A Rudajevová

K Mili

Residual and thermal strain in AX41 magnesium alloy reinforced with short Saffil fibres

Keywords: A. Metal-matrix composites, Short -fiber composites, B. Thermal properties, C. Stress relaxation

Thermal expansion characteristics of AX41 magnesium alloy reinforced by 12 vol. % of short Saffil fibers were investigated at the temperature range of 25 to 380 ºC. Specimens cut at various angles involving random planar distribution of fibers were used for the experiments. From the thermal expansion characteristics, residual and thermal strains and their dependence on the orientation were evaluated. Tensile thermal strains were observed from 0° to 45° angles between the axis sample and the preferential plane of the fiber distribution. For greater angles, i.e., 45°-90º, the compression thermal strains were observed. The thermal stresses and the thermal strain connected with them head towards stress-free state by elastic-plastic mechanism. The temperature of the elastic-plastic transition does not depend on the angle between sample axis and the short fiber direction.

Introduction

Metal matrix composites reinforced by short ceramic fibers represent typical systems of phases with different coefficients of thermal expansion (CTE). Because of these differences, local strains occur inside these materials in the matrix as well as in the reinforcement. In principle, two types of the macroscopic strains can be distinguished in the composite. First, residual strains are a consequence of material preparation, e.g., mechanical procedures, and as a rule, can be simply removed by heating. The nature of these strains is usually tensile [1,2]. Residual strains can also be introduced any time by additional deformation of the sample. Second, the thermal strains are attributes of the system in any state and can be assigned exclusively to differences in CTE of phases.

These strains cannot be removed by any process from the composite because they occur during cooling and they release during heating. Releasing of the thermal strains takes place by the elastic-plastic mechanism [1].

During fabrication cooling, the composite goes through the so-called stress-free state where no internal stresses exist in a composite material. The flow stress of the metallic matrix is usually very low so plastic deformation of the matrix occurs during cooling almost instantaneously. This plastic deformation begins within the first few degrees of cooling. Levy et al. [3] have shown on Al alloy/SiC composite that plastic deformation finishes at about 225 ºC. No plastic deformation occurs between 225 and 65 ºC. In this paper FEM-simulation were made with assumption one direction ordering of fibres in the matrix and the material was cooled from 500 o C to room temperature.

Thermal plastic deformation disappeared due to the temperature dependence of the yield strength of the matrix alloy. Plastic deformation in the composite is localized in the matrix near the interface between matrix/reinforcement. This region of the matrix can produce complex effects on the composite responses during its mechanical loading. It has 3 been reported that the thermal stresses can result in asymmetric stress-strain responses under tensile and compressive loading [4,5,6].

Both types of the local strains have been detected by several experimental procedures such as X-ray diffraction [7] and dilatation techniques [8]. In the latter, the measured coefficient of thermal expansion of a given material includes the changes not only in atom vibrations but also in all deformations with temperature. Therefore, measurements of CTE can serve well in identifying the integral changes in local strains.

The distribution of reinforcing fibers in metal matrix composites is usually not regular; their arrangement strongly depends on the procedure of fabrication of the composite. The present paper consists of an investigation of the influence of the specific arrangement on directional dilatation characteristics of a composite with a magnesium alloy AX41 matrix with short ceramic Saffil fibers in a wide temperature interval from 25 to 380 ºC.

Experimental details

The materials for the present study were magnesium composites based on AX41 (Mg-4Al-1Ca) alloy, which was reinforced by 12 vol. % Saffil fibers. The composites were supplied by the Centre of Advanced Materials, Clausthal, and were prepared by squeeze casting. The molten alloy (700 ºC) was inserted into a preheated die (350 ºC) with Saffil preform. The two-stage application of pressure was used (40 MPa for 15 s followed under 70 MPa for 90 s). The ingot dimensions were 100 x 100 x 30 mm. Short fibers in the composite held their original arrangement existing in the preform; they were planar randomly arranged, i.e., axes of fibers lay randomly in parallel planes xy (Fig. 1). The length of the fibers was in order of tens of µm and their diameter The linear thermal expansion of the composite specimens was measured in a helium atmosphere by using a Netzsch 402 C/4/G dilatometer from room temperature to 380 ºC at heating and cooling rates of 2 ºC/min. The thermal expansion curves for composites were measured during three consequent heating and cooling cycles. In all cases, results obtained in the second thermal cycle were the same as those in the third cycle. Therefore, in the following, dilatation characteristics obtained in the first and second thermal cycles only will be presented and discussed. The first cycle was performed in the as-cast state.

Experimental results

The substantial difference between the dilatation characteristics obtained in the first and the second thermal cycles was a permanent reduction of the sample length after the first thermal cycle. The value of the reduction of the sample length was about 25 m.

For a better understanding of the processes occurring in composites during thermal cycling, the measured relative elongation on several contributions can be divided. These (CTE) AX41 = 24.9 10 -6 K -1 ). The residual strain for all composites as well as for pure alloy AX41 is shown in Figure 2. The residual strain was obtained as the difference between the first and second thermal cycles. angle is presented in Figure 7.

Figure 8 reveals the temperature dependence of the residual strain that occurred in the composite when various cooling rates were used. The composite C-0 was used for this experiment. The composite was heated 24 h at 400 o C (this temperature was used for the heat treatment) and then it was quenched in air, water, and liquid nitrogen. The dilatation characteristics were then measured during two thermal cycles. The residual strain was calculated from relation (1). Figure 8 shows that character of the residual strain after quenching was different from the residual strain that occurred during preparation of the composite.

Discussion

The dilatation characteristics of the AX41 alloy had a standard course. After the first thermal cycle, a reduction of the sample length occurred. The residual strain was released only during heating. Figure 2 shows that the residual strain in the alloy was practically the same as the residual strain in the composites. The temperature dependence of the relative elongation and the CTE in the second and the third thermal cycles were the same. No hysteresis was found during heating and cooling. It is necessary to note that the alloy sample was prepared from the same ingot as composites studied.

The residual strain in the composites was found only in the as-prepared composites.

Figure 2 shows the release of the residual strain that was not practically dependent on the direction of the fibers to the axes of the sample. The results reveal that the alloy and the matrix of the composite in as-prepared state were always in tension (after the first thermal cycle reduction of the sample length occurs). This effect is evidently connected with solidification when the volume of the solid is lower than the volume of the liquid. The temperature gradient in the ingot during cooling decreased from the ingot center to its margin. So the margin of the ingot solidified first. The interior of the ingot cannot reduce its volume and the composite is therefore deformed in tension. This tensile deformation is then removed in the following thermal cycle. Amount of this removed deformation depends on the maximum thermal cycle temperature and on the heating rate.

The thermal strain occurred in the composite as consequence of the difference of the CTE of the alloy and reinforcement during cooling. The existence of the thermal strain in composites was connected with the hysteresis on the temperature dependence of the relative elongation. This means that the development and release of the thermal strain did not occur in the same manner (Fig. 3). Similar results were presented by Kumar et al. ( )

T F M th ∆ - = α α ε (2)
where M is the matrix coefficient of thermal expansion and F is the inclusion coefficient of thermal expansion. Term T is the difference between T o , that is temperature where the stress-free state exists, and actual temperature T. It was evident that the thermal mismatch strain was highest at lowest temperature; it decreased with increasing temperature and reached zero at the stress-free state. The thermal stresses and the thermal strain in the components connected with them depended on other factors such as the size and shape of inclusions and the character of the interface. For example, Yih and Chung [13] have shown that the composite reinforced with the Cu-coated SiC whisker had a lower linear CTE than that of the corresponding composites with the uncoated one. The thermal strain in the composite was determined by the character and by the density of the dislocations in metal matrix near the interface between the matrix and reinforcement.

Anisotropy of the thermal strain was perceptible from all the results (Fig. 123456).

With regard to the results obtained for C-0 and C-90 composites, during heating, the thermal stress in the composite decreased at first only elastically. When the thermal stress reached the yield stress of the matrix, at a certain (high) temperature, plastic zones near the interfaces between the matrix and fibers were reduced (yield stress decreases with increasing temperature). The elastic stress field was modulated by this plastic deformation and decrease (C-0) or increase (C-90) in the thermal strain was faster than in the case of only the elastic deformation range. The temperature boundary between elastic and elastic-plastic mechanism may be defined as bend on the temperature dependence of the CTE during heating (Fig. 4). The transient temperature is about 220 ºC. It is assumed that the matrix is strained in tension in the direction parallel to the fiber planes. The decrease in the thermal stress (strain) in this direction is then associated with the reduction of the specimen length ( TS l l ∆ 0 <0). On the other hand, the matrix is deformed in compression in the direction perpendicular to the fiber planes. The decreasing thermal stress (strain) leads to an expansion of the specimen length in this direction (

TS o l l ∆ >0).
The yield stresses for heating and cooling do not coincide so that hysteresis is observed.

The C-45 composite has practically zero thermal strain (Fig. 6). The composites C- The highest thermal strain is in the direction of the fibers and in the direction perpendicular to a planar random arrangement.

Figure 8 reveals the temperature dependence of the residual strain that has occurred by the quenching of C-0 composite from 400 ºC up to air, water, and liquid nitrogen.

Release of this residual strain has not the same course as in the case the residual strain that occurred because of manufacturing cooling. Substantial difference is perceptible on dependence of the residual strain that was obtained by the quenching in liquid nitrogen.

This quenching of the composite C-0 into liquid nitrogen leads to compression macroscopic deformation in the fibers' direction. Release of the residual strain during heating is connected with an increase of above 200 ºC. This effect was not found during release of the manufacturing thermal strain and is not probably connected with precipitation because heating of the pure alloy and its quenching into liquid nitrogen do not change the dilatation characteristics.

Conclusions

The residual strain was found in all as-prepared samples of the composites and the pure alloy. This residual strain was tensile in all cases and it was not dependent on the place of the sample in the ingot. The residual strain occurs also during quenching of the composite from a high temperature up to air, water, or liquid nitrogen. This residual strain, however, has different character from the residual strain after manufacturing cooling. The thermal strain depends on direction of the short fibers to the sample axis. In direction where angle of the sample axis and fibers is 45º, zero thermal strain exists. The highest thermal strain was found for side angles; compression for the case when the axes of the sample was perpendicular to the place of a planar randomly arranged short fibers, and tensile when the axis of the sample was parallel to the fibers. Increasing temperature leads to release of the thermal strain. The sample length increases/decreases when the compression/tensile strain is released. This process has elastic-plastic character. At low temperatures, below 220 ºC, the thermal strain relaxation has only elastic character.

Above this temperature the plastic zones in the matrix near fibers disappear and this process accelerated relaxation of the thermal strain.

List of captions

  (thickness) approximately 3 µm. Particles of secondary phases, namely, CaAl 2 , were randomly distributed in the structure. From the composite part of the ingot, parallelepipeds, which contain different angles α with preferential plane xy of the fiber distribution (Fig. 1), were cut. Cylindrical specimens of 6 mm in diameter and 25 mm or 20 mm long were prepared for dilatation measurements. The composite samples with angle = 0, 30, 45, 60 and 90 ˚ are further called C-0, C-30, C-45, C-60 and C-90.

  contributions were additive. Measured relative elongation ( l/l o ) meas can be expressed as by the rule of mixtures and it increases with increasing temperature ((CTE) Saffil = 7.6 10 -6 K -1 ,

Figure 3

 3 Figure 3 shows the temperature dependence of the relative elongation for all

  in the works[9,10] on the Mg fiber composites. The hysteresis and the residual strain were found in their work for transversal and perpendicular orientation of the fibers to the sample axis.The temperature dependence of the CTE during heating for all composites studied is shown in Figure4. On each curve were linear section and section where curvature occurred above 220 ºC. This curvature was connected with the decrease in the CTE for C-0 and C-30 composite and increase in CTE for C-90, C-60, and C-45 composites. These departures from the linear dependence mean that the relative elongation was caused by thermal vibration and some further deformation. If the CTE increased as in the case of C-90 and C-60, then deformation was positive and the sample length increased during heating; the sample was in compression deformation before heating. On the other hand, when the temperature dependence of the CTE was curveted to lower values of the CTE, the sample was in tensile deformation and during heating the sample length would be reduced when tensile deformation was released. In a previous work[11], the CTE of the predeformed composite in compression increased and it decreased when the composite was predeformed in tension.During cooling of composite, thermal stresses can be introduced into each constituent because of a high thermal mismatch between a ceramic reinforcement and a metal matrix. The linear thermal mismatch strain resulting from a temperature variation T is often published as[12]

  30 and C-60 behave similarly as the composites C-90 and C-0; only the values of the thermal strain are lower in the entire temperature range studied. The plastic zones disappear at about 220 ºC, the bend on the temperature dependence of the CTE occurs at about this temperature. The scheme of the thermal strain components at angle and dependence of the measured values of the thermal strain on angle is shown in Figure 7.

Fig. 1 -

 1 Fig. 1 -Scheme of composite ingot and manner of cutting of samples (a), illustration of

Fig. 2 -Fig. 3 -Fig. 4 -Fig. 5 -Fig. 6 -Fig. 7 -Fig. 8 -Fig. 2 temperature

 23456782 Fig. 2 -Temperature dependence of the residual Fig strain in as-prepared samples

Acknowledgments

The authors are grateful for the support offered by the Grant Agency of the Czech Republic under Grant 106/06/1354. This work is also a part of the research program MSM 0021620834 that is financed by the Ministry of Education of the Czech Republic.


Nattakan Soykeabkaew

Noriko Arimoto

Takashi Nishino

Ton Peijs

All-Cellulose Composites by Surface Selective Dissolution of Aligned Ligno-Cellulosic Fibres

Keywords: A. Natural fibres, B. Mechanical properties, B. Interfacial strength, C. X-ray diffraction (XRD), C. Scanning electron microscopy (SEM)

All-cellulose composites were successfully prepared by a surface selective dissolution method of aligned ligno-cellulosic fibres using lithium chloride/N,Ndimethylacetamide as a solvent. The effect of the immersion time of the aligned fibres in the solvent during preparation was investigated. The structure and mechanical properties of the composites were characterized by X-ray diffraction, scanning electron microscopy, and tensile testing. Optimization of the immersion time resulted in allcellulose composites with excellent mechanical properties, i.e. a longitudinal tensile strength and Young's modulus of 460 MPa and 28 GPa, respectively. Strong interfacial interaction was also observed for these all-cellulose composites with good interface dominated properties like transverse tensile strengths in the range of 22-40 MPa. The significant advantages of these composites are their biobased and biodegradable character combined with excellent mechanical properties due to their very high fibre volume fraction which makes them as a potential alternative to glass-fibre-reinforced composites.

Introduction

Nowadays, the growing environmental awareness throughout the world has triggered a paradigm shift towards designing environmentally friendly materials.

Consequently, in recent years, natural fibres have attracted more and more interest as reinforcements for both thermoplastic and thermosetting polymer composites [START_REF] Heijenrath | Natural-fibre-mat-reinforced thermoplastic composites based on flax fibres and polypropylene[END_REF][START_REF] Peijs | Thermoplastic composites based on flax fibres and polypropylene: Influence of fibre length and fibre volume fraction on mechanical properties[END_REF][START_REF] Garkhail | Mechanical properties of natural-fibremat-reinforced thermoplastics based on flax fibres and polypropylene[END_REF][START_REF] Stamboulis | Environmental durability of flax fibres and their composites based on polypropylene matrix[END_REF][START_REF] Peijs | Composites turn green[END_REF][START_REF] Singleton | On the mechanical properties, deformation and fracture of a natural fibre/recycled polymer composite[END_REF].

However, most of the commercially available polymers used as composite matrices are currently petroleum-based, non-biodegradable and regarded as non-sustainable materials [START_REF] Mohanty | Surface modification of jute and its influence on performance of biodegradable jute-fabric/Biopol composites[END_REF][START_REF] Lu | Self-reinforced melt processable composites of sisal[END_REF][START_REF] Toriz | Novel cellulose esterpoly(furfuryl alcohol)-flax fiber biocomposites[END_REF][START_REF] Wibowo | Chopped industrial hemp fiber reinforced cellulosic plastic biocomposites: thermomechanical and morphological properties[END_REF]. On the other hand, current biobased composites based on biodegradable polymers are often of modest strength and not cost-effective at present [START_REF] Wibowo | Chopped industrial hemp fiber reinforced cellulosic plastic biocomposites: thermomechanical and morphological properties[END_REF][START_REF] Nishino | Kenaf reinforced biodegradable composite[END_REF][START_REF] Soykeabkaew | Preparation and characterization of jute-and flax-reinforced starch-based composite foams[END_REF][START_REF] Puglia | Processing, properties and stability of biodegradable composites based on Mater-Bi and cellulose fibres[END_REF][START_REF] Lu | Morphological, thermal and mechanical properties of ramie crystallites-reinforced plasticized starch biocomposites[END_REF][START_REF] Averous | Biocomposites based on plasticized starch: thermal and mechanical behaviours[END_REF][START_REF] Luo | Interfacial and mechanical properties of environmentfriendly green composites made from pineapple fibers and poly(hydroxybutyrateco-valerate) resin[END_REF]. Moreover, for composites which are generally composed of two chemically foreign components, a strong interfacial interaction between fibre and matrix is required to obtain efficient reinforcement because only a well formed interface allows good stress transfer from matrix to fibre. In case of using natural fibres as reinforcement, an improvement in fibre-matrix adhesion is usually achieved by fibre surface-or matrix modifications, addition of compatibilizers or coupling agents or using other techniques at the expense of increased processing cost and time [START_REF] Wollerdorfer | Influence of natural fibres on the mechanical properties of biodegradable polymers[END_REF][START_REF] Mohanty | Effect of process engineering on the performance of natural fibre reinforced cellulose acetate biocomposites[END_REF][START_REF] Eichhorn | Composite micromechanics of hemp fibres and epoxy resin microdroplets[END_REF][START_REF] Shanks | Composites of poly(lactic acid) with flax fibres modified by interstitial polymerization[END_REF].

The most desirable solution to all these problems is possibly the idea of selfreinforced composites such as the all-polypropylene composites [START_REF] Ward | Novel composites by hot compaction of fibers[END_REF][START_REF] Ward | The science and technology of hot compaction[END_REF][START_REF] Peijs | Composites for recyclability[END_REF][START_REF] Cabrera | Processing of all-polypropylene composites for ultimate recyclability[END_REF], which have recently been developed. These composites are basically monomaterials and therefore fully recyclable and environmentally friendly. Moreover, since both fibre and matrix are composed of the same material they show excellent interfacial compatibility. Next to more traditional ways of creating all-polymer composites through the impregnation of polymer fibres with a polymer matrix of a slightly lower melting temperature, recently two more innovative routes have been proposed for the manufacture of all-polymer composites. First, the 'hot compaction' process was developed at the University of Leeds [START_REF] Ward | Novel composites by hot compaction of fibers[END_REF][START_REF] Ward | The science and technology of hot compaction[END_REF], which is based on the selective melting of the fibre surface and subsequently 'welding' fibres together rather than impregnating them with polymer matrix. In this approach part of the highly oriented polymer fibre is melted and upon cooling under pressure, the molten fibre material recrystallises into a matrix, which bonds the fibres together and forms a perfect interface [START_REF] Ward | Novel composites by hot compaction of fibers[END_REF][START_REF] Ward | The science and technology of hot compaction[END_REF]. In order to overcome the extremely small processing temperature window which is needed to transform the optimum amount of fibre material into matrix material an alternative route was proposed by Peijs and co-workers [START_REF] Peijs | Composites for recyclability[END_REF][START_REF] Cabrera | Processing of all-polypropylene composites for ultimate recyclability[END_REF], which is based on the consolidation of coextruded fibres. In this method a high modulus polypropylene homopolymer tape (read: fibres) is co-extruded with a thin coating of a lower melting temperature copolymer (read: matrix). The resulting all-polypropylene composites have a large processing window and their exceptionally high fibre volume fraction of around 90% makes them highly competitive with conventional glass-fibre-reinforced composites of much lower fibre loadings in various potential applications particularly the automotive industry.

Following on the successes of all-polymer composites like all-PP [START_REF] Ward | Novel composites by hot compaction of fibers[END_REF][START_REF] Ward | The science and technology of hot compaction[END_REF][START_REF] Peijs | Composites for recyclability[END_REF][START_REF] Cabrera | Processing of all-polypropylene composites for ultimate recyclability[END_REF], allcellulose composites have recently been introduced [START_REF] Nishino | All-cellulose composite[END_REF][26]. In a similar fashion to allpolymer composites an approach can be followed where cellulose fibres are impregnated with a cellulose matrix. Such an approach was followed for the creation of high-strength all-cellulose composites where ramie fibres are the reinforcement and dissolved Kraft pulp [START_REF] Nishino | All-cellulose composite[END_REF] or dissolved ramie fibre [26] is used for the matrix. Due to the high fibre volume fraction in these composites, the tensile strength of these uniaxially reinforced all-cellulose composites was as high as 480-540 MPa which compared very favourably to other nature fibre based composites. The all-cellulose composites described were obtained by dissolving pre-treated cellulose fibres in lithium chloride/N,N-dimethylacetamide (LiCl/DMAc) and then impregnation of the cellulose solution into the aligned ramie fibres followed by coagulation in methanol and drying.

Ligno-cellulosic or natural fibres from annual plants, wood, and agricultural byproducts is an abundant renewable resource [START_REF] Gindl | All-cellulose nanocomposite[END_REF]. Ramie fibre was selected for this study because of its excellent fibre characteristics. Ramie or china grass (Boehmeria nivea (L.) Gaud.) is a perennial herbaceous plant of the Urticaceous family. Ramie fibres are strong, very fine and silk-like, naturally white in colour, and have a high lustre. Other advantages are its good resistance to bacterial, mildew, and insect attack. Furthermore, the fibres are stable in alkaline media and not harmed by mild acids [START_REF] Lu | Morphological, thermal and mechanical properties of ramie crystallites-reinforced plasticized starch biocomposites[END_REF]. Due to the excellent fibre properties previously mentioned, ramie fibres have, therefore, a high potential as a raw material for preparing high performance cellulose based composites.

As mentioned earlier, one potential route to the creation of all-cellulose composites is through a traditional impregnation method. However, similar to other composite systems the impregnation of fibre bundles with high viscosity polymer systems has always been a difficulty. Another technique to prepare all-cellulose based composites has also been previously proposed by Matsumura et al. and Lu et al. [8,[START_REF] Matsumura | Cellulosic nanocomposites. I. Thermally deformable cellulose hexanoates from heterogeneous reaction[END_REF].

In these works, wood pulp and sisal fibres were partially converted to the thermoplastic cellulose esters which were afterwards thermally consolidated into a continuous matrix reinforced with the remained (unsubstituted) cellulose. The various extent of chemical modification influences a melt processability and reinforcing effect of these composites.

The present study focuses on an alternative approach for the preparation of all-cellulose composite. Rather than impregnating cellulose fibres with a highly viscous cellulose matrix or chemically modifying cellulose fibres as were reported previously [START_REF] Lu | Self-reinforced melt processable composites of sisal[END_REF][START_REF] Nishino | All-cellulose composite[END_REF][26][START_REF] Matsumura | Cellulosic nanocomposites. I. Thermally deformable cellulose hexanoates from heterogeneous reaction[END_REF], here surface selective dissolution of aligned cellulose fibres in the solvent by controlling the immersion time was employed. A similar approach has been used previously to prepare random all-cellulose composites from filter paper by Nishino et al. [START_REF] Nishino | All-cellulose composite prepared by selective dissolving of fiber surface[END_REF]. As the cell wall of a natural fibre is made up of a number of layers, the surface layer of the fibres can be partially dissolved and transformed into the matrix phase of the composites. Meanwhile, the remaining fibre cell cores maintain their original structure and impart a reinforcing effect to the composite [START_REF] Lu | Self-reinforced melt processable composites of sisal[END_REF][START_REF] Klemm | Cellulose. Biopolymers[END_REF][START_REF] Krässig | Cellulose: Structure Accessibility and Reactivity[END_REF]. This approach is similar to the 'selective melting' approach for self-reinforced composites where the fibre skin is also transformed into a matrix phase but now through melting [START_REF] Ward | Novel composites by hot compaction of fibers[END_REF][START_REF] Ward | The science and technology of hot compaction[END_REF][START_REF] Peijs | Composites for recyclability[END_REF][START_REF] Cabrera | Processing of all-polypropylene composites for ultimate recyclability[END_REF].

Clearly, in the case of cellulose where melting is not an option the matrix phase needs to be created through a surface selective dissolution process rather than melting as illustrated in Figure 1. The effect of immersion time of the aligned fibres in the solvent during preparation, which is the determining step of how much of the outer layer of the fibres is dissolved to form a matrix phase, was investigated in this study. With increasing immersion time, larger fractions of fibre can be dissolved to form a matrix phase, leading to composites of different fibre volume fractions. Since both the fibre and matrix phases of this cellulose composite are of the same origin and hence are chemically identical, a strong interfacial adhesion can be expected between them [START_REF] Soykeabkaew | Preparation and characterization of jute-and flax-reinforced starch-based composite foams[END_REF][START_REF] Cabrera | Processing of all-polypropylene composites for ultimate recyclability[END_REF]. The structure of the all-cellulose composites was examined by X-ray diffraction and scanning electron microscopy. Tensile testing was used to characterize the mechanical properties of the prepared all-cellulose composites.

Experimental details 2.1 Sample preparation

Ramie fibres, kindly supplied by Toyobo Co., Ltd., Japan were aligned in the longitudinal direction and were then fixed at both ends in a metal mould (dimension 50 × 50 mm) to prevent shrinkage and distortion. Table 1 summarizes the characteristic information of the as-received ramie fibres. The activation of the fibres was performed by immersing the fibres in distilled water, acetone, and DMAc, respectively, each for 2 hours at room temperature. Then, the activated fibres (0.36% wt/v) were immersed in 8% wt/v LiCl/DMAc solvent for a specified immersion time of 1, 2, 3, 4, 5, 6, 9, and 12 hours. The fibres were then removed from the solvent and the partially dissolved fibres started to gel by exposing them to ambient conditions for 12 hours. Subsequently, this fibre-incorporated gel was immersed in methanol for 12 hours to extract the DMAc and LiCl from the system. During this step, the methanol was exchanged by fresh methanol repeatedly after 1 hour and 6 hours of the immersion. Next the specimens were dried at room temperature for 12 hours, and then further under vacuum at 60 °C for 24 hours.

Measurements

The structure of the prepared composites was examined with a scanning electron microscope (SEM), JEOL JSM 6300 at an accelerating voltage of 10 kV. Prior to examination, the surface of the specimen was coated with a thin layer of gold.

X-ray diffraction profiles were detected using Cu Kα radiation, generated with RINT-2000 (Rigaku Co.) at 40 kV, 20 mA. The X-ray beam was operated in reflection mode and irradiated on the specimen perpendicular to the fibre orientation. After subtracting the air scattering, the diffraction profile was curve resolved into noncrystalline (amorphous) scattering and crystalline reflections using Rigaku multi-peaks separation software, whereby the amorphous contribution was estimated from the fully dissolved/regenerated cellulose matrix profile. The apparent crystallinity (%) was determined from the ratio of their area [START_REF] Nishino | All-cellulose composite prepared by selective dissolving of fiber surface[END_REF]. X-ray diffraction photographs were taken with a flat camera with a camera length of 37.5 mm. Mechanical properties of the composites were assessed with a universal tensile tester, Instron 5584, at room temperature. The gauge length of the specimens with a width of 3 mm was 20 mm and a cross-head speed of 20 mm/min was utilized for the tests similar to Nishino et al. [START_REF] Nishino | All-cellulose composite[END_REF] which previously prepared all-cellulose composites by an impregnation method. Elongation at break, ultimate tensile strength, and Young's modulus of the composites were evaluated. The results were reported as the average value of at least five measurements.

Prior to all measurements, the specimens were conditioned at a controlled relative humidity of 55.9 + 0.3 % at 15 °C (according to ASTM E104).

Results and discussion

Comparison of the X-ray diffraction patterns of all-cellulose composites (Figure 2) shows that the crystallinity of the composites decreased with the immersion time of the ramie fibres in the solvent. Without doubt, at longer immersion times, larger fractions of fibres are dissolved to form an amorphous matrix phase (non-crystalline domains). This directly results in a reduction of the overall crystallinity of the composites which was calculated from the XRD data and is shown in Figure 3.

Processing X-ray diffraction data by means of Scherrer's equation (Equation 1) also reveals that the lateral crystallite size normal to the (200) plane, in cellulose composites is reduced with immersion time (Figure 3). The size (width) of the cellulose crystallites was estimated from the width of the peak at 2θ = 22.8° at half-height using the following equation. 1)

D (crystal size) = λ / β . cos θ (Equation
where λ = 1.5418 Å, β: corrected integral width, θ: Bragg angle for the 200 reflection [START_REF] Nishino | All-cellulose composite[END_REF].

At longer immersion times, more cellulose is dissolved and hence smaller cellulose crystallites remain with larger non-crystalline domains being formed. This is also illustrated by the X-ray diffraction photographs of the composites (Figure 4) which indicate that the intensity of the non-crystalline scattering increased with immersion time. Furthermore, the reduction in the sharpness of the reflections for the composites prepared with longer immersion time also indicates lower molecular orientations in these composites. This is caused by an increase in the fraction of the formed amorphous phase (no orientation) with immersion time [START_REF] Kong | Influence of domain orientation on the mechanical properties of regenerated cellulose fibers[END_REF]. Correspondingly, the scanning electron micrographs (SEM) of the cross-section of the composites (Figure 5) show that longer immersion times lead to a reduction in fibre size and the formation of thicker matrix layers between the remaining fibre cores. From these scanning electron micrographs, the estimated volume fractions of the composites were determined by distinguishing each fraction and weighing. These results are illustrated in Figure 6.

As shown in Figure 7, in plant fibres, the outer layers of the fibres mainly consists of unordered or poorly oriented crystalline cellulose when compared to the inner core layers [START_REF] Lu | Self-reinforced melt processable composites of sisal[END_REF][START_REF] Klemm | Cellulose. Biopolymers[END_REF][START_REF] Krässig | Cellulose: Structure Accessibility and Reactivity[END_REF]. This should be beneficial for our surface selective dissolution process as in this approach, only the thin, less oriented, outer layers of the fibres are dissolved which reform into a matrix phase, leaving the majority of the oriented high crystalline core of the fibre unaffected. From X-ray diffraction results, the composites prepared with 1 to 6 hours immersion time still exhibit a high crystalline character which is close to that of the original ramie fibres [START_REF] Nishino | All-cellulose composite[END_REF]. The scanning electron micrographs of these composites also reveal that the original fibres are largely retained.

This would certainly explain that the fibre's strength is essentially maintained in the composites.

The tensile tests of the composites tested in the longitudinal (fibre) direction (Figure 8) show that the composite prepared with 2 hours immersion time exhibits the best properties. At this preparation condition, the amount of outer layer of the fibres which is dissolved to create a matrix phase is adequate to bond the remaining core fibres efficiently together (Figure 5; 2h), leading to a good interfacial bond and stress transfer in the composite. As also shown in Figure 6, the amount of voids in the composites are decreased from 6 vol.% to less than 1 vol.% for 2 hours immersion time and longer.

Moreover, after partial dissolution of 2 hours, still only a relatively small amount of fibre is dissolved, leading to a high fibre volume fraction in the composite of ~84%

(Figure 6). The good interfacial interaction together with the high fibre volume fraction and high remaining fibre strength, results in an optimum in properties for the composites with a high longitudinal tensile strength and Young's modulus. For the composite of 1 hour immersion time, a smaller amount of fibre surface is dissolved to form a matrix phase which apparently is not sufficient to provide a good interfacial bonding between the fibres in the composite. As illustrated by the SEM photographs (Figure 5), the composite of 1 hour immersion time displays cracks and voids in between the fibres over the cross-sectional area. Only a discontinuous phase of very thin films of regenerated cellulose is formed between the fibres. Usually, a discontinuous phase connecting fibres together such as in particle board, is considered as a binder rather than a matrix phase. Although, for some of the all-cellulose composites here, the matrix is more like a binder, we will refer to it in this paper as a matrix. For the composite prepared with 1 hour immersion time, the SEM photograph (Figure 5; 1h) obviously points-out an inadequate formation of a matrix phase in this composite which causes a reduction in its stress transfer capability. The failure mode of this composite appears brush-like with extensive debonding along the fibres as shown in Figure 9. Due to the poor bonding between the fibres, this composite exhibits inferior mechanical properties compared to the composite of 2 hours immersion time even though for the 1 hour condition a smaller fraction of the fibres is dissolved. On the other hand, composites prepared at 3 hours immersion time results in enhanced interfacial bonding between fibre and matrix since a large fraction of the fibre surfaces is dissolved, forming a matrix phase to unite the aligned fibres. The SEM photographs in Figure 5 reveal that cracks and voids over the cross-sectional area of the composites were found to diminish and a thicker matrix phase between the reinforcing fibres is observed. In addition, Figure 9 illustrates that the failure mode of these composites tends to become more brittle with less debonding between fibre and matrix phases and a smaller amount of fibre pull-out, indicating strong interfacial adhesion [START_REF] Wibowo | Chopped industrial hemp fiber reinforced cellulosic plastic biocomposites: thermomechanical and morphological properties[END_REF][START_REF] Mohanty | Effect of process engineering on the performance of natural fibre reinforced cellulose acetate biocomposites[END_REF][START_REF] Nishino | All-cellulose composite[END_REF] when the immersion time is increased. However, with increasing immersion time more of the fibre core is dissolved and as a result a significant reduction in composite strength is found compared to the original fibre strength. This causes an overall reduction in longitudinal composite properties, which ultimately gets close to that of the pure cellulose matrix. In Figure 10, the stress-strain curves of the composites and the pure cellulose matrix show that the behaviour of the composites becomes similar to that of the pure cellulose matrix when the immersion time is increased. With increasing immersion time, the remaining fibre volume fraction in the resulting composites is reduced, which according to the 'rule of mixtures' theory for unidirectional composites, should lead to a linear reduction in mechanical properties of the composites [START_REF] Hull | Elastic deformation of long-fibre composites[END_REF].

A good indication for the level of interfacial adhesion between fibres in a composite can be determined through the evaluation of the transverse properties of a unidirectional composite laminate as shown in Figure 8. In this case, the composites prepared with the longer immersion times exhibit the better transverse tensile strength. The improvement in the transverse tensile strength with immersion time implies a better interfacial adhesion in these composites. In addition, the observation of optical transparency (Figure 11) is another indication for an improved interfacial adhesion of the composites, as this transparency requires a perfect interphase with a perfect bonding between matrix and fibre [START_REF] Gindl | All-cellulose nanocomposite[END_REF][START_REF] Nishino | All-cellulose composite prepared by selective dissolving of fiber surface[END_REF]. Nevertheless, the elongation at break of the transverse composites is very low compared to that of the pure cellulose matrix, even for the composites prepared with the longest immersion times of 12 hours. This is due to the highly oriented character of the fibres which causes cracks to be easily initiated and propagated along these anisotropic fibres compared to a crack propagating in an isotropic cellulose matrix.

According to the previous work of Nishino et al. [START_REF] Nishino | All-cellulose composite[END_REF], the all-cellulose composites prepared by impregnation resulted in a transverse tensile strength of nearly 12 MPa which was further improved to around 17 MPa after pre-treatment of the fibres.

In this work, the composites of 2 and 3 hours immersion time already exhibit a better transverse tensile strength than the composites prepared by matrix impregnation with values of approximately 22 MPa and 31 MPa, respectively. It appears that the present preparation method can provide a much better interfacial adhesion between the fibres and the matrix than in the previously used impregnation method because the selective dissolution method results in an interphasial region, which minimises stress concentrations and voids that may lead to the initiation of cracks. The strong interfacial bond in these composites can be ascribed to the presence of strong hydrogen bonding within the cellulose fibre, matrix phase and interphasial region [START_REF] Soykeabkaew | Preparation and characterization of jute-and flax-reinforced starch-based composite foams[END_REF]. The tensile strength (in the longitudinal direction) of previously reported all-cellulose composites prepared by a cellulose matrix impregnation technique averaged 480 MPa [START_REF] Nishino | All-cellulose composite[END_REF] and 440 MPa [26]. For the present work a composite of 2 hours immersion time, results in a similarly high average longitudinal tensile strength of 460 MPa. This value is relatively high especially if we bear in mind that in this case the slightly oriented fibre skins were dissolved to form the matrix, while in another method the oriented fibres were kept intact and impregnated with an isotropic cellulose matrix. However, this reason appears to cause only a slight difference in tensile strength compared to the composites prepared with the impregnation technique which indicates that the surface selective dissolution process at the optimum condition only affects the low oriented fibre skins with the high oriented core of the fibre remaining intact. Supposedly after 2 hours immersion time, the present preparation method results in the dissolution of only the thin outer layer of the fibres, which mainly consists of disordered or less oriented crystalline cellulose that does not contribute that much to the original fibre's strength. With only the less oriented fibre skin transformed into an isotropic matrix phase the highly crystalline core fibre remains largely unaffected and imparts a highly efficient reinforcing effect into the composites [START_REF] Lu | Self-reinforced melt processable composites of sisal[END_REF][START_REF] Klemm | Cellulose. Biopolymers[END_REF][START_REF] Krässig | Cellulose: Structure Accessibility and Reactivity[END_REF].

Figure 12 shows a comparison in mechanical properties of the all-cellulose composites prepared in this work to all-cellulose composites (ACC) in previous works and other unidirectional natural fibres based composites. For comparison, all composites are unidirectional except for two all-cellulose composites (in the rectangular box) which reinforcements are randomly oriented. The all-cellulose based composites (in the grey area) exhibit superior performances over other unidirectional natural fibres based composites especially, the three all-cellulose composites (in the circle) from Qin et al. [26], Gindl et al. [START_REF] Gindl | Drawing of self-reinforced cellulose films[END_REF] and the present study.

Conclusions

All-cellulose composites were successfully prepared by a surface selective or partial dissolution method of aligned fibres. During preparation, as the immersion time of the aligned ramie fibres in the solvent is increased, larger fractions of the fibre skin are dissolved to form a matrix phase resulting in an assembly of highly oriented fibre cores imparting an effective reinforcing effect to the all-cellulose composites. It was found that with increasing dissolution time a better interfacial adhesion between cellulose fibre and matrix was created which allows for a good stress transfer capability in the composite. Longitudinal tensile tests on unidirectional laminates showed that an immersion time of 2 hours is the optimum processing condition to produce all-cellulose composites with the best overall properties using lithium chloride/N,Ndimethylacetamide as a solvent. At this condition, the amount of fibre surface selectively dissolved to form the matrix phase is adequate to provide sufficient interfacial adhesion to the composite, while the remaining fibre cores maintain most of their initial strength. The obtained all-cellulose composites show excellent mechanical properties which are similar or better than those prepared by a previously reported cellulose matrix impregnation method. The improvement in interface dominated properties like the transverse tensile strength indicates the stronger interfacial interaction in the composites obtained by the present surface selective dissolution preparation method. The outstanding properties of the all-cellulose composites originate from excellent mechanical properties of cellulose itself, the creation of a strong interface between the chemically identical cellulose reinforcement and matrix, resulting in a high efficiency of cellulose fibres in combination with very high fibre volume fractions.

Caption of Figures

Fig. 1 Surface selective dissolution process to prepare all-cellulose composites.

  The transverse tensile strength of composites prepared with 3 to 6 hours immersion time remain fairly constant and around 29-33 MPa, while longer immersion time results in the composites' properties approaching those of pure cellulose matrix properties. The transverse tensile strength of the composites of 9 and 12 hours immersion time were in 37 and 40 MPa, respectively, compared to pure cellulose matrix strength of 59 MPa.

Fig. 2 X

 2 Fig. 2 X-ray diffraction profiles of the all-cellulose composites, indicating the

Fig. 3

 3 Fig. 3 Effect of immersion time on % crystallinity and cellulose crystallite size (nm) of

Fig. 4 XFig. 5 Fig. 6

 456 Fig. 4 X-ray diffraction photographs of the all-cellulose composites, showing the

Fig. 7 Fig. 8 Fig. 9 Fig. 10

 78910 Fig. 7 Structural design of plant cell wall exemplified by cotton fibres. C = cuticula

Fig. 11

 11 Fig. 11 Optical transparency observation of the all-cellulose composites, indicating the

Fig. 12

 12 Fig. 12 Comparison in mechanical properties of the all-cellulose composites prepared in

Figure 1 Figure 2

 12 Figure 1

Figure 7 Figure 8 ImmersionFigure 9 Figure 10 Figure 11

 7891011 Figure 7

  Figure 12

Table 1

 1 The properties and characteristic of the as-receive ramie fibres (reported with the standard deviation in parentheses)

	Tensile strength (MPa)	768 (154)
	Young's modulus (GPa)	42.0 (7.9)
	Elongation at max. load (%)	2.57 (0.66)
	Average diameter (µm)	24.4 (2.8)

Acknowledgments N.S. gratefully acknowledges the financial support from the Royal Thai Government. Ramie fibres were kindly supplied by Toyobo Co., Ltd. Both N.S. and N.A. acknowledge financial support from the Daiwa Anglo-Japan Foundation. The authors wish to thank to Dr. M. Philips for material characterization discussions, Dr. N. Stingelin-Stutzmann for general discussions, Dr. Z. Luklinska, and Mr. M. Willis for SEM assistance, Dr. K. Berketis and Dr. S. Savona for mechanical testing assistance.


Giovanni Belingardi

Maria Pia Cavatorta
email: maria.cavatorta@polito.it

Davide Salvatore Paolino

A NEW DAMAGE INDEX TO MONITOR THE RANGE OF THE PENETRATION PROCESS IN THICK LAMINATES

Keywords: Low velocity impact, damage accumulation, single and repeated impact tests, polymer matrix composites

A damage variable (damage degree DD) representing the ratio between the absorbed energy and the impact energy was introduced in 1998 by Belingardi and Vadori to assess damage accumulation caused by low-velocity impacts. More recently, repeated impact tests carried out on thick laminates pointed out the significance and extent of the penetration process in thick laminates, which the DD is unable to monitor as, by definition, it reaches the value of one at penetration to remain unchanged over the entire penetration process. In the present paper, a new damage variable (damage index DI) is proposed to overcome shortcomings of the DD with respect to thick laminates. By introducing the displacement of the impactor into the definition of the DI, the depth of the penetration process is taken into account. Normalization by the displacement of the quasi-static perforation test allows for a non-dimensional damage variable which is shown to reach the value of one at perforation. Validity of the approach is proven against impact data obtained for different fibre-matrix architectures and laminate thickness. Results show that the DI can effectively differentiate between penetration and perforation thresholds, increasing monotonically within the range of the penetration process. In particular, the DI is shown to increase linearly with the impact energy up to penetration and to rise quite abruptly within the range of the penetration process. Results for repeated impact tests prove that at first the DI increases quite linearly impact after impact, owing to a steady accumulation of damage. A few impacts before penetration a sudden rise in the DI value points out a change in the rate of damage accumulation.

INTRODUCTION

Energy balances have often being used to evaluate the level of damage accumulation during impact events. In [START_REF] Belingardi | Energy absorption and damage degree in impact testing of composite materials[END_REF][START_REF] Belingardi | Low velocity impact tests of laminate glass-fiberepoxy matrix composite materials plates[END_REF][START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF] Belingardi and Vadori introduced the Damage Degree (DD) defined as the ratio between the absorbed energy and the impact energy. The impact energy E i is the kinetic energy of the impactor right before contact takes place and it is indeed the energy introduced into the specimen. The energy absorbed by the specimen E a can be calculated from the load-displacement curve as the area surrounded by the curve in case of closed load-displacement curves (impact event with rebound) or the area bounded by the load-displacement curve up to a constant level of force and the horizontal axis in case of open load-displacement curves (impact event with no rebound).

Based on the energy viewpoint, penetration should take place the first time the absorbed energy reaches the level of impact energy. Therefore the DD is below one for impact events with rebound while reaches the value of one in case the impactor is stopped with no rebound and specimen penetration is achieved. In [START_REF] Belingardi | Low velocity impact tests of laminate glass-fiberepoxy matrix composite materials plates[END_REF][START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF], it was shown that the relationship between the DD and the impact energy increases monotonically until saturation and a fairly good data interpolation was achieved by a linear regression curve [START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF]. A saturation energy level E sa was defined as the impact energy at which the DD regression curve reaches the value of one. This energy threshold is of practical and theoretical interest since it defines the maximum energy level the laminate can dissipate by means of internal damage mechanisms only [START_REF] Belingardi | Energy absorption and damage degree in impact testing of composite materials[END_REF].

The linear relationship between the DD and the impact energy found in [START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF] agrees well with the second-order relationship proposed by Mian and Quaresimin [4] between the absorption coefficient (defined as the ratio between the absorbed energy E a and the penetration energy E p ) and the intensity coefficient (defined as the ratio between the impact energy E i and the penetration energy E p ). The penetration energy E p is defined in accordance to reference [START_REF] Caprino | Influence of material thickness on the response of carbon-fabric/epoxy panels to low velocity impacts[END_REF] as the absorbed energy depurated by the contribution of friction and it is conventionally measured in perforation tests as the energy level at which the force signal flattens [START_REF] Caprino | Influence of material thickness on the response of carbon-fabric/epoxy panels to low velocity impacts[END_REF]. As it will be explained hereafter, for thick laminates the defined penetration energy E p would rather be an approximate measurement of the perforation energy. However, in the case of thin laminates as the ones examined in [START_REF] Mian | A model for the energy absorption capability of composite laminates[END_REF][START_REF] Caprino | Influence of material thickness on the response of carbon-fabric/epoxy panels to low velocity impacts[END_REF], conditions of laminate penetration and perforation basically coincide.

Going back to the original definition proposed in [START_REF] Mian | A model for the energy absorption capability of composite laminates[END_REF]:

2 = p i p a E E E E (1)
an empirical master curve can be defined, which is shown to hold true for different lay-ups and different composite materials.

A second-order polynomial regression curve was also proposed by Liu [START_REF] Liu | Size effect on impact response of composite laminates[END_REF][START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] to describe the absorbed energy vs. impact energy curve (named by Liu the energy profile) up to penetration:

c bE aE E i i a + + = 2 (2)
Depending on the laminate under study, the linear term and the constant c can be smaller than the quadratic term so that equation ( 2) can be simplified as:

2 i a aE E ≅ (3)
It is worthwhile noticing that by rewriting equation (1) in the form:

2 1 i p a E E E = (4)
the linear coefficient a of Liu's regression curve acquires a specific meaning, being the inverse of the laminate penetration energy.

As pointed out in [START_REF] Liu | Size effect on impact response of composite laminates[END_REF][START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF], while a single energy threshold is generally sufficient to define the impact characteristics of thin laminates, for thick laminates two different threshold values are to be defined:

the penetration threshold P n and the perforation threshold P r .

The penetration threshold is identified at the first time the absorbed energy reaches the level of impact energy and it is therefore conceptually the same as the saturation energy. For impact energies above the penetration threshold, the impactor moves deeper into the laminate. Once the impact energy is high enough, perforation eventually takes place. Between the penetration and perforation thresholds, there exists a range, named by Liu "the range of the penetration process", in which the impact energy and the absorbed energy are equal to each other but which represent different stages of the penetration process with the impactor moving deeper and deeper into the specimen as the impact energy increases.

Damage variables based on the energy viewpoint are obviously unable to catch the different stages of the penetration process as they reach a value of one at the penetration threshold to remain unchanged over the entire penetration process. Penetration and perforation thresholds increase with thickness, so does the range of the penetration process. In other words, while for thin laminates the difference between the penetration and the perforation thresholds can be negligible, for thick laminates the same can become quite significant. For cross-ply glass-epoxy composite laminates, Liu [START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] found that the ratio between the penetration threshold P n and the perforation threshold P r is a function of the laminate thickness t: Equation [START_REF] Caprino | Influence of material thickness on the response of carbon-fabric/epoxy panels to low velocity impacts[END_REF] indicates that for the investigated glass/epoxy laminates, the penetration threshold is about 80% of the perforation threshold. In case of 3-mm thin laminates, the range of penetration process (P r -P n ) is less than 2 J. For 6-mm laminates, a difference of 15 J is found, while for 12-mm thick laminates, (P r -P n ) exceeds 100 J and by far can not be neglected.

As more and more composites have gained ground in automotive, nautical and military applications, fibre-reinforced polymer matrix composites are also utilised in thick-laminate form. One important aspect differentiating thick from thin laminates is indeed the extent and significance of the penetration process up to laminate perforation. In the present paper a new formulation of the DD introduced by Belingardi and Vadori is presented which seems to effectively differentiate between the penetration and the perforation thresholds. Experimental data obtained on laminates of different fibre-resin architectures and thickness are reported to test validity of the approach.

EXPERIMENTAL

Experimental impact tests were performed according to ASTM 3029 standard [START_REF] Astm D | Standard Test Method for Impact Resistance of Rigid Plastic Sheeting or Parts by means of a Tup (Falling Weight)[END_REF] using an instrumented free-fall drop dart testing machine. The impactor has a total mass of 20 kg; its head is hemispherical with a radius of 10 mm. Stainless steel was chosen for its high hardness and resistance to corrosion. The maximum falling height of the testing machine is 2 m, which corresponds to a maximum impact energy of 392 J. The drop-weight apparatus was equipped with a motorized lifting track. The collected data were stored after each impact and the impactor was returned to its original starting height. Using this technique, the chosen impact velocity was consistently obtained in successive impacts. Because, the target holder was rigidly attached to the frame of the testing device, the tup struck the specimen each time at the same location. By means of a piezoelectric load cell, force-time curves were acquired and, with a double integration, forcedisplacement curves were obtained. By additional integration, deformation energy-displacement curves were plotted. Initial conditions were given with the time axis having its origin at the time of impact. At time t=0, the dart coordinate is zero and its initial velocity can be obtained by the well known relationship:

h g v ∆ = 2 0 ( 6
)
where ∆h is defined as the height loss of the centre of mass of the dart with respect to the reference surface [START_REF] Belingardi | Low velocity impact tests of laminate glass-fiberepoxy matrix composite materials plates[END_REF][START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF]. The impact velocity was also measured by an optoelectronic device.

Square specimen panels, with 100 mm edge, were clamped with a 76.2 mm inner diameter, and fixed to a rigid base to prevent slippage of the specimen (Figure 1). The clamping system was designed to provide an uniform pressure all over the clamping area.

Prior to impact tests, a series of quasi-static perforation tests were performed to get information on the laminate strength characteristics. Specimens were tested using a servo-hydraulic machine with maximum loading capacity of 100 kN. The hydraulic actuator was electronically controlled in order to perform constant velocity tests. Signals of the force applied by the actuator and of the actuator displacement were acquired in time with an appropriate sampling rate. [START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] and Sutherland & Guedes Soares [START_REF] Sutherland | Effects of laminate thickness and reinforcement type on the impact behaviour of e-glass/polyester laminates[END_REF] were also employed. Unfortunately, no other literature data could be taken into consideration since not all the information required in the analysis were available from the papers.

FROM THE DAMAGE DEGREE TO THE DAMAGE INDEX

The idea of an improved definition for the DD came up during a series of repeated impact tests on 12.31 mm thick laminates for nautical applications [START_REF] Belingardi | Comparative response in repeated impact tests of hand lay-up and vacuum infusion glass reinforced composites[END_REF]. Four impact energies were considered (25 J, 49 J, 98 J and 147 J corresponding to impact velocities of 1.5 m/s, 2.2 m/s, 3.1 m/s and 3.8 m/s) and a minimum of four specimens for any given energy were subject to forty repeated impacts or up to perforation. The two higher impact energies lead to perforation, while the lower two did not.

However, apart from the 25 J tests, the value of the DD at the first impact was around 0.90 regardless of the impact energy (Figure 2). Moreover, the non-monotonic behaviour of the curves was difficult to explain considering that the DD is a measure of the level of damage induced in the laminate and as such should grow with the impact number.

Another aspect of concern was linked to the fact that a DD of one was not always associated to complete perforation of the laminate. As underlined by Liu [START_REF] Liu | Size effect on impact response of composite laminates[END_REF][START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF], a significant range for the penetration process was to be expected considering the laminate thickness; however, the DD was not able to make any distinction among impact energies above the penetration threshold since by definition it saturates to one [START_REF] Belingardi | Energy absorption and damage degree in impact testing of composite materials[END_REF][START_REF] Belingardi | Low velocity impact tests of laminate glass-fiberepoxy matrix composite materials plates[END_REF][START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF]. The value s MAX in equation ( 7) refers to the displacement value recorded at the instant when the force approximately reaches a constant value, in case of impact tests that cause specimen perforation; while it corresponds to the maximum displacement recorded during the test below the perforation threshold.

In order to make the DI a non-dimensional quantity, the displacement s MAX was normalised by the corresponding displacement s QS measured in quasi-static perforation tests (Figure 3). The choice of normalising by s QS was taken so to leave apart possible strain-rate effects on the s MAX values. Indeed, it is not possible to assume a priori that the value of s MAX would be equal when measured in perforation tests performed at different impact velocities. Therefore, the choice of the quasi-static perforation test is a way of defining an absolute reference test. It is in any case worthwhile saying that results presented in [START_REF] Schoeppner | Delamination threshold loads for low velocity impact on composite laminate[END_REF] suggest that, even in the presence of significant strain-rate effects on the delamination threshold load (DTL), the displacement value measured at DTL remains almost constant. Indeed, at least for the laminates investigated in the study, the s MAX of perforation tests was constant regardless of the impact velocity and equal to the s QS value.

DI vs. DD: ANALYSIS OF IMPACT DATA

As already discussed, results obtained on 12.31 mm thick glass/vinylester laminates showed that the DD value was not able to effectively tell apart impact tests performed at different impact energies, at least with reference to the first impact.

Figure 4 plots the DD and DI data against the impact energy. As it can be observed, the DI increases for increasing impact energies. Data scatter is very limited and a remarkable correlation exists with a linear regression curve.

The overall data referring to the series of repeated impacts tests are shown in Figure 5. As it can be observed, the DI data, not only show a different value at first impact for different impact energies, but, given the impact energy, increase monotonically with the impact number owing to the process of damage accumulation.

As with the DD, the DI remains basically constant for the 25 J tests while it slowly increases impact after impact for the 49 J tests, denoting a slow but steady accumulation of damage. For both perforation tests (98 J and 147 J tests), the DI shows an initial steady increase followed by an abrupt growth up to perforation. Figures 67are close ups of the 147 J and 98 J repeated impact tests, respectively. They clearly display that the initial portion of steady damage accumulation corresponds to a linear growth of the DI. In Figure 6 it can be observed how the DI effectively differentiates between penetration and perforation, while the DD reaches the value of one as soon as penetration occurs. Another advantage of the DI over the DD can be noticed in Figure 7. Again the repeated impact test was carried out up to laminate perforation. Starting from the 18 th impact, the DI visibly shows that a change in the rate of damage accumulation is taking place helping foreseeing laminate penetration. In this respect, the DD appears less sensitive.

When considering Figure 4, it is worthwhile noticing that the fitting curves of both the DD and DI do not intersect the origin of the axes, meaning that a non-zero damage is present at zero impact energy. To investigate the initial portion of the DD/DI-impact energy curves, additional tests were performed at very low impact energies. Results are reported in Figure 8. As expected, the previously evaluated linear regression (Figure 4) does not hold true for very low impact energies. Nevertheless, while for the DD the initial step rise is quite abrupt and extrapolation of the linear fit to impact energies close to zero leads to high positive DD values which cannot represent the damage induced by impacts at almost null energies; for the DI the initial step rise is rather small so that the extrapolated DI values are still very close to zero.

In the attempt to prove the potentiality of the approach also in case of single impact tests up to laminate perforation, the open literature was reviewed in search of suitable impact data obtained on thick laminates. Unfortunately, almost all reviewed papers provide impact and absorbed energies but make no reference to displacement data. The only viable literature sources were [START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] and [START_REF] Sutherland | Effects of laminate thickness and reinforcement type on the impact behaviour of e-glass/polyester laminates[END_REF]. In [START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] examination of the load-displacement curves revealed that, in impact tests where perforation occurred, the displacement value at which the force signal becomes constant is about the same regardless of the impact energy. The curves also show that no significant strain-rate effect exists.

Not having access to the quasi-static perforation curve, it was assumed that the quasi-static displacement s QS was equal to the s MAX at perforation, similarly to what observed in thick glass/vinylester laminates [START_REF] Belingardi | Comparative response in repeated impact tests of hand lay-up and vacuum infusion glass reinforced composites[END_REF]. Figure 9 depicts impact data for a 6.25 mm thick glass-epoxy laminate [START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF] analysed in terms of DD and DI. As it can be observed, the DI vs. impact energy curve is linear up to the penetration threshold. Also the DI effectively distinguishes between the penetration threshold and the perforation threshold, while the DD stays at the value of one over the entire range of the penetration process.

In [START_REF] Sutherland | Effects of laminate thickness and reinforcement type on the impact behaviour of e-glass/polyester laminates[END_REF] a rather complete set of impact data including impact energy, absorbed energy and maximum displacement is reported in the Appendix for the seven glass/polyester laminates under study.

Unfortunately for most tested laminates, impact energies are below the penetration threshold.

Moreover, definition of the maximum displacement is explicitly given only in case of impact tests with rebound for which the datum is said to refer to the displacement corresponding to the maximum force. When penetration is achieved, given data are difficult to interpret as the reported values are extremely variable and, in some cases, more than four times the displacement value just before penetration. Only for a 10-ply chopped-strand-mat, about 10.50 mm thick, data appear to be quite consistent and were used in the analysis. Again the quasi-static displacement s QS was assumed to be equal to the displacement s MAX at perforation. Figure 10 reports the impact data analysed in terms of DI and DD. The main interest for data shown in Figure 10 lies in the fact that impact tests were performed with impactors of mass ranging from 2.853 to 10.853 kg, i.e. data referring to a given impact energy were obtained at different impact velocities. As it can be seen, data scattering is rather limited for both the DD and DI curve showing that, at least in the analysed case, the damage variables are not strain-rate sensitive.

Provided that the range of the penetration process is less significant for thin laminates, it was decided to prove the DI against the DD in the case of thin laminates for which the DD was proven to work quite satisfactory. 2. It can be observed that, given the lay-up, the slope (i.e. the rate of accumulated damage) decreases with the number of layers, while, given the number of layers, the slope is lower in the case of the [0/90] n lay-up. A slower accumulation of damage well correlates with a higher penetration threshold [START_REF] Belingardi | Influence of the laminate thickness in low velocity impact behaviour of composite material plate[END_REF].

CONCLUSIONS

A new damage variable, the damage index DI, has been presented in the paper aimed at overcoming shortcomings of the damage degree (DD) in case of thick composite laminates. In particular, displacement of the impactor during the test has been introduced into the DI definition so that the depth of the penetration process within the laminate can be correctly investigated; whereas the DD, by definition, stays at a value of one over the entire penetration process. Normalization by the displacement of the quasi-static perforation test allows for a non-dimensional damage variable which is shown to reach the value of one at laminate perforation.

Analysis of single impacts on different fibre-matrix architectures and laminate thickness have pointed out suitability of the DI to differentiate between penetration and perforation thresholds.

Below penetration, the DI increases linearly with the impact energy while it undergoes an abrupt rise within the range of the penetration process. When used to elaborate impact data on thin laminates, the DI is in good agreement with results obtained for the DD. In any case, the correlation coefficient for the linear regression of the impact energy curve is higher for the DI than it is for the DD. Tests run at low impact energies pointed out that the linear regression does not hold true for very low impact energies. However, while for the DD the initial step rise is quite abrupt and extrapolation of the linear fit to impact energies close to zero leads to high positive DD values which cannot represent the damage induced by impacts at almost null energies; for the DI the initial step rise is rather small so that the extrapolated DI values are still very close to zero.

When introduced to analyse data of repeated impact tests, the DI is shown to initially increase linearly impact after impact, owing to a steady accumulation of damage, to then grow quite abruptly a few impacts before penetration, signalling a change in the rate of damage accumulation.

1 ,

 1 The idea of a new damage variable, named hereafter the damage index (DI), aroused considering that in the range of the penetration process, the impactor moves deeper and deeper into the specimen as the impact energy increases. It was therefore decided to introduce into the damage variable a measure of how far the impactor had penetrated into the laminate:

Figure 11

 11 Figure 11 reports the DI and the DD values for impact tests performed on 4.50 mm glass-epoxy laminates [12]. The range of the penetration process is only a few Joules, however the DI once again permits to differentiate between the two energy thresholds, signalling laminate penetration with an abrupt growth of the DI and reaching the value of one at perforation. The linear regression curve up to laminate penetration is again characterised by an excellent correlation coefficient.Figures 12-13 plot the DD and the DI for the thin carbon-epoxy laminates originally used to test the DD concept [3]. In case of very thin laminates, plots of the DD against the impact energy are quite satisfactory; however, Figures 13-14 demonstrate that the correlation coefficient for the DI is always higher than the one associated to the DD. Once again, while the DD stays at a value of one over the entire range of the penetration process, the DI reaches the value of one only at perforation pointing out the onset of the penetration process with a sudden abrupt growth. Slopes of the DI vs. impact energy plots of Figures 12-13 are reported inTable 2. It can be observed

Figure 3 .

 3 Figure 3. An example of quasi-static perforation tests and impact tests to perforation[START_REF] Schoeppner | Delamination threshold loads for low velocity impact on composite laminate[END_REF]. Definition of the displacement variables s MAX and s QS ..

Figure 4 .

 4 Figure 4. Value of the DD and DI at first impact vs. impact energy. Data for glass/vinylester + polyester 12.31 mm laminates.

Figure 5 .

 5 Figure 5. A comparison between the DD and the DI for repeated impact tests on glass/vinylester + polyester 12.31 mm laminates.

Figure 6 .

 6 Figure 6. The DD and DI parameters in repeated impact tests up to laminate perforation. Impact energy: 147 J.

Figure 7 .Figure 8 .

 78 Figure 7. The DD and DI parameters in repeated impact tests up to laminate perforation. Impact energy: 98 J

Figure 9 .

 9 Figure 9. A comparison between the DD and the DI for impact tests on glass/epoxy 6.25 mm laminates[START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF].

Figure 10 .

 10 Figure 10. DI and DD plotted against impact energy for 10.50 mm glass-polyester laminates[START_REF] Sutherland | Effects of laminate thickness and reinforcement type on the impact behaviour of e-glass/polyester laminates[END_REF]. The impacting mass varies from 2.853 to 10.853 kg.

Figure 11 .

 11 Figure 11. A comparison between the DD and the DI for impact tests on glass/epoxy 4.50 mm laminates.

Figure 12 .Figure 1 .

 121 Figure 12. A comparison between the DD and the DI for impact tests on carbon/epoxy laminates. Lay-up: [0/60/-60] n

Figure 2 .Figure 3 .

 23 Figure 2. DD vs. impact number. Series of repeated impact tests on glass/vinylester + polyester 12.31 mm laminates.

Figure 4 .

 4 Figure 4. Value of the DD and DI at first impact vs. impact energy. Data for glass/vinylester + polyester 12.31 mm laminates.

Figure 5 .

 5 Figure 5. A comparison between the DD and the DI for repeated impact tests on glass/vinylester + polyester 12.31 mm laminates.

Figure 6 .

 6 Figure 6. The DD and DI parameters in repeated impact tests up to laminate perforation. Impact energy: 147 J.

Figure 7 .Figure 8 .

 78 Figure 7. The DD and DI parameters in repeated impact tests up to laminate perforation. Impact energy: 98 J

Figure 9 .

 9 Figure 9. A comparison between the DD and the DI for impact tests on glass/epoxy 6.25 mm laminates[START_REF] Liu | Characterization of impact properties and damage process of glass/epoxy composite laminates[END_REF].

Figure 10 .

 10 Figure 10. DI and DD plotted against impact energy for 10.50 mm glass-polyester laminates[START_REF] Sutherland | Effects of laminate thickness and reinforcement type on the impact behaviour of e-glass/polyester laminates[END_REF]. The impacting mass varies from 2.853 to 10.853 kg.

Figure 11 .

 11 Figure 11. A comparison between the DD and the DI for impact tests on glass/epoxy 4.50 mm laminates.

Figure 13 .

 13 Figure 13. A comparison between the DD and the DI for impact tests on carbon/epoxy laminates. Lay-up: [0/90] n

Table 1

 1 reports main characteristics of the laminates used in the study. Together with test data obtained by the authors, test results by Liu

Table 1 .

 1 Main characteristics of the laminates analysed in the paper

				Nominal
	Reference Fibre /Matrix	Lay-up	Thickness
				[mm]
	[10]	Glass/Vinylester	[random/0 2 /90/random/90/0 2 /random]	12.31
	[9]	+Polyester Glass/Polyester	10-ply chopped-strand-mat	≈10.50
	[7]	Glass/Epoxy	[0/90/0/…] 9	6.25
	[11]	Glass/Epoxy	[random/-45/+45/0 2 ] 2	4.50
			[0/90] 4	0.35
			[0/90] 8	0.75
			[0/90] 16	1.55
	[3]	Carbon/Epoxy	[0/60/-60] 4	0.40
			[0/60/-60] 8	0.85
			[0/60/-60] 16	1.75

Table 2 -

 2 Slope of the DI vs. impact energy curves (Figures12-13) Testing fixture for impact testing (dimensions are in mm). Figure 2. DD vs. impact number. Series of repeated impact tests on glass/vinylester + polyester 12.31 mm laminates.

	Slope of the DI-impact energy curve (× × × × 10 4 )
		[0/60/-60] n	[0/90] n
	n=4	160	64
	n=8	46	19
	n=16	15	9

Figure 12. A comparison between the DD and the DI for impact tests on carbon/epoxy laminates. Lay-up: [0/60/-60] n