3rd EASN Association International Workshop on Aerostructures PDF
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In te rn a tio ISSN 1757-9864 n Volume 5 Number 3 2014 a Volume 5 Number 3 2014 l J o u rn a l o f S tru International Journal of c tu International Journal of Structural Integrity ra l In Structural Integrity te g Number 3 rity 3rd EASN Association International Workshop on Aerostructures Guest Editors: Professor Mario Guagliano and Professor Spiros Pantelakis 169 Editorial advisory board 3rd EASN Association 170 Guest editorial International Workshop 171 Development of a cohesive zone model for three-dimensional simulation of joint de-bonding/ delamination under mixed-mode I/II fatigue loading on Aerostructures A. Pirondi, G. Giuliese and F. Moroni 187 Assessing the quality of adhesive bonded joints using an innovative neural network approach Guest Editors: Professor Mario Guagliano Christos Vasilios Katsiropoulos, Evangelos D. Drainas and Spiros G. Pantelakis and Professor Spiros Pantelakis 202 Chebyshev descriptors for SHM with acoustic emission and acousto ultrasonics Davide Crivelli, Mark Eaton, Matthew Pearson, Karen Holford and Rhys Pullin 214 Design, analysis and optimization of thin walled semi-monocoque wing structures using different structural idealization in the preliminary design phase Odeh Dababneh and Altan Kayran 227 Modelling of small CFRP aerostructure parts for X-ray imaging simulation Published in partnership with the V Kristina Bliznakova, Zacharias Kamarianakis, Aris Dermitzakis, Zhivko Bliznakov, Ivan Buliev o European Aeronautics Science Network and Nicolas Pallikarakis lu m e 5 N u m b e r 3 2 0 1 4 w w w .e m e ra ld in s ig Access this journal online h t.co www.emeraldinsight.com/ijsi.htm ISBN 978-1-78350-859-4 www.emeraldinsight.com m EDITORIALADVISORYBOARD Editorial D.Angelova L.Marsavina advisory board UniversityofChemicalTechnologyand UniversitateaPolitehnicaTimisoara,Romania Metallurgy–Sofia,Bulgaria JohnE.Moon CharisApostolopoulos QinetiQ,UK UniversityofPatras,Greece A.Navarro J.N.Bandyopadhyay UniversityofSeville,Spain 169 IndianInstituteofTechnology,India Sp.Pantelakis LeslieBanks-Sills UniversityofPatras,Greece Tel-AvivUniversity,Israel P.Peyre SimonBarter LALP/CNRS,France DSTO,Australia B.PurnaChandraRao ClaudioDalleDonne IndiraGandhiCenterforAtomicResearch(IGCAR), EADSDeutschlandGmbH,Germany India PaulodeCastro A.Pistek UniversidadedoPorto,Portugal BrnoUniversityofTechnology,CzechRepublic BahramFarahmand StephenReed TechnicalHorizonInc.,USA MinistryofDefence,DefenceScienceand TechnologyLaboratory,UK A.Giannakopoulos UniversityofThessaly,Greece R.Ritchie UniversityofCalifornia,Berkeley,USA M.M.I.Hammouda Al-AzharUniversity,Egypt HamidSaghizadeh TheBoeingCompany,USA SeungHoHan Dong-AUniversity,SouthKorea KojiTakahashi YokohamaNationalUniversity,Japan PeterHorst TechnischeUniversita¨tCarolo-Wilhelminazu V.Troshchenko Braunschweig,Germany NationalAcademyofSciences,Ukraine Y.H.Huh JaimeTupiassu´ PinhodeCastro KRISS,Korea PUC-Rio,Brazil MadabhushiJanardhana L.Wagner Directorate-GeneralTechnicalAirworthiness, TechnischeUniversita¨tClausthal,Germany RAAF,Australia GengShengWang RhysJones FOI,TheSwedishDefenceResearchAgency, MonashUniversity,Australia Sweden J.P.Komorowski AliYousefiani CNRC,InstituteforAerospaceResearch,Canada TheBoeingCompany,USA DanielKujawski WesternMichiganUniversity,USA G.Labeas UniversityofPatras,Greece InternationalJournalofStructural Integrity Vol.5No.3,2014 p.169 rEmeraldGroupPublishingLimited 1757-9864 IJSI Guest editorial 5,3 170 The 3rd International Workshop on Aerostructures of the European Aeronautics ScienceNetwork(EASN),foundedin2008asanindependentEuropeanAssociationfor coordinating and supporting the interests of the European universities and facilitate academia to perform funded research, was hosted by Politecnico di Milano on 9-11 October2013.Itwasincludedamongtheeventstocelebratethe150thAnniversaryof the foundation of PolitecnicodiMilano. The workshop was a successful event with about 120 participants from academia andindustry.Atotalof90paperswerepresented.Mostofthemweredevelopedinthe frameworkofrunningprojectsfundedinthe7thFrameworkProgramandwereobject ofinterestingdiscussions,spanningawidevarietyofmattersinaerostructuredesign: from composite materials to new coating processes as repairing techniques, from securityandreliabilitytocostefficiencyandmuchmore.Intotalscientificresultsfrom 27runningresearchprojects,werepresented,thusaccentingtheWorkshopasamajor Europeandisseminationeventfornewknowledgeandemergingtechnologiesrelatedto aerostructures. ThepresentspecialissueoftheInternationalJournalofStructuralIntegrityincludes aselectionofthepaperspresentedinashorterversionattheworkshopregardingthe subjects of this journal. They are representative of the high-scientific quality and technological merit of aeronautics research carried out inEurope. Wewouldliketothankthereviewers,fortheirpatienceandfortheircommentsand suggestions, andthe authors, for their valuablecontributions. Hoping that you will share thisview. ProfessorMario Guagliano Dipartimento di Meccanica, Politecnicodi Milano, Milano, Italy Professor Spiros Pantelakis University of Patras,Patras,Greece InternationalJournalofStructural Integrity Vol.5No.3,2014 p.170 ©EmeraldGroupPublishingLimited 1757-9864 DOI10.1108/IJSI-08-2014-0037 Thecurrentissueandfulltextarchiveofthisjournalisavailableat www.emeraldinsight.com/1757-9864.htm Development of a cohesive zone Development of a cohesive model for three-dimensional zone model simulation of joint de-bonding/ delamination under mixed-mode I/II 171 fatigue loading Received27February2014 Revised29April2014 Accepted12May2014 A. Pirondi and G. Giuliese Dipartimento di Ingegneria Industriale, Università di Parma, Parma, Italy, and F. Moroni Centro Interdipartimentale SITEIA.PARMA, Università di Parma, Parma, Italy Abstract Purpose–Inthiswork,thecohesivezonemodel(CZM)developedbysomeoftheauthorstosimulate thepropagationoffatiguedefectsintwodimensionsisextendedinordertosimulatethepropagation ofdefectsin3D.Thepaperaimstodiscussthisissue. Design/methodology/approach – The procedure has been implemented in the finite element (FE) solver (Abaqus) by programming the appropriate software-embedded subroutines. Part of the procedureisdevotedtothecalculationoftherateofenergyreleaseperunit,G,necessarytoknow thegrowthofthedefect. Findings – The model was tested on different joint geometries, with different load conditions (pure mode I, mode II pure, mixed mode I/II) and the results of the analysis were compared with analyticalsolutionsorvirtualcrackclosuretechnique(VCCT). Originality/value – The possibility to simulate the growth of a crack without any re-meshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elementsmakestheCZMattractivealsoforthefatiguecrackgrowthsimulation.However,differently from VCCT, three-dimensional fatigue de-bonding/delamination with CZM is not yet state-of-art in FEsoftwares. KeywordsFatigue,Delamination,Finiteelementanalysis,Cohesivezone,De-bonding PapertypeResearchpaper 1.Introduction Composite and hybrid metal/composite structures are nowadays present in several fieldsbesidetheaerospaceindustrythankstothecontinuousperformanceimprovement andcostreduction.Thisrequires,inturn,extensiveuseofadhesivebondingandamore and more sophisticated capability to simulate and predict the strength of bonded connections. For this purpose, analytical methods are being progressively integrated or replaced by finite element analysis (FEA). In engineering applications, it is well establishedthatfatigueistherootcauseofmanystructuralfailures.Inthecaseofbonded joints, fatigue life is related to the initiation and propagation of defects starting at free edgesofjoiningregionsorotherfeatures,suchasthrough-thicknessholes.Inthecaseof InternationalJournalofStructural composite or metal/composite joints, fatigue can start also from defects at the same Integrity Vol.5No.3,2014 pp.171-186 ThisworkwaspartiallysupportedbyEmilia-RomagnaRegionwithinPORFESR2007-2013and ©EmeraldGroupPublishingLimited 1757-9864 byConsorzioSpinner,Bologna,Italy,throughPhDprojectno.067/11. DOI10.1108/IJSI-02-2014-0008 IJSI locations cited above, then the crack may either run into the adhesive or become a 5,3 delamination crack. Especially in the case of damage tolerant or fail safe design, it is necessarytoknowhowcracks,oringeneraldefects,propagateduringtheservicelifeofa component. A numerical method able to reproduce three dimensionally the fatigue debondinginstructuresisthereforenecessarytoimprovetheirperformances. The relationship between the applied stress intensity factor and the fatigue crack 172 growth(FCG)rateofadefectisgenerallyexpressedasapowerlaw(ParisandErdogan, 1961). In the case of polymers, adhesives and composites, the relationship is traditionally written as afunction of the rangeof strain energy release rate (ΔG) as: da ¼BDGd (1) dN where B and d are the parameters depending on the material and mode mixity ratio, and a the defect length. In this simple form, the presence of a FCG threshold and an upperlimittoΔGforfracturearenotrepresentedalthough,whenneeded,expressions accountingfortheselimitscanbeeasilyfound(Curleyetal.,2000).Inthesameway,the influenceofthestressratio,R,ontheFCGratecanbeintroducedintoEquation(1)bya termderivedfromextensionsoftheParislawexpressedintermsoftherangeofstress intensity factor, ΔK (Formanet al.,1967). If a closed-form solution for the strain energy release rate as a function of crack length exists, then the number of cycles to failure comes out from the numerical integration between the initial crack length (a ) and the final crack length (a) of the 0 f inverse ofEquation(1)(Curleyetal.,2000;PirondiandMoroni,2009).Whenaclosed- form solution for the strain energy release rate does not exist, finite element (FE) simulation is commonly used to compute it. A stepwise prediction of crack growth is then carried out, each step corresponding to a user-defined crack growth increment. Tospeeduptheprocess,insomeFEsoftwaresthisprocedureisintegratedinspecial features (e.g. the *Debonding procedure in Abaqus®, where the strain energy release rate is obtainedusing thevirtualcrackclosure technique (VCCT). The cohesive zone model (CZM) is commonly used for the simulation of the quasi static fracture problems, especially in the case of interface cracks such as in bonded joints and delamination in composites (Hutchinson and Evans, 2000; Blackman et al., 2003; Li et al., 2005 among others). The possibility to simulate the growth of a crack withoutanyremeshingrequirementsandtherelativelyeasypossibilitytomanipulate the constitutive law of the cohesive elements makes the CZM attractive also for the FCGsimulation(MaitiandGeubelle,2005;RoeandSiegmund,2003;Muñozetal.,2006; Turon et al., 2007; Khoramishad et al., 2010,2011; Naghipour et al., 2011; Harper and Hallett,2010;BeaurepaireandSchuëller,2011;MoroniandPirondi,2012).InMaitiand Geubelle (2005), the damage of the cohesive element is related to both the monotonic quasi-staticloadingandthenumberofcycles.Inparticularfatiguecyclingaffectsthe tensile stiffness, K ,whichevolution is: 22 ds (cid:1) (cid:3) N (cid:2)b K ¼ 22 ¼(cid:2)g N s ¼(cid:2) f s (2) 22 dd f 22 a 22 22 whereN representsthenumberofcyclestodamageinitiationinthecohesiveelement, f β and α two parameters that can be calibrated by comparison between FE modelling and FCG experiments. Concerning interfaces Roe and Siegmund (2003), introduced a cyclic degradation Development of the monotonic cohesive strength based on a damage variable, D, representing of a cohesive theratiobetweentheeffective(damaged)andnominal(undamaged)cross-sectionofa zone model representative interface element. At the same time the damage variable D relates thecohesivezonetractionvector(T )withtheeffectivecohesivezonetractionvector ~ CZ T ,by the equation: CZ 173 T~ ¼ TCZ (3) CZ 1(cid:2)D The cyclic damage evolutionlaw is then: (cid:4) (cid:4)(cid:5) (cid:6) D_ ¼(cid:4)Du_(cid:4) T (cid:2) sf (4) dS smax smax;0 where Δu_ is the mixed mode equivalent displacement jump between crack surfaces, T the equivalent traction, σ ¼σ (1 − D) the maximum stress of the damaged max max,0 cohesivelaw,dStheaccumulatedcohesivelength,σfthecohesivezoneendurancelimit andσ themaximumstressofthecohesivelawpriortodamage.Inthisformulation max,0 thetwo parameters dS and σf have to be calibrated by FCG experiments. An approach similar to Roe and Siegmund (2003) was developed in Muñoz et al. (2006) where the robustness of the model in predicting crack growth rate was demonstrated, with an upper bound for the cohesive element length and number of cycles perincrement inorder to preservethe accuracy. A different approach was proposed by Turon et al. (2007): in this model the calibration of cohesive parameter for cyclic loading is not required. In fact a damage homogenisationcriterionisusedforrelatingtheexperimentalFCGrate,representedby Equation(1),withthedamageevolutionofthecohesiveelements.Inthiswayacycle- by-cycleFEanalysisisnotnecessaryfortheintegrationofdamagerate,whichmeansa significant computational time saving. However, only simple geometries where the strain energy release rate is not dependentfrom the cracklength, were treated. IntheworkofKhoramishadetal.(2010,2011),thedamage(D)evolutionwithrespect to the number of cycles is expressed in term of strain (or crack opening) by the equation: ( DD ¼ aðemax(cid:2)ethÞb emax4eth (5) DN 0 emaxpeth where e is the maximum principal strain in the cohesive element (therefore a max combination of the normal and shear component of strain), ε the threshold strain th (value of strain below which no damage occur) and α and β are material constants. The set of parameters ε , α and β has to be calibrated by comparison with th experimentaltests.Thefatiguedegradationdoesnotaffectthestiffnessofthecohesive element, but the value of tripping stress for damage initiation. ThemodelofTuronetal.(2007)wasrevisitedbyNaghipouretal.(2011)improving the cohesive zone area definition under mixed-mode I/II loading and the integration scheme of the cohesive law in the user-defined element (UEL) developed in the FEA softwareAbaqus®.Thisworkyieldedabetter,thoughnotfull,agreementbetweenthe IJSI FCG rate(B,dparametersinEquation(1))inputtotheanalysisand theFCG ratesin 5,3 outputwith respect to the work of Turon et al.(2007). A fatigue damage formulation that preserves the direct link with linear elastic fracturemechanicswaspresentedinHarperandHallett(2010),basedonstrainenergy releaserateextractionfromcohesiveinterfaceelements.Thisformulation,thoughvery practical from the computational point of view, requires a detailed understanding 174 ofthecohesivezonestressdistribution,thatisamuchfinermeshsizewithrespecttoa quasi-static analysis. In Beaurepaire and Schuëller (2011), a law for FCG has been developed including a memoryvariablethataccountsforthedegradationofthematerialunderalternatingload, similarly to Roe and Siegmund (2003). The variability of fatigue crack initiation and propagationwasaccountedforusingrandomcohesiveparametersgeneratedusingMonte Carlosimulation.Anextrapolationschemeisproposedtospeedupthesimulationtime, skipping cycle by cycle simulation. In fact, it is worth emphasising that in Roe and Siegmund(2003)andMuñozetal.(2006)damageevolutionissimulatedonacycle-by-cycle basis, whereas the schemes proposed in Maiti and Geubelle (2005), Muñoz et al. (2006), Turon et al. (2007), Khoramishad et al. (2010,2011), Naghipour et al. (2011), Harper and Hallett(2010),workincrementallyoncyclesonly,andarethereforemuchlessexpensive fromthecomputationalpointofview.Additionally,themodels(MaitiandGeubelle,2005; RoeandSiegmund,2003;Muñozetal.,2006;Turonetal.,2007;Khoramishadetal.,2010, 2011;Naghipour etal., 2011;Harper andHallett,2010;BeaurepaireandSchuëller,2011), wereappliedessentiallytotwo-dimensional(planar)crackgeometries. The model presented in this paper was initially developed by some of the authors (Moroni and Pirondi, 2012) starting from the framework proposed by Turon et al. (2007).Themaindifferenceswithrespecttothatworkconcern:first,thedamageDis related directly to its effect on stiffness and not to the ratio between the energy dissipatedduringthedamageprocessandthecohesiveenergyandthen,inturn,tothe stiffness;second,theprocesszonesizeA isdefinedasthesumofA ofthecohesive CZ e elementsforwhichthedifferenceinopeningbetweenthemaximumandminimumload ofthefatiguecycle,Δδ¼δ −δ ,ishigherthanathresholdvalueΔδth;therefore,it max min is evaluated by FEA during the simulationand not derived from a theoretical model. Moreover,thestrainenergyreleaserateiscalculatedusingthecontourintegralmethod over the cohesive process zone and the model is implemented as a user-defined field subroutine (USDFLD) in Abaqus acting on standard cohesive elements, instead of a user element. This model was demonstrated to yield a FCG rate that are exactly as thoseinputwiththevalueofBanddEquation(1),usingameshsizesuchastoinclude only afew cohesive elements withinthe process zone. The extension of the model to full 3D cracks undergoing mixed-mode I/II fatigue loading is presented in this work, with a special emphasis on the changes done with respect to the 2D model. 2. Two-dimensional fatigue CZM description 2.1 Generalfeatures Althoughseveraldifferentshapesofthecohesivelawareproposedintheliterature,the triangular one (Figure 1) is often good enough to describe crack growth behaviour. Inthatcase,damagestartsoncethetrippingstressS hasbeenattained,decreasing max progressively the element stiffness K. Considering a representative surface element (represented in the simulation by the cohesive element section pertaining to one integration point (IP), damage initiation Development (cid:2) 22 of a cohesive damage evolution zone model (cid:2) 22,0 D = damage K220 (* = mode l) 175 22 Γ 22 Figure1. K =(1–D)K 0 22 22 Exampleofatriangular cohesivelaw (cid:2) (cid:2) 22,0 22,c (Figure2)withanominalsurfaceequaltoA,theaccumulateddamagecanberelatedto e thedamaged area due to microvoids or crack (A ): d A K D¼ d ¼1(cid:2) (6) Ae K0 Referring to the mode I loading case represented in Figure 1, the behaviour is characterised by a stiffness K , constant until δ . Beyond this limit the stiffness 22,0 22,0 isprogressivelyreducedbydamage,untiltotaldegradationatδ .Betweenδ and 22,c 22,0 δ the stiffness K varies according to: 22,c 22 K22 ¼K22;0ð1(cid:2)DÞ (7) TheareaΓ underlingthecohesivelawistheenergytomakethedefectgrowofaunit 22 area and itis therefore representative of the fracture toughness, G : IC Zd22;C G ¼ s dd (8) 22 22 22 0 Inthemonotoniccase,thedamagevariableDiswritten,asusual,asafunctionofthe opening(δ )andofthedamageinitiationandcriticalopening(respectively,δ and 22 22,0 δ ): 22,c (cid:1) (cid:3) D¼d22;(cid:1)c d22(cid:2)d22;0(cid:3) (9) d22 d22;c(cid:2)d22;0 Ad Ae–Ad Figure2. Nominalanddamaged areainarepresentative surfaceelement(RSE) middle surface crack propagation direction IJSI When the element is unloaded, the damage cannot be healed, therefore, looking at 5,3 Figure 1, the unloading and subsequent loadings will follow the dashed line, until a further damage is attained. This simple model is able to describe the monotonic damagein case of modeI loading. Consideringtheentirecohesivelayer,thecrackextensionarea(A)canbecomputed asthesumofdamagedareasofallthecohesiveelementsIPs(A )(Turonetal.,2007): d 176 X A¼ A (10) d Whenthefatiguedamageisconsidered,fromthepreviousequation,thecrackgrowth (dA)canbewrittenasafunctionoftheincrementofthedamageareaofallthecohesive elements (dA ),therefore: d X dA¼ dA (11) d However,thedamageincrementwouldnotconcernthewholecohesivelayer,butitwill be concentrated in a relatively small process zone (A ) close to the crack tip. CZ In order to estimate the size of A , analytical relationships can be found in the CZ literature (Harper and Hallett, 2008), where the size per unit thickness is defined as the distance from the crack tip to the point where σ is attained. In this model, 22,0 adifferentdefinitionandevaluationmethodisproposed:A correspondstothesumof CZ thenominalsectionsofthecohesiveelementswherethedifferenceinopeningbetween themaximumandminimumloadofthefatiguecycle,Δδ ¼δ −δ ,ishigher 22 22,max 22,min thanathresholdvalueΔδth.ThevalueΔδth isakenasthehighestvalueofΔδ inthe 22 22 22 cohesivelayerwhenΔGinthesimulationequalsΔG obtainedexperimentallybyFCG th tests.IthastobeunderlinedthatinthiswayFCGmaytakeplaceevenatΔδ ⩽ 22,max Δδ , which is a condition that should be accounted for since δ results from 22 22,0 the calibration of cohesive zone on fracture tests and may not be representative of a threshold for FCG. The process zone size A has therefore to be evaluated CZ byFEAwhileperformingtheFCGsimulationbut,ontheotherhand,doesnotneedto be assumed from a theoretical model. Equation (11) can be rewritten as (Turon et al., 2007): X dA¼ dAi (12) d iAACZ whereonlytheelementslyingintheprocesszone(namelyA )areconsideredandthe CZ subscripti stands for the ithIP inthe process zone. Inordertorepresentthecrackgrowthduetofatigue(dA/dN),thelocaldamageof the cohesive elements (D) has to be related to the number of cycles (N). This is done using the equation: dD dD dA ¼ d (13) dN dA dN d Thefirsttermontherighthand-sideofEquation(13)canbeeasilyobtainedderiving Equation(2): dD 1 ¼ (14) dA A d e The process to obtain the second term requires to define the derivative of Development Equation (12)with respect to the number of cycles: of a cohesive dA X dAi zone model ¼ d (15) dN dN iAACZ then it is assumed that the increment of damage per cycle is the same for all the 177 IPs lying in the process zone. Therefore the crack growth rate can be rewritten as (Turon et al.,2007): X dA dA dA ¼ d ¼n d (16) dN dN CZ dN iAACZ wheren isthenumberofIPslyingontheprocessareaA .Forconstantsizecohesive cz CZ elements n ¼A /A leading to the equation: cz CZ e dA A dA ¼ CZ d (17) dN A dN e and, therefore: dA dA A d ¼ e (18) dN dNA CZ CombiningEquations(14)and(18),thedamagegrowthratecanbefinallyexpressedas a function of the applied strain energy release rate, in the simplest version using Equation (1): dD 1 ¼ BDGd (19) dN A CZ 2.2 Strain energy release rate computation A general method to evaluate the strain energy release rate as a function of crack length via FEA is needed to feed Equation (19). Common methods are the contour integral(J)andtheVCCT.ThesetwomethodsareusuallyavailableinFEsoftwares, but VCCT is intended in general as alternative to using cohesive elements while the softwareusedinthiswork(Abaqus®v.6.11)doesnotoutputthecontourintegralforan integrationpath including cohesive element. In order to compute the J-integral, a path surrounding the crack has to be selected. x 2 x 1 Figure3. n ExampleofJ-integral q Cohesive surroundingthecohesive elements elementlayer Ω
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