A Bouaziz

F Zaïri

M Naït-Abdelaziz

J M Gloaguen

J M Lefebvre

Micromechanical modelling and experimental investigation of random discontinuous glass fiber polymer matrix composites

Keywords: A. Polymer-matrix composites (PMCs), B. Modelling, B. Microstructure, B. Debonding, D. Videoextensometry

Videomeasurements were used to estimate the damage in chopped random glass fiber polymer matrix composites. In order to predict the overall mechanical behaviour, voiding evolution induced by fiber debonding is incorporated into a micromechanics-based constitutive model. The comparison between the experimental data and the numerical predictions shows a very good agreement.

Introduction

Fiber-reinforced polymer matrix composites are widely used in industry as structural materials and then there is an evident need for the prediction of their mechanical properties. In this kind of materials, various damage phenomena can occur such as matrix cracking, interfacial debonding, fiber pull-out and fiber fracture. The predominant damage mechanism may vary according to fiber volume fraction and aspect ratio, orientation and distribution in the composite, strengths of the interface and each constituent, and loading mode. Progressive damage accumulation in the composite is known to affect the overall mechanical properties.

In order to estimate the overall response of the material, the accumulated damage must therefore be included in the constitutive relations. Furthermore, in order to achieve a rigorous description of material, the constitutive equations must be derived from micromechanical considerations. However, due to the complexity of the microstructure, the damage mechanisms in fiber-reinforced polymer matrix composites are not fully understood from the experimental point of view. Nevertheless, some micromechanical analyses have been proposed in literature to simulate the damage response of discontinuously fiber-reinforced composites. Meraghni and Benzeggagh [START_REF] Meraghni | Micromechanical modeling of matrix degradation in randomly discontinuous-fibre composites[END_REF] and Meraghni et al. [START_REF] Meraghni | Effect of interfacial decohesion on stiffness reduction in a random discontinuous-fibre composite containing matrix microcracks[END_REF][START_REF] Meraghni | Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures[END_REF] identified damage mechanisms in a random discontinuous fiber-reinforced composite based on acoustic emission. The authors proposed a micromechanical analysis based on a modified version of the Mori-Tanaka model to investigate the effect of damage mechanisms on the overall response. Similar analyses were made by Fitoussi et al. [START_REF] Fitoussi | Prediction of the anisotropic damaged behavior of composite materials: introduction of multilocal failure criteria in a micro-macro relationship[END_REF][START_REF] Fitoussi | A statistical micromechanical model of anisotropic damage for SMC composites[END_REF] and Derrien et al. [START_REF] Derrien | Prediction of the effective damage properties and failure properties of nonlinear anisotropic discontinuous reinforced composites[END_REF] relying on the ultrasonic method and the Mori-Tanaka approach. Considering fibers randomly oriented in a ductile polymer matrix, Lee and Simunovic [START_REF] Lee | Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites[END_REF][START_REF] Lee | A damage constitutive model of progressive debonding in aligned discontinuous fiber composites[END_REF][START_REF] Lee | A damage mechanics model of crack-weakened, chopped fiber composites under impact loading[END_REF] recently proposed a micromechanical model. In all these investigations, the damage evolution was introduced into the micromechanical approach from probabilistic considerations in the form of a Weibull statistical density function. This probability function introduces additional parameters generally calibrated on an experimental stress-strain curve.

In the present paper, the damage behaviour of glass mat fiber-reinforced polymer matrix composite is investigated using a combined approach of micromechanical modelling and experimental characterization. A representative composite, consisting of a polyester matrix incorporating various volume fractions of randomly oriented glass fibers, was chosen. Rather than using the methods (acoustic emission and ultrasonic) usually employed, an alternative technique based on volume strain variation is retained to quantify the progressive interfacial damage in the material. The progressive damage observed on the macroscopic level was identified at the microscopic level by SEM observations. Damage evolution is introduced into a micromechanical model based on the Eshelby formulation and the ensemble-volume averaging homogenization process. The resulting micromechanical model is implemented numerically and used to simulate uniaxial loading for the sake of comparison with experimental results.

Experiments

Material

The composite under study consists of randomly oriented chopped (E-glass) fibers embedded in an unsaturated polyester matrix. The material was fabricated by compression molding at room temperature from mat densities of 300 and 450g/m 2 . Each fiber is constituted by a bundle of 50 filaments of about 10µm in diameter and 50mm in length. The fibers, randomly distributed in the plane of the material, exhibit an aspect ratio α of about 100. The fiber volume fraction, obtained by burning off the polyester matrix, is found to be 13 and 21%. For convenience in the remaining of the paper, the glass fiber reinforced polyester (GFRP) composites are coded as follows: GFRP -21R and GFRP-13R for the 21 and 13% fiber volume fractions respectively.

Experimental method

In literature, the damage response in fiber reinforced polymer composites is experimentally addressed from acoustic emission or ultrasonic techniques. In these methods, the void nucleation at the interfaces is not explicitly quantified and is completely ignored in the associated modelling. In this paper, video-controlled tensile tests and scanning electron microscope (SEM) observations were achieved in order to understand the basic mechanisms governing deformation in the composite material.

Parallelepipedic plates were machined to the specimen shape presented in Fig. 1. Rather than using a normalized specimen with constant cross-section, we have designed this specific geometry of the specimen in order to localize the damage in the central part. The large radius of curvature allows to be freed from the stress triaxiality dependence.

The mechanical behaviour of the composite material was determined at room temperature by tensile tests on an Instron © (model 5800) machine equipped with videotraction © extensometer. The videotraction © set-up consists of a CCD videocamera and an unit for image digitizing and analyzing as schematically represented in Fig. 2 [START_REF] François | Volume strain measurements by optical extensometry: application to the tensile behaviour of RT-PMMA[END_REF][START_REF] Sell | Experimental characterization of deformation damage in solid polymers under tension, and its interrelation with necking[END_REF]. Contrary to standard strain measurement methods such as gauge which impose a measure with contact, the optical extensometer allows to avoid the potential damage initiation on the specimen surface. The technique consists in following, in real time, the location of the center of gravity of ink marks drawn on the sample surface (Fig. 1). Five round markers (A, B, C, D and E) are aligned along the tensile axis 1, each located 1mm apart (center-to-center). Two others (F and G) are placed on the perpendicular axis 2 and are separated as much as possible. Their diameter is about of 0.5mm. The objective of the method is to determine the three principal strains in the representative volume element (RVE) defined by the three transversal markers [START_REF] Sell | Experimental characterization of deformation damage in solid polymers under tension, and its interrelation with necking[END_REF]. The thickness of the RVE is about 0.2mm. The surface containing the seven markers is digitized and the coordinates of their gravity centers are provided 50 times per second with a precision of about 0.05 pixel, which gives a precision on the deformation of about 0.0002. The axial strain is determined from the partial axial strains induced by the relative displacement of markers dispos ed along the axis 1. The partial axial strains are given by: ( ) where ( 00 AB , 00 BC , 00 CD, 00 DE ) and ( AB , BC , CD , DE ) are initial and extended distances defined in Fig. 1. The axial strain in the RVE is obtained by a nonlinear polynomial interpolation from the four partial axial strains [START_REF] Sell | Experimental characterization of deformation damage in solid polymers under tension, and its interrelation with necking[END_REF]:

( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) 1111111111 Enonlinear interpolation from E,E,E,E =   FCG ABBCCDDE (2)
The transversal strain is given by: ( )

00 2222 00 FGFG EEFG FG - == (3)
where 00 FG and FG are initial and extended distances of the transversal markers. Note that since only one camera is used, 22 E and 33 E are assumed equal.

Once the three principal strains are measured in the RVE, the local volume variation measuring the dilatation in the material can be calculated from the following relation:

( )( ) ( ) 0 112233 0 1111 v VV EEEE V - ==+++- (4)
where 0 V and V are the initial and current volume of the RVE.

The damaged local volume variation is given by:

de vvv EEE =- (5)
where e v E is the elastic part of the volume variation defined by: ( ) 11 12

e v E E ν Σ =- (6)
In ( 6) ν is the Poisson's ratio, E is the Young's modulus and 11 Σ is the stress given by: ( ) ( )

11 02233 11
F SEE Σ= ++ ( 7
)
where F is the applied load on the specimen and 0 S is the initial cross-section.

Experimental results

The local axial strain rate, during a tensile test at a constant cross-head speed of 0.2mm/min, is displayed in Fig. 3a as a function of time. The global strain rate is determined from the cross-head speed and the initial grip to grip distance (80mm). It is clear that the local strain rate is not constant during deformation. Indeed, it shows a decrease followed by an increase due to an heterogeneous deformation. In order to model the local behaviour of the damaged composites for a strain driven test, it is fundamental to keep the local strain rate constant. The system used in this study is able to control the local strain rate. Fig. 3b shows result of a test at a local constant strain rate of 4.10 -5 s -1 . Monitoring of the cross-head speed by the videotraction system is clearly seen. This control is achieved in real time with the simultaneous data measurements.

The stress-strain curves of composites conducted at a local constant strain rate of 10 -4 s -1 are given in Fig. 4. The strain at break of these composite specimens is of the order of 0.01.

Therefore, these chopped random fiber composites are brittle in nature.

As shown in Fig. 5, a whitening phenomenon is observed in the central part of the specimen.

This phenomenon is generally associated in the literature with voids occuring in the material.

The whitening appears because the void size is larger than the light wavelength (about 0.6µm). It provides an optical verification of nucleation and propagation of voids in the material.

The damaged volume variation is presented as a function of axial strain in Fig. 4. The nucleation and growth stages of microvoiding are both revealed in this figure. It is evident that there exists an incubation strain where no damaged volume strain is observed. Note that for GFRP -21R, there is a small increase and decrease o f the damaged volume strain at the beginning of the loading; this measure has however no meaning since it is in the scattering range of the measurement system. The incubation strain depends on fiber volume fraction since it is equal to 0.004 for GFRP-21R and 0.0055 for GFRP-13R. In this incubation period, the volume variation is associated to the purely elastic dilatation due to the Poisson effect.

Subsequently, an exponential damage increase is observed and the behaviour is approximately the same for the two materials. The scaling of the volume strain depends on fiber volume fraction. For an axial strain of 0.01, a damaged volume variation of 0.007 for GFRP -21R and 0.005 for GFRP-13R is found.

In order to identify the local damage mechanisms and the location of voids, microscopic observations on fracture surfaces at the RVE were achieved by SEM. Fig. 6 shows that the material contains numerous voids. These voids are localised around the fibers. The origin of these voids is attributed to the interfacial damage which seems to be the predominant microscopic damage mechanism in the composite. However, fiber fracture was also seen. Due to high hydrostatic stress, the region of broken fibers is also the site of void nucleation in the matrix. Furthermore, no significant matrix cracking was observed.

Modelling

Constitutive relationships

Traditional continuum mechanics cannot directly predict the correct behaviour of the composite since such an approach is based on continuity and homogeneity of the mater ial.

Indeed the concept of micromechanics is required to perform a rigorous analysis of the material and to predict the effect of microstructure on its overall mechanical properties. The constitutive law of the homogeneous medium equivalent to the heterogeneous material is established from a micromechanical modelling, taking into account both the existence of discontinuous randomly dispersed and oriented glass fibers, and damage evolution.

Chopped glass fibers are assumed to be elastic spheroids (prolate: α >1) randomly dispersed and oriented in the elastic polymer matrix. As the spheroidal fibers are in the 1-2 plane, the composite as a whole is transversely isotropic.

The constitutive equations of the equivalent homogeneous medium is defined by:

: = SCE (8)
where S and E are the macroscopic stress and macroscopic strain tensors, respectively, and C is the fourth-order elastic stiffness tensor of the composite polymer (":" signifies the tensor contraction).

The volume-averaged stress S and strain E tensors are given respectively by:

( )

1 = ∫ V dV V Ssx and
( )

1 = ∫ V dV V E ex (9)
where s and e are the microscopic stress and microscopic strain tensors, respectively and V is the volume of a RVE.

The fiber-reinforced composite presents initially p erfect interfacial bonding between the matrix (phase 0) and fibers (phase 1). After its nucleation, damage (phase 2) is taken into account as an added phase in the composite. Therefore, the initial two-phase composite becomes a three-phase composite from the onset of damage nucleation.

According to the explicit formulation derived by Ju and Chen [START_REF] Ju | Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities[END_REF] for unidirectionally aligned spheroid-reinforced composites, the macroscopic stiffness tensor of the equivalent homogeneous medium is defined by the following expression:

( )

2 1 0 1 - =  =+-  ∑ rrr r CCIBISB ( 10
)
where I is the fourth-rank identity tensor, 0 C is the elasticity tensor of the matrix material, r S is the Eshelby's tensor for phase r and r B is a fourth-rank tensor defined by:

( )

1 1 00 φ - -  =+-  rrrr BSCCC (11)
where r C and φ r are respectively the elasticity tensor and the volume fraction of the phase r.

The Eshe lby's tensor r S is a function of the Poisson's ratio of the matrix and the aspect ratio of the phase r. Its formulation for a spheroidal inclusion embedded in an isotropic linear elastic medium can be found in literature [START_REF] Lee | A damage constitutive model of progressive debonding in aligned discontinuous fiber composites[END_REF][START_REF] Ju | A novel formulation for the exterior-point Eshelby's tensor of an ellipsoidal inclusion[END_REF].

Since for the studied material the fibers are randomly oriented in the 1-2 plane, it is necessary to introduce global axes denoted by the unprimed axes and local axes of each fibers denoted by the primed axes (Fig. 7). The random orientation of glass fibers can be then described by introducing the angle θ between the primed and unprimed axes:

' iijj xQx = (12)
where the transformation matrix ij Q is given by: cossin0 sincos0 001

θθ θθ   =-   ij Q (13)
In [START_REF] Ju | A novel formulation for the exterior-point Eshelby's tensor of an ellipsoidal inclusion[END_REF], θ ( 0 θπ ≤≤) is the angle between 1 x and ' x .

According to the studies of Tandon and Weng [START_REF] Tandon | Average stress in the matrix and effective moduli of randomly oriented composites[END_REF] and Lee and Simunovic [START_REF] Lee | Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites[END_REF], the orientational averaging process for all orientations for the macroscopic stiffness tensor can be written as:

( )

0 sin minjmnpqpkql QQCQQpd π θθθ = ∫ C ( 14
)
where ( ) p θ is the probability density function of the random orientation which is equal to 1 π for uniformly random orientation.

In order to achieve more realistic behaviour predictions, the damage experimentally identified must be included in the modelling. Based on experimental evidence, the debonding along the interface between the matrix and fibers is the major failure mechanism in this material. The interfacial debonding under increasing deformation leads to the creation of new surfaces inducing void volume variation in the material. The increase of the void volume fraction is assumed to be a coupled effect of nucleation of voids and growth of these voids. The rate of void volume fraction is governed by the following evolution relation:

2 nuclgrow φφφ =+ &&& ( 15
)
where nucl φ & is the nucleation rate of voids and grow φ & is the growth rate of existing voids.

The nucleation rate, linked to the local hydrostatic stress applied on the fiber, is expressed in a simple empirical way. The progressive partial debonding between fibers and the matrix can be taken into account with the Weibull statistical function [START_REF] Weibull | A statistical distribution function of wide applicability[END_REF]:

( )

1 1 1exp m h dh u P σ σ σ    =--    ( 16
)
where 1 h σ is the average internal hydrostatic stress of the fibers, m and u σ are the Weibull parameters to be estimated from experiments. m controls the shape of the Weibull function and u σ its scale.

From the Eshelby inclusion theory, the stress inside fibers is assumed uniform and is given by [START_REF] Lee | Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites[END_REF]:

( )

1 2 1 11111 1 : rr r φ - - =  =--  ∑ sCISBISBE (17)
The cumulative volume fraction of debonded fibers is then given by:

( )

1 ddh P φφσ = ( 18
)
where φ is the original volume fraction of bonded fibers.

After partial debonding, the debonded portion of the fiber does not transmit any more stresses to the matrix. The debonding process is mechanically complex because it introduces a local induced anisotropy which is not easy to account for. In order to simplify the problem, the debonded part of the fiber is substituted by an equivalent volume of matrix material. By this way, replacing elastic mechanical properties of the debonded fibers by that of the matrix leads to a global weakening of the composite. Moreover, the void volume fraction which is introduced as a third phase, also acts as supplementary weakening factor. The nucleation rate of interfacial voids by the debonding of fibers and the matrix is assumed to be controlled by the stress in the fibers:

( )

1 1 1 dh nucldh h P σ φγφγφσ σ ∂ == ∂ && & (19)
where γ is a scaling coefficient for void nucleation rate and is assumed to be constant.

The growth rate of the previously nucleated microvoids at the interface is given by [START_REF] Steenbrink | Void growth in glassy polymers[END_REF]:

3 4 grownuclh φφ µ =Σ & & ( 20
)
where µ is the shear modulus of the composite. Void growth is governed by the macroscopic hydrostatic stress. The voids are assumed to be spheroidal and to remain of uniform size during deformation. Furthermore, the interactions between the different phases are not taken into consideration in the present model.

The model introduced into a computer algorithm based on the strain driven scheme; the unknown macroscopic stress history is determined by a given macroscopic strain:

: ttttt +∆+∆ =+∆ SSCE (21)
The incremental nonlinear equations for damage are solved using the Trapezoidal scheme:

222 ttt φφφ +∆ =+∆ (22)
where:

222 2 ttt t φφφ +∆ ∆  ∆=+  && (23)
The hydrostatic stress inside the fibers is computed according to (17) and the current volume fraction of bonded fibers is updated in the following way:

1ttdtt φφφ +∆+∆ =- (24)
The volume fractions of damage ( 22) and bonded fibers (24) are updated at each time increment step and are used to compute the progressive evolution of the stiffness tensor. After computation of the current stiffness tensor, the stresses are updated.

Considering the width (23mm) of the specimens used in the mechanical tests (Fig. 1), the geometrical distribution of the fibers (nominal length of fibers is 50mm giving α =100) is expected to be inhomogeneous. Fig. 8 shows the influence of the aspect ratio α of the fibers on the predicted Young's modulus of the composite. It is clear that α influences strongly the Young's modulus for smaller values of α and its effect saturates when considering higher values (about α >30). Therefore, it is worth assuming that all fibers have identical geometry.

Comparison between predicted and measured behaviour

The formulation given in the previous section is now applied to uniaxial loading condition.

The material properties of the unsaturated polyester matrix and fibers are: 0 E =4400MPa, 0 ν =0.35, 1 E =72000MPa, 1 ν =0.25. The Young's modulus and the Poisson's ratio of the matrix are measured from video-controlled tensile tests. The aspect ratio α of fibers is 100.

The parameters of the voids nucleation rate (19) are numerically determined using a least squares regression fitting on the accumulated damage curves observed in the experiments.

They are found to be: m =5, u σ =118MPa and γ =0.08. These values are taken independent of the fiber volume fraction.

The simulated stress-strain responses and damaged volume strain are given in Fig. 9. The model predictions are in very good agreement with experiments. However, the final stage of damage, leading to brutal fracture, is not well represented. In this final stage, the simulated damage evolution underestimates the experimental data since no threshold stage is taken into account in the present modelling. Indeed, during the rupture various damage mechanisms (debonding, fiber pull-out and breakage) simultaneously accumulate leading to a sudden coalescence of voids which produce a drastic increase of the damaged volume strain.

The volume fraction evolution of debonded fibers predicted by the model is displayed in Fig. 10 for the two volume fractions of fibers. The case without damage representing an upper bound and the damaged case are shown in Fig. 11. The weakening effect due to damage can be clearly seen. This weakening is more emphasized for GFRP-21R than GFRP -13R.

Conclusion

The damage behaviour of chopped random glass fiber unsaturated polyester matrix composites was investigated. The experimental results have demonstrated the importance of taking into consideration the volume strain in the accurate characterization of composites damage, especially for the composites having a weak interfacial bond strength. The experimental results were used for the validation of a micromechanical model based on the

Figure captions

Fig. 1. Specimen dimensions (in mm) and configuration of the seven markers for strains measurement.

Fig. 2. Schematic illustration of the optical extensometer system.

1

 1

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 3456 Fig. 3. Local and global strain rates for GFRP -13R: (a) non strain-controlled and (b) straincontrolled tests.Fig. 4. Experimental stress-strain and damaged volume strain cur ves for: (a) GFRP -21R and (b) GFRP -13R.

Fig. 7 .Fig. 8 .

 78 Fig. 7. Local and global coordinates for a composite containing randomly located and oriented sphe roidal fibers.Fig. 8. Influence of the shape parameter α on the predicted macroscopic Young's modulus.

Fig. 9 .

 9 Fig. 9. Predicted stress-strain and damaged volume strain curves compared to experimental data for: (a) GFRP-21R and (b) GFRP-13R.

Fig. 10 .

 10 Fig. 10. Predicted volume fraction of debonded fibers.

Fig. 11 .Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 6 .

 1112346 Fig. 11. Effect of damage on the overall behaviour.

Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .

 7891011 Fig. 7. Local and global coordinates for a composite containing randomly located and oriented spheroidal fibers.

Fig. 5. Photograph of a fractured GFRP -21R spec imen.

ensemble -volume averaged homogenization procedure introduced by Lee and Simunovic [START_REF] Lee | Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites[END_REF].

The damage evolution law was incorporated into the modelling in terms of nucleation and growth of voids. The predictions of the micromechanical damage model were found in good agreement with the measured behaviour.

The modelling is clearly able to connect the complex microstructure and the dissipative mechanisms with the macroscopic behaviour of the material. Comparison with experiments was done only for in-plane mechanical behaviour. Therefore, data collection with other mechanical tests than uniaxial tension is required. Furthermore, the micromechanical constitutive model is going to be implemented into a finite ele ment code.


Zuhair Saleem

Heinrich Rennebaum

Frank Pudel

Eckhard Grimm
email: eckhard.grimm@obst.uni-hannover.de

Treating bast fibres with pectinase improves mechanical characteristics of reinforced thermoplastic composites

Keywords: A. Short-fibre composites, B. Mechanical properties, D. Environmental scanning electron microscopy (ESEM), E. Extrusion, Injection moulding

The effect of pectinase treatment of hemp (Cannabis sativa L.) fibres on mechanical properties of fibre reinforced polypropylene was investigated. Incubating technical fibres with pectinase (SIHA-Panzym ® DF) reduced their cross-sectional area (8.72•10 -3 vs. 3.67•10 -3 mm 2 , control vs. pectinase incubation) and decreased tensile strength (455.4 vs. 171.2 MPa). Polypropylene (PP) was reinforced with these fibres using conventional extrusion and injection moulding techniques. Maleic anhydride grafted PP was applied as compatibilizer. The cross-sectional area of fibres in the composite decreased from 2.58•10 -4 to 1.21•10 -4 mm 2 for control vs. pectinase. Tensile strength (43.7 vs. 47.6 MPa for control vs. pectinase incubation), flexural strength (49.9 vs. 56.6 MPa) and moduli of elasticity (tensile, 2.62 vs. 3.25 GPa and flexural, 2.28 GPa vs. 2.87 GPa, respectively) all increased when using fibres incubated in pectinase. Qualitatively and quantitatively similar effects, albeit on a decreased level, were obtained when reinforcing PP in absence of the compatibilizer. The data indicate the refining of technical fibres in response to pectinase treatment. This effect was accomplished by (1) enzymatic decomposition of the middle lamellae, (2) mechanical stress exerted by compounding and (3) compression of cell lumina. The separation of technical fibres into smaller bundles and single fibre cells, in turn, resulted in improved tensile and flexural characteristics of thermoplastic composites.

Introduction

In the past decade mechanical properties, processing technologies and the interfacial compatibility of cellulose fibre reinforced composites were investigated extensively [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF][START_REF] Mohanty | Biofibres, biodegradable polymers and biocomposites: An overview[END_REF][START_REF] Mohanty | Surface modifications of natural fibres and performance of the resulting biocomposites: An overview[END_REF][START_REF] Belgacem | The surface modification of cellulose fibres for use as reinforcing elements in composite materials[END_REF]. Using vegetable fibres in reinforced thermoplastics and thermosets has a number of technological and environmental benefits [START_REF] Mohanty | Sustainable bio-composites from renewable resources: opportunities and challenges in the green materials world[END_REF]. Vegetable fibres are obtained from a range of sources, including stem (bast) and leaf fibres from flax, hemp, jute, ramie, sisal and other fibre crops. In the plant body fibres provide structural support by absorbing mechanical stress. By using these fibres in reinforced composites key properties of plant fibres are transferred to the composite: tensile strength and stiffness similar to those of E type glass fibres [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF], low density (range 1.15 to 1.6 g•cm -3 ) similar to aramide fibres (1.4 g•cm -3 [START_REF] Mohanty | Biofibres, biodegradable polymers and biocomposites: An overview[END_REF]). Additional benefits result from low energy consumption and CO 2 pollution in processing as well as from recyclability. However, for advanced technical applications vegetable fibres have to be prepared regarding (i) the chemical and physical homogeneity of fibre batches, (ii) the degree of degumming and elementarization of fibre bundles, (iii) the degree of polymerization and crystallization, (iv) the adhesion between fibres and matrices, (v) the moisture repellence, and (vi) the flame retardant properties [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF].

Technical fibres are coarse and inhomogeneous when extracted mechanically from hemp straw using industrial scale decortication equipment. The quality of these fibres may be considerably improved when decortication is followed by further refining treatments. Here we focused on incubation with pectinase that is expected to decompose the middle lamellae selectively and to separate technical fibres into smaller bundles and single fibre cells. The objective of the present study, therefore, was to establish the effect of pectinase treatment on the physical properties of hemp fibres and on the mechanical characteristics of a model composite consisting of these fibres and polypropylene.

Experimental

Plant material

Hemp (Cannabis sativa L. cv. Kompolti) for fibre production was grown according to the current agricultural practice (seeding date: 25 April; seeding density: 450 m -2 ; N supply: 120 kg•ha -1 ; no measures for growth regulation and crop protection; harvest date: 8 September) at the Experimental Station of the Martin-Luther-Universität Halle-Wittenberg in Leipzig-Seehausen (51°21Ń, 12°25É; Germany). Stands were harvested with a combine at 10 to 20 cm above the ground surface and cut to 60 to 80 cm length.

Stalks remained in a swath for dew retting until a medium degree of retting was attained. The stalks were baled (19 October). Fibres were extracted mechanically using a custom build roller device equipped with rollers for breaking stalks, rotating sieves for separating shives and further refining units (LaRoche, Vernaro GmbH, Gardelegen, Germany). The product obtained by this process is referred to as technical fibres. In botanical terms technical fibres represent fibre bundles consisting of numerous fibre cells. Unless stated otherwise we use the term fibres for fibre bundles and for those filamentous products arising from pectinase treatment (see also [START_REF] Vincent | A unified nomenclature for plant fibres for industrial use[END_REF]).

Enzyme treatment, composite manufacture

Hemp fibres were cut into shorter segments of 8 mm length, and incubated in 8% (v/v) SIHA-Panzym ® DF (EC 3.2.1.15, Novozyme A/S, Bagsvaerd, Denmark) in 1 M sodium hydrogen carbonate, 1 M citric acid, 10 mM ethylenediaminetetraacetic acid (EDTA) at 35°C and pH 4.5. EDTA was added to the incubation medium to destabilize pectins by complexing cell wall bound calcium [START_REF] Akin | Biobased fiber production: enzyme-retting for flax/linen fibers[END_REF][START_REF] Henriksson | Influence of chelating agents and mechanical pretreatment on enzymatic retting of flax[END_REF][START_REF] Adamsen | Chelating agents and enzyme retting of flax[END_REF]. After 4 h fibres were removed from solution, rinsed twice using tap water, centrifuged, and air-dried for 2 to 3 d. There were two independent preparations (prep1, prep2). Non-treated fibres served as controls. For physical characterization of fibres a subsample was taken before milling (SM 2000, Retsch GmbH, Haan, Germany) and sieving using a sieve of 2 mm pore size.

For compounding a co-rotating twin-screw extruder (ZSE 27 GL-44D, Leistritz Extrusionstechnik GmbH, Nürnberg, Germany) was used. The temperature gradient was set at 190°C and 160°C between heating zones 1 and 10. Polypropylene (Atofina PPH 7060, Total Petrochemicals, Felny, Belgium) and hemp fibres were fed in heating zones 1 and 6 of the extruder, respectively. For fibres, a FlexWall ® Plus feeder (DDW-MD-FW40/4plus-ISC, Brabender Technologie KG, Duisburg, Germany) and a twin-screw volumetric feeding system (T-35, K-Tron AG, Niederlenz, Switzerland) was used. In some batches 2% (w/w) maleic anhydride modified polypropylene (SCONA TPPP 7112 FA, Kometra GmbH, Schkopau, Germany) was added as a compatibilizer. Following cooling strands were pelletized to 3 mm length (SP 30, Pell-Tec Pelletizing Technology GmbH, Niedernberg, Germany).

Analyses

Physical characteristics of fibres were determined on subsamples obtained prior to milling. Fibres free of splices and splinters were used as test specimen. Thickness was recorded along a 45-mm part of the specimen at a 90° angle using a two-axial laser micrometer (ODAC 15Y-JM, Zumbach, Orpund, Swizerland). As a first approximation cross-sectional area of fibres was estimated assuming a cylindrical shape of the specimen and using mean thickness as mean diameter of a circle. Tensile tests were performed using a universal instrument for material testing (model 1446, Zwick AG, Ulm, Germany). Gauge length, initial load and test velocity were set at 2 mm, 0.05 N and 3 mm•min -1 , respectively. Test parameters were calculated using the software For microscopy compound pellets (prep1) were cut with the help of a diamond saw.

Surface was ground and polished using 30, 9, 6, and 1 µm-diamond polishes. Surface images were obtained from environmental scanning electron microscopy (XL30, ESEM-FEG, Philips Eindhoven, Netherlands). Cross-sectional areas of fibres on the microscopic images were measured using the imaging software Analysis 3.0 (Soft Imaging Systems GmbH, Münster, Germany)

Statistics

Analysis of Variance (ANOVA) and bootstrap analysis were performed using SAS Systems for Windows 8.02 (SAS Institute Inc., Cary, USA) and 2SAMPLE [START_REF] Mudelsee | Quantifying effects in two-sample environmental experiments using bootstrap confidence intervals[END_REF] (software free available from Mudelsee, University of Leipzig, Germany; http://www.uni-leipzig.de/∼meteo/MUDELSEE/), respectively. All statistical tests were carried out at P = 0.05. For ANOVA, data on fibre characteristics (cross-sectional area, tensile strength) were transformed using the cubic root to obtain normal distributions.

Data are displayed as box-whisker plots with box, whiskers and crosses giving the 25 th to 75 th , 10 th to 90 th and 5 th to 95 th percentiles, respectively. The horizontal line in the box shows the median. The numerical data given above the boxes represent the backtransformed arithmetic mean. Bootstrap comprised 1999 simulations. Significant median differences were stated when the 95%-confidence interval did not include zero.

Results

Incubating technical hemp fibres in pectinase significantly decreased cross-sectional area by 42 and 46% in two independent preparations, respectively (Fig. 1A; prep1 and prep2). Furthermore, tensile strength of fibres significantly decreased by 37 and 52% (Fig. 1B). Both statistical procedures, i.e., ANOVA (on transformed data) and bootstrap (on non-transformed data; analysis not shown), yielded the same conclusion.

In the hemp fibre polypropylene composite (HFPP) fibres incubated in pectinase significantly increased tensile strength and tensile modulus of elasticity regardless of the absence and presence of the compatibilizer maleic anhydride (±MA) (Table 1). Ultimate elongation either decreased or was not affected by pectinase treatments. There was no consistent effect of pectinase on elongation at break. Flexural strength and flexural modulus of elasticity increased markedly in composites with fibres from pectinase treatments. Further, there was no consistent effect of pectinase treatment on charpy impact strength of the composite (Table 1). In prep1, but not in prep2 charpy impact strength was increased (control: HFPP-E±MA), when fibres were incubated in pectinase (HFPP+E±MA).

Comparison of all pectinase and maleic anhydride effects revealed that the highest tensile and flexural strengths and the corresponding moduli of elasticity were generally obtained in composites containing pectinase treated fibres and maleic anhydride (HFPP+E+MA). Furthermore, effects of pectinase on tensile strength were smaller than those of MA (2.1 to 8.9% vs. 29.7 to 34.8% for pectinase vs. MA). However, effects of pectinase on flexural strength were larger than those of MA (13.4 to 34.4% vs. 4.8 to 24.1% for pectinase vs. MA). Thus, flexural properties were more affected by pectinase than by MA, but the reverse was true for tensile properties.

Micrographs obtained by ESEM of HFPP pellets showed a deformed structure of embedded fibres (Fig. 2AB), that did not allow identification of individual fibre cells.

Cell lumina were mostly collapsed and cell walls appeared condensed with numerous cracks along middle lamellae of fibre bundles or across cell wall layers of fibre cells resulting in numerous fragments. The of the fibres in the PP matrix appeared randomized. Cross-sectional areas of fibres differed significantly between non-treated control (2.58•10 -4 mm 2 ) and pectinase treatments (1.21•10 -4 mm 2 ; Fig. 2C). It is interesting to note that cross-sectional area of fibre cells in the composite were about ten-fold smaller than those determined prior to processing by milling and compounding (see Fig. 1A). In absence of MA (HFPP-MA) fibres were often surrounded by wide gaps that prevented contact between fibre and PP matrix (Fig. 2A). These gaps were not apparent in samples with MA grafted PP (HFPP+MA; Fig. 2B).

Discussion

Fibre refining

Bast and leaf fibres represent elongated sclerenchyma cells that are assembled in bundles forming a part of the phloem. In the plant fibre cells are surrounded by thin walled tissues, e.g., sieve elements, companion cells, parenchyma of rays, bark and mesophyll. Mechanical decortication equipment breaks the thin cell walls of the latter structures thereby releasing fibre bundles of varying dimensions (technical fibres).

Residual cell wall fragments remain on the surface of the fibre bundles leaving behind a pattern of imprints of the neighbouring cells. To improve hemp fibre quality additional refining procedures are required, i.e., cleaning the surface and splitting fibre bundles into finer units, ideally into individual fibre cells. For refining various methods may be adapted including steam explosion [START_REF] Kessler | Steam explosion of flax -a superior technique for upgrading fibre value[END_REF], ball milling of thermally treated fibres [START_REF] Prasad | Mechanical properties of thermally treated hemp fibers in inert atmosphere for potential composite reinforcement[END_REF][START_REF] Prasad | Structure property correlation of thermally treated hemp fiber[END_REF][START_REF] Prasad | Properties of ball milled thermally treated hemp fibers in an inert atmosphere for potential composite reinforcement[END_REF], chemical degumming in alkaline media [START_REF] Mwaikambo | The effect of chemical treatment on the properties of hemp, sisal, jute and kapok for composite reinforcement[END_REF][START_REF] Keller | Influence of the growth stage of industrial hemp on chemical and physical properties of the fibres[END_REF], enzymatic separation of technical fibres, and scouring [START_REF] Dreyer | Comparison of enzymatically separated hemp and nettle fibre to chemically separated and steam exploded hemp fibre[END_REF][START_REF] Ouajai | Morphology and structure of hemp fibre after bioscouring[END_REF].

Alternatively, the stalks of fibre plants may be subjected to complex microbial and enzymatic decomposition processes referred to as retting. Effective retting allows the isolation of fibre bundles of reduced thickness [START_REF] Hobson | Quality of fibre separated from unretted hemp stems by decortication[END_REF]. Retting organisms release cell wall degrading enzymes including pectinases. This group of enzymes comprises polygalacturonases, pectin esterases, pectin lyases and pectate lyases. Pectinases are also used in biotechnological processes [START_REF] Jayani | Microbial pectinolytic enzymes: A review[END_REF]. In particular the alkaline forms are often applied for degumming of vegetable fibres [START_REF] Hoondal | Microbial alkaline pectinases and their industrial applications: a review[END_REF]. Chelators support fibre refining by retting [START_REF] Akin | Effect of retting enzymes on the structure and composition of flax cell walls[END_REF][START_REF] Akin | Retting of flax with endopolygalacturonase from Rhizopus oryzae[END_REF][START_REF] Akin | Progress in enzyme-retting of flax[END_REF]. However, cellulase activity may be associated with retting and degumming agents. Cellulases corrode the cellulose of the primary and secondary cell wall layers particularly, at the nodes and dislocations of the fibres [START_REF] Akin | Progress in enzyme-retting of flax[END_REF][START_REF] Khalili | Fibernodes in flax and other bast fibers[END_REF].

We focussed on pectinase treatment of mechanical decorticated hemp fibres.

Preliminary data established that SIHA-Panzym ® DF was the most effective for separating technical hemp fibres into smaller bundles and single fibre cells among thirty preparations investigated (data not shown). It represents a blend of pectinases developed for must processing in the wine industry. As expected, SIHA-Panzym ® DF also degraded the middle lamellae of hemp fibre as indexed by a markedly decreased crosssectional area of fibres (Fig. 1A). Since cross-sectional area of fibre is closely related to fineness [START_REF] Rennebaum | Fibre quality of linseed (Linum usitatissimum L.) and the assessment of genotypes for use of fibres as a by-product[END_REF], pectinase treated fibres should have a low fineness. Microscopy of fibres revealed that imprints of neighbouring cells disappeared upon incubation in pectinase (data not shown) analogous to scouring. [START_REF] Ouajai | Morphology and structure of hemp fibre after bioscouring[END_REF].

The structural changes induced by the pectinase treatment altered the mechanical properties of the fibres as indicated by decreased tensile strength (Fig. 1). This effect is primarily accounted for by loosening of the pectin lamellae. Clearly, side effects of residual cellulytic activity in the SIHA-Panzym ® DF preparation cannot be excluded.

However, there was no evidence from microscopy in support of the latter activity.

Similar findings are reported on bioscouring of hemp fibres [START_REF] Ouajai | Morphology and structure of hemp fibre after bioscouring[END_REF]: Pectate lyase (Scourzyme L from Novozyme, Australia) smoothed the fibre surface, separated fibre cells, removed pectin and increased the surface area as well as the pore size. However it also decreased tensile strength and E-modulus when incubation was extended to more than five hours.

Composite characteristics

HFPP prepared using pectinase treated fibres exhibited improved tensile and flexural characteristics (Table 1). These effects may be attributed to the refinement resulting in separation of technical fibres into smaller bundles and single fibre cells. The decrease in tensile strength of the fibres did not translate into decreased tensile strength of the composite (Fig. 1 vs. Table 1). This effect may be surprising at first sight. However, refining fibres increased the surface to mass ratio of the fibres leading to a markedly enlarged interfacial area between fibre and matrix. Support for this hypothesis comes from literature data: Flax fibre reinforced PP (±MA) exhibited a higher tensile and flexural strength when hackled (fine) instead of scutched (coarse) fibres were compounded [START_REF] Van Den Oever | Influence of the physical structure of flax fibres on the mechanical properties of flax fibre reinforced polypropylene composites[END_REF]. Similarly, studies on wood fibre PP composites reported increased tensile and flexural properties as a result of an increased aspect ratio (length per cross-sectional diameter) [START_REF] Stark | Effects of wood fiber characteristics on mechanical properties of wood/polypropylene composites[END_REF]. In addition the removal of pectins may provide a sound base for interfacial binding between cellulose and PP matrix [START_REF] Lethi | Realization of polypropylene/sisal fibre composites by reactive extrusion[END_REF].

It is interesting to note that despite the order of magnitude decrease in cross-sectional area of fibres during compounding the relative difference in fibre cross-sectional area between composites containing pectinase treated and non-treated fibres remained about the same (Fig. 1A vs. Fig. 2C). Clearly, this comparison is somewhat skewed, since orientation of fibres in the pellet was random and hence, apparent cross-sectional areas of fibres in the pellet are not representative for the true cross-sectional area of the fibre.

Thus our estimates of fibre areas from the pellet are conservative underestimating the effect of compounding on area. This, however, applies equally to both non-treated and pectinase treated fibres. The absence of a consistent effect of pectinase treatment on impact strength may be attributed to the complex mechanistic basis comprising matrix fracture, fibre-matrix debonding, pull-out of fibres, and fibre fracture. The relative importance of these processes and the effect of pectinase treatment thereon are currently unknown.

The effect of pectinase treatment of fibres on mechanical characteristics of HFPP was independent of the compatibilizer MA. That MA was effective in our experiments is demonstrated by data in Table 1. Graft co-polymerisation of hot PP and MA results in a covalent and cohesive coupling of cellulose hydroxyl groups to the PP matrix (for summary see [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF]). This effect is mechanistically different from those of the pectinase treatment discussed above.

Conclusion

In summary our data provide evidence for an effective refinement of hemp fibres when incubated with a commercially available pectinase. The use of pectinase treated fibres in reinforced PP significantly improved tensile and flexural characteristics of the composite.

Table 1: Mechanical characteristics of hemp fibre reinforced polypropylene (HFPP).

Fibres were treated without (-E) and with pectinase (+E) before compounding in polypropylene without (-MA) and with 2% (w/w) maleic anhydride (+MA) grafted polypropylene. Data were obtained from two independent preparations (prep1, prep2).

Different letters within preparations indicate significant difference of arithmetic means by ANOVA at P=0.05 (n = 10; * n = 5).

TestXpert 6 .

 6 0 (Zwick AG, Ulm, Germany). Mechanical characteristics of the composite were established according to the standards DIN EN ISO 527-1 and 2 (tensile test) and DIN EN ISO 178 (flexural test) on a universal test instrument (Z010/TH2S, Zwick AG, Ulm, Germany). Specimens were prepared on an injection moulding machine (Allrounder 320 C 500-250, Arburg GmbH & Co KG; Lossburg, Germany) at a maximum temperature of 180°C and an injection pressure of 160 MPa. Impact testing was carried out with the Pendelschlagwerk 5.102.102 (Zwick AG, Ulm, Germany) according to the standard DIN EN ISO 179.

Fig. 1 :

 1 Fig. 1: Cross-sectional area (A) and tensile strength (B) of hemp fibres (HF) without (-E, contr) and with pectinase incubation (+E). Data for pectinase treated fibres were

Fig. 2 :

 2 Fig. 2: Micrographs obtained from environmental electron microscopy (ESEM) of cross-sections of hemp fibre reinforced polypropylene (HFPP) pellets (A,B) and

Fig. 1 )

 1 Fig.1

Fig. 2 "

 2 Fig.2

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Table 1

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Acknowledgements

The research was supported by the German Federal Ministry of Economics and Technology. The authors thank Moritz Knoche for critical discussion and Frank Syrowatka, Interdisciplinary Centre of Material Science at the University of Halle, for preparation and ESEM microscopy of composite pellets.


M Tarfaoui
email: tarfaomo@ensieta.fr

S Choukri

A Neme

Effect of fibre orientation on mechanical properties of the laminated polymer composites subjected to out-of-plane high strain rate compressive loadings

Keywords: E glass/epoxy composites, dynamic response, fibre orientation, strain rate, damage

published or not. The documents may come

Effect of fibre orientation on mechanical properties of the laminated polymer composites subjected to out-of-plane high strain rate compressive loadings

Mostapha Tarfaoui, S. Choukri, A.

Introduction

The composite materials with organic matrix found important applications in the shipbuilding industries. New applications of the composites are identified, including their current and potential use in superstructures, platforms and some large military equipment, such as destroyers and aircraft carriers. The mechanical characteristics of these materials are well known for static loading, they are likely to evolve with the strain rate [START_REF] Bouette | Effect of strain rate on interlaminar shear properties of carbon/epoxy composites[END_REF][START_REF] Zhao | An experimental investigation of compressive failure strength of fibre-reinforced polymer matrix composite plates under impact loading[END_REF][START_REF] Zhao | Material behavior characterization using SHPB techniques, tests and simulations[END_REF][START_REF] Fitoussi | Experimental methodology for high strain-rates tensile behaviour analysis of polymer matrix composites[END_REF].

The behaviour of structures subject to impact has been of interest to many scientists for purposes of design as well as developing constitutive models of the materials tested [START_REF] Hou | Measurement of the properties of woven CFRP T300/914 at different strain rates[END_REF][START_REF] Gilat | Experimental study of strain rate dependent behavior of carbon/epoxy composite[END_REF]. The study of the composite materials behaviour at high strain rates is still relatively new and reliable data on strain rate effects is very scarce. Although the problem of obtaining reliable data is accentuated by difficulties encountered in designing and conducting of impact tests on composites [START_REF] Harding | The Effect of High Strain Rate on Material Properties[END_REF]. The qualitative relationship between the dynamic constitutive response and the dynamic damage evolution for composites at high strain rates are still far from understanding. To investigate the ratedependent constitutive relations of materials at high strain rates, the Split Hopkinson Pressure Bar (SHPB) technique has been extensively accepted [START_REF] Kolsky | An investigation of the mechanical properties of materials at very high rates of loading[END_REF]. The experience of the use of SHPB for the investigation of metals led to the adaptation of this technique for the laminated polymer composites characterization at medium strain rates.

Significant efforts has been made to examine the high strain rate behaviour using the split Hopkinson bar, of more brittle materials such as composites and ceramics, to measure dynamic response of materials under varying loading conditions [START_REF] Kumar | Dynamic compressive behavior of unidirectional GFRP for various fiber orientations[END_REF][START_REF] El-Habak | Mechanical behavior of woven glass fiber-reinforced composites under impact compression load[END_REF][START_REF] Harding | Effect of strain rate and specimen geometry on the compressive strength of woven glass-reinforced epoxy laminates[END_REF][START_REF] Sierakowski | Dynamic compressive strength and failure of steel reinforced epoxy composites[END_REF]. Most recently, the study conducted by Hosur et al. [START_REF] Hosur | Studies on the o.-axis high strain rate compression loading of satin weave carbon/epoxy composites[END_REF] presents the effect of in-plane off-axis testing of an 8-harness satin weave carbon fabric/SC15 composite specimens. Specimens were tested in the in-plane direction of 0°, 15°, 30°, 45°, 60°, 75°, and 90° in a range of strain rates from 1092 to 2425 s -1 . From this study it was noted that the high strain rate tested specimens showed considerable increase in the stress to failure and stiffness of the composite compared to the quasistatic loaded specimens. Depending on the fibre orientation of the specimens, the ultimate strength and strain varied considerably and exhibited a nonlinear stress-strain response that increases with angle up to 45°. Tsai and Sun [START_REF] Tsai | Constitutive model for high strain rate response of polymeric composites[END_REF] have reported the difference between tensile and compressive behaviours in a unidirectional glass fibre-reinforced composite, and developed a nonlinear rate-dependent viscoplasticity model to characterize its compressive stress-strain relationship. Many different models [15-17] have been developed to predict failure stress and modes in composites subjected to quasi-static loading. However, few criteria have been developed and experimentally validated for high strain rate loading.

In this study, specimens of glass/epoxy composite used in marine applications were subjected to a static and dynamic compression loading. Quasi-static tests were conducted on an Instron universal machine to evaluate the elastic properties and quasistatic response, while the split-Hopkinson pressure bar (SHPB) is used for dynamic tests. Samples were tested in the thickness direction. The fibre orientations of the samples were 0°, ±20°, ±30°, ±45°, ±60°, ±70° and 90°. Stress-strain curves at increasing strain rates were obtained for different cases. However, no experimental data for the intermediate range of strain rates between (80s -1 to 300s -1 ) was obtained, because the Instron universal testing machine and the SHPB employed in the experimental tests are designed respectively for low and high strain rates. Off-axis composites and angle ply laminates exhibited significant nonlinear and strain dependent behaviour. Finally experimental observations enable us to draw up the history of the dynamic damage in the specimens according the fibre orientation and strain rate evolution.

Material and specimens

The material used in this study consists of 2400 Tex E-glass fibres impregnated with an epoxy matrix. The resin is a EPOLAM pre-polymer, EPOLAM 2020 hardener and 2020 accelerator from Axson. Glass fibres are commonly used for naval applications because of their high strength/mass ratio and their low cost compared to other reinforcements. The reinforcement consists of a plain weave fabric with 90% warp yarns and 10% weft yarns. Panels were made by infusion process and seven orientations are studied: 0°, ±20°, ±30°, ±45°, ±60°, ±70° and 90°. The square panels, 500 × 500 mm, were cut into samples of the geometry which dimensions are shown in Table 1.

The standard deviations are indicated in brackets. Laminate properties given in Table 2 are calculated by laminate theory expressions [18].

Elastic properties

Two types of static compression tests are used to obtain the elastic properties of the lamina. In-plane loading (IP), parallel to the plies plane; plane (1,2), and out-of-plane loading (OP), according to the thickness; direction 3. Table 2 compares the elastic values of the characteristics drawn from relations of micromechanics with those resulting from experimental work.

One can note that the damage for out-of-plane loading case appears by a cracking along the diagonal of the cube, which means that cracking crossed the weft yarns which represent the weakest part of the fabric. On the other hand, the matrix cracks and delamination occur in the privileged interlaminar planes for in-plane loading, Figure 1.

Dynamic tests

The split Hopkinson bar test is the most commonly used method for determining material properties at high strain rates, Figure 2a. This technique of characterization, based on the response of a material to wave propagation for high strain rate from 100s -1 to 5000s -1 , was improved by Kolsky [START_REF] Kolsky | An investigation of the mechanical properties of materials at very high rates of loading[END_REF].

The experimental set-up consists of (1) a stress generating system which is comprised of a split Hopkinson bars and the striker, (2) a specimen, (3) a stress measuring system made up of sensors (typically resistance strain gauges), and (4) a data acquisition and analysis system. The signals are treated with Maple Software package using Fast Fourier Transformation to obtain the evolution of the dynamic parameters: stress vs. strain, strain rate vs. time, incident and transmitted load and velocity at the interfaces input bar/sample and output bar/sample vs. time.

Data processing procedure

The subjected to dynamic compression loading in the thickness direction. Nine different impact level were applied to the input bar by varying the pressure acting on the striker bar, from 0.5 to 1.6 by step of 0.1/0.2 bar : 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.4 and 1.6bar witch correspond to the impact velocities: 3.6, 6.3, 8.1, 9.9, 11.7, 13.5, 15.1, 17.1 and 18.9 m/s. Many processing schemes are necessary before obtaining stress, strain and strain rate in the specimen, namely the Fast Fourier Transform of the sampled signals and their transport from strain gauges location to the specimen loaded faces (Figure 1), under non dispersive hypothesis of the wave propagation in the bars. Figure 2 shows typical signals time variations and the stress/strain curve for a given strain rate.

Strain rate dependencies of dynamic mechanical properties

Before launching the experimental study for dynamic case, it is necessary to be ensured of the tests reproducibility. For this objective, for each fibre orientation, a minimum of two tests was carried out at the same impact pressure to analyze dispersion.

As figure 4 shows it, it is noted that dispersion is weak and that was checked for all the tests.

For out-of-plane (OP) tests, results for compressive strain rates between 200s -1 and 2000s -1 are obtained using SHPB. Figure 5 shows the evolution of the strain rate versus time. The maximum value is considered for the analysis of the experimental results.

The strain rate evolution is sensitive to the entry pressure in the chamber of compressed air P (impact pressure of the striker on the input bar), the loading direction and the sample lay-up (angle θ ). we will analyze that in detail in the following section.

For the results analysis and exploitation, we will be interested in the evolution of: initial dynamic modulus ( dynamic E ) witch is evaluated for the linear part of ).

In a concern of simplifying the graphic representations, the analyzed parameters:

dynamic E , Max σ , Max σ ε
and Max ε will be given according to the impact pressure (P) and the fibre orientation θ (Teta). The evolution of ε is approximated by a quadratic equation, Figure 6. Table 3 gives the coefficients of this function. ) where the increase is fast and the second phase where the variation is less marked. The fibre orientation has an effect on the strain rate evolution. Indeed, one notices on blue curves that the evolution of ε is relatively similar for samples 20/70, 30/60 and 45/45 whereas for samples 0/90 it is different. with the increase in the impact pressure. There is not threshold effect for OP loading; the transitional pressure does not exist, Figure 11.

Damage

The damage tolerance is an important parameter for the use of composite materials in the technologically advanced sectors and in particular for military naval applications. This characterization passes by drawing up the history and the damage kinetics of material from initiation until the complete failure. Several techniques are used to examine the extent of damage. First, during the dynamic compression, High-speed photography and infrared camera were used to follow the damage in the samples.

Frames taken in real time are used for illustrating the evolution of the damage. Impacted samples were inspected by optical techniques and fluorescent dye was applied to improve damage visualization. The damage can also be located by the presence of a second peak on the ( )

t f = ε
curve. To the formation of this peak a fall of stress corresponds, Figure 10.

The first observation that one can make, for out-of-plane tests, is that material shows a greater strength. The damage appears only for the great impact pressures: 0.8bar for 13. In fact for these specimens multiple mode fracture is depicted. As the strain rate increase more damage mechanism is involved; from matrix cracking to delamination with multiple paths to final fracture. For 0/90 and 45/45 specimens a dominant path is observed along the weakest link, respectively across weft yarns and plies interfaces, witch may explain the lower strength. The kinetics of damage for this direction of loading is strongly conditioned by the specimen's fibre orientations. Figure 13 summarizes the history of damaging modes for the various laminates.

Conclusion

In this work, the high strain rate material response of Samples were subjected to OP tests. The effects of fibre orientation and strain rates in a glass/epoxy composite material under compressive dynamic loading are examined.

Moreover, a family of compressive stress-strain curves, as well as failure modes, at dynamic strain rates at a series of fibre orientation were determined. All of the stressstrain curves had similar shapes: an initial linear elastic portion followed by a nonlinear behaviour until failure. The stress-strain curves of the composite materials show that the material is strongly sensitive to fibre orientation at the same impact pressure: the initial modulus of elasticity, maximum failure stress, strain at maximum stress and the maximum strain are all dependent on fibre orientation and strain rates. The initiation and propagation of failure mechanisms at different strain rates have been examined. The most pronounced effect of increasing the strain rate results in changes in the failure modes. Specimen fails by fibre kinking at low strain rates, with delamination and interfacial separation dominating the high strain rate failure regime. Off-axis composites and angle ply laminates exhibited significant nonlinear and strain dependent behaviour.

15. Soden P., Hinton M., Kaddour A. Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates. Composite Science and Technology, Special issue on "Failure criteria in fibre reinforced polymer composites" part A, 1998;58 [START_REF] Harding | The Effect of High Strain Rate on Material Properties[END_REF]:1011-1022.

List of Figure headings

  specimens [0] 40 , [±20] 20 , [±30] 20 , [±45] 20 , [±60] 20 , [±70] 20 and [90] 40 were

Figure 7

 7 Figure 7 gives the experimental curves in blue and the envelope surface. The evolution of ε follows two phases: a first phase (bar 2 . 1 P 5 . 0 ≤ ≤

Figure 8

 8 Figure 8 give the evolution of the strain rate of [0/90], [20/70], [30/60] and [45/45] samples for 9 impact pressures. The appearance of a second peak is around 0.9bar for [0/90] and 1.4bar for the other orientation, Table 4. The dynamic behaviour for OP tests is dominated by compressive properties of the polymeric matrix and the damage is created for high impact pressure. The fibres orientation affects the initiation and propagation of damage. For undamaging tests, the fall of strain rate passes by negative values, which correspond to the springback in the sample. The glass/epoxy composite materials present a high strength on compressive dynamic loading for OP tests.

  [0/90°] 40 , 1.4 -1.6bar for ([20/70°] 20 and [30/60°] 20 ) and 1.4bar for [45/45°] 20 . For this lower range of impact pressure there were only residual "plastic" deformations due to matrix cracks. One can also notice that the nature of the damage is strongly affected by the laminates orientation, Figure 11-12, witch still a parameter in improving also out of plane dynamic compressive strength. The multiplication of the microscopic cracks involves the catastrophic failure. The high strength recorded for 20/70 and 30/60 can be correlated with damaging modes observed and reported in figure

  [0] 40 , [±20] 20 , [±30] 20 , [±45] 20 , [±60] 20 , [±70] 20 and [90] 40 E-glass/epoxy composite material systems was investigated.

  16. Gotsis P. K., Chamis C. C. and Minnetyan L. Application of progressive fracture analysis for predicting failure envelopes and stress-strain behaviors of composite laminates: a comparison with experimental results. Composite Science and Technology, Special issue on "Failure criteria in fibre reinforced polymer composites" part B, 2002;62(12/13): 1545-1559. 17. Travis A. Bogetti, Christopher P. R. Hoppel, Vasyl M. Harik, James F. Newill and Bruce P. Burns. Predicting the nonlinear response and failure of composite laminates: correlation with experimental results. Composite Science and Technology, Special issue on "Failure criteria in fibre reinforced polymer composites" part C, 2004;62(3/4): 449-476. 18. Chamis, C.C. Simplified micromechanics equations for hygral, thermal, and mechanical properties. SAMPE Quarterly, 1984.

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 Figure 12 .Figure 13 .

 12345678910111213 Figure 1. Damage in static tests

Figure 2 .Figure 3 .

 23 Figure 2. Typical compressive split Hopkinson bar apparatus

Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 11

 456711 Figure 4. Tests reproducibility, OP test P=1.4 bar

Table 1 .

 1 Geometry and fibre mass fraction of the samples, standard deviation in brackets

Table 2 .

 2 Elastic properties of E-glass/epoxy lamina

Table 3 .

 3 Coefficients of quadratic functions

Table 4 .

 4 Critical impact pressure for appearance of second peak

	Panel	Thickness, (mm)	Surface (mm 2 )	void fraction (%)	Stacking sequence	Fibre volume Fraction (%)
	A	13.00 (0.1)	13×13 (0.2)	9.26	[0]40	53.5 (0.5)
	B	12.52 (0.3)	13×13 (0.2)	9.00	[±20] 20	54.0 (0.5)
	C	13.00 (0.1)	13×13 (0.2)	8.78	[±30] 20	55.0 (0.5)
	D	12.78 (0.2)	13×13 (0.2)	8.69	[±45]20	54.3 (0.5)

Table 1 .

 1 Geometry and fibre mass fraction of the samples, standard deviation in brackets

	Characteristics	E 1 (MPa)	E 2 (MPa)	E 3 (MPa)	ν	12	ν	13	ν	23	G 12 (MPa)	G 13 (MPa)	G 23 (MPa)
	Experimental	46217	16086	9062	0.28	0.41	0.097	2224	3500	4540
	Rules law	42030	14524	9130	0.31	-	0.01	3441	3273	4508

Table 2 .

 2 Elastic properties of E-glass/epoxy lamina

	OP Tests	0°/90°	20°/70°	30°/60°	45°/45°/
	α	-135.5	-676.66	-341.17	-329.77
	β	1581	2444.9	1801.9	1585.9
	γ	-336.33	-830.42	-560.75	-34173

Table 3 .

 3 Coefficients of quadratic functions

	OP Tests	0°/90°	20°/70°	30°/60°	45°/45°/
	P c (bar)	0.9	1.6	1.6	1.4

Table 4 .

 4 Critical impact pressure for appearance of second peak

	Table(s)


Isabel Koke
email: isabel.koke@ltm.uni-paderborn.de

Wolfgang H Müller
email: wolfgang.h.mueller@tu-berlin.de

Ferdinand Ferber
email: ferdinand.ferber@ltm.uni-paderborn.de

Rolf Mahnken
email: rolf.mahnken@ltm.uni-paderborn.de

Herbert Funke
email: herbert.funke@fh-dortmund.de

Measuring mechanical parameters in glass fiber-reinforced composites: Standard evaluation techniques enhanced by photogrammetry

Keywords: A. Glass fibers, A. Fabrics/textiles, B. Mechanical properties, B. Stress/strain curves, C. Elastic properties

This paper demonstrates how the usual standard tests for characterization of mechanical stiffnesses of glass fiber-reinforced composites can be enhanced by means of photogrammetry. This method allows to reveal and study local imperfections and damage inherent to the production process of the material (e.g., weaving flaws) as well as during loading (e.g., fiber breakage). Moreover it is capable of quantifying the impact of these imperfections on design and construction in terms of (local) deformation or overall stiffness.

Introduction

For design purposes it is desirable to know as much as possible about the threedimensional local deformation response in a structure made of fiber-reinforced materials. Accurate knowledge of their current anisotropic mechanical characteristics, in particular of the stiffness matrix, is required to reach this goal. Once the stiffnesses are known Finite Element (FE) studies in combination with suitable damage models can be used in order to assess and to predict the reliability of the whole structure. In order to quantify the stiffnesses key experiments, based on the concepts of laminate theory, have been conceived resulting in certain engineering standards, such as [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF][START_REF] Funke | Standard test method for tensile properties of fiber reinforced composites[END_REF]. …

Introduction

For design purposes it is desirable to know as much as possible about the threedimensional local deformation response in a structure made of fiber-reinforced materials. Accurate knowledge of their current anisotropic mechanical characteristics, in particular of the stiffness matrix, is required to reach this goal. Once the stiffnesses are known Finite Element (FE) studies in combination with suitable damage models can be used in order to assess and to predict the reliability of the whole structure. In order to quantify the stiffnesses key experiments, based on the concepts of laminate theory, have been conceived resulting in certain engineering standards, such as [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF][START_REF] Funke | Standard test method for tensile properties of fiber reinforced composites[END_REF].

However, useful as these may be for a first mechanical assessment in terms of overall initial properties and, consequently, FE analysis of the initial stress-strain response, these standards are insufficient when the objective is a straightforward in-depth characterization of the quality of the production process leading to the laminate structure or of its residual properties during or after use.

Optical field measurement techniques are excellent tools that allow to retrieve this kind of information, the most prominent being classical photoelasticity [START_REF] Föppl | Praktische Spannungsoptik[END_REF], and more modern ones, such as Moiré or micro-Raman interferometry, e.g., [START_REF] Dewolf | Stress measurements in silicon devices through Raman spectroscopy: Bridging the gap between theory and experiment[END_REF][START_REF] Pezzotti | Micromechanics of fracture in a ceramic/metal composite studied by in-situ fluorescence spectroscopy I: Foundations and stress analysis[END_REF], speckle techniques [START_REF]Handbuch für experimentelle Spannungsanalyse[END_REF] and, in particular, photogrammetry [START_REF]Handbuch für experimentelle Spannungsanalyse[END_REF]. Depending on the material the structure is made of, all or at least some of these methods allow, in principle, to monitor the local 3D deformation. In combination with a suitable material law and the corresponding material parameters it then becomes possible to predict the local stresses, which together with the strains may eventually be entered in damage equations. However, these parameters are often unknown and, consequently, it becomes necessary to apply an "inverse method" by running an FE analysis with a suitable constitutive equation, assuming reasonable starting values for its material constants, predicting the deformation pattern, comparing it with the experimental one, and reiterating this procedure until a "best fit" is achieved.

Clearly, to reach this objective in perfection is very ambitious. In this paper we will present a first attempt towards a solution of the full problem. More specifically, we will concentrate on a combination of experiments according to the standards described in [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF][START_REF] Funke | Standard test method for tensile properties of fiber reinforced composites[END_REF] together with photogrammetry to determine the in-plane elastic properties of a selfmade glass fiber-reinforced laminate. This will allow us

•

to discuss the non-linear stress-strain behavior of a virginal as well as a preconditioned laminate in terms of an average, a secant, and a second modulus;

• to determine the in-plane lateral contraction coefficient;

• to visualize and to quantify the onset and growth of local damage during loading of the structure due to ondulation, weaving flaws, warpage, and fiber breakage;

• to monitor the mechanical quality of a manually fabricated laminate and the corresponding production process.

Aside from this we will also briefly touch on the problems involved in the mechanical characterization of glass-fiber reinforced materials as indicated in the standard specifications. We will also outline the use and difficulties inherent to photogrammetry and put it in context with previous work in this field. The paper will end with a discussion of the results that were achieved so far, and how to improve them in the near future, e.g., by combining the deformation patterns obtained in photogrammetry with a finite element analysis in order to extract all current local elastic properties.

Specimen fabrication

In order to determine the mechanical characteristics of handmade glass-fiber reinforced plastics (GRP) tensile test specimens were fabricated according to [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF] as indicated in Fig. 1. More specifically, a glass fabric with a specific weight of 163 g/m² and finish FRP 144 (Interglas 92110), in twill weave fashion was embedded in epoxy resin L1100 with a slow hardener EPH294 from R&G Faserverbundwerkstoffe GmbH, guaranteeing a processing time between 500 to 600 minutes [START_REF] R&g Catalogue | [END_REF]. Six or twelve of such fiber layers were required to produce specimens of 1 or 2 mm thickness, respectively. Some details of the manufacturing process are indicated in Fig. 2: The fabric is laminated on a base plate with a separation agent and a tearing fabric on top. The tearing fabric leads to a rough specimen surface which is very useful for firm attachment of tabs (see below).

The laminated fibers obtain a label for identification. Moreover, strips of tearing fabric, plastic foil, cover and cushion are attached. After that the whole setup is sealed in a vacuum bag and left at room temperature for approximately 12 hours. Finally the testing laminate is tempered at approximately 70°C for 10 hours. The fiber volume fraction F ϕ is determined with the following formula [START_REF] Carlsson | Experimental Characterization of Advanced Composite Materials[END_REF]:

F R R F F R L F F m m m V V ⋅ + ⋅ ⋅ = = ρ ρ ρ ϕ (1)
where F V denotes the volume of fibers in the laminate, L V is total volume of the testing laminate, R ρ and F ρ are the (known) mass densities of the resin and of the fibers, respectively, F m refers to the mass of the fibers in the laminate (the mass of the fibers per square meter is known and the area can easily be measured), and L m is the mass of the laminate (to be obtained by weighing). Expected values of F ϕ for hand laminates range between 35 % and 50 %; industrial laminates achieve 60 % or more.

The next step of preparation consists of attaching tabs (cf.,

Setup and evaluation of tensile tests

In order to characterize the mechanical properties of the manufactured laminates tensile tests were carried out according to [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF], as indicated in Fig. 3. The tests were displacement controlled, i.e., the force was recorded as a function of displacement y u

(measured with a mechanical extensometer) while increasing the load up to specimen failure. Displacements and forces were converted into axial engineering strain y ε and uniaxial engineering stress y σ . A typical result is shown in Fig. 4 (for the laminate GRP [0/90] 12 with a fiber volume fraction of 36%). Clearly the stress-strain relationship is not perfectly linear as it is commonly assumed in laminate theory. As we shall see shortly this is due to several effects, non-linearity of the resin, local imperfections of the material, imperfect alignment of the fibers, etc. Consequently the question arises how, on the basis of the available data, the linear-elastic stiffnesses of the material in question can rationally be determined. Two procedures were used for this purpose: In a simplified approach (shown in the left picture of Fig. 4) the stressstrain data was approximated by linear regression where the slope of the regression line served directly as a measure of Young's modulus. This is easily achieved. Note that the regression line does not quite lead through the origin of the stress-strain coordinate system. Moreover it is well known in experimental mechanics that this origin is always hard to determine, which is due to slight fluctuations of the displacement control of the machine and to unavoidable (slight) initial misorientation of the specimen as well as (slight) deviation from proper uniaxial tensile loading conditions at the beginning of each test. This in turn renders it almost impossible to determine Young's modulus exactly as the initial slope of a stress-strain curve, even if the material is fully isotropic and without need for pre-conditioning (see below). It is for this reason that in more complex evaluation techniques the determination of the origin and follow-up readjustment of the stress-strain data points has become part of an iterative procedure for the determination of Young's modulus (see, e.g., [START_REF] Andersson | Characterization of Mechanical Properties of Eutectic Sn-Co-Cu Lead Free Alloy[END_REF]). However, in order to avoid mathematical intricacies we follow in the present paper a procedure known as the bimodal approach [START_REF]Faserverbundwerkstoffe Band[END_REF]: The stress-strain curve is divided into two regions (see Fig. 4, right, and Fig. 5) which can be distinguished by a bent, the so called "knee." Up to 0.1 % of strain the stress-strain data form almost a straight line the slope of which essentially coincides with that of a secant to the stress-strain curve. This slope, another measure of Young's modulus, is also known as the "secant modulus" (the DIN standards [START_REF]Bestimmung der Zugeigenschaften. Teil 1[END_REF] and [START_REF]Glasfaserverstärkte Kunststoffe[END_REF] recommend = (0.05 % , 0.25 %) and = (0.05 % , 0.1 %) to be used as the base points of the secant). In fact, the secant modulus represents the highest gradient (slope) and results at the beginning of the first loading of a virginal specimen.

At ca. 0.4 % of strain the stress-strain curve of the virginal specimen flattens. The stress-strain data to the right of this knee are also fitted linearly and, consequently, result in a third measure of stiffness, the so-called "second modulus." The corresponding slope is clearly smaller than that of the secant modulus.

We conclude that the stress-strain behavior of a virginal test specimen is not strictly linear and cannot be described by a single stiffness. It is for this reason that we perform "cyclic" tensile tests by, first, applying a tensile load which steadily increases up to a maximum value of 7.5 kN, followed by unloading to 1 kN and subsequent reloading to 7.5 kN, etc., until failure of the specimen. Fig. 5 presents the stress-strain curves after three such loading cycles. As previously discussed the stress-strain response during first load is non-linear and can be evaluated in the manner described above. However, the stress-strain curves of follow-up unloading and loading processes essentially "approximation"), the secant and, finally, the second modulus for GRP [0/90] 6 with 38.5 and 37.2 vol. %. We conclude that the impact of the fiber volume fraction on stiffness seems insignificant at least within the accuracy of measurements and for the range of volume fractions considered. This is confirmed by the two Young's moduli stemming from laminate theory which were calculated using the software LamiCens [START_REF] Funke | Software[END_REF]. For the calculation several input parameters are required, such as the type of reinforcement fabrics or uni-/multidirectional inlays, the type of epoxy resin and the hardener. In addition the stacking sequence, the direction of the fibers and, of course, the fiber volume fraction need to be added.

Note that the average secant modulus from the test series essentially agrees with the LamiCens prediction according exceeding it by a maximum of 7 %. The stiffness values resulting from linear regression and the second modulus are smaller and close to each other.

Setup and evaluation of field optical measurements (photogrammetry)

In the past field optical measurement techniques have frequently been used by the authors. In [START_REF] Pezzotti | Micromechanics of fracture in a ceramic/metal composite studied by in-situ fluorescence spectroscopy I: Foundations and stress analysis[END_REF] Raman spectroscopy was used to reveal and quantify the local stressstrain distributions in particle reinforced ceramics. In [START_REF] Ferber | Bruchmechanische Analyse der Entstehung und Ausbreitung von Matrix-und Grenzflächenrissen in thermisch belasteten Faserverbundwerkstoffmodellen[END_REF][START_REF] Ferber | Numerische und experimentelle Untersuchungen rissbehafteter Strukturen. Berichte aus der Mikromechanik[END_REF][START_REF] Ferber | Elementary failure analysis of composite models by using optical methods of stress analysis and modern digital image systems[END_REF] the mechanics of interface cracking was investigated by means of photoelasticity and other optical methods of experimental mechanics. In this paper photogrammetry will be used to visualize and quantify the full deformation fields in laminates subjected to uniaxial stress. More specifically, GOM's commercial hardware/software package Aramis was used. An introduction to the fundamentals as well as details of how and where this package can be used are compiled in [START_REF]Aramis v5.4[END_REF][START_REF] Galanulis | Optical measuring technologies in sheet metal processing[END_REF]. By definition photogrammetry is a measurement technique where three-dimensional coordinates of points on an object are determined by using two photographic images taken at different positions [START_REF]Handbuch für experimentelle Spannungsanalyse[END_REF]. To this end it is necessary to print a recognizable stochastic pattern onto the specimen's surface.

As indicated in Fig. 8 a picture is taken by each camera during every step of the experiment, which can be both, load or displacement controlled (as it was in our case).

A 3D displacement vector and (by differentiation) the corresponding strains on the specimen surface can then be obtained numerically in an automated fashion. It is worth mentioning that the Aramis-4M-system, which was used, consisted of two CCD cameras with a resolution of four mega pixel each. According to the manufacturer this will guarantee an accuracy of 0.01 % during strain measurements. These forces can give rise to tension in the laminates which are strong enough to lead to bending when they have not been laid up uniformly [19].

Note that the first fibers cracked audibly at step 16. This was investigated closer by looking at the axial strain on the specimen surface along a virtual line (the so-called "section line"): Fig. 10, left. At the beginning of the experiment the strain along the section line is nearly homogeneous. Then at step 16 some fibers break and the strain at the corresponding location jumps: Fig. 10, right, red curve.

This effect is examined closer in Fig. 11 which presents the development of the strain component y ε for three different points on the specimen surface. "Stage point 2" corresponds to the location where the fiber cracking took place. And, indeed, for this point we observe a sudden jump, i.e., a strain discontinuity y ε (i.e., crack opening) after a certain stress has been applied, whereas the strain in the other points increases monotonically.

The same procedures can now be applied to study the behavior of the lateral strain field x ε of the GRP specimen: Fig. 12. By combining the strain results for the x-and y- direction another macroscopically relevant material parameter can be obtained: the lateral Poisson's ratio (see Fig. 13). Specifically, we choose two section lines within the undamaged region of the specimen as shown in the strain carper plot on the right hand side of Fig. 13 and compute: 1 (all values in MPa, nomenclature corresponding to Fig. 7).

Summary and outlook

In this paper it was shown how industry standards can be used for evaluation of stressstrain data resulting from uniaxial tensile tests to deliver stiffness coefficients of handmade glass-fiber reinforced laminates. It was shown that the stress-strain response of a virginal laminate is somewhat non-linear necessitating use of different stiffnesses, such as an average, a secant and a second Young's modulus. Moreover, it was demonstrated that pre-conditioning of a laminate by subjecting it to a sequence of loading and unloading states resulted in a linear stress-strain curve, which could be characterized by a single stiffness coefficient. The reason for this behavior is micromechanical, at least in part, stemming from realignment of the fibers as well as relaxation of the epoxy matrix.

Finally photogrammetry was used to determine several material characteristics in one experiment, namely Young's modulus and Poisson's ratio from field information regarding the displacements x u and y u or strains x ε and y ε , respectively.

Photogrammetry is also capable of assessing heterogeneities, i.e., the micromechanical behavior of composites, in particular the onset of fiber fracture, and inhomogeneities induced by the fabrication process.

Clearly, the vast amount of information hidden in the local displacement fields should be further analyzed. Several options exist, for example, a computer simulation of the tensile test could be performed, using FE in combination with suitable material laws, to predict the stress-strain fields during loading. This data could then be compared with the real stress-strain fields leading to an iterative procedure with the objective to extract optimum average or, if desired, optimized local material properties of GRPs. For this purpose we will built upon the "inverse method" techniques presented in [START_REF] Nguyen | Parameter identification of SMT solder materials using the small punch test[END_REF], [START_REF] Albrecht | Nanoindentation: A suitable tool to determine local mechanical properties in microelectronic packages and materials?[END_REF]. shown on the right hand sight Tables Table 1: Young's moduli predicted from virtual extensometry (for nomenclature see shown on the right hand sight Tables Table 1: Young's moduli predicted from virtual extensometry (for nomenclature see

Figure captions

Fig. 1 )

 1 to the ends of the laminate. Tabs are required so that the load at the fixing grips of the tensile testing machine is properly transferred to the laminate giving rise to only very small stress concentrations and ensure that uniaxial stress conditions prevail. The last stage of manufacturing consists of cutting out the tensile test specimens according to the German industry standard DIN EN ISO 2818: 1997, page 3, number 3.2. This is done with a diamond saw blade at a slow feeding speed (0.025 m/s) and a high number of revolutions (2950 1/min) assisted by water-cooling. Humidity absorption (determined according to DIN EN ISO 53495) was experimentally monitored showing that it is reversible by tempering the laminates for a short while.

  coincide and, what is more, they are linear resulting in only one slope and, consequently, a single stiffness value. In other words after pre-conditioning the mechanical response of the laminate can sufficiently be described within the framework of linear, anisotropic elasticity, i.e., simple laminate theory. The pre-conditioning effect might eventually be explained micro-mechanically. It seems very likely that during first loading and subsequent unloading the fibers will start to align properly which, macroscopically speaking, would result in a reproducible stiffness value. Other explanations of the pre-conditioning phenomenon are that some kind of relaxation might take place between the fiber and the matrix, that the ondulated fibers are stretched in loading direction, or that this effect results from the grips, i.e., the fixation of the specimen. Microsectioning of the virginal as well as of the pre-conditioned specimens should be able to confirm these suppositions. For now we conclude that unloading and subsequent uploading leads to a linear stress-strain response. The corresponding slope is in between the secant and the second modulus.Clearly, there is a certain scatter involved in the stress strain data of virginal laminates of the same sort. This is demonstrated in Fig.6where five specimens of the GRP [0/90] 6 type with a fiber volume fraction of 38.5 % were tested leading to average secant and second moduli of 20 GPa and 15 GPa, respectively, with a standard deviation of roughly 500 MPa. Moreover, the photogrammetry experiments described below will show that there are also local fluctuations of the stiffness within each specimen. This in turn explains the standard deviation observed for the global specimen stiffnesses which are characterized by the secant and second moduli as outlined above.

Fig. 7

 7 Fig. 7 allows to compare the stiffness obtained by linear regression (denoted as

Fig. 9

 9 Fig. 9 shows the axial strain field y ε of a GRP specimen [0/90] 6 at various steps of

  Finally the slopes of the stress-strain curves corresponding to different points on the laminates, such as the ones shown in Fig.'s 10-13, can be used to calculate Young's moduli characteristic of the overall stiffness behavior of the laminate in question. This has been done for a GRP [0/90] 6 laminate using three such "virtual extensometers" resulting in the stiffness values of Table

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 11 .Fig. 12 .Fig. 13 .

 123456789111213 Fig. 1. Dimensions of tensile test specimen

Section 3 )Fig. 1 .Fig. 2 .Fig. 3 .

 3123 Fig. 1. Dimensions of tensile test specimen

Fig. 5 .Fig. 6 .

 56 Fig. 5. Stress strain curve of a cyclic tensile test using GRP [0/90] 12 , fiber volume fraction 36% (see text)

Fig. 8 .Fig. 9 .Fig. 11 .Fig. 12 .Fig. 13 .

 89111213 Fig. 8. The principle of photogrammetry demonstrated for a tensile test

  Fig. 7. Comparison of Young's moduli for GRP [0/90] 6 with 38.5 and 37.2 vol. % of fibers determined with different methods (see text)

		25.000					ϕ F =38.5% ∅ laminate 07
		20.000	18.976	18.402		20.281	19.336	ϕ F =37.2% ∅ laminate 09
					15.147	14.863	14.628	14.583
	E / N/mm²	10.000 15.000	calculated	calculated
		5.000
		0
			LamiCens LamiCens	E Regression approximation secant modulus Sekantenmodul	2. Modul nd modulus 2

Acknowledgments

We thank R&G Faserverbundwerkstoffe GmbH, Waldenbuch, for supporting the experimental work. One of the authors (I.K.) would also like to thank for financial support of this work as part of the BMBF project Nemesis -Virtual Engineering Labs.

A detailed analysis of the material anisotropy, i.e., the determination of the different Young's moduli, Poisson's ratios, and shear moduli depending on the fiber orientation and weaving is left to future research.