Int J Fract (2008) 149:119–141DOI 10.1007/s10704-008-9220-8

ORIGINAL PAPER

Prediction of initiation and growth of single leveldelaminations in a transversely loaded compositespecimen using fracture mechanics

Zoltan Mikulik · Donald W. Kelly ·B. Gangadhara Prusty · Rodney S. Thomson

Received: 31 October 2007 / Accepted: 17 May 2008 / Published online: 10 July 2008© Springer Science+Business Media B.V. 2008

Abstract The behaviour of a composite test specimen with an embedded delaminationsubjected to transverse tension has been investigated through experimental testing and finiteelement (FE) analyses. The testing program consisted of specimens in two geometrical con-figurations; square and rectangular delamination. The initiation and growth of the delamina-tion was numerically predicted by fracture mechanics. FE models were analysed with bothMSC.Nastran and Abaqus FE codes. The MSC.Nastran model was used to calculate strainenergy release rates employing a crack tip element methodology. The Abaqus model wasevaluated using the virtual crack closure technique. Both approaches accurately predictedfailure initiation locations as observed in the test specimens. Failure loads were also wellpredicted. The mode mix at the crack tip in the proposed specimen was found to be similarto the mode mix expected in a conventional in-plane compression specimen.

Keywords Composites · Fracture mechanics · Energy release rate · Delamination · Mixedmode fracture · Crack tip element · Virtual crack closure technique

1 Introduction

Delamination is an important failure mode in carbon fibre reinforced laminated compositesand can result from manufacturing imperfections, foreign object impact, or at free edgesdue to mismatch in properties of the individual layers. Delaminations can cause a significantdegradation of stiffness and strength of a composite part. In composite structures subjected totensile loading, matrix cracking and fibre breakage play a significant role, while delamination

Z. Mikulik · D. W. Kelly · B. G. Prusty (B)School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW,2052 Australiae-mail: g.prusty@unsw.edu.au

R. S. ThomsonCooperative Research Centre for Advanced Composite Structures Limited, 506 Lorimer Street,Fishermans Bend, Melbourne, Vic., 3207 Australia

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is a critical parameter in compression (Pavier and Clarke 1995). With the increased use ofcarbon fibre reinforced plastics in aircraft structures, it is essential for numerical analysesto accurately characterise delamination initiation and progression. Widely accepted method-ologies for predicting the onset and growth of this failure mechanism are based on fracturemechanics. The approaches consist of determining a total strain energy release rate (SERR)along a delamination front and the mode mix. The mode mix is defined as a ratio of ModeI (opening mode), Mode II (in-plane shearing mode), and Mode III (out-of-plane shearingmode) to the total SERR. These are subsequently compared to a critical SERR value, GC ,coupled with an appropriately formulated mixed mode failure criterion. An essential require-ment for all fracture mechanics methodologies is a pre-existing crack or imperfection witha finite length. The onset of the crack growth must be initiated from a crack-like flaw sinceSERR vanishes at zero crack length. In composite damage tolerance design and analysismanufacturing flaws and/or in-service damage manifested as interlaminar cracks are almostalways assumed (Rousseau 2003).

Numerous analytical fracture mechanics based methods have been proposed to determineSERRs and their components. A commonly employed approach is the virtual crack closuretechnique (VCCT) which was first developed by Rybicky and Kanninen (1977). Alterna-tive general methods for prediction of the SERR are the so-called crack tip element (CTE)methodology proposed by Davidson (Davidson et al. 1995; Davidson 1996) or an approachdeveloped by Williams (Williams 1988; Yap et al. 2002). Williams’ theory is based on lin-ear elastic fracture mechanics in which the intact structure is separated into substructuresadjacent to the crack plane. Section loads in the substructures, distributed according to theirstiffness, alter the displacement state compared to the intact region. The transition from onedisplacement condition to the other at the crack front is used for the calculation of the SERR.Mode I delamination is represented by pairs of moments and transverse shear forces actingin opposite directions. Mode II is obtained when the curvatures in two delaminated substruc-tures are identical. The VCCT and CTE approaches are used in this paper and are discussedin detail in Sect. 2.

Besides fracture mechanics, there are alternative numerical formulations to predict theonset and growth of delaminations. A micromechanical 3D approach was proposed by Liet al. (2003) who used the Strain Invariant Failure Theory (SIFT) developed by Gosse andChristensen (2001). It is based on a model that predicts failure initiation when the dilatational(volumetric) or distortional (equivalent) effective strain exceeds a critical value. The meth-odology includes a global three-dimensional finite element (FE) analysis on a ply-by-plybasis. Unlike fracture mechanics methodologies, an initial delamination or disbond is notrequired, thus the SIFT approach is capable of the analysis of pristine composite structures.To date, the use of SIFT is relatively new and requires further validation. In addition, it isbased on pre-determined element size and localised solid ply-by-ply FE modelling that canbe computationally very expensive for large scale analysis.

Delamination initiation and growth can additionally be modelled by cohesive elementswhich govern opening stresses and displacement at a delamination interface (Camanho andDavila 2002). The cohesive element approach incorporates damage initiation by a strength-based criterion and propagation is controlled by fracture mechanics. In general, a cohesivezone is assumed to support a nominal traction field in both normal and tangential directions.The response of cohesive elements is described through a constitutive law (Chowdhury andNarasimhan 2000). Cohesive elements are limited to very fine mesh size and can produceunacceptably inaccurate predictions when large elements are employed (Alfano and Crisfield2001).

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Prediction of initiation and growth of single level delaminations 121

A considerable amount of work has been conducted into failure predictions in laminatedcomposites subjected to axial compression using non-linear FE analyses and in some casescoupled with the above mentioned numerical methodologies. Single level delamination isdiscussed by various researchers such as Pavier and Chester (1990), Greenhalgh (1993),Bolotin (1996), and Short et al. (2001, 2002). Publications dealing with multiple delam-inations include Larsson (1991), Kutlu and Chang (1995a,b), Kouchakzadeh and Sekine(2000) and recently Cappello and Tumino (2006). Compression tests address an importantfailure mode in aircraft structures but can be very sensitive to manufacturing imperfectionsor test setup misalignment. Consequently, this can affect delamination growth behaviour andresidual strength of the specimens or increase scatter of the results. Failure of compressivecoupons is a sudden and catastrophic mode. The buckling mode and failure load are affectedby the specimen geometry, delamination length and depth (Short et al. 2002). Global buck-ling occurs when the sub-laminates above and below the delamination buckle in the samedirection. In local buckling, the more flexible sub-laminate buckles out of plane causingdelamination opening.

In this work, alternative single level delamination specimens were designed and tested intransverse tension. The experimental method was developed to substitute for a typical com-pression test, while keeping comparable delamination behaviour and mixed mode growththat occurs in the locally buckled compressive specimen. The objective of this research wasto validate computationally efficient fracture mechanics based approaches to estimate thefailure load and the location at which the onset of delamination occurs for use in the designenvironment.

Additionally, relatively few papers address the influence of mesh size and mesh refinementon the computation of SERR. Tay et al. (1999) presents a convergence study for the VCCTand crack closure technique which shows that a symmetric crack tip mesh is relatively insen-sitive to mesh refinement. The current research outlines discrepancies when mesh refinementis applied to VCCT and CTE FE models and the effect on the resulting prediction of SERRsand failure initiation loads.

2 Theoretical background

2.1 Crack tip element methodology

The CTE approach is a computational methodology to predict delamination growth developedby Davidson (Davidson et al. 1995; Davidson et al. 2000; Davidson 2001). The methodologywas successfully applied to various standardised fracture mechanics coupon specimens suchas the Mode I double cantilever beam, the Mode II end notch flexure, and the mixed modebending specimens. Further evaluation included the analysis of hat stiffened panels. The CTEapproach is based on a set of equations that yields total SERR and the mode mix from theknowledge of the forces and moments in the vicinity of the crack tip (Davidson 2001). Thegeneric three-dimensional CTE with force and moment resultants is shown in Fig. 1. Theelement uncracked region dimension is denoted b while crack region length is a. The totalthickness of the CTE, denoted as t , is a summation of thicknesses of lower sub-laminate, t2,and upper sub-laminate, t1. Generic definition of the CTE assumes that dimensions a, b andthe width of the element, W , are considerably larger than thicknesses t1, t2 or t . The coordi-nate system origin is defined at the crack tip at the midplane of the uncracked region. Sincethe CTE methodology developed here is to be employed with the MSC.Nastran FE program,the z-axis of the coordinate system has been inverted compared to the original formulation

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Fig. 1 Definition of the 3D CTE

x

yz

21M

26N

11N

16N

u6N

u1M

u1N

11M

21N

presented in Yu and Davidson (2001). By this modification, plies of the laminate are num-bered from the bottom surface which is consistent with the numbering of the MSC.Nastranlayered composite element property (PCOMP) card definition.

The total energy release rate and the three fracture modes are determined as (Davidson etal. 2000):

Gt = 1

2

[(�Ni�ε0

i + �Mi�κi)

p=1 + (�Ni�ε0

i + �Mi�κi)

p=2

], i = 1, 2, 6 (1)

G I = 1

2

[−√c11 Nc sin � + √

c22 Mc cos (� + �)]2 (2)

G I I = 1

2

[√c11 Nc cos � + √

c22 Mc sin (� + �)]2 (3)

G I I I = Gt − G I − G I I (4)

For detailed derivation of Eqs. 1–4, refer to Davidson (2001). To calculate the total energy re-lease rate, Gt , at any location along the delamination front plate theory forces, {N1, N2, N6}p ,and moments, {M1, M2, M6}p , are obtained for the upper sub-laminate (denoted with a sub-script p = 1) and the lower sub-laminate (denoted with a subscript p = 2). These are takenfrom the centroidal points of all quadrilateral elements located directly ahead and behindthe delamination or debond front. Values of �N and �M are the differential quantities ofthe in-plane forces and moments calculated from the cracked and intact regions. The ModeI and Mode II components are derived from the crack tip force, Nc, and moment, Mc. Anon-classical mode mix definition, designated as � in Eqs. 2 and 3, is dependent on thethickness ratio of the upper and lower sub-laminates and is given by (Davidson 2001):

� =⎧⎨⎩

−24 η < −0.46860.409η − 41.738η3 if −0.468 < η < 0.46824 η > 0.468

⎫⎬⎭ (5)

where

η = log10t2t1

(6)

The CTE numerical methodology has been integrated into a post-processing tool developedby Cooperative Research Centre for Advanced Composite Structures Limited (CRC-ACS).The tool is incorporated into MSC.Patran pre- and post-processing software. It is an analyticalsemi-automatic program written in Patran Command Language (PCL) and FORTRAN. The

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Prediction of initiation and growth of single level delaminations 123

program is based on a global-local modelling philosophy, which has the capability to iden-tify critical failure regions in composite structures and perform an assessment of compositebonds and delaminations.

2.2 Virtual crack closure technique

The most commonly employed fracture mechanics based approach in predictive failure anal-ysis of composite structures is VCCT. The technique and its applications are extensivelycovered by Krueger (2004). This method originated from the finite crack extension methodand the virtual crack extension method firstly discussed in the mid 1970’s (Hellen 1975). TheVCCT methodology, which requires only a single FE analysis, is based on the assumptionthat the energy released when a crack is extended is identical to the energy required to closethe crack. Additionally, the single-step method also presumes that a crack extension of �adoes not significantly alter the state of the crack tip.

The technique uses nodal forces at the delamination front and the displacements behindthe delamination front to determine the SERR components. Derivation of the equations tocalculate these quantities for three-dimensional plate/shell problems employing two differentFE modelling approaches is presented by Wang and Raju (1996). In the first approach, thenodes of the upper and lower sub-laminate at the crack front are constrained in all six degreesof freedom. The second technique allows the crack front nodes to have independent rotation;restraining only translational degrees of freedom. The later technique proved to realisticallysimulate behaviour at the delamination front and therefore yielded more accurate SERRs(Wang and Raju 1996). The SERR components for four-noded shell elements using thismodelling approach are determined as:

G I = − 1

2�AZLi (wLl − wLl∗) (7)

G I I = − 1

2�AX Li (uLl − uLl∗) (8)

G I I I = − 1

2�AYLi (vLl − vLl∗) (9)

where according to Fig. 2, �A is the virtually closed area; X Li , YLi and ZLi are the forcesat the crack front in the global x , y and z-directions, respectively. Corresponding globaldisplacements behind the crack front at the upper sub-laminate are denoted as uLl , vLl andwLl , whereas displacements at the lower sub-laminate are designated as uLl∗ , vLl∗ and wLl∗ .For a geometric non-linear problem these forces and displacements must be transformed toa local coordinate system.

The total strain energy release rate is calculated as a summation of three fracture compo-nents:

Gt = G I + G I I + G I I I (10)

The VCCT is applicable to both three-dimensional plate/shell models and solid models.Krueger and O’Brien (2001) presented a hybrid shell/3D modelling technique for whichsolid brick elements were employed only in the close vicinity of the crack tip. This combinedthe accuracy of the full three-dimensional solution with the computational efficiency of aplate/shell FE model. In the work presented in this paper, continuum shell elements wereused in the VCCT numerical simulations.

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Fig. 2 VCCT for shell models

Fig. 3 Test specimen geometry

3 Structural testing program

3.1 Specimen geometries and manufacturing

The assessment of the accuracy of the CTE and VCCT formulations involved an evaluationof SERR for single level delaminations. The geometry of the specimens developed for thisresearch is presented in Fig. 3. The flat composite plates were 130 mm×130 mm with thenominal thickness of 4.4 mm. The specimens were fabricated with Cytec bi-directional plainweave T300/970 carbon fibre reinforced epoxy prepreg. The material properties were pro-vided by the industrial partner of CRC-ACS which are presented in Table 1. For the analyses,it was assumed that the out-of-plane shear moduli were equal to the in-plane shear modulus.

All plies were cut according to the desired orientations having the initial dimensionsof 150 mm×150 mm. Specimens were hand laid up in a 20-ply [0/90, ± 45, ± 45, 0/90,0/90, ± 45, ± 45,0/90, 0/90, ± 45]S configuration. The first 16 plies were placed on aTeflon-coated caul plate. Subsequently, the delamination was established by a 0.05 mm thickAirtech Wrightlon 5200 high performance fluoropolymer release film cut to the requiredshape. The location of the delamination insert was marked on the lay-up tool and the speci-mens themselves. The remaining four plies were then laid over the Teflon insert. In this study,two delamination configurations were considered: square and rectangular. The rectangulardelamination aspect ratio was selected as 1.0:1.5, keeping the area of delaminations identical

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Prediction of initiation and growth of single level delaminations 125

Table 1 Material properties of T300/970

Material property Value Unit

Longitudial Young’s modulus, E11 55,840 MPaTransverse Young’s modulus, E22 55,840 MPaPoisson’s ratio, V12 0.06In-plane shear modulus, G12 3,650 MPaNominal ply thickness 0.22 mmCritical energy release rate for Mode I, G I C 0.45 kJ/m2

Critical energy release rate for Mode II, G I I C 2.46 kJ/m2

in both configurations (4,900 mm2). Thus, the embedded square delamination geometry haddimensions of 70 mm×70 mm and rectangular delamination 57.2 mm×85.7 mm.

Following the lay-up, the specimens were covered with a layer of release film and breathercloth. Finally, the vacuum bag with installed vacuum fitting was placed over the specimenand sealed. The bag was checked for any leaks. The test panels were cured in an autoclaveat 177 ± 4 ◦C and the pressure of 610 ± 10 kPa for 2 h. After curing, the reference markswere used to trim the panels to their final dimensions. The testing program consisted of sixspecimens of each configuration. Two concentric bolt holes were introduced at the locationsshown in Fig. 3 using a specially designed jig. The first hole with diameter of 10 mm wasdrilled through the thickness of the flat plate, whereas the later 20 mm bolt hole was preciselydrilled by a hole-saw only up to the Teflon insert. This enabled a bolt and a washer to beused to introduce a transverse tension load at the delamination interface. Prior to testing, thepresence of undesired defects was checked using the ultrasonic C-scan technique. The non-destructive inspections (NDI) showed no flaws or voids and confirmed the correct locationof the embedded delamination in all specimens.

3.2 Test setup and procedure

The specimen was designed to be clamped onto the fixture by two steel plates, as shownin Fig. 4. The specimen was placed in the test fixture after inserting a loading bolt with awasher. It was precisely aligned to the pre-set position in order to ensure consistent loadingand clamping conditions for all tested specimens. The clamping regions were measured as90 mm in a longitudinal direction by 10 mm in a width direction. Due to a size limitation ofthe test fixture, in reality, the right clamping region was found to be 12 mm in width. The testassembly was then installed in the testing machine. Two 30 mm linear variable displacementtransducers (LVDTs) were attached to the test fixture by magnetic grips at the diagonal cor-ners. These were used to increase accuracy of displacement measurements. The entire testingsetup is presented in Fig. 5.

The test was performed in the Solids Laboratory at the University of New South Wales.Testing of the specimens was carried out using an INSTRON 8504 universal testing machinewith a load cell of 5 kN capacity. Tests were conducted at room temperature dry (RTD) con-ditions. Testing was performed in displacement control at a rate of 0.1 mm/min. The loadand out-of-plane displacements were monitored in real-time during the tests. The specimenwas observed carefully during testing for any audible cracking. Test specimens were gener-ally tested until ultimate pull-through failure. Subsequently, all specimens were inspected bynon-destructive means using C-scan technology.

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Fig. 4 Clamping and loading of the specimen

Fig. 5 Test setup

4 Numerical analysis

4.1 CTE numerical model

FE models for the CTE methodology were created using MSC.Patran 2005r2 software. Dou-ble plate FE models with four-noded QUAD4 elements were implemented. Three differentFE models, with various levels of crack tip element mesh refinement, were generated. Thenominal element edge lengths of these FE models were 2.5, 1 and 0.055 mm. The final FEmodel had the edge length equal to 25% of the single ply thickness as recommended for con-verged predictions by Davidson et al. (1995). Previous work (Mikulik et al. 2007) showed thatthe CTE methodology strongly depends on mesh size at the crack front. It was demonstratedthat accurate failure predictions can be achieved by linear extrapolation of two numericalestimates. This approach has been used in this research to predict the onset of embeddeddelamination growth.

Shell elements were located on the physical midplanes of the upper and lower sub-lami-nates. The element connections were modelled with RBE2 rigid bar elements, joining all sixdegrees of freedom. This definition of the RBE2 connections retained interface compatibil-

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Prediction of initiation and growth of single level delaminations 127

ity by tying displacements and rotations such that both sub-laminates deformed as a singlelaminate. The rigid connections were established in a way that the upper sub-laminate nodeswere dependant on the lower sub-laminate nodes. The kinematic constraints are given by thefollowing set of equations:

u1,mx −

(t12

)ψ1

y = u2,mx +

(t22

)ψ2

y (11)

u1,my −

(t12

)ψ1

x = u2,my +

(t22

)ψ2

x (12)

u1,mz = u2,m

z (13)

ψ1x = ψ2

x (14)

ψ1y = ψ2

y (15)

ψ1z = ψ2

z (16)

where superscripts 1 and 2 refer to the upper sub-laminate and the lower sub-laminate,respectively, superscript m refers to the sub-laminate midplane, ux , uy , uz are transla-tional displacements in the respective directions, ψx ,ψy,ψz are rotations about x , y andz-axes, respectively, and t1 and t2 are the corresponding thicknesses of upper and lowersub-laminates.

Even though contact was not expected, gap elements were used between the delaminatedsub-laminates to prevent physically inadmissible interpenetration of the elements during theanalysis. The FE modelling technique used for the rectangular delamination configuration isillustrated in Fig. 6. The baseline rectangular delamination FE model (2.5 mm) consisted of6,088 nodes, 5,852 quadrilateral elements, 895 bar elements and 2,136 RBE2 elements. Thesquare delamination model comprised of 5,400 nodes, 5,120 quadrilateral elements, 2,183bar elements and 1,296 RBE2 elements. The total degrees of freedom of the refined models

x

z

Intact region Delaminated region

x

y

Not to scale

GAP element

Uppersub-laminate

shellelements

Lowersub-laminate

shellelements

RBE2 element –dependent node

Fig. 6 Modelling of the rectangular delamination MSC.Nastran FE model

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128 Z. Mikulik et al.

Fig. 7 Applied boundaryconditions

Boundary

Y

X

condition(123) applied at nodes

Out of planedisplacement applied

at nodes

1

3

1

2

1

3 2

Analytical rigidbody

Uppersub-laminate

Lowersub-laminate

Not to scale

Fig. 8 Modelling of the rectangular delamination Abaqus FE model

was limited by applying the mesh refinement only locally in the vicinity of the delaminationfront. It was important to ensure that the shell element orientations were in agreement with theCTE definition, thus, all sign conventions for forces and moments were carefully checked.Inconsistency in orientations would yield incorrect calculation of SERR. Both geometricalconfigurations contained four plies for the upper sub-laminate and 16 plies for the lowersub-laminate.

The clamping area was modelled asymmetrically as per the test conditions with the trans-lational degrees of freedom of all nodes corresponding to the location of the clamping platesrestrained. The applied out-of-plane displacement of magnitude 3 mm was initially evenlydistributed over the entire region which geometrically represented the loading bolt. However,it was found that this boundary condition was overly stiff and did not represent the physi-cal behaviour of the contact between the bolt and the upper sub-laminate. The tendency ofthe loaded portion of the upper sub-laminate and the washer to bend was confirmed by FEanalysis. Therefore, transverse displacement was applied at the inner nodes only as shownin Fig. 7. This FE model provided better correlation with test load-displacement behaviour.

Models were run using MSC.Nastran 2005r2 non-linear solution sequence 106 (SOL106)with a full Newton-Raphson procedure and default convergence residual criteria. The initialload increment was defined as 5%. FE models were run to the full displacement of 3 mm.

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Prediction of initiation and growth of single level delaminations 129

Locations ofboundaryconditions

Applieddisplacement

Bonded region Initially bonded region

Delaminated region

1

2

23

1

Fig. 9 Meshing, contact definitions and boundary conditions of the FE model

4.2 VCCT numerical model

FE models for VCCT evaluation were created in Abaqus/CAE 6.6-3 pre- and post-processingsoftware. The VCCT has been commercially implemented into an Abaqus add-on modulecalled VCCT for Abaqus. It provides simulation capabilities for prediction of the onset andpropagation of interlaminar fracture in laminated composite materials. The continuum three-dimensional FE model and its cross-sectional illustration are shown in Fig. 8. It consisted ofthree parts: upper sub-laminate, lower sub-laminate and analytical rigid body. The rigid bodyrepresented a contact face of the loading bolt and the washer. Surface-to-surface interactionwas also generated between the rigid body and the bolt region at the upper sub-laminateto represent the physical contact during testing. In all contacts in the Abaqus FE models,the rotational degrees of freedom of the nodes that constitute the interface surface were notconstrained between the master-slave nodal pair.

The sub-laminates were connected using another surface-to-surface interaction at the ini-tially bonded and delaminated regions that are depicted in Fig. 9. The initially bonded regionidentified a part of the FE model where crack propagation was considered. During analysis,the constraints between nodal pairs are released when the delamination growth failure crite-rion is satisfied. The failure criterion is discussed in the following section. The delaminatedregion represented a precise size and location of the artificial delamination. The contact pairswere defined with the upper sub-laminate as a slave region. The remaining part, designated asthe bonded region, was constrained by a TIE contact creating a surface-to-surface connectionfor the duration of the simulation. The translational degrees of freedom of the slave nodalpoints were dependant on the corresponding master nodes. This contact definition satisfiedphysical interface compatibility. Note that a three-dimensional FE model was used so thatall constraints were applied at the physical interface not at the midplane of shell elements.

The 3D FE model was meshed by 8-noded continuum shell elements with reduced inte-gration (SC8R). These elements provide the efficiency of conventional shell elements withthe advantages of three-dimensional elements, such as generation of boundary conditions andcontact interactions at the physical interfaces. Furthermore, SC8R elements allow rotationsof interfacial nodes in each sub-laminate ahead and behind the crack front. This has beenfound to be the preferable modelling technique to yield converged SERR results (Glaessgenet al. 2002). FE models with two mesh densities were generated. A baseline model had the

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nominal element edge set to 2 mm and mesh refinement was created by halving the nominalelement edge. In total, the square delamination FE model consisted of 21,661 nodes and12,521 hexahedral elements, while the rectangular delamination model consisted of 22,126nodes and 12,807 elements. In the through-the-width direction, both models had two ele-ments in the lower sub-laminate and one element in the upper sub-laminate. The numericalmodel is shown in Fig. 9.

The transverse loading was modelled by assigning the displacement at the referencepoint of the rigid body. Exact modelling of the physical contact improved representationof the real loading case. Even though there was a slight difference in the modelling of thetransverse displacement in the two FE models, it is shown later that numerical predictionsof the load-displacement curves correlated very well. To simulate the test fixture clampingof the specimen, boundary conditions restraining all translational degrees of freedom wereapplied to the highlighted regions shown in Fig. 9. The clamped boundary conditions in theAbaqus model were applied at the surfaces of the specimen, which closely represented the testconditions, while in the MSC.Nastran model they were applied at the sub-laminate midplanelocations.

Geometrical non-linear analyses were run in Abaqus Standard 6.6-3 using the automaticincrementation mode with the maximum increment set to 1%. To improve the convergencerate of the model, global stabilisation using an energy dissipation fraction of 1 × 10−6 wasused. Comparing static dissipation energy and total strain energy for the whole model indi-cated that the global stabilisation was appropriate and did not significantly over-damp theFE model.

4.3 Failure criterion

In order to determine the onset of crack propagation, the linear mixed-mode failure criterionwas implemented in both FE approaches. This was given by:

G I

G I C+ (G I I + G I I I )

G I I C= 1 (17)

where G I , G I I , and G I I I , are the SERR components calculated in the Mode I, Mode II andMode III, respectively. Fracture toughness of the material system in Mode I, G I C , was deter-mined by double cantilever beam (DCB) tests. Mode II critical SERR, G I I c, was obtainedby end notched flexure (ENF) tests.

VCCT for Abaqus has the capability to predict irregular crack growth. The built-in sub-routines calculate three fracture components of the SERR at each increment for every nodalpair at the crack front. These are measured against the fracture toughness of the laminateusing the mixed-mode criterion implemented by Eq. 17. When the criterion is satisfied, thepropagation occurs by releasing the constraint for the failed nodal pair. A new crack front isformed and the entire process is repeated in a subsequent load increment.

5 Results and discussions

5.1 Experimental results

Experimental load-displacement curves for the square delamination specimens, shown inFig. 10a, revealed very consistent non-linear behaviour with increasing magnitude of tan-gent stiffness due to membrane stiffening. The occurrences of crack growth initiation were

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Prediction of initiation and growth of single level delaminations 131

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

Displacement (mm)

Lo

ad (

kN)

Square 1 Square 2

Square 3 Square 4

Square 5 Square 6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

Displacement (mm)

Lo

ad (

kN)

Rectangular 1Rectangular 2Rectangular 3Rectangular 4Rectangular 5Rectangular 6

(a) (b)

Fig. 10 Experimental load-displacement plots for (a) square delamination and (b) rectangular delaminationspecimens

Table 2 Summary of the experimental results

Specimen Experimental crackinitiation (N)

Specimen Experimental crackinitiation (N)

Square 1 880 Rectangular 1 500Square 2 850 Rectangular 2 400Square 3 950 Rectangular 3 420Square 4 870 Rectangular 4 480Square 5 790 Rectangular 5 510Square 6 880 Rectangular 6 600Average 870 485Standard deviation (N) 51.77 71.48Coefficient of variation (%) 5.95 14.74

clearly identified by sudden load drops. The onset of the crack growth did not catastrophicallydegrade the load carrying capability of the specimens since the load continually increaseduntil subsequent delamination growth occurred. Failure of the specimens occurred under theloading bolt characterised by pull-through failure of the laminate.

Experimental results for rectangular delaminations, presented in Fig. 10b, were not asregular as the square delaminations. Specimens denoted as Rectangular 1 and Rectangular2 exhibited noteworthy load flattening which corresponded to small continuous cracking.Crack initiation of the remaining specimens was detected by a single audible crack followedby a visible load drop. Comparison of the two charts in Fig. 10 reveals that the onset ofcrack growth of the rectangular delamination panels occurred at lower load levels than forthe square delamination specimens. A summary of test observations is presented in Table 2.The average crack initiation load was determined to be 870 N and 485 N for the square andrectangular configurations, respectively.

5.2 Load versus displacement comparison

The numerical results are compared with a typical load versus displacement experimental plotin Fig. 11. Both FE approaches exhibited almost identical initial stiffness and displayed simi-lar global behaviour to the test observations. The Abaqus VCCT model correctly captured thenon-linear region up to delamination initiation followed by a sudden load drop and a region ofload increase up to subsequent crack advancements. Since crack propagation was not simu-lated in the CTE FE models, this phenomenon was not captured. The predicted stiffness for thesquare delamination specimen was higher than the test observations. Although the deviation

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132 Z. Mikulik et al.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

Displacement (mm)

Lo

ad (

kN)

Square 1

CTE analysis

VCCT analysis

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

Displacement (mm)

Lo

ad (

kN)

Rectangular 1

CTE analysis

VCCT analysis

(a) (b)

Fig. 11 Experimental and numerical load versus displacement plots for (a) square and (b) rectangular delam-ination models

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2

Displacement (mm)

Lo

ad (

kN)

2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Displacement (mm)

Lo

ad (

kN)

1mm FE model

2mm FE model

1mm FE model

2mm FE model

(a) (b)

Fig. 12 Abaqus/VCCT load-displacement predictions for (a) square and (b) rectangular delamination models

from the experimental load-displacement curve was evident due to the discrepancy in stiffnessbetween 0 and 100 N, the crack initiation load was satisfactorily captured. For the rectangulardelamination specimen, the numerical and experimental stiffness matched very well.

5.3 Mesh refinement effects

The impact of mesh refinement on the numerical predictions is discussed in the followingsection. The results of Abaqus VCCT models meshed with 1 mm and 2 mm element sizeare compared in Fig. 12. The refined FE models were analysed only slightly beyond crackinitiation, while the 2 mm models were run up to the third crack propagation phase. The ini-tial stiffness of both models matched well. The phenomenon of increasing load levels aftercrack initiation was observed in the numerical results. For the square delamination models,it was found that crack initiation occurred at 857 N in the model with 1 mm mesh size andat 811 N in the model with 2 mm mesh size. Similarly, the rectangular model predictionsincreased when the crack front mesh size was refined. The 2 mm model crack initiation wasdetermined to be 447 N while the failure prediction of the 1 mm FE model was 464 N. In allcases, the discrepancy between numerical predictions was in the range of approximately 5%.Post-initiation tangent stiffness of the original and refined models was similar.

An additional preliminary study on the effect of modelling technique on calculated SERRswas conducted. The research of Glaessgen et al. (2002) showed that the discrepancy betweena plate FE model and a 3D brick model could be up 27% depending on the mesh size and slen-derness ratio. To address the impact of the modelling approach on the predicted failure load,

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Prediction of initiation and growth of single level delaminations 133

y = 0.3073x + 0.8377

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5 2 2.5

Crack tip element size (mm)

Fai

lure

pre

dic

tio

n (

kN)

3

y = 0.0847x + 0.5033

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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0 0.5 1 1.5 2 2.5

Crack tip element size (mm)

Fai

lure

pre

dic

tio

n (

kN)

3

(a) (b)

Fig. 13 MSC.Nastran/CTE two-point h-convergence analysis for (a) square and (b) rectangular delaminationmodels

y = 0.2726x + 0.91R2 = 0.9906

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8(a) (b)

0 0.5 1 1.5 2 2.5 3

Crack tip element size (mm)

Fai

lure

pre

dic

tio

n (

kN)

y = 0.0966x + 0.4786R2 = 0.9912

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3

Crack tip element size (mm)

Fai

lure

pre

dic

tio

n (

kN)

Fig. 14 MSC.Nastran/CTE three-point h-convergence analysis for (a) square and (b) rectangular delamina-tion models

the continuum shell model was converted to a full three-dimensional model. The failure ini-tiation between 1 mm continuum shell and 3D brick models differed by 8%. The results indi-cated that the discrepancy between the two numerical models reduced with mesh refinement.However, the analysis of composite 3D brick models with a fine mesh is impractical due tosignificant demands on the computational power. A balance between numerical accuracy andcomputational efficiency is important and therefore continuum shell approach was adopted.

All three MSC.Nastran/CTE numerical models displayed identical stiffness behaviourregardless the level of mesh refinement at the vicinity of the crack front. Unlike VCCT pre-dictions, CTE failure analyses showed a significant dependency on the mesh size. Crackinitiation estimates for the square delamination model decreased by almost 30% between the2.5 mm (1606 N) and 1 mm model (1145 N). The discrepancy for the rectangular delamina-tion FE model was calculated to be approximately 18%; 715 N for the 2.5 mm model and588 N for the 1 mm model. Further reduction of the crack initiation load was predicted withthe final (0.055 mm) model. The numerical estimates of the 0.055 mm model showed gooddegree of agreement with the test; 948 N for square delamination model and 476 N for therectangular delamination model.

In accordance with the approach previously developed by the authors (Mikulik et al.2007), an h-convergence study was conducted. Previous work showed that accurate fail-ure estimates could be determined by linear extrapolation of two sets of failure predictions.Numerical estimates from the 2.5 and 1 mm models were therefore used to predict a theoreticalzero element edge length failure initiation load. Results of the h-convergence extrapolationstudy, shown in Fig. 13, demonstrated that considerable improvements to accuracy could be

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134 Z. Mikulik et al.

Table 3 Numerical predictions for delamination growth initiation for the square delamination model

FE model Numericalprediction (N)

Difference to theaverage test value (%)

Abaqus/VCCT numerical methodology2 mm crack element 811 −6.781 mm crack element 857 −1.49

MSC.Nastran/CTE numerical methodology2.5 mm crack element 1606 84.601 mm crack element 1145 31.611/4 ply thickness (0.055 mm) 948 8.97h-convergence (2-points) 838 −3.68h-convergence (3-points) 910 4.60

Table 4 Numerical predictions for delamination growth initiation for the rectangular delamination model

FE model Numericalprediction (N)

Difference to theaverage test value (%)

Abaqus/VCCT numerical methodology2 mm crack element 447 −7.841 mm crack element 464 −4.33

MSC.Nastran/CTE numerical methodology2.5 mm crack element 715 47.421 mm crack element 588 21.241/4 ply thickness (0.055 mm) 476 −1.86h-convergence (2-points) 503 3.71h-convergence (3-points) 479 −1.24

achieved compared with single run predictions. The influence of the 0.055 mm model wasadditionally assessed in the three-point h-convergence predictions presented in Fig. 14. Thetheoretical zero element edge length failure initiation load was determined to be 910 N and479 N for square and rectangular delaminations, respectively. When compared to the base-line two-point h-convergence predictions, the three-point h-convergence estimate of failureinitiation increased by approximately 9% for the square delamination while in case of therectangular delamination a 5% reduction was found. The linear mesh size dependency wasstill valid confirmed by the R2 values of 0.99. Accuracy comparisons of all FE models areprovided in Tables 3 and 4.

Mesh refinement of the VCCT models caused a slight increase in the predicted failureload. In contrast, CTE models exhibited a large decrease of the failure initiation predictionsas the mesh was refined. These results indicate that a coarse mesh can yield slightly conserva-tive failure predictions when VCCT is employed, but can be very unconservative when CTEis used. The highest degree of accuracy and most consistency were delivered by the 1 mmVCCT FE models, under-predicting the average onset of crack initiation by a maximum of4.3%, and by the two CTE h-convergence analyses for which the predictions were within arange of −3.7–4.6%.

5.4 Distribution of SERR

Figures 15–18 show the distribution of the total SERR and its fracture mode componentsalong the right hand delamination boundary (refer to Fig. 3). The horizontal axis defines the

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Prediction of initiation and growth of single level delaminations 135

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode IMode IIMode IIITotal

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

(a) (b)

Fig. 15 SERR distribution estimated by VCCT for the square delamination at initiation load (a) 2 mm FEmodel: 811 N (b) 1 mm FE model: 857 N

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

(a) (b)

Fig. 16 SERR distribution estimated by CTE for the square delamination at initiation load (a) 2.5 mm FEmodel: 1606 N (b) 1 mm FE model: 1145 N

0

0.2

0.4

0.6

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0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode IMode IIMode IIITotal

(a) (b)

Fig. 17 SERR distribution estimated by VCCT for the rectangular delamination at initiation load (a) 2 mmFE model: 447 N (b) 1 mm FE model: 464 N

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

(a) (b)

Fig. 18 SERR distribution estimated by CTE for the rectangular delamination at initiation load (a) 2.5 mmFE model: 715 N (b) 1 mm FE model: 588 N

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136 Z. Mikulik et al.

Fig. 19 Failure initiationpredictions for (a) square and (b)rectangular delaminations

Delamination growth initiation

(a) (b)

normalised length where 0 corresponds to the upper edge of the delamination and 1 corre-sponds to the lower edge. The magnitudes of the SERR for the square delamination model inFig. 15 are presented at load increment 60 which corresponded to the predicted onset of thecrack growth of the baseline 2 mm model. Similarly SERR values of the rectangular delam-ination model in Fig. 17 are shown at the crack initiation load (increment 37) as estimatedby the baseline FE model.

For the VCCT, it is evident that mesh refinement process did not affect the calculated mag-nitude of the total SERR. The delay of crack initiation of the refined 1 mm models, foundin both delamination configurations, was caused by a slight difference in estimated modemixities. The G I /G I I mode mix ratio decreased with mesh refinement which eventuallyresulted in a reduction of failure indices. However, mesh refinement resulted in a significantincrease in the magnitude of the total SERR for the CTE models for both the square andrectangular delaminations. In refining the mesh from 2.5 mm to 1 mm, the peak total SERRvalue increased by approximately 40%, causing the significant decrease in the predictedfailure loads.

It was also observed that the maximum total SERR at which the onset of delamination waspredicted, as well as location of the peak value, for both VCCT and CTE methodologies wasalmost identical. The maximum SERR was consistently found to be approximately 0.8 kJ/m2

for the square delamination model and 0.7 kJ/m2 for the rectangular panel. Generally, thecalculated mode mix ratio also showed good agreement between baseline CTE and VCCTmodels.

5.5 Delamination initiation location and growth

Both FE analyses predicted the delamination to initiate at a similar location at the right edgeof the initial artificial delamination in the vicinity of the bolt hole. Delamination growth ini-tiation for two specimens is illustrated Fig. 19. Crack propagation analysis using the VCCTfor the square delamination specimen revealed a secondary initiation site at the bottom edge.This was predicted at a load of 935 N which corresponded to a transverse displacement of2.0 mm. For the rectangular configuration, delamination growth was predicted only at theright edge which was also confirmed by NDI. Qualitative comparisons of the numericaldelamination growth predictions with the C-scan images are presented in Fig. 20 and showstrong agreement.

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Prediction of initiation and growth of single level delaminations 137

Fig. 20 Qualitative comparisonof delamination growthpredictions from Abaqus/VCCTwith C-scan images from test

Specimen FEA C-scan

Squaredelamination

Rectangulardelamination

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1

Normalised length

Cra

ck p

ropa

gatio

n (m

m)

FE prediction Square 4specimen

Square 3specimen

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1

Normalised length

Cra

ck p

ropa

gatio

n (

mm

)

FE prediction

Rectangular 6 specimen

Rectangular 5specimen

(a) (b)

Fig. 21 Crack propagation comparison between test and Abaqus/VCCT for (a) square and (b) rectangulardelaminations

Predictions of delamination growth are also quantitatively compared with the actual NDImeasurements in Fig. 21. The x-axis of the charts represents normalised length at the initialcrack front location. Thus, it corresponds to a distance of 30 mm for the square delaminationspecimen and 36.4 mm for the rectangular delamination specimen measured from the rightedge of these specimens. The x = 0 indicates the upper edge of the specimen while x = 1refers to the bottom edge. Given the different lengths of the initial delaminations, the delami-nated regions are between 0.23 ≤ x ≤ 0.77 and 0.17 ≤ x ≤ 0.83 for square and rectangulardelaminations, respectively. The y-axis gives the crack extension at the given location. Theexperimental results indicated that asymmetric loading had a greater influence on crackextension in the rectangular delamination specimen. In this case the maximum extensionwas measured to be approximately 8.2 mm, while the maximum crack propagation for thesquare delamination was 7.4 mm. The overall delamination area was, however, larger for thesquare delamination specimen. The FE analyses under-predicted the actual crack propaga-tion length which was determined to be 6 mm in both configurations. Note that the maximumextension was shorter by approximately one row of elements since the element size in thenumerical models was 2 mm. It is believed that mesh refinements, causing significant increaseof computational run time, would improve the correlation with the test measurements. Thelocations of delamination were captured well, especially for the rectangular delaminationspecimens and the Square 3 specimen.

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138 Z. Mikulik et al.

Fig. 22 FE models and applied loading (a) transverse tensile case (b) in-plane compression case

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode IIITotal

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

Normalised length

SE

RR

(kJ

/m2 )

Mode I

Mode II

Mode III

Total

(a) (b)

Fig. 23 Variation of the SERR for (a) transverse tensile and (b) compression cases

5.6 Numerical comparison of the tensile and the in-plane compression case

A numerical study was conducted to demonstrate that the proposed transverse tensile testgenerates a similar mode mix at the crack front to an equivalent in-plane compression test.The investigation was based on an identical square delamination specimen as presented in thispaper with minor changes to ensure symmetrical loading. Thus, the transverse tensile loadintroduction location was shifted to the delamination centre and the specimen clamping wasapplied symmetrically. FE models, shown in Fig. 22, were created in Abaqus/CAE 6.6-3 andthe mode mix determined using the VCCT. The aim of this study was to compare the SERRsand mode mix of the specimen under in-plane compression loading in the post-bucklingregime with the specimen loaded in transverse tension.

The non-linear FE analysis of the compression specimen revealed local buckling of theupper sub-laminate. Consequently, in the post-buckling regime the increasing compressionload caused progressive crack opening until it reached the critical fracture toughness for agiven mode mix. Figure 23 shows the variation of the SERR along the crack front priorto crack initiation. The peak magnitude of the total energy release rate was found to be0.65 kJ/m2 for the transverse tensile case, which increased to 0.78 kJ/m2 in the in-plane com-pression model. The magnitude of the Mode I SERR showed excellent agreement betweenthe two models while an increased contribution of Mode II was identified in the compressionmodel. The contribution of Mode III was negligible in both cases.

Substituting G IG I C

= F I I and G I I +G I I IG I I C

= F I I I the failure criterion presented in Eq.17 can be expressed as a summation of opening and combined shear fracture mode failureindices as:

F II + F II I = 1 (18)

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Prediction of initiation and growth of single level delaminations 139

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

Fai

lure

ind

exMode I

Mode II+III

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalised length

Fai

lure

ind

ex

Mode I

Mode II+III

(a) (b)

Fig. 24 Fracture mode criticality for (a) transverse tensile and (b) compression cases

The fracture mode failure indices indicate criticality or relative contribution of the givenfracture mode to the prediction of failure initiation. Since Mode I fracture toughness is lowerthan Mode II, criticality of F II is higher than for the shear modes (F II I ). This indicatesthat when comparing transverse tensile and in-plane compression models, correlation of theMode I is the most critical factor. Figure 24 shows that Mode I contributes 90% to the failureinitiation index (F I = 1) in the transverse tensile case while a contribution of 85% wasdetermined in the in-plane compression case. The remaining fractions of 10% and 15% werecontributions of Mode II and Mode III for tensile and compression models, respectively.Thus, the numerical analysis confirmed a high degree of agreement of fracture mode criti-cality between the two FE models. On the other hand, the post-buckling deformations of twomodels were not identical which affects the crack tip stress field. Since differences betweenthe two loading cases were found, an experimental investigation should be conducted tovalidate the numerical simulations.

6 Conclusion

This paper presents the design, analysis and testing of an alternative composite specimencontaining an embedded delamination. The specimen is proposed as an analogous test torepresent similar crack front conditions to typical compression experiments, but without theinherent problems of compression testing. Specimens with square and rectangular delamin-ations were subjected to transverse tension. The results of the test were used to validate twofracture mechanics based approaches, CTE methodology using shell elements and VCCTusing continuum shell elements, for estimating the failure load and initiation location. Thepurpose of validation was to demonstrate that the two methods represent a balance betweencomputational efficiency and accuracy demanded in aircraft design.

Quantitative comparison of experimental and numerical results showed very good cor-relation in terms of failure load predictions. The results of the FE analyses indicated thatevaluation of the total SERR and its components using VCCT was not strongly sensitive tomesh refinements. Thus, a reasonably coarse mesh was adequate. FE models with coarsermesh gave slightly more conservative estimates of the failure initiation load as a result ofa minor change in the mode mix. The growth of the artificial delamination was accuratelycaptured in all cases.

In contrast to the VCCT, it was found that the CTE methodology was very sensitive tomesh size in the vicinity of the delamination front. The FE model with 2 mm and 1 mm meshsize significantly over-estimated the actual test delamination growth initiation load. Accurate

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140 Z. Mikulik et al.

predictions were limited to a fine crack tip element mesh or to h-convergence analysis. Thefailure load prediction approach based on linear extrapolation of results obtained by h-con-vergence presented in previous work was successfully validated. A high degree of agreementbetween numerical predictions and tests was achieved for both geometrical configurations.The maximum discrepancy between the test results and the estimates from CTE analyses withthe crack tip element size equal to one quater of the ply thickness was found to be less than9%. The failure initiation locations agreed with the VCCT predictions and test observations.

The numerical comparison study demonstrated that the mode mix in the vicinity of thedelamination front for in-plane compression load and transverse testing implemented in thisresearch showed satisfactory agreement. Excellent correlation was achieved for damage criti-cality where opening and combined shear mode failure indices differed by 5%. It is thereforeproposed that the transversely loaded specimen could be used as a test for resistance todelamination growth in laminates. This configuration provides a simpler testing and analysisenvironment than an in-plane compression specimen. Since differences in the post-bucklingdeformations and stress field in the vicinity of the crack tip were noted, further numericaland experimental investigations are required.

Acknowledgements This work was undertaken as a part of the research program in CRC-ACS. The authorswould like to acknowledge the support of CRC-ACS in providing a research scholarship for the first author.They also would like to express their appreciation to all personnel involved for their scientific contributionsand particularly to Dr Roger Li and Mr Luis Ramirez for the participation in the design and testing phase ofthe project.

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