amplitude. Then, damage kinetics decreases progressively to level off around an average kinetic, which appears to be quite independent of the orientation and applied stress amplitude. However, for very high amplitude, this stabilized second stage may disappear because of early failure. • The higher levels of damage and plastic strain are generally obtained for the lowest applied maximum stress. Indeed, when applying high-stress amplitude, the plastic strain barrier around the fibers may be crossed more easily due to higher local stress concentration. Consequently, the redistribution of the local stress and strain may be limited, and microcrack coalescence may occur earlier leading to precocious failure. • For very low amplitudes, the coupling curves during fatigue begin to follow the monotonic one; then damage seems to saturate. This leads to a plasticity dominant stage where the coupling curve remains almost flat. Finally, a third-drastic damage stage occurs leading to the fracture of the specimen.

Figure 18 resumes the different stages of the damage plasticity evolution for different applied stress amplitudes.

| Fracture surfaces

Figure 19 illustrates the SEM fracture surfaces for tensile and fatigue tests. For the three direction and for both monotonic and fatigue loading, the creation of cavities or microvoids can be observed around the fiber matrix interface, indicating local plasticity before debonding. A lot of studies have been interested in the creation of these cavities, we can, for example, cite those of Achour et al [START_REF] Achour | Modélisation multi-échelle et analyse expérimentale du comportement de composites à matrice thermoplastique renforcés fibres de verre sous sollicitations dynamiques modérées[END_REF] who reported a damage scenario starting with the creation of cavities and microcracks at the glass fiber ends. The second stage of the damage is characterized by the propagation of microcracks around the fiber; the coalescence of microcracks lead to a fast crack growth leading to failure.

For fatigue loading, plastic deformation can be also observed in the form of striations located around the fibers. This confirms the above interpretation of a plastic deformation barrier located around the fibers, which allows avoiding microcracks propagation through the matrix and leading to larger damage and deformation.

The SEM images reveal higher ductility for tensile tests. In fact, under monotonic loading, the matrix just around the fibers does not accumulate plastic deformation while under fatigue, local cyclic loading can result in highplastic strain concentration around the fibers. This high ductility observed for monotonic loading leads to more fiber pullout in comparison with the fatigue loading. The same remark was advanced in the works of Noda et al. [32]

| CONCLUDING REMARKS

The overall mechanical properties of PPGF40 are studied based on of monotonic, loading-unloading, and fatigue tensile tests. The effects of the temperature and the strain rate are illustrated. Fatigue tests are performed at two different frequencies and a slight improvement of the fatigue strength is observed at 10 Hz. The dynamic modulus, the plastic strain and the self-heating evolution are used to analyze the evolution of the macroscopic properties of the composite during fatigue. Under fatigue loading, the fatigue stiffness reduction vs plastic strain increment curves always starts as the monotonic curve, but they do not show the same kinetics. Indeed, a sharp increase in damage and plasticity is emphasized for cyclic loading. A comparison between monotonic and fatigue fracture surfaces obtained by SEM observations provides an interpretation of the specific coupling effect between damage and plasticity occurring at the local scale during cyclic loading at its effect on the macroscopic properties of the composite.

1

 1 Principle of the ultrasonic method: determination of the speed V 0 [Color figure can be viewed at wileyonlinelibrary.com]

F

  I G U R E 2 Principle of the ultrasonic method: determination of speed V OL [Color figure can be viewed at wileyonlinelibrary.com] F I G U R E 3 A, Sample holder used for ultrasonic characterization allowing control of angle of incidence (i) as well as direction of propagation of the transverse waves. B, Principle of ultrasonic method: determination of speed of transverse waves [Color figure can be viewed at wileyonlinelibrary.com]

F

  I G U R E 4 Loading-unloading tests procedure F I G U R E 5 Specimen geometry It can be noted that the shell layers represent about 66% of the sample thickness.

F

  I G U R E 6 Skin: A, shell. B, core. C, microstructure, inducted by injection molding optionally the transcrystallization at the fiber matrix interface.

F I G U R E 8

 8 Storage modulus during dual cantilever DMA test at different frequencies F I G U R E 9 Tensile normalized stress-strain curves of PPGF40 at room temperature for 0 , 45 , 90 directions and PP at a crosshead speed of 2 mm/min corresponding to strain rate of 0.0004 s -1 . PP, polypropylene F I G U R E 7 Position in plate of 16 pieces used for ultrasonic measurements and corresponding polar diagrams [Color figure can be viewed at wileyonlinelibrary.com]

F I G U R E 1 0

 1 Tensile normalized stress-strain curves of PPGF40 at 23 C, -30 C, and 85 C for 0 , 45 , and 90 directions at crosshead speed of 2 mm/(min 0.0004 s -1 )

F I G U R E 1 1

 1 Tensile normalized stress-strain curves of PPGF 40 at different strain rates and room temperature F I G U R E 1 2 Loading-unloading and monotonic normalized stress-strain curves for 0 , 45 , and 90 F I G U R E 1 3 Stiffness loss and plasticity evolution during loading-unloading tests F I G U R E 1 4 Stiffness loss as a function of plastic strain at damage threshold

3. 3 |

 3 Fatigue behavior 3.3.1 | Effects of loading amplitudes and frequency

Figure 15

 15 Figure 15 represents the 10 Hz and 1 Hz S-N curves for the three directions. In concordance with tensile results, the longitudinal direction shows the fatigue strength

F I G U R E 1 7

 1 Stiffness loss as function of plastic strain subtracted by plastic strain at the damage threshold during fatigue loading F I G U R E 1 8 Schematic of damage plasticity coupling as function of fatigue amplitudes [Color figure can be viewed at wileyonlinelibrary.com]

  Summary of mechanical properties of tested configurations E (MPa) σ max (MPa) ε max (mm/mm)

	0	Avrg 7883.3	84.85	0.02
		devi	277.8	1.58	0.001
	45	Avrg 5090	55.89	0.03
		devi	432	1.14	0.002
	90	Avrg 4466.7	44.01	0.025
		devi	155.6	1.38	0.002
	Pure PP Avrg 1045	31	0.39
		devi	75	2	0.003

T A B L E 1

Abbreviation: PP, polypropylene.

ACKNOWLEDGMENT This work is carried out as part of a Phd thesis ( CIFRE number 2016/1520) in collaboration between Arts et Metiers Institute of Technologie and Flex N gate Exteriors Europe. ORCID Mohamed A. Imaddahen https://orcid.org/0000-0002-5681-0024 Mohammadali Shirinbayan https://orcid.org/0000-0002-2757-8529

Funding information Grant/Award Number: scholarship; FLEX-N-GATE Exteriors Europe, Grant/Award Number: scholarship + Materials


MD Erwan Donal
email: erwan.donal@chu-rennes.fr

MDà Arnaud Hubert

PhD Virginie Le Rolle

MD Christophe Leclercq

PhD Raphael Martins

MD, PhD Philippe Mabo

MD, PhD Elena Galli

PhD Alfredo Hernandez

New Multiparametric Analysis of Cardiac Dyssynchrony: Machine Learning and Prediction of Response to CRT

come   L'archive ouverte pluridisciplinaire

àDrs. Donal and Hubert contributed equally to this manuscript.

Although previous studies have suggested that the analysis of mechanical dyssynchrony can improve prediction of response to cardiac resynchronization therapy (CRT), current guidelines still neglect the value of left ventricular (LV) mechanical dyssynchrony assessed by imaging technics, particularly echocardiography. Recently, machine-learning methods have offered new opportunities to analyze complex features in cardiology [START_REF] Omar | Artificial intelligence-based assessment of left ventricular filling pressures from 2-dimensional cardiac ultrasound images[END_REF]. We hypothesized that a multiparametric evaluation, based on the combination of electrocardiographic and echocardiographic parameters, analyzed by an automated machine-learning system based on the random forest (RF) method, could enhance the appraisal of the likelihood of reverse remodeling and prognosis of favorable clinical evolution after CRT.

A total of 154 heart failure patients, with an ejection fraction <35% and QRS duration >120 ms, who had a CRT device implanted in Rennes University Hospital between 2010 and 2017, were retrospectively studied. A total of 109 patients (71%) were responders, defined by a decrease in LV endsystolic volume >15% at 6-month follow-up. The mean age of the overall population was 65 ± 10 years, there were 103 (67%) men. Mean QRS width and LV ejection fraction were 164 ± 18 ms and 28 ±7%, respectively. Ischemic cardiomyopathy was identified in 45 (29%) patients. All patients had a complete baseline echocardiography before implantation (Ve9, Ve95, GE Healthcare, Horten, Norway) and at 6month followup, with offline parameters measurement according to the current guidelines by a certified senior echocardiographer. Custom-made signal processing methods, developed with MATLAB software (MathWorks Inc.), were used to analyze automatically the 4-chamber longitudinal strain, providing 60 different features, particularly dyssynchrony parameters and integrals of regional longitudinal strain signals, as described in Bernard et al. [START_REF] Bernard | Impact of cardiac resynchronization therapy on left ventricular mechanics: understanding the response through a new quantitative approach based on longitudinal strain integrals[END_REF]. QRS duration was also included in the analysis as an additional feature. Electrocardiogram (ECG) and echocardiographic parameters were selected first, based on a filtering cutoff of Pearson's coefficient >0.8. The R) method was then applied to analyze the relative importance of the remaining features and to obtain the 6 most significant features. A final RF method was applied to the 6 selected features, with the objective of predicting response to CRT. A Monte Carlo crossvalidation method with 30 runs was applied, using, in each run, different random sets of 70% of patients for training and 30% for testing.

Results showed a mean area under the curve (AUC) of 0.804 with a standard deviation of 0.03 (0.77 to 0.94) (Figure 1). In contrast, the best classification performance for a single variable was obtained with a strain-based measurement of myocardial wasted energy of the septal wall, with an AUC of 0.686, followed by QRS duration with an AUC of 0.668.

Our study demonstrates that the machine-learning approaches may be useful to improve the estimation of good candidates for CRT. Linear models are useful to find variables that are significantly different between groups, but these variables are not necessarily associated with outcomes. Through the iterative creation of models from a significant number of variables, machine learning allows the identification of the model that best fits the primitive clinical question. It optimally combines complementary information on the patients' susceptibility to respond favorably to a predefined treatment [START_REF] Cikes | Machine learning-based phenogrouping in heart failure to identify responders to cardiac resynchronization therapy[END_REF][START_REF] Kalscheur | Machine learning algorithm predicts cardiac resynchronization therapy outcomes: lessons from the COMPANION Trial[END_REF]. Combing multiple data might allow a move to "precision medicine" [START_REF] Califf | Future of personalized cardiovascular medicine: JACC State-ofthe-Art Review[END_REF]. Moreover, this study underlines the complementary value of LV dyssynchrony parameters with respect to standard ECG analysis and proposes a method to estimate CRT response by combining a limited number of sensitive ECG and echocardiography parameters. Finally, this approach demonstrated that a fast semiautomated echocardiographic method, based only on a longitudinal strain curves that is strongly reproducible even for novice readers, could provide useful information to better select CRT candidates. Although our population is limited, the Monte Carlo cross-validation method is robust through many tests using subgroups for learning and a subgroup for testing.

When analyzed in a multiparametric approach using machine-learning algorithms, a combination of echo-based parameters of LV dyssynchrony and QRS duration helped to improve the prediction of the response to CRT.

Figure 1

 1 Figure 1


Orianne Dumas
email: orianne.dumas@inserm.fr

Audrey J Gaskins

Krislyn M Boggs

Scott A Henn

Nicole Le Moual

Raphäelle Varraso

Jorge E Chavarro

Carlos A Camargo

Raphaëlle Varraso

Occupational use of high-level disinfectants and asthma incidence in early-to mid-career female nurses: a prospective cohort study

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

INTRODUCTION

Disinfectants and cleaning products (DCPs) are widely used in the healthcare industry to protect patients and workers against healthcare-related infections [START_REF] Quinn | Cleaning and disinfecting environmental surfaces in health care: Toward an integrated framework for infection and occupational illness prevention[END_REF]. In addition to 'common' DCPs, specific chemicals are used for high-level disinfection of critical or semicritical items (e.g., surgical instruments, endoscopes), including aldehydes (e.g., glutaraldehyde), peracetic acid or hydrogen peroxide [START_REF] Henn | Precautionary practices of healthcare workers who disinfect medical and dental devices using high-level disinfectants[END_REF].

Evidence for adverse health effects of exposure to DCPs has grown in the last two decades [START_REF] Folletti | Update on asthma and cleaning agents[END_REF][START_REF] Dumas | Damaging effects of household cleaning products on the lungs[END_REF]. Many studies have reported an association between these exposures and poor respiratory health, including asthma symptoms and poor asthma control [START_REF] Folletti | Update on asthma and cleaning agents[END_REF][START_REF] Dumas | Occupational exposure to disinfectants and asthma control in US nurses[END_REF][START_REF] Su | Clustering asthma symptoms and cleaning and disinfecting activities and evaluating their associations among healthcare workers[END_REF]. However, most of these studies are cross-sectional, and results from longitudinal studies on asthma incidence are not entirely consistent. Three longitudinal population-based studies in Europe have reported associations between occupational exposure to DCPs and asthma incidence [START_REF] Kogevinas | Exposure to substances in the workplace and new-onset asthma: an international prospective population-based study (ECRHS-II)[END_REF][START_REF] Ghosh | Asthma and occupation in the 1958 birth cohort[END_REF][START_REF] Lillienberg | Occupational Exposure and New-onset Asthma in a Population-based Study in Northern Europe (RHINE)[END_REF]. In contrast, in a longitudinal cohort of late-career nurses from the Nurses' Health Study II, no association was observed between exposure to DCPs and asthma incidence, potentially because of a healthy worker effect [START_REF] Dumas | Occupational exposure to disinfectants and asthma incidence in U.S. nurses: A prospective cohort study[END_REF]. To limit this bias, it is important to actively follow-up workers from the beginning of their careers. Therefore, we investigated the prospective association between use of high-level disinfectants (HLDs) and incident asthma in a large cohort of early to mid-career female nurses in North America.

METHODS

The Nurses' Health Study 3 (NHS3) is an ongoing, prospective, internet-based open cohort of nurses in the US and Canada [START_REF] Bao | Origin, Methods, and Evolution of the Three Nurses' Health Studies[END_REF]. Female nurses (registered nurse, licensed practical/vocational nurse or nursing student) born on or after 1 January 1965 were eligible for the study. From 2010 to 2018, 46167 nurses enrolled in the study. Follow-up questionnaires are sent every 6 months. The Institutional Review Board of the Brigham and Women's Hospital (Boston, Massachusetts) approved the study. Completion of the web-based questionnaires implied informed consent. Occupational use of HLD was evaluated in the baseline questionnaire [START_REF] Gaskins | Occupational use of high-level disinfectants and fecundity among nurses[END_REF].

Participants were first asked if they had ever used HLDs (""In your career, have you ever used disinfectants to disinfect medical instruments, devices or supplies [such as endoscopes, thermometers or other items which cannot be sterilized] by either manual or automatic methods? (This does not include the cleaning of countertops or other surfaces)"). The questionnaire then listed several examples of disinfectants. Participants were also asked to report the duration of use during the career, and the type of HLD (e.g., aldehydes, hydrogen peroxide) used in the past month for disinfecting medical instruments. Finally, women reporting use of HLD in the past month were asked about the frequency of protective equipment use (never, sometimes, always) when handling HLDs, including disinfection system with dedicated local exhaust ventilation or respiratory protection (not including a surgical mask).

At baseline, participants were asked if they ever had clinician-diagnosed asthma. In follow-up questionnaires, they were asked to report clinician-diagnosed illnesses that they had in the past 12 months, including asthma. Incident asthma was defined by absence of asthma at baseline and report of new clinician-diagnosis of asthma in follow-up questionnaires.

Information on potential confounders was assessed on the baseline questionnaire, including age, race/ethnicity, height, weight, and smoking history.

Associations between occupational use of HLD and asthma incidence was evaluated by Cox proportional hazard models, adjusted for age, race (white, black, other), ethnicity (Hispanic vs non-Hispanic), smoking habits (non-smoker, ex-smoker or current smoker) and body mass index (BMI, <25, 25-29.9, ≥30 kg/m2). As we hypothesized that conducting analyses in a group of early career nurses would help minimize a potential healthy worker effect, we performed an age-stratified analysis using median age (34 years) as the cut-off.

RESULTS

Among the 46,167 NHS3 participants, 35,119 were employed full-time in nursing at baseline. Among them, 769 women with missing data for HLD use or potential confounders, and 6,895 women who reported asthma diagnosis before or at baseline, were excluded.

Among the 27,455 women without asthma at baseline, follow-up data were available for 17,280 (63%), who were eligible for the current analysis (online supplementary Figure E1).

At baseline, participants were on average 34 years old (range 20-52 years; age did not differ according to asthma status, p=0.14); 93% were white, 19% were current smokers and 5% were ex-smokers. Regarding HLD use, 16% of the nurses reported 1-5 years of use, and 11% reported >5 years of use, in their career until baseline. Nurses reporting >5 years of HLD use were older, more often ex-or current-smokers and more often had BMI ≥30 kg/m2 (online supplementary Table E1). Among 800 (5%) nurses reporting current HLD use at baseline (at least 1h per week in past month), 17% reported using a disinfection system with dedicated ventilation and 13% reported using respiratory protection sometimes or always.

During 67,392 person-years of follow-up (mean follow-up: 3.8 years), 391 nurses reported incident clinician-diagnosed asthma. In multivariable models, nurses who reported 1-5 years of HLD use did not differ from nurses who reported never using HLD or <1 year of use (Table 1). In contrast, nurses who reported >5 years of HLD use had a significantly increased risk of incident asthma (adjusted hazard ratio [95% CI], 1.38 [1.03-1.85]).

We examined the number and type of HLDs currently used among nurses with >5 years of HLD use, using as reference group nurses who never used HLD or had ≤5 years of use. The risk of incident asthma was elevated but not statistically significant in those reporting current use of ≥2 products (1.72 [0.88-3.34]). The risk of incident asthma was significantly increased in women with >5 years of HLD use but no current use (1.46 [1.00-2.12]). When examining the types of HLDs (Table 1) or use of protective equipment (online supplementary Table E2) in the past month, effect estimates were imprecise due to low numbers and we observed no significant associations. Statistical power also was limited for the age-stratified analysis (online supplementary Table E3) but we observed the association between >5 years of HLD use (vs. never or ≤5 years) and incident asthma among the nurses <34 years old at baseline (1.75 [1.03-2.98]) and not among the older nurses (1.27 [0.90-1.78]; Pinter=0.23).

DISCUSSION

We found that occupational use of HLD among US and Canadian female nurses was associated with increased risk of developing asthma. These findings are based on a prospective study of 17,280 early to mid-career nurses (mean age: 34 years) with a mean follow-up time of ~4 years.

Our results are consistent with many cross-sectional and a few longitudinal studies on disinfectants and cleaning products (DCPs) [START_REF] Folletti | Update on asthma and cleaning agents[END_REF]. Three European cohorts reported a prospective association of occupational exposure to DCPs with increased risk of asthma development [START_REF] Kogevinas | Exposure to substances in the workplace and new-onset asthma: an international prospective population-based study (ECRHS-II)[END_REF][START_REF] Ghosh | Asthma and occupation in the 1958 birth cohort[END_REF][START_REF] Lillienberg | Occupational Exposure and New-onset Asthma in a Population-based Study in Northern Europe (RHINE)[END_REF], although none of these studies specifically examined the role of HLDs. In contrast, in a longitudinal study in an older population (aged 55 years at baseline on average), drawn from a related cohort of US registered nurses, we did not observe any association between current occupational exposure to DCPs, including HLDs, and asthma incidence [START_REF] Dumas | Occupational exposure to disinfectants and asthma incidence in U.S. nurses: A prospective cohort study[END_REF].

We hypothesized that this result was due to a healthy worker survivor effect, as the study selected women free of asthma after several decades in nursing, and, therefore, likely excluded the most susceptible individuals. In the current study of early-to mid-career nurses, despite the significant association between HLD use and asthma incidence, sensitivity analyses also hinted a healthy worker effect. First, although the association with asthma incidence was observed for duration of HLD use >5 years, it was only observed among younger nurses (≤33 years old at baseline) in analyses stratified by age group, where age is considered as a surrogate for the number of years in nursing. Second, when examining the number of products used currently in addition to duration of use, the association was only observed for nurses with no current use of HLD at baseline. These findings emphasize the challenge of addressing the healthy worker effect, even in longitudinal studies. The literature suggests that respiratory health effects of DCPs should be investigated from very early career onward. Moreover, since workers may reduce the use of products before asthma diagnosis, complete exposure history is preferable.

The fact that the association between HLD use and asthma incidence was observed among nurses who no longer used HLD at baseline may also suggests that for many nurses, asthma diagnosis possibly occurred several years after reduction of exposure. In occupational asthma, an average duration of several years between first symptoms and diagnosis has been reported [START_REF] Descatha | Factors associated with severity of occupational asthma with a latency period at diagnosis[END_REF], and it is common that symptoms persist after exposure reduction or cessation [START_REF] Rachiotis | Outcome of occupational asthma after cessation of exposure: a systematic review[END_REF]. In addition, HLD are thought to cause asthma predominantly through an irritant mechanism [START_REF] Folletti | Update on asthma and cleaning agents[END_REF], and irritant-induced occupational asthma is particularly difficult to diagnose [START_REF] Vandenplas | EAACI position paper: Irritant-induced asthma[END_REF]. Thus, our results may reflect a delayed diagnosis or under-diagnosis of irritant-induced occupational asthma in nurses.

In our study, asthma was defined based on a single question on clinician-diagnosed asthma at baseline and in follow-up questionnaires, which is a limitation. However, the validity of self-reported health outcomes in cohorts of nurses is generally high [START_REF] Colditz | Validation of questionnaire information on risk factors and disease outcomes in a prospective cohort study of women[END_REF].

Moreover, in analyses conducted in a similar nursing cohort in which more detailed information on asthma was collected, results were unchanged regardless of the asthma definition (single question or a refined definition based on supplementary questionnaires) [START_REF] Dumas | Asthma history, job type and job changes among US nurses[END_REF]. Occupational use of HLD was also self-reported, which may raise questions regarding both differential and nondifferential exposure misclassification [START_REF] Donnay | Under-estimation of self-reported occupational exposure by questionnaire in hospital workers[END_REF]. As history of HLD use was evaluated before the report of asthma diagnosis, differential recall bias is unlikely.

However, the HLD use was only evaluated at baseline, and the use of specific products was evaluated in the past month, which may not reflect past exposure. Moreover, nurses may not know precisely the chemicals they use for high-level disinfection [START_REF] Donnay | Under-estimation of self-reported occupational exposure by questionnaire in hospital workers[END_REF]. Thus, non-differential misclassification may have affected the analyses of duration of HLD use and specific HLDs, and driven associations toward the null. This may partly explain why no significant associations with asthma were observed in analyses of specific HLDs. In addition, the occupational questionnaire was not specifically designed to study risk factors for asthma [START_REF] Gaskins | Occupational use of high-level disinfectants and fecundity among nurses[END_REF].

Consequently, questions were limited to HLDs and a potential role of low/medium level DCPs in asthma could not be evaluated. Similarly, no information regarding the use of latex gloves was available in NHS3. However, our work in the Nurses' Health Study II [START_REF] Dumas | Occupational exposure to disinfectants and asthma control in US nurses[END_REF] and other studies [START_REF] Wiszniewska | Occupational allergy: respiratory hazards in healthcare workers[END_REF] suggest that latex exposure is no longer the major concern for respiratory health among healthcare workers, most likely because of the reduction in the use of powdered latex gloves.

The use of ventilation systems or respiratory protections when handling HLDs was relatively limited, as previously reported [START_REF] Henn | Precautionary practices of healthcare workers who disinfect medical and dental devices using high-level disinfectants[END_REF]. Low numbers prevented a meaningful analysis on their impact on the association between HLD use and asthma. Although elimination of hazardous substances is generally a preferred measure in the prevention of work-related asthma, the role of protective equipment in modulating asthma risk warrants further investigation.

In summary, our results add longitudinal evidence to an association between occupational exposure to disinfectants and asthma development, and encourage the development of asthma prevention strategies compatible with infection control in healthcare settings [START_REF] Quinn | Cleaning and disinfecting environmental surfaces in health care: Toward an integrated framework for infection and occupational illness prevention[END_REF].

Table 1

 1 Prospective association between use of high-level disinfectants (HLDs) and asthma incidence in female nurses, n=17,820 HR, hazard ratio; CI, confidence interval; HLD, high-level disinfectant. Multivariable models were adjusted for age, race, ethnicity, smoking status and body mass index. Use of HLD was evaluated by questionnaire at baseline. Results in boldface are statistically significant. * In the past month. † HR not calculated because of low number of exposed cases.

		Person-	No. of	Age-adjusted HR	Multivariable-
		years	cases			adjusted HR
				HR	95% CI	HR	95% CI
	Duration of HLD use
	Never or <1 year (ref.)	48,100	276	1	-	1	-
	1-5 years	10,247	58	0.98	0.74-1.30	0.96	0.73-1.28
	>5 years	6,761	57	1.42	1.06-1.90	1.38	1.03-1.85
	Never or ≤5 years (ref.)	58,347	334	1	-	1	-
	>5 years	6,761	57	1.42	1.07-1.90	1.39	1.04-1.86
	Duration of HLD use and number of HLDs currently* used
	Never or ≤5 years (ref.)	58,347	334	1	-	1	-
	>5 years of use
	No current use	3,540	31	1.48	1.01-2.15	1.46	1.00-2.12
	Current use of 1 HLD	2,357	17	1.22	0.75-1.99	1.17	0.72-1.92
	Current use of ≥2 HLDs	864	9	1.77	0.91-3.45	1.72	0.88-3.34
	Duration of HLD use and type of HLDs currently* used
	Never or ≤5 years (ref.)	58,347	334	1	-	1	-
	>5 years of use
	Glutaraldehyde*	1869	18	1.61	1.00-2.59	1.55	0.96-2.49
	Ortho-phtalaldehyde*	529	4	1.24	0.46-3.34	1.20	0.44-3.22
	Peracetic acid* †	400	1	-	-	-	-
	Hydrogen peroxide*	841	9	1.79	0.92-3.48	1.73	0.89-3.37
	Other*	574	4	1.17	0.44-3.13	1.12	0.42-3.01
	Abbreviations:

Acknowledgments

The Nurses' Health Study 3 is coordinated at Harvard T.H. Chan School of Public Health and the Channing Division of Network Medicine, Brigham and Women's Hospital -both located in Boston, MA, USA. We would like to thank the participants and staff of the Nurses' Health Study 3 for their valuable contributions. We also thank Christina C Lawson (National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention, Cincinnati, Ohio, USA) for her participation in the creation of the occupational exposure questionnaires.

Funding

National Institute for Occupational Safety and Health R01 OH-10359; National Institutes of Health R24-ES028521-01, and U01-HL145386-01.

Authors' contributions: OD contributed to the study conception, the analysis and interpretation of the data, and primary manuscript preparation. AJG, SAH and JEC contributed to the acquisition and interpretation of the data and critical revision of the manuscript. KB, NLM, and RV were involved in the data interpretation and critical revision of the manuscript. CAC participated in the study conception, data interpretation and critical revision of the manuscript. All authors approved the final version of the manuscript and agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Competing Interests: Dr. Camargo reports grants from NIOSH/CDC and NIH during the conduct of the study. Dr. Chavarro reports grants from National Institute of Occupational Safety and Health, grants from National Institute of Environmental Health Sciences, grants from National Heart, Lung and Blood Institute, during the conduct of the study.

Disclaimer

The findings and conclusions in this report are those of the author(s) and do not necessarily represent the official position of the National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention.


V Savaux

Y Louët

PAPR Analysis of Non-Contiguous Duplex Multicarrier Signals

This paper deals with the peak to average power ratio (PAPR) of duplex multicarrier signals. A simple but accurate expression of the complementary cumulative distribution of the PAPR is suggested, based on both empirical and theoretical analyzes of the mean PAPR of such a continuous duplex signal. To this end, we show that the mean PAPR can be written in function of the frequency distance between the two signals composing the duplex one. The relevance and the accuracy of the suggested analysis are shown through simulations, and a discussion paves the way to further analyzes involving general multiplex signals with different powers and subcarriers numbers.

Introduction: Multicarrier signals (MC) are well known to be prone to high power fluctuations due to the inherent summation of independent information carried on different tones. These power fluctuations can be characterized through the ratio of the maximum instantaneous power and the mean power of the transmitted signal, which leads to the definition of the peak to average power ratio (PAPR). PAPR is a metric that is directly related to the instantaneous power fluctuations of a signal. When considering a power amplifier, the power budget is the ratio of the output power of the amplified signal and the supply power. As the output power is a function of the input power, the efficiency of the power amplifier is generally inversely proportional to the PAPR of the input signal. This is why PAPR reduction methods aim to mitigate the PAPR so as to drive the signal as close as possible to the saturation point of the power amplifier where the efficiency is the highest [START_REF] Louët | Global power ampliïň Ąer efïň Ąciency evaluation with PAPR reduction method for post-OFDM waveforms[END_REF].

While PAPR derivation is well known considering a single-band multicarrier signal [START_REF] Van Nee | Reducing the peak-to-average power ratio of OFDM[END_REF][START_REF] Van Nee | OFDM for wireless multimedia communications[END_REF][START_REF] Ochiai | On the Distribution of the Peak to Average Power Ratio in OFDM Signals[END_REF], very few works have been suggested for noncontiguous multiplex of signals [START_REF] Rajbanshi | Peak-to-Average Power Ratio Analysis for NC-OFDM Transmissions[END_REF][START_REF] Kryszkiewicz | PAPR analysis in noncontiguous OFDM systems[END_REF][START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF]. Nevertheless, this situation raises in contexts of heterogeneous signals transmission such as cognitive radio or 5G, when several non-contiguous signals, each associated to different users, have to be transmitted and amplified all together. In this context the resulting PAPR should not only depend on the signals themselves (respective number of subcarriers, respective mean powers, number of users) but on the frequency distance between the signals as well. Given these features, any opportunistic spectrum access or frequency resource allocation has to be evaluated on the PAPR criteria.

In [START_REF] Rajbanshi | Peak-to-Average Power Ratio Analysis for NC-OFDM Transmissions[END_REF][START_REF] Kryszkiewicz | PAPR analysis in noncontiguous OFDM systems[END_REF], the PAPR is analyzed only through simulations [START_REF] Rajbanshi | Peak-to-Average Power Ratio Analysis for NC-OFDM Transmissions[END_REF], and through upper bounds of the complementary cumulative distribution functions (CCDFs) [START_REF] Kryszkiewicz | PAPR analysis in noncontiguous OFDM systems[END_REF]. More recently, the authors in [START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF] derived a thorough study of the PAPR of multiplex signals with different numerology for an application to 5G technology. Although the theoretical expression of the PAPR generally well matches the simulations results, it is not easily tractable in practice. Furthermore, the authors in [START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF] did not specifically analyze the effect of the frequency gap between signals on the PAPR behavior.

In this paper we suggest handling this PAPR issue by considering the combination of two non contiguous OFDM signals with the same number of carriers and power. A simple and tractable expression of the CCDF of PAPR is proposed, based on both theoretical and empirical original analyzes of the mean PAPR of duplex multicarrier signals. The resulting PAPR is evaluated with the frequency distance between the two spectra, and we show the relevance of the derived results through simulations. In particular, we show that the PAPR of a duplex signal increases when the frequency distance between signal increases, but it reaches an upper bound. Moreover, we discuss the results to provide leads for further studies including more general multiplex of multicarrier signals as in [START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF]. This PAPR analysis can be useful to any engineer or researcher seeking to rapidly evaluate the PAPR of duplex multicarrier signals without need of sophisticated functions.

The remainder of the paper is organized as follows. The PAPR of the duplex signal is derived in Section after the statement of the problem given in Section . Simulations are provided in Section and a conclusion ends the paper in Section .

Problem Statement:

We consider a duplex multicarrier signal x(t) composed of two signals x 1 (t) and x 2 (t) as

x(t) = x 1 (t) + x 2 (t), (1)
or x 2 (t) is then Bw = N Bsc.
The time-frequency representation of x 1 and x 2 is illustrated in Fig. 1. The sampled version of x i (t), i ∈ {1, 2}, at Nyquist rate ts, is noted x i,n with n = 0, 1, .., N -1. In this case, the observation window can be rewritten as T = N ts. If N is larger than about ten subcarriers, it can be reasonably assumed that the samples x i,n are independent and identically distributed (iid) and x i,n obey a complex Gaussian distribution, i.e.

x i,n ∼ CN (0, σ 2 ), where σ 2 = E{|x i,n | 2 } [8]
, with E{.} the mathematical expectation. Under this assumption, Van Nee et al. suggested an expression of the CCDF of the PAPR of x i (t), i = 1, 2, expressed as [START_REF] Van Nee | Reducing the peak-to-average power ratio of OFDM[END_REF][START_REF] Van Nee | OFDM for wireless multimedia communications[END_REF][START_REF] Ochiai | On the Distribution of the Peak to Average Power Ratio in OFDM Signals[END_REF]:

CCDF (λ) =P max t∈ 0,T |x i (t)| 2 σ 2 ≥ λ (2) ≈1 -(1 -e -λ ) αN , (3)
where P(E) means "probability of the event E", and α is an adjusting parameter that has been empirically set to α = 2.8 in [START_REF] Van Nee | Reducing the peak-to-average power ratio of OFDM[END_REF]. The popularity of the CCDF expression in (3) lies in its simplicity and its good accuracy.

In fact, the PAPR of a continuous multicarrier signal can be properly approximated by knowing its subcarriers number only. Therefore, it is relevant to suggest a simple expression of the CCDF of the PAPR of the duplex multicarrier signal x(t) in a Van Nee's fashion. To this end, we empirically set different α values in function of ∆ f thanks to the mean PAPR of the duplex multicarrier signal. The developments are hereby derived. Nevertheless, limitations of Van Nee's model have been stated in [START_REF] Ochiai | On the Distribution of the Peak to Average Power Ratio in OFDM Signals[END_REF][START_REF] Jiang | Derivation of PAPR Distribution for OFDM Wireless Systems Based on Extreme Value Theory[END_REF], such as the lack of theoretical justification. We hereby use this approach for its simplicity, but we will, in turn, fairly discuss the suggested adaptation of (3) to duplex signals in Section .

PAPR Analysis:

We assume that the CCDF of the PAPR of a multicarrier duplex signal x(t) in ( 1) can be expressed as in [START_REF] Van Nee | OFDM for wireless multimedia communications[END_REF], where the coefficient α needs to be defined. This assumption will be verified through simulations.

To do so, on one hand we theoretically derive the mean of the PAPR as a function of α (it must be emphasized that the mean of PAPR has no practical significance, but in this paper, it is used as a trick of arithmetic to derive α). On the other hand, we empirically express the mean of PAPR as a function of the frequency distance ∆ f . From these two developments, we obtain a simple expression of the CCDF of PAPR with a coefficient α as a function of ∆ f .

Proposition 1: We define µ as the mean PAPR of the signal x(t) in [START_REF] Louët | Global power ampliïň Ąer efïň Ąciency evaluation with PAPR reduction method for post-OFDM waveforms[END_REF]. For large N value (N ≥ 128), the mean PAPR can be simply expressed as

µ = γ + ln(αN ), ( 4
)
where γ is the Euler-Mascheroni constant, γ ≈ 0.577, and ln(.) is the natural logarithm.

ELECTRONICS LETTERS 12th August 2020 Vol. 00 No. 00

Proof: In order to develop the mean of PAPR, we rewrite the CCDF in (3) by using the binomial series expansion of (1e -λ ) αN as

CCDF (λ) =1 - +∞ k=0 αN k (-1) k e -kλ (5) = - +∞ k=1 αN k (-1) k e -kλ , (6)
where αN k is the generalized binomial coefficient. The distribution of the PAPR, defined as f (λ) = ∂(1-CCDF (λ)) ∂λ , is then obtained as

f (λ) = - +∞ k=1 αN k (-1) k ke -kλ , (7)
hence the mean is derived as

µ = +∞ 0 λf (λ)dλ = - +∞ k=1 αN k (-1) k k . (8)
For large αN value, we have

αN k ∼ (αN ) k k! , then (8) yields µ = - +∞ k=1 (αN ) k (-1) k kk! . (9)
From [START_REF] Abramowitz | Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables[END_REF], we know that the series expansion of the exponential integral defined for any z ∈ C\R -as

E 1 (z) = +∞ z e -t
t dt leads to

E 1 (z) = -γ -ln(z) - +∞ k=1 (-1) k z k kk! . ( 10
)
Since lim z→+∞ E 1 (z) = 0, and reminding that we assume large αN , then the substitution of z = αN into (10) leads to (4), which concludes the proof.

It can be noticed that this result is very similar to those in [START_REF] Ochiai | Peak-Power Reduction Schemes in OFDM Systems : A Review[END_REF][START_REF] Savaux | PAPR Analysis as a Ratio of Two Random Variables: Application to Multicarrier Systems with Low Subcarriers Number[END_REF] where Nyquist-sampled signals are considered. Thus, µ in (4) can be seen as a generalized expression of the mean PAPR. From (4), we notice that the α coefficient can in turn be expressed in function of the mean µ as

α = exp(µ -γ) N . (11)
In order to obtain α relatively to the frequency distance ∆ f , we empirically express µ as a function g of ∆ f such as suggested in Proposition 2. For convenience, and in order to make the expression g independent of the bandwidth Bw, we set θ = ∆ f Bw .

Proposition 2: Consider a non-contiguous duplex multicarrier signal x(t) such as defined in [START_REF] Louët | Global power ampliïň Ąer efïň Ąciency evaluation with PAPR reduction method for post-OFDM waveforms[END_REF]. Let θ ∈ R + , then the mean PAPR µ of x(t) can be expressed as a function of θ as µ =g(θ) [START_REF] Savaux | PAPR Analysis as a Ratio of Two Random Variables: Application to Multicarrier Systems with Low Subcarriers Number[END_REF] =βν exp(-q.θ c ), (13) where β, ν, q, and c are positive parameters that need to be determined. It can be noted that µ in (13) is a strictly increasing function of θ, which is upper bounded by β.

The four parameters can be assessed as follows:

• β = lim θ→+∞ µ, even though in practice θ should feature low values due to the limitations of the transmitter in term of bandwidth.

• Once β is obtained, we deduce ν by means of the equality g(0) = βν, which corresponds to the mean PAPR of a continuous (at least largely oversampled) signal featuring N subcarriers. In practice, this case should not happen since it means that x 1 and x 2 overlap since f 1 = f 2 , but for the sake of the analysis, it allows us to deduce ν. • Similarly, q can be deduced thanks to g(1) = βνe -q , which corresponds to the mean PAPR of a continuous signal featuring 2N contiguous subcarriers. 1.5

• Let us note θ o = sup θ∈R + ∂g(θ)
∂θ , then c can be deduced by solving

∂ 2 g(θ o ) ∂θ 2 = 0.
In fact, a unique solution θ o exists, leading to a unique

solution to ∂ 2 g(θ o ) ∂θ 2
= 0 as well. Alternatively, the parameter c can be empirically set to fit the behavior of µ in function of θ obtained through simulations.

To summarize our approach, we suggest estimating the CCDF of PAPR of duplex multicarrier signal x(t) in (1) by using a simple Van Nee-like expression as in [START_REF] Van Nee | OFDM for wireless multimedia communications[END_REF] where the coefficient α must be defined. To this end, we theoretically express α as a function of the mean PAPR µ in (11) on one hand. On the other hand, we empirically derive an expression of µ in (13) as a function of the frequency distance ∆ f (or equivalently θ) between the two multicarrier signals that compose the duplex. Then, substituting the empirical mean µ into (11) finally leads to the simple expression of CCDF of PAPR [START_REF] Van Nee | OFDM for wireless multimedia communications[END_REF].

Simulations: This section aims to evaluate the relevance of the previous developments through simulations. Both signals x 1 and x 2 are composed of N subcarriers with N ∈ {128, 256, 512}, carrying elements that are randomly taken from a 16-QAM constellation. We assume that x 1 and x 2 are synchronized in time, even though time synchronization should not have influence on the PAPR value, according to "remark 2" in [START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF]. A large oversampling rate of R = 32 is considered in order to approximate continuous signals, and at least to respect the condition ∆ f << R ts for reasonable ∆ f range. When this condition does not hold, some simulations artifacts appears when ∆ f > R 4ts (i.e. when ∆ f is too close to the sampling frequency), which are not further described in this paper. All the simulations results have been averaged over 10000 independent runs. Fig. 2 shows the mean PAPR µ (linear scale) versus θ for a duplex signal x(t) featuring 128 subcarriers per signal x i (t), i = 1, 2. The behavior of µ has been obtained by simulation, and allows us to deduce the four parameters β, ν, q, and θ o (leading to c), such as highlighted by the different markers. The corresponding values have been reported in Table 1, for N = 128, 256, and 512. We observe from Fig. 2 that µ is strictly increasing with θ, and reaches an upper bound for θ ≥ 4.

It is worth noticing from Table 1, that β and ν depend on θ, whereas q and c are constant. Furthermore, ν tends to 1.5 when N increases. We deduce that, for N large (typically N ≥ 512) it is sufficient to assess β for θ ≥ 4 to estimate µ for any θ, which further simplifies the PAPR estimation. Otherwise, further simulations have shown that both β and ν must be set when N < 512. In Fig. 3, we compare the mean PAPR µ versus θ for 128, 256, and 512 subcarriers per signal, obtained through simulations and from (13) using the parameters in Table 1. It can be observed that the empirical µ values in function of θ perfectly match the trajectories obtained through simulations, therefore validating (13). For applications, we deduce from results in Fig. 3 that it is preferable to transmit the signals x 1 and x 2 in contiguous bands (i.e. θ = 1), when possible, as it minimizes the PAPR. However, in practice, other parameters should be considered to properly design the system, such as the synchronization between signals (synchronization mismatch between x 1 and x 2 would lead to interference), or the possible intermodulation distortions that may cause disruptions in both x 1 and x 2 , but this is not dealt with in this paper.

Fig. 4 compares the trajectories of CCDF (λ) versus λ (dB) obtained through simulations with that obtained with (3). N = 256 subcarriers are considered, and θ = 1, 3. The corresponding α values are 5.68 and 11.45, respectively. It can be seen that the curve obtained from analysis for θ = 1 matches that obtained through simulations. Moreover, it should be noticed that α/2 = 2.82, which almost corresponds to the empirical value α =2.8 defined in [START_REF] Van Nee | Reducing the peak-to-average power ratio of OFDM[END_REF] by Van Nee. Note that we find α/2 = 2.7 and α = 3.02 for N = 128, and N = 512, respectively. We then deduce that the suggested approach allows to adapt α value according N in Van Nee model (i.e. θ = 1). It can be seen for θ = 3 that the results obtained from analysis slightly underestimate the CCDF of PAPR obtained through simulations (of about 0.05 dB). The suggested analysis is nevertheless an accurate approximation of the CCDF of PAPR regarding the simplicity of the expression.

Discussion: Developments and simulations results have shown that the PAPR of duplex multicarrier signals can be simply but accurately approximated in a Van Nee's fashion where the α coefficient is function of the frequency distance ∆ f between the signals x 1 and x 2 . However, we voluntary limited the analysis to the case where x 1 and x 2 are equipowered and share the same number of subcarriers. A similar but more general study case could then be carried out in case the two signals do not share the same parameters. In this case, the four parameters β, ν, q, and c should be tuned with respect to the different powers and subcarriers numbers of x 1 and x 2 . To go further, the present analysis could even be extended to derive simple expressions of the CCDF of PAPR of multiplex multicarrier signals such as considered in [START_REF] Liu | Peakto-Average Power Ratio Analysis forOFDM-Based Mixed-Numerology Transmissions[END_REF][START_REF] Jiang | Derivation of PAPR Distribution for OFDM Wireless Systems Based on Extreme Value Theory[END_REF]. In that case, a more general mean PAPR expression µ = g(θ 1 , θ 2 , .., θ M -1 ) should be considered, where M is number of signals composing the multiplex one, and θ i are the corresponding frequency distances.

In addition, it must be emphasized that the function g in ( 13) is empirically derived. Although Fig. 3 shows that g accurately matches simulations, an analytical derivation of g should be investigated as well. Other studies could be undertaken from the present paper, such as the analyze of the instantaneous signal envelope |x(t)| instead of |x(t)| 2 , and its adaptation to duplex signals featuring low subcarriers numbers (typically N ≤ 64) by using results in [START_REF] Savaux | PAPR Analysis as a Ratio of Two Random Variables: Application to Multicarrier Systems with Low Subcarriers Number[END_REF].

Conclusion:

This paper highlights the dependency between the frequency distance between signals composing a non-contiguous duplex signal and the resulting PAPR. By deriving the mean PAPR of such kind of signal, we came to the conclusions that (i) the lowest PAPR value of the duplex is given when the two signals are contiguous in frequency, corollarilly (ii) the larger the frequency gap the larger the PAPR, but (iii) the mean PAPR is upper bounded for large frequency distance between the signals that compose the duplex. To go further, this study could be enriched by considering more than two users of unequal powers and different subcarriers numbers.

V. Savaux (Network Interfaces Lab, b<>com, Rennes, France), Yves Louët (CentraleSupélec, Rennes, France) E-mail: vincent.savaux@b-com.com

Fig. 2

 2 Fig. 2 Mean PAPR µ as a function of θ, for 128 subcarriers per signal. Markers indicate the values from which the parameters β, ν, q, and θ o (leading to c) are deduced.

Fig. 3

 3 Fig. 3 Mean PAPR µ as a function of θ, for 128, 256, and 512 subcarriers per signal. Comparison of simulations and analysis (13).

1 Fig. 4 CCDF

 14 Fig. 4 CCDF (λ) versus λ (dB) for N = 256, θ = 1, 3. Comparison between simulations and analysis.

  Time-frequency representation of duplex of multicarrier signals x 1 and x 2 transmitted at frequencies f 1 and f 2 .where t belongs to an observation window of duration T , i.e. t ∈ [0, T ]. Typically, T corresponds to the duration of an OFDM symbol. Moreover, we assume that x 1 and x 2 are non-contiguous in the frequency domain, i.e. x 1 is transmitted at frequency f 1 and x 2 at frequency f 2 such that we define the frequency distance ∆ f = f 2f 1 . Without loss of generality, we arbitrarily consider that f 2 ≥ f 1 . Furthermore, we assume that x 1 and x 2 are composed of the same number of subcarriers denoted by N with a common subcarrier spacing Bsc. The total bandwidth of each signal x 1 (t)

			t
	amplitude	T	B w x 1		x 2 B w
			...
	0	B sc	f 1	✁ f	f 2	f
	Fig. 1

Table 1 :

 1 Parameters β, ν, q, and c obtained from simulations.

	parameter	N	value
	β	{128, 256, 512}	{7.83, 8.6, 9.36}
	ν	{128, 256, 512}	{1.45, 1.49, 1.5}
	q	{128, 256, 512}	0.7
	c	{128, 256, 512}