ch位错位错与晶体缺陷作用详解实用

会计学1ch位错位错与晶体缺陷作用详解实用22.1位错理论的产生一、晶体的塑性变形方式二、单晶体的塑性变形三、多晶体的塑性变形四、晶体的理论切变强度五、位错理论的产生六、位错的基本知识第1页/共47页32.2位错的几何性质一、位错的几何模型二、柏格斯矢量三、位错的运动四、位错环及其运动五、位错与晶体的塑性变形六、割阶第2页/共47页42.3位错的弹性性质一、弹性连续介质、应力和应变二、刃型位错的应力场三、螺型位错的应力场四、位错的应变能五、位错的受力六、向错七、位错的半点阵模型第3页/共47页52.4位错与晶体缺陷的相互作用一、位错间的相互作用力二、位错与界面的交互作用三、位错与点缺陷的交互作用第4页/共47页6InteractionsBetweenDislocationsWewillfirstinvestigatetheinteractionbetweentwostraightandparalleldislocationsofthesamekind.Ifwestartwithscrewdislocations,wehavetodistinguishthefollowingcases:

第5页/共47页7Inanalogy,wenextmustconsidertheinteractionofedgedislocations,ofedgeandscrewdislocationsandfinallyofmixeddislocations.Thecaseofmixeddislocations-thegeneralcase-willagainbeobtainedbyconsideringtheinteractionofthescrew-andedgepartsseparatelyandthenaddingtheresults.

Withtheformulasforthestressandstrainfieldsofedgeandscrewdislocationsonecancalculatetheresolvedshearstresscausedbyonedislocationontheglideplaneoftheotheroneandgeteverythingfromthere.Butforjustobtainingsomebasicrules,wecandobetterthanthat.Wecanclassifysomebasiccaseswithoutcalculatinganythingbyjustexaminingoneobviousrule:Ifthesuperpositionofthestrainfieldsofdislocationsadduptovaluesofthecompressiveortensilestrainlargerthanthoseofasingledislocations,theywillrepulseeachother.Ifthecombinedstrainfieldislowerthanthatofthesingledislocation,theywillattracteachother.第6页/共47页8Thisleadstosomesimplecases:1.Arbitrarilycurveddislocationswithidentical

bonthesameglideplanewillalwaysrepeleachother.

第7页/共47页92.Arbitrarydislocationswithopposite

bvectorsonthesameglideplanewillattractandannihilateeachother

EdgedislocationswithidenticaloroppositeBurgersvectorbonneighboringglideplanesmayattractorrepulseeachother,dependingontheprecisegeometry.Thebluedoublearrowsinthepicturebelowthusmaysignifyrepulsionorattraction.第8页/共47页10ThegeneralformulafortheforcesbetweenedgedislocationsinthegeometryshownaboveisFx

=

[Gb2/2p(1–n)]

·

[x·(x2–y2)/(x2+y2)2]Fy

=

[Gb2/2p(1–n)]

·[

y·(3x2+y2)/(x2+y2)2]

Fory=0,i.e.thesameglideplane,wehavea1/xor,moregenerallya1/rdependenceoftheforceonthedistancerbetweenthedislocations.Fory<0ory>0wefindzonesofrepulsionandattraction.Atsomespecificpositionstheforceiszero-thiswouldbetheequilibriumconfigurations;itisshownbelow.TheformulaforFyisjustgivenforthesakeofcompleteness.Sincethedislocationscannotmoveiny-direction,itisoflittlerelevancesofar.第9页/共47页11Theillustrationinthelinkgivesaquantitativepictureoftheforcesactingononedislocationonitsglideplaneasafunctionofthedistancetoanotherdislocation.第10页/共47页12一、位错间的相互作用力第11页/共47页13第12页/共47页14（一）相互平行的两个螺位错间的作用力（二）相互平行的两个刃位错间的作用力（三）其它情况的位错之间的作用力（四）位错运动的晶格阻力－P-N力第13页/共47页15（一）相互平行的两个螺位错间的作用力第14页/共47页16上式说明，两平行螺位错之间只有径向交互作用，因而交互作用力是一中心力。（即Fθ=Fz=0,Fr≠0）第15页/共47页17（二）相互平行的两个刃位错间的作用力σyy

与σzz

不考虑，它们对位错运动无影响σxx

使b2攀移σyx使b2滑移第16页/共47页18根据F=τb有：Fyx=σyx•b，Fxx=σxx•b第17页/共47页19第18页/共47页20第19页/共47页21第20页/共47页22第21页/共47页23ForcesbetweenEdgeDislocationsShownistheforcebetweenedgedislocationsofidenticalandoppositeBurgersvectorsasafunctionoftheirnormalizeddistance.Thedistancexbetweenthedislocationsisexpressedinunitsofy,thedistanceoftheglideplanes.第22页/共47页24Theforcechangesfromrepulsivetoattractiveorviceverseforadistancex=y;i.e.ifthedislocationsareatanangleof45orelativetotheglideplane.The45opositionisastableequilibriumpositionforoppositeBurgersvectors,becauseatthispositionF=0,anddF/dx<0.Fordislocationswithidenticalbvectors,thestablepositionisatx=0.第23页/共47页25示。第24页/共47页26（三）其它情况的位错之间的作用力1.两相互垂直的螺位错之间的作用力2.相互垂直的螺位错与刃位错之间的作用力3.平行螺位错与刃位错之间的相互作用4.具有任意伯格斯矢量的平行位错第25页/共47页271.两相互垂直的螺位错之间的作用力恒值。第26页/共47页282.相互垂直的螺位错与刃位错之间的作用力第27页/共47页293.平行螺位错与刃位错之间的相互作用因为无驱使对方运动的应力分量，所以无交互作用。＝A•b1

•b2=0第28页/共47页304.具有任意伯格斯矢量的平行位错具有任意伯格斯矢量的平行位错大于第29页/共47页31Thedislocationannihilationbycross-slipAnnihilationofascrewdipolebycross-slip:Twodislocationsofoppositesignglideinneighbouringparallelslipplanesandannihilateeachotherbychangingtheirslipplanes.

第30页/共47页32Thedislocationdoublecross-slipObstacleby-passing:Ascrewdislocationcanby-passanobstacle,hereasessiledislocationsegmentofsamesign,byadoublecross-slipprocess.第31页/共47页33（四）位错运动的晶格阻力－P-N力第32页/共47页34上第33页/共47页35表,与实验数据相符。第34页/共47页36二、位错与界面的交互作用第35页/共47页37第36页/共47页38三、位错与点缺陷的交互作用（一）刃位错与点缺陷的交互作用（二）螺位错与点缺陷的交互作用（三）关于空位与位错的作用第37页/共47页39（一）刃位错与点缺陷的交互作用设置换式溶质原子R`>基体原子R柯垂耳(Cottrell)处理:假设(1)晶体为连续弹性介质;(2)溶质原子为刚球;(3)溶质原子引起的点阵畸变是球形对称畸变.则溶质原子溶入,相当于在(r,θ)处挖一个R的球形洞,再挤入一个R`的刚球.交互作用能=刚球挤入过程中反抗位错应力场做的功=位错应力场做的负功由第38页/共47页40第39页/共47页41溶质原子R`>基体原子R,即第40页/共47页42第41页/共47页43（二）螺位错与点缺陷的交互作用因为螺位错是纯切应力场，所以当点缺陷引起球形对称畸变时，两者无交互作用；若点缺陷引起的是非球形对称畸变时，则溶质原子与位错仍发生交互作用，结果使溶质原子向位错偏聚，形成溶质原子气团；例如，钢中的C、N溶入bcc铁的八面体间隙时，引起非球形对称畸变（称为四方畸变），其应力场既有正应力，又有切应力，能与位错发生交互作用；螺型位错的纯切应力场可以等效一个正应力场，使溶质原子择优分布，形成史诺克（Snock）气团，对位错有强烈的钉扎作用。第42页/共47页44第43页/共47页45（三）关于空位与位错的作用第44页/共47页46ThefundamentalinteractionsbetweendislocationsandelasticobstaclesThegoaloftheworkistounderstandthefundamentalinteractionsbetweendislocationsandelasticobstacles.Theprimarytoolthatwillbeusedisthein-situTEMdeformationtechnique.Withthistechniqueitispossibletodirectlyobservetheinteractionbetweendislocationsandelasticobstaclesathighspatialresolution.Fromtheseobservations,themagnitudeofthepinningstrength,thebypassmechanism,andtheprocessbywhichdislocationloopsaredestroyedcanbeascertained.Copperwasselectedsimplyforeaseofcomparisonwithcomputersimulationstudies.In-situTEMstrainingspecimensof99.999%purepolycrystallineCuwerecutfrom250mmthickcoldrolledstripinto11mmby2.7mmpieces.Holesforthestrainingpinsinthestageweredrilledintheendsofthetensilebarsfollowedbypolishingthesurfacestoa600-gritfinish.Sampleswe