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1、12.1 2.1 位错理论的产生位错理论的产生一、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22.2 2.2 位错的几何性质位错的几何性质一、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32.3 2.3 位错的弹性性质位错的弹性性质一、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42.4 2.4 位错与晶体缺陷的相互作用位错与晶体缺陷的相互作用一、位
2、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5Interactions Between DislocationsWewillfirstinvestigatetheinteractionbetweentwostraightandparalleldislocationsofthesamekind.qIfwestartwithscrewdislocations,wehavetodistinguishthefollowingcases:第5页/共47页6Inanalogy,wenextmustconsidertheinteractionofedgedislocat
3、ions,ofedgeandscrewdislocationsandfinallyofmixeddislocations.qThecaseofmixeddislocations-thegeneralcase-willagainbeobtainedbyconsideringtheinteractionofthescrew-andedgepartsseparatelyandthenaddingtheresults.Withtheformulasforthestressandstrainfieldsofedgeandscrewdislocationsonecancalculatetheresolve
4、dshearstresscausedbyonedislocationontheglideplaneoftheother oneandgeteverythingfromthere.Butforjustobtainingsomebasicrules,wecandobetterthanthat.Wecanclassifysomebasic caseswithoutcalculatinganythingbyjustexaminingoneobviousrule:qIfthesuperpositionofthestrainfieldsofdislocationsadduptovaluesofthecom
5、pressiveortensilestrainlargerthanthoseofasingledislocations,theywillrepulseeachother.Ifthecombinedstrainfieldislowerthanthatofthesingledislocation,theywillattracteachother.第6页/共47页7Thisleadstosomesimplecases:1.Arbitrarilycurveddislocationswithidenticalbonthesameglideplanewillalwaysrepeleachother.第7页
6、/共47页82.Arbitrarydislocationswithoppositebvectorsonthesameglideplanewillattract and annihilateeachotherEdge dislocations with identical or opposite Burgers vector b on neighboring glide planes may attract or repulse each other,depending on the precise geometry.The blue double arrows in the picture b
7、elow thus may signify repulsion or attraction.第8页/共47页9ThegeneralformulafortheforcesbetweenedgedislocationsinthegeometryshownaboveisFx=Gb2/2p(1n)x(x2y2)/(x2+y2)2Fy=Gb2/2p(1n)y(3x2+y2)/(x2+y2)2qFory=0,i.e.thesameglideplane,wehavea1/xor,moregenerallya1/rdependenceoftheforceonthedistancerbetweenthedisl
8、ocations.qFory0wefindzonesofrepulsionandattraction.Atsomespecificpositionstheforceiszero-thiswouldbetheequilibriumconfigurations;itisshownbelow.qTheformulaforFyisjustgivenforthesakeofcompleteness.Sincethedislocationscannotmoveiny-direction,itisoflittlerelevancesofar.第9页/共47页10Theillustrationinthelin
9、kgivesaquantitativepictureoftheforcesactingononedislocationonitsglideplaneasafunctionofthedistancetoanotherdislocation.第10页/共47页11一、位错间的相互作用力第11页/共47页12第12页/共47页13（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14（一）相互平行的两个螺位错间的作用力第14页/共47页15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
10、是一中心力。（即F=Fz=0,Fr0）第15页/共47页16（二）相互平行的两个刃位错间的作用力yy与zz不考虑，它们对位错运动无影响xx使b2攀移yx使b2滑移第16页/共47页17根据F=b有：Fyx=yxb，Fxx=xxb第17页/共47页18第18页/共47页19第19页/共47页20第20页/共47页21第21页/共47页22Forces between Edge Dislocations ShownistheforcebetweenedgedislocationsofidenticalandoppositeBurgersvectorsasafunctionoftheirnormal
11、izeddistance.qThedistancexbetweenthedislocationsisexpressedinunitsofy,thedistanceoftheglideplanes.第22页/共47页23qTheforcechangesfromrepulsivetoattractiveorviceverseforadistancex=y;i.e.ifthedislocationsareatanangleof45orelativetotheglideplane.qThe45opositionisastableequilibriumpositionforoppositeBurgers
12、vectors,becauseatthispositionF=0,anddF/dx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,)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39第39页/共47页40溶质原子R基体原子R,即第40页/共47页41第41页/共47页42（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
13、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43第43页/共47页44（三）关于空位与位错的作用第44页/共47页45The fundamental interactions between dislocations and The fundamental interactions bet
14、ween dislocations and elastic obstacleselastic obstaclesThegoaloftheworkistounderstandthefundamental interactions between dislocations andelasticobstacles.Theprimarytoolthatwillbeusedis the in-situ TEM deformation technique.With thistechnique it is possible to directly observe theinteractionbetweend
15、islocationsandelasticobstacles at high spatial resolution.From theseobservations,themagnitudeofthepinningstrength,the bypass mechanism,and the process by whichdislocation loops are destroyed can be ascertained.Copper was selected simply for ease of comparisonwithcomputersimulationstudies.In-situTEMs
16、trainingspecimensof 99.999%pure polycrystallineCuwerecutfrom250mmthickcoldrolledstripinto11mmby2.7mmpieces.Holesforthestrainingpinsin the stage were drilled in the ends of the tensilebarsfollowedbypolishingthesurfacestoa600-gritfinish.Samples were then annealed at 750 C in avacuumfurnacefor2hoursand
17、allowedtofurnace-coolinordertoproducelargeequiaxedgrains.Thinfoilswereproducedbytwin-jetelectropolishinginasolution of 33%nitric acid in methanol cooled to 20Catacurrentof0.11A/cm2.第45页/共47页46Figure1.Thecapturedvideoframecontainsapinneddislocationattheinstantbeforebreakingfree(Left).Thedistancebetwe
18、enobstacles,l,ismeasured.Inanimageeditingcomputerapplication,circlesaredrawntoasizewhereaportionofthecircleapproximatesthedislocationcurvatureonbothsidesoftheobstacle(Right).Tangentlinesaredrawnonthecircleswiththeiroriginatthepinningpoint.Theangle2ismeasuredbetweenthetangentlines.第46页/共47页47感谢您的欣赏！第47页/共47页