16TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS

1

Abstract

To study the behaviour of fibre reinforced compositelaminates under in-plane complex stress states abiaxial loading frame has been developed. Usingfour independent servo-hydraulic actuators acruciform type specimen is biaxially loaded in itsplane. For obtaining reliable biaxial failure data thedesign of the cruciform specimen is of paramountimportance. Finite element simulations of thecruciform specimen in combination with experimentsusing DIC for strain determination has led to theproposal of an optimized geometry which was usedto obtain strength data at different loading ratio’s.For the identification of the in-plane orthotropicelastic constants an inverse method is presented.The full field displacements and strains areidentified by digital image correlation techniqueand compared with finite element strain results. Theengineering constants are unknown parameters inthe finite element model. Starting from initial values,these parameters are updated till the computedstrain field matches the experimental strain field.

1 Introduction

Although the use of composite materials inaerospace, aviation and automotive industry hasincreased rapidly over the last decades, reliable rulesfor the prediction of structural behavior are generallynot available and consequently excessive safetyfactor are used to cover the high level of uncertainty.The ability to successfully model and simulate thebehavior of these materials for optimum use instructural applications, depends largely on thematerial description (constitutive relations, damage

evolution laws, failure criteria, ..) employed in theanalytical/numerical formulations. For validation ofproposed material models rigorous experimentalcharacterization under a variety of complex loadingconditions is mandatory. The current practice ofusing solely uniaxial test results is simplyinadequate. In general, composite laminates aredeveloping multi-axial stress states [1] andconsequently testing closer to reality is needed. Eventhough large demand exists for experimentalmultiaxial test data, there is little existingexperimental capability to evaluate the multiaxialresponse of composite materials [2,3,4]. One of themajor difficulties on performing these multiaxialtests is to design specimens and loading devices sothat a uniform plane stress state can be produced.

2 Biaxial testing equipment

Different experimental techniques andspecimens have been used to produce biaxial stressstates. These techniques may be classified into twocategories [5], (i) tests using a single loading systemand (ii) tests using two or more independent loadingsystems. In the first category the biaxial stress ratiodepends on specimen’s geometry or on the loadingfixture configuration, whereas in the secondcategory it is specified by the applied loadmagnitude.

Examples of the first category include bendingtests on cantilever beams, anticlastic bending tests ofrhomboidal or rectangular shaped composite plates,bulge tests, equibiaxial loading of disc- shapedspecimens and tests on cruciform specimens with aspatial pantograph.

BIAXIAL TESTING OF FIBRE REINFORCEDCOMPOSITES

D. Van Hemelrijck1, C. Ramault1 , A. Makris1 , , A. Clarke2, C. Williamson2,M. Gower3, R. Shaw3, R. Mera3, E. Lamkanfi4, W. Van Paepegem4

1Vrije Universiteit Brussel, Mechanics of Materials & Constructions, Brussels, Belgium2QinetiQ, Cody Technology Park, Ively Road, Farnborough Hampshire GU 14 OLX - UK3National Physical Laboratory, Hampton Road Teddington Middlesex TW 11 OLW, UK

4Ghent University, Laboratory Soete, Mechanical Construction & Production, Ghent, Belgium

Keywords: biaxial testing, digital image correlation, inverse methods

Van HEMELRIJCK D., Ramault C.

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Examples of the second category are round barsunder bending-torsion, thin-wall tubes subjected to acombination of axial loading and torsion or internal /external pressure, and cruciform specimens under in-plane biaxial loading.The technique with the thin-wall tube is the mostpopular one [6] and seems to be very versatile,because it allows tests with any constant load ratio tobe performed. However, it presents someinconveniences [5,7,8] as for instance (i) dependingon the thickness of the tube and the applied load theradial stress gradients may not be negligible, (ii) realconstruction components in fibre reinforcedcomposite materials are often flat or gently curvedand differ a lot from tubular specimens, (iii) thin-wall tubes are not easy to fabricate, (iv) obtaining aperfect alignment and load introduction is notstraightforward, (v) thin tubular specimens canexperience various forms of elastic instability whenthey are subjected to circumferential or axialcompression or torsion loads, and (vi) tubes mayexhibit changes in geometry during loading, butthese effects are usually ignored when processingexperimental results. There for the most appropriatemethod for biaxial testing of fibre reinforcedcomposite laminates consists of applying in-planebiaxial loads to cruciform specimens. In order to doso, a biaxial test device was developed at the FreeUniversity of Brussels (VUB) at the Department ofMechanics of Materials and Constructions (MeMC)[9]. This device employs four servo-hydraulicactuators for testing cruciform specimens understatic and cyclic loading conditions. Finite elementsimulations of the cruciform specimen geometry incombination with experiments using both straingages and a full field optical-numerical method forthe strain measurements in the biaxially loaded testzone have been carried out, leading to the proposalof an optimized geometry.

3. Plane biaxial test bench for crucifom testspecimens

The biaxial test rig, see Figure 1, developed atVUB has a capacity of 100kN in each perpendiculardirection, but only in tension, limiting theexperimental results to the first quadrant of the two-dimensional stress space. As no cylinders withhydrostatic bearing used, failure or slip in one armof the specimen will result in sudden radial forceswhich could seriously damage the servo-hydrauliccylinders and load cells. To prevent this, hingeswere used to connect the specimen to the load cells

and the servo-hydraulic cylinders to the test frame.Using four hinges in each loading direction results inan unstable situation in compression andconsequently only tension loads can be applied. Thestroke of the cylinders is 150mm. The loading maybe static or dynamic up to a frequency of 20Hz.Each cylinder is independently controlled and anytype of loading waveform, including spectralsequences of variable amplitude, can be efficientlyintroduced using the dedicated software and controlsystem.

Fig. 1 Biaxial test bench developed at the VUB

4. Design of the cruciform test specimen

Traditionally, a successful biaxial strength testwith cruciform specimens required the followingconditions: (i) maximization of the region ofuniform biaxial strain, (ii) minimization of the shearstrains in the biaxially loaded test zone, (iii)minimization of the strain concentrations outside thetest zone, (iv) specimen failure in the bi-axiallyloaded test zone and (v) repeatable results[3,8,10,11,12]. It has been proven extremely difficultto develop cruciform specimens that simultaneouslyfulfil all these requirements. Conditions (i) and (ii)were required if strains were measured at the centreof the specimen with a strain gage or extensometerwhere one average strain value was obtained overtheir length. This average value should berepresentative for the whole length of the strain gageor extensometer. Thanks to the development of fullfield methods for strain determination, non-uniformities in strain and occurring shear strains canbe quantified getting round these requirements. Thestrain symmetry condition however remains to befulfilled and the strains should at least be constantover the length of the strain gage and the subset sizeof the digital image correlation software, since anaverage value is given over that size. Conditions (iii)

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BIAXIAL TESTING OF FIBRE REINFORCED COMPOSITES

and (iv) are required if reliable strength data underbiaxial loading are needed, avoiding failure in thearms or at the corner fillet of the cruciformspecimen. These conditions will be checked bycomparing the failure strains obtained on standardbeamlike specimens with failure strains onuniaxially loaded cruciform specimens measured atthe centre of the specimen. For a suitable cruciformgeometry, the failure strain values should be equalindicating no early failure occurred elsewhere in thecruciform specimen.

To investigate the influence of parameters like(i) the radius of the corner fillet at the intersection ofthe arms, (ii) the thickness of the bi-axially loadedtest zone in relation to the thickness of the uniaxiallyloaded arms and (iii) the geometry of the bi-axiallyloaded test zone, orthotropic finite elementsimulations were carried out, allowing a selection offinal candidate geometries to be testedexperimentally. Afterwards, the numerical resultswere compared with experimental ones using thedigital image correlation technique for full fieldstrain measurements.

The finite element simulations were performedwith the commercial software Ansys using elementtype plane 42, which is used here as a plane stresselement. It is defined by four nodes having twodegrees of freedom at each node: translations in thenodal x and y directions. The element coordinatesystem was parallel to the global coordinate system.The material modelled was glass fibre reinforcedepoxy with a [(±45/0)4/±45]T lay-up. The materialsystem and stacking sequence are typical of windturbine rotor blade construction. Cruciformspecimens were machined from plates produced byLM Glasfiber, Denmark, using RTM (resin transfermoulding) technology. When cured, the [±45] plieshave a thickness of 0.61 mm and the [0] ones of 0.88mm. This gives a total thickness of 6.57 mm for thelaminate of the cruciform specimen and of 3.59 mmwhere one group of [±45/0] was milled away at eachside of the specimen. Homogenized elasticproperties for the composite laminate, derived bymeans of Classical Lamination Theory, were usedfor the simulations. The load ratio between the x-and y-directions was chosen equal to the respectivestrength ratio of the laminate, Fx/Fy = 46.2 kN/12kN. The width of the arms is 25 mm; the total lengthof the specimen is 250 mm. In Fig.2, finite elementresults are shown of the first principal strain for foursubsequent geometries while in Fig.3 the occurringshear strain is presented. The bi-axially loaded test

zone was zoomed in, but the finite elementcalculations were performed with the arms included.

A full field experimental technique that enablesthe assessment of the overall strain distribution inthe cruciform specimens is absolutely necessary.Strain measurements using a strain gage orextensometer are not sufficient because both give anaverage value of the deformation along their gaugelength. To be able to study the symmetry of thestrains and the occurring shear strainsexperimentally, a full field strain method isnecessary.

0 0,3 0,6 0,9 1,2 1,5 2,1 2,4 2,71,8 [%]0 0,3 0,6 0,9 1,2 1,5 2,1 2,4 2,71,8 [%]

Fig.2. Finite element results of the first principalstrain for four cruciform geometries.

-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]

Fig.3. Shear strain distributions for four cruciformgeometries .

Digital image correlation (DIC) is anexperimental technique, which offers the possibilityto determine displacement and deformation fields atthe surface of objects under any kind of loading,based on a comparison between images taken at

25mm X

Y

R=6.25mm

25mm X

Y

R=6.25mm

Van HEMELRIJCK D., Ramault C.

4

different load steps. The software processes andvisualizes the data gathered in order to obtain animpression of the distribution of strains in themeasured object. A measurement session consists oftaking several pictures of the object of interest with aCharge Coupled Device (CCD) camera. In this case,see Fig.4, two cameras were used to be able tomeasure both in-plane and out of planedisplacements on specimens not entirely flat as is thecase for the specimens with a milled surface in thecentre. Each picture corresponds to a differentloading step. The camera uses a small rectangularpiece of silicon, which has been segmented into anarray of 1392 by 1040 individual light-sensitivecells, also known as photo sites or pixels. Everypixel stores a certain grey scale value ranging from 0to 255, in agreement with the intensity of the lightreflected by the surface of the tested specimen.

Specimen

CCD CamerasAcquisitionboard

Screen

Computer

Fig. 4 Digital Image Correlation system

The same cruciform geometries as studied inthe finite element simulations were testedexperimentally. Results for the first principal strainare shown in Fig.5. Similar distribution of the strainis obtained as in the finite element simulations. Onlyin the transition zone between the intact laminateand the milled area, high strains are observed withthe digital image correlation technique but not in thefinite element simulations. This is due to the factthat the milling requires more detailed finite elementmodels to simulate the decrease in number of layersgradually.

Shear strain distributions for the four testedgeometries are presented in Fig. 6. The results aresimilar as the finite element simulations with zeroshear stains in the uniaxially loaded arms and in thecentre of the specimen and shear strains at the cornerfillets.

-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]

Fig.5. Digital image correlation results of the firstprincipal strain of the selected geometry.

-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]-1,35 -1,05 -0,75 -0,45 -0,15 0,15 0,75 1,05 1,350,45 [%]

Fig. 6. Digital image correlation results of the shearstrains of the selected cruciform geometry.

In figure 7 the experimental biaxial test results aregiven for different loading ratio’s.

Fig. 7. Biaxial test results for different load ratio’s

biaxial failure envelope:stresses calculated from area

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600

stress east-west (kN) 0°

stre

ssno

rth-s

outh

(kN

)90

°

GEV207_S0105_1/0_st.GEV207_S0105_7,7/1_st.GEV207_S0105_5,775/1_st.GEV207_S0105_3,85/1_st.GEV207_S0105_2,567/1_st.GEV207_S0105_1,925/1_st.GEV207_S0105_0,9625/1_st.GEV207_S0105_0,5/1_st.GEV207_S0105_0/1_st.GEV207_S0105_1/0_st.incr.GEV207_S0105_7,7/1_st.incr.GEV207_S0105_5,775/1_st.incr.GEV207_S0105_3,85/1_st.incr.GEV207_S0105_2,567/1_st.incr.GEV207_S0105_1,925/1_st.incr.GEV207_S0105_1/0,9625_st.incr.GEV207_S0105_0,9625/1_st.incr.GEV207_S0105_0,5/1_st.incr.GEV207_S0105_0/1_st.incr.GEV307_S0105_1/0_st.GEV307_S0105_7,7/1_st.GEV307_S0105_5,775/1_st.GEV307_S0105_3,85/1_st.GEV307_S0105_2,567/1_st.GEV307_S0105_1,925/1_st.GEV307_S0105_0,9625/1GEV307_S0105_0,5/1_st.GEV307_S0105_1/3,85_st.GEV307_S0105_0/1_st.GEV307_S0105_1/0_st.incr.GEV307_S0105_7,7/1_st.incr.GEV307_S0105_5,775/1_st.incr.GEV307_S0105_3,85/1_st.incr.GEV307_S0105_2,567/1_st.incr.GEV307_S0105_0,9625/1_st.incr.GEV307_S0105_0,5/1_st.incr.GEV307_S0105_0/1_st.incr.

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BIAXIAL TESTING OF FIBRE REINFORCED COMPOSITES

Pictures recorded immediately prior to (upper frame)and during failure (lower frame) are shown in Fig.8

48.7kN failure, 48.7kN

Fig. 8 Pictures of the failure modes

5. Inverse method

5.1 Introduction

For uniaxial testing the conversion from force tostress is straightforward because the cross section isknown and consequently stiffness data can be easilycalculated. In order to define stiffness data usingbiaxial loaded cruciform test specimen an alternativemixed numerical experimental technique belongingto the category of inverse problems was developed.The method developed at the Royal MilitaryAcademy (RMA), which integrates an optimizationtechnique, a full-field measurement technique and afinite element method [13,14]. In this paper, amethod is proposed for the identification of the in-plane engineering constants E1, E2, G12 and ν12 of anorthotropic material based on surface measurements.The responses of the system, i.e. the surfacedisplacements are measured with digital imagecorrelation. Strains are subsequently calculated,based on the measured displacement field. A finiteelement model of the cruciform specimen serves asnumerical counterpart for the experimental set-up.The difference between the experimental andnumerical strains (the cost function) is minimized ina least squares sense by updating the values of theengineering constants. The optimization of theparameters is performed by a Gauss-Newtonmethod.

In contrast to a direct problem which is theclassical problem where a given experiment issimulated in order to obtain the stresses and thestrains, inverse problems are concerned with thedetermination of the unknown state of a mechanicalsystem, using information gathered from theresponse to stimuli on the system [15]. Not only theboundary information is used, but relevantinformation coming from full-field surfacemeasurements is integrated. The inverse method

described here can be narrowed to parameteridentification, as the only item of interest is thedetermination of the constitutive parameters. Thevalues of these parameters cannot be derivedimmediately from the experiment due to thespecimen geometry. A numerical analysis isnecessary to simulate the experiment. However, thisrequires that the material parameters are known. Theidentification problem can be formulated as anoptimization problem where the function to beminimized is an error function that expresses thedifference between numerical simulation andexperimental results. In the present case the strainsare used as output data. (Fig. 9) represents the flowchart of the inverse modeling problem.

Fig. 9 - Flow-chart of determination process

5.2 Optimization algorithm

The optimization of the apparent engineeringconstants is performed by a Gauss-Newton method.The cost function that is minimized is a simple leastsquares formulation. Expression (1) shows the formof the least-squares cost function that is minimized.The residuals in the function are formed by thedifferences between the experimental and thenumerical strains.

n

1i

2

expi

expi

numi

εεpε

ppεCpC (1)

The necessary condition for a cost function to attainits minimum is expressed by equation (2). Thepartial derivative of the function with respect to the

Van HEMELRIJCK D., Ramault C.

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different material parameters has to be zero. Bydeveloping a Taylor expansion of the numericalfinite element strains around a given parameter set,an expression is obtained in which the differencebetween the present parameters and their newestimates is given (3).

0pε

εεpε

pC1

ppC n

1j i

numj

expi

expi

numi

i

(2) (2)

kjj

m

1j j

knumiknum

inumi pp

p

pεpεpε

(3) (3)

When substituting this last expression intoexpression (2) and after rearranging some terms,expression (4) yielding the parameter updates isobtained.

knumexpt1t pεεSSSpΔ

(4) (4)

in which the following elements are:

Δp : column vector of the parameter updates of

E1, E2, G12 and v12expε : column vector of the experimental strains

)p(ε knum : column vector of the finite element

trains as a function of the parameters at iteration kkp : the four parameters at iteration step k

S : sensitivity matrix

5.3 Sensitivity calculation

The sensitivity matrix (5) groups thesensitivity coefficients of the strain components inevery element of the finite element mesh withrespect to the elastic material parameters. Theindex n in equation (5) stands for the total numberof elements. The components of this sensitivitymatrix can be derived analytically from theconstitutive relation between stress and strain,which is given by expression (6) in the case of aplane stress problem.

The stresses that are used in the calculation ofthe derivatives are taken from the convergedsimulation in the actual iteration step. The values of

the parameters are taken from the previous iterationstep.

12

nxy

12

nxy

2

nxy

1

nxy

12

ny

12

ny

2

ny

1

ny

12

nx

12

nx

2

nx

1

nx

12

1xy

12

1xy

2

1xy

1

1xy

12

1y

12

1y

2

1y

1

1y

12

1x

12

1x

2

1x

1

1x

GEE

ε

G

ε

E

ε

E

ε

εGε

Eε

E

GEE

εGε

Eε

Eε

εGε

Eε

E

S

ε

ε

(5)

xy

y

x

12

21

12

1

12

1

xy

y

x

τ

σσ

G100

0E1

Ev

0Ev

E1

γ

εε

(6)

5.4 Experimental results

5.4.1 Tests on rectangular specimen

An extended database of experimental staticand fatigue results on beamlike glass fibre reinforcedepoxy specimens with a [(+45° -45° 0°)3(+45°-45°)]-lay-up has been set-up within the frameworkof the Optimat Blades project [16]. For the glassfibre reinforced composite laminate with thementioned lay-up the average and standard deviationmaterial parameter results of about four hundredtraditional beamlike tests are given in (Tabel 1). Noinformation about the shear modulus is available forthis lay-up. Only for a single unidirectional ply,information exists from off-axis tests and tests on a(+45°/-45°) lay-up given in (Tabel2). Based on theply data, the theoretically expected properties of thelaminate can be calculated using classical laminatetheory (Tabel 3).

Table 1. Material properties of the laminate obtained onbeamlike specimens

E1 E2 G12 ν12

GPa GPa GPa -average 27.03 14.21 - 0.455standard deviation 1.19 0.85 - 0.042

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BIAXIAL TESTING OF FIBRE REINFORCED COMPOSITES

Tabel 2. Material properties of the ply used in thelaminate obtained on beamlike specimens

E1 E2 G12 ν12GPa GPa GPa -

average 39.10 14.44 5.39 0.294standard deviation 2.10 0.98 1.77 0.027

Tabel 3. Calculated material properties of the laminateusing classical laminate theory (the apparent engineeringconstants of the laminate)

E1 E2 G12 ν12

GPa GPa GPa -average 28.48 16.27 8.33 0.407

5.4.2 Tests on cruciform specimen (engineeringconstants)

For the identification of the four independentelastic orthotropic parameters, a perforated and anon-perforated specimen are used. The reason oftesting a specimen with a hole is the aim to influencethe overall deformation field and to make themeasured strain fields more sensitive to the differentmaterial parameters. Because we are dealing with anexperimentally obtained strain field, this can beimportant. The specimens are subjected to threedifferent ratios of biaxial tensile loads : 2.56/1,3.85/1 and 5.77/1. Five successive load steps areimposed per ratio, so this means that fifteenindependently measured strain field triplets areavailable per specimen for the identification process.The same loads are used in the finite elementsimulation. A plane stress model is used with auniformly distributed load as boundary condition.The convergence criterion used in the optimizationphase ends the iteration process when the relativevalue of the parameter updates is inferior to 0.01%.In all of the optimization runs, the convergencecriterion is reached in less than 13 iterations.

The results of the identification process areshown in (Table 4) and (Table 5) for both perforatedand non-perforated specimen, in terms of the meanparameter value and its corresponding standarddeviation. They are obtained based on the fifteenimposed load steps considered per specimen. Thestarting values for each of the parameters arementioned as well.

It can be observed that the difference betweenthe results for both specimen types is reasonablysmall. The stability of the results obtained with thenon-perforated specimen is slightly larger. This isprobably due to the fact that the strain field is lesscomplex and therefore easier to measure with the

digital image correlation technique than in the caseof the perforated specimen.

Table 4. Material properties of perforated cruciformspecimen

E1 E2 G12 ν12GPa GPa GPa -

starting values 15 10 10 0.3average 25.11 12.17 7.05 0.483standard deviation (%) 5.4 6.8 8.9 7.7

Table 5. Material properties of non-perforatedcruciform specimen

E1 E2 G12 ν12

GPa GPa GPa -

starting values 15 10 10 0.3

average 25.11 13.31 7.69 0.467

standard deviation (%) 2.8 6 6.8 6.6

6. Conclusions

The combination of finite element simulationsand experiments performed on different cruciformgeometry types using the digital image correlationtechnique for full field strain measurements, led tothe selection of a suitable geometry for biaxialtesting of fibre reinforced composite laminates. Thisgeometry has a reduced thickness in the centralregion of the specimen, in combination with a filletcorner between two arms inside the material. Thesefeatures cause failure to occur in the bi-axiallyloaded test zone, rather than in the uni-axially loadedarms giving failure strains comparable to strainsobtained on beamlike specimens for the uniaxialload ratios. The digital image correlation techniqueused for full field strain measurements offerssignificant advantages over conventional techniquessuch as strain gauges. The spatially resolved strainsled to a better understanding of the behaviour ofcomposites under bi-axial loads. The strain valuesobtained with the digital image correlation techniqueare comparable with those calculated in the finiteelement simulations. Using the proposed geometrystrength data was obtained for different load ratio’s.An inverse method has been proposed to determinethe elastic parameters (E1, E2, G12 and v12) of aglass fibre reinforced epoxy with a [(+45° -45°0°)3(+45°-45°)]-lay-up. Two specimen geometriesare used: a regular cruciform specimen and acruciform specimen into whom a central hole isdrilled. The latter is made in order to enhance thealready heterogeneous deformation field. The

Van HEMELRIJCK D., Ramault C.

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method is based on a finite element calculated strainfield of a cruciform specimen loaded in bothorthogonal axes and the measured strain fieldobtained by digital image correlation. The obtainedmaterial parameters agree reasonably well with thevalues obtained by traditional uni-axial tensile tests.However, the results based on the regular cruciformspecimen without hole, show less variance than theresults obtained with the perforated specimen. Thisis possibly due to the fact that the digital imagecorrelation technique has some difficultiesmeasuring steep deformation gradients, henceinducing errors in the measurement of thedisplacement and strain maps. Further investigationis needed to clarify this inconvenience. Theobjective of the experiment is to enforce a materialbehaviour that exposes the different elastic materialparameters. If this is achieved by a non-perforatedspecimen, there is no need for a more complexgeometry which will possibly lead to moremeasurement errors.

7. Acknowledgements

This project is supported by the Belgian SciencePolicy through the IAP P05/08 project and theEuropean Commission in the framework of thespecific research and technology developmentprogram Energy, Environment and SustainableDevelopment with contract number ENK6-CT-2001-00552. The authors also express their gratitudeto Hans Tommerup Knudsen from LM-Glassfiber inDenmark for his effort in producing the cruciformspecimens.

8. References

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[2] Boehler JP, Demmerle S, Koss S, A new directbiaxial testing machine for anisotropic materials,Experimental Mechanics, vol 34 (1), 1-9, 1994

[3] Soden PD, Hinton MJ, Kaddour AS, Biaxial testresults for strength and deformation of a range of E-glass and carbon fibre reinforced compositelaminates : failure exercise benchmark data,Composites Science and Technology, vol 62 (12),1489-1514, 2002

[4] Welsh JS, Adams DF. Development of anelectromechanical triaxial test facility for compositematerials. Exp Mech 2000; 40(3): 312-320.

[5] Zouani A, Bui-Quoc T, Bernard M, A proposeddevice for biaxial tensile fatigue testing, Fatigue andFracture, ASME PVP-323, vol 1, 331-339, 1996

[6] Swanson SR, Christoforou AP, Colvin GE, Biaxialtesting of fiber composites using tubular specimens,Experimental Mechanics, vol 28 (3), 238-243, 1988

[7] Pascoe KJ, de Villers JWR, Low cycle fatigue ofsteels under biaxial straining, Journal of StrainAnalysis, vol 2 (2), 117-126, 1967

[8] Parsons MW, Pascoe KJ, Development of a biaxialFatigue testing rig, Journal of Strain Analysis, vol10, 1-9, 1975

[9] Smits A, Van Hemelrijck D, Philippidis TP, CardonA, Design of a cruciform specimen for biaxialtesting of fibre reinforced composite laminates,Composites Science and Technology, vol 66 (7-8),964-975, 2006

[10] Yu Y, Wan M, Wu XD, Zhou XB. Design of acruciform biaxial tensile specimen for limit strainanalysis by FEM. Journal of Materials ProcessingTechnology 2002; 123(1): 67-70.

[11] Mayes JS, Welsh JS, Key CT. Biaxial failureenvelope for a glass fabric reinforced compositelaminate. Final Report PO N00167-01-M-0246Mayes Consulting Engineers. 2002. p. 1-13.

[12] Welsh JS, Adams DF. An experimental investigationof the biaxial strength of IM6/3501-6 carbon/epoxycross ply laminates using cruciform specimens.Compos Part A- Appl S 2002; 33(6): 829-839.

[13] Lecompte D, Smits A, Sol H, Vantomme J, VanHemelrijck D, Mixed Numerical-Experimentaltechnique for orthotropic parameter identificationusing biaxial tensile tests on cruciform specimens,International Journal of Solids and Structures, vol44 (5), 1628-1642, 2007

[14] Lecompte D, Elastic and elasto-plastic materialparameter identification by inverse modeling ofstatic tests using digital im age correlation, PhDThesis, Free University of Brussels (VUB), 1-220,2007

[15] Bui HD, Inverse problems in the Mechanics ofMaterials : An introduction, CRC Press Inc. Florida,1-224, 1994

[16] Reliable optimal use of materials for wind turbinerotor blades, Optimat Blades, contract n° ENK6-CT-2001-00552, project n° NNE5-2001-00174