周萧明
,
胡更开
复合材料学报
doi:10.3321/j.issn:1000-3851.2004.06.026
提出了预测复合材料非线性电位移和电场强度关系的一种解析方法,该方法基于各向材料的割线介电常数,将非线性问题转化成一系列线性问题来求解.该方法适用于任意各向异性复合材料和组分材料的非线性性质,而常用的Stroud和Hui的模型只适用于各向同性复合材料和组分材料的弱线性.证明了本文方法具有Ponte Castaneda提出的变分结构.计算结果表明,当基体非线性较小时,本文模型的预测与Stroud和Hui的模型一致,但当基体非线性系数增大时,本文模型能给出合理的预测结果,而Stroud和Hui的模型则会超出基体和夹杂的性能范围.
关键词:
复合材料
,
介电常数
,
非线性
,
割线方法
金属学报(英文版)
桑危郑牛樱裕桑牵粒裕桑希巍。希啤。龋伲模遥希牵牛巍。桑危模眨茫牛摹。模眨茫裕桑蹋拧。拢遥桑裕裕蹋拧。裕遥粒危樱桑裕桑希巍。桑巍。罚保罚怠。粒蹋眨停桑危眨汀。粒蹋蹋希?##2##3##4##5INVESTIGATIONOFHYDROGENINDUCEDDUCTILEBRITTLETRANSITIONIN7175ALUMINUMALLOY$R.G.Seng:B.JZhong,MG.ZengandP.Geng(DepartmentofMaterialsScierce,ScienceCollege,NorthearsternUniveisity,Shenyang110006,ChinaMaruscriptreceived4September1995inrevisedform20April1996)Abstrac:Effectsofhydrogenonthemechanicalpropertiesofdifferentlyaged7175aluminumalloyswereinvestigatedbyusingcathodicH-permeation,slowstrainratetensionandsoon.Theresultsindicatethatboththeyieldstressandthepercentagereductionofareadecreasewithincreasinghydrogenchargingtime,andthedegreeofreductiondecreasesasagingtimeincreasesforthesamehydrogenchargingtime.Keywords:hydrogeninducedductile-brittletransition,7175aluminumalloy,mechanicalproperty,cathodicH-permeation1.IntroductionForalongtimehydrogenembrittlementproblemwasthoughttobeabsentinhighstrengthaluminiumalloybecausethesolutiondegreeofhydrogeninaluminumatcommontemperatureandpressureisverysmall.However,hydrogenembrittlementphenomenonwasfoundinaluminumalloyduringtheinvestigationofstresscorrosionandcorrosionfatigue[1-5].Therehavebeenonlyafewreportsofhydrogeninducedsofteningandhardening.Inthispaper,theeffectsofhydrogenonmechanicalpropertiesof7175aluminumalloywereinvestigatedbyusingcathodicalchargingwithhydrogenandslowtensiontests.2.ExperimentalProcedureTheexperimentalmaterialwas7175aluminumalloyforgingintheformofa43mminthicknessandwithcomposition(wt%).5.41Zn,2.54Mg.1.49Cu,0.22Cr,0.1Mn.0.1Ti,0.16Fe.0.11Si,balancedbyA1.Alloyplateof1.5mminthicknesswasobtainedbyhot(465℃)andtoldrollingto83%reductioninthickness.Thelongaxisofhydrogenchargedspecimensisalongtherollingdirection.Allspecimensweresolidsolutionedat480℃for70min,followedtyimmediatequenchinginwaterandthenagedat140℃for6h(A),16h(B)and98h(C).Thetreatmentof6hiscorrespondingtotheunderagedstate.16hthefirstpeak-agedstateand98hthesecondpeak-agedstate.Thespecimenswerepolishedsuccessivelyusingemerypaperbeforehydrogencharging.Thetensilespecimenswerecathodicallychargedina2NH_2SO_4solutionwithasmallamountofAs_2O_3forpromotinghydrogenabsorption,andwithacurrentdensityof20±1mA/cm￣2atroomtemperature.ThehydrogencontentanalysiswascarriedoutonanLT-1Amodelionmassmicroprobeafterthesputteringdepthreached8nm.Theioncurrentsofhydrogenandaluminuminvariousagedstateswererecordedunderthesamecondition.ThetensiletestswereperformedonanAG-10TAmodeltestmachinewhichwascontrolledbycomputer.3.ExperimentalResultsTheratioofioncurrentstrengthofhydrogentoaluminumisrelatedtohydrogenconcentrationinhydrogenchargedspecimen.TheresultswereshowninTable1Thehydrogencontentincreaseswiththeincreaseincharingtime.Ofthethreeagedstates,theunderagedspecimenhasthehighesthydrogencontent.Theratioofyieldstrengthofhydrogenchargedandunchargedspecimenschangeswithhydrogenchargingtime,asshowninFig.1Itcanbeseenthattheyieldstrengthofhydrogenchargedspecimendecreasewithincreasinghydrogenchargingtime.Atthesamechargingtime,theyieldstressdecreasestheleastinthesecondpeak-agedstate,anddecreasesthemostintheunderagedstate.Itindicatesthattheunderagedspecimenismostsensitivetohydrogeninducedsoftening,whichisconsistentwiththeresultsofanotherhighstrengthaluminumalloy[6].TherelativechangesoftheradioofreductionofareawithhydrogenchargingtimearesummarizedinFig.2,whereΨ￣0andΨ￣Harethepercentagereductionofareaofthesamplewithoutandwithhydrogenchargingrespectively.Theradioofreductionofareareduceswhenhydrogenchargingtimeincreases,andthedecreasingdegreeofreductionofareaincreaseswithincreasingagingtime,ie,,theunderagedstateisthemostsensitivetohydrogenembrittlement.4.DiscussionItisknownfromtheresultsabovethatcathodicalchargingwithhydrogenleadstotheobviousdecreaseinthetensilestrengthandplasticityThisisbecausealargeamountofsolidsolutionhydrogenentersthespecimenintheprocessofhydrogenchargingSolidsolutionhydrogenisliabletoenterthecentreofdislocationundertheactionofdislocationtrap,henceraisingthemovabilityofdislocation.Thereforethedislocationsinhydrogenchargedspecimenmoveeasierthaninunchargedspecimen.soresultinginthereductionofyieldstrength[7].Whendislocationstartstomove,thecrystallatticeresistance(P-Nforce)whichitmustovercomeisgivenby:whereμismodulusofshear,visPoissonratio,aisspanofslipplane,bisatomspanofslipdirection.Moreover.theotherresistanceofdislocationmotionmayarisefromtheelasticinteractionofdislocation,theactionwithtreedislocationandetc.,itcanbeexpressedasfollows:whereαisconstant,XisdislocationspanSotheresistanceofdislocationmotioncanbewrittenasfollows:Becausehydrogenatomsreducetheatombondingstrengthafterhydrogencharging,shearmodulusμdecreasesandresultsinthereductionoff,therebytheyieldstressdecreases.Asthecentreofdislocationistheseriousdistortionzoneoflattice.thestresscanberelaxedafterhydrogenatomstuffing,andthesystemenergydecreases.Thusthecentreofdislocationisastrongtrapofhydrogen[8].Therefore,amovabledislocationcaptureshydrogenandmigratestograinboundaries.phaseboundariesorsurfaceofthespecimen,promotingthecrackiesformationandgrowth,thuscausingthelossofplasticity.Sincethelocalenrichmentofhydrogenisrealizedbydislocationtransporting(inthestageofdeformation),thelargerthereductionofyieldstress.theearlierarehydrogenatomstransportedtotheplaceofenrichment.Inaddition,thedamageofatombondingstrengthinducedbyhydrogenmakesthefracturestressdecrease[9]:whereCHishydrogenconcentration.σ_thisfracturestrengthbeforehydrogenchargingandisfracturestrengthafterhydrogencharging.Eq.(4)showsthatthematerialsmaybefracturedatalowerstraini.e.,brittlefractureoccurs.5.Conclusions(1)Hydrogencontentofdifferentlyagedspecimensincreaseswithincreasinghydrogenchargingtimethecapabilityofthealloytoabsorbhydrogeninunderagedstateisthestrongest.(2)Theyieldstressaswellasthepercentagereductionofareaof7175aluminumalloydecreaseashydrogenchargingtimeincreasesundervariousagedstates.(3)Underagedstateismostsensitivetohydrogeninducedsofteningandhardening.(4)Anexplanationwasofferedforthephenomenonofhydrogeninducedsofteninginthestageofdeformation,andhardeninginthestageoffracture.REFERENCES｜｜1G.KKock,Corrosion35(1979)73.2M.K.TsengandH.LMarcus,Scr.Metall.15(1981)427.3PSFao.M.GaoandR.P.Wei,Scr.Metall.19(1985)265.4R.G.SongandM.K.TsengJ.NortheasternUniversity15(1994)5(inChinese).5R.K.Viswanadham,T.S.sunandJ.A.S.Green,Metall.Trans.11A(1980)85.6J.Liu,M.KTsengandB.R.Liu.NonferrousMiningandMetallrgy5(1989)33(inChinese).7LChen,WXChen,ZHLiuandZ.Q.Hu,InFrocofthe1stNationalConfonAl-LiAlloys(Sheryang.China,1991)p.328(inChinese).8Z.HLiuL.ChenW.XChenY.X.ShaoandZ.Q.Hu,InProc.ofthe1stNationalConfonAl-LiAlloys(Shenyang,China,1991)p.334(inChinese).9R.A.OrianiandF.H.Josephic,ActaMetall.22(1974)1065.##61G.KKock,Corrosion35(1979)73.2M.K.TsengandH.LMarcus,Scr.Metall.15(1981)427.3PSFao.M.GaoandR.P.Wei,Scr.Metall.19(1985)265.4R.G.SongandM.K.TsengJ.NortheasternUniversity15(1994)5(inChinese).5R.K.Viswanadham,T.S.sunandJ.A.S.Green,Metall.Trans.11A(1980)85.6J.Liu,M.KTsengandB.R.Liu.NonferrousMiningandMetallrgy5(1989)33(inChinese).7LChen,WXChen,ZHLiuandZ.Q.Hu,InFrocofthe1stNationalConfonAl-LiAlloys(Sheryang.China,1991)p.328(inChinese).8Z.HLiuL.ChenW.XChenY.X.ShaoandZ.Q.Hu,InProc.ofthe1stNationalConfonAl-LiAlloys(Shenyang,China,1991)p.334(inChinese).9R.A.OrianiandF.H.Josephic,ActaMetall.22(1974)1065.##A##BINVESTIGATION OF HYDROGEN INDUCED DUCTILE BRITTLE TRANSITION IN 7175 ALUMINUM ALLOY$$$$R.G.Seng: B.J Zhong, MG. Zeng and P. Geng(Department of Materials Scierce, Science College,Northearstern Univeisity, Shenyang 110006, China Maruscript received 4 September 1995 in revised form 20 April 1996)Abstrac:Effects of hydrogen on the mechanical properties of differently aged 7175 aluminum alloys were investigated by using cathodic H-permeation, slow strain rate tension and so on. The results indicate that both the yield stress and the percentage reduction of area decrease with increasing hydrogen charging time, and the degree of reduction decreases as aging time increases for the same hydrogen charging time.
关键词:
:hydrogen induced ductile-brittle transition
,
null
,
null
,
null
金属学报(英文版)
粒裕希停桑谩。疲希遥茫拧。停桑茫遥希樱茫希校佟。希拢樱牛遥郑粒裕桑希巍。希啤。停粒牵危牛裕遥希巍。樱校眨裕裕牛遥牛摹。粒蹋眨停桑危眨停樱桑蹋桑茫希巍。粒蹋蹋希佟。疲桑蹋停?##2##3##4##5ATOMICFORCEMICROSCOPYOBSERVATIONOFMAGNETRONSPUTTEREDALUMINUM-SILICONALLOYFILMSJ.W.Wu,J.H.FangandZ.H.Lu(NationalLaboratoryofMoleculeandBiomoleculeElectronics,SoutheastUniversity,Nanjing210096,ChinaManuscriptreceived27October1995)Abstrcat:Twodifferentsurfacemorphologycharacteristicsofmagnetronsputteredaluminumsilicon(Al-Si)alloyfilmsdepositedat0and200℃wereobservedbyatomicforcemicroscopy(AFM).Oneisirregularlyshapedgrainsputtogtheronaplane.TheotherisirregularlyshapedgrainsPiledupinspace.Nanometer-sizedparticleswithheightsfrom1.6to2.9nmwerefirstobserved.Onthebasisoftheseobservationsthegrowthmechanismofmagnetronsputteredfilmsisdiscussed.Keywords:magnetronsputtering,Al-Sialloy,surfacemorphology,atomicforcemicroscopy,filmgrowthmechanism1.IntroductionTheuseofaluminumalloys[1,2],inparticularAl-Si,isacommonfeatureinmanysinglelevelandmultilevelinterconnectionschemesadoptedinthemanufactureofmicroelectronicdevicesbecauseofseveraldesirableproperties.TheAl-Sigrainmorphology(size.geometryanddistributionofgrainsisassociatedwithstepcoverage[3],electromigration[4]andinterconnectsresistivity[5]etc..Thus,characterizationofAl-Sialloysurfacemorphologyisveryimportant,especiallywhenintegratedintensityincreasesandlinewidthsof0.3to0.5μmbecomecommon.Inthepasttwentyyears,theAl-Sialloysurfacemorphologywhichaffectsthereliabilityofmicroelectronicdeviceshasbeenwidelyinvestigatedbyscanningelectronmicroscopy(SEM),transmissionelectronmicroscopy(TEM)etc.[5-7].However,SEMandTEMhavetheirlimitationorinconvenience,forexample,theverticalresolutionofSEMisnothighandTEMneedscomplexsamplepreparation.Recently,anewgrainboundaryetchingmethodwasproposed￣[8]whichalsoneedstroublesomechemicaletching.Atomicforcemicroscopy(AFM),sinceitsemerging,hasbecomemoreandmoreusefulinphysics,chemistry,materialsscienceandsurfacescience,becauseofitshighresolution,easeofsamplepreparationandrealsurfacetopography.Recently,discussion[9,10]waspresentedonhowAFMwillplayaroleinsemiconductorindustry.Asaresponsetothisdiscussion,weusedAFMtoinvestigateAl-SialloysurfacemorphologyandhaveobtainedsomeresultswhichcannotberevealedbySEMorTEM.ThisindicatesthatAFMisagoodcharacterizationtoolinsemiconductorindustry.2.SamplePreparationInourexperiments,aluminumwith30ppmsiliconwassputteredonsiliconsubstrateinbatchdepositionmodeAllthreefilmswiththicknessof1.6μmweredepositedusinganargonsputteringpressureof4.2×10￣-3Pa.TheotherdepositionparametersaredescribedinTable1.Thesubstratewascleanedusingstandardpremetallizationcleaningtechniquespriortofilmdeposition.3.ExperimentalResultsandDiscussionTheAFMmeasurementswereperformedonacommercialsystem(NanoscopeIII,DigitalInstruments,SantaBarbara).Thetipismadeofmicrofabricatedsiliconnitride(Si_3N_4)Itisattachedtoa200μmcantileverwithaforceconstantofabout0.12N/m.Beforethesurfaceofsamplewasexamined.agoodtipwithananometer-sizedprotrusionatitsendwasselectedbeforehand,whichcanbeobtainedbyimagingtheatomicstructureofmicasubstrateandagoldgrid.AtypicaloperatingforcebetweenthetipandAl-Sisamplesurfaceisoftheorderof10￣-8Nandallimagesweretakenatroomtemperatureinair.AtypicaltopographicviewoftheAl-SifilmsisshowninFig.1(allimagescansizeis5by5μma,bandcarerespectivelyforsample1,2,and3).FromFig.la,itcanbeseenthatirregularlyshapedgrainstiltinginvaryingdegreespileupinspace,andgroovesamongtheirregularlyshapedgrainsaredifficulttodecideatacertainarea(wedefineitascharacteristicA).Toourknowledge,onreportsonthesurfacemorphologyhavebeenpresentedbefore.InFig1b,however,irregularlyshapedgrainsassembleonaPlaneandgroovesamongtheirregularlyshapedgrainsareeasytodecide(wedefineitascharacteristicB),whichisinagreementwithmanypreviousreports[5-7].InFig.1c,bothcharacteristicA(arrowA)andcharacteristicB(arrowB)wereobserved.IndoingAFMexperiments,weselectedfivedifferentscanareastobeimagedforeachsampleandfoundthatallimagesofeachsamplearerespectivelysimilartoFig.1a,bandc.Also,wenotedthatthesurfaceofinFig.1a.WethinkthatdepositionparameterswillinfluenceAl-Sisurfacemorphology,andthetiltedgrainsmaybesusceptibletomicrocracking.Byreducingthescansizeareato2by2μm(Fig.2aandb).Weobtainedmanyidenticalresultsasdescribedabove,suchasirregularlyshapedgrainsetc.Forthefirsttime,wefoundnanometersizedparticlesonirregularlyshapedgrainsurfacewhichcannotberevealedbySEMbecausethediameterofthesenanoparticlesisabout10nmandtheheightofthesenanoparticlesisintherangeof1.6to2.9nm.Inimaging,wenotedthatrotatingthescandirectionandchangingthescanfrequencydidnotaffectthestructureofthesegrainsasshowninFig.2aandb,rulingoutthepossibilitythatscanninginfluencedtheshapeoftheseparticlesorcausedsomesimilarimagingartifacts.Also,wenotedthatthenanoparticleswerenotobservedontheslopesofthegrooves(Fig.2aandb).Thisphenomenoncanbeexplainedasfollows:thepotentialenergyattheslopeislargerthanthatelsewhere,sotheparticlesseemmorelikelytobedepositedontheseareaswithlowerpotentialenergy.Fig.2c,scansize250by250nm,isazoomtopographicimage(whiteoutlineinb).Itshowsunevendistributionofthenanoparticles.Andtheheightdifferenceofthenanoparticlesindicatesdifferentgrowingspeed.Wethinkbasedonthemorphologyofnanoparticles,thattheheightdifferenceandunevendistributionofthesenanoparticlesshowdifferentgrowingadvantageandindicatethatatomshaveenoughenergytomovetoasuitablegrowingspot.Theenergymaybefromthefollowingsources:surfacetemperaturefluctuation,stressdifferenceorcollisionbetweenhighspeedsputteredatoms.Thesenanoparticlesgoongrowingandformmanyirregularlyshapedgrains.AndtheseirregularlyshapedgrainsfurtherconnecteachotheraccordingtocharacteristicAorB,finallyformingtheAl-Sisurfacemorphology.4.ConclusionWecandrawthefollowingconclusionsfromtheabove.First,theexperimentalresultsshowedthatAFMisapowerfultooltoinvestigatethedetailsofAl-Sisurfacemorphologywhichcangreatlyenrichourknowledgeofthefilmgrowthmechanism.Second,depositionconditionsplayanimportantroleindeterminingtheAl-Sisurfacemorphology.Third,thetwoAl-Sisurfacemorphologycharacteristicsarethatirregularlyshapedgrainsassembleonaplaneandirregularlyshapedgrainstiltinginvaryingdegreespileupinspace.Fourth,forthefirsttime,nanoparticleswereobservedonirregularlyshapedgrainsurfacewhichsuggestedthatthefilmgrowthmechanismwasbyinhomogeneousnucleation.Acknowledgements-BeneficialdiscussionswereheldwithDr.ZhenandMr.Zhu.ThisworkwaspartiallysupportedbytheNationalNaturalScienceFoundationofChina.RFFERENCES｜｜1D.pramanikandA.N.Saxena,SolidStateTechnol.26(1983)127.2D.pramanikandA.N.Saxena,SolidStateTechnol.26(1983)131.3D.pramanikandA.N.Saxena,SolidStateTechnol.33(1990)73.4S.S.IyerandC.Y.Worg,J.Appl.phys.57(1985)4594.5J.F.Smith,SolidStateTechnol.27(1984)135.6D.GerthandD.Katzer,ThinSolidFilm208(1992)67.7R.J.WilsonandB.L.Weiss,ThinSolidFilm207(1991)291.8E.G.Solley,J.H.Linn,R.W.BelcherandM.G.Shlepr,SolidStateTechnol33(1990)409I.SmithandRHowland,SolidStateTechnol.33(1990)53.10L.Peters,SemiconductorInternational16(1993)62.##61D.pramanikandA.N.Saxena,SolidStateTechnol.26(1983)127.2D.pramanikandA.N.Saxena,SolidStateTechnol.26(1983)131.3D.pramanikandA.N.Saxena,SolidStateTechnol.33(1990)73.4S.S.IyerandC.Y.Worg,J.Appl.phys.57(1985)4594.5J.F.Smith,SolidStateTechnol.27(1984)135.6D.GerthandD.Katzer,ThinSolidFilm208(1992)67.7R.J.WilsonandB.L.Weiss,ThinSolidFilm207(1991)291.8E.G.Solley,J.H.Linn,R.W.BelcherandM.G.Shlepr,SolidStateTechnol33(1990)409I.SmithandRHowland,SolidStateTechnol.33(1990)53.10L.Peters,SemiconductorInternational16(1993)62.##A##BATOMIC FORCE MICROSCOPY OBSERVATION OF MAGNETRON SPUTTERED ALUMINUM-SILICON ALLOY FILMS$$$$J.W.Wu,J.H. Fang and Z.H.Lu (National Laboratory of Molecule and Biomolecule Electronics,Southeast University,Nanjing 210096, China Manuscript received 27 October 1995)Abstrcat:Two different surface morphology characteristics of magnetron sputtered aluminumsilicon(Al-Si)alloy films deposited at 0 and 200℃ were observed by atomic force microscopy(AFM).One is irregularly shaped grains put togther on a plane.The other is irregularly shaped grains Piled up in space. Nanometer-sized particles with heights from 1.6 to 2.9 nm were first observed. On the basis of these observations the growth mechanism of magnetron sputtered films is discussed.
关键词:
:magnetron sputtering
,
null
,
null
,
null
,
null
