力學(xué)大會(huì)2015集夾雜相變對(duì)裂紋偏轉(zhuǎn)及擴(kuò)展的影響機(jī)理

* 展的效應(yīng)以及引起裂紋偏轉(zhuǎn)的力學(xué)機(jī)理。首先，針對(duì)裂紋尖端附近含有單個(gè)相變顆粒的情況，方向的裂紋擴(kuò)展能量釋放率J1tip，J2tip的解析解。并基于裂尖Jktip與遠(yuǎn)場(chǎng)Jk∞的相對(duì)變化量△Jk相紋反了臨果紋尖布粒變紋的受的顆離裂尖位置等參數(shù)的影響。其次，基于Auricchio本構(gòu)模型開(kāi)發(fā)的形狀合金單元，針對(duì)基體中含隨（1，J2）積分判定了的反相分對(duì)的作粒相的，粒生用反內(nèi)反并且相變?cè)鲰g，相變顆粒，構(gòu)型力理論，裂紋偏轉(zhuǎn)，Jk積分引1本文基于材料構(gòu)型理論的擴(kuò)展，獲得了受相變影響下(3)可得斷裂力學(xué)中著名的Jk-積分[10,11]形式如下： JJ1bj1njds(Wn1σjkuk,1nj)ds\*MERGEFORMAT J

nds

(Wnσ

n

\*MERGEFORMAT j2

jkk,2 bjiWδjiσjkuk \*MERGEFORMAT其中，W代表彈性系統(tǒng)的應(yīng)變能密度；δji為Kronecker

j jσjk為應(yīng)力張量 (K2K2 2K

II

J2 III\*MERGEFORMAT)y)y(r,Γα圖1ε積分的裂尖Jk積分；沿包含所有相變顆粒和裂尖的路徑積分的遠(yuǎn)場(chǎng)JkJktiplimbkjnjdsbkjnjdsAbkj,ε \*MERGEFORMAT JkGkJkJktip MERGEFORMAT其中，Jk代表與應(yīng)力強(qiáng)度因子相關(guān)的遠(yuǎn)場(chǎng)Jk-積分，如式\*MERGEFORMAT gW i且滿(mǎn)足平衡方程由式\*

bji,jgi \*MERGEFORMAT值表示顆粒相變使得裂尖Jktip積分相對(duì)遠(yuǎn)場(chǎng)Jk減少。此時(shí)，相變扮演了裂紋的角色。構(gòu)型力增量Gk的正值表示裂尖表現(xiàn)為反效應(yīng)。積分定義為裂紋沿平行于裂紋面方向擴(kuò)展單位長(zhǎng)度所需的總勢(shì)能釋放率。G(α)J1tipcosαJ2tip \*MERGEFORMAT

0

\*MERGEFORMAT2ijdWσeT \*MERGEFORMATij其中，σij為I/II型混合加載下，不考慮相變顆粒時(shí)的裂尖附近應(yīng)力場(chǎng)[17]σ σ

2πrcos 2σ

MERGEFORMAT

(1sin 由方程\*MERGEFORMAT(7),(11)和\*(12)，考慮包含體積膨脹應(yīng)變和剪切應(yīng)變的相變應(yīng)變[8,9]，eTeTeTeTλeT其中，eT代表膨脹應(yīng)變， 2 3

3θ

G=JπRer

22π22π

2 2

2

2 2KII 2 3

3θ

3θ

G=J=πRer

2

K2

22π 22π

2 2I 2 2 2 2KII MERGEFORMAT圖2給出了利用r32eTπR2K正則化后的J eTeT的值從0到5變化，載荷假定為純I型加載。由圖2可知，受遠(yuǎn)場(chǎng)純I型載荷KI作用時(shí)，含單個(gè)相變顆粒材料的效應(yīng)和反效應(yīng)之間具有一些臨界角。例如，含單變顆粒的位置角在(40110)范圍內(nèi)時(shí)，相變對(duì)裂紋具 作用因而可增強(qiáng)材料的斷裂韌性[18]

50-10020140160()。裂紋偏轉(zhuǎn)角。裂紋偏轉(zhuǎn)角()20-6 20406080100120140160θ(同時(shí)，根據(jù)方程(9)和\*(10)最大能量釋放率準(zhǔn)則，利用式\*MERGEFORMAT(4)和\*MERGEFORMATαarctanGyJ2 GxJ1

2

3

K E'πRer2 2I

KK42π III

2 2cos3θ

5θK E'πR2eTr32

2I

(K2K2)2 2sin

22λcos23λsinθsin2KII MERGEFORMAT3應(yīng)力應(yīng)力0

σσσσσσ σAS rr H

2

2

cos213sin2

n?2其中θ822

sin

cos221

2 \*MERGEFORMAT eeg g其中，s865 體積分?jǐn)?shù)定隨機(jī)情況在數(shù)值過(guò)程中的誤差，以獲得最后的數(shù)值結(jié)果?；诜匠毯蚛*4 EvansA.Tougheningmechanisminzirconiaalloys.Adv.Ceram,1984,12:HutchisonJW.Mechanismsoftougheninginceramics.TheoreticalandAppliedMechanics.ElsevierSciencePublishersB.V.(North-Holland),IUTAM,1989.139～144ShimamotoA,FuruyaY,TayaM.Activecontrolofcrack–tipstressintensitybycontractionofshapememoryTiNifibersembeddedinepoxymatrixcomposite.InligentMaterialsandRobots,7thInternationalSymposium,1996.463～466ClaussenN.FracturetoughnessofA12O3withanunstabilizedZrO2dispersedphase.J.Am.Soc,1976,59:PorterDL,EvansAG,HeuerAH.Transformation-tougheninginpartiallystabilizedzirconiaActaMetall,1979,27:EvansAG,BurlingameN,DroryM,KrivenWM.Martensitictransformationsinzirconiaparticlesizeeffectsandtoughening.ActaMetall,1981,29:447～456MauginGA.Materialinhomogeneitiesinelasticity.London:ChapmanHall,StamGThM,GiessenEvander.Crackgrowthinnon-homogeneoustransformableceramics.PartConstrainedstraightcracks.Int.J.Fract,1996a,79:Stam,GThM.,Giessen,E.vander.:Crackgrowthinnon-homogeneoustransformablePartII:Crackdeflection.Int.J.Fract,1996b,79:Chen,Y.H.:Advancesinconservationlawsandenergyreleaserates.KluwerAcademicPublishers:TheNetherlands,2002RiceJR.Apathindependentintegralandtheapproximateysisofstrainconcentrationbynotchandcracks.J.Appl.Mech,35,1968,379～386LiebowitzH.Fracture:anadvancedtreatise.NewYork:AcademicPress,IrwinGR.ysisofstressesandstrainsneartheendofacracktraversingate.Appl.Mech,1957,24:BudianskyB,RiceJR.Conservationlawsandenergyreleaserates.J.Appl.Mech,1973,40:EshelbyJD.Theelasticenergy-momentumtensor.J.Elasticity,1975,5:321-HerrmannAG,HerrmannG.Onenergy-releaseratesforanecrack.J.Appl.Mech.,1981,48:525～528McMeekingRM,EvansAG.Mechanicsoftransformationtougheninginbrittlematerials.J.Ceram.Soc.,1982,65:LiZH,YangLH.Thenear-tipstressintensityfactorsforashortcrackpartiallypenetratinganinclusion.J.Appl.Mech.,2004,71:465～469FavierD,LiuY,OrgeasL,etal.InfluenceofthermomechanicalprocessingonthesuperelasticpropertiesofaNi-richnitinolshapememoryalloy.Mater.Sci.Eng.,A.,2006,429:130～136AuricchioF,TaylorRL,LublinerJ.Shape-memoryalloys:macro-modelingandnumericalsimulationsofthesuperelasticbehavior.Comput.Method.Appl.Mech.Eng.,1997,146:281～312AuricchioF,PetriniL.Improvementsandalgorithmicalconsiderationsonarecentthree-dimensionalmodeldescribingstress-inducedsolidphasetransformations.Int.J.Numer.Method.Eng.,2005,55:AuricchioF,FugazzaD,DesRochesR.Numericalandexperimentalevaluationofthedampropertiesofshape-memoryalloys.J.Eng.Mater.Tech.,2006,128:312～319XiongF,LiuY.Effectofstress-inducedmartensitictransformationonthecracktipstress-intensityfactorinNi-Mn-Gashapememoryalloy.ActaMater.,2007,55:5621～5629YiS,GaoS.Fracturetougheningmechanismofshapememoryalloysduetomartensitetransformation.Int.J.SolidsStruct.,2000,37:5315～5327SunQ,HwangK.Micromechanicsmodelingfortheconstitutivebehaviorofpolycrystallineshapememoryalloys.J.Mech.Phys.Solids.,1993,41:1～19SunQ,HwangK.Micromechanicsmodelingfortheconstitutivebehaviorofpolycrystallineshapememoryalloys.J.Mech.Phys.Solids.,1993,41:20～33MouraB,ShihCF.Atreatmentofcracktipcontourintegrals.Int.J.Fract.,1987,35:ShivakumarKN,RajuIS.Anequivalentintegralmethodforthree-dimensionalmixed-modefractureproblem.Eng.Fract.Mech.,1992,42:935～959CrackdeflectionbythetransformableparticlesdispersedinJunlingHou,RongWang,QunLi,Hong*Correspondingauthor,:StateKeyLaboratoryStrengthandVibrationofMechanicalStructures,SchoolofAerospace,Xi’anJiaotongUniversity,Xi’anThisworkwassupportedbytheNationalNaturalScienceFoundationofwithgrantNo. ,No. ,No. andtheFundamentalResearchFundsfortheCentralUniversitiesin.Transformationtougheningisoneoftheimportantwaystoimprovethesticityandfracturetoughnessofmaterials.Inrecentyears,onthebasicoftheTRIPeffect,manyproductshavebeenwidelyusedinmanyfields.However,theresearchontheeffectofthephasetransformationonthefracturetoughnessmechanismofthematerialisinsufficiencysofar.Ourpreviousresearchshowsthattheeffectofphasetransformationonthefracturetoughnessofthematerialisnotconsistentwiththedifferentstagesofthematerialfractureprocess.Itisfoundthattheeffectofthephasetransformationnearthecracktiponthefracturetoughnessofthematerialneedstobefurtherstudied.Inthispaper,thecrackdeflectioninfluencedbyphasetransformationoftheausteniteparticleembeddedinthecrackedmaterials,isstudied yticallyandnumericallyinaustenite-martensitedualmaterial.Firstly,forasinglephaseparticlenearthecracktip,thetougheningmechanismduetothephasetransformationaccountingforbothdilatationandshearstraincanbeinvestigatedbytheconfigurational theory,the solutionofthecrackpropagationenergyreleaserateJ1tip,J2tiphasbeenobtained.Moreover,basedoncomparisonofthecracktipJktipandfar-fieldJk∞,theshieldingzoneandanti-shieldingzoneinducedbythephasetransformationhavebeendiscussedbyqualitative ysis,an