Gilles Lubineau

ACCEPTED MANUSCRIPT

Keywords: A -Laminate, C -Residual stress, C -Transverse cracking, D -Optical microscopy

Today, advanced damage models taking into account residual stresses are available. In particular, microcracking as a degradation mechanism in laminates is very sensitive to manufacturing-induced stresses. However, these stresses are often introduced through a model parameter whose identification remains difficult or requires time-consuming and costly additional tests. Here, we propose a relatively simple method based on the observation of the displacement field associated with the creation of a transverse crack in a crosswise laminate. Subsequently, this displacement field can be reinterpreted according to the model being used in order to build the quantity required by the model.

Introduction

Because of their manufacturing process, laminated composites are subject to residual stresses which can be significant and lead to various consequences between the manufacturing stage and the end of the application's life [START_REF] Parlevliet | Residual stresses in thermoplastic composites -a study of the literature. part iii: Effects of thermal residual stresses[END_REF]. These residual stresses can have different sources: thermomechanical sources (different expansion coefficients for the reinforcement and the matrix), chemical sources (matrix shrinkage during polymerization) . . . (a review can be found in [START_REF] Parlevliet | Residual stresses in thermoplastic compositesa study of the literature-part i: Formation of residual stresses[END_REF]).

A well-known consequence of these initial residual stresses is the problem of the dimensional stability of molded pieces [START_REF] Huang | Warping in advanced composite tools with varying angles and radii[END_REF]. As far as mechanical degradation models are concerned, these stresses were long ignored, but today most approaches take them into account in behavior prediction. A classical example, which is reported here, is transverse cracking, a degradation mechanism which is well-documented in the literature (see [START_REF] Berthelot | Transverse cracking and delamination in cross-ply glass-fiber and carbonfiber reinforced plastic laminates: Static and fatigue loading[END_REF] [5] for reviews). Several authors pinpointed the need to take into account the residual stresses associated with the manufacturing process in estimating the fracture criterion [START_REF] Nairn | Fracture mechanics of composites with residual thermal stresses[END_REF] [7] [START_REF] Perreux | The effect of residual stress on the non-linear behaviour of composite laminates part ii. layer, laminate non-linear models and the effect of residual stress on the model parameters[END_REF]. However, even when the models do manage to integrate these residual stresses, these parameters often remain difficult to identify and evaluate precisely.

A first approach to the resolution of this problem consists in simulating the process as exhaustively as possible in order to deduce these residual stresses from the simulation ([9] [START_REF] Ruiz | Numerical analysis of cure temperature and internal stresses in thin and thick rtm parts[END_REF] . . . ). This is probably the best solution for the long-term future. Today, however, the number of parameters and physical phenomena involved is too large for the whole evaluation to be controlled. A second solution consists in evaluating these residual stresses within the structure. Thus, a series of destructive or non-destructive experimental approaches was gradually derived for this purpose [START_REF] Parlevliet | Residual stresses in thermoplastic compositesa study of the literature-part ii: Experimental techniques[END_REF].

A classical estimation technique

Email address: lubineau@lmt.ens-cachan.fr (Gilles Lubineau).

consists in observing the effects of these residual stresses on a geometric modification of the structure. Among other works along these lines, one could mention, for example, studies on bimetallic strips [START_REF] Jun | Effect of residual shear strain on the cured shape of unsymmetric cross-ply thin laminates[END_REF] or applications of what is known as the "incremental hole" method [START_REF] Zhandanov | Determining the residual welding stresses at depth in metals[END_REF] [14] [START_REF] Bateman | Measurement of residual stress in thick section composite laminates using the deep-hole method[END_REF] [16] [START_REF] Baldi | Full field methods and residual stress analysis in orthotropic material. ii: Nonlinear approach[END_REF]. Each of these tests must be carried out carefully and represents an additional experiment in the series needed to identify a material.

Here, we propose a simple approach in order to obtain a first approximation of the residual stress state within a ply's material in the context of a study of transverse microcracking.

The method consists in observing (using a numerical camera) then analyzing the displacement field generated by the opening of a transverse crack. The multicracking test is classically used in micromechanics to observe crack density/load ratios in order to identify the associated material model [START_REF] Hoover | Transverse cracking of symmetric and unsymmetric glassfibre/epoxy-resin laminates[END_REF] [19] [START_REF] Highsmith | Stiffness reduction mechanism in composite laminates[END_REF]. During such a test, each occurrence of a transverse crack results in a localized perturbation of the energy density in its vicinity.

The displacement field associated with this perturbation can be calculated through the resolution of a residual problem which can take seemingly different, but actually very similar, forms depending on the authors [START_REF] Berthelot | Transverse cracking and delamination in cross-ply glass-fiber and carbonfiber reinforced plastic laminates: Static and fatigue loading[END_REF] [21] [START_REF] Nairn | The strain energy release rate of composite microcracking: a variational approach[END_REF]. Under linear elasticity assumptions, this perturbation is proportional to the residual field which existed along the crack's lip prior to its occurrence. Therefore, by observing this field one can gain some information about the internal stress state of the composite material [START_REF] Takeda | Micromechanical characterization of local deformation in interlaminar-toughened cfrp laminates[END_REF].

In the first section, we review the reference problem, which is about the occurrence of a transverse crack in an initially crack-free crosswise laminate. Through a classical decomposition by superposition, we pinpoint the respective roles of the mechanical loading and the initial residual loading in each component of the field. We also emphasize in the related appendix some properties of the residual field thus introduced.

The second section describes the measurement method itself. The objective is to measure the displacements caused by initial residual stresses. The construction of these displacements requires the comparison of two fields, one obtained experimentally through image analysis, the other obtained numerically through finite element simulation. The experi-in the case of a carbon/epoxy laminate with [0/90] s lay-up.

In the third section, these residual displacements are interpreted in terms of residual stresses and used to measure the "equivalent polymerization temperature" referred to by several microcracking models [START_REF] Nairn | Applications of finite fracture mechanics for predicting fracture events in composites[END_REF]. The value obtained is fully consistent with the usually accepted orders of magnitude.

The reference problem

Let us consider the general case of a cracked cross-ply laminate under generalized plane strains. A more detailed description of the problem is given in Appendix A. Here, we are considering only the two states (cracked and uncracked) of the laminate described in

∆U = λ Ā F + U R ( 1
)
where F is the external loading, λ Ā a linear operator (see Appendix A) and U R the part of the displacement field associated with the relaxation of the residual stresses over the crack's lips. Here, the objective is to evaluate the residual field U R to obtain the residual stresses; therefore, we simply transform this equation into: Thus, we are going to use this relation to recover the field U R associated with the initial residual stresses.

U R = ∆U -λ Ā F ( 2
3 Estimation of the residual displacement U R Thus, the construction of the residual displacement field U R from Equation 2requires / an experimental field: ∆U / and a numerical field: λ Ā F .

Here, we will illustrate the method in the case of a crosswise laminate consisting of a [0/90] s lay-up of width b=20mm. The elementary ply has a width of 0.142mm and its material characteristics are given in Table 1.

E ll E tt ν lt ν tt G lt (M P a) (M P a) (MPa)
157,000 8,500 0.29 0.4 5,000

Table 1 Elastic properties of the carbon-epoxy material being used

The material is an IM7/977-2 carbon-epoxy provided by EADS, which was in charge of optimizing the polymerization cycle for a supersonic application (a completely stable polymerized material free from post-baking effects). In order to achieve a minimal residual Of course, the method can also be applied to Component 3 in order to supplement the identification and make it more robust.

Construction of Field [λ Ā F ]

The operator Ā is obtained simply as the displacement field of the finite element problem described in Figure 7. This is a generalized plane strain problem subjected to a uniform unit residual along the crack's lip with zero loading at infinity. (In practice, a finite problem with length L > 10H provides a good approximation.) This is a problem with natural boundary conditions alone which is slightly different from that described in [START_REF] Ladevèze | On a damage mesomodel for laminates: micro-meso relationships, possibilities and limits[END_REF]. Then, the component Ā2 associated with the displacement in the N 2 direction is illustrated in Figure 7.

This displacement is shown in Figure 8 for the macroscopic load corresponding to the experimental observation F = 6, 000N on the observation zone S Obs . This field can now The comparison of Fields ∆U 2 | S Obs and [λ Ā2 F ] (figure 9) tells us about the magnitude of the initial residual stresses. Thus, the displacement field U 2 R can be estimated. It is shown in Figure 10.

Estimation of the initial residual stresses

At this point, the interpretation of the residual displacement U 2 R in terms of initial stresses requires that a number of assumptions be made. Here, we will consider the most common and simplest case:

the elementary ply (of course, only through the thickness of the ply of interest; they may vary between plies.) Under this assumption, the residual field must read:

U 2 R = Ā2 σ R (3)
Thus, the initial residual stress is obtained by minimizing a distance D between the measured field and the theoretical field. Here, this distance is defined simply by:

D(σ R ) = S Obs U 2 R -Ā2 σ R 2 S Obs dS Obs ( 4
)
Function D is shown in Figure 11. For the measurement which was carried out, we observe an initial residual stress level of about 22MPa, which is fully consistent with classical orders of magnitude. Numerous microcracking models assume the existence of an initial prestress. This prestress is usually calculated as a "thermal prestress" related to a temperature variation ∆T . With a very coarse approximation of the laminate in 1D, one obtains classically

∆T = E ll + E tt E ll • E tt • (α l -α t ) σ R (5)
For the material being considered, α l ≈ 0 and α t ≈ 30.10 -6 . Thus, in this case, the temperature variation equivalent to the process would be around -75 o C, which is in agreement with commonly accepted values. Let us note that the exact interpretation of the quantity obtained here differs from that presented in other approaches, such as in [START_REF] Nairn | Applications of finite fracture mechanics for predicting fracture events in composites[END_REF].

In the "master plot analysis" type of approach, the determination of the thermal prestress is achieved through a microcracking development model. Therefore, the temperature variation which must be introduced is highly dependent on the cracking model. Thus, in the case of an AS4/3501 -6, [START_REF] Nairn | Applications of finite fracture mechanics for predicting fracture events in composites[END_REF] ends up with two different values (-95 o C and -143 o C) depending on whether cracking is assumed to occur under prescribed displacement or prescribed load. In our approach, no degradation model is introduced. Cracking is introduced only to create the heterogeneous field necessary to give rise to residual stresses.

Therefore, this quantity is common to all subsequent mechanisms. This approach also has the advantage of allowing one measurement point for each transverse crack, which enables dozens of possible evaluations from a single multicracking test.

Conclusion

In this paper, we propose a method for the estimation of residual stresses based on post-processing a displacement field measured with a numerical camera on a crosswise laminate, then comparing this field with a finite element calculation. This method has the advantages of being relatively simple to implement and using a test already included in classical identification procedures for laminates. The use of a field measurement enables one to make the measurement robust because it is relatively insensitive to the profile of the crack being considered. Of course, this method can be used throughout the multicracking test and reused at the occurrence of each new crack. This will significantly enhance both the accuracy of the method and its robustness, and will be the subject of forthcoming works.

A Detailed reference problem

Let us consider a crosswise laminate subjected to a macroscopic solicitation in traction

(Figure A.1[a]
). Two states are being considered: State A before cracking (with the traction load F A ), and State B after cracking (with the traction load F B > F A ). The whole study will be carried out under the following assumptions:

• Assumption A1: the problem is independent of the direction N 1 . This is equivalent both to neglecting the edge problem and to assuming a crack crossing through the ply width.

Here, this assumption is legitimate (the edge effect has been verified to be negligible by a FE analysis, and the crossing of the crack has been observed by X-Ray), but this may not always be the case depending on the sequence being used. In that case, the method presented here can still be applied using a 3D finite element reanalysis in order to improve its accuracy. This will be the subject of a forthcoming paper.

• Assumption A2: the material's behavior is linear elastic.

A1 enables us to define simplified problems over a plane domain S (Figure A. 1 [b]). These are generalized plane strain problems, and all the displacement fields will be expressed in the coordinate system [O; N 2 , N 3 ], O being the "center" of the crack. In the following sections, we will consider only the plane part of these displacements.

Remark: a bold quantity X designates a field over S, and an underlined quantity X denotes a vector. A quantity both bold and underlined X designates a vector field over S. Thus, X i is the scalar field associated with the component i of the vector field X.

For State A, the field of the displacement vectors

U A = [U 2 A N 2 + U 3 A N 3
] can be expressed as:

U A = [ Ã2 N 2 + Ã3 N 3 ] FA = Ã FA (A.1)
where à is the field of the displacement vectors which corresponds to a unit macroscopic load. In the case of Assumption A1, this operator can be easily obtained analytically using the classical theory of laminates.

For state B, the field of the displacement vectors U B can be expressed as the superposition of a crack-free solution U B x and a residual solution

U B y (see Figure A.2): U B = U B x + U B y (A.2)
Of course, as far as Solution x is concerned:

U B x = Ã FB (A.3)
Then, this healthy solution is corrected through the residual problem in order to build the exact solution. Problem y is linear with respect to the residual loading onto the crack's lip, denoted P . showed that the perturbations due to the cracks' local profile subside very quickly, which confirms the advantage of a field measurement compared to a local measurement of the lip's opening.

Thus, in practice, the size of the exclusion zone is guided mainly by constraints related to the field measurements. If the interpolation zones are N px * N px pixels, this exclusion zone must obviously be at least N px + L c pixels wide, L c being the width of the crack generated by its waviness. In the example given here, N px = 16px and L c ≈ 60px. The minimum size of the exclusion zone is about 80px. In practice, we recommend a size of the order of the ply's thickness.

C Suppression of the rigid body mode

The measured field ∆U 2 | S Obs is the superposition of a residual field of interest ∆U 2r | S Obs and a rigid body field (due, for example, to the variation in the stiffness of the sample The residual part is generated by an ideal "virtual" crack whose abscissa is, of course, unknown, but bounded by X -and X + . Let X ref 2 denote the abscissa of the theoretical crack chosen between X -and X + .

• Step 1: Choose an arbitrary value of X ref

QU AL = 1 2 • Z1∪Z2 ∆U 2 | step2 S Obs (x) + ∆U 2 | step2 S Obs (-x) dx (C.4)
The quality indicator is minimum (theoretically zero in the case of perfect measurements) when X ref 2 corresponds to the position sought for the virtual crack. The whole approach relies on the fact that the exact residual field is skew-symmetric with respect to x 2 .

Figure 1 .

 1 Figure 1.

Fig. 1 .

 1 Fig. 1. Cross-ply laminate in traction (A being the healthy state, B the cracked state)

) Equation 2

 2 involves the mechanical loading (Part [λ Ā F ]), the observed displacement fields (Part [∆U]) and the displacements associated with the residual stresses (Part [U R ]).

  a post-baking cycle was added to the customary cycle used for this material in subsonic applications. The cycle chosen consisted of a 3-hour gelation phase at 150 • c followed by a 2-hour polymerization phase at 180 • C. Cooling and heating were applied at a rate of 2 • C/mn. A pressure of 7 bars was applied from the beginning of the cycle until the return to ambient temperature. Post-baking consisted of heating at a rate of 3 • C/mn until 210 • C, followed by 2 hours at constant 210 • C temperature, then cooling at a rate of 3 • C/mn until the return to ambient temperature.3.1 Measurement of Field ∆U This measurement was carried out based on an observation of the sample area using a numerical camera. A numerical camera mounted on a long-distance QUESTAR microscope (Figure 2) enabled us to acquire data on the edge of the sample. The macroscopic loading was incremented in ∆F steps. For each load level (F n = n∆F ), a series of pictures was taken through automatic scanning of the sample area. (This step was required because the position of the future crack was of course unknown.) The procedure was repeated for each increment. When a transverse crack was detected, the load level was reduced down to the previously recorded level. Then, a picture of the cracked zone was taken in order to play the role of Picture B. Thus, we had pictures of the zone before and after cracking (Figure 3) corresponding to the same load level (F A = F B = F ). The size of both pictures was 1024 * 1280px 2 . The resolution was 1.66 pixel/micron. Next, the field of the displacement vectors ∆U A→B between the two pictures A and B was obtained by image analysis. The classical technique [25] [26] consists in dividing the zone of interest of Picture A (hereafter denoted S Obs ) into elementary patterns following a regular grid (Figure 4). Then, each elementary zone of Picture A is sought in Picture B by correlation, leading to the displacement of the center of the elementary pattern. Thus,

Fig. 2 .Fig. 3 .

 23 Fig. 2. Setup for the optical observation and incremental scanning of the edge of the crosswise laminate

Fig. 4 .

 4 Fig. 4. The zone of interest S Obs and the decomposition grid of the reference picture for image analysis purposes

Fig. 5 .

 5 Fig. 5. Processing of the observed displacement field

Fig. 6 .

 6 Fig. 6. The displacement field ∆U 2 | S Obs

Fig. 7 .

 7 Fig. 7. The FE problem for the determination of Operator Ā and the displacement field Ā2 associated with a unit macroscopic load

Fig. 8 .

 8 Fig. 8. The displacement field λ Ā2 F associated with a macroscopic load b. F = F = 6000N

Fig. 9 .

 9 Fig. 9. Superposition of Fields ∆U 2 | S Obs and [λ Ā FB ]

Fig. 10 .

 10 Fig. 10. The residual displacement field U 2 R

Fig. 11 .

 11 Fig. 11. D as a function of σ R

Fig. A. 1 .

 1 Fig. A.1. [a]: crosswise laminate in traction (A is the healthy state and B the cracked state) [b]: simplified problems in generalized plane strain ( F = F b )

  in the vicinity. Various levels of smoothing (L=1, L=2, L=3) were tested and no significant difference was found (Figure B.2). L = 2 was chosen for all the plots.

Fig. B. 2 .

 2 Fig. B.2. Comparison of the measured and smoothed fields over different characteristic lines. The dots correspond to direct measurements and the lines to progressive approximation levels

Fig. B. 3 .

 3 Fig. B.3. Comparison of the residual displacements for lips with varying roughness caused by the crack, a poor repositioning of the camera between shots A and B, small differences in macroscopic loads between shots,. . . ). Here, first of all, we give the key steps to suppress this rigid body mode when it reduces to a pure translation along N 2 . In order to simplify, let us consider the diagram of Figure C.1 [a], representing the displacement field ∆U 2 | S Obs (here, again for the sake of simplicity, a curve with normal N 3 ).

2 • 2 :• Step 3 :∆U 2 • Step 4 :

 22324 Fig. C.1. Step-by-step construction of the residual field for a predefined position of the "ideal" crack • Step 3: Remove the "rigid body" part for this test; Z1 and Z2 are two symmetrical zones in the new coordinate system, chosen to be as large as possible depending on the available data (Figure C.1[c]):

ACCEPTED MANUSCRIPT

In the absence of residual internal stresses, P consists only of a part associated with the mechanical loading FB , denoted P M . Of course, P M is proportional to FB with a known proportionality coefficient denoted λ. Thus, in that case:

The crack also introduces a residual displacement field of the form:

where Ā is the field of the displacement vectors associated with a unit residual and uniform over the crack's lip.

In the presence of internal residual stresses P R , the residual P becomes:

P R is a priori not necessarily uniform over the cracked surface. Therefore, in general, the displacement of the residual problem y can be written as:

U R is the part of the displacement field associated with the relaxation of the residual stress over the crack's lip. The objective of the rest of this paper is to measure, then Configuration B:

Let ∆U = U B -U A be the field of the displacement jump vectors between State A and State B. From A.1 and A.8, one has:

Now, assuming that FB = FA = F , Equation A.9 reduces to:

B Smoothing and truncation

The solution chosen is based on an interpolation of the measured field in the vicinity of each point M . One defines the plane Π M which provides the best fit, in the least-squares sense, to the displacement field in the vicinity of V(M ). Then, the "smoothed" value of For a square smoothing zone, let (2L+1) 2 denote the number of points taken into account

ACCEPTED MANUSCRIPT

Thus, this procedure enables one both to determine effectively the underlying "perfect" crack (which is needed for comparison with the subsequent finite element analysis) and to remove the rigid body mode very precisely. The extension to the case of a general in-plane rigid body mode (two translations and one rotation) is straightforward.


R M O'higgins

M A Mccarthy

C T Mccarthy
email: conor.mccarthy@ul.ie

Comparison of Open-Hole Tension Characteristics of High Strength Glass and Carbon Fibre-Reinforced Composite Materials

Keywords: A. Carbon fibres, A. Glass fibres, B. Fracture, B. Mechanical properties 1

An experimental study was carried out to determine the open hole tension (OHT) characteristics of carbon fibre-reinforced plastic (CFRP) and high-strength S2-glass fibrereinforced plastic (GFRP). Tests to failure and percentages of ultimate load were carried out and non-destructive techniques were used to map damage progression. It was found that the CFRP OHT specimens were stronger, while the GFRP OHT specimens had greater ultimate strain. However, damage progression mechanisms in the two material systems were very similar. This contrasts with previous findings on E-glass composites, indicating that S2-glass FRP notched failure behaviour is closer to a high performance CFRP. Higher levels of damage formation prior to failure were found to result in higher OHT strength (S OHT ).

Blocked ply stacking sequences were found to give higher damage levels and S OHT than sublaminate level stacking sequences, and similar trends were found when laminate thickness was reduced. Non-linear transverse behaviour in GFRP resulted in lower levels of matrix cracking in OHT specimen 90º plies, compared to CFRP, providing a barrier to the growth of stress relieving axial splits in 0º plies.

Introduction:

With the increasing cost of fuel and worries about the environmental impact of air travel, great efforts are being made to improve the efficiency of air transportation systems.

One practical way of reducing structural weight and increasing payload efficiency is increasing the structural application of fibre-reinforced plastics (FRP), which offer improved specific properties compared to traditional metallic materials and allow more efficient manufacturing processes. It is estimated that a weight reduction of 1kg on an aircraft equivalent in size to an Airbus A320 saves over 2,900 litres of fuel per year [START_REF] Flower | Materials for Airframes[END_REF]. Generally, carbon fibre-reinforced plastics (CFRP) have been the composite material of choice for use in primary structures due to their high specific strength and modulus. As such, a considerable literature exists on the damage characteristics of notched CFRP laminates [START_REF] Awerbuch | Notched Strength of Composite Laminates: Predictions and Experiments -A Review[END_REF][START_REF] Backland | Tensile Fracture of Laminates with Holes[END_REF][START_REF] Coats | A Progressive Damage Methodology for Residual Strength Predictions of Notched Composite Panels[END_REF][START_REF] De Morais | Open-Hole Strength of Quasi-Isotropic Laminates[END_REF][START_REF] Eriksson | Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes[END_REF][START_REF] Harris | On the Use of Crack-Tip-Opening Displacement to Predict the Fracture Strength of Notched Graphite/Epoxy Laminates[END_REF][START_REF] Harris | Fracture of Thick Laminated Composites[END_REF][START_REF] Harris | A Fractographic Investigation of the Influence of Stacking Sequence on the Strength of Notched Laminated Composites[END_REF][START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF][START_REF] Lee | A Study on the Compressive Strength of Thick Carbon Fibre-Epoxy Laminates[END_REF][START_REF] Higgins | Experimental and numerical Study of the Open-Hole Tensile Strength of Carbon/Epoxy Composites[END_REF][START_REF] Pinnell | An Examination of the Effect of Composite Constituent Properties on the Notched Strength Performance of Composite Materials[END_REF][START_REF] Soutis | Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole[END_REF][START_REF] Spearing | Fatigue damage mechanics of composite materials I: Experimental measurement of damage and post-fatigue properties[END_REF][START_REF] Wang | Experimental and Numerical Investigation of the Tension and Compression Strength of Un-notched and Notched Quasi-Isotropic Laminates[END_REF][START_REF] Green | An experimental investigation into the tensile strength scaling of notched composites[END_REF].

It has been widely reported that notch tip damage prior to ultimate failure has a direct effect on CFRP laminate notched strength [START_REF] De Morais | Open-Hole Strength of Quasi-Isotropic Laminates[END_REF][START_REF] Eriksson | Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes[END_REF][START_REF] Harris | Fracture of Thick Laminated Composites[END_REF][START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF]. Intralaminar damage at the notch tip provides stress relief as the notch geometry changes and the stress concentration is reduced, hence increasing the notched strength. Larger damage zones typically provide more stress relief and hence greater notched strength. Conversely interlaminar damage, if extensive, reduces the notched strength as individual uncoupled plies are free to fail by the fracture mode of least resistance [START_REF] Harris | A Fractographic Investigation of the Influence of Stacking Sequence on the Strength of Notched Laminated Composites[END_REF]. Damage initiation and progression is dependent on a number of variables such as stacking sequence, notch geometry, loading rate, test temperature etc.

Concerning laminate lay-up and stacking sequence, Eriksson & Aronsson [START_REF] Eriksson | Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes[END_REF] showed 0º ply dominated laminates had higher notched strengths and exhibited more damage prior to failure than ±45º and 90º ply dominated laminates. Harris and Morris [START_REF] Harris | A Fractographic Investigation of the Influence of Stacking Sequence on the Strength of Notched Laminated Composites[END_REF] carried out an in-depth study of the effect of laminate lay-up and stacking sequence and showed that laminate notched strength varied considerably with both the specified set of ply fibre orientations (i.e. lay-up), as well as the order in which the specific plies were arranged in the laminate (i.e. stacking sequence). Axial splits in the main load-carrying 0º plies were found to be particularly effective at reducing the notch stress concentration. Kortschot & Beaumont [START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF] showed that cross-ply laminates with blocked stacking sequences ([90 2 /0 2 ] s ) exhibited more damage prior to failure and had 50% higher notched strength than laminates with a sublaminate stacking sequence ([90/0] 2s ), even though both had an equal number of 0º and 90º plies. Similarly, Green et al. [START_REF] Green | An experimental investigation into the tensile strength scaling of notched composites[END_REF] studied scaling effects for quasi-isotropic stacking sequences and found that sub-laminate scaled S OHT decreased with increasing specimen size, but conversely, S OHT increased with increasing specimen size for blocked stacking sequences. [START_REF] Harris | Fracture of Thick Laminated Composites[END_REF] examined the effects of laminate thickness and found that in thick laminates, pre-failure damage near the notch only occurred in the outer plies; thus the greater the laminate thickness, the less effect damage had on the stress distribution prior to failure.

Harris and Morris

Depending on the type of damage the laminate lay-up was susceptible to, the notched strength either increased or decreased with thickness until a constant value for notched strength was achieved for laminates of 60 plies or more.

It has been shown by a number of researchers [START_REF] Coats | A Progressive Damage Methodology for Residual Strength Predictions of Notched Composite Panels[END_REF][START_REF] De Morais | Open-Hole Strength of Quasi-Isotropic Laminates[END_REF][START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF][START_REF] Wang | Experimental and Numerical Investigation of the Tension and Compression Strength of Un-notched and Notched Quasi-Isotropic Laminates[END_REF] that CFRP laminate notched strength decreases with increasing notch size. One possible explanation for this was proposed by Whitney & Nuismer [START_REF] Whitney | Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations[END_REF] for open hole laminates who showed that even though the stress concentration factor, K T , is approximately 3 for holes of all sizes in quasi-isotropic OHT specimens, the stress drops off more steeply moving away from the hole, for smaller holes. It was reasoned that this increased the probability of having a large flaw in the highly stressed region around a large hole, resulting in a lower average strength for a laminate with a large hole.

A variety of through-thickness discontinuities have been used to determine the notched characteristics of CFRP laminates, viz. centre-cracked [START_REF] Coats | A Progressive Damage Methodology for Residual Strength Predictions of Notched Composite Panels[END_REF][START_REF] Harris | On the Use of Crack-Tip-Opening Displacement to Predict the Fracture Strength of Notched Graphite/Epoxy Laminates[END_REF], double edged notched [START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF] and open hole laminates [START_REF] Eriksson | Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes[END_REF][START_REF] Wang | Experimental and Numerical Investigation of the Tension and Compression Strength of Un-notched and Notched Quasi-Isotropic Laminates[END_REF]. However, the open hole laminate has been adopted as the industry standard for determining the notched strength of FRP laminates [19 -21]. Data presented in the literature for centre cracked and open hole tension laminates with the same lay-up and notch length indicates that the notched strength for both specimen types is not significantly different [START_REF] Eriksson | Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes[END_REF][START_REF] Daniel | Engineering Mechanics of Composite Materials[END_REF].

The specific failure characteristics of individual FRPs are dependent on their constitutive material properties. Pinnell [START_REF] Pinnell | An Examination of the Effect of Composite Constituent Properties on the Notched Strength Performance of Composite Materials[END_REF] showed that fibres with high tensile strength and modulus give greater strength as they provide better resistance to fibre-dominated tensile failure and enhance the ability to dissipate the stress concentration at the notch edge. In addition, a thermoplastic matrix system provided greater notched strength than a thermoset matrix system due to its greater strength and toughness [START_REF] Pinnell | An Examination of the Effect of Composite Constituent Properties on the Notched Strength Performance of Composite Materials[END_REF]. Dimant et al. [START_REF] Dimant | Evaluation of a Damage-Mechanics Approach to the Modelling of Notched Strength in KFRP and GRP Cross-Ply Laminates[END_REF] compared the damage characteristics of notched, cross-ply Kevlar ® fibre-reinforced plastic (KFRP) and Eglass fibre-reinforced plastic (GFRP). It was shown that the KFRP specimens exhibited similar damage initiation and growth behaviour as CFRP. Damage patterns were consistent and well-defined, involving transverse matrix cracks in the 90º plies and axial splits at the hole in the 0º plies, though the delaminations accompanying the axial splits form with a narrower tip angle than in CFRP. A greater density of transverse ply cracks and a greater tendency to delaminate was observed with increasing transverse ply thickness in GFRP. Fibre failure in the 0º ply occurred in the same plane coinciding with the transverse ply crack that extended from the notch tip. The higher statistical variation in E-glass fibre strength lead to a more variable failure pattern in GFRP with multiple axial splits which spread far from the notch.

In recent years, high strength S2-glass fibre-reinforced composite materials have found increasing application in armour systems [START_REF] Hosur | Studies on the repair of ballistic impact damaged S2-glass/vinyl ester laminates[END_REF] and as a constituent material in the fibre metal laminate (FML) GLARE ® , which is used in the upper fuselage of the Airbus A380 as well as other aerospace structural applications [START_REF] Hosur | Studies on the repair of ballistic impact damaged S2-glass/vinyl ester laminates[END_REF]. However, little data appears to be available in the literature on the damage characteristics of notched S2-Glass/epoxy composites.

The objective of this paper is to characterise and compare damage initiation and growth in open-hole tension CFRP and high strength S2-Glass FRP laminates. An experimental test series was carried out to determine laminate unnotched and open hole ultimate strength and strain of a CFRP and S2-glass FRP currently used in the aerospace industry. In addition, non-destructive inspection techniques were used to map damage growth with increasing applied load for both material systems. Four different stacking sequences were examined and in explaining the results, reference is made to basic material property tests which were also carried out on both systems.

Experimental Methods

The specimen geometry for the OHT specimens is shown in Fig. 1. All OHT specimens tested had a 2a/W ratio of 1/6, where 2a is the notch length (hole diameter) and W

is the laminate width. The test procedure and specimen geometry were based on ASTM Standard D5766 [START_REF]Standard Test Method for Open Hole Tensile Strength of Polymer Matrix Composite Laminates[END_REF]. Two FRP material systems were studied viz. Hexcel Materials Ltd. All test specimens were manufactured at the University of Limerick. Panels of the desired lay-up were prepared from prepreg and cured in an autoclave according to ASTM D5687 [START_REF]Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials[END_REF]. Test specimens were cut from the panels using a dedicated composite cutting machine with a diamond-coated cutting blade. In order to examine the initiation and growth of damage around the hole in the specimen, high quality holes free from defects associated with solid-tool drilling of composite materials, e.g. chip-out, surface delamination, internal delamination and fibre/matrix pull-out were generated using jigs and drilling methods developed as part of a previous study [START_REF] Mccarthy | Bolt-hole clearance effects and strength criteria in single-bolt, single-lap, composite bolted joints[END_REF]. Laminates were sandwiched between two Perspex plates, to prevent chip-out on entry and exit, in a specialised jig. Holes were drilled and then reamed to their final dimensions using carbide tools, producing high quality holes for research purposes.

Five specimens of each laminate stacking sequence for both material systems were tested to failure to determine the average OHT strength (S OHT ). Three unnotched specimens, with the same dimensions as the OHT specimens, were also tested to failure to determine the and [90 2 /0 2 ] s (65%, 75%, 85% and 95% S OHT ). Damage progression in the vicinity of the hole in the CFRP specimens was examined using penetrant radiography; the penetrant used was iodomethane 99%. As damage voids (i.e. cracks and delamination) tend to close upon laminate unloading, the penetrant had to be applied to the laminate while it was subjected to a tensile load (usually 75% of the load it was previously subjected to; this allowed reopening of existing damage voids without causing new damage to form). A novel approach was developed to infuse penetrant into damage voids in the test specimens. A reservoir was created at the hole using two notched rubber blocks, stiffened with a steel backing plate, shown in Fig. 3a, and held in place using a G-clamp, as shown in Fig. 3b. The rubber blocks were carefully tightened onto the specimen to provide a liquid-tight seal around the hole, but not too tight to prevent re-opening of damage voids. Penetrant was added to the reservoir with a dropper and the specimen was held at the designated load for approximately 5 minutes. The penetrant level in the reservoir had to be repeatedly topped up during this time as firstly, the level drops as the penetrant infuses into the damage voids and secondly, Iodomethane 99% evaporates slowly at room temperature. Once sufficient time had elapsed for the penetrant to infuse into the damage voids, the laminate was unloaded and x-rayed. The quality of the radiograph was dependent on how quickly it was x-rayed after being removed from the straining frame, since the penetrant tended to evaporate out of the voids relatively quickly (10 -15 minutes) after infusion. The above procedure was developed using considerable trial and error.

Both constituents of GFRP are translucent and so damage progression in specimens was examined using a backlight technique. Placing a bright light source behind the laminate reveals damage in the form of shadows. This method was found to produce damage progression images of a quality similar to that achieved by penetrant radiography and it was possible to examine (and video) the damage growth in real time.

In addition to the above tests, basic material tests were performed on 0º, 90º and ±45º specimens according to the appropriate standards [START_REF]Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials[END_REF][START_REF]Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45º Laminate[END_REF] to provide reference properties for both material systems. Further details on these tests can be found in [30].

Results and Discussion

Stress-strain curves and failure properties

Figure 4 shows the stress-strain curves for CFRP and GFRP unnotched and OHT specimens for each of the stacking sequences. Note that the unnotched curves are not to failure since the extensometers had to be removed prior to rupture to avoid damaging them. It is clear from these curves that the CFRP OHT specimens have greater strength and significantly greater stiffness than the GFRP OHT specimens; though not shown on these graphs, the same was also true for the unnotched specimens. However, the GFRP specimens (both unnotched and OHT) have a significantly greater ultimate strain and absorb greater strain energy (i.e. area under the stress-strain curve). These general property trends can be attributed to the fibre direction properties of each material. From the basic material property tests, it was found that CFRP is slightly stronger and has significantly greater stiffness in the fibre direction than GFRP, but has a significantly lower ultimate strain, as shown in Table 1.

Examination of unnotched and OHT stress-strain curves suggests that the presence of the hole has no effect on the stiffness of the CFRP laminates and only slightly reduces the stiffness of the GFRP laminates. This phenomenon can be attributed to the placement of the extensometers on the specimen (see Fig. 2). When load is applied, the unnotched specimen displacement within the extensometer gauge length is uniform across the laminate width.

However, for the OHT specimen, greater strain occurs along the centre away from the edges due to the stress concentration at the hole, and as the load increases, due to damage initiation and propagation in the region around the hole. This is not detected by the extensometers as their attachment points are relatively remote from the high strain region. Therefore, the stressstrain ratio appears similar for OHT and unnotched specimens.

Strength data is presented in Table 2 showing good repeatability for each data series, with a maximum coefficient of variance of 5%. The unnotched strength is seen to be significantly greater than the OHT strength for all laminate stacking sequences of both material systems. Normalised strength (S OHT /S UN ) data is presented for each laminate. The normalised strength is a measure of the notch sensitivity of each of the laminate lay-ups.

According to [START_REF] Soutis | Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole[END_REF], a material is ideally notch insensitive (ideally ductile) if the failure stress is proportional to the net-sectional area, whereas it is ideally notch sensitive (brittle) if it fails when the local stress at the edge of the hole equals the unnotched strength (S UN ). In general, an open hole specimen with a 2a/W ratio of 1/6 has a notch insensitive normalised strength (1-2a/W) of 5/6 ( 83%) [START_REF] Soutis | Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole[END_REF]. Conversely, an open hole specimen (again with 2a/W = 1/6) has a notch sensitive normalised strength = 1/K T [START_REF] Soutis | Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole[END_REF], where K T is the stress concentration factor.

For a quasi-isotropic lay-up, K T is approximately 3, yielding a notch sensitive normalised strength of 0.32 [START_REF] Soutis | Static Compression Failure of Carbon Fibre T800/924C Composite Plate with a Single Hole[END_REF], while a cross-ply lay-up yields 0.22 for GFRP and 0.19 for CFRP (K T for each laminate was determined analytically according to the equations given in [START_REF] Daniel | Engineering Mechanics of Composite Materials[END_REF] with finite-width correction factors determined from [31]). This type of analysis gives the range of notch sensitive -notch insensitive bands using in the following analysis. Examination of the modulus reduction curves in Fig. 5 shows that for GFRP a reduction in modulus between 0% and 0.5% strain occurs in all cases. This is not seen in the CFRP curves. This reduction in modulus is attributed to yielding of the matrix in the 90º plies.

GFRP exhibits significant non-linear transverse behaviour and modulus reduction as demonstrated by experimental curves obtained from 90º specimen tensile tests shown in Fig. 6. The 90º specimen exhibits a steady reduction in modulus between 0% and 0.5% strain, after which the modulus starts to plateau, similarly to the behaviour exhibited by the GFRP OHT specimens. In contrast CFRP 90º specimens show that no such non-linear behaviour (see Fig. 6) and consequently no such modulus reduction in the OHT configuration (apart from slight variations due to bedding in of the specimens in the grips).

Damage Progression Mapping

The progression of damage in CFRP and GFRP quasi-isotropic OHT specimens is shown in Fig. plies is again faint in comparison to CFRP. The apparently lower level of matrix cracks in the 90° plies in the GFRP OHT specimens compared to the CFRP OHT specimens may be due to the less brittle nature of the matrix material in GFRP, as evidenced in Fig. 6. The welldefined, consistent pattern of damage in the GFRP specimens is in contrast to the findings of Dimant et al. [START_REF] Dimant | Evaluation of a Damage-Mechanics Approach to the Modelling of Notched Strength in KFRP and GRP Cross-Ply Laminates[END_REF] for E-glass FRP, which showed a variable pattern of multiple axial splits across the width of the specimens; the variability in behaviour was attributed in [START_REF] Dimant | Evaluation of a Damage-Mechanics Approach to the Modelling of Notched Strength in KFRP and GRP Cross-Ply Laminates[END_REF] to the relatively high statistical variance in the strength of E-glass fibres. The present results demonstrate that high-strength S2-glass FRP is closer to a high-performance CFRP material in its notched failure behaviour, than it is to E-glass FRP.

Radiographs of damage progression in CFRP [90/0] 2s and [90 2 /0 2 ] s OHT laminates, presented in Fig. 9, show that damage is again characterised by axial splits in the 0° plies accompanied by matrix cracks in the 90° plies. However, the damage zones in the [90 2 /0 2 ] s OHT laminate are much more extensive than those in the [90/0] 2s laminate (or indeed the [90/0] 4s laminate in Fig. 8). The length of the axial splits observed in the [90 2 /0 2 ] s laminate radiographs indicates that blocked stacking of 0° plies facilitates the growth of this form of damage, whereas placing 90° plies between each 0° ply, as in the sub-laminate stacked [90/0] 2s laminate, tends to arrest the growth of the splits more. This result is consistent with the findings of [START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF]. In addition, areas of triangular delamination are evident along the length of the axial splits in both stacking sequences, particularly from 75% S OHT to failure. The edge of the delamination zone in the [90 2 /0 2 ] s radiographs appears as a 'tide-mark', due to evaporation of penetrant prior to x-ray exposure. Again, the extensive matrix cracking in the 90° plies occurs mainly outside of the axial splits showing the effective stress concentration blunting of this form of damage.

Backlight images of damage progression in GFRP [90/0] 2s and [90 2 /0 2 ] s OHT laminates presented in Fig. 10 show a similar trend to that exhibited by CFRP. However, as with the [90/0] 4s GFRP laminates evidence of 90° ply matrix cracking, while clearer than in the [90/0] 4s case, is quite faint in comparison to the CFRP specimens.

Comparison of the damage in the [90/0] 4s (Fig. 9) and [90/0] 2s (CFRP in Fig. 9 and GFRP in Fig. 10) OHT laminates shows that although both have the same stacking sequence 2) shows that there is a correlation between the extent of damage sustained by a laminate prior to failure and the S OHT . The [90 2 /0 2 ] S laminate achieves the highest S OHT value and also exhibits the greatest amount of damage prior to failure, for both material systems. Conversely, the [90/0] 4s laminate has the lowest S OHT of the cross-ply laminates while exhibiting the least damage prior to failure. In addition, stress-strain curves (Fig. 5) indicate that laminates that sustain significant damage prior to failure absorb greater energy before failure. The principal at work here is that damage formation, effectively blunts the stress concentration due to the notch, allowing the specimen to achieve higher S OHT values and energy absorbed to failure. These findings are consistent with those in [START_REF] Harris | Fracture of Thick Laminated Composites[END_REF][START_REF] Harris | A Fractographic Investigation of the Influence of Stacking Sequence on the Strength of Notched Laminated Composites[END_REF][START_REF] Kortschot | Damage Mechanics of Composite Materials: -I -Measurements of Damage and Strength[END_REF].

Comparing the quasi-isotropic and [90/0] 4s configurations, which both have the same thickness, a similar principle can be seen to be at work. Even though the [90/0] 4s laminate has a much higher unnotched strength than the quasi-isotropic laminate (1112 MPa versus 705

MPa for CFRP and 937 MPa versus 654 MPa for GFRP), the normalised strength (S OHT /S UN ) is significantly higher for the quasi-isotropic configuration for both material systems indicating lower notch sensitivity. Comparing Figs. 7 and8, it can be seen that more extensive damage occurs prior to failure in the quasi-isotropic configuration.

Concluding Remarks

Comparing the two materials tested in this study, the CFRP OHT specimens had the greater stiffness and strength, while the GFRP OHT specimens exhibited greater strain to failure and significantly higher toughness. Comparison of damage progression in the two materials however indicates a very similar damage and failure sequence. In the quasi-isotropic configuration, this consisted of matrix cracks in the ±45º and 90º plies followed by extensive delamination prior to failure. In the cross-ply configuration, it consisted of matrix cracks in the 90º plies, a pair of axial splits emanating from each side of the hole in the 0º plies and triangular areas of delamination extending from the splits. This regular and consistent pattern of damage formation in the current S2-glass composite is in contrast to the more variable damage patterns involving multiple axial splits exhibited by E-glass composite in [START_REF] Dimant | Evaluation of a Damage-Mechanics Approach to the Modelling of Notched Strength in KFRP and GRP Cross-Ply Laminates[END_REF].

A correlation was found for all lay-ups between the extent of damage prior to failure and the resulting S OHT and energy absorbed. Higher levels of damage formation (provided plies are still coupled to each other) reduce the stress concentration and result in higher S OHT values and energy absorbed to failure. The large difference in S OHT between blocked and sublaminate level stacking sequences in the cross-ply laminates is an illustration of this point, with blocked sequences allowing easier growth of the splits in the 0º plies, resulting in more extensive damage in the specimen and greatly increased energy absorbed. Thicker cross-ply laminates with the same stacking sequence were also found to have shorter axial splits and consequently lower S OHT and energy absorbed.

The transverse behaviour of GFRP is highly non-linear as exhibited by tests on 90º specimens. In the OHT tests this shows up in the form of a drop in stiffness early in the test (between 0 and 0.5% strain), and a reduced level of matrix cracking in the 90º plies (compared to CFRP). This reduced level of matrix cracking in the 90º plies may have knock on effects in cross-ply OHT configurations in that it provides more resistance to growth of splits in the adjacent 0º plies than the highly cracked 90º plies in the CFRP specimens. As seen above, limiting the growth of axial splits results in lower S OHT values and this may be the reason why GFRP was found here to be more notch sensitive (i.e. having lower S OHT /S UN values) than CFRP.

ACCEPTED MANUSCRIPT

  6376C-HTA(12K)-5.5-29.5% CFRP and Cytec Engineered Materials Ltd. FM94-27%-S2-187-460 S2-glass GFRP. Four laminate stacking sequences were examined, one quasiisotropic ([45/0/-45/90] 2s ) and three cross-ply ([90/0] 4s , [90/0] 2s , [90 2 /0 2 ] s ). These stacking sequences were chosen as quasi-isotropic type stacking sequences are very common in aircraft structures, while cross-ply stacking sequences of GFRP are used in GLARE ® [25]. In addition, the [90/0] 2s and [90 2 /0 2 ] s stacking sequences were studied to examine the effects of sub-laminate and blocked stacking of plies in OHT laminates.

  average unnotched strength (S UN ) of each laminate. Each OHT specimen tested to failure was instrumented with two axial extensometers as shown in Fig.2to measure the localised displacement in the vicinity of the hole; extensometers remained attached right through to laminate final failure. Each extensometer had a gauge length of 25 mm and was placed on the specimen so that the hole was in the centre of the gauge length. Unnotched specimens were instrumented with one extensometer (that was removed prior to ultimate failure to prevent it being damaged) to determine displacements for comparison with OHT data. The use of hydraulically pressurised grips with specially machined faces for gripping composite materials ensured that all unnotched laminates failed in the gauge length. All specimens were loaded quasi-statically in tension, in stroke control at a rate of 0.03 mm/s (approximately 2 mm/min).Having determined the S OHT for each laminate, tests to percentages of S OHT were carried out to map the initiation and progression of damage for each stacking sequence of both material systems. These OHT specimens were not instrumented with extensometers. Three percentage of S OHT tests were carried out for quasi-isotropic laminates one each for 75%, 85% and 95% of S OHT . Similarly, three percentage of failure tests were carried out for the [90/0] 4s laminate (65%, 80% and 95% S OHT ), and four percentage of failure tests each for the [90/0] 2s

For

  the current study, the [90 2 /0 2 ] S laminate achieves the highest normalised strength (S OHT /S UN ), 0.85 for CFRP and 0.59 for GFRP. Based on the above analysis, the high normalised strength achieved by the CFRP [90 2 /0 2 ] S laminate indicates that it is notch insensitive. This is supported by the radiograph shown in Fig. 9h, which shows long axial splits in the 0º plies on each side of the hole at 95% S OHT , indicating that the load is only being supported by the two outer unnotched ligaments of the laminate, the stress concentration at the hole is completely blunted. All the other laminates fall well within the notch sensitive -notch insensitive bands. The CFRP and GFRP quasi-isotropic laminates have approximately the same normalised strength, 0.53 and 0.54 respectively. However, the CFRP cross-ply laminates attain higher normalised strengths than the GFRP laminates, suggesting that overall, CFRP is less notch sensitive. Comparison of the strength data for [90/0] 4s and [90/0] 2s in Table 2 shows the effect which laminate thickness has on notched strength. Both laminates have the same stacking sequence, but [90/0] 4s is twice as thick. The S UN values for [90/0] 4s and [90/0] 2s are not significantly different for both material systems. However, the S OHT of the [90/0] 2s laminate is significantly higher than that of the [90/0] 4s laminate for both material systems. Comparison of the data for [90/0] 2s and [90 2 /0 2 ] S shows the effect which stacking sequence has on notched strength. Both laminates have the same thickness and contain equal numbers of 0º and 90º plies, but the [90/0] 2s laminate has a sub-laminate stacking sequence, while the [90 2 /0 2 ] S laminate has a blocked-ply stacking sequence. The S UN of the [90/0] 2s and [90 2 /0 2 ]s laminates are not significantly different for both material systems. However, the [90 2 /0 2 ] s laminate S OHT is significantly higher than the [90/0] 2s laminate S OHT for both CFRP (56 %) and GFRP (35 %). This finding is similar to observations made by Kortschot and Beaumont [10] for CFRP double-edged notched specimens with the same stacking sequences.A comparison of OHT laminate stress-strain and modulus reduction curves for all layups is presented in Fig.5. The modulus reduction curves were generated by calculating the slope of the stress-strain curves using a moving average window size of 7. For CFRP, the quasi-isotropic OHT laminate has the lowest modulus (approximately 47 GPa), the [90/0] 2s and [90 2 /0 2 ] s laminates achieve a higher modulus of about 65 GPa, and the [90/0] 4s laminate achieves the highest modulus of approximately 70 GPa. A similar trend is observed for the GFRP OHT laminates. The quasi-isotropic laminate has the lowest modulus (approximately 17 GPa), while all the cross-ply laminates achieve a slightly higher modulus of about23.5 GPa. This data indicates that notched laminate stiffness depends on the stiffness of the reinforcing fibres as well as the percentage of fibres aligned in the direction of loading, i.e. the stiffer laminates have a greater percentage of plies aligned with the direction of loading, as expected.

7 .

 7 Damage does not occur until a relatively high load is reached (i.e. approximately 75% of S OHT ). Radiographs of the CFRP specimen at 75% and 85% S OHT shows that damage mostly consists of matrix cracking in the ±45° and 90° plies in the vicinity of the hole, accompanied by some delamination around the hole; cracks in the 90° plies extend to the laminate edge at 85% S OHT . However, between 85% and 95% S OHT large triangular delamination zones emanate from the hole, decoupling plies and leading to rapid failure of the laminate (Note: areas of delamination shown around the hole at 75% and 85% S OHT in Figs. 7a and 7c, are not visible at 95% S OHT in Fig. 7e due to evaporation of the penetrant). Backlight images of the GFRP laminate show a quite similar trend for damage propagation. At 85% and 90% of S OHT shadows in the vicinity of the hole indicated the presence of matrix cracks in the ±45° and 90° plies; the shadows are quite faint however and matrix cracking does not appear to be as extensive as in CFRP at this point in the loading cycle. At 95% of S OHT however, deep shadows around the hole indicate the formation of delamination zones just prior to failure, in a similar manner to that of CFRP. Damage progression in CFRP and GFRP [90/0] 4s laminates is presented in Fig. 8. Damage in the [90/0] 4s laminate is characterised by axial splits at each side on the hole in the 0° plies. Radiographs of the CFRP laminate indicate that axial splits occur in the 0° plies prior to 65% S OHT and are accompanied by matrix cracks in the 90° plies. As the load increases, the damage zone increases in size, but the matrix cracks in the 90° plies only occur outside (i.e. towards the laminate edge) of the 0° ply axial splits indicating that the splits effectively blunt the stress concentration from the hole. Backlight images of the GFRP [90/0] 4s OHT laminate indicate a similar well defined pattern of two axial splits in the 0° plies (shown as linear shadows either side on the hole) which increase in length with increasing load. The splits are longer than those observed in the CFRP laminates but evidence of matrix cracking in the 90°

  and exhibit similar damage patterns, the damage zones, and particularly the length of the axial splits, are significantly greater in the [90/0] 2s OHT laminate, for both material systems. This can be attributed to the formation of triangular zones of delamination along the length of the axial splits, particularly evident at 85% and 95% S OHT , which facilitate their increasing growth as they are freed from transverse reinforcing provided by the 90° ply fibres. The thin [90/0] 2s laminate (8 plies) is more susceptible to delamination than the thicker [90/0] 4s laminate (16plies) as interlaminar stresses tend to be higher in the surface plies of laminates, hence a greater percentage of the plies in the [90/0] 2s laminate are subjected to these higher interlaminar stresses than in the [90/0] 4s laminate. Comparison of the damage progression maps for the cross-ply laminates ([90/0] 4s , [90/0] 2s and [90 2 /0 2 ]s) with strength data (Table

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .

 12345678910 Fig. 1. Open hole tension specimen geometry (all dimensions in mm)

Table 1

 1

	Material properties
	Property	CFRP	GFRP
	E 11 (GPa)*	139	52
	E 22 (GPa)*	10	10
	G 12 (GPa) †	5.2	3.0
	ν 12 *	0.32	0.28
	S 11 (MPa)*	2170	1840
	S 22 (MPa)*	73	44
	S 12 (MPa) †	83	39
	e 11 (%)*	1.5	3.8
	e 22 (%)*	0.8	1.0
	* calculated according to ASTM D3039 [28] † calculated according to ASTM D3518 [29]

Table 2 Unnotched (UN) and open hole tension (OHT) laminate strength data

 2

	Lay-up	[45/0/-45/90] 2s		[90/0] 4s			[90/0] 2s			[90 2 /0 2 ] s
	CFRP Data
		S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN
		(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)
	Average	710	380	53	1110	480	45	1060	550	52	1010	860	85
	Value
	S.D.	17	7	-	16	12	-	54	28	-	39	22	-
	(C.V. {%})	(2.4)	(1.9)		(1.5)	(2.4)		(5.2)	(5.1)		(3.8)	(2.6)
	GFRP Data
		S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN	S UN	S OHT	S OHT /S UN
		(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)	(MPa)	(MPa)	(%)
	Average	660	350	54	940	370	40	900	410	46	960	560	59
	Value
	S.D.	12	10	-	8	4	-	37	14	-	20	17	-
	(C.V. {%})	(1.8)	(2.9)		(1.0)	(1.0)		(4.1)	(3.4)		(2.1)	(3.0)

O'Higgins RM. An Experimental and Numerical Study of Damage Initiation and Growth in High Strength Glass and Carbon Fibre-Reinforced Composite Materials. PhD Thesis, University of Limerick, Department of Mechanical and Aeronautical Engineering, 2007.

Tan SC. Finite-width correction factors for anisotropic plate containing a central hole. Journal of Composite Materials 1988; 22: 1080 -1097.

Acknowledgements

This work was funded by the Irish Research Council for Science, Engineering and Technology (IRCSET) Basic Research Project Grant: A Study of Damage Initiation and Growth in Composite Bolted Joints; Project No. SC/02/191. One author (R.M. O'Higgins) would like to acknowledge the funding provided by the University of Limerick Foundation H.T. Hallowell scholarship. The authors would like to thank Mr. Declan Kenihan for his advice and help with the radiographs.


Jan Kalfus
email: kalfus@fch.vutbr.cz

Josef Jancar

Reinforcing mechanisms in amorphous polymer nanocomposites

Keywords: nano composites, elastic properties, dynamic mechanical thermal analysis

published or not. The documents may come

Reinforcing mechanisms in amorphous polymer nanocomposites

(DMTA)

Considerable volume of literature has been published on the experimental observations of the deformation response of amorphous polymer composites with rigid nano-scale inclusions. Their mechanical response deviates substantially from that observed for polymers filled with micrometer sized inclusions 1, 2. Presence of rigid particles results in enhancement of the elastic modulus of polymer composite compared to that of the neat polymer. The reinforcement can be caused in principle by one of the three main mechanisms: (i) the stress transfer from matrix to the non-isometric particles 3, (ii) the partial substitution of soft matrix with stiffer filler 3 and (iii) the segmental immobilization caused by the interaction of polymer chains with filler surface 2. The stress transfer mechanism depends on the inclusion aspect ratio, its orientation to the applied load, the strength of adhesion and, thus, it is considered as size independent contribution for the case of sufficiently flexible matrix chains. The second mechanism is independent of particle size as well. On the other hand, the segmental immobilization mechanism contributes to the overall composite reinforcement with the extent primarily affected by the size of the inclusions, becoming important for submicron particles with large surface to volume ratio.

As shown in Figure 1, the reinforcement in nanocomposite is very temperature sensitive variable and two principal temperature regions can be identified 4. Bellow the T g , the concentration dependence of the relative storage modulus, E r , only small deviations from the prediction based on the simple Kerner-Nielsen substitution model were observed [START_REF] Nielsen | In: Mechanical Properties of Polymers and Composites -second edition[END_REF]. At temperatures above matrix T g , the E r increased well above the continuum micromechanics prediction suggesting that the segmental immobilization is the primary mechanism responsible for the polymer reinforcement. It has been proposed that the filler surface area per unit weight of nano-composite is the most suitable structure variable in modeling compositional dependence of elastic moduli of polymer nano-composites. This phenomenon has not been observed in the case of polymers filled with micrometer-sized fillers due to their small surface to volume ratios 1. In these systems, the observed deviations were attributed to the change in Poisson's ratio or relief of internal stresses upon heating 3.

At low filler content, the main reinforcing mechanism in polymers, above their T g , filled with high specific surface area nanoparticles results from processes occurring in the large interphase matrix surrounding nano-inclusions. In order to derive a suitable conceptual framework to describe the chain immobilization based reinforcing mechanisms active in the nanocomposites, basic physical principles governing molecular mobility in amorphous polymers have to be outlined. Entangled amorphous polymers are unique systems with macroscopic viscoelastic response driven by the relaxation processes on the molecular level 5. These relaxation processes represent specific motions of a portion of chains occurring within some characteristic volume, V c , at various temperatures. The characteristic volume varies from 10 -3 nm 3 for localized bond vibrations to 10 6 nm 3 for the non-local normal mode relaxation (Figure 1). In the later case, the characteristic volume is the boundary value still displaying strong dependence on the chain size, V c  R 3  N 3/2 , where R is the chain end-to-end distance and N is the number of monomer units in a chain. The characteristic time,  c , for each particular relaxation process varies from 10 -14 s for bond vibrations to the infinitely long times for the chain diffusive motion below T g . Thus, the macroscopic viscoelastic response is a manifestation of a range of molecular relaxations localized in a characteristic volume and the relaxation rate is indirectly proportional to its localization.

The individual relaxations are a consequence of thermal agitation of chain subunits. One may consider the polymer chain as a set of linearly linked Brownian particles executing thermally activated motion primarily via the torsion around the single bonds.

Due to the intra-and inter-chain potential field, kinetic energy of a Brownian particle must be sufficient to overcome the energy barrier caused by the torsion potential. Thus, particular activation energy, E A , can be ascribed to each particular relaxation mode. In general, neglecting any secondary process being of Arrhenius nature, the relaxation times typical for the -relaxation (glass transition) and normal mode are persistence times displaying temperature dependence well described by the Vogel-Fulcher-Tamann equation in the approximate form 5:

            0 exp * T T k E B A   . (1)
In. Eq. ( 1

G glass =  * /V e , (2)
where  * is the single bond torsion force constant of the order  * = 10 -19 -10 -20 J 7.

At higher temperature, when the log-time sufficiently advanced the enormous frequency of the chain conformational changes results in normal mode fluctuations able to completely relief the applied load. Thus, the characteristic volume increased from V e  10 -3 nm 3 to the value typical of random coil dimensions, V c  10 5 10 6 nm 3 . In high molecular weight polymers the rubbery plateau can be detected. The rubbery region exhibits primarily entropy driven behavior and the elastic modulus, G rubber , in entangled polymers can be approximated as [8]:

G rubber = 4RT/5M e . ( 3
)
Because the characteristic volume of the entangled network, V c , can be expressed as:

V c = (M e C N b 2 /M 0 ) 3/2 , (4)
the modulus of elasticity may be then written in the form:

G rubber = 4RTC N b 2 /5M 0 (6V c ent /) 2/3 , ( 5
)
where M e is the entanglement strand molecular weight, M 0 is the monomer unit molecular weight, C N is the chain characteristic ratio, b is the bond length,  is the rubber density and R is the universal gas constant.

Let us compare the molecular characteristic volumes with those of filler inclusions (Figure 3). In the glassy polymer filled with micrometer-sized particles, the ratio r v = V p /V c (V p is the particle volume) is of the order of 10 15 (Table 1). Obviously, the rubber (T>T g ) filled with micrometer-sized inclusions exhibits r v equal to the ratio characterizing the glassy polymer (T<T g ) filled with nanometer-sized inclusions. On the other hand, the rubbery matrix filled with nano-inclusions represents a unique system specific by the very low value of r v , which means that the volume characteristic of the relaxation process is considerably larger compared to the stiff nano-inclusion (Table 1).

At high r v , matrix characteristic structural unit in which relaxation mode occurs is small enough being negligible compared to the inclusion size. At higher temperatures, the r v decreases suggesting that the matrix loses its continuum character under given conditions.

In addition, the physical reasons for the breakdown of continuum elasticity on the nano-scale include increasing importance of surface energy due to appreciable surface to volume ratio [9], the discrete molecular nature of the polymer matrix discussed above [10], presence of the nano-scale inclusions [11, 12] and the internal strain due to molecular motion within a non-primitive lattice [13, 14]. Quantum confinement effects can also play a role inducing a strain gradient on the nano-scale without presence of any external loading, however, its importance is limited to the size range below 2 nm [15] and it is not considered here. Heterogeneity of the polymer structure at the nano-scale resulting from the long chain nature of the molecules is further complicated by adding stiff nano-sized filler particles.

In order to estimate the length scale at which the classical elasticity becomes non-valid, the molecular dynamics on a model amorphous polyethylene-like chain was performed under periodic boundary conditions at 50K [16]. The corresponding length scales for the longitudinal and transverse directions were 1.85 and 3.81 nm, respectively. Nikolov et al. [17] estimated that rubbers above their T g should have nonlocal length scale approximately 5 nm. The high non-locality in polymers most probably stems from a cooperative behavior of large number of chain segments characteristic for entangled polymers. As a result, parts of the material system may undergo considerable non-affine deformation associated with occurrence of high moment stresses.

Consequently, for such systems, taking strain-gradient effects into account while investigating nano-scale elastic phenomena may impart significant size-dependent corrections to the results obtained from classical continuum elasticity [10,16].

Although the immobilization is a reasonable reinforcing mechanism and its Tables:

Table 1: Ratios of the particle volume/polymer characteristic volume, r v , and particle diameter/polymer characteristic length, r l , for microcomposite and nanocomposite below and above the glass transition.

Table(s) 1

  ), * is the time characteristic of torsion vibration, k B is the Boltzmann constant and T 0 is Vogel temperature typically some 50°C bellow the experimentally measured T g . Note that the torsion vibrations represent very localized relaxation. The time characteristic of torsion vibrations does not manifest such a strong temperature dependence compared to the other microscopic motions, and Considering the hypothesis put forward above, one can see that the characteristic time, temperature and volume represent variables correlated to each other (Figure 2). At low temperatures, the microscopic modes are too slow compared to the time scale considered unable to maintain equilibrium values of the extensive thermodynamic quantities. Glassy chains can relax only due to extremely rare conformation transitions of low-mobility chain segments trapped in the energy landscape. Hence, the glassy polymer response is principally energy driven and the torsion vibrations with V e of value about 10 -3 nm 3 are the primary microscopic motion governing response of a majority of polymer units in a glassy solid. Polymer glass is composed of individually vibrating chain segments; rotational isomeric state (RIS) jumps represent rare cooperative events very sensitive to the local density of monomer units. Consequently, one may express the modulus of elasticity, G glass , of the glassy polymer in the approximate form:

  molecular origin has been well documented in literature [18-21], precise prediction or simulation of its extent for various composite systems under changing external conditions still represents intriguing problem unresolved yet. This contribution attempted to set the reinforcing mechanism responsible for the observed peculiarities of the mechanical response of polymer nano-composites, under given conditions, into a conceptual physical framework. The emphasis was put on the estimation of the boundary between length scales where the continuum mechanics is still valid and the length scales, where the discrete molecular structure has to be taken into account resulting in the need to apply molecular dynamics models. It was shown that the boundary does not represent a simple constant characteristic of a given composite system; however, it can change under varying test conditions such as time, temperature or strain. It seems that combining the strain gradient continuum elasticity with the molecular dynamics could provide suitable bridging law capable of transforming the peculiarities of the nano-scale effects into the behavior of continuous matter at larger length scales. Sternstein SS, Zhu AJ. Macromolecules 2002;35:7262. 20 Kalfus J, Jancar J. J Polym Sci: Part B: Polym Phys 2007;45:1380. 21 Sen S, Thomin J D, Kumar S K, Keblinski P. Macromolecules 2007;40:4059.

Figures:Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2: Microscopic relaxation processes on the background of the time, temperature

Figure 3 :

 3 Figure 3: Contrast between the filler particle size and volume characteristic of given