16TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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 ratios.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.
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  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 , (i) tests using a single loading systemand (ii) tests using two or more independent loadingsystems. In the first category the biaxial stress ratiodepends on specimens 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.
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  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). 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)
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 cur