中文翻译材料.docx

中文翻译材料.docx

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中文翻译材料

FractureToughnessofSi3N4/S45CJointwithanInterfaceCrack

LiedongFu,YukioMiyasitaandYoshiharuMutoh

CopyrightAD-TECH.;licenseePtyLtd.

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Posted:

September2005

TopicsCovered

Abstract

FracturetoughnesstestswerecarriedoutforSi3N4/S45Cspecimenswithinterfacecracksofdifferentlengths.  Itwasfoundthatthespecimenwithacrackof4mmhashigherapparentfracturetoughnessthanthosewithcracksof1mmand2mmduetothereductionoftheresidualstress.  FracturepropagatedintoSi3N4 fromthecracktipinthedirectionof40o forcracksof1mmand2mmwhileitpropagatedalongtheinterfaceforcrackof4mm. Elasto-plasticanalysiswascarriedoutconsideringS45CasthelinearhardeningmaterialandSi3N4 astheelasticmaterial.  Itwasfoundthatthestressaroundthecracktipisdominatedbyanelasto-plasticsingularstressfield,whichissubstantiallythesameastheelasticsingularstressfieldofaninterfacecrack.  Evaluationofthefracturepathandtoughnesswascarriedoutbasedonthestressintensityfactorsoftheelasto-plasticsingularstressfield.

Keywords

InterfaceCrack,FractureToughness,Si3N4/S45CJoint,ThermalResidualStress,Elasto-plasticAnalysis

Introduction

Theceramic/metaljointshavebeenincreasinglyappliedinawiderangeofengineeringfieldsbecausetheceramichasstablemechanicalpropertiesathightemperatureandgoodresistancetowear,erosionandoxidation. However,thedifferenceofmaterialpropertiesbetweenmetalandceramicinducesstresssingularitiesattheinterfaceedge.  Moreover,highthermalresidualstresswillbeinducedduringthecoolingprocessduetothemismatchofthethermalexpansioncoefficients.  Thestresssingularitytogetherwiththethermalresidualstressdegradesthestrengthofceramic/metaljointandmakestheevaluationofthestrengthdifficult.  Manyworkshavebeendoneabouttheresidualstressandthestrengthevaluationofceramic/metaljoints.  Forexample,Kobayashietal.[1,2]haveinvestigatedthebendingstrengthandresidualstressofSi3N4/S45Cjointandtheeffectofthesizeofthespecimenonthebendingstrength.  Qiuetal.[3]haveinvestigatedtheinfluenceofresidualstressandcyclicloadonthestrengthofSi3N4/S45Cjoint.  However,duetothecomplexityoftheproblem,ageneralizedevaluationmethodfortheceramic/metaljointhasnotyetbeenproposed.

Theelasticsolutionofthesingularstressfieldoftheinterfacecrackhasbeenstudiedsince1959[4-9].  Rice[10]hassummarizedtheworkinthisfieldandsetuptheelasticfracturemechanicsconceptsforinterfacialcracks.  Yuukietal.[11,12]haveproposedthemaximumnormalstresscriteriaforpredictingfracturepathandstrengthofceramic/metaljointbasedontheelasticplasticdeformationofmetalwillinevitablyappearnearthecracktipduetothestresssingularity.  Formostoftheceramic/metaljoints,theplasticdeformationofmetalhasasignificantinfluenceonthestrengthoftheceramic/metaljoint.  Duetotheanalyticalcomplexity,theevaluationofthefracturepathandstrengthofceramic/metaljointbasedontheelasto-plastictheoryhasnotyetbeenmade.

Inthisstudy,fourpointbendingtestsofSi3N4/S45Cjointspecimenswithaninterfacecrackwerecarriedout.  Evaluationofthefracturepathandfracturetoughnesswasattemptedbasedontheelasto-plasticanalysis.

Experimental

Specimen Preparation

Figure1showsthegeometryanddimensionsofSi3N4/S45Cjointspecimen. Thesilverbasedbrazingalloy（wt%is:

Ag,71%,Cu,27%,Ti,2%）with60μmthicknesswasusedforthebondingbetweenSi3N4 ceramicsandS45Csteel. Brazingwascarriedinavacuumfurnace Torr）.  Thetemperatureofthefurnacewasincreasedatarateof20oC/minuptothebrazingtemperatureof850oCandkeptfor10min,thendecreasedatarateof10oC/min.  Thejoiningsurfaceswerepolishedwithdiamondpowderofμmdiameter. Duringthebrazing,acontactpressureofMPawasapplied.

Afterbrazing,aninterfacecrackwasintroducedbytheelectricdischargemethodwiththecuttingwireof0.1mmdiameter.  Fourspecimenswithdifferentcracklengthswereprepared.  Twoofthespecimenshadcracklengthsof4.0mmandtheothertwospecimenshadcracklengthsof1.0mmand2.0mm.

Figure1. Fracturetoughnessspecimen.

ExperimentalResults

Fourpointbendingtestswerecarriedoutonthefracturetoughnessspecimensatacrossheadspeedof0.5mm/min.  Table1showstheresultsofthefracturetoughness.  Theapparentfracturetoughnessisdefinedas:

（1）

with

（2）

                （3）

WherePf isthefractureload,aisthecracklength,wthespecimenwidth,tthespecimenhighness,L2 theouterspanandL1 theinnerspan.

Table1. Resultofthefracturetoughnesstests.

No.

Cracklengtha（mm）

Pf （N）

σ f （MPa）

FI

KIApparent（MPa√m）

1

2

3

4

AscanbeseeninTable1,thespecimenswithacracklengthof4.0mmindicateahigherfractureloadthanthosewithshortercracklengthsofand2.0mm.  Astheresidualstresswillredistributeaftercutting[2],therelaxationofthermalresidualstressforlongercracklengthmaybeapossiblereason.

Figure2showsthemacroscopicobservationofthefracturedspecimen.  Forthespecimenswithacracklengthofand2.0mm,crackpropagatedintoSi3N4 directlyfromtheinitialcracktipinthedirectionofabout40o.  Forthespecimenswithacracklengthof4.0mm,thecrackpropagatedalongtheinterfaceforabout1.0mmandthenkinkedintoSi3N4 inadirectionofabout10o totheinterface.

（a）a=1.0mm

（b）a=2.0mm

（c）a=4.0mm

（d）a=4.0mm

Figure2. Fracturedspecimens.

OscillatorySingularStressFieldofTheInterfaceCrackandTheMaximumNormalStressCriteria

TheelasticsolutionofthestressfieldofaninterfacecrackhasbeenaccomplishedbytheWillims[4],Erdogan[5,6],England[7]andSihetal.[8,9].  Ithasbeenfoundthatthestressfieldneartheinterfacecracktiphastheoscillatorysingularity.  Underthepolarcoordinatewiththeoriginlocatedatthecracktip,thestressfieldcanbeexpressedas

                （4）

Here 

 isthebi-materialconstantthatcanbeexpressedas

               （5）

             （6）

whereµj and vj aretheshearmodulusandthePoisson’sratioofthematerials,respectively.

Thestressintensityfactorsoftheoscillatorysingularstressfieldaredefinedas

               （7）

where, l isthereferencelengthtoeliminatethedimensionoftheoscillatoryterm.  Usually l takesthevalueofthewholecracklength,.l=2a.

Whenthestressalongtheinterfacehasbeenknown,thestressintensityfactorscanbecanbeextrapolatedas:

               （8）

              （9）

Yuukietal.[11,12]haveproposedupthemaximumnormalstresscriteriaforthefractureofinterfacecrack.  Consideringthatthevalueof 

 isverysmall,thenormalstresscanbeapproximatelyexpressedas

              （10）

where

           （11）

W1=e-ε（π-θ）,W2=eε（π+θ）                （12）

                 （13）

Thedirectionofthemaximumnormalstresscanbedeterminedfrom:

∂B（θ,ε,y）/∂θ=0           （14）

Letθ0 representthedirectionofthemaximumnormalstress,thecorrespondingstressintensityfactorcanbeexpressedas:

               （15）

Fracturewilloccuralongthedirectionof θ0 whenKθmax reachestheKIC valueofthebasematerial.  Itshouldbenotedthatfracturemayoccuralongtheinterfacewhen θ0 becomessmallerthancertainvalue,sincethestrengthofinterfaceisusuallylowerthanthatofthebasematerial.

Elasto-PlasticSingularStressFieldatTheInterfaceCrackTip

Theelasto-plasticsingularstressfieldforalinearhardeningmaterial[13]hasbeenfoundtobesubstantiallythesameasthatofelasticmaterialwhoseelasticconstantsaredefinedas:

            （16）

whereEistheYoung’smodulusandH’thehardeningcoefficient.

Therefore,theelasto-plasticsingularstressfieldattheinterfacecracktipissubstantiallythesameastheelasticsingularstressfieldoftheinterfacecracktip.  Thegoverningregionoftheelasto-plasticsingularstressfieldwillbeconfinedinasmallregionaroundthecracktipinsidetheyieldzone.  Forceramic/metaljoint,consideringthatthevalueofhardeningcoefficientismuchlessthanthevalueofYoung’smodulus,itcanbefoundfromEq.（16）andEq.（5）that

        （17）

FEMAnalysisandEvaluationofFracturePathandToughnessBasedontheElasto-PlasticStressIntensityFactors

FEManalysiswascarriedoutunderplanestressconditionusingtheprogramofABAQUS.  Si3N4 isassumedasanelasticmaterialwhosematerialconstantsareindependentoftemperatureandE=289GPa, v=andCTE=.  S45CsteelisassumedasalinearhardeningmaterialwiththematerialconstantslistedinTable2[14].  Thestressfreetemperatureisconsideredtobe550oCfortheanalysisofthethermalresidualstress.

Table2. MaterialconstantsofS45C

25oC

100oC

200oC

300oC

400oC

500oC

600oC

E  （GPa）

206

206

201

197

192

187

183

v

σY- （MPa）

375

348

333

309

280

241

193

H’（MPa）

1381

2056

2680

2325

1685

1026

687

CTE（10-6）

Forcomparison,theelasticanalysiswasalsocarriedout.  Calculatedfromtheelasticconstantsof25oC,thebi-materialconstant

forelasticcaseis.  Table3liststhestressintensityfactorsaswellasthedirect