Z Aboura
email: aboura@utc.fr

N Talbi

S Allaoui

& M L Benzeggagh

Elastic behavior of corrugated cardboard: Experiments and Modeling

Keywords: Corrugated cardboard, Experimental procedure, Homogenization, Finite element

Motivated by computed homogeneous of linear corrugated cardboard behavior, an analytical model related to the assessment of equals behavior is proposed. This model takes into account the geometrical and mechanical properties of the corrugated cardboard constituents. An experimental methodology is also proposed to obtain both the in-plane elastic properties of each constituents and the corrugated cardboard. After model validation by a comparison with the experiment results, a parametric study is conducted studying the effect of geometrical parameters on in-plane elastic properties. Moreover, in order to assess the relevance of the homogenization method, a finite element model for 3 point bending test is created. Two approaches are adopted: the first one models separately the core and liner of the corrugated cardboard with thin shell element (3D approach), whereas the second approach being of particular interest in this work, considers the corrugated cardboard sandwich as a homogeneous plate and modeled therefore by a plate elements. It is shown that the simplified homogenized procedure is adequately accurate and ten time faster than the 3D approach for effectively analyzing corrugated cardboard panel in the preliminary and optimum design stages.

Introduction "The packing must protect what it sells and must sell what it protects ", this citation

summarizes the big functions of the packing that are divided in six principal families: paper, plastic, glass, metal, wood and composed material. The more used, the corrugated cardboard packing does not stop its increasing every year. This is due to its numerous advantages, notably the protection of the environment (completely recyclable) and its reduce coast.

Nevertheless, its use in an optimum manner requires the knowledge of its mechanical behavior : elastic, inelastic, failure, etc…

The problem can be viewed by considering the corrugated cardboard as a structure and then be by norms relative to the composite or metallic sandwich structure. The main tests are 3 or 4-point bending (ASTM C393-62), as well as shear tests (ASTM C273-61). Norstrand et al [START_REF] Nordstrand | Evaluation of transverse shear stiffness of structural core sandwich plates Composite structures[END_REF] have evaluated the transverse shear stiffness of corrugated cardboard by ASTM block shear test and by three-point bending test. It has been found that the shear moduli determined by the bending test, are significantly lower than those obtained by the block shear test.

Nevertheless, this approach doesn't allow to determine the stiffness matrix of such a material and makes therefore its homogenization for a finite elements calculation impossible. It is obvious that the possibility exists always to mesh the structure completely (skins and core) [START_REF] Patel | Local buckling and collapse of corrugated cardboard under biaxial stress Composite structures[END_REF][START_REF] Gilchrist | Nonlinear finite element modeling of corrugated cardboard[END_REF][START_REF] Nordstrand | Parametric study of the post-buckling strength of structural core sandwich panels Composite structures[END_REF] leading to an extremely expensive process. In this study, an other alternative being well developed consists the replacing the corrugated cardboard by an equivalent orthotropic layer. This approach articulating around two points, will permit after homogenization to simplify the numerical calculations.



The first point is to dedicate the different experimental protocols finalized for the sake of determination the mechanical properties of the constituents (skins and core) as well as those of the corrugated cardboard. The main difficulty resides in the experimental precautions in order to identify the necessary parameters in the absence of the pre-workbenches protocols.



The second point is to dedicate the analytical modeling. Thus, by using the mechanical properties and geometrical parameters of the constituents (step of fluting, thickness of skins and core), this model should be able to predict the homogenized elastic behavior of the corrugated cardboard.

A comparison between the experimental observations, analytic model and finite elements prediction allows to judge the performances of the proposed model. It is accompanied by a parametrical study highlighting the effect of the structural parameters on some elastic properties.

Experimental procedure

Material

The corrugated cardboard is an orthotropic sandwich with the surface plies (facing) providing bending stiffness, separated by a lightweight corrugated core (fluting) that provides shear stiffness. The core and facing plates are glued along the edges of the facing plates to form a wide sandwich panel. Two main dirctions characterise this material. The first noted MD (machine direction) corresponds to the direction of manufacturing of the material. It coincides with the x axis. The second noted CD (cross direction) corresponds to the transverse direction and coincides with the y axis (Fig. 1).

The cardboard is manufactured by SMURFIT company and is made from chemical Kraft fibres. The geometric material characteristics are presented in table 1.

Preparation of specimens is conducted for whole of tests, according to the recommendations of French norms NFQ 03-002 and NFQ 03-029.

Tensile tests

The used specimens are receptively inspired from ISO type NF T51-034 and NF Q03-002 on the mechanical characterization of plastic materials, paper and cardboard (Fig. 2). Each specimen is instrumented by a bi-directional strain gage. The most important difficulty of the tensile tests on the corrugated cardboard resides in the bruising of the specimen heads at the griping time.

To increase the rigidity of the specimen heads, a polyester resin is injected between flutings and the cardboard skins to fill the existing emptiness. A particular precaution is taken at the time of the specimen preparation in the CD. As a matter of fact, the resin risks to flow in the useful part and distort the test.

With regard to the skins preparation, the specimen extremities are rigidified by impregnating in the resin. This technique allows consequently to avoid the recourse to the special bits recommended by the norm NF Q03-002. All specimens are conditioned at 23°C and 50% RH for at least 24 h before testing. The tests are conducted under 3 mm/min cross head speed using a sensitive load cell of 500 N.

A representative example of the normal stress-strain curve of the corrugated cardboard is pointed out in figure 3. This curve exhibits a linear part following by a non-linear one. The later seems to be governed by a damage phenomenon which is mainly localized on the skins.

This phenomenon is more obvious in load-displacement curves of skin notably in the transverse direction of cellulose fibers (CD). It characterizes by small load falls (Fig. 3b). The obtained results under tensile tests are presented in table 2. It is important to note that the result dispersion remains acceptable with a maximum value of 15.47% for E CD. . The mechanical properties are more important in the MD than CD. One can conclude that these results are in an appropriate accordance with those results presented in the literature [START_REF] Patel | Local buckling and collapse of corrugated cardboard under biaxial stress Composite structures[END_REF][START_REF] Nordstrand | Parametric study of the post-buckling strength of structural core sandwich panels Composite structures[END_REF][START_REF] Damatty | Finite element modelling and analysis of a cardcardboard shelter Thin[END_REF].

Shear tests

The shearing tests represents a suitable manner to determine the two equivalent moduli of the transverse shearing: G xz and G yz . Such tests are carried out according to ASTM 273-61. The following limits, relative to the geometry of test-tubes are to respect hc <b/2 and hcs <l/12 [START_REF] Nordstrand | Evaluation of transverse shear stiffness of structural core sandwich plates Composite structures[END_REF][START_REF] Desrumaux | de technologie de Compiègne[END_REF] where hc is the core thickness of the sandwich and b and l are respectively the width and the length of the specimen. The specimen is glued to loading blocks with a twocomponent epoxy glue (araldite) that cures 24 hours at room temperature (Fig. 5). Then, it is conditioned at 23°C and 50% RH for 24h. As far as the loading measurement is concerned a load cell of 20 000 N load capacity is used.

The shear moduli are determined according to the ASTM C273-61 recommendation. The corresponding effective shear moduli in MD and CD are defined as follows : The in-plane shear moduli of the skin and the corrugated are calculated using Baum's approximation [START_REF] Baum | Orthotropic elastic constants of paper[END_REF] as follows

    l b H G iz iz iz    i = x,y
y x B xy E E G 387 . 0 
The measured values obtained from these tests are summarized in table 3. The dispersion concerning the out-plane shear remains acceptable (lower than 10%).

Let's analyze the load evolution during the displacement for this test. In the case of MD, this evolution can be described by four phases before the failure (Fig. 6). The first stage is characterized by a linear shape (elastic phase). A first load fall is observed at the end of this stage corresponding to the downfall of flutings under shearing effect. Once the minimal fluting thickness reaches, the material enters in the third stage during which the load increases again. In this phase, the shear loading of fluting-skins interfaces takes place. The fourth stage represents a total damaging of the material. The glue of starch gives up and provokes the detachment of skins. With regard to the CD behavior, this later is characterized by an linear elastic phase before reaching the failure as the detachment of flutings (Fig. 7).

Bending tests

The specimens of the 3-points bending tests do not require any particular preparation. Their dimensions are 200 x 60 x 4.01 mm. The span value is 160 mm giving the span-to-thickness ratio (L/h) equal to 39 minimizing therefore the shearing effect. The specimens are conditioned at 23°C and 50% RH for at least 24h.

Beam deflection is measured by an LVDT transducer attached directly to the specimen. The overall capacity of this transducer is 50 mm and the load is measured by a sensitive load cell of 50 N. The employed cross head speed is 2 mm/min.

The figure 8 presents a typical example of load-displacement in MD. Position and diameter of the load nose have a significant influence on the maximal value of the downfall load.

However, the elastic behavior is practically the same under these experimental conditions. Hence, in the case of 10 mm load nose diameter positioned between two tops of undulation (case 1), the downfall load is less important and the loss of linearity is more pronounced in comparison with the case where the load nose is applied on the top of the undulation (case 2). This phenomenon can be explained by the apparition of a local distortion under the load noses on the superior skin. It is important to note that such distortion is less important in the second case. In order to minimize this phenomenon and to avoid the localization of the load in a particular point, other tests are carried out using 40 mm load nose diameter. The obtained results indicate an increase of the downfall load whereas the elasticity remains unchanged.

Formulation of the analytical model

To analyze the elastic behavior of the corrugated cardboard, the proposed technique is a pointwise lamination approach using the classical laminate theory. This approach is inspired from Ishikawa et al [START_REF] Ishikawa | Stiffness and strength behavior of woven fabric composites[END_REF], Aboura [START_REF] Aboura | Etude du processus de délaminage Mode I, Mode II et Mode mixte (I et II) de matériaux composites à renforts tissés à différentes vitesses de sollicitation[END_REF][START_REF] Aboura | Analytical model of woven composite laminate. Superposition effect of two plies[END_REF] and Scida et al. [11] related to the elastic behavior modeling of woven composites materials.

A unit cell representative of the corrugated cardboard is defined as in figure 9 and considered fthe skins and the undulated fluting as an assembling of many infinitesimal elements dx of unidirectional lamina oriented at different angles.

The classical laminate theory is then applied to each element. The relationship between the inplane stress and moment resultants N i and M i , and in-plane strains, curvature  j and  j is given by :

                   j j ij ij ij ij i i k D B B A M N  (i,j =1,2 and 6) (1)
in which A ij , B ij and D ij are the in-plane stiffness for each infinitesimal element dx. These are defined by

   2 : 2 / 2 ) , , 1 ( ) , , ( h h ij dz Q z z D B A ( 2
ij G E E E E Q 0 0 0 1 1 0 1 1           (i,j = 1,2,6) (3)
Q ij is evaluated for each constituent of the corrugated cardboard unit cell. This means that the superior and inferior skins and the fluting undulation are taken into account. The local stiffness of each infinitesimal element depends on the constituent elastic properties as well as on the fluting orientation defined by the local off-axis angle (x). This angle is calculated from the fluting median fiber function

H t (x) : ) ) ( ( tan ) ( 1 dx x dHt x    (4) H t (x)
is assumed to be of sinusoidal form with a maximum thickness of hc :

) 2 ( sin 2 ) ( P x hc x Ht   (5)
The existence of these angles leads to a reduction in the effective elastic moduli in x and y direction. Thus, the elastic constants for the fluting can be calculated as follows. Table 5 presents the global matrix [B] evolution of for three integration steps dx : 0.1mm, 0.005 mm and 0.0005 mm. One notes that from the second step of integration, the global matrix [B] approaches to zero. Therefore, the step integration dx equal to 0.005 mm will be used for the model validation.

                                                                                  
) ( 1 4 2 2 2 / 1 ) ( 1 1 1 ) ( ) ( ) ( 2 1 / 1 ) ( 2 1 / 1 ) ( G m f f m G E E E G f m G E E f m E E E m f m E G E f E E f f m E G E m E xy x xy y x           (6) m=cos(), f =sin(), E 1 , E 2 ,
  P globale dx x D x B x A P D B A 0 ) ( ), ( ), ( 1 ) , , ( (7)

Model validation

In order to validate the analytical model, its predictions are compared with experimental results. The geometrical parameters of the unit cell are already summarized in Table 1. By using the mechanical properties of the skins and the fluting experimentally identified (Tab. 2 and 3), the predicted values compared with the experimental results are obviously demonstrated in Table 6.

It is worth noting that the predictions describe fairly well the tensile and bending experimental results. The error remains lower than 5% for all values except for E MD and  xy where these errors are respectively 10.57% and 15.8%. This difference can be explained by the sensitivity of the model to the geometrical parameters values.

The evaluation of the impact of these geometrical parameters on the numerical results is performed by simulation. In fact, the elastic properties variation according to the step of the undulation, the corrugated thickness and the skin thickness are first determined. The predictions are then well demonstrated as in figures 10, 11 and 12. It is obvious that the variation of the step undulation has a little influence on the E MD modulus. However, the other moduli are strongly influenced by this parameter. So, a gap of 20% on this parameter can provoke an error of 7.5% on the E CD modulus. This influence is even more perceptible concerning the curves in figures 11 and 12. Moreover, a variation of 20% of the total thickness drags an error between 5% and 15 % related to the elastic parameters. A variation of 10% on skin thickness leads to a variation of 10% on the Young and shear modulus . Note that 10% on skin thickness variation represents 0.016 mm, therefore a particular attention should be taken during the measure of this parameter.

 Effect on membrane properties

The first observation concerns the influence of the global thickness of the corrugated cardboard. The E x modulus (E MD ) is strongly influenced. Actually, for a constant undulation step, the fall is about 60% (2400 MPa for a thickness of 1.5 mm against 1000 MPa for a thickness of 4 mm). The E y modulus (E CD ) is less affected. It displays a fall of 45% (of 1100 MPa for 1.5 mm to 600 MPa for 4 mm).

With regard to the fluting step influence, it appears that the modulus E x remains almost insensible to this value whereas the value of E y modulus increases about 40% when the fluting step decreases from 8 mm to 3 mm. The influence of the thickness remains perceptible on the in-plane shear modulus G xy . An increase of 62.5 % of the thickness induces a decrease about 50% of the G xy modulus.

The effect of the fluting step is more important for the strong thickness (4 mm). The modulus G xy value decreases by 25 % when the step evolves from 3 mm to 8 mm. Whereas, this fall is only 6% for 1.5 mm thickness situation.

 Effect on bending properties

The bending rigidities are more sensitive to the thickness than the membrane properties (Figures 16 and17). Thus, whatever the undulation step, the fall of the bending rigidities D 11 and D 22 is practically 90 % when the thickness varies from 4 mm to 1.5 mm. On the other hand, as for the elastic modulus E x , the bending rigidity D 11 remains insensible to the step undulation except for 4 mm thickness. Indeed, a fall of 15% is calculated when the step undulation increase from 3 to 5 mm followed by a constants values until a step of 8 mm.

The bending rigidity in cross direction exhibits an other behaviour. In fact, the influence of the step undulation is important for 4 mm thickness. The D 22 fall by 56 % when the fluting step increases from 3 mm to 8 mm. This influence remains perceptible for higher thickness (4 mm to 3 mm). However the CD bending rigidity, for the lower thickness, are not influenced by the step undulation. This parametric study shows an antagonist evolution of membrane and bending rigidities versus total thickness. Nevertheless, the fluting step affect the E y and G xy more than the other parameters. The highest values are obtained for the lowest step undulation. Thus, the choice of geometrical parameters for optimal elastic parameters depends on the nature of loading.

For a complex loading, a compromise between membrane and bending rigidities is necessary. This analytical model seems to be an interesting tool for making decision regarding the geometrical parameters choice for an optimum elastic solution.

Finite element analysis

The main advantages of the mechanical behavior simulating of corrugated cardboard product are:

 decreased development costs, since less experiments are necessary in the process development phase;  a faster development phase, since more information on the mechanical properties of a corrugated cardboard is obtained in an early stage of its design;  the possibility of testing packages made from new corrugated cardboard materials, even if these materials have to be developed;

 being able to study the local phenomena (as local stresses and displacements).

In order to assess the relevance of the developed homogenization method, a finite element model is created for the 3-point bending. The geometrical characteristics of this model are chosen similar to those used in the corresponding experiments.

The used element is the basic triangular 3-nodes flat shell. It's a combination of CST plane stress and DKT plate bending elements [START_REF] Batoz | A Search for the Optimum Three-Node Triangular Plate Bending Element[END_REF][START_REF] Batoz | A study of Three-Node Triangular Plate Bending Elements[END_REF], based on the Kirchhoff hypotheses under a discreet manner and proposed by Dhatt [START_REF] Dhatt | Numerical Analysis of Thin Shells by Curved Triangular Elements Based on Discrete Kirchhoff Hypothesis[END_REF] and Stricklin et al. [START_REF] Stricklin | A rapidly Converging Triangular Plate Element[END_REF] for the linear analysis of thin plates. The stiffness matrix integration is performed by using three point Gauss quadrature rule in area coordinates. To determine the element stiffness matrix in local coordinates of a particular element, the global coordinate of each node in this element is transformed into the local coordinate. The stiffness matrix in local coordinates is then transformed into corresponding global coordinates. A transformation is required for this purpose which is discussed in detail in Zienkiewicz [START_REF] Zienkiewicz | The Finite Element Method, 4 th Ed[END_REF]. The DKT facet shell element seems to be the best element of its category while taking into account the aspects: simplicity in the calculations, efficiencies in the displacement and stress estimations and results reliability.

The FE program Reflex-v.1 [START_REF] Batoz | Modélisation des structures par éléments finis[END_REF] is used to calculate and GID-v.7 to model the actual corrugated cardboard sandwich panel. Two approaches are adopted:

 Shell approach (3D) which model separately the core and liner (skin) of the corrugated cardboard with thin shell element (Fig. 18). It is an association of two triangular elements (DKT plate element for bending and classical CST membrane). The adhesive between the liner (skin) and medium (core or undulation) is modeled as a perfect bonding. As a matter of fact, the extreme positions of the medium are connected directly to the liner by sharing the same node. Gilchrist et al. [START_REF] Gilchrist | Nonlinear finite element modeling of corrugated cardboard[END_REF] are modeled the corrugated board by this method and a second one. In this later, a multi-point constraint (MPC) technique is utilized. The MPC chosen acts as a beam element between the two nodes that connects the liner and the medium and imposes the same rotations and translation on each nodes. They find, in all of the two models, that the predictions are almost the same. However, such an approach is bound to have a high number of elements and degrees of freedom which increase computational coast when one is interested in the overall response of the structure. In the CD model, 900 elements and 1070 nodes are required. The skin and flute elastic properties are assumed to be the same and are presented in table 2.

 Plate approach (2D) considers the corrugated cardboard sandwich as a homogeneous plate and is modeled therefore by a triangular 3-node DKT plate element. For this model, the effect of the mesh refining on the solution convergence is investigated. Thus, 80, 160 and 240 elements are used. The elastic properties introduced in the FE analysis are those obtained by the analytical model and presented in table 6.

First, let's analyze the effect of the number of elements on the 2D model. Refining the mesh has not a significant influence on the result accuracy (Table . 7). For this reason, the 2D model with 160 elements is considered for analysis after mesh convergent studies.

Table 8 presents a comparison between experimental and the two FE approaches results. The calculation times (CPU) of personnel computer with AMD Duron 850 MHz processor are also indicated for the two approaches. The ratio FE / experiment for the 3D approach is 1.07. These same ratios are 1.08 and 0.88 respectively for MD and CD for the simplified homogenization procedure. The correlation between experimental and the two FE approaches is correct. However, for an overall behavior, the time calculation of the 2D approach is 10 time lower than that of the 3D approach. It appears that the simplified homogenization procedure is adequately accurate and fast for effectively analyzing corrugated cardboard panel in the preliminary and optimization design stages.

Conclusions

Although the corrugated cardboard has a constitution of a sandwich structure, its structural properties are revealed once the packing structure is constituted. This fact leads to consider that this sandwich is like a monolithic material. Hence, an experimental protocol is developed to determine its 2D orthotropic stiffness matrix.

As far as the modeling is concerned, an analytical model, taking into account the geometrical and mechanical properties of the cardboard constituents, is also proposed to predict these inplane properties. This model is also able to predict the bending properties.

After the model validation showing a good correlation between experimental and analytical results, a parametric study is conducted. This allows to analyze the effect of geometrical parameters on in-plane elastic properties. Thus, it appears that the E MD modulus and bending properties (D 11 and D 22 ) are strongly influenced by the total thickness of the corrugated whereas the E CD modulus is more affected by fluting step. The proposed model should be an interesting tool for a help to decision on the choice of geometrical parameters for an optimum elastic solution

In order to assess the relevance of the homogenization method developed for this purpose, a finite element analysis is used. The main goal of this work is to verify the possibility to use a 2D meshing of the corrugated cardboard, in stead of of a 3D meshing extensively used in the literature. It was found that the simplified homogenization procedure is adequately accurate and fast for effectively analyzing corrugated cardboard panel in the preliminary and optimum design stages.



  iz : shear stress  iz : shear strain : slope of the linear part of the load-displacement curve H : total sandwich thickness b : specimen width l : length of the specimen



  : slope of the load displacement curve l : length between supports b : width of the specimen H : thickness of the specimen The bending moduli are considerably close to the tensile moduli giving us a certain legitimacy to validate the tensile experimental procedure established for this material.

   12 and G 12 are the elastic properties of the fluting and skins in the orthotropic plane. Once the Q ij terms are calculated, the in-plane stiffness coefficients can be evaluated for each element in different regions of the unit cell by using equation (2). The global matrices A global , B global and D global for the corrugated cardboard unit cell are calculated numerically from the local matrices A, B and D evaluated for each infinitesimal element with an average in the x direction by

From

  the global matrices [A], [B] and [D], the effective Young's moduli, shear modulus and Poisson's ratio of the corrugated cardboard can be obtained as *] = [A]/H, H is the total unit cell thickness. The relation (8) remains valid only in the case of symmetric laminate, that means that the global matrix [B] is equal zero. The solution convergence depends on the integration step dx.

Figures 13 and 14

 14 Figures 13 and 14 summarize the combined effect of the thickness of the corrugated and undulation step on the evolution of the elastic properties of the material obtained by the analytical model. The geometrical characteristics of the micro fluting and middle fluting are fixed like limits of the interval (thickness: H1 = 1.55 mm for micro fluting and H2= 4.01 mm for middle fluting, and the undulation step: P1 = 3.26 for micro fluting and P2 = 8 mm for middle fluting).

Figure 1 :

 1 Figure 1 : Cardboard panel geometry

Figure 3 :

 3 Figure 3 : Cardboard corrugated stress-strain tensile curve.

Figure 4 :Figure 6 :

 46 Figure 4 : Skin load displacement tensile curve

Figure 7 :

 7 Figure 7 : CD load-displacement shear curve.

Figure 8 :

 8 Figure 8 : MD load-deflection curves for different load nose diameters.

Figure 9 :Figure 10 :

 910 Figure 9 : Unit cell representative of the corrugated cardboard

Figure 11 :

 11 Figure 11 : Variation of elastic properties versus skin and flute thickness variation.

Figure 12 :

 12 Figure 12 : Variation of elastic properties versus total thickness variation.

Figure 13 :Figure 14 :Figure 15 :Figure 17 :

 13141517 Figure 13 : Evolution of E MD versus thickness and flute step

Figure 18 :

 18 Figure 18 : 3D and 2D finite elements meshing.

Table 1 :

 1 Geometrical parameters

Table 2 :

 2 Tensile properties of skins and cardboard corrugated.

	Gxz Corrugated	G yz Corrugated	B xy G Skins	xy B G Corrugated
	(Mpa)	(Mpa)	(Mpa)	(Mpa)
	2.32  0.12	3.926  0.14	2052.76	267.83

Table 3 :

 3 Shear properties of cardboard corrugated and skins

	E MD (MPa)	E CD (MPa) E MDflex /E MDtensile E CDflex /E CDtensile
	844.4571.29 605.7324.54	0.97	1.09

Table 4 :

 4 Bending properties.

Table 5 :

 5 Influence of the step integration dx on the global matrix[B]

		E	MD (Mpa)		xy		MD	(Mpa)	E	CD (Mpa)		yx		CD	(Mpa)
	Skins	8258.53744.03 0.390.061	50.071.60	3406.84258.4 0.140.01	23.510.71
	Corrugated	863.0599.50	0.270.03	4.440.14	554.9785.89	0.220.03	2.7600.28

* Obtained by Baum's relation

Table 6 :

 6 Comparison between analytical and experimental results

	N x M	2 x 10	4 x 20	6 x 30
	d.o.f	99	315	651
	MD deflection (mm)	1.3479	1.3563	1.3562
	CD deflection (mm)	2.4650	2.4788	2.4787

Table 7 -

 7 Convergent studies

		Plate FE	Plate FE	Shell FE	Exper.	Exper.
		MD	CD	CD	CD	MD
	Bending rigidity	3.68	2.017	2.47 2,290,09 3.390.36
	(N/mm)
	CPU Time (s)	0.3	0.3	3	/	/
	Total load is 5 N.

Table 8 :

 8 Comparison between FE and experimental results

Scida, D., Aboura, Z., Benzeggagh, M.L. and Bocherens, E., Prediction of elastic behaviour of hybrid and non-hybrid woven composite, Composites, science and


Keywords: Paperboard, corrugated cardboard, behaviour, damage, coating

Paperboard exhibits a complex mechanical behaviour, which is governed by several phenomena. This work proposes a contribution to the identification of these phenomena. Uniaxial tensile tests under various configurations were carried out on the paperboard and corrugated cardboard. Observations under scanning electron microscopy were thereafter done in order to identify the microscopic phenomena produced in the structure. These observations made possible to highlight the presence of damage and its various appearance mechanisms.

Due to the continuous nature of the materials process, two main directions characterize paper and paperboard (figure1): transverse or cross direction denoted CD and machine direction denoted MD that corresponds to the feel orientation of the filter, therefore the privileged orientation of the cellulose fibres. To refer to out-of-plane direction (through-thickness), a third direction denoted ZD is introduced as depicted by figure 1. We observe the same directions for the corrugated cardboard. Let us note that the manufacture direction of the sandwich coincides with the machine direction of the corrugated cardboard and the paperboards (figure 2).

Due to its various virtues, corrugated cardboard sandwich is the paper family the most used in packing. The more utilized configuration is the simple wall. It is composed by three paperboard components: upper layer, core and lower layer. Therefore, for a better optimization of its use, previous studies were restricted to model its elastic behaviour. Corrugated cardboard is regarded as structure [START_REF] Biancolini | Evaluation of equivalent stiffness properties of corrugated board[END_REF][START_REF] Beldie | Paperboard packages exposed to static loads-finite element modelling and experiments[END_REF], sandwich [START_REF] Nordstrand | Parametric study of the post-buckling strength of structural core sandwich panels[END_REF][START_REF] Allansson | Stability and collapse of corrugated cardboard; numerical and experimental analysis[END_REF] or monolithic material [START_REF] Aboura | Elastic behavior of corrugated cardboard: experiments and modeling[END_REF]. All these approaches need the knowledge of mechanical properties of the corrugated cardboard components, indeed the sandwich behaviour is governed by those of its constituents.

Paper and paperboard are fibrous materials. They are built from cellulose fibres jointed by hydrogen bonds and some additional elements like talc. Due to the non-homogeneous and anisotropic nature of the paper materials, it is difficult to predict accurately the materials responses. Therefore, they exhibit complex mechanical behaviour, commonly characterized by a highly anisotropic linear elastic response (under moderate mechanical loading) and non-linear response (attributed to a plastic response) under high loading [START_REF] Baum | Subfacture mechanical properties[END_REF].

Under cyclic tensile test, when the paper is cycled at low strain there was little evidence of non-linear elastic behaviour. Beyond the yield stress, wide hysteresis loops appear and stress relaxation phenomena is highlighted [START_REF] Sawyer | An experimental description of the response of Paper[END_REF]. Unloading from some point of the non-linear part of the stress strain curve further results in a permanent deformation. Tryding shows that the unloading stiffness generally coincides well with the elastic modulus [8]. Sawyer and al. [START_REF] Sawyer | An experimental description of the response of Paper[END_REF] suggest that the molecular structure deformation mechanics are dominating the inelastic flow of paper.

This work purposes a contribution to a better comprehension of phenomena governing uni-axial tensile behaviour of the paperboard and corrugated cardboard. It will use in next works to model the global corrugated cardboard behaviour.

Material

Corrugated cardboard used in this study is single wall of type C . An upper and lower layer and a core compose it. They are respectively denoted Recto, Verso and Well. All the constituents are composed with 100% cellulose recycled fibres. Their thicknesses are 0.26 mm, for the Recto and the Verso and 0.21 mm for the Well. The total sandwich thickness is 4.1 mm and the flute step is P=8 mm.

Static tensile tests

Static tensile tests were carried out on corrugated cardboard and its constituents in the two-plane direction (MD and CD). The aim of these tests is to identify elastic and failure properties and highlight the different stages of their uni-axial tensile behaviour. The specimens were inspired from ISO type NF T51-034 and NF Q03-002 on the mechanical characterization of plastic materials, paper and cardboard. The most important difficulty of the tensile tests on the corrugated cardboard resides in the bruising of the specimen heads at the griping time. To increase the rigidity of the specimen heads, a polyester resin was injected between flutings and the cardboard skins to fill the existing emptiness. With regard to the paperboard preparation, the specimen extremities were rigidified by impregnating in the resin. This technique allows consequently avoiding the use of the special bits recommended by the norm NF Q03-002 [START_REF] Aboura | Elastic behavior of corrugated cardboard: experiments and modeling[END_REF].

All the specimens were conditioned at 23°C and 50% RH for at least 24 hours before testing. The tests were conducted under 2 mm/min crosshead speed using a sensitive load cell of 500 N. The instrumentation used is a camera which makes possible to follow the displacements of four points positioned, on each specimen, as shown in figure 3 [9]. We note that these specimen preparations before testing were used during the various tests of this work.

Table 1 shows the elastic and failure properties obtained. For all tested materials, Young modulus and failure loads are more significant in machine direction that corresponds to the cellulose fibres and flute orientations. In the case of paperboard layers, they are twice more significant than those measured in CD.

Concerning the corrugated cardboard, it appears that the failure load in MD is equal to the sum of the maximum failure loadings of the two main layers (Recto and Verso). On the other hand, it is equal to the sum of those of the three constituent s failures loads (layers and flute) in cross direction. The failure strain is twice more significant in CD than MD. In each direction, we note the quasi equivalence of the strains between the various constituents and the sandwich.

Characteristic stress-strain curves (figure 4 for layers and figure 5 for corrugated cardboard) show that mechanical behaviour in the two in-plane directions is composed by linear part followed-up by non-linear part. This phenomenon depends on the cellulose fibres, the hydrogen bonds and the rate of the moisture content. The nonlinearity is accentuated in the cross direction. This more marked non-linearity can be due to the fact that the paperboard mechanical behaviour is more governed by hydrogen bonds that are more requested in CD than the cellulose fibres.

To investigate this effect and to better understand phenomena that govern mechanical behaviour of paperboard, other mechanical tests are necessary. Therefore, the following tests were first carried out on the paperboard in order to best apprehend its behaviour. Thereafter, this permits to better understand the global uni-axial behaviour of the sandwich.

a) Strain rate effect

The viscous behaviour of paperboard can be highlighted by uni-axial tensile tests at different strain rate (ε& ). The tests were conducted on tensile testing machine INSTRON 4411 using speed strain range going from 6*10-5 s -1 to 12*10-3 s -1 , which correspond to different displacement speeds as illustrated in table 2. For each rate strain, ten specimens were tested for each paperboard in the two directions MD and CD. Two instrumentations were used:

extensometer and camera (figure 3).

Figures 6 to 9 present examples of stress-strain curves obtained at various strain rates request. In all cases (Well, Recto and Verso), the effect of the strain rate (ε& ) is not negligible in both directions MD and CD. Indeed, failure and yield stress increase according to strain rate.

This confirms well the presence of a viscous behaviour of paperboard that appears rather at high strains rates.

This tendency is quantified in tables 3 and 4. We note that the standard deviations are less than 7% for all the results.

At the strain rate 12*10 -3 s -1 , the maximum evolution of the failure stress (σ f ) compared to strain rate 6*10 -5 s -1 is obtained for the skins Recto and Verso. It is about 24.92% and 30.43% respectively for the Recto skin in the machine direction and Verso skin in the cross direction.

The smallest evolutions (about 19%) are obtained for the Well paperboard in the two directions.

The more significant evolution in the case of the skins Recto and Verso can be attributed to the behaviour of the coating used to treat the skins surfaces and which, undoubtedly, interferes on the material behaviour. Indeed, the paperboards Recto and Verso underwent a more significant coating than the Well paperboard as we will see it further.

The Young modulus evolution is more marked in the case of the Well paperboard in both directions (about 22% between minimum and maximum rates strains request). The same rate of evolution is raised in the case of the Verso skin in the cross direction (table 4). Therefore, the linear part of the paperboard behaviour is also governed by a viscous phenomenon. If the viscous effect is well highlighted, we can wonder whether the non-linearity beyond yield stress is due only to this phenomenon, or other additional phenomena intervene in the process. In order to answer this interrogation, other tests are necessary.

b) Strain recovery

The goal of the strain recoveries tests is to check the existence or not of a permanent deformation after unloading. The tests were carried out on uni-axial dynamic testing machine INSTRON 1341, with a cell of 1KN. This machine controls either in strain or in stress rates.

The specimens were loaded in stress controlled with a stress rate of

s MPa / 5 , 0 = σ& .
Once in non-linear part, the specimens were unloaded to a value near zero without reaching zero (in order to avoid the buckling) with the same stress rate. Then, they were heeded at a fixed stress during 24 hours. Throughout the test, the strain was measured by an optical method.

Figures 10 and 11 present examples of loading-unloading-holding response of the Verso skin in MD and Recto layer in CD. Specimen of Verso skin was requested, until a strain of 2.8% (Figure 10). After unloading and load holding, the material covers a strain of 1.53% in 3 hours of time. Beyond, the strain covers is unimportant, less than 0.03% during 21 hours (Figure 12). At the end of the test, the residual strain is about 1.27%. Therefore, paperboard recovers 55% of the initial strain.

For the skin Recto, it was requested in the direction CD until a deformation of 2.05% (Figure 11). After unloading and load holding, the strain recovered is about 1.47%, during 3 hours. After 24 hours of holding, the residual strain is about 0.59% and the covers strain represents 71% of the initial strain. Note that the recovered strain is more important in the Cross direction, due to the fact that the phenomenon is mainly managed by the connections inter fibres, whereas in the machine direction the fibres govern the behaviour.

Loading-unloading-holding tensile tests carried out on the skins, in the two directions, revealed a residual plastic strain. Thus, non-linearity of the paperboard is governed by a viscoplastic phenomenon. The slopes of unloading are curved. This indicates the presence of energy dissipation, so a loss of stiffness. This dissipation can be due to the presence of a damage coupled with the viscoplastic phenomenon. The next step of this study concerns the checking and quantification of the damage presence by using cycling loading tests.

Cyclic loading tensile tests

Generally, the quantitative evaluation of damage is done through the evolution of an elastic variable, which characterizes the studied phenomenon. For the needs for this study, this variable is the Young modulus. Cyclic tensile tests were carried out on ten specimens for each paperboard in the two directions. The specimens were loading and unloading at the same strain rate ( = 24*10 -5 s -1 ). The increments of loading were fixed at 20N for the machine direction and 10N for the cross direction. Once the data acquisition made, the parameter D was established for each level of loading as follows:

100 ) 1 ( 0 x E E D d - =
Where E 0 is the Young modulus measured in initial linear part and E d the Young modulus measured for each level of loading, during the unloading beyond the zones with stronger nonlinearity. The measurement domain was established between 0.85% and 0.25% of the reached load.

Parameter D allows following the evolution of the material behaviour. It includes the damage parameter, but also taking into account the presence of a viscous phenomenon. This parameter cannot be used as a damage parameter in a modelling approach.

Figures 13 and14 illustrate the examples of Verso skin behaviour, in machine and cross directions, during the loading-unloading tensile tests. During the first cycles, at low stress, there is no evidence of non-linear elastic behaviour and residual strains. Thus, the skins have a reversible linear behaviour. By increasing the increment of the load, in nonlinear field, loops of hysteresis appear synonymous with energy dissipation. These loops become more open while advancing in the nonlinear field.

An average of the evolution curves of the parameter D is represented on Figure 15. The stiffness loss occurs earlier in the cross direction than in MD. This phenomenon starts at a stress of 10 MPa in MD and 3 MPa in CD (Figure 15). Moreover, the evolution of parameter D, which is represented by the curves shape, is more significant in cross direction than in machine direction.

The maximum value reached by the parameter D in the case of Recto and Verso skins (Upper and Lower layers) is about 15% in both in-plane directions. On the other hand, in the case of Well paperboard used for the flute, stiffness loss is twice more significant in the machine direction than the cross direction (respectively 16.6% and 7.4%). This difference in the behaviour between the skins (upper and lower) and the paperboard of the flute can be due to the coating treatment undergone by the upper and lower skins. This surface coating improves printing quality on external skins of the corrugated cardboard packing. Therefore, it is little used for the flute paperboard. Indeed, it is denoted that the coating on the Recto and Verso skins, is about few tens of microns and is present on all the skins surfaces (Figure 16). A perpendicular sight of the treated surface reveals this facing with the detriment of the cellulose fibres that are not visible. On the other hand, this coating is weak (< 10µm) for the Well paperboard and its presence is not homogeneous on all the skin face (Figure 17). The cellulose fibres are well distinguished on the treated face. This film used for coating is made up of polymeric materials. It probably attenuates the damage of the two skins Recto and Verso, which is not the case of the paperboard Well that arrived at failure rather quickly.

Nevertheless, whatever the components of the sandwich, a significant loss of rigidity is observed contrary to precedent works [8] where the stiffness under unloading, from each point on the non-linear field, coincides well with the elastic modulus. This pushes us to believe that there is presence of damage phenomenon that occurs in material. In order to confirm this presence and the moment of its apparition, uni-axial tensile tests under scanning electron microscopy (SEM) were carried out.

Relaxation tensile tests under SEM

To be able to note the damage presence and its coupling with viscoplasticity, in-situ tensile tests with holding at fixes strains under SEM were carried out on the paperboard (figure 18). The load cell capacity is 300 N. It was assembled inside the SEM and then connected to an acquisition system. The minimal length between the two jaws of the device is 10mm and the maximum race is 10mm. Micro specimens were cut out for the three paperboards in the two directions MD and CD. The Length of the useful part between jaws of specimens is 10mm and their width is 5mm. Paperboard being a no conducting material, the specimens underwent a metallization with a film of gold before testing in order to ensure conductivity. Thereafter, they were assembled on the device inside the SEM, and tested with rate strain control of 12*10 -6 s -1 . In order to highlight the effect of stress relaxation and its appearance, each test was carried out with holding at various strain levels. During these material relaxations, fractographies were taken to show the nature of damage. Mechanical parameters obtained by theses tests will not be exploited because of the scale effect. Only physical phenomena will be considered. shown. At the first one, corresponding to the linear field of curve, stress falls synonymous of relaxation. On the other hand, the stress relaxation in linear part is weak in the machine direction (Figure 20). This observation consolidates the results of precedents tensile tests at various rates strains control. It confirms the presence of viscoelastic phenomenon at the elastic phase. This phenomenon is more significant in the cross direction than in the machine direction. This is due to the fact that the hydrogen bonds between fibres, which can have a viscous behaviour, are requested more in CD.

a) Results and discussions

Stress relaxation of paperboard increases with the increase of load level. This is due to the viscoplastic behaviour, which becomes more important in the nonlinear phase. As previously, these stress relaxations are more significant in the cross direction than in the machine one.

For the Well paperboard in CD, the damage intervenes with the second strain holding (ε=0.23%) beyond the linear part. Microscopic cracks appear locally. By increasing load level, microscopic cracks appear in greater number on the entire specimen surface as we can notice it at strain ε=0.89% on Figure 19. In fifth holding, the starting of macroscopic crack appears between the diffuse microscopic cracks. This crack increases and another one appears with the following holding. The final failure of material occurs according to the macroscopic crack appeared in first and according to a cross-section. Like in the cross direction, microscopic cracks appear at the second strain holding (ε=0.36%) beyond the linear phase on specimens loaded in machine direction. We note a presence of few microscopic cracks located in only some areas of the specimen in spite of the strain holding in the nonlinear part (Figure 20). The material failure intervenes abruptly in an area, which is not very reached by the damage, other that which saw germinating the most microscopic cracks.

b) Damage mechanisms

This part of the article relates the damage phenomena observed under the microscope and consequently details the preceding phenomenological explanations. At first holdings, the areas where appear first microscopic cracks were located. Thereafter, pictures of these areas were taken at each holding, in order to follow the microstructure evolution. One of the explanations to this phenomenon is that damage, in direction CD, occurs in the form of failure of the bonds between fibres. These bonds control the behaviour of paperboard in cross direction and are less rigid than cellulose fibres. These micro cracks coalesce to generate a macro crack, which appears in bottom of the sample. It is obvious that the edge effect is partly responsible for the localization of this macro crack. The figure 21d, zoom of the figure 21a, confirms this report and brings an additional explanation. Indeed, it appears that the effect of cutting and the radius curvature of the specimen take part in the failure initiation. This macroscopic crack becomes extensive until causing the failure (figure 21 b andc). On all the tested specimens, failure intervened according to the first appeared macroscopic crack. Figure 22 shows an example of crack from its appearance to the failure for specimen tested in cross direction. Evolution of the crack occurs while skirting fibres. Badly directed fibres being on its trajectory are broken (figure 22 b ε=1.01%). Figure 22d shows an example of the presence of badly directed fibres broken or torn off in-depth of the paperboard. The final failure intervenes according to a cross-section of the specimen. These failure facieses are in agreement with those found during tensile tests off-axis carried out in precedent study [10].

Contrary to the paperboard behaviour in cross direction, where the microscopic cracks are diffuse, in the case MD they are really localized near the edges of the specimen (figure 23). Here again, the effect of the specimen size and the nature of the cutting play a part in the crack initiation. (figure 23b). The first macroscopic crack (high part of photography b) appears in one of these zones and extends along the section. At the same time, another crack starts (down part of photography b). This second crack is propagated more quickly than the first one until causing the failure (figure 23 c andd). The final failure occurs according to a crack, which found the most direct way of fibres skirting therefore requiring less energy. This phenomenon is due to the damage mechanisms governing the behaviour of paperboard in this direction. Indeed, the crack is propagated in the transverse direction of cellulose fibres. Therefore, fibres failure is the prevalent damage mechanism in paperboard tested in machine direction. Crack develops by first circumventing the fibres and then after by breaking them. That is what explains its sinuous shape [10]. On the whole of the tested specimens, the section where occurs the final failure could not be predicted precisely.

Therefore, damage of the paperboard intervenes in several forms. We can note fibre skirting (Figure 24a), fibres failures (figure 24b) or even the coating damage (figure 24c). These mechanisms are found in the two in-plane directions (MD and CD), but with more or less significant proportions.

Cyclic loading tensile tests on corrugated cardboard

Several complex phenomena coexist on paperboard behaviour. Therefore, after having highlighted them, it would be interesting to know their influence on the corrugated cardboard behaviour. For this reason, cyclic tensile tests were carried out on the sandwich. Static tensile machine INSTRON 4411 is used.

Ten specimens were tested in each in-plane direction of the material. To measure strains, each specimen was instrumented by extensometer and camera and then loaded and unloaded with the same strain rate ( = 24*10 -5 s -1 ). Increments of loading were fixed at 20N for the machine direction and 10N for the cross direction. For each test, load-strain tensile was plotted.

Thereafter parameter D, considering previously, was established for each load level.

The Corrugated cardboard behaviour during these tests is similar to that of the paperboard in the two directions (Figure 25 and26). During the first unloading, at low strains, there is not evidence of non-linear elastic behaviour and residuals strains. By increasing increment of load, in nonlinear field, loops of hysteresis appear synonymous with energy dissipation. These loops become more open while advancing in the nonlinear domain.

Evolution of the parameter D, representing the evolution of mechanical behaviour of the sandwich, was established for each test. An average of these evolutions in the two directions is represented on figure 27. The stiffness lost is earlier and its evolution is more significant in the cross direction. Its starting occurs towards a stress of 0.4MPa in this direction and 0.7MPa in MD. The value of D in the direction MD is about 20%. It is very near to that of the paperboards (around 16%). The request of the corrugated cardboard in this direction is distributed primarily on the external skins [START_REF] Baum | Subfacture mechanical properties[END_REF], which explains this report. The small difference can be due to the interference of the interfaces skin-flute on sandwich behaviour. The damage of these interfaces, which are rigid, generates a local damage of the paperboard. These interfaces intervene more in cross direction, where they are requested at the same time than the skins and the flute. This explains why the parameter D is twice more significant than those of paperboards, because their damage is added to that of the rigid interfaces.

These observations carry out us to think that mechanical behaviour of corrugated cardboard, in uni-axial tensile, is controlled by the skins behaviour, even if it would be appropriate to add a small effect of the core and the interfaces skin-flute.

Conclusions

Due to its particular microstructure, paperboard presents a complex tensile behaviour governed by several phenomena. Tests carried out in this study confirm the presence of viscoelastic phenomenon, in the linear part, and viscoplastic one in the non-linear part. In addition, damage of paperboard was highlighted through cyclic and relaxation tensile tests. The behaviour of this material is thus more complex compared to what is described in literature, since this coexistence is synonymous with a coupling of viscosity-plasticity-damage.

The damage, whose evolution and importance are more increased in the cross direction, was highlighted very early during the tests. It is governed mainly by hydrogen bonds between cellulose fibres but also by fibres skirting. Moreover, cyclic tests showed the effect of the coating on damage evolution. In the case of corrugated cardboard sandwich, this complexity is increased with the interference of the rigid interface skin-flute. Nevertheless, it is not aberrant to think that the global behaviour remains to be controlled by the skins that reduce the structure effect on tensile test.

From a phenomenological point of view, the works in progress relate to the environmental effect on the mechanical behaviour. Whereas, from a modelling point of view, future works will try to approach, with the sight of the results of this study, the prediction of tensile behaviour beyond elasticity of corrugated cardboard, by taking into account the complex mechanical behaviour of its constituents. .

Stress (MPa)

  Phenomena governing uni-axial tensile behaviour of paperboard and corrugated cardboard S.ALLAOUI * , Z.ABOURA ** and M.L.BENZEGGAGH *** Introduction Paper materials are widely used in packing industry, media platform and number of other applications. They are made from chemical and mechanical pulp in a continuous process. The pulp is sprayed through the head box into a filter screen and dried under tension and pressure.

Figure 19

 19 Figure 19 illustrates the example of Well paperboard behaviour during relaxation test

Figure 21

 21 Figure 21 presents an example of damage evolution of specimen until failure in CD. The

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 1234567 Figure 1: Principal directions of paperboard

Figure 9 :

 9 Figure 9: Stress-strain curves of the paperboard Recto in CD according to ε& solicitation

  ±2.40 35.94 ±2.50 42.77 ±1.54 42.03 ±2.20 43.01 ±3.26 45.27 ±1.57 Recto

		Direction	6 * 10 -5		12 * 10 -5		Strain rates ε& (s -1 ) 6 * 10 -4 12 * 10 -4	6 * 10 -3	12 * 10 -3
	Direction Corrugated cardboard σ f (MPa) MD 36.24 σ f (MPa) 14.72 ±0.93	Material Upper layer (Recto) Lower layer (Verso) 15.77 ±1.27 17.09 ±0.61 16.95 ±0.55 17.28 ±1.10 17.949 ±0.81 Flute (Well)
		CD
		σ f (MPa)	36.02 ±1.19	Young Modulus (MPa) 40.51 ±1.95 41.61 ±0.71 43.01 ±1.87 44.24 ±1 .92 43.86 ±2.12
	MD Verso	MD σ f (MPa)	644.45 15.15 ±0.85	4322.20 15.86 ±0.80 16.42 ±0.74	4433.48 17.85 ±1.22	18.02 ±0.70	5106.67 19.76 ±0.56
	CD	CD σ f (MPa)	433.10 41.02 ±2.32	2048.27 42.35 ±2.53 45.61 ±1.62	2032.91 46.83 ±0.92	46.12 ±2.19	1962.35 48.97 ±3.58
	MD Well	CD MD σ f (MPa)	285.35 15.83 ±0.75	Load (N) 134.83 16.24 ±0.65 16.67 ±0.51	146.81 17.52 ±0.96	18.82 ±0.44	123.75 18.83 ±065
	CD		185.79		60.710			61.87		43.58
					Strain failure (%)
	MD		1.71		1.66				1.83		1.60
	CD		4.12		3.68	3.16 Strain rates ε& (s -1 )		3.51
	44.5% Direction	Machine direction 6 * 10 -5 12 * 10 -5		6 * 10 -4		12 * 10 -4		6 * -3	12 * 10 -3
	Recto	34.5% 39.5% E (MPa) MD E (MPa)	4718 ±125 Cross direction 4868 ±112 1944 ±148 2017 ±77	5265 ±166 2123 ±68		5191 ±83 2137 ±64		±186 2213 ±76	5408 ±99 2255 ±79
		29.5% CD
	E (MPa)	5086 ±184		5065 ±190	4952 ±207		5468 ±129		±125	5246 ±380
	9.5% 24.5% MD E (MPa) D (%) 19.5% Strain rate ε& (s -1 ) Verso CD E (MPa) 14.5% Control displacement (mm/min) 2056 ±99 5122 ±168 MD Well E (MPa) 2067 ±78		2062 ±108 6 * 10 -5 5155 ±244 0.5 2203 ±54	2072 ±73 12 * 10 -5 5336 ±198 1 2223 ±82	2306 ±66 6 * 10 -4 12 * 10 -4 5609 ±194 5 10 2291 ±124	2389 ±83 6 * 10 -3 ±121 50 ±108	2518 ±84 12 * 10 -3 6259 ±185 100 2529 ±146
		CD
		4.5%
		0	0.5	1	1.5	2	2.5		3	3.5		4	4.5	5
							Stress (Mpa)

Table 1 :

 1 Elastic and failure parameters of the materials

Table 2 :

 2 Range strain rates

Table 3 :

 3 Evolution of the failure stress (MPa) according to strain rate request

Table 4 :

 4 Evolution of the Young modulus (MPa) according to strain rate request


Cédrick Fairon
email: fairon@tedm.ucl.ac.be

Sébastien Paumier
email: paumier@tedm.ucl.ac.be

Patrick Watrin
email: watrin@tedm.ucl.ac.be

Can we parse without tagging ?

come

Introduction

Syntactic parsing is a major problem in Natural Language Processing and has been widely studied with the help of different methods, such as statistical parsing [START_REF] Charniak | Statistical Parsing with a Context-Free Grammar and Word Statistics[END_REF][START_REF] Collins | A New Statistical Parser Based on Bigram Lexical Dependencies[END_REF][START_REF] Magerman | Statistical Decision-Tree Model for Parsing[END_REF] and linguistic-based methods [START_REF] Roche | Analyse syntaxique transformationnelle du français par transducteurs et lexique-grammaire[END_REF][START_REF] Abney | Partial Parsing via Finite-State Cascades[END_REF][START_REF] Koskenniemi | Compiling and Using Finite-State Syntactic Rules[END_REF][START_REF] Ait-Mokhtar | Incremental Finite-State Parsing[END_REF]. Traditionally, at least for Romance languages, parsers take in input tagged texts in which each lexical unit is given to grammatical and/or inflectional information, such as lemma, grammatical category, gender and number. There are many taggers that use a mix of probabilistic and linguistic information: [START_REF] Church | A Stochastic Parts Program and Noun Phrase Parser for Unrestricted Text[END_REF], TreeTagger [START_REF] Schmidt | Probabilistic part-of-speech tagging using decision trees[END_REF]), Brill's Tagger [START_REF] Brill | Some Advances in Transformation-Based Part-of-Speech Tagging[END_REF], [START_REF] Cutting | A Practical Part-of-Speech Tagger[END_REF], Xerox part-of-speech tagger, GREYC parser [START_REF] Giguet | From Part-of-Speech Tagging to Memory-Based Deep Syntactic Analysis[END_REF], etc. Most of these tag about 95% of all lexical units correctly. This means that there is always a certain percentage of eroneously tagged units which will disrupt the behavior of parsers.

In this paper we will discuss the possibility of parsing texts without prior tagging. Therefore we will apply the same parsing method to two versions of the same text: one which was first disambiguated by automatic tagging and one which was not (in the latter case, a dictionary provides morphological information, but without disambiguation). Results will be compared in order to measure the impact of disambiguation. The method used is a common approach based on precise linguistic descriptions: electronic dictionaries [START_REF] Silberztein | Dictionnaires électroniques et analyse automatique de textes: le système INTEX[END_REF] and lexicon-grammar tables (Gross, 1975).

The framework

The question of whether or not tagging is needed for parsing arose within the framework of an applied research project which aims at developing a linguistic index engine 1 . In this particular context, indexation is viewed as the ultimate step towards an information extraction process. Parsing is therefore understood in a restrictive way: it is used on texts that resort to a technical sublanguage (as opposed to general language) and is used to analyse sentences that contain predefined verbs 2 in 1 This research was partly financed by Bureau Van Dijk. We wish to thank them for their collaboration. 2 The full process involves also the analysis of nominal forms. As we do not elaborate on this part in this order to extract their various complements. We built extraction graphs wich enable us to correctly extract the syntactic structures described in the linguistic databases of the lexicon-grammar. The following question then arose: should these extraction graphs be applied to a disambiguated text (where each word of the text is associated with one -and only one -POS tag) or could the system rely on a "simple" dictionary lookup procedure that would provides all the possible analyses for any given word but which would offer no disambiguation.

Before discussing these two possibilities, we will first describe the parsing method and the linguistic resources format.

The parsing method

Contrary to many others parsers, our method is based on an exact linguistic description and does not use statistics of any kind. The main part of this description consists of tables that, for each verb, describe the elementary structures in which it can appear. We can automatically generate grammars from such tables, and subsequently, apply them to texts via the advanced pattern matching function offered by the Unitex3 software. This approach has already been illustrated by several works [START_REF] Roche | Analyse syntaxique transformationnelle du français par transducteurs et lexique-grammaire[END_REF][START_REF] Senellart | Reconnaissance automatique des entrées du lexique-grammaire des phrases figées[END_REF][START_REF] Paumier | De la Reconnaissance de Formes Linguistiques à l'Analyse Syntaxique[END_REF].

Lexicon-grammar tables

Lexicon-grammar tables where introduced by Maurice Gross who analysed completive verbs in French (Gross 1975). These tables have since then been extended to the rest of French simple verbs [START_REF] Boons | La structure des phrases simples en français: constructions intransitives[END_REF][START_REF] Guillet | La structure des phrases simples en français: les constructions transitives locatives[END_REF] as well as to other kind of predicates (nouns, adjectives) and various languages.

The tables consist of a formal description of verbs represented as a matrix, as shown in Figure 1. Each line corresponds to a verb, and each row represents a formal syntactic property 4 . A '+' sign in a cell, paper, we will not give more details. respectively '-', means that the verb can, respectively cannot, appear in the corresponding structure. For instance, the property N0 V N1 is verified for both alimenter and allumer; we can therefore have sentences like:

N0 alimente N1 N0 allume N1

But the property N0 V en N2 is verified for alimenter and not for allumer; as a result we can have:

N0 alimente N1 en N2 but not: N0 allume N1 en N2 V N0 V N1 N1 est Vpp par N0 N0 V en N2 N0 V à partir de N3 N0 V à N4 N0 V dans N5 abattre + + - - - - absorber + + - - - - acheminer + + - - - - alimenter + + + + - - allumer + + - - - - approvisionner + + + - - - broyer + + + - - - brûler + + - - - - chauffer + + - + - - collecter + + - - - - comporter + - - - - - composer + + - - - - comprendre + + - - - - concentrer + + - + - - Figure 1: French verb table

Parametrized graphs

We exploit the content of the table using parametrized graphs, drawn with the help of Recursive Transition Network (RTN) formalism. Such a graph describes linguistic constructions that are relevant to the lexicongrammar table.

Each construction is described by a path in the parametrized graph as shown in Figure 2. The graph contains parameters. The value of each parameter is given depending on lexical entries and is given in the columns of the table. The parameters are named after the corresponding columns @A, @B, etc (@A=first column, @B=second column, etc). For Figure 1, the variable @A corresponds to the verb column.

A table can contain property marks ('+' and '-') and lexical elements. For each line of the table, a graph is then generated by substituting the variables as follows:

-if the variable @X refers to '-', the path is removed; -if it refers to '+', the path is maintained; -if it refers to a lexical item, it is replaced by this item.

impact on the method presented in this paper.

Properties marks + and -are used as conditions in the parametrized graph. We describe a set of possible constructions in the parametrized graph which condition each construction by referring to its corresponding property in the table. An automatic process5 then generates a graph for each entry of the table which only contains the constructions that are possible for this entry. Figure 3 shows the graph obtained for the verb allumer.

Parsing

Our method does not distinguish between pattern matching and parsing. Once we have generated graphs, we consider them as patterns. We use the pattern matching function of Unitex to find all matching sequences in a text. If sequences are matched by a graph, then we can say that we have parsed these sequences, because we can insert outputs in the graph, and therefore, tag matching sequences. In order to apply this method, we must define all of our patterns, which implies having a description of noun phrases. This is why we use a graph that is an approximative description of noun phrases.

The experiment

We have applied our parsing method on both tagged and untagged versions of the same corpus in order to compare results. In this section we describe our experiment.

Corpus and patterns

Our experiment aimed at extracting information in the area of energy. Our 1,500,000 word corpus is a collection of texts taken from the web. To evaluate our method we selected 5 verbs representative of the most common syntactic structures found in the domain of energy:

-alimenter : N0 V N1 en N2 à partir de N3 -chauffer : N0 V N1 à partir de N3 -consommer : N0 V N1 -contenir : N0 V N1 -produire : N0 V N1 à partir de N3

Naturally, there are other syntactic structures for theses verbs, but for the purpose of our study, we were particularly interested in structures containing complements that were relevant from a semantic point of view.

Tagged text

As most famous taggers have similar precision scores, we arbitrarily chose to use the TreeTagger because it was easy to install and use in our experiment.

We first applied the TreeTagger to our corpus. A script then rewrites the output of the tagging so that it can be manipulated by Unitex. This rewriting step basically consists of changing the tagset. For example, if we consider the following text:

Ce rapport veut en effet alimenter le débat social

The TreeTagger will turn it into:

Untagged text

By untagged text we do not mean that we use no linguistic information. We use the DELAF electronic dictionaries for French that are included in Unitex. These dictionaries provide the list of possible tags for each word. For instance, the French word est can be considered as a verb (a form of to be) or an adjective (east). In other words we do not assign a tag to each word a priori, as opposed to a tagger that always decides on a particular tag. This ambiguity is illustrated in the graph shown in Figure 4.

Is this comparison relevant ?

One can object that the comparaison is irrelevant because decisions of the statistical guesser are not based on the same dictionary as the one used for the "no-tagger" approach. This is not really a limitation since the words that are found in the TreeTagger's lexical resources are also present in the DELAF dictionary which covers a very large part of the lexicon. However there are some differences between the outputs of the TreeTagger and that of the dictionary lookup program:

some words could be absent from our dictionary (neologisms, proper names, misspelt words) but the TreeTagger will always provide a tag for these. This point will be disscussed below in the "results" section ; -the dictionary contains a large number of compound lexical forms (over 100.000 compound words); however the tagger cannot analyse compounds. This has no influence on the results since the noun phrase grammar we have developed contains patterns which match the internal structure of compound words (N de N, N à N, AN, NA, etc.).

Naturally, this argumentation is valid for any tagger with a comparable level of accuracy. The small difference in precision scores (3.61%) may indicate that tagging is not absolutely necessary. Precision errors are dued to the matching algorithm that gives priority to longest matches. For instance, the French word est can be an adjective (east) or a verb (a from of to be). Consequently, if the matching program considers it as an adjective, it will provide the following erroneous analysis: <N0>L'air</N0> alimentant <N1>la combustion est injecté par des buses à la base de la chambre</N1>

Results

Precision

In the example above, est is a verb, and the correct N1 complement is only la combustion. Such errors occur when the text is not disambiguated or when a word has been erroneously disambiguated.

Recall

Tagged text: 47.84 % (598/1250) Untagged text: 39.44 % (493/1250) The analysis of these results has highlighted two main reasons of this difference (8.4 %):

• Incompleteness of electronic dictionaries: even if they have a very large coverage, these resources cannot be exhaustive. In a domain such as energy, there are many neologisms and technical terms that are not in dictionaries. Therefore an unknown word is a fatal error with a dictionary-based approach, whereas a tagger always gives it a tag. When this tag is correct, the tagger approach is more efficient than the dictionary one. • Numbers: in its current state, our prototype contains no graph able to handle numbers. This fact blocks the analysis in the same way as unknown words do. On the other hand, the tagger gives tags to numbers so that the grammar can deal with them if they are tagged as determiners.

These poor recall scores are mainly due to complex structures that occur in texts and that are not taken into account in our grammars. For example, verb coordination, anaphora and relatives have not been described (or very briefly). The reason for this is that, within the framekork of indexation, we gave priority to precision in order to extract relevant complements. We did not try to make a complete parsing of our corpus, but only to parse sentences that contain enough information to be useful for indexation.

Conclusion

In this paper, we have presented a parsing method which is based on a precise linguistic description and which can be applied to tagged texts as well as untagged texts. The analysis of the results obtained with and without disambiguation shows that precision is not significantly greater if we use a tagger. On the contrary, we have observed that recall is better with a tagger, because our method is currently blocked by unknown units such as neologisms and numbers.

Figure

  Figure 2: parametrized graph

Figure 3 :

 3 Figure 3: graph obtained for the verb allumer

Figure 4 :

 4 Figure 4: ambiguous text after dictionary lookup

Unitex is an LGPL-licensed software, available at: http://igm.univ-mlv.fr/~unitex/

Usually, a lexicon-grammar table contains verbs that have the same main structure (for instance, N0 V N1). For convenience sake, we proceeded differently in our experiments. This is why there are properties referring to N4 or N5, which is not standard in the lexicon-grammar frame. However, this detail has no

For a complete description of this process, see Unitex manual at: http://igm.univ-mlv.fr/~unitex/manuel.html