text:
Dahoun

J Martin

M Ponçot

J M Hiver

P Bourson

A Dahoun

Real-time Raman spectroscopy measurements to study the uniaxial tension of isotactic polypropylene: a global overview of microstructural deformation mechanisms

Keywords: Polymer, Deformation, Crystallinity index, Molecular orientation, Real-time

Real-time Raman spectroscopy measurements to study the uniaxial tension of isotactic polypropylene: a global overview of microstructural deformation mechanisms

Introduction

Macroscopic properties of materials, such as the mechanical behaviour, are closely related to their microstructures [START_REF] Ward | Mechanical Properties of Solid Polymers[END_REF] . In the case of semi-crystalline polymers, the crystallinity index and the molecular orientation in crystalline and amorphous phase are considered to be essential factors to understand this relationship and to optimise their end-use properties [START_REF] Ward | Mechanical Properties of Solid Polymers[END_REF][START_REF] Samuels | Structured Polymer Properties: The Identification, Interpretation, and Application of Crystalline Polymer Structure[END_REF][START_REF] Young | Introduction to Polymers[END_REF] . At the macroscopic scale, mechanical properties of such materials are determined on normalized sample shapes using conventional uniaxial tensile tests [START_REF] Sell | Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] . At the microscopic scale, a number of indirect analytical techniques can be used to investigate the microstructure such as thermal analysis, microscopic observations, X-ray scattering, birefringence and Nuclear Magnetic Resonance (NMR) [START_REF] Wunderlich | Macromolecular Physics: Crystal Structure, Morphology, Defects[END_REF][START_REF] Gedde | Polymer Physics[END_REF][START_REF] De Vries | In Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] . By collecting both these macroscopic and microscopic data, numerous experimental works have attempted to associate one state of deformation (such as the strain level) to one state of microstructure (such as molecular orientation) in order to propose elementary descriptive models of the deformation micro-mechanisms [START_REF] Hay | [END_REF][9][START_REF] Schultz | Polymer Materials Science[END_REF][START_REF] Petermann | [END_REF][START_REF] Friedriech | Advances in Polymer Science, Crazing in Polymers[END_REF] . A good review of these deformations mechanisms has been published by Bowden and Young [START_REF] Bowden | [END_REF] . In that vein, the papers of Peterlin 9 , focused on polyethylene and polypropylene, developed the first models showing how the crystalline structure are sheared, rotated and fragmented under uniaxial tension. Numerous studies have improved existing models by introducing the metallurgical concept of dislocation and glide systems involving slip within the lamellar crystals during the yielding [14][15][16] . Contribution of amorphous phase was then introduced by Treloar et al. [START_REF] Treloar | The Physics of Rubber Elasticity[END_REF] , Young et al. [START_REF] Young | [END_REF] and Bartczak et al. 19 and then computed by Van der Giessen et al. 20 and G'Sell et al. 21 by considering a composite approach of the material. Central role of tie molecules localized in the interlamellar layers in determining viscoelastic, plastic deformation, and failure was evidenced in pioneering works by Nitta and Takayanagi 22,23 .

However, in many cases, evidence of these mechanisms is debatable for two major experimental limits. i) In the case of ductile materials which experience a pronounced necking due to their plastic instability (such as polymers), conventional mechanical tests used widely by the past and giving access to the nominal stressstrain curve are inappropriate to reveal their intrinsic mechanical behaviour at prescribed temperature and strain rate [START_REF] Sell | In Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] . In order to perform quantitative measurements, geometry variations in the necking zone of the stretched sample have to be taken into account along the entire course of the tensile test [START_REF] Sell | [END_REF]26 . ii) Furthermore, conventional analytical techniques suffer from a common difficulty related to their rather elaborate instrumental set-up, often costly and bulky, which requires in most of the cases post mortem analysis and destructive sampling procedure coupled with serious risks of structural damage. For accurate measurements, one has to consider the microstructural evolution in real-time with the deformation especially to avoid the material recovering which occurs after sample unloading [START_REF] Treloar | The Physics of Rubber Elasticity[END_REF][27][28][START_REF] Escaig | In Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] . The main purpose of this work is thus to overcome these two experimental difficulties by coupling two original experimental instruments: i)

On the one hand, by using a video-controlled testing device (called VidéoTraction TM ), developed in our laboratory by G'Sell and Hiver [START_REF] Sell | French Patent #010542100[END_REF][31][32] , the true constitutive mechanical behaviour of semi-crystalline polymers is determined under a constant true strain rate by taking into account the plastic instability of the polymer which occurs during de deformation.

ii) On the other hand, a Raman spectrometer is coupling to the tensile test machine allowing in situ acquisitions. Due to its recent instrumental improvements in particular the advent of laser radiations and the development of Couple Charge Device (CCD) detectors, Raman spectroscopy is adapted for polymer microstructure characterization with reliability, rapidity and commodity [33][START_REF] Spells | Characterization of Solid Polymers: New Techniques and Developments[END_REF][START_REF] Xue | [END_REF] . It gives access to the vibrational frequencies of the covalent chemical bonds of polymers and allows analysis of molecular species at different scales, from the chemical repetitive unit to the conformational architecture of the macromolecular chain 36, In this paper, we propose to apply this experimental set-up in a practical application e.g. to follow the microstructural evolution of an isotactic polypropylene in real-time with its uniaxial stretching over a large true strain range, from the elastic to the stress hardening deformation domains. Major microstructural features are considered such as the crystallinity index, the molecular orientation (both in crystalline and amorphous phase) and the stress distribution at the chemical bonds scale. On this point, Colomban et al. [START_REF] Colomban | [END_REF]39 report some valuable in situ results performed on polyethylene terephtalate (PET), polyamide 66 (PA66)

and isotactic polypropylene (iPP). However these investigations are based on the lowwavenumber spectral range of the Raman spectrum (collective modes) and the deformation domain under consideration was limited to the viscoelastic response of the polymers.

Moreover numerous studies relating Raman spectroscopy in situ measurements deal with the stress-induced Raman wavenumber shifts [40][START_REF] Hendra | Polymer Spectroscopy[END_REF][START_REF] Rodriguez-Cabello | [END_REF][43] but only few papers about Raman bands intensity 44,45 .

On the basis of previous elementary descriptive models, our results are principally discussed in terms of deformation micro-mechanisms explaining relationship between the polymer mechanical behaviour and its microstructure.

Experimental details

Material

The investigated polypropylene was manufactured by Atochem under the reference 3050 MN1. This natural isotactic grade is characterized by a relatively broad molecular weight distribution, as assessed by gel permeation chromatography, with M w = 262000 g.mol -1 and M n = 75900 g.mol -1 . Pellets of the polymer were subsequently processed by injectionmolding into 4 mm thick plates (Apollor, Lunéville, France). The density of the material is firstly determined by hydrostatic weighting,  = 0.916 g.cm -3 . Based on density values published in the literature for perfectly crystalline and amorphous phase ( c = 0.946 g.cm -3 and  a = 0.854 g.cm -3 , respectively [START_REF] Wunderlich | Macromolecular Physics: Crystal structure, Morphology, Defects[END_REF] ), the weight index of crystallinity, <X c >, is found to be equal to 67 %. This value is confirmed by Differential Scanning Calorimetry (DSC) measurements performed at a heating rate of 10 °C.min -1 showing a melting point located at T m = 165 °C with an enthalpy of fusion, H m , equal to 109J.g -1 . This corresponds to a weight index of crystallinity of about 66 % (the theoretical enthalpy of fusion considered for a perfect crystal of infinite size, H t,m is 165 J.g -1 ) [START_REF] Wunderlich | Macromolecular Physics: Crystal structure, Morphology, Defects[END_REF] . The glass transition temperature, T g , is measured Observations show spherulites of about 55 µm average diameter.

Experimental set-up and samples

To follow evolution of the iPP microstructure in real-time with its uniaxial deformation, we customized a system coupling a video-controlled tensile machine with a Raman microspectrometer. A schematic view of this experimental set-up are displayed inref. 56.

The video-controlled mechanical testing method used here is the latest version of the VidéoTraction  system developed by G'Sell and Hiver [START_REF] Sell | French Patent #010542100[END_REF] . This device provides direct access to the true mechanical behaviour of polymers under uniaxial tension at prescribed temperature, T, and strain rate, zz ε .

, up to very large levels of deformation, even plastic instabilities (necking) appear. Along the entire course of a tensile test, geometry instabilities localized in the necking zone of the polymer sample are taken into account by video measurements. The VideoTraction  system, widely described in previous papers by G 'Sell et al. 31,32 and Addiego et al. 48 Raman spectra are collected in backscattered geometry using an iHR250  spectrometer developed by Horiba Jobin Yvon (Lille, France) linked to a remote head of probe by means of two optic fibres: one fibre for sending the incident radiation to the sample and the second one for collecting and sending the backscattered radiation to the spectrometer. The head of probe, placed in face to face to the video-controlled system, is equipped with an Olympus long working distance objective lens (x 50 as objective length, x 500 as total magnification, 12 mm as focal distance). Laser radiation coming from a diode laser, producing a  = 785 nm wavelength radiation, is maintained focused onto the flat surface in the predefined RVE zone of the test sample where necking is expected. At maximum laser power (300 mW), the probe typically delivers an illumination power density of about 15 mW.µm -2 . The head of probe is also equipped with a linear polarizer and analyser which allow polarizing the incident laser beam and the Raman scattering radiation, respectively. Rayleigh scattered light is eliminated through a holographic Notch filter placed on the light path just before the diffraction grating (1200 grooves.mm -1 ). The spectral resolution achieved is about 0.5 cm -1 . Previously, the Raman shift is calibrated using a reference sample of pure silicon which shows a well reported scattering band at 521 cm -1 . A micro-computer interfaced with the spectrometer allows recording raw spectra by means of the Labspec  acquisition software (Horiba Jobin Yvon, Lille, France). A self-written fitting least-square procedure based on the Levenberg-Marquardt method is used to process raw data 49 . Residual fluorescence background is eliminated by a polynomial baseline cutting procedure. A mixed Gaussian-Lorentz function is used to decompose each scattering band and the final adjustment gives access to the useful spectral features such as position,  (cm -1 ), integrated intensity, I (a.u), and full width at half maximum, FWHM (cm -1 ).

The test specimens are machined out from the injection-molded plates using a computercontrolled milling machine (CharlyRobot CRA4) following a thin film geometry as described in ref.

Measurement procedures

To describe microstructure of iPP under deformation, 4 microstructural features are considered such as i) the cristallinity index, ii) the orientation of macromolecules in the crystalline phase, iii) the orientation of macromolecules in the amorphous phase, iv) the distribution of stress at the chemical bonds scale. For each, we adopted a particular Raman spectral criterion developed in our previous study [51][52][53][54][55][56] on the basis of fundamental works on vibrational mode assignments [57][58][59][60][61] . Table 1 summarized the vibrational mode assignments and the phase belonging (crystalline and/or amorphous) of the Raman scattering bands used to design theses spectral criterions.

The crystallinity, index noted <X c >, is deduced from depolarized Raman spectroscopy measurements by determining the criterion R c = (I 809 +I 842 ) / (I 835 +I 809 +I 842 ) of integrated intensity of scattering bands located at 809 (60 % crystalline), 835 (0 % crystalline) and 842 cm -1 (65 % crystalline) (Table 1). Due to the fact that bands at 809 and 842 cm -1 are not pure crystalline bands, we proposed in a previous study to adjust R c by balancing factors in order to estimate <X c > according to the following matching relation :

(

The molecular orientation is estimated from Raman spectroscopy by performing measurements in a particular polarization geometry of the incident and scattered radiations noted x(zz)x (as Porto's notation 62 ) where both the incident and scattered radiations are polarized along the z-stretching direction. In these conditions, we demonstrate in previous papers that the ratio R orient,c = I 973 / I 998 of the integrated intensity of the two particular Raman The position dependence of Raman bands versus applied stress, commonly called stressinduced Raman shifts, is of fundamental importance in understanding how a macroscopic stress is distributed at the chemical bonds scale [START_REF] Hendra | Polymer Spectroscopy[END_REF][START_REF] Rodriguez-Cabello | [END_REF][43] . These wavenumber shifts are interpreted on the basis of the anharmonicity of chemical bonds, stress inducing an interatomic distance alteration which changes the atomic vibration frequencies 39 . Shifts are expected different according to the nature of the chemical bonds and their orientation towards the macroscopic applied stress direction. A shift towards the low wavenumbers means that bonds are under an extension stress while a shift towards the high ones is related to a compressive stress. In a depolarized configuration, we proposed to follow the normalized shift evolution, R s 809 = 809 / 0 809 , R s 835 = 835 / 0 835 and R s 842 = 842 / 0 842 of bands at 809, 835 and 842 cm -1 in function of the true axial strain  zz .  0 809 is the reference position of the 809 cm -1 band reported for no applied stress. Objective is to explore the evolution of stress distribution both in crystalline (809 and 842 cm -1 ) and amorphous phase (835 cm -1 ) during the deformation.

Results

Mechanical behaviour

Uniaxial tension of the iPP was performed at T = 30 °C remaining a constant axial true strain rate .

ε zz = 5.10 -3 s -1 . Evolution of the true axial stress -strain curve ( zz - zz ) is presented in ref. 56. Three different stages are noted. The first one,  zz = 0 -0.09, corresponds to the elastoviscoelastic behaviour of the iPP. The initial slope of the curve corresponds to the elastic Young's modulus, E = 1.7 GPa. The yield point is defined when stress  y zz achieves 36 MPa and passes through a round-off maximum at strain  y zz = 0.09. The second stage,  zz = 0.09 -0.8, corresponds to the soft-plastic deformation. At the beginning, stress is marked by a small but significant stress decrease while the deformation localizes in a sharp neck in the RVE (structural softening). This is then followed by a symmetric propagation of the neck shoulders towards the specimen heads at almost constant stress,  zz = 32 MPa (easy plastic flow). The last stage,  zz = 0.8 -1.6, termed as the plastic stress-hardening regime, shows a nearly exponential increase of the stress from 32 to 71 MPa.

Cristallinity index

Figure 1 shows fitted Raman spectra recorded in the useful spectral range 780 -860 cm -1 at growing true axial strain level,  zz = 0, 0.1, 0.8 and 1.4. Intensity of bands at 809 and 842 cm - 1 , which are characteristics of the crystalline phase, decreases regularly with the increasing deformation. On the contrary, intensity of one at 835 cm -1 , exclusively associated to the amorphous phase, increases with the increasing deformation. This observation evidences qualitatively a loss of crystallinity in iPP with deformation, chains initially present in the crystalline phase going through the amorphous one. On the same figure, we note shifts of bands. This point will be discussed further in details. Figure 2 presents evolution of the crystallinity index of iPP, <X c >, versus the axial true strain,  zz . It confirms the general decrease of the crystalline phase amount with the increasing deformation. Evolution marked a three-stage behaviour with the true axial strain,  zz : i) in the elasto-viscoelastic regime, from 0 to 0.09, the crystallinity index is high and quite constant, <X c > = 0.67, ii) then drops drastically in the soft-plastic deformation regime, from 0.09 to 0.8, passing from <X c > = 0.67 to 0.57 and iii) finally decreases softly in the stress-hardening regime, from 0.8 to 1.6. Just before the rupture, the crystallinity index is low and equal to <X c > = 0.54. achieved their maximal orientation level before the material rupture. proportion oriented parallel to the z-polarization direction which is also the stretching direction. Thus, chains of amorphous phase tend to be preferentially oriented along the ztensile direction. Figure 6 presents the evolution of the orientation function of the amorphous phase F am/z , and the true axial stress  zz in function of the true strain  zz from 0 to 1.6.

Orientation of macromolecules in the crystalline phase

Orientation of macromolecules in the amorphous phase

Increasing evolution of F am/z with deformation confirms our preliminary observations: macromolecular chains tend to be oriented towards the z-tensile direction. It can be delimited with respect to the true axial strain,  zz : i) In the elasto-viscoelastic regime, from 0 to 0.09, chains are profoundly affected by the deformation since F am/z raises from 0.03 to 0.3. ii) In the soft-plastic deformation regime, from 0.09 to 0.8, orientation of amorphous is milder passing from F am/z = 0.3 to 0.6 and iii) becomes more and more moderate F am/z = 0.6 -0.7 in the stress-hardening regime, from 0.8 to 1.6. Approaching the fracture deformation, F am/z exhibits a maximal and quite constant value, F am/z = 0.7, suggesting that amorphous chains have almost achieved their maximal orientation level before rupture.

Stress distribution

In figures 1 and 3 we have noted that bands at 809, 835 and 841 cm -1 exhibit opposite wavenumber shifts with deformation. Bands at 809 and 835 cm -1 possessing both a high contribution of the C-C skeletal backbones moves towards lowwavenumbers. This indicates that these chemical bonds experience an increasing extension stress with the increasing deformation as described by. On the contrary, crystalline band at 842 cm -1 , principally attributed to the CH 2 lateral groups, moves up to highwavenumbers. This evidences the compressive solicitation that endures C-H lateral bonds during stretching. These observations are in good agreement with previous studies of Wool et al. 64 in case of polyethylene. Figure 7 shows evolution of the normalized position, / 0 of the crystalline bands at 809 and 842 cm -1 whereas figure 8 plots the amorphous one at 835 cm -1 .  0 represents position of bands for the non-deformed iPP. Despite that shift of crystalline bands at 809 and 842 cm -1 have an opposite behaviour, their evolutions are comparable in function of the true axial strain,  zz : i)

In the elasto-viscoelastic regime, from 0 to 0.09, normalized shifts of both bands are very low.

This indicates that application of extension-stress on the C-C skeletal backbones and compressive-stress on C-H lateral bonds is weak as if crystalline chains are not yet regarded by the deformation. ii) In the soft-plastic deformation regime, from 0.09 to 0.8, positions of bands move gently meaning that stress is progressively applied on chemicals bonds. ii) In the last stress-hardening regime, from 0.8 to 1.6, bonds are strongly constrained since shifts exhibit important variations. By comparing evolution of the extension-stress on C-C bonds between crystalline (Figure 7) and amorphous chains (Figure 8), we note major differences particularly in the elasto-viscoelatic regime where amorphous C-C bonds are highly constrained while crystalline ones are not yet affected.

Discussion

Discussion will turn to the description of the deformation micro-mechanisms occurring in the semi-crystalline structure of iPP by clearly discerning the three different regimes of the mechanical behaviour, i) elasto-viscoelastic regime, ii) soft-plastic regime and iii) stresshardening regime. It will be based on the cross-checking of the results obtained previously and summarized in Table 2. Such a rigorous description has to take into account two special crystal features of the -iPP spherulites. : i) The high dependence of the initial orientation of lamellae, distributed in equatorial, diagonal and polar regions of the spherulite, with respect to the macroscopic applied stress z-direction [START_REF] Haudin | In Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] . ii) The cross-hatch type lamellar branching which exhibits radial ("mother") and tangential ("daughter") lamellae oriented nearly orthogonally [START_REF] Lotz | [END_REF] . Radial lamellae correspond to the c 1 -crystallographic axis and the tangential ones to the c 2 -axis. This last point explains strongly the mechanical behaviour differences observed with the -iPP spherulites which consist of broad, locally stacked radial lamellae, just as in spherulites of polyethylene [START_REF] Aboulfaraj | [END_REF]67 . Under tensile loading, it has been shown that the -iPP spherulites exhibit brittle behaviour whereas the -ones deform plastically with little damage (occurrence of cavitation) up to strain of about  zz = 0.25.

Elasto-Viscoelastic regime

In the elasto-viscoelastic regime (Figure 9),  zz = 0 -0.09, results demonstrate that it is only the amorphous phase which plays a major role in the deformation process: orientation of amorphous chains is high and accompanied by the application of an important extension-stress level on the amorphous C-C skeletal backbones. On the contrary, deformation mechanisms involving crystalline phase are not yet active: neither the crystalline chains orientation nor the crystallinity index change. This is usually explained by considering the soft amorphous phase behaviour compared with the rigid crystalline blocks. In the analogous case of polyethylene, Schultz et al. [START_REF] Schultz | Polymer Materials Science[END_REF] show that the nanoscopic elastic modulus of one chain is sixteen times higher than the macroscopic one evidencing the essential contribution of the soft amorphous phase. For T > T g , the Van der Waals interactions are overcome and the amorphous part exhibits a rubber-like behaviour. Initially under an interpenetrating coils configuration, chains in the interlamellar layers have enough molecular mobility to orient themselves towards the z-tensile direction in order to accommodate the deformation. It involves disentanglement, extension and alignment of tie molecules between two adjacent crystalline lamellae. This is particular true for stacked lamellae oriented perpendicularly to the stretching direction such as for the radial and tangential ones in equatorial and polar regions respectively. Adjacent lamellae are separated and the average length of the amorphous interlamellar layer increases [START_REF] Bowden | [END_REF] . The important extension-stress measured on the amorphous C-C skeletal backbones is in good agreement with this interpretation. On the contrary, lamellae in polar regions undergo locally a compressive stress leading to move lamellae closer.

Amorphous chains are confined in the interlamellar layer. Radial and tangential lamellae in diagonal regions, inclined at  45 ° with respect to the macroscopic z-tensile direction are locally subject to a shear stress which promotes lamellae sliding. This leads to a progressive extension and alignment of amorphous chains. Deformation of amorphous phase is always at least partially reversible in the elastic domain and time-dependent in the viscoelastic one [START_REF] Treloar | The Physics of Rubber Elasticity[END_REF][START_REF] Young | [END_REF] . This is due to the thermodynamic tendency of the stretched chains to return to their coiled geometry.

Soft-plastic deformation regime

In the soft-plastic deformation regime (Figure 9),  zz = 0.09 -0.8, results show that orientation of the crystalline chains towards the z-tensile direction is dominant, the crystallinity index drops drastically, the macroscopic stress is more and more disseminated on the chemical bonds of the crystalline macromolecules and the volume damage is activated.

These important changes noted for the crystalline phase signal clearly the activation of new deformation mechanisms differing from these encountered during the viscoelastic regime.

After a critical stress is achieved corresponding to the yield point, amorphous phase cannot accommodate any more the increasing deformation because interlamellar extension and/or shearing process is limited by the finite extensibility of the highly entangled chains (or tiemolecules). Therefore these are crystals which are affected at their turn by dissipative deformation mechanisms as plastic flow and formation of micro-voids in the amorphous layers and / or at inter-spherulitic boundaries [START_REF] Bowden | [END_REF] . In the true stressstrain curve of iPP, the stress drop occurring just past the yield point, is caused by the catastrophic and cooperative failures of the lamellae accompanying deformation. In the equatorial regions, Nitta and Takayanagi 22,23 proposed that tie molecules between two adjacent lamellae support the external force and produce locally a concentrated load on lamellae surfaces leading to the lamellae bending, as shown in figure 9. They show that under a critical bending stress value, calculating as a function of the tie molecules fraction, lamellae are break up into smaller blocks. In parallel, our results on crystallinity show that a part of crystalline chains is pulledout from the folded-chains lamellae. This is commonly termed as the mechanically-induced melting process. At the same time, micro-voids appear in the amorphous layers where density of tie-molecules is lower, and transform progressively into cavities with the increasing deformation [START_REF] Friedriech | Advances in Polymer Science, Crazing in Polymers[END_REF] . In polar regions, the existence of a local compressive stress induces also a lamellar bending in the meaning of Nitta and Takayanagi 22,23 . Crystal blocks are at first pulled out of the lamellae, then rotate towards the z-tensile axis and are subject in part to disintegration [START_REF] Schultz | Polymer Materials Science[END_REF] . Deformation mechanisms in diagonal regions are quite different since radial and tangential lamellae are oriented at  45 ° versus the z-tensile axis which promotes fine crystallographic slips by generation and glide of dislocations leaving the lamellae intact 15,16 .

In uniaxially stretched isotactic polypropylene, it was demonstrated that minimum value of the Critical Resolved Shear Stress (CRSS) is firstly achieved for chain slip mode along the (100)[001], (010)[001], (110) [001] and ( 10)[001] glide systems 63 . For further deformation, this crystal plasticity, that readily accommodates most of the applied deformation, leads to consecutives secondary effects such as i) plastic tilt of crystallites towards the z-tensile axis, ii) lamellae fragmentation owing to coarse slip process, iii) crystalline phase destruction by chains pull-out process and iv) micro-voids formation in the amorphous layers [START_REF] Hay | [END_REF][9][START_REF] Schultz | Polymer Materials Science[END_REF][START_REF] Petermann | [END_REF][START_REF] Friedriech | Advances in Polymer Science, Crazing in Polymers[END_REF][START_REF] Bowden | [END_REF] . On this last point, it is worth to note that voiding appears earlier in the equatorial and polar regions of the spherulites where plastic slip is less favourable compared to the diagonal ones. These interpretation were assessed by previous microscopy studies on the transition from yielding to crazing in polypropylene concluding to a competition between crystal slip and voiding in governing the propagation of cavitation across the spherulite 68 . In addition, the fact that voids occur at the same time in the equatorial and polar regions is related to the cross-hatched structure of the -iPP spherulites and gives credit to the assumption that radial lamellae in equatorial position deformed similarly as the tangential ones in the polar regions and viceversa. In the case of polyethylene and polybutene which present both only radial lamellae, Addiego et al. 48 and Weynant et al. 69 show respectively, that the structural damage occurs firstly in the equatorial regions and long after in the polar ones.

Strain hardening regime

In the last strain-hardening domain (Figure 9),  zz = 0.8 -1.6, results show principally that deformation mechanisms involving crystalline and amorphous phase become stable: orientation of the crystalline and amorphous chains is less active, the loss of crystallinity slow down and volume strain achieves practically its maximum level. This means that mechanisms of plastic deformation are depleted and the initial isotropic lamellar structure is transformed into a highly anisotropic and damaged micro-fibrillar structure oriented towards the tensile direction [START_REF] Bowden | [END_REF] . Contrary to the soft-plastic regime, deformation mechanisms in the strainhardening one are quite identical in the equatorial, diagonal and polar regions of the -iPP (having a critical size) breaking craze fibrils as it grows [START_REF] Kramer | In Plastic Deformation of Amorphous and Semi Crystalline Materials, B. Escaig and C. G'Sell[END_REF] .

Conclusion

The deformation mechanisms of isotactic polypropylene during its uniaxial tension were investigated at the macroscopic scale by means of a 2D video extensometer (VidéoTraction TM ) giving access to the intrinsic stressstrain curve of the polymer for a constant true strain rate at constant temperature, and at the microscopic scale by micro-Raman

List of figures

at 5

 5 °C. X-ray scattering measurements obtained with a Bruker AXS (ref. D8 Advance) equipped with a Cu-K 1 ( CuK1 = 0.1542 nm) Johansson monochromator proves the semi-crystalline nature of the investigated iPP. The narrow peaks located at 2 = 14.1, 16.9, 18.5, 21.2 and 21.8 degrees evidences the presence of the -monoclinic form of the iPP crystals because they are due to the selective diffraction of the (110), (040), (130), (111) and (31) crystallographic planes of the -monoclinic unit cell respectively[START_REF] Lotz | [END_REF] . The spherulitic morphology is observed by means of polarized optical microscopy performed on thin slices (20 µm thickness).

  56.. Thickness is considerably reduced from 4 mm to 500 µm (by polishing flate surfaces) in order to obtain a film geometry. Main reason is to minimize the deflection of the necking zone to ensure a suitable focalisation of the laser onto the sample all along the mechanical test. All specimens are stretched at T = 30 °C under a constant true strain rate  zz = 5.10 -3 s -1 until their rupture at  zz = 1.6. During the entire course of the tensile test 40 Raman spectra are recorded. For each Raman spectrum, acquisition time is fixed at 5 s. . Note that results are based on the repetition of 10 tensile tests in exactly the same experimental conditions in order to ensure reproducibility.

  scattering bands at 973 (symmetric stretching mode of the C-C skeletal backbones in crystalline phase) and 998 cm -1 (rocking mode of CH 3 lateral alkyl groups in crystalline phase), enable to estimate orientation of crystalline phase chains in the z-tensile direction. In uniaxial tension, G'Sell and Dahoun63 show the development of a fiber texture which can be characterized by the determination of only one orientation function, F c/z , describing the spatial distribution of the crystallographic c-axis towards the z-tensile direction. A matching relation between R orient,c and F c/z was established as follow :Keeping the same polarization configuration, x(zz)x, we used the ratio R orient,am = I 835 / I tot of the unique band at 835 cm -1 (stretching mode of the C-C skeletal backbones in amorphous phase) as a spectral criterion of amorphous chains orientation . I tot is the integrated intensity of the entire recorded spectrum. By the same reasoning, a linear relation was established between R orient,am and orientation function of the amorphous phase F am/z describing the spatial distribution of amorphous macromolecules towards the z-tensile direction .

Figure3reports

  Figure3reports fitted Raman spectra recorded in polarized configuration, x(zz)x, at growing

Figure 5

 5 Figure5shows fitted Raman spectra recorded in polarized configuration, x(zz)x, at growing true axial strain level,  zz = 0, 0.1, 0.8 and 1.4. In the spectral range considered, 780 -880 cm - 1 , is only plotted the useful polarized scattering band at 835 cm -1 which allows calculation of

spherulite as illustrated in figure 9 .

 9 The microstructure accommodates the continuing deformation only by the extension and the valence angle opening of the chemical bonds. The force required for displacing the C-C bonds from their equilibrium distance (related to the Morse's potential) is such important that the stress increases drastically in this last deformation regime. Our results showing important variations of the local stresses at the chemical bonds assesses this interpretation: C-C skeletal backbones of both the crystalline and amorphous macromolecules are more and more under extension since they are oriented in the tensile direction. In contrast, the C-H lateral bonds are more and more compressed since they are practically oriented towards the compressive direction of the uniaxial stress tensor. At large deformations, the ellipsoidal geometry of the voids observed in numerous microscopy studies is directly related to the application of a dilatation and a compaction stress (hydrostatic stress) along the axial and transversal directions, respectively. Approaching the polymer rupture, crystalline and amorphous chains have achieved their maximal orientation level, the proportion of crystalline phase is low and degraded in favour of the amorphous one, microstructure is highly damaged by the generation of crazes resulting from the nucleation, growth and coalescence of micro-voids (cavity). When chemical bonds cannot support the applied stress anymore, rupture of the polymer occurs by the rapid propagation of a crack

  spectroscopy. The new combination of these both techniques was introduced in this work and allows characterizing microstructure in real-time with its deformation by being free of the undesirable effects of the microstructure relaxation widely observed during post-mortem analysis. By this means, we demonstrate that rapidity of the spectral acquisitions presents a particular advantage in performing time-resolved measurements such as to follow the deformation mechanisms step by step. On the basis of the use of simple but reliable (previously validated) Raman spectral criterions appropriated for crucial features of the iPP microstructure (crystallinity index, chains orientation of both amorphous and crystalline phase and volume strain), we described evolution of the iPP microstructure in a large deformation domain from its elastic response to its rupture. Deformation of the spherulite microstructure results from a number of mechanisms involving both amorphous and crystalline phase. Such mechanisms are highly dependent on the orientation of structural elements with respect to the stress axis (equatorial, diagonal and polar regions). Results evidence clearly the transformation of the initial isotropic lamellar structure into a highly anisotropic and damaged micro-fibrillar structure oriented towards the stress direction. The main results show: the major role played by the amorphous phase during the initial elasto-viscoelastic deformation regime leading to interlamellar and / or shearing mechanisms. the major role played by the crystalline phase during the soft-plastic deformation regime such as crystal plasticity (for diagonal regions), lamellae destruction owing to a chains pulling-out mechanism, crystal tilting towards the stress direction, fragmentation, and voids generation,  the major role played by the chemical bonds in resisting to the deformation during the last strain-hardening regime.Further works should be devoted to a closer examination of the amorphous and crystalline phase evolution during loading and unloading cycles in order to have a better understanding of structural mechanisms occurring in the material relaxation.

Figure1: ( a )

 a Figure1: (a) Depolarized Raman spectra and (b) fitted scattering bands at 809, 835 and 842 cm -1 of iPP stretched at different strain levels.

Figure 2 :

 2 Figure 2 : Evolution of the true axial stress,  zz , and the crystallinity index, <X c >, in function

Figure 3 :

 3 Figure 3 : (a) Polarized x(zz)x Raman spectra and (b) fitted scattering bands at 973 and 998 cm -1 of iPP stretched at different strain levels.

Figure 4 :

 4 Figure 4 : Evolution of the true axial stress,  zz , and the orientation function of the crystalline

Figure 5 :

 5 Figure 5 : Fitted Raman scattering band at 835 cm -1 for different strain levels of iPP recorded

Figure 6 :

 6 Figure 6 : Evolution of the true axial stress,  zz , and the orientation function of the

Figure 7 :

 7 Figure 7 : Evolution of the true axial stress,  zz , and the normalized position,  /  0 , of crystalline bands at 809 (C-C) and 842 cm -1 (CH 2 ).

Figure 8 :

 8 Figure 8 : Evolution of the true axial stress,  zz , and the normalized position,  /  0 , of

Figure 9 :

 9 Figure 9 : A schematic illustration of micro-structural mechanisms occurring in uniaxially

Figure 1 :Figure2:Figure 4 : 1 T = 30 °CFigure 5 : 4 Figure 6 :Figure 7 :Figure 8 :Figure 9 :

 14130546789 Figure 1: (a) Depolarized Raman spectra and (b) fitted scattering bands at 809, 835 and 842 cm -1 of iPP stretched at different strain levels.

Table 2 :

 2 Raman spectroscopy results on major microstructural aspects of iPP uniaxially stretched at T = 30 °C under a constant true strain rate = 5.10 -3 s -1 from the elastic to the stress-hardening regime.

	deformation regime


Antoine Loriette

Diemo Schwarz

Elicitation of 2D expressive gestures through interactive soni cation

Gesture-based input devices for controlling music software should support expressivity. However, it is challenging to effectively design new gestural interactions that both exploit the capabilities of existing devices and afford user expressivity. To further the understanding of expressive interactions, we propose a demo that interactively supports users in the production of new gestural movements. Precisely, the demo implements an elicitation algorithm which rewards the originality of gesture dynamics to support users in the exploration of the space of motions they can perform. This demo is targeting 2D interactions supported by, for example, a mouse, trackpad or Sensel device. As users interact with their input device, movement dynamics (e.g.

speed profile and orientation derivative) are computed and 2D strokes are segmented into small primitives. The originality of a new segment is then measured as the minimum distance to previously observed segments and fed back to the users as an audio cue; the greater the distance, the louder the feedback. Such sonification scheme encourages users to produce new behaviours. This elicitation produces a map of motion primitives wherein clusters identify prototypical user behaviour. The properties of these clusters, such as user specificity or time of invention, could be used to reflect on the user practice and identify new opportunities for interface design.

Requirements

The demo will provide a self-contained Max project for download that can be run by anyone with a Windows or Mac computer, after installing Max by Cycling'74. For running the provided patches it is not necessary to buy a Max license.

Antoine Loriette, STMS -Ircam CNRS Sorbonne Université, Paris, France Diemo Schwarz, STMS -Ircam CNRS Sorbonne Université, Paris, France Elicitation of 2D expressive gestures through interactive soni cation 3

The demo will explore expressive touch and movement on 2D input devices. It will work with a mouse or touchpad, but we will also provide input modules for typical 2D input devices such as Sensel Morph, ROLI Lightpad Block, Wacom tablet, MIDI pads and joysticks, OSC streams.

Program Description

We observe that well-established gesture elicitation methods are usually targeting movement-to-action mappings (instead of expressivity) and that most recognition algorithms rely on geometrical features for discriminating users' intention. In parallel, there is little information about how users interact with their input devices in the context of music software control.

After an introduction of the method and aims of this research, we will spend time to get the demo patch running for everyone, and connect the participants' 2D controllers.

We will then let participants explore expressive 2D gestures first without, then with the help of the elicitation algorithm's audio feedback. The built-in visualisation will help participants see how much they could extend their personal expressive space through "rewarding" original movements by audio feedback.

At the end of the demo, participants will have the choice to save and send us their recorded movement data in order to constitute an anonymised movement dataset that will allow more in-depth analysis of a larger panel of users, leading to better generalisation and helping further research on this topic.

Media

This demo heavily draws inspiration from the works of Williamson et al. [START_REF] Williamson | Rewarding the original: explorations in joint user-sensor motion spaces[END_REF] and Kulić et al. [START_REF] Kulić | Incremental learning of full body motion primitives and their sequencing through human motion observation[END_REF]. While the first reference investigated the sonification of user movements based on the distance with previously observed movements in order to foster original behaviours, the second reference formalised a process that learns the structure of human movement by iteratively clustering motion primitives.

We relied on the dataset Unistroke In this demo, we propose to explore movement dynamics as the main feature for computing similarity between input sequences, with the hypothesis that these could be better suited as a proxy for movement expressivity. In addition, they provide interesting invariances to translation and orientation.

The elicitation process produces an embedding of motion primitives which can then be explored to identify specific patterns. In the figure below, the top row displays the Unistroke dataset embedded with t-sne, based on pairwise distances taking only movement dynamics into account. We observe different clusters with similar dynamics, produced by very different time series, such as the 4 samples drawn in the vicinity of the black cross for which the position data and dynamics can be compared (last two rows).

Position data and associated dynamics of four sample strokes taken from the dataset Unistroke.

  [3] to tune our algorithm. This dataset contains 2D strokes produced by 11 users and representing 16 different shapes executed at various speeds. The figure below shows 4 samples from 3 different classes (triangle, caret and rectangle) and 3 different speeds (slow, medium and fast). The first and second row represent position data and dynamics, respectively.

Acknowledgements

This work is supported by ELEMENT project -Enabling Learnability in Embodied Movement Interaction, (ANR-18-CE33-0002).