A set of essential requirements towards standardising the numerical simulation of blast-loaded windows and facades

2015

Editors: Martin Larcher, European Commission Alexander Stolz, Fraunhofer Institute Oliver Millon, Fraunhofer Institute Authors: Chiara Bedon, University of Trieste Kevin C. Ans van Doormaal, TNO Christof Haberacker, WTD 52 Götz Husken, BAM Martin Larcher, European Commission Oliver Millon, Fraunhofer Institute Arja Saarenheimo, VTT George Solomos, European Commission Alexander Stolz, Fraunhofer Institute Laurent Thamie, CEA Georgios Valsamos, European Commission Andy Williams, CAST

The research leading to these results has received funding from the European Union as part of the European Reference Network for Critical Infrastructure Protection project.

ERNCIP thematic group Resistance of structures to explosion effects

EUR 27807 EN

A set of essential requirements towards standardising the numerical simulation of blast-loaded windows and facades

This publication is a Technical report by the Joint Research Centre, the European Commission’s in-house science service. It aims to provide evidence-based scientific support to the European policy-making process. The scientific output expressed does not imply a policy position of the European Commission. Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication. Contact information European Commission Joint Research Centre Institute for the Protection and Security of the Citizen Georgios Giannopoulos Address: Joint Research Centre, Via Enrico Fermi 2749, TP 721, 21027 Ispra (VA), Italy E-mail: erncip-office@jrc.ec.europa.eu Tel.: +39 0332 78 6211 Fax: +39 0332 78 5469 JRC Science Hub https://ec.europa.eu/jrc JRC100438 EUR 27807 EN ISBN 978-92-79-57507-5 ISSN 1831-9424 doi:10.2788/684747 © European Union, 2015 Reproduction is authorised provided the source is acknowledged. All images © European Union 2015.

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European Reference Network for Critical Infrastructure

Protection (ERNCIP) thematic group

Asetofessentialrequirements

towardsstandardisingthenumericalsimulationofblast-loadedwindows

andfacades

Thematic group:

Resistance of structures to explosion effects

Coordinator: Dr Alexander Stolz, Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut (EMI) Deputy coordinator: Dr Oliver Millon, Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut (EMI)

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Editors: Martin Larcher Oliver Millon Alexander Stolz Authors (in alphabetical order): Chiara Bedon Kevin C. Ans van Doormaal Christof Haberacker Götz Hüsken Martin Larcher Oliver Millon Arja Saarenheimo George Solomos Alexander Stolz Laurent Thamie Georgios Valsamos Andy Williams Acknowledgements: The research leading to these results received funding from the European Union within the European Reference Network for the Critical Infrastructure Protection project hosted at the Joint Research Centre (JRC) — European Commission — Via E. Fermi 2749 — Ispra, Varese (VA), Italy.

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Abstract

Thedeterminationoftheblastprotectionleveloflaminatedglasswindowsandfacadesisofcrucialimportance,andit isnormallydonebyusingexperimental investigations.Inrecentyearsnumericalmethodshavebecomemuchmorepowerfulalsowithrespecttothiskindofapplication.Thisreportattempts to give a first idea of a possible standardisation concerning such numerical simulations.Attentionisdrawntotherepresentationoftheblastloadingandofthebehaviourofthematerialofthementionedproducts,tothegeometricalmeshing,aswellastothemodellingoftheconnectionsof theglasscomponents to themainstructure.Theneedtovalidatethenumericalmodelsagainstreliableexperimentaldata,someofwhichareindicated,isunderlined.

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Contents

1. Introduction....................................................................................................................................5

2. Generalconsiderations:Whattoexpectfromnumericalsimulations...........................................5

3. Selectionofrepresentativeloadscenarios.....................................................................................7

4. Loadcharacterisation.....................................................................................................................7

5. Modeldiscretisation.......................................................................................................................8

6. Materialmodels............................................................................................................................10

Glass..................................................................................................................................................10

Interlayers.........................................................................................................................................11

Adhesivesandstructuralsealantsjoints...........................................................................................11

Steelandaluminiumcomponents....................................................................................................11

7. Boundaryconditions.....................................................................................................................11

8. Applicationofloading...................................................................................................................12

9. Sensitivitystudyforessentialcalculationparameters.................................................................13

Meshsizedefinitionandelementshape..........................................................................................13

Parametersformaterialmodelling...................................................................................................16

10. Validationandassessmentofperformance.............................................................................16

Validationofnumericalmodels........................................................................................................16

Examplesforvalidationexperimentsfromliterature.......................................................................17

Assessmentofperformance.............................................................................................................17

11. Numericalsimulationdomainsofapplicationregardingactualstandards..............................17

12. Conclusions...............................................................................................................................19

13. References................................................................................................................................19

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1. Introduction Numericalsimulationsareusedforstructuralanalysisandcanbebasedonnon-linearmethodsandmaterial models representing the expected real behaviour under a given type of loading andenvironmental conditions. Numerical simulation techniques constitute another way of assessingstructural performance and are an addition to the physical testing in a laboratory or on the site.Unlike in real testing, it could be claimed that simulation is not limited by structural size, loadmagnitudeandtesting facility.However, thepossibilitiesprovidedbynumericalsimulationsshouldnotbeoverestimatedandadequatechecksintermsofvalidationshouldbeperformedtoverifytheresultsandconclusions.Severalothertechnicallimitsarealsoknown.Forexample,thedevelopmentoftheglassfragmentshasuntilnownotbeenpossiblewithnumericalmethods.

Clearly, themodel formulationmust be based on principles of mechanics, namely itmust satisfyrequirementsofequilibriumofforces,compatibilityofdisplacementsandmaterialconstitutivelaws.Theinevitableerrorsduetonumericalapproximationsshouldalwaysbecontrolledbysolution-errorcriteria. It is also known that the complexity of a model grows with each new feature added.Therefore,itisappropriatetoincludeonlythosefeatureswhicharesignificantforthegivencase,inordertokeepthemodelassimpleandefficientaspossible.

The finite elementmethod aswell as similarmethods like finite volumes or finite differences aretypically used for the numerical solution of continuum mechanics problems. A finite elementformulation should satisfy the requirement of convergence to the exact solution by reducing theelement size (and increasing the number of degrees of freedom). It is understood that,independently of the material model, the approximations introduced by the finite elementformulationcanbeasignificantsourceoferrorsinnumericalanalysis.Similarlywithothernumericalmethods, the errors due to these approximations should be adequately checked as shown forconcretein[1].

2. General considerations: What to expect from numerical s imulations

European as well as American testing standards for laminated glass windows (e.g. [2]) define ahazardlevelthatismeasuredbythefragmentsthatarefoundaftertheexperimentbehindtheglasspane. More details can be found in US General Services Administration [3] and ISO-standard [2](Table1),andalsointhepreviousreports[4]and[5].Scientificandtechnicalliteraturehasshownthatnumericalsimulationscanbeusedwithconfidencetodeterminethefailureofthelaminatedglassanditsinterlayerandmaybeusefultoapproximatethe launch conditions of the splinters. The bearing capacity and the glazing damage level of thewindow of full window systems and their components can also be determined by numericalsimulations. However, the prediction of the formation and development of splinters or slivers ofblast-loaded laminated glass has until now not been accurate enough and is a challenge fornumerical simulations. Also the splinter velocity and dispersion behind the window cannot bedeterminednumerically.

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Table1:Hazard-ratingcriteriaforarenatestsaccordingtoISO16933:2007[2]Hazard

rating

Hazard-ratingdescription

Definition

A Nobreak The glazing is observed not to fracture and there is no visible damage to theglazingsystem.

B Nohazard Theglazingisobservedtofracturebuttheinner,rearfaceleafisfullyretainedinthefacilitytest frameorglazingsystemframewithnobreachandnomaterial islostfromtheinteriorsurface.Outerleavesfromtheattackfacemaybesacrificedandmayfallorbeprojectedout.

C Minimalhazard

The glazing is observed to fracture. Outer leaves from the attack face may besacrificed and may fall or be projected out. The inner, rear face leaf shall besubstantially retained,withthetotal lengthof tearsplusthetotal lengthofpull-outfromtheedgeoftheframelessthan50%oftheglazingsightperimeter.

Also,therearenomorethanthreerateableperforationsor indentsanywhere inthewitnesspanelandanyfragmentsonthefloorbetween1mand3mfromtheinterior face of the specimen have a sum total united dimension of 250mm orless.Glazingdustandsliversarenotaccountedforinthehazardrating.

Ifbydesignintentthereismorethan50%pull-outbuttheglazingremainsfirmlyanchored by purpose-designed fittings, a rating of C (minimal hazard) may beawarded, provided that the other fragment limitations are met. The survivalconditionandanchoringprovisionsshallbedescribedinthetestreport.

D Very lowhazard

The glazing is observed to fracture and significant parts are located no furtherthan 1m behind the original location of the rear face. Parts are projected anydistancefromtheattackfacetowardstheblastsource.

Also,therearenomorethanthreerateableperforationsor indentsanywhere inthewitnesspanel,andanyfragmentsonthefloorbetween1mand3mfromtheinterior face of the specimen have a sum total united dimension of 250mm orless.Glazingdustandsliversarenotaccountedforintherating.

E Lowhazard The glazing is observed to fracture, and glazing fragments or the whole of theglazingfallbetween1mand3mbehindtheinteriorfaceofthespecimenandnotmorethan0.5mabovethefloorattheverticalwitnesspanel.

Also,thereare10orfewerrateableperforationsintheareaoftheverticalwitnesspanelhigher than0.5mabove the floorandnoneof theperforationspenetratemorethan12mm.

F Highhazard Glazingisobservedtofractureandtherearemorethan10rateableperforationsin the area of the vertical witness panel higher than 0.5m above the floor, orthereareoneormoreperforationsinthesamewitnesspanelareawithfragmentpenetrationmorethan12mm.

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3. Selection of representative load scenarios Theloadingscenariodependsonthespecificprotectionrequirementsandlocalconditions.Detailedinstructionsfordefiningloadingscenariosaregiveninnationalregulationsormustbediscussedwiththe infrastructure operator/owner or the responsible authorities. Loads to be considered indesigning a structure are usually expressed in terms of equivalent mass of TNT and stand-offdistance, e.g. the distance between the structure to be designed and the postulated explosionsource.

In general, numerical simulations are able to handle an almost arbitrary loading scenario for thestructural element considered. Taking these capabilities concerning loading into account, it isimportanttoensurethatthemodelledscenarioscanbecomparedtotheexperimentalresults.Forthis,itwouldbenecessarytocapturetheactualloadingofthestructuralcomponentexaminedwiththesamelogicasintheexperiments.Therefore,itisrecommendedtorecordineachsimulationtheresulting loading pressure and impulse for the considered structural elements, especially incalculationsthatarecombiningfluidandstructures.

4. Load characterisation Blastwavesarecharacterisedbyacompressionphase(positivephase)withaveryhighpeakover-pressure and a following under-pressure (negative phase). The compression phase starts with astrongincreaseinthepressurefromtheambientpressure(p0)tothepeakpressure(p0+pmax)withinatimescaleofmicroseconds.Figure1showsasimplifiedformofthepressure-timehistoryofablastwave,andindicatestherelevantparameters.Ofimportancefortheloadingofglasswindowsisalsothe negative phase since this could be strong enough to pull outwards fragments that weredevelopedbythepositivephase.

Figure1:Pressurehistoryforafree-fieldair-blastwave

For a blasted structure different loading conditions can be distinguished: impulsive, dynamic andquasi-static loading (Figure 2). Loads with very short duration (relative to the structure’s naturalperiod)areknownasimpulsiveloading,andinlaminatedglasswindowstheyoftenresultinashear

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failure next to the border or at the boundary itself. Loadswith longer duration (dynamic loading)tend to causebendingmode failuresofglasspanels.Onlyvery slowlydevelopedpressures (quasi-staticloading)wouldbesimulatedbyusingastaticload.Forthestructureunderconsiderationtheseloadingregimescanbeschematicallyshownintheso-calledPI(Pressure-Impulse)diagram,Figure2.

Figure2:PIdiagram:impulsive,dynamicandquasi-staticloading

5. Model discretisation Model discretisation is based on the transformation of real structural components in a numericalrepresentationusingfiniteelements.Elementsarecharacterisedbythreemainparameters:

• Elementtype(anddegreesoffreedom)• Numberofnodes/elementorder• Integration

Someof theelementtypesthatareused inastressanalysisarepresented inFigure3.Oneof themain differences between those entire element types is their geometry. Elements may also bedistinguishedbetweensolidelements,shell,beamandtrusselements.

Figure3:Someclassicalelementtypes

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Dependingonthesoftwareusedtoassessthestructuralmodel,differentelementtypesareavailableandcanbeemployed.Thenumberofdegreesoffreedomisassociatedwiththeelementtype,andisthe fundamental variable calculated during the analysis. For a stress/displacement simulation thedegreesoffreedommaybetranslationaland,forshell,pipe,andbeamelements,translationalandrotational.

Specificelementtypesandotherfeaturescanalsobeavailablesuchasconnectorelements,infiniteelements,multi-point constraint (MPC) links. As an example, those element types can be used todefine the link between the window and the frame. Cohesive links can be used between twoseparatedglasslayers.Thistypeofelementcanbeveryusefulinordertoevaluatethedelaminationprocessinsidemulti-layerglasspanels.

Displacementsand rotationsarecalculatedat thenodesof theelement.Atanyotherpoint in theelement, the values are obtained by interpolating them from the nodal ones. Usually theinterpolationorderisdeterminedbythenumberofnodesusedintheelement.

• Elements that have nodes only at their corners, such as an 8-node brick use linearinterpolationineachdirectionarecalledlinearelementsorfirst-orderelements.

• Elementswithmid-sidenodes,suchasa20-nodebrickelementusequadraticinterpolationandarecalledquadraticelementsorsecond-orderelements.

As a rule, the increase of the element order improves the accuracy of the result for the sameelementsize.However,theincreaseoftheelementorderincreasestheCPUtime(calculationtime).

Numericalmethodsareusedtointegratevariousquantitiesoverthevolumeofeachelement.Usingfor example Gaussian quadrature for the simulation, the code evaluates thematerial response ateachintegrationpointineachelement.Elementscanoftenbeusedinfullorreducedintegration,achoicethatcanhaveasignificanteffectontheaccuracyoftheelementforagivenproblem.Useofreduced integrationcanalsodecreasetheneededCPUtime.Reduced integration ismainlyused inorder to reduce the locking of the elements. This could result in hourglassmodes that should beavoided.

Shell,pipe,andbeamelementpropertiescanbedefinedasgeneralsectionbehaviours.Eachcross-sectionof theelement canbe integratednumerically, so thatnon-linear responseassociatedwithnon-linear material behaviour can be tracked accurately when needed. In addition, a compositelayeredsectioncanbespecifiedforshellelements.

Inmodellingawindowpanelorafacade,thefollowingissuesshouldbetakenintoconsideration:

• Thegeometricalshapeofthewindowpanel• Thedesignofthestructure(laminated,multilayered,etc.)• Thetypeofsolverusedtoanalysethestructure(explicitorimplicittimeintegration)• Typeofdamagestudied(brittlefailure,delamination,etc.)• Typeoflinksbetweenthestructuralcomponentsconsidered• Boundaryconditions

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An example of an insulated laminated glass panel and its frame is given in Figure 4. Additionalinformationaboutsimulationsofisolatedglassinfacadesisforexamplegivenby[6].

Figure4:Detailofafaçadesystemusinglaminatedglass

6. Material models Theappropriatematerialmodelsshouldbechosentobestrepresentthematerialbehaviourunderthe examined loading conditions and in compatibility with the model discretisation described inSection5.Themechanicalcalibrationofallwindowcomponentsshouldbecarriedout,dependingontheglazingsystemtypology,bytaking intoaccountthespecificdamageconstitutivebehaviourandpossiblestrainrate-dependentphenomena.

Materialmodelsforthesimulationoflaminatedglasswindowsandfacadesareusuallybasedonthefollowingtheories:

• Linearbehaviourwithbrittlefailurelimit(cracking)• Theoryofplasticitywithplasticflowrule• Damagetheory• Visco-elasticandvisco-plastictheory

Thechoiceofanappropriatetheorydependsonthespecificapplication.

Glass Glassisaverybrittlematerial.Alinear-elasticrepresentationwithafailureorerosioncriterionworkswellinmostcases.Sometimesaplasticpartisaddedinordertofadeoutthestressinaslowerwayandtoalsoreducenumericalinstabilityproblemsifsuchamaterialmodelisnotphysical.Thestrainratebehaviourofglassisstillnotsufficientlyinvestigated.Firstresultsshowthatthefailurestrengthincreasesatveryhighstrainrates[7].TypicalmaterialparametervaluesforannealedaswellasfortemperedglassaregiveninTable2.

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Interlayers ThematerialmodelforthePVBinterlayerstronglydependsonthedamagelevelconsidered.Itsbehaviouruntilthefirstglasscrackingcanbeassumedtobeelasticsincethestrainisstillverysmall.Amoreaccuratedescriptionofthebehaviouroftheinterlayerbecomesimportantwhentheglassiscracked.Alsoaplasticmateriallawcould,forexample,representtheloadingbehaviourunderhigherstrainratesquitewellwhentheunloadingbehaviourofPVBbecomesmoreviscoelastic.Somevaluesfortheinterlayermaterialaregivenin[8]andTable2.

Adhesives and structural sealants joints Adhesive joints and structural sealants are usually introduced between the glass panels and themetalframes.Literaturereferencesareavailablefortheirmechanicalcharacterisation,e.g.fromtheproducers. In general, adhesives and sealants of common use in structural glass applications aretypically characterised by low modulus of elasticity, limited tensile/shear resistance and largeultimate strain. The simplest numerical modelling approach for the mechanical description ofstructural sealants in tension takes the form of equivalent linear elastic materials with brittlebehaviour[9].

Steel and aluminium components Thestrainrateeffectofaluminiumisgenerallysmallwhilethatofsteelcouldbehigh.Dependingonthe structural configuration, the strain rates in the bearing construction could be smaller.Nevertheless, a Johnson–Cook material law could represent the strain rate behaviour of manymetallicmaterials.Examplesaregiveninthepreviousreport[4].

Table2:Typicalmaterialpropertiesforglass,PVBandsealant

Property Annealedglass Temperedglass PVB Sealant

InitialYoung’smodulus[Pa] 7.0e10 7.0e10 2.2e8 1.8e5-6.2e5

Poissonratio[-] 0.23 0.23 0.45 0.49

Elasticstresslimit[Pa] - - 11e6 -

Density[kg/m³] 2500 2500 1100 1000

Failurestrain[-] 0.0012 0.00228 2.0 4-4.6

Failurestress[Pa] 84e6 196e6 28e6 9.4e5-12e5

7. Boundary condit ions For theanalysisof theblast responseofaglasswindowor facade,FEnumericalmodelsshouldbeproperlyvalidatedandassessednotonlyintermsofmechanicalcharacterisationofmaterials,butbyproperlytakingintoaccountallthemaininfluencingparameters.

Specifically,carefulattentionshouldbegiventothenumericalmodellingofeachwindowcomponent(e.g.glasspanel,metalframeworkandpossibleadhesivejointsbetweenthem)andtheconnectiontothebuildingstructure.

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Bothgeometricallysimplifiedmodelsandcomputationallyexpensivedetailedmodelscanbeused,ifproperlyvalidatedforthespecificcase.

Anexampleofsimplifiedmodelscanbethedescriptionofawindowintheformof3Dshellelements(glasspanels),beamelements(metalframe)andmechanicalpointconnectors(properlycalibratedsothat they could adequately reproduce the physical interaction between the glass panel and theframe). The same modelling approach can be extended to glazing systems in general, namelyconsistingofcurtainwallmodularunits,cable-netsystemsandmetalpointconnectorsfortheglasspanels(Figure5).

Theappropriatenumericaldescriptionofeachwindowcomponentshouldbesuitablycheckedandvalidated against simple analytical models or experiments derived from small specimens/singlefacadecomponents.

(a) (b)

Figure 5: Example of point-supported glass panel. (a) Typical ‘spider’ connector and (b)correspondinggeometricallysimplifiedFEmodel[10].

Beforeperformingdynamicanalysesonfull3DsolidFEmodels,carefulconsiderationshouldbegivento the assessment of the correct description of adhesive joints and/or mechanical connectors.Regarding the boundary conditions of the FEmodels, the presence of special devices/connectionsystemsorbracketsbetweentheglazingwindowandthestructuralsystem(e.g.theconcreteslabofabuilding)shouldbeproperlytakenintoaccount,sothattheaccuracyofthepredictedeffectsdueto the design blast load on glass as well as the maximum reaction forces transmitted to thesubstructurecanbeensured.

8. Application of loading Thenumericalapproachescanbedividedintotwomaingroups:coupledanduncoupledcalculationapproaches.A coupled approachmaybeneeded in a casewhere the structure-fluid interaction is

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substantial,e.g.inthecaseofaveryflexiblestructure,isolatedglass,fragmenttrajectories,openingsintheglass.Ingeneral,theloadingdefinitionisbasedontheTNT-equivalentmethod.

Uncoupledapproach

Pressure,loadingperpendicularlyaplanewall,causedbyblastwavescanbecalculatedaccordingtothetheoryofnormalandobliqueshockwavereflection,wheretheparametersofthesphericalblastwaveareestimatedfromempiricalequationsordiagrams(e.g.KinneyandGraham[11],KingeryandBulmash [12]). These load functions can be applied if there are no alterations of the propagatingblastwavebetweenthedetonationpointandthestudiedstructure(duetoterrainanomalies,otherobstructions,etc.).Clearlythismethodconsidersexclusivelythedynamicbehaviourofthestructure(andnotthesurroundingair),anditsadvantageisthemuchlowercomputationalcost.

Coupledapproach

More comprehensive explosion simulations use a coupled Eulerian-Lagrangian (CEL) simulationscheme.InCELtheexplosiveandsurroundingairaremodelledusinganEulerianapproach,typicalinfluidmechanics.ThebehaviourofbothgaseousmaterialsismodelledusingEquation-of-State(EOS)modelsthatrelatethepressuretothedensityofthematerial.Forairthisistypicallytheidealgaslawand for explosives, such as TNT, a Jones–Wilkins–Lee (JWL)model can be used [5]. The structuresubjected to the blast loads is modelled using the traditional Lagrangian approach. The couplingbetween the Eulerian and Lagrangian elements is included so that the solid Lagrangian structureoccupiesEulerianspaceandpressuresontheinterfaceactasloadsonthesolidstructure.

9. Sensit ivity study for essential calculation parameters Thetopicofsensitivitystudyisbroadandcancovera lotofaspects.Thischapterfocusesonsomeimportantparameterstobeanalysedsuchas

• Meshsizedefinition• Elementsshape• Materialparameters

Mesh size definit ion and element shape Somerecommendationshavebeenwrittenin[4]and[5].Table3presentstypicalparameterstobecheckedbeforeandduringthesimulation.Mostnumericalcodesprovidetheirownqualitychecksthatmighthelpengineerstodesignthenumericalmodel.

Aftertheelementqualitycheck,ameshsensitivitystudyshouldbeperformedbyusingmodelswithdifferent mesh refinement and comparing the main results, such as failure location and size,maximumdeflectionof the structure,maximum strain (plastic strain) value. At least twodifferentmeshrefinementsshouldgivesimilarresultsinordertominimisemeshsensitivity.Someexamplesofmeshrefinementstudiesofclassicalsimulationscanbefoundin[2].

Anotherwaytoguidethemeshgenerationistoevaluatewherethehigheststressvaluesoccurandthentoverifythatthemeshsizeisabletomodelthegradientofthestresses.Ifthegradientistoosteep, it can generate a wrong estimation of stress maximum value. A general example of meshconvergenceisgivenin[14].

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Table3:Meshconformityrecommendationsforshellandsolidelements(seealso[13])

Mesh Description

Meshuniformity It is admitted mesh is as homogenous aspossible. In case ofmesh sizemodification, sizeof two adjacent elements shouldn’t differmorethan1.5times(ratioofelementsize)

Minimum number of integration pointsthroughthethicknessofashellelement

In case of linear material model, threeintegration points may be sufficient. In case ofnon-linear deformation, number of integrationpointsshouldbesevenormore.

In case of layered structure, the number ofintegrationpointsshouldfollowpreviousruleperlayer.

Skewness:

Measures the deviation of an element’sanglesαi from90°forquadrilateralelementsand60°fortriangularelements

Quadrilateral:𝑆𝑘𝑒𝑤 = (90 − 𝛼!)!!!!

Triangular:𝑆𝑘𝑒𝑤 = (60 − 𝛼!)!!!!

Warp:

Measures the deviation in an element facefromamaximumallowableplanarwarp

Taper:

𝐴𝑎 = 0.25× 𝐴1 + 𝐴2+𝐴3 + 𝐴4

𝐴𝑖 − 𝐴𝑎𝐴𝑎

> 0.5

Aspectratio:

Should be chosen as it is defined for theelementtype

The ratio of themaximum element edge lengthto the minimum length (it might also be thethickness).

Stretch:(examplefortriangularelement)

stretch=(R/Lmax)actual*(Lmax/R)target

A:Target,B:Actual

Anexampleof localdiscretisation isgivenbelow,representingablast-loaded laminatedglassplatesimilar to theexperimentofKranzer [16].The simulation isdone in the samewayasproposedbyLarcher[8]usinglayeredelements(linear)throughthethickness.Theglassplateisclampedbetweentwo steel frames as defined by ISO 16933. The element sizes, the number of elements and thecalculationtimeisgiveninTable4.Theresults(Figure6andFigure7)showthatthecoarsestmeshresultsinadifferentdisplacementhistory.Thismayresultfromthewiderboundaryconditions.Onlythe finest mesh can represent the failure behaviour of the laminated glass as indicated by theexperiment. The displacement history is therefore also quite different for the finest mesh size,especiallyinthereboundphase.

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Table4:Meshsensitivityanalysisforablast-loadedlaminatedglass)

elementsize[m] elements calculationtime[s]0.1 63 8

0.05 396 330.025 1280 233

0.0125 5120 19230.00625 20480 13821

0.003125 81920 95635

Figure6:Displacementat10msfordifferentelementsizes

Figure7:Displacementhistoryfordifferentmeshsizesforablast-loadedlaminatedglass

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Parameters for material modell ing Thechoiceofamaterialmodeldefinesthenumberof inputparameters.Forexample, forapurelyelasticmaterial (suchasglass)witha stress limit, thematerialparametersneeded for theanalysisare:

• Young’smodulus• Poisson’sratio• Density(duetodynamicstructureresponse)• Stresselasticlimit

In many cases, the number of material parameters is much bigger. For example, the number ofparametersfortheJohnson–Cookmodel(strainrateandtemperature-dependentmodel)isgenerallysix.Typically,themore‘advanced’thematerialmodelis,themoreinputparametersareneeded.

Inordertoevaluatetheinfluenceofeachmaterialparameter,itisusefultodeterminethedegreeofuncertainty of the value. Then, an option is to generate a sensitivity analysis on each materialparameterinordertocheckitsinfluenceontheresults.

Differentmathematicalapproachescanbeusedinordertosolvethistypeofproblem.Basedonaniterative process, several simulation codes provide a numerical approach to conduct this type ofanalysis(optimisationproblem,forexampleLS-OPT,toolbasedonLS-DYNAsoftware).

10. Val idation and assessment of performance

Validation of numerical models The numerical method and the material model should be validated by experimental data. Thisvalidationshouldinclude:

• Basicmaterialtests:namelyintendedforthepropermechanicalcharacterisationofglassandtheotherwindowcomponents (e.g. interlayers inpresenceof laminatedglassand frames,adhesive joints,mechanical connectors, etc.). Basicmaterial testing would be appropriateeven if this is inmost casesneitherpossiblenor costefficient.Data from literatureor themanufacturesoftheproductscouldreplacethematerialtests.

• Structuraltests:theindividualglazingwindowcomponents(glasspane,frame,connectors),aswellastheirreciprocalstructuralinteraction,shouldbesufficientlyvalidated.

• Ameshsensitivity study: itmustbeperformed,asoutlinedabove, inorder tovalidate themodel.

Theobjectiveofanon-linearanalysis is to simulate thestructuralbehaviourand todetermine thestructural resistance. Such a task can also be formulated as a prediction of the most probableresistance, which would then be the mean value of ultimate resistance. Therefore, the meanresistanceischosenasareferenceforsafetyassessmentbynon-linearanalysis.Theuncertaintydueto randomvariationofmaterialproperties (andpossiblyofotherparametersof resistance)canbedescribedbytherandomvariationof resistance. Inadditionamodeluncertaintymustbe includedseparately.

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Examples for val idation experiments from l iterature Inorder tovalidatenumericalmodelsexperimentaldataareneeded.Appropriateexperimentsarenot often available in advance. Table 5 includes some sets of experiments, published in the openliterature,whichcouldbeusedforthemodeldevelopmentandvalidationinthisfield.

Table5:Blast-loadedlaminatedglassexperimentspublishedintheopenliterature

Glasstype/plies

Panelsize[m]

Blast wavesource

Charge(equivalent)

Distance[m]

Failure

Morison[15]

Float glass3mm

1.25 ×1.55

Solidexplosive 60kgTNT 12 Interlayer

Kranzer[16] Float glass

3mm 1.1×0.9Solidexplosive/shocktube

0.5/0.25/0.125kgPETN

5.75/3.7/2.0

Glass

Hooper[17]

Float glass3mm 1.5×1.2 Solidexplosive 15kgC4 10/13 Interlayer

Morison[15]

Float glass3mm

1.25 ×1.25

Shocktube (100/500kgTNT)

31/65 Interlayer

Larcher[8]

Temperedglass6mm 1.1×0.9 Shocktube (820-

4500kg)45-83 Glass/interlayer

Zhang[9] Float glass3mm,6mm

1.5×1.2Solidexplosive

10/207.2-12.3 Glass/interlayer

/boundary

Assessment of performance The interpretationof theresultscanbedone inseveralways.Adamageparameteror failure limittogetherwithanerosion criterion can identify cracks in theglass, in the interlayeror in theotherstructuralcomponents.Asimulationresultinginacompletelyundamagedstatecanbeidentifiedasafullprotection,withoutanyglasssplintersintheinterior.Assumingamodelthatcanrepresentthefailure of the interlayer is available, for simulation resulting in an undamaged interlayer it can bestatedthattheinterioroftheroomisprotectedfrommajorglasssplinters.Alsothewindowfailurecan be distinguished between shear failure near the window borders and bending failure in themiddle of the pane. Finally, point connectors may have a different local failure mechanism. Theinteracting force between anchors/links and the surrounding structures should also be checked inordertoavoidtheirfailure.

11. Numerical s imulation domains of application regarding actual standards

Table1 shows thehazard levels thatarenormallydeterminedexperimentally.They represent inaway the formationandprojectionof splintersor fragmentsbehinda laminatedglasswindow.Thefragmentation of laminated glass cannot yet be represented very well by numerical simulations.Therefore,withregardtohazardlevels,numericalsimulationscanonlybeseenasasupplementtotheexperimentalinvestigations.

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ConcerningspecificallythehazardlevelsinISO16933:2007[2],somecorrespondencesofnumericalresultstothehazardlevelsA,BandCcanbedrawn,asindicatedinTable6.Eventualdevelopmentsofcalculationmethodsandmodelsshouldenablereliableresultsonhigherhazardlevels,too.

Table6:Hazard-ratingcriteriaforarenatestsaccordingtoISO16933:2007[2]Hazard

rating

Hazard-ratingdescription

Definition Example of interpretation ofnumericalresults

A Nobreak The glazing is observed not to fracture andthere is no visible damage to the glazingsystem.

No failure in the glass, i.e. thereis elastic behaviour of the glass.Some very small failed zonesnear the boundary conditionsmayoccur.

B Nohazard The glazing is observed to fracture but theinner, rear face leaf is fully retained in thefacilitytestframeorglazingsystemframewithno breach and no material is lost from theinterior surface. Outer leaves from the attackface may be sacrificed and may fall or beprojectedout.

Both glass plies could fail toreach their stress limit. Smallstrains inthe interlayer,no largeplastic (permanent) deformationof thewindowat theendof thesimulation (this way thedelaminationshouldbesmall).

C Minimalhazard

The glazing is observed to fracture. Outerleaves from the attack face may be sacrificedand may fall or be projected out. The inner,rear face leaf shall be substantially retained,with the total length of tears plus the totallength of pull-out from the edge of the framelessthan50%oftheglazingsightperimeter.

Also, there are no more than three rateableperforations or indents anywhere in thewitness panel and any fragments on the floorbetween1mand3mfromtheinteriorfaceofthe specimen have a sum total uniteddimensionof250mmorless.Glazingdustandslivers are not accounted for in the hazardrating.

Ifbydesignintentthereismorethan50%pull-outbuttheglazingremainsfirmlyanchoredbypurpose-designed fittings, a rating of C(minimal hazard) may be awarded, providedthat the other fragment limitations are met.Thesurvivalconditionandanchoringprovisionsshallbedescribedinthetestreport.

Both plies fail. Failure of theinterlayer. Distinction betweenclassCandthehigheronescouldperhaps be possible using thevelocity of the fragments andtheirtrajectories.

D Very lowhazard

The glazing is observed to fracture andsignificant parts are located no further than1m behind the original location of the rear

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face.Partsareprojectedanydistancefromtheattackfacetowardstheblastsource.

Also, there are no more than three rateableperforations or indents anywhere in thewitnesspanel, andany fragmentson the floorbetween1mand3mfromtheinteriorfaceofthe specimen have a sum total uniteddimensionof250mmor less.Glazingdustandsliversarenotaccountedforintherating.

E Lowhazard Theglazingisobservedtofracture,andglazingfragments or the whole of the glazing fallbetween1mand3mbehind the interior faceof the specimen and not more than 0.5mabovethefloorattheverticalwitnesspanel.

Also, there are 10 or fewer rateableperforations in theareaof theverticalwitnesspanel higher than 0.5m above the floor andnoneof theperforationspenetratemore than12mm.

F Highhazard Glazing is observed to fracture and there aremorethan10rateableperforationsintheareaoftheverticalwitnesspanelhigherthan0.5mabove the floor, or there are one or moreperforations in the same witness panel areawithfragmentpenetrationmorethan12mm.

12. Conclusions Areviewhasbeenmadeofthecapabilitiesofnumericalsimulationstoassessblast-loadedlaminatedglasswindowsandfacades,andtobeusedundercertaincircumstancestodeterminerelatedhazardlevels. As emphasised, special attentionmust be given to the validation of the numericalmodelssince the choiceof loading conditions,material parameters andboundary conditions couldhaveastronginfluenceontheresults.ThisreportshowsthefirststepstowardsEuropeanstandardisationinthat field. Thenext stepwouldbe to further elaborate these findings and contact the responsibletechnicalcommitteeatCEN.

13. References [1] Fib:ModelCodeforconcretestructures2010,Ernst&Sohn2010,Paragraph7.11.[2] ISO 16933:2007/Cor1:2008, Glass in building— Explosion-resistant security glazing— Test and

classificationforarenaair-blastloading.[3] GSA-US General Services Administration 2003, Standard Test Method for Glazing and Window

SystemsSubjecttoDynamicOverpressureLoadings,GSA-TS01-2003.[4] Stolz, A., Kevin, C., vanDoormaal, A., Haberacker, C., Hüsken, G., Larcher,M., Saarenheimo, A.,

Solomos,G., Thamie, L. andValsamos,G., ‘Resistance of structures to explosion effects: Review

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report of testingmethods’, ERNCIP thematic area, Resistance of structures to explosion effects.DeliverableD1,PublicationsOfficeoftheEuropeanUnion,2013.

[5] Stolz, A., Kevin, C., vanDoormaal, A., Haberacker, C., Hüsken, G., Larcher,M., Saarenheimo, A.,Solomos, G., Thamie, L. and Bedon, C., ‘Numerical simulations for classification of blast-loadedlaminatedglass:possibilities,limitationsandrecommendations’,ERNCIPthematicarea,Resistanceofstructurestoexplosioneffects,PublicationsOfficeoftheEuropeanUnion,2014.

[6] Rong-bing Deng, Xian-long Jin, ‘Numerical Simulation for Blast Analysis of Insulating glass in acurtain wall’, International Journal for computational Methods in Engineering Science andmechanics,11:3,pp.162-171,2010.

[7] Peroni,M., Solomos,G.,Pizzinato,V.andLarcher,M., ‘Experimental investigationofhigh strain-ratebehaviourofglass’,AppliedMechanicsandMaterials,82,pp.63-68,2011.

[8] Larcher, M., Solomos, G., Casadei, F. and Gebbeken, N., ‘Experimental and NumericalInvestigations of Laminated Glass Subjected to Blast Loading’, International Journal of ImpactEngineering39,pp.42-50,2012.

[9] Weggel,D.C.,Zapata,B.J.,‘LaminatedGlassCurtainWallsandLaminatedGlassLitesSubjectedtoLow-LevelBlastLoading’,JournalofStructuralEngineering134(3),2008.

[10] Amadio, C. and Bedon, C., ‘Viscoelastic spider connectors for themitigation of cable-supportedfaçadessubjectedtoair-blastloading’,EngineeringStructures,42:190-200,2012.

[11] Kinney, G.F. and Graham, K. J., Explosive Shocks in Air, Springer, Berlin; Heidelberg; New York;Tokyo,1985.

[12] Kingery, C.N. and Bulmash, G., ‘Air-blast parameters from TNT spherical air burst andhemispherical surface burst’, Technical report, Defence Technical Information Centre, BallisticResearchLaboratory,AberdeenProvingGround,Maryland,1984.

[13] IDEASSimulation:FiniteElementModellingUser’sGuide,SiemensProductLifecycleManagementSoftwareInc.,2014.

[14] Science de l’ingénieur: Raffinement du maillage et convergence, http://www.si.ens-cachan.fr/accueil_V2.php?page=affiche_ressource&id=174,2012.

[15] Morison, C., Zobec,M. and Frenceschet, A., ‘Themeasurement of PVB properties at high strainrates, and their application in thedesignof laminatedglassunderbombblast’, In: ISIEMS2007,International symposium on interaction of the effects of munitions with structures, 17e21September,Orlando,US,2007.

[16] Kranzer,C.,Gürke,G.andMayrhofer,C.,‘Testingofbomb-resistantglazingsystems,Experimentalinvestigationof thetimedependentdeflectionofblast loaded7.5mmlaminatedglass’, In:Glassprocessingdays,2005.

[17] Hooper,P.,Dear, J.,Blackman,B.,Smith,D.,Hadden,D.andSukhram,R., ‘Strengthof structuralsilicone glazing joints under blast loading’, In: Department of defense explosives safety boardseminar,12e14August,PalmSprings,CA,USA,2008.

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doi:10.2788/684747 ISBN 978-92-79-57507-5

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