C Bouvet

S Rivallant

J J Barrau

MODELLING OF IMPACT DAMAGE AND PERMANENT INDENTATION ON LAMINATE COMPOSITE PLATE

This paper deals with impact damage and permanent indentation modelling. A model enabling the formation of damages developing during a low velocity / low energy impact test on laminate composite panels has been elaborated. The different impact damages developing during an impact test, i. e. matrix cracking, fibres failure and interfaces delamination, are simulated. The interlaminar damages, i.e. interfaces delamination, are classically simulated thanks to interface finite elements based on the fracture mechanics. The particularity of this model is to account for the intralaminar damages, i.e. matrix cracks, thanks to interface finite elements which respect their discontinue character. These interface elements allow equally to simulate the permanent indentation during the impact unloading. This impact mark modelling is very original in the literature, and should allow to entirely design a composite structure thanks to impact damage tolerance.

Introduction

Composite materials are being increasingly used in airframe and spatial applications thanks to their interesting mechanical characteristics and low specific weight. Nevertheless, for structures submitted to low energy impacts or minor objects drop, like tools during assembly or maintenance operation, composite laminates reveal a brittle behaviour and can undergo significant damages in terms of matrix cracks, fibres breakages or delamination. These damages are particularly dangerous because they drastically reduce the residual mechanical characteristics of the structure, and at the same time can leave very little visible mark onto the impacted surface. Consequently, it is essential to define a damage tolerance demonstration to ensure that, with accidental damage occurring within the operational life, the remaining structure can withstand reasonable loads without failure until the damage is detected. The accidental damage is characterised by its visual detectability and compared to the so called barely visible impact damage (BVID) which is a basic concept in relation to the damage tolerance evaluation (JAR 25.571). So in order to numerically optimise the design of composite structures in impact damage tolerance, it is necessary to model in a first step the impact phase, and in particular the permanent indentation, and in a second step the residual strength phase. And the challenge of a numerical design optimisation of a composite structure is to simulate these 2 phases with the same modelling in order to be able to foresee the effect of a design modification on the residual strength but equally on the permanent indentation let by impact. This paper deals with the first step of this work, that is the numerical modelling of the impact phase. It consists in simulation of the damages created during the impact test and in particular the permanent indentation. Many authors have studied the impact modelling of composite structures ( [START_REF] Allix | Mesomodelling of delamination: towards industrial applications[END_REF][START_REF] Choi | A model for predicting damage in graphite / expoxy laminated composites resulting from low-velocity point impact[END_REF][START_REF] Li | Modelling damage of multiple delaminations and transverse matrix cracking in laminated composites due to low velocity lateral impact[END_REF][START_REF] Finn | Delaminations in composite plates under transverse static or impact loads[END_REF][START_REF] Moura | Modelling the interaction between matrix cracking and delamination in carbon-epoxy laminates under low velocity impact[END_REF]) but to our knowledge, the permanent indentation is never taken into account in these simulations when this data is necessary to define a damage tolerance concept. The impact damages are classically divided in 2 parts:

• The intralaminar damages, i.e. the damages developing inside the ply like matrix cracking, fibre/matrix debonding or fibres failure. To our opinion, these damages are equally responsible of the formation of the permanent indentation ( [START_REF] Abi | Experimental analysis of damage creation and permanent indentation on highly oriented plates[END_REF]), even if a lot of work is still necessary to confirm this hypothesis. • The interlaminar damages, i.e the damages developing at the interface between 2 consecutive plies namely delamination. Where E l t is the Young Modulus in tension in longitudinal direction, E l c in compression, E t in transverse direction, ν lt the Poisson ratio, G lt the shear modulus, σ t f the failure stress in transverse direction, τ lt f the failure shear stress, ε l f the failure strain in longitudinal direction and G I c and G II c the critical energy release rates, respectively in mode I and II, obtained in propagation with a 0°/45° interface. The stacking sequence of the laminate plate is [0°2, 45°2, 90°2, -45°2] S corresponding in a total thickness of 4.16 mm. An impact test is performed at a 30 J energy corresponding in an initial velocity of 5.4 mm/s with the used 2.05 kg-mass impactor. The curves of the impact force versus the time and the impactor displacement are drawn respectively figures 6a and 6b. The interfaces delaminations, obtained by ultrasonic investigation on impacted side, are reported figure 9. Thanks to the relatively simple stacking sequence used in this study, it is easy to identify each delaminated interface on this C-Scan. It can be noted on this figure the interfaces are numbered from non-impacted side toward impacted side. The permanent indentation has been equally measured 48 h after impact and evaluated to 0.7 mm. This permanent indentation is typical of BVID which is classically taken equal to about 0.6 mm without humidity aging ( [START_REF] Alderliesten | Damage tolerance of bonded aircraft structures[END_REF][START_REF] Tropis | Certification of the composite outer wing of the ATR72[END_REF]).

E l t (GPa) E l c (GPa) E t (GPa) ν lt G lt (GPa) σ t f (MPa) τ lt f (MPa) ε l f (%) G I c (N/m) G II c (N/

Permanent indentation investigation

In order to study the phenomenon of permanent indentation after impact and the impact damages morphology, 2 different post mortem cuts and microscopic photos were done (fig. 1). These micrographs show clearly the impact damages like matrix cracks, delaminations or fibres failures. In particular, permanent openings of these cracks are clearly observed. For example a very large delamination opening of the first interface non-impacted side of about 0.5 mm is observed. These observations show that the permanent openings of these cracks are due to the presence of debris that get infiltrated in the different cracks and create a blocking system ( [START_REF] Abi | Experimental analysis of damage creation and permanent indentation on highly oriented plates[END_REF]). This explanation of the permanent indentation formation is to be confirmed and should not be the alone responsible phenomenon, and other phenomena like permanent strains of resin should equally play a role. Nevertheless this phenomenon of blocking system due to impact debris of matrix cracking has been supposed preponderant in the formation of the permanent indentation. And there has been taken into account in the finite element (FE) model (cf. § 3.2) in order to simulate the permanent indentation after impact.

Numerical modelling

The proposed modelling is quickly described in this paper but more details can be found in [START_REF] Bouvet | Low velocity impact modelling in laminate composite panels with discrete interface elements[END_REF].

Intralaminar damage modelling

The 2 principal damages developing inner the plies are the matrix cracks and the fibres failures. The matrix cracking is simulated thanks to interface elements, then the ply mesh consists in volumic elements with a side parallel to the fibres directions and one element in the thickness (fig. 2). These elements strips, representative of strips of fibres and resin, are jointed together with interface elements of null thickness and very high stiffness (typically 10 6 MPa/mm). When this interface element is safe, 2 consecutive strips are perfectly jointed, but when a matrix crack exists, the interface stiffnesses are put to zero and 2 consecutive strips are disjointed. The matrix crack is derived from a classical quadratic equation:

( ) 1 2 2 2 2 ≤ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + f lt tz lt f t t τ τ τ σ σ (1)
where σ t is the transverse stress, τ lt and τ tz the shear stresses in the (lt) and (tz) planes, < > + the positive value and σ t f and τ lt f the failure stresses mentioned above. A particularity of this modelling is to drive this matrix cracking criterion of these interface elements thanks to stresses in adjacent volumic elements and not thanks to stresses in the interface elements. This allows to avoid stress concentration in the tip of matrix cracks but imposes a discussion between the volumic elements and the interface elements. This ply modelling enables to correctly take into account the matrix cracks discontinuities observed in experiments but it obliges to build a particular and refined meshing. In fact the ply model imposes a special meshing for the ±45° plies with diamond shaped elements to allow for the coincidence between 2 consecutive plies (fig. 3). The fibres failure is simulated with a classical strain failure criterion in the volumic elements:

(2)

f l l ε ε ≤
where ε l is the longitudinal strain and ε l f is given table 1. When this criterion is reached, the longitudinal stress σ l and the 3 shear stresses τ lt , τ tz , and τ lz are put to zero.

Permanent indentation modelling

In order to simulate the permanent opening of the matrix cracks observed in experiments, the interface elements of matrix cracking, which are broken, are avoid to close. Practically if the opening displacement d t in the transverse direction or the shear displacement d z in the zdirection are greater than a fixed value d 0 , an interface stiffness k is imposed to avoid the crack closure. Moreover the non-closure of a matrix crack can only exist for d t positive but can exist for d z positive or negative: In fact the d 0 value represents the minimum crack opening necessary to the formation of debris in order to create a blocking system. Moreover, as the matrix cracks direction is 45°, the d 0 values in opening displacement d t and in shear displacement d z are supposed equal. This modelling of permanent indentation is original and must be confirmed thanks to other experimental investigations. In fact the values of d 0 and k have been evaluated thanks to permanent indentation measured at 30 J-impact and prevents actually the use of this permanent indentation modelling as a predictive tool but rather as a qualitative tool.

(3) ( ) ( ) ( ) ( ) ( ) ( ) ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ ⎩ ⎨ ⎧ + = ⇒ > = ⇒ - ≤ ⇒ - ≤ ⎩ ⎨ ⎧ - = ⇒ < = ⇒ ≥ ⇒ ≥ ⎩ ⎨ ⎧ - = ⇒ < = ⇒ ≥ ⇒ ≥ ≤ ≤ ≤

Interlaminar damages modelling

The interlaminar damages consist with delaminations between 2 consecutive plies. This damage is classically simulated thanks to interface elements of null thickness driven by the fracture mechanics ( [START_REF] Crisfield | Progressive delamination using interface elements[END_REF]). A classical softening behaviour is imposed between the stress σ and the displacement d I to allow the dissipation of the energy release rate G I c at the interface (fig. 3a): in the 3 directions are supposed very high (in fact 10 6 MPa/mm) and the limit stresses σ I 0 and σ II 0 are chosen equal respectively to σ t f anf τ lt f . Once more time, the direction III is supposed equivalent to the direction II and σ III 0 is supposed equal σ II 0 . In fact the equality of the σ I 0 , σ II 0 and σ III 0 stresses with the matrix cracking stresses allows to use the same criterion for the initiation and the propagation of the delamination.

Experimental validation of the modelling

Finally, this modelling was set up in the FE software abaqus ® explicit and the 30 J impact test above mentioned was simulated. The half composite plate is meshed with 1 volumic element by plies sequence of same orientation, then 7 elements in the thickness [0°2, 45°2, 90°2, -45°4, 90°2, 45°2, 0°2] with a double thickness element in the middle, and axial symmetry condition around the z-axis is imposed (fig. 5). The curve of the impact force versus time is drawn figure 6a. A good correlation is observed between the experiment and the modelling, even if a little overestimation of the force is obtained between 1 and 2 ms. This overestimation should be due to the numerous fibre fractures observed experimentally which are not well taken into account by the modelling. The fibre failure criterion should be improved and in particular the post failure degradation. In fact, the question on the stresses to degrade after failure and on the energy release rate dissipated by the fibres failure should be studied. The curve of the impact force versus the displacement is drawn figure 6b. A good correlation is also observed with the overestimation of the force previously mentioned. Cuts of the plate in the 0° and 90° direction at the time of 2 ms are drawn figure 7. The openings of the matrix cracks and of the delaminations are clearly observed. In particular the large opening of the first interface non-impacted side is obviously visible in the 0° cut. In the same time, this large opening is not visible in the 90° cut. This is due to the direction of the fibres. In fact the first ply, non impacted side, is directed in the 0° direction and tends to open the first interface non impacted side and to propagate it in the 0° direction. This large propagation in the 0° direction is clearly observed on the delamination picture obtained by ultrasonic investigation (fig. 9). This opening is equally observed after impact as on the experimental micrograph (fig. 1) as on the FE modelling cut (fig. 8). Indeed, when the impact force is come back to zero, a permanent displacement is still present on the FE modelling thanks to the non-closure system of matrix cracking interface elements. Nevertheless the permanent opening of the first interface non-impacted side obtained by modelling is too high compared to the experiment (fig. 1). It should be to the non-closure parameters k and d 0 or more generally to the non-closure modelling principle. Indeed the development of this modelling is still in an early stage and need to be improved. Nevertheless the general shape of the laminate plate after impact obtained numerically (fig. 8) is in good agreement with the experimental observations (fig. 1). For example, the large opening of the first ply (non-impacted side) matrix crack located just under the impactor is clearly observed in the 90° cut, as numerically (fig. 8), as experimentally (fig. 1). It is equally the case for the important middle ply matrix crack. This matrix crack is oriented at 45° in the experimental observations (fig. 1) and should be due to shear stress particularly important in the middle of the thickness. Of course this 45° direction can not be taken into account by the modelling but this matrix cracking is numerically found and its opening after impact is equally simulated (fig. 8). The value of the permanent indentation given by simulation of 0.6 mm impacted side is in good agreement with the measured value of 0.7 mm. We want to point out that this comparison should be considered with caution because of the evaluation of the k and d 0 parameters was performed thanks to the experimental permanent indentation. Then this modelling of post impact deformation should be considered as a qualitative tool rather as a quantitative tool. But it could be user to better understand the permanent indentation formation which is a dominating parameter for the impact damage tolerance. The delaminated interface areas obtained after the impact test by experiment and by calculation are drawn figure 9. The comparison between these 2 delamination pictures is good and confirms the proposed modelling allows to account for experimental scenario of impact damage. In particular the delamination propagation is always driven by the direction of the lower ply, which is well taken into account by the modelling. Moreover, contrary to the permanent indentation modelling, no one material parameter has been identified thanks to impact test. This allows to confirm the good behaviour of the proposed modelling and to confirm its ability to foresee the impact damages.

Conclusion

An impact damage has been set up to simulate the different damage types forming during an impact on composite panel. The 3 principal damages, which are matrix cracks, interfaces delamination and fibres failure, are well taken into account by the proposed modelling thanks to interface elements. In particular the interaction between the matrix cracking damage and the delamination, which is a crucial point for the impact damages, is directly simulated without addition of interaction parameter. The modelling parameters are directly identified thanks to classical material tests. The modelling allows equally to simulate the permanent indentation which is a dominating parameter to certify a composite structure in damage tolerance concept. Unfortunately this part of this modelling imposes the introduction of supplementary parameters which are not until now evaluated thanks to classical material tests. But this inconvenience could be solved in the future and more work is still necessary to improve this modelling. This permanent indentation modelling should be considered as a qualitative tool rather as a quantitative tool. Nevertheless this modelling idea is totally original and could help to better understand the formation of permanent indentation which is until now a not well known phenomenon. Afterwards this modelling will be used as an initial condition to simulate a test of compression after impact in order to evaluate the residual strength in compression due to impact damages. In effect, in order to completely optimize the design of composite structure in damage tolerance, it is necessary to simulate each phase of the problem: the damages development during impact, the permanent indentation creation during impact and the damages propagation and the final failure during compression after impact.

Figure 1 .

 1 Figure 1. Post-mortem microscopic cuts in the 0° and 90° direction

Figure 2 .

 2 Figure 2. Ply modelling

Figure 3 .

 3 Figure 3. Meshing of the 4 ply types

Table 2 :

 2 Material characteristics for permanent indentation of the T700/M21 composite These d 0 and k values should be tested on other experimental tests and in particular on different energies of impact.

Figure 3 .

 3 Softening law of the stress-displacement curve (a) and linear mixed mode of fracture (b) Where a decreasing exponential law is chosen to avoid the shock of the final fracture: 7-10 June 2010, Budapest, β I is determined to dissipate the energy release rate G I c under the strainstress curve. Moreover a linear mixed mode of fracture is imposed (fig. 3b): Where G I , G II and G III are the energy release rates respectively in mode I, II and III and G I c , G II c and G III c are the critical energy release rates respectively in mode I, II and III. The critical energy release rates G I c and G II c are evaluated thanks to table 1, and the critical energy release rate in mode III is supposed equal to the one in mode I. The initial stiffnesses k I 0 , k II 0 and k III 0

Figure 5 .

 5 Figure 5. Finite element modelling of the plate

Figure 6 .

 6 Impact force versus time (a) and versus displacement (b)

Figure 7 .Figure 8 .

 78 Figure 7. Cuts of the FE modelling at 2 ms-time in the 0° and 90° directions

Figure 9 .

 9 Experimental (a) and modelled (b) delaminations

2 Experimental investigation 2.1 Impact test

Impact tests have been performed on laminate composite 100*150 mm 2 plates simply supported by a 75*125 mm 2 shadow (IGC 04.26.383 N_4 Airbus) with a spherical impactor of 16 mm-diameter. The material used is a prepreg with carbon unidirectional fibres and epoxy matrix T700/M21 manufactured by HEXCEL of 0.26 mm-thickness ply. The material characteristics evaluated by test (

[START_REF] Prombut | Caractérisation de la propagation de délaminage des stratifiés composites multidirectionnels[END_REF]

) are summarized on table 1.

Table 1 :

 1 Material characteristics of the T700/M21 composite

	m)

7-10 June 2010, Budapest, Hungary Paper ID: 672-ECCM14


Amir Shahdin
email: amir.shahdin@isae.fr

Joseph Morlier

Yves Gourinat

Damage monitoring in sandwich beams by modal parameter shifts: A comparative study of burst random and sine dwell vibration testing

Keywords: Vibration Testing, Modal Parameters, Structural Health Monitoring, Honeycomb Sandwich Beams

published or not. The documents may come

Damage monitoring in sandwich beams by modal parameter shifts: a comparative study of burst random and sine dwell vibration testing

Amir Shahdin, Joseph Morlier, Yves

Introduction

Laminated honeycomb sandwich materials are being used widely in weight sensitive structures where high flexural rigidity is required, such as in the aerospace industry. By inserting a light weight core between the two face sheets, the bending stiffness and strength are substantially increased compared with a single layer homogeneous structure, without adding much weight. When the beam or plate undergoes flexural vibration, the damped core is constrained primarily to shear. This shearing causes energy to be dissipated and the flexural motion to be damped. However damage in these structures may negate many of the benefits of sandwich construction. Impact can induce various types of damage in the structure. The facesheets can be damaged through delamination and fibre breakage; the facesheet and core interface region can be debonded and the core can be damaged through crushing and shear failure mechanisms. Safe and functional effectiveness of stressed sandwich structures can often depend on the retention of integrity of each of the different materials used in its manufacture. Therefore lightweight sandwich materials used in next generation of more advanced aircraft, marine craft, road and rail vehicles must possess the capability to absorb higher impact energy and retain a high degree of structural integrity. For aeronautical structures, a field where this problem has been quite studied, the components have to undergo low energy impacts caused by dropped tools, mishandling during assembly and maintenance, and in-service impacts by foreign objects such as stones or birds. In these low energy impacts normally, a small indentation is seen on the impact surface. This level of damage is often referred to as barely visible impact damage (BVID). There has been considerable research on the impact performance and damage development in carbon fiber composite materials and sandwich composite materials; see for example references [START_REF] Schubel | Impact and post impact behaviour of composite sandwich panels[END_REF][START_REF] Dear | Impact damage processes in composite sheet and sandwich honeycomb materials[END_REF][START_REF] Petit | Impact and compression after impact experimental study of a composite laminate with a cork thermal shield[END_REF][START_REF] Bull | Compressive strength after impact of CFRP-foam core sandwich panels in marine applications[END_REF][START_REF] Abrate | Impact on composite structures[END_REF].

Although not visually apparent, low energy impact damage is found to be quite detrimental to the load bearing capacities of sandwich structures, underscoring the need for reliable damage detection techniques for composite sandwich structures. In recent years, structural health monitoring (SHM) using vibration based damage detection has been rapidly expanding and has shown to be a feasible approach for detecting and locating damage. The purpose of structural health monitoring systems is to provide information about the condition of a structure in terms of reliability and safety before the damage threatens the integrity of the structure. So the diagnosis of the damage in structural systems requires an identification of the location and type of damage, as well as the quantification of the degree of damage. Therefore, several techniques have been used to detect damage in structures. A detailed and comprehensive overview on the vibration based damage detection methods has been presented in references [START_REF] Doebling | Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review[END_REF][START_REF] Doebling | A summary review of vibration-based damage identification methods[END_REF][START_REF] Yan | Development in vibration-based structural damage detection technique[END_REF][START_REF] Sohn | A review of structural health monitoring literature[END_REF][START_REF] Carden | Vibration based condition monitoring: A review[END_REF][START_REF] Van Der Auweraer | International research projects on structural damage detection[END_REF]. The basic principle of vibration based damage detection can be explained as follows. Any structure can be considered as a dynamic system with stiffness, mass and damping. Once some damages emerge in the structures, the structural parameters will change, and the frequency response functions and modal parameters of the structural system will also change. This change of modal parameters can be taken as the signal of early damage occurrence in the structural system. Although vibration-based structural damage detection is a newly emergent research topic, its development can still be divided into traditional-and modern-type.

The traditional-type refers to detection method for structural damage by using only the structural characteristics, such as natural frequencies, modal damping, mode shapes, etc.

These methods are among the earliest and most common, principally because they are simple to implement on any size structure. Structures can be excited by ambient energy, an external shaker or embedded actuators. Accelerometers and laser vibrometers can be used to monitor the structural dynamic responses. A variety of broadband excitation signals have been developed for making shaker measurements with FFT analyzers e.g., burst random, burst chirp etc. Since the FFT provides a spectrum over a broad band of frequencies, using a broadband excitation signal makes the measurement of broadband sprectral measurements much faster than using sine dwell or swept sine excitations [START_REF] Schwarz | Experimental modal analysis, CSI Reliability week[END_REF]. Despite the fact that sine dwell or swept sine modal testing requires large acquisition times, but they have the capability of detecting non linear structural dynamic behavior unlike the broadband excitations [START_REF] Gloth | Influence and characterisation of weak non-linearities in swept-sine modal testing[END_REF].

Several modern techniques e.g., statistical process control, neural networks, advanced signal processing, genetic algorithm, wavelet analysis etc., have been researched for detecting damage in composite materials, many of them showing the effectiveness of dynamic response measurements in monitoring the health of engineering structures [START_REF] Fugate | Vibration-based damage detection using statistical process control[END_REF][START_REF] Waldron | Damage detection using finite elements and laser operational deflection shapes[END_REF][START_REF] Sundaresan | Methods of distributed sensing for health monitoring of composite material structures[END_REF][START_REF] Leclerc | Impact detection in an aircraft composite panel -a neural network approach[END_REF][START_REF] Banks | An experimentally validated damage detection theory in smart structures[END_REF][START_REF] Krawczuk | Identification of delamination in composite beams by genetic algorithm[END_REF][START_REF] Yan | Online detection of crack damage in composite plates using embedded piezoelectric actuators/sensors and wavelet analysis[END_REF][START_REF] Kao | Detection of structural damage via free vibration responses generated by approximating artificial neural networks[END_REF][START_REF] Wojtowicki | New approach for the measurements of damping properties of materials using oberst beam[END_REF][START_REF] Vanhoenacker | The use of multisine excitations to characterise damage in structures[END_REF]. These methods are generally classified as modern-type methods for damage detection.

Change in natural frequency is the most common parameter used in the identification of damage [START_REF] Gadelrab | The effect of delamination on the natural frequencies of a laminated composite beam[END_REF][START_REF] Tracy | Effect of delamination on the natural frequencies of composite laminates[END_REF][START_REF] Shahdin | Correlating low energy impact damage with changes in modal parameters: A preliminary study on composite beams[END_REF]. Various methods of damage detection that use natural frequency information are reported by salawu [START_REF] Salawu | Detection of structural damage through changes in frequency: a review[END_REF]. Kim and Hwang investigated the effect of the debonding extent on reduction in the flexural bending stiffness and on the natural frequency of honeycomb sandwich beams, and concluded that increasing face-layer debonding progressively reduces the flexural bending stiffness of the beams [START_REF] Kim | Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams[END_REF]. Lestari and Qiao extracted dynamic characteristics of a sandwich structure by collecting dynamic response data from piezoelectric smart sensors, in order to evaluate the location and magnitude of the damage [START_REF] Lestari | Damage detection of fiber-reinforced polymer honeycomb sandwich beams[END_REF]. Adams and Cawley localized damage in structure from measurements of natural frequencies [START_REF] Adams | The localisation of defects in structures from measurements of natural frequencies[END_REF]. Yam and Chang showed that with the increase in delamination size the natural frequency decreases, by artificially creating a crack and then vibrating the structure with the help of an embedded actuator [START_REF] Yam | Damage detection of composite structures using dynamic analysis[END_REF]. Arkaduiz found that the presence of a self created delamination reduces the natural frequencies of a composite beam when harmonically excited [START_REF] Arkaduiz | Non-linear vibration of a delaminated composite beam[END_REF]. Kim et al. also proposed a methodology to non-destructively locate and estimate the size of damage in structures using a few natural frequencies. They formulated a damagelocalization algorithm in order to locate damage from changes in natural frequencies and a damage-sizing algorithm to estimate crack-size from natural frequency perturbation [START_REF] Kim | Damage identification in beam-type structures: frequency-based method vs. mode-shape based method[END_REF]. They used resonant poles to identify the modes, especially those modes that exhibit relatively large pole shifts are believed to be affected by damage [START_REF] Khoo | Structural damage assessment using vibration modal analysis[END_REF]. S.G. According to them, false negatives give no indication of damage when damage is present. [START_REF] Mattson | Damage detection and localization based on outlying residuals[END_REF]. The advantage of using the change of structural natural frequency to detect damage is its convenient measurement and high accuracy. However the measurement of natural frequency cannot provide enough information for structural damage detection. Furthermore, the natural frequency is often not sensitive enough to initial damage in structures. Usually, this method can only ascertain existence of large damage, but may not be able to give the damage location because the structural damage in different location may cause the same frequency change.

However, in structures made of composite materials there seems to be a tendency to use damping as a damage indicator tool, as it tends to be more sensitive to damage than the stiffness variations. The introduction of damage into a material generally results in an increase of damping, which is related to energy dissipation during dynamic excitation. As friction is an energy dissipation mechanism, it is reasonable to assume that damping may be used for SHM, when this type of damage is concerned. Therefore, damping has also been proposed as a potentially sensitive and attractive damage indicator [START_REF] Montalvao | A method for the localization of damage in a CFRP plate using damping[END_REF], though research works related to damping are fewer in number than those on natural frequency. The main sources of internal damping in a composite material arise from microplastic and viscoelastic phenomena in the matrix together with the interface effects between the matrix and the reinforcement [START_REF] Adams | Damping in composites[END_REF]. The importance of damping as a parameter for damage detection is explained in scientific literature and has also been verified by the experimental results in this article. Zhang and Hartwig recommended damping in the evaluation of damage process which seemed more sensitive than the natural frequencies [START_REF] Zhang | Relation of damping and fatigue damage of unidirectional fibre composites[END_REF]. Gibson carried out vibration tests on composite specimens and found that for higher modes damping loss factor measurements are more significant than frequency measurements [START_REF] Gibson | Modal vibration response measurements for characterization of composite materials and structures[END_REF]. Similarly, Saravanos and Hopkins experimented on composite beams, and showed that the delamination has a more profound effect on modal damping than the natural frequencies [START_REF] Saravanos | Effects of delaminations on the damped dynamic characteristics of composites[END_REF]. Colakoglu showed that the damping factor increased with the number of fatigue cycles [START_REF] Colakoglu | Description of fatigue damage using a damping monitoring technique[END_REF]. Richardson and Mannan found that the loss of stiffness in a structure corresponds to a decrease in natural frequency combined with an increase in damping [START_REF] Richardson | Correlating minute structural faults with changes in modal parameters[END_REF].

The main motivation of the work presented in this article, is to carryout modal testing on intact and damaged sandwich beams by using both burst random and sine dwell testing in order to study the influence of impact damage and core-only damage on the global modal parameters (frequency and damping). The testing methodology used falls under the traditional-type vibration-based structural damage detection methods. In the end, a design of experiments is carried out on the experimental results, to determine that which modal testing method among burst random and sine dwell is more efficient for estimation in the presence of damping.

Material and specimen

In order to investigate the effect of impact and core-only damages on the modal parameters, honeycomb sandwich beams shall be used in this article. As this is a preliminary experimental study, therefore standard sandwich material like honeycomb is chosen for the instance. In future, this study will be extended to more complex sandwiches like entangled sandwich materials.

Resin-containing carbon-fiber/epoxy prepreg of T700/M21 is used to fabricate the skin materials [START_REF] Hexply | Data Sheet[END_REF]. The material is supplied by Hexcel composites, the physical properties are set out in Table 1. The upper and lower skins consist of four plies each with a stacking sequence of [0/90/90/0]. The thickness of each ply is 0.125mm.

The core material is honeycomb and can be selected from a wide range of metallic and non-metallic honeycomb cores. The honeycomb sandwich beams in this article are made of Nomex-aramid honeycomb core (HRH 10) supplied by Hexcel composites [START_REF] Hexweb | Honeycomb attributes and properties[END_REF]. The honeycomb core has a nominal cell size of 6.5 mm and a core thickness of 10 mm.

Mechanical properties of the honeycomb core is listed in Table 2. The sandwich beam specimens are fabricated using an autoclave and an aluminum mold. The skin and the core are cured simultaneously in order to have an excellent bond. The final dimensions of the six identical honeycomb sandwich beams used in this article are 480 x 50 x 11 mm.

The vibration tests are carried out with two steel masses (50 x 25 x 5 mm) attached at the ends [START_REF] Vanhoenacker | The use of multisine excitations to characterise damage in structures[END_REF][START_REF] Shahdin | Correlating low energy impact damage with changes in modal parameters: A preliminary study on composite beams[END_REF]. The aim of putting these masses at the ends is to enhance the difference in the modal parameters between the undamaged and the damaged test specimens.

Experimental methods

Vibration tests

The experimental equipment used for vibration testing is shown in Fig. 1. The experimental set-up is that of a free-free beam excited at its center, based on Oberst method [START_REF] Wojtowicki | New approach for the measurements of damping properties of materials using oberst beam[END_REF]. The Oberst method states that a free-free beam excited at its center has the same dynamical behavior as that of a half length cantilever beam. The test specimen is placed at its center on a B&K force sensor (type 8200) which is then assembled on a shaker supplied by Prodera having a maximum force of 100 N. However the force sensor is not capable of measuring reliable response below 5 Hz. A fixation system is used to place the test specimens on the force sensor. The fixation is glued to the test specimens with a HBM X60 rapid adhesive. The response displacements are measured with the help of a non-contact and high precision Laser Vibrometer OFV-505 provided by Polytec. The shaker, force sensor and the laser vibrometer are manipulated with the help of a data acquisition system supplied by LMS Test Lab for burst random testing and Ideas Test (B&K) for sine dwell testing.

The center of the test specimens is excited at Point 17 as shown in Fig. 2. Each sandwich specimen is tested with two types of excitations i.e., burst random and sine dwell.

For both the testing systems (LMS and B&K), the resolution is kept 0.25 Hz in order to obtain a good shape of the resonance peaks at low frequency range and to have a reliable comparison of modal parameters between the two systems. Response is measured at 33 points that are symmetrically spaced in three rows along the length of the beam to have reliable identifiable mode shapes. The level of the excitation signal for both the excitations is chosen as 1N which is kept fixed during all the vibration tests conducted in this paper. With the help of LMS by using burst random excitation, we have the advantage of having in quick time the overall dynamic (modal) response of our structure if we are mostly concerned with frequency and mode shapes. In addition, this broadband type of testing helps us identify the modes that we can use later on for sine-dwell testing. However if we need precise damping measurements then sine-dwell testing becomes inevitable but the problem with it is the lengthy acquisition times.

Burst random excitation is a broadband type excitation signal for which a 50% burst percentage is used. Normally burst random excitations are leakage free but after trying different window functions, it was found that by putting Hanning windows on both the excitation and response signals, better quality signals FRFs are obtained. The signal is averaged 10 times for each measurement point and the frequency band chosen is 0-2650Hz.

Sine-dwell excitation is the discrete version of sine sweep. The frequency is not varied continuously, but is incremented by discrete amounts at discrete time points. The advantage of sine-dwell testing is its capability of detecting non linear structural dynamic behavior unlike the broadband excitations. As sine dwell testing requires larger acquisition times, so instead of studying the whole frequency band (0-2650 Hz), acquisition is carried out only around the first four bending modes previously identified by burst random testing by keeping the same resolution.

The modal parameters are extracted by Polymax and Polyreference, integrated in the data acquisition systems for burst random and sine-dwell testing respectively. The Polymax estimation method used by LMS acquisition system is a new non-iterative frequency domain parameter estimation method based on weighted least squares approach and uses measured FRFs as primary data. For the B&K system, one similar concept is used but in time-domain (Polyreference LSCE method), which typically require impulse responses (obtained as the inverse Fourier transforms of the FRFs) as primary data. Practically both of these methods work in similar fashion as follows:

• Firstly all the 33 FRFs are sort of superimposed along with a FRF sum. Limited frequency band estimation is then performed by taking each resonance separately.

• For accurate assessment of damping, a frequency interval of ± 20 Hz is chosen for each resonance peak for both Polymax and Polyreference, because by changing the frequency interval damping values can be affected.

• In the next step a stability diagram is constructed containing the poles i.e., frequency, damping information. For each mathematical model order, the poles are calculated from the estimated denominator coefficients of Equation 3. The order of the mathematical model is shown on the right vertical end of the stability diagram. For reliable damping measurement, that value of pole should be chosen which displays a stable value for several model orders and if possible for each mode the value of poles should be chosen at the same model order to ensure that there is minimum uncertainty while comparing the damping values between different damage states.

One of the specific advantages of these two techniques lies in the very stable identification of the system poles and participation factors as a function of the specified system order, leading to easy-to-interpret stabilisation diagrams. This implies a potential for automating the method and to apply it to "difficult" estimation cases such as high-order and/or highly damped systems with large modal overlap. As discussed previously, both Polymax and Polyreference are based on least-squares complex optimization methods, so both of them calculate the optimal pole value (frequency and damping) based on the 33 measurement points. We do not have access to the average values, variances or standard deviations for the 33 FRFs as the estimated modal parameters are the results of an optimized process.

The reference [START_REF] Peeters | The PolyMAX frequencydomain method: a new standard for modal parameter estimation[END_REF] explains these two estimators in detail.

So from the above discussion it can be said that both Polymax and Polyreference methods work in similar fashion, so the difference in the resulting modal parameters if it is the case, is due to the difference in excitations than due to the different estimation methods.

Impact tests

The six sandwich beams tested in this article are damaged in two different ways. The first four are damaged by drop weight impacts around the barely visible impact damage limit (BVID), in order to simulate damage by foreign impact objects such as stones or birds. The other two are damaged by piercing a hole all along the width in the honeycomb core by a hand drill, simulating mishandling during assembly and maintenance. The impact tests are carried out by a drop weight system as shown in Fig. 3, and a detailed cut away of the drop assembly is shown in Fig. 4.

The impactor tip has a hemispherical head with a diameter of 12.7 mm. A force sensor (type 9051A) provided by Kistler is placed between the impactor tip and the free falling mass of 2 kg. The impact velocity is measured with the help of an optic sensor. The combined weight of the impact head, freefalling mass, force sensor and the accelerometer is 2.03 kg. In the calculation of impact height, a factor of 1.1 is used to compensate for the losses due to friction between the guidance tube and the drop assembly. The size of the impact window is 80 x 40 mm 2 which allows all the impact points to have the same boundary conditions and all the four ends are clamped. Further details on the impact test methodology of this drop tower can be found in the references [START_REF] Petit | Impact and compression after impact experimental study of a composite laminate with a cork thermal shield[END_REF][START_REF] Shahdin | Correlating low energy impact damage with changes in modal parameters: A preliminary study on composite beams[END_REF].

In this article, a simple case with symmetric impacts is chosen. If satisfactory results are obtained, then asymmetric damage shall be studied in the future. Honeycomb sandwich beams are impacted by taking into account the barely visible impact damage limit (BVID).

BVID corresponds to the formation of an indentation on the surface of the structure that can be detected by detailed visual inspection and can lead to high damage. In the aeronautical domain, BVID corresponds to an indentation of 0.3 mm after relaxation, aging etc (according to Airbus certifications). In this study, it is decided to take 0.6-0.8 mm of penetration depth as detectability criterion just after the impact [START_REF] Petit | Impact and compression after impact experimental study of a composite laminate with a cork thermal shield[END_REF] which corresponds to an indentation depth of approximately 0.3 mm by taking into account the above mentioned factors such as relaxation, aging, humidity etc. The idea behind the impact tests is to damage the specimens below the BVID limit, in order to detect by vibration testing the damage that is not visible through naked eye. Four of the six sandwich beams are impacted symmetrically at four points with the same impact energy, as shown in Fig. 2. However in honeycomb sandwich beams, it is difficult to induce the same amount of damage at different points in the same specimen, even if it is impacted with the same energy i.e., impacting at the honeycomb cell center and at the corner leads to different damages. Therefore, it is not possible to have the same density of damage in honeycomb sandwich specimens at all the different impact points.

The first two honeycomb sandwich beams (H1 and H2) are impacted at 4J that produces a very small damage (not measurable by NDT methods) which is not visible on the surface. The reason for having the same impact energy for these two beams is to study the effect of end masses i.e., H1 is without and H2 is with end masses. The next honeycomb beam (H3) is impacted at 6J, which produces an indentation depth from 0.1 to 0.3 mm at the four impact points. However, the greatest dispersion in damage is seen in the honeycomb beam H4 which is impacted at 8J as shown in Fig. 5.

The damage depth for two impact points at one side of the beam is approximately 0.7 mm which corresponds to the BVID limit. But at the two impact points on the other end of the beam, the impactor head has induced severe damage due to impact at honeycomb cell center.

This phenomenon introduces asymmetry in the beams and highlights the difficulty in inducing a global symmetric damage. The impact parameters for these four sandwich beams are listed in Table 3.

The data obtained during the drop weigh impact tests carried out on the honeycomb beams (H2, H3 and H4) is shown in Fig. 6. The impact test data for the honeycomb beams (H1 and H2) is similar as they are impacted with the same energy.

Four similar impacts have been performed on each specimen. However, in order to clarify these plots, only one impact test result for each specimen is plotted. All the impact curves presented in Fig. 6 are filtered at 15 kHz to avoid a free frequency of the impactor at about 20 kHz. These curves, representative of all performed impact tests, are very classic in the literature [START_REF] Bull | Compressive strength after impact of CFRP-foam core sandwich panels in marine applications[END_REF][START_REF] Abrate | Impact on composite structures[END_REF]. In Fig. 6 a, the impact forces are drawn as a function of time. These curves are globally smooth and almost sinusoidal at low impact energy. The curves for all the three beams (H2, H3 and H4) show an important force signal fall followed by oscillations which is characteristic of delamination onset i.e., the appearance of first major damage in the sandwich beams. This is also evident in the force-displacement plot (Fig. 6 b). The evolution of the peak force signal for the three beams (H2, H3 and H4) shows a logical increase with the increase in the impact energy.

As discussed previously, the second way of inducing damage is by piercing a hole all along the width in the honeycomb core by a hand drill. This type of damage can be referred to as core-only damage. In case of the honeycomb beams (H5) and (H6), approximately 5 mm and 10 mm diameter holes are pierced all along the width at the same positions as the impact points as shown in Fig . 2. For the 5 mm holes (Beam H5), some honeycomb material is present between the hole and the skins, however in case of 10 mm holes (Beam H6), no honeycomb material is present between the damage and the skin. The aim of inducing coreonly damage is to check that whether this type of damage induces the same effect on the modal parameters as the impact damage. This will help us in future to develop algorithms based on modal parameters to detect these kinds of damages (impact and core-only damage) in sandwich structures.

The sandwich beams have three states. First one is the undamaged state (UD), the second is the damage state due to two impacts or two holes (D1) and the third is the damage state due to four impacts or four holes (D2). Vibration tests are carried out on the six sandwich beams after each of these three states. The effect of the impact damage and coreonly damage on the modal parameters is studied in the following sections of this paper with the help of frequency and damping changes between the undamaged (UD) and the damaged states (D1 and D2) with the help of Eq. 1 and Eq. 2.

Change in frequency between UD and D1, (Δf

) = UD D UD f (k) f (k) f (k) -1 (1)
Change in damping between UD and D1, (

Δ ζ ) = D U D UD (k) (k) (k) ζ -ζ ζ 1 (2)
where f UD (k) is the damped natural frequency for the undamaged specimen for the k th mode and f D1 (k) is the damped natural frequency for the specimen damaged at two impact points (D1) for the k th mode. Nomenclature in case of Eq. 2 is the same. Furthermore, in order to calculate the frequency and damping change ratios between UD and D2 the same procedure is used.

Tracking of poles for damage detection by modal analysis

Modal parameter estimation is a special case of system identification where the a priori model of the system is known to be in the form of modal parameters. The identification process consists of estimating the modal parameters from frequency response function (FRF) measurements. Modal identification uses numerical techniques to separate the contributions of individual modes of vibration in measurements such as frequency response functions. Each term of the FRF matrix can be represented in terms of pole location and a mode shape. The FRF matrix model is represented mathematically by:

[ ] [ ] [ ] mod es k 1 R(k ) R(k ) * H( ) (j (k) p(k )) (j (k) p(k )*) = ⎧ ⎫ ω = + ⎨ ω - ω - ⎩ ⎭ ∑ ⎬ (3)
The numerator R(k) is the residue of the FRF and is a function of the product between mode shape components at all points. The denominator gives the modal frequency and modal damping (second term in Equation ( 3) is the complex conjugate term). The poles p(k), are the roots that satisfy this equation and are related to modal frequency and damping as follows:

p(k ) (k ) j (k ) = -σ + ω (4)
The magnitude of each pole is the undamped natural frequency (ω n ). The undamped natural frequency (ω n ) and the modal damping ( σ ) are related to mass, stiffness and damping as follows: given by

2 2 n d K (k ) M ω = ω + σ = (5) C 2 (k) M σ = (6)
The effect of physical properties on poles in the complex s-plane is illustrated in Fig. 8.

From Fig. 8, it can be observed that a change in stiffness affects only the frequency, while changes in mass and structural damping affect both modal damped frequency (ω d ) and modal damping ( ). For this study, the primary interest is to study the decrease in the modal damped frequency (ω d ) and the increase in modal damping ( σ σ ) due to damage in the sandwich specimens [START_REF] Meyers | Response surface methodology 1995[END_REF].

Results and discussion

Significance of end-masses

End-masses have been placed in case of composite laminate beams in scientific literature [START_REF] Shahdin | Correlating low energy impact damage with changes in modal parameters: A preliminary study on composite beams[END_REF] in order to enhance the difference between the modal parameters for the undamaged and the damaged cases. But in case of sandwich composite beams, this phenomenon has to be verified. So in this article, vibration tests are carried out on honeycomb sandwich beams (H1 without end-masses) and (H2 with end masses) to verify that whether in case of honeycomb sandwich beams the end-masses have as effect on modals parameters or not.

This study is conducted by studying the frequency and the damping change ratios presented in Table 4 between the undamaged (UD) and the two damaged cases (D1 and D2)

for the honeycomb sandwich beams (H1 without end-masses) and (H2 with end-masses) for both burst random (BR) and sine dwell (SD) testing based on Eq. 1 and Eq. 2. From Tables 4, it can be said that on the whole the changes in frequency and damping ratios are more prominent in case of the beam H2 with end masses. A closer examination of the results reveals that by adding end-masses, the damping ratios seem to be affected more as compared to the natural frequencies. A plausible explanation can be that the end-masses increase the effect of shearing forces which causes an increase in friction in the material, consequently leading to a higher change in damping ratios as compared to natural frequencies. Table 4 shows that by putting end-masses, the change in natural frequency (between the undamaged and the damaged cases) is increased by around 3 %. However in case of damping ratios, this increase is as high as 93 %. So clearly the damping ratios are more affected by the endmasses. It can also be noticed that the change in damping ratios is greater in case of sine dwell testing, because the damping ratio estimated by sine-dwell testing is always higher in case of the two damaged states (D1 and D2) as compared to the burst random testing (also seen in Figure . 12 and Table 6). Therefore, the rest of the honeycomb sandwich beams (H2 to H6) except beam H1 in this article have been tested with end-masses.

Estimation of modal parameters at the undamaged state

Theoretically all the beams at the undamaged state should possess similar natural frequency and damping values, but due to fabrication anomalies there can be some dispersion.

As all the beams are at the undamaged state and the testing parameters have been kept the same for all beams so the authors think that it is logical to compare the average natural frequency and average damping ratio values for all the beams for the first four bending modes with their respective standard deviation values to give an idea about the dispersion at the undamaged state.

In this section the modal parameters of the five honeycomb sandwich beams with endmasses (H2 to H6) are discussed. In order to have a clear picture, the average values of natural frequencies and damping ratios for the first four bending modes of these five beams (H2 to H6) with both burst random and sine dwell testing are plotted in Fig. 9. The standard deviation associated with each average value is also represented for both burst random and sine dwell testing. In case of natural frequencies, the two types of testing, give similar results at the undamaged states as shown by the standard deviation values. However the dispersion at the 3 rd bending mode for the natural frequency is a bit on the higher side, which is due to the fact that the beam H5 at the 3 rd bending mode has a natural frequency of 1429 Hz whereas the average for the other four beams is 1338 Hz. This dispersion in natural frequency at Mode 3 occurs in case of both of testings. This anomaly outlines the inherent possibility of false negatives which can arise due to boundary conditions and gives no indication of damage when it is present as discussed in the reference [START_REF] Mattson | Damage detection and localization based on outlying residuals[END_REF].

In case of damping ratios, the results at the undamaged state give a good comparison as well for the two types of testings with small standard deviation values. However the exception in case of the damping ratios is the 1 st bending mode for burst random testing which has a high standard deviation value of 0.116 (Fig. 9b). This is because of the honeycomb beam H2, which has a damping ratio of 0.161 % for the 1 st bending mode, whereas the average damping ratio for the other four beams estimated by burst random testing is 0.389 %.

This dispersion is not present in case of sine dwell testing, so this result gives us a first indication that the sine dwell testing might be better suited for damping estimation.

Effect of impact damage on modal parameters

The effect of impact damage on the honeycomb sandwich beams is studied with the help of modal parameter changes for the first four bending modes as they have the largest amplitudes for the type of test configuration presented in this article. The variation of natural frequency and damping ratio due to impact damage is studied for the honeycomb beams (H2, H3 and H4) with end-masses. Frequency and damping ratios are the global parameters of the specimen, and are extracted from high quality measurements carried out on the 33 measurement points. The modal parameters (natural frequency and damping) help in monitoring globally the health of a specimen. For the first four bending modes, the variation of damped natural frequency as a function of the undamaged (UD) and the two damage states (D1 and D2) for the honeycomb beams (H2, H3 and H4) for both burst random (BR) and sine-dwell (SD) testings is presented in Fig. 10.

As discussed before in section 4.1, that damage in the specimens prompts a decrease in natural frequencies. So from Fig. 10, it is clear that the decrease in the natural frequencies for the three honeycomb beams is more prominent in case of the beam H4 impacted at 8J. In case of natural frequencies, both burst random and sine-dwell testing give similar results. But the interesting fact is that, even for beam H2 impacted at 4 J which does not produce a visible damage on the surface, the average change in frequency for the first four bending modes between the undamaged and the damaged cases is 14 %, which proves that the beam H2 has a notable loss of rigidity without any signs of damage on the beam surface. It is particularly in these cases that vibration testing becomes a very useful tool for structural health monitoring.

It is noticed that in case of honeycomb beams H3 and H4 impacted at 6 and 8 J respectively, the level of damage is not the same on both sides of the beams as it depends on whether the honeycomb cell center or corner is impacted as discussed previously and shown in Fig. 5. So this asymmetric damage leads to distortion of the resonance peaks or the appearance of twin peaks instead of one. This is evident in Fig. 11, which shows a comparison of the sum of the frequency response functions (FRF), estimated by burst random testing, for the honeycomb sandwich beams (H2, H3 and H4) for the undamaged case (UD), damaged at 2 points (D1) and damaged at 4 points (D2) for the 2 nd bending mode. The sum of the FRF can be compared as for each sandwich beam 33 symmetric measurement points have been chosen that are symmetric on both sides of the two major axes of symmetry.

Fig. 11 (a) shows that the resonance peaks for the beam H2 impacted at 4J are pretty much intact even for the damaged cases, showing that on the whole the beam is lightly damaged. But for the beams H3 and H4, as the damage level increases and with the addition of the asymmetric distribution of damage as discussed previously, the shape of peaks becomes distorted. This distortion of peaks does not affect the estimation of natural frequencies as such, as shown in Fig. 10 i.e., both burst random and sine-dwell testing give similar natural frequency results in the presence of damage. However, for the estimation of damping ratios for the damage states D1 and D2, there is a notable difference between the results of burst random and sine dwell testing as shown in Fig. 12.

It can be seen in Fig. 12 that in general the damping increases with the increase in damage in the sandwich beams. However, in case of burst random testing, for the beam H2

for the 4 th bending mode (Fig. 12d) and for the beam H4 for the 1st bending mode (Fig. 12a) the damping does not increase with damage. However sine dwell testing shows a logical increase of damping for these beams. Furthermore, the estimation of damping by sine-dwell testing for the damage state (D2) is always notably higher as compared to burst random testing with the exception of the beam H3 for the 1st bending mode. It confirms the fact that sine dwell testing is more capable of detecting non linear structural dynamic behavior (due to accumulation of high damage as in state D2) unlike the broadband excitations [START_REF] Gloth | Influence and characterisation of weak non-linearities in swept-sine modal testing[END_REF].

Effect of core-only damage on modal parameters

As discussed previously, in case of the honeycomb beams (H5) and (H6), approximately 5 mm and 10 mm diameter holes are pierced all along the width at the same positions as the impact points. The aim of inducing core-only damage is to see that whether this type of damage induces the same effect on the modal parameters as the impact damage.

The effect of core-only damage on the natural frequency and damping is studied similarly as the impact damage and is shown in Fig. 13 and Fig. 14.

Fig. 13 shows that the core-only damage induces a smaller change in natural frequencies as compared to the impact damage. The change in frequencies between the damaged states and the undamaged state is below 7 % for both the honeycomb beams H5 and H6 as shown by the frequency change ratios in Table 5. Both burst random and sine-dwell testing give relatively similar results for natural frequencies with the exception of beam H5

for the 4 th bending mode. It is interesting to note that there is no remarkable change in damping ratios for the beams H5 and H6 in the presence of core-only damage, with the exception of the damping for the 1 st bending mode estimated by burst random testing for both beams H5 and H6. Whether the damping increases or decreases with damage, the change in damping ratio is generally very small between the undamaged (UD) and the damaged cases (D1 and D2). So it can be concluded that the core-only damage does not reduce much the stiffness of the honeycomb sandwich beams as compared to the impact damage. As the change in modal parameters is slight for the core-only damage, so it shall be more difficult to carryout core-only damage detection with the help of modal parameter changes.

The effect of impact and core-only damage on the frequencies and damping ratios can be further elaborated by studying the frequency and the damping change ratios between the undamaged (UD) and the damaged cases (D1 and D2) for the impact damaged beams H3 and H4 and for the core-only damaged beams H5 and H6 in Tables 5 and6. Same procedure as explained in section 4.2 is followed. It can be clearly seen that the change in modal parameters is by far more prominent in case of the impact damaged beams (H3 and H4).

Furthermore, the results in Tables 5 and6 underline the fact that the damping change ratios are more prominent than the frequency change ratios. The maximum damping change ratio is 968 % whereas the maximum frequency change ratio is 38 %. As discussed previously, the damping change ratio estimated by sine-dwell testing is higher as compared to burst random testing. It can be concluded from the above results that damping seems more sensitive to damage than the natural frequency variations in case of honeycomb sandwich beams. So it is reasonable to assume that damping may be used instead of natural frequency as a damage indicator tool for structural health monitoring purposes. However, the fact that damping is a parameter that is relatively difficult to estimate as compared to natural frequency has to be taken into account [START_REF] Morlier | Original Statistical Approach for the Reliability in Modal Parameters[END_REF].

Effect of sine-dwell frequency direction on modal parameters

The aim of carrying out sine dwell testing in both up and down frequency directions is to be able to detect structural non-linearities in the damaged honeycomb beams. In literature it has been shown that frequency response functions (FRF) vary for the different sweep directions [START_REF] Gloth | Influence and characterisation of weak non-linearities in swept-sine modal testing[END_REF]. In this article, the effect of sweep directions is studied only for the beams with the highest level of damage i.e., impact damaged beams H3 and H4 for the damage state (D2) as presented in Table 7.

Table 7 shows the presence of nonlinear behavior in the honeycombs beams H3 and H4, as the natural frequencies and damping ratios show a slight discrepancy when tested in the increasing and decreasing frequency order. This is also shown graphically in Fig. 15 by plotting the frequency response functions from sine-dwell sweeps upwards and downwards in frequency. It is observed that in the presence of non-linearity, there is always a change in amplitude coupled with a slight shift in frequencies.

Design of Experiments (DOE)

Design of experiments (DOE) is a powerful analysis tool for highlighting the influence of key parameters that affect an experimental process and the output of that process [START_REF] Meyers | Response surface methodology 1995[END_REF]. This study is carried out on the modal parameters (natural frequency and damping ratio) of the three impact damaged sandwich beams with end-masses (H2, H3 and H4) tested by both burst random and sine-dwell testing. The aim is to find out that which testing method gives a more logical estimation of damping in the presence of damage i.e., damping increases with the increase of damage in the specimen [START_REF] Richardson | Correlating minute structural faults with changes in modal parameters[END_REF]. The design of experiments shall also help us identify the factors which have the most significant effect on the experimentally obtained modal parameters.

The two factors chosen for the design of experiments are the energy of impact (IE) and the density of damage (DD). For the energy of impact there are three levels (4, 6 and 8J) and for the density of damage there are also three levels (the undamaged state (UD), damage at 2 impact points (D1) and damage at 4 impact point (D2)). By keeping in view the levels of the two factors, a full factorial design is chosen. The linear regression model associated with the full factorial design, based on the two variables discussed above is expressed as follows: In Eq. 7, coefficients represent model constants (a i ) that are the contribution of independent variables on the response. E is the random error term representing the effects of uncontrolled variables, i.e., not included in the model. The model constants (a i ) are determined by multi-linear regression analysis and are assumed to be normally distributed.

The error is assumed to be random and normally distributed. These constants (a i ) are obtained with 90% confidence level. The significance of each variable on a given response (modal parameters in our case) is investigated using t test values based on Student's distribution. The t ratio is the ratio of the parameter estimate (constants) to its standard deviation. A t ratio greater than 2 in absolute value is a common rule of thumb for judging significance of the variable. The derived constants (a i ) and t ratios for the natural frequencies and the damping ratios estimated by burst random testing are presented in Tables 8 and9. Negative values of the model constants and t ratios indicate that the response decreases with the increase in the value of the parameter. In our case, this is most of the times true for the natural frequencies as they decrease with the increase in damage in the specimens.

By comparing the t ratios for the energy of impact (IE) and the density of damage (DD) in Tables 8 and9, it can be seen that the density of damage (DD) has a more significant effect on the modal parameters than the impact energy (IE) for the first four bending modes.

The second order interaction term (IE x DD) is more significant in case of the natural frequencies as compared to the damping ratios. Similar results are observed in case of sinedwell testing. The design of experiment results based on the modal parameters estimated by sine-dwell testing are laid out in Tables 10 and11.

Sine-dwell testing also proves the significance of density of damage (DD) as the parameter that has the most significant effect on the results. If the t ratios for the damping ratios estimated by burst random and sine-dwell testing are compared in Tables 9 and11, it can be seen that the two factors (IE and DD) have higher t ratios in case of the damping ratios estimated by sine-dwell testing. So it can be concluded that sine-dwell testing gives more reliable estimation of damping in the presence of damage as compared to burst random testing. Although the main disadvantage of sine-dwell testing is the lengthy acquisition times as compared to broadband excitations, but if quality damping estimations are required then sine-dwell excitation based vibration testing becomes indispensable.

Conclusion

Vibration tests have been carried out on pristine and damaged honeycomb sandwich beams using burst random and sine dwell excitations in order to compare that which testing method gives a more logical estimation of damping in the presence of damage, because damping is much harder to estimate as compared to natural frequency. Vibration tests are carried out by placing steel masses at the two ends of the sandwich beams in order to enhance the shift between the modal parameters between the undamaged and the damaged cases. The six sandwich beams tested in this article are damaged in two different ways. The first four are damaged by drop weight impacts around the barely visible impact damage limit (BVID), in order to simulate damage by foreign impact objects such as stones or birds. The other two are damaged by piercing a hole all along the width in the honeycomb core by a hand drill (coreonly damage), simulating mishandling during assembly and maintenance. Results show that with the accumulation of damage in the specimens, there is a decrease in natural frequency accompanied by an increase in damping ratio. The impact of core-only damage seems feeble on the modal parameters as compared to impact damage. Furthermore, damping seems to be more sensitive to damage than the natural frequency. So it is reasonable to assume that damping may be used instead of natural frequency as a damage indicator tool for structural health monitoring purposes. Presence of non-linearity in the impacted sandwich beams is proved by carrying out sine-dwell testing upwards and downwards in frequency. It is observed that in the presence of non-linearity, there is always a change in amplitude coupled with a slight shift in frequencies in the FRFs. Design of experiments carried out on the extracted modal parameters show highlighted density of damage as the factor having the most significant effect on the modal parameters, and prove that sine-dwell excitation based modal testing gives more reliable estimation of damping in the presence of damage as compared to burst random testing. In future similar vibration tests shall be carried out with different excitation levels and asymmetric impacts in order to study their effects on modal parameters.

Acknowledgments

The authors gratefully thank Professor B. Castanié from Université de Toulouse and research project student Hanno Niemann from TU Braunschweig for their technical support during the experimental work.

Nomenclature


P Rahmé

C Bouvet

S Rivallant

V Fascio

G Valembois

MECHANICAL PROTECTION FOR COMPOSITE STRUCTURES SUBMITTED TO LOW ENERGY IMPACT

Composite materials are widely used in aeronautical structures. These materials can be submitted to low energy impacts like tool drop, routine operations… Such impacts can generate damages in the material that significantly reduce the structure strength. A solution to reduce the severity of damages due to impact is to add a mechanical protection on composite structures (patent n° 2 930 478). In this paper, an experimental study on different concepts of protective layers is presented. This protection is made of a certain thickness of low density energy absorbent material (foam, honeycomb or stacking of hollow spheres) and a thin layer of composite laminate (Kevlar).

Experimental impact tests with a spherical impactor of 20 mm diameter at low velocity and low energy are made on aluminum plates, with different protections, and for different levels of energy. Analyses of Load/Displacement curves enable to study the capability of each mechanical protection to absorb energy. Resistance of these protections is then compared and discussed, taking into account the thickness and the surface density of the protections.

Introduction

Composite materials are widely used nowadays in aeronautics. This growing interest is due to the strength/mass ratio relatively high for these materials compared to metals. These materials are sometimes subjected to low energy impacts during manufacture, maintenance or machining, which can have an influence on the residual mechanical properties of the structure [START_REF] Abrate | Impact on composite structures[END_REF]. That is why during design of composite structures, damage tolerance must be taken into account ( [START_REF] Coutellier | Presentation of a methodology for delamination detection within laminated structures[END_REF], [START_REF] Alderliesten | Damage tolerance of bonded aircraft structures[END_REF]). Several authors ([4]- [START_REF] Ballère | Damage tolerance of impacted curved panels[END_REF]) studied the resistance of composite structures against impact at low velocity. They tried to explain the scenarios of damage during impact.

However, the core materials (honeycomb, foam, hollow spheres ...) are of significant scientific interest due to their good specific resistance and high capacity of energy absorption. These materials can also be used to protect structures against impact. For example, the cockpit of the aircraft is often protected against bird strikes by a honeycomb sandwich layer covered by aluminum skin to improve the capacity of energy absorption. Wang [START_REF] Wang | Impact behavior and energy absorption of paper honeycomb sandwich panels[END_REF] showed that the energy absorption has a linear increase trend with the increase of relative density of honeycomb cores. Therefore, increasing the relative density of honeycomb cores can efficiently improve the dynamic cushioning properties of the sandwich panels. Yi Li et al. [START_REF] Li | Energy-absorption performance of porous materials in sandwich composites under hypervelocity impact loading[END_REF] used different materials in their impact at high velocity. They determined and compared the energy absorption of these materials. They concluded that porous silicon carbide materials 7-10 June 2010, Budapest, Hungary Paper ID: 541-ECCM14 2 present a greatest ability to reduce impacting energy. On the other hand, Apetra et al. [START_REF] Apetre | Low-velocity impact response of sandwich beams with functionally graded core[END_REF] studied the impact at low velocity of honeycomb sandwich beams with variable density and rigidity in thickness. They showed that the variable features core reduces maximum deformation corresponding to maximum impact effort. Furthermore, Shin et al. [START_REF] Shin | An experimental study of low-velocity impact responses of sandwich panels for Korean low floor bus[END_REF] presented impact tests at low velocity on several types of sandwiches. They concluded that the glass skin sandwich plates have a better resistance against impact compared to aluminum skin. In the same context, Petit et al. [START_REF] Petit | Impact and compression after impact experimental study of a composite laminate with a cork thermal shield[END_REF] showed that a layer of thermal protection (cork) is also a good mechanical protection against impact. The use of such protections increases the residual strength of compression after impact tests.

Anyway, the main objective is to obtain a maximum residual strength for a minimum mass of the structure. Here, the mechanical protector layers become interesting. These layers must possess an ability to absorb impact energy. The addition of these layers can also help to detect easily the impact on these layers since it is more deformable than the structure.

In this paper, several types of protective layers against impact are tested. Impact tests at low velocity (<10 m/s) and low energy (<90J) are performed using a 20 mm diameter impactor on a falling weight device. Finally, a comparison is made between the different layers tested.

Experimental study

Falling weight device

There are many testing procedures to simulate an impact on a structure. However, the falling weight remains the most used device [START_REF] Abrate | Impact on composite structures[END_REF]. Such a device has been used in this study to perform impact tests according to standards AITM 1-0010 [START_REF]Determination of compression strength after impact-stress[END_REF]. The principle of this falling weight is to drop a mass guided in a tube on a composite plate, as illustrated in Figure 1. This device is dedicated to impact tests at low velocity (<10 m/s) and low energy (<90J). A 4.02 kg impactor with a 20 mm diameter hemispherical head is used. The impactor is instrumented with a force sensor, installed between the impactor head and its body. This KISTLER piezoelectric sensor having a max capacity of 120 kN is calibrated to measure the Paper ID: 541-ECCM14 3 impact effort. An optical sensor (Laser diode, Figure 1) measures the initial velocity of the impactor just before the impact. By integrating the equations of the fundamental principle of dynamics, velocity and displacement versus time curves are obtained from the measured effort provided by the sensor KISTLER, knowing the impact velocity.

Protective layers

Two configurations of protective layers have been tested. Configuration 1 is designed for 50 J energy impacts (see Figure 2). It is composed of a skin having a number (a) of Kevlar fabric plies (aK) and of three types of core: hollow spheres made by ATECA Company, honeycomb (Nomex Aramid fiber/phenolic resin honeycomb, HRH-10-3/16-3.0) and foam (HEREX 70.75). The patent "Peau amortissante de protection de pièces composites" n° 2 930 478 has been filed about the hollow spheres protective layers [START_REF]Peau amortissante de protection de pièces composites[END_REF]. The mechanical properties of the skin and the different cores are given in Table 1 and Table 2 respectively. The assembly is glued onto an aluminum plate. Configuration 2 consisting of two skins and two core layers is developed in order to withstand 90 J energy impacts. The design of this configuration is based on a gradual stop of the impactor. The two core layers are separated by a number (b) of Kevlar fabric plies (bK) as shown in Figure 2. The thickness of core layers is about 6 mm.

Test results

The specimens were impacted at several impact energies. Indeed, configuration 1 specimens were tested at 15, 30 and 50 J impact energies. Impact energies of 15, 50 and 90 J were used for the thick layers (configuration 2). An example of Load/Displacement curve is presented in Figure 3, for a 50 J energy impact, on a configuration 1 specimen with hollow spheres. The other tests on protective layers present similar curves. The initial impact velocity measured in this test is 5.1 m/s. The maximum displacement of the impactor is then about 6.8 mm. This displacement is lower than the layer thickness (7.4 mm, represented on the curve by the vertical line). Hence, the impactor will not touch the aluminum plate, which is not the case for highest energy impacts. The various steps of the impactor displacement through the layer are identified during impact. Thus, in Figure 3, the impact effort starts to increase after the contact of the impactor with the skin. The skin remains in bending until the beginning of the hollow spheres crash. During the first phase, the damage of the skin and the hollow spheres is shown until the failure of the skin. Breaking the skin is identified by the significant drop in effort. After this break, the skin damage continues and the hollow spheres densification is held up to the maximum effort and the return of the impactor.

Figure 4 shows the cross-sections of the different layers after impact, at the centre of the impacted area. The skins failure and the cores crushing are clearly visible on this figure. In some cases, under the impactor head, the whole thickness of the protective layer is crushed, leading to a plastic indentation of the aluminum plate (visible on the figure).

Comparison and discussion

Impact energy absorption capability for a given layer thickness

In this subsection, the impact resistance of configuration 1 and configuration 2 of various specimens is studied. The different Load/Displacement curves, corresponding to the specimen's core of hollow spheres, honeycomb or foam, are compared. Figure 5 shows the impact curves of various specimens of configuration 1 at three levels of impact energy 15, 30 and 50J. For best efficiency when impacting with a given energy, maximum impact effort must be the lowest possible. This leads to securely protect the structure impacted. In Figure 5-a, the significant difference between slopes of different impact curves at 15J proves a significant difference between the efficiencies. Indeed, the hollow spheres (HS1) exhibit the highest capability to absorb energy without a peak of load, and with a short displacement, followed by the honeycomb (HC1). The foam core (F1) has low efficiency due to lower compression resistance at this energy compared to other materials. The densification occurs when the impactor tends to touch the aluminum plate, thus the core material is crushed. At impact Paper ID: 541-ECCM14 7 energy of 30J, the best efficiency of hollow spheres is confirmed. The behavior of the foam and the honeycomb is nearly identical. In this case, the impactor tends to plastify the aluminum plate and the layer is no more protective against impact (Figure 5-b). In Figure 5-c, it is remarkable that the impactor plastify the aluminum plate in both cores HC1 and F1. By cons, it is still at a distance of approximately 1 mm in the case of HS1 and therefore only the layer HS1 continues to be a good candidate for protection against impact. These results was identified and observed on the Figure 4-a after impact. This first study shows the advantage when using hollow spheres and its better efficiency to 50J impact energy in the case of configuration 1. In the case of configuration 2, the three energies tested are 15, 50 and 90J (see Figure 6). Similarly, on the different Load/Displacement curves obtained, the best efficiency and capability to absorb energy are found for the hollow spheres. In Figure 6-c, it is remarkable that the impactor plastify the aluminum plate in the case of HC2 and F2 and stays at about a distance of 2 mm in the case of HS2. This shows that the layers HC2 F2 are not candidate to absorb impact energy of 90J without load peak. However, the layer HS2 can rather resist to this energy. Similarly, observations on the Figure 4-b prove these results deducted from the impact effort curves. The comparison between the same configurations (or same thickness) shows initially the better efficiency of hollow spheres. Nevertheless, the mass is an important interest in the aeronautical domain. Moreover, for a given mass, it is preferable to optimize the thickness of protector layers in order to obtain less volume. A comparison between different specimens of the same surface density must then be made.

Impact energy absorption capability for a given surface density

The layers of the same configuration have different surface densities. The surface density of hollow spheres is about twice that of honeycomb and foam of the same configuration (see Table 1). To obtain the same surface densities, configuration 1 of the hollow spheres must be compared to configuration 2 of honeycomb and foam. The corresponding surface densities are then respectively 50, 50 and 48 g/dm² for the hollow spheres, honeycomb and foam. However, configuration 2 has a further advantage in that it contains intermediate skin of fabric Kevlar plies (bK). Paper ID: 541-ECCM14 9

Figure 7 shows the impact effort curves of layers referred at 15 and 50J impact energy as a function of the displacement. The difference of the energy absorption capability is also remarkable in Figure 7-a at 15J impact energy. At 50J impact energy, the curves are different. The thicknesses are not equal and thus the displacement of the impactor. This entails a max impact effort for the hollow spheres larger than honeycomb and foam. However, the distance between the impactor and the aluminum plate is about 1 mm in all cases. This follows close efficiency for the three layers of the same surface density but with different thicknesses. Note that the intermediate Kevlar skin increases significantly the resistance against impact. The hollow spheres present then an important efficiency and acceptable energy absorption capability when impacting. Furthermore, the hollow spheres can be used to optimize the thickness when this thickness is a constraint for a given structure. Note that the hollow spheres have an advantage over other materials for energy absorption due to their easy installation on non-flat structures.

In a subsequent study, these protective layers must be tested on composite plates to compare the different residual strength and thus to check the best protection against impact.

Conclusion

In this paper, the efficiency of composite structures mechanical protection against impact has been studied. This protection includes a Kevlar skin and cores of several types. The tested cores consist of hollow spheres, honeycombs or foams. Two configurations of two different thicknesses have been impacted at several impact energies. The curves comparison of impact effort for a given constant thickness shows better energy absorption capability for the hollow spheres. Another comparison between different types of cores at different configuration with constant surface density was conducted. The hollow spheres have also increased capacity to absorb energy comparable to two stages layers of foam or honeycomb separated by a number of fabric Kevlar plies and having the same density. These results can be used to protect composite structures with hollow spheres having important resistance against impact. Theses composite structures can have complex shapes such as non-flat surfaces as well as a circular surface. This paper is limited to study the protective layer against impact, on metallic plates. A future study on composite plates protected by these layers will be lead.

Figure 1 :

 1 Figure 1 : Falling weight device

Figure 2 :

 2 Figure 2 : Geometry and material configuration of protective layers

Figure 3 :

 3 Figure 3 : Load/Displacement curve example: 50 J impact test on HS layer

Figure 4 :

 4 Figure 4 : Cross-sections of impacted protective layers (HS: Hollow Spheres, HC: Honeycomb, F: Foam -1 for configuration 1, 2 for configuration 2) a) at 50 J impact energy -b) at 90 J impact energy Results observed on the different layers are compared and discussed in the following paragraph.

Figure 5 :

 5 Figure 5 : Load/Displacement curves of configuration 1 layers. a) 15 J -b) 30 J -c) 50 J

Figure 6 :

 6 Load/Displacement curves of configuration 2 layers. a) 15 J -b) 50 J -c) 90 J 7-10 June 2010, Budapest, Hungary Paper ID: 541-ECCM14 8

Figure 7 :

 7 Figure 7 : Load/Displacement curves for same surface density layers : a) 15 J -b) 50 J

Guide Tube Force sensor Protective layer Optical sensor 7

  -10 June 2010, Budapest, Hungary

Table 3

 3

sums up the material and geometrical configurations for each different tested protective layer, and the global surface density obtained.

Table 1 : Skin properties Al plate Honeycomb Configuration 1 aK bK Configuration 2 Al plate Hollow spheres

 1

	6 mm
	Al plate	Al
	6 mm
	6 mm

plate Foam aK Al plate Al plate Honeycomb Hollow spheres Foam 14

TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS 7-10 June 2010, Budapest, Hungary Paper ID: 541-ECCM14 4 Material

Failure stress in compression (MPa) Young's modulus in compression (MPa) Density (kg/m 3 )

	Hollow Spheres (HS)	0.35	30	166
	Honeycomb (HC)	2.2	137	48
	Foam (F)	1.3	83	80

Table 2 :

 2 Core materials properties

	Specimen	Core	Number of skins	Thickness (mm)	Surface density (g/dm²)
	HS1	Hollow	1	7.4	50
		spheres
	HC1	Honeycomb	1	7.6	29
	F1	Foam	1	7.8	27
	HS2	Hollow	2	13.3	100
		spheres
	HC2	Honeycomb	2	14.7	50
	F2	Foam	2	14.6	48

Table 3 :

 3 Characteristics of protective layers

Acknowledgements

The authors would like to acknowledge Région Midi-Pyrénées and DRIRE for the funding of this study through EPICEA 2008 program, in project "bielle HCM".