第七章 固体材料的塑性变形.docx

第七章 固体材料的塑性变形.docx

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第七章固体材料的塑性变形

第七章固体材料的塑性变形

Chapter7PlasticDeformation

1.比较塑性变形两种基本形式：

滑移与孪生的异同点；

2.滑移的临界分切应力；

3.滑移的位错机制；

4.多晶体塑性变形的特点；

5.细晶强化与Hall-Petch公式；

6.屈服现象与应变时效；

7.弥散强化；加工硬化；

8.形变织构与残余应力；

QuestionforChapter7

1.Thedifferencebetweenslipandtwining;

2.Criticalresolvedstressesforslip;

3.Mechanismofslip;

4.Thecharacteristicsofpolycrystallinedeformation;

5.GrainrefinementandPetch-Hallequation;

6.Yieldandstrainaging;

7.Precipitationhardeningandwork（orstrain）hardening;

8.Deformationtexturesandresidualstresses

7-1应力－应变曲线

Sec.7.1Stress-strainCurves

材料受力变形的特性，可以用“应力一应变”曲线来描述，如图7.1所示。

工程上应力、应变可按下式确定：

图7.1工程力学应力-应变曲线

stress

strain

oA:

elasticdeformation;

Hooke’slaw:

σ=Eε

E—elasticmodulus

AtpointA’;σe—elasticlimit.

AbovepointA’:

plasticdeformation

εT=ln

=ln（1+）（指数曲线）

AtpointA.σs—yieldstrengthoryieldlimit.;

AtpointCσb—tensilestrength;

C—necking;

AtpointK:

σk—fracturestrength;.

elongation

contractionofareaorpercentagereductionofarea.

图7.2真应力-真应变曲线和工程应力应变曲线

金属材料发生塑形变形（即所谓材料开始屈服）后，应力应变关系摆脱了Hoke定律的约束，进入了一个新的极其复杂的领域。

通常我们把从屈服点开始到最大载荷点，这一步均匀塑性变形的真应力—真应变曲线称作流变曲线，所对应的真应力称作流变应力。

流变曲线可用经验公式表示，即

（指数曲线）（7-7）

式中K是强化系数，n是应变硬化指数。

K和n都跟材料本身有关，一些金属材料的K和n值如表7-1所示。

试样产生颈缩后，由于颈缩区受了三向应力状态，使形

表7-1一些金属材料的K和n值（室温）

金属材料

状态

n值

K值

0.05%C钢

退火

0.26

532

0.6%C钢

淬火+538°回火

0.10

1575

0.6%C钢

淬火+704°回火

0.19

1230

铜

退火

0.54

320

7-3黄铜

退火

0.49

897

变受到约束，使真应力真应变又变到近似直线关系。

如果欲求得不受三向应力影响的真应力，还要加以修正。

不过这个修正是很难做到精确的。

应变指数n反映了材料抵抗塑性变形的能力。

n愈大，变形时应变强化愈显著，即材料继续塑性变形时，所需要的应力要提高。

n=0表示材料呈完全塑性；

n=1表示材料呈完全弹性。

对于大多数金属材料来说：

n=0.10~0.50。

所谓材料的韧性就是指试棒断裂前所吸收的能量，即

也就是流变曲线下面所包围的面积。

7-2单晶体的塑性变形

Sec.7.2PlasticDeformationofSingleCrystals

常温下塑性变形的主要方式：

滑移和孪生。

1.滑移

（1）滑移：

在切应力作用下，晶体的一部分相对于另一部分沿着一定的晶面（滑移面）和晶向（滑移方向）产生相对位移，且不破坏晶体内部原子排列规律性的塑变方式。

光镜下：

滑移带（无重现性）。

（2）滑移的表象学

电镜下：

滑移线。

（3）滑移的晶体学

滑移面（密排面）SLIPPLANES

（a）几何要素

滑移方向（密排方向）SLIPDIRECTIONS

（b）滑移系SLIPSYSTEMS

Thecombinationofaslipplaneandoneofitsclose-packeddirectionsdefinesapossibleslipmodeorslipsystem.

滑移系：

一个滑移面和该面上一个滑移方向的组合。

滑移系的个数:

（滑移面个数）×（每个面上所具有的滑移方向的个数）

典型滑移系

晶体结构

滑移面

滑移方向

滑移系数目

常见金属

面心立方

{111}×4

<110>×3

12

Cu,Al,Ni,Au

{110}×6

×2

12

Fe,W,Mo

体心立方

{121}×12

<111>×1

12

Fe,W

{123}×24

×1

24

Fe

{0001}×1

×3

3

Mg,Zn,Ti

密排六方

{1010}

<1120>

3

Mg,Zr,Ti

{1011}

6

Mg,Ti

一般滑移系越多，塑性越好；

滑移系数目与材料塑性的关系：

与滑移面密排程度和滑移方向个数有关；

与同时开动滑移系数目有关（c）。

Itisanexperimentalfactthatinmetalcrystalsslip,orglide,occurspreferentiallyonplanesofhigh-atomicdensity.Itisageneralrulethattheseparationbetweenparallellatticeplanesvariesdirectlyasthedegreeofpackingintheplanes.Therefore,crystalsareshearedmosteasilyonplanesofwideseparation.Thisstatementdoesnotmeanthatslipcannotoccurinagivencrystalonplanesotherthanthemostcloselypackedplane.Rather,itmeansthatdislocationsmovemoreeasilyalongplanesofwidespacingwherethelatticedistortionduetothemovementofthedislocationissmall.

Notonlydoessliptendtotakeplaceonpreferredcrystallographicplanes,butthedirectionofshearassociatedwithslipisalsocrystallographic.Theslipdirectionofacrystal（sheardirection）hasbeenfoundtobealmostexclusivelyaclose-packeddirection,alatticedirectionwithatomsarrangedinastraightline,onetouchingthenext.Thistendencyforsliptooccuralongclose-packeddirectionsismuchstrongerthanthetendencyforsliptooccuronthemostcloselypackedplane.Forpracticalpurposes,itcanusuallybeassumedthatslipoccursinaclose-packeddirection.

Thefactthattheexperimentallydeterminedslipdirectioncoincideswiththeclose-packeddirectionsofacrystalcanbeexplainedintermsofdislocations.Whenadislocationmovesthroughacrystal,thecrystalisshearedbyanamountequaltotheBurgersvectorofthedislocation.Afterthedislocationhaspassed,thecrystalmustbeunchangedinthegeometryoftheatoms;thatis,thesymmetryofthecrystalmustberetained.Thesmallestshearthatcanfulfillthisconditionequalsthedistancebetweenatomsinaclose-packeddirection.

（c）滑移的临界分切应力CRITICALRESOLVEDSHEARSTRESS（c）

Itisawell-knownfactthatpolycrystallinemetalspecimenspossessayieldstressthatmustbeexceededinordertoproduceplasticdeformation.Itisalsotruethatmetalsinglecrystalsneedtobestressedaboveasimilaryieldpointbeforeplasticdeformationbyslipbecomesmacroscopicallymeasurable.Sinceslipiscausedbyshearstresses,theyieldstressforcrystalsisbestexpressedintermsofashearstressresolvedontheslipplaneandintheslipdirection.Thisstressiscalledthecriticalresolvedshearstress.Itisthestressthatwillcausesufficientlylargenumbersofdislocationstomovesothatameasurablestraincanbeobserved.Mostcrystalspecimensarenottesteddirectlyinshear,butintension.Therearegoodreasonsforthis.Themostimportantreasonisthatitisalmostimpossibletotestacrystalindirectshearwithoutintroducingbendingmomentswherethespecimenisgripped.Theeffectofthesebendingmomentsistoproduceshearstresscomponentsonslipplanesotherthantheoneonwhichitisdesiredtostudyslip.Ifslipontheseplanesisnotmeasurablymoredifficultthanontheplanetobetested,oneobtainsaconditionwhereslipoccursonseveralslipplanesoverthosepartsofthespecimennearthegrips.Theeffectofthisdeformationmaybetocausebendingofthespecimennearthegrips,andoneisthusleftwithadeformationthatisfarfromhomogeneous.Therearealsoproblemsassociatedwiththeuseofsinglecrystaltensilespecimens,butthesearelessseriousand,byproperdesignofthegrips,theymaybelargelyeliminated.

Anequationwillnowbederivedthatrelatestheappliedtensilestresstotheshearstressresolvedontheslipplaneandintheslipdirection.

Lettheinclinedplaneatthetopofthecylindricalcrystalcorrespondtotheslipplaneofthecrystal.Thenormaltotheslipplaneandtheslipdirectionareindicatedbythelinespandd,respectively.Theanglebetweentheslipplanenormalandthestressaxisisrepresentedbyθ,andthatbetweentheslipdirectionandthestressaxisbyф.Theaxialtensileforceappliedtothecrystalisdesignatedbyfn.

Thecross-sectionareaofthespecimenperpendiculartotheappliedtensileforceistotheareaoftheslipplaneasthecosineoftheanglebetweenthetwoplanes.Thisangleisthesameastheanglebetweenthenormalstothetwoplanesinquestionandistheangleθinthefigure.Thus,

or

WhereAnisthecross-sectionareaperpendiculartothespecimenaxis,andAsptheareaoftheslipplane.Thestressontheslipplaneequalstheappliedforcedividedbytheareaoftheslipplane:

WhereσAisthestressontheslipplaneinthedirectionoftheoriginalforcefn.Thisisnot,however,theshearstressthatactsintheslipdirection,butthetotalstressactingontheslipplane.ThecomponentofthisstressparalleltotheslipdirectionisthedesiredshearstressandmaybeobtainedbymultiplyingσAbycosф,whereфistheanglebetweenσAandτtheresolvedshearstress.Asaresultoftheabove,wecannowwrite

Whereτistheshearstressresolvedontheslipplaneandintheslipdirection.Finally,sincefn/Anistheappliedtensileforcedividedbytheareanormaltothisforce,thistermmaybereplacedbyσthenormaltensilestress:

SeveralimportantconclusionsmaybedrawnfromEq.

.Ifthetensileaxisisperpendiculartotheslipplane,theangleфis90˚andtheshearstressiszero.Similarly,ifthestressaxisliesintheslipplane,theangleθis90˚andtheshearstressisagainzero.Thus,itisnotpossibletoproducesliponagivenplanewhentheplaneiseitherparallelorperpendiculartotheaxisoftensilestress.Themaximumshearstressthatcanbedevelopedequals0.5σandoccurswhenbothθandфequal45˚.Forallothercombinationsofthesetwoangles,theresolvedshearstressissmallerthanone-halfthetensilestress.

InregardtoEq.

itisimportanttonotethattheresolvedshearstressτduetoatensilestressσdependsonthecosinesoftheanglesbetweentwopairsofdirections;thatis,thecosineoftheangleθbetweenthetensilestressaxisandtheslipplanepoleandthecosineoftheangleфbetweenthetensilestressaxisandtheslipdirection.Assumingthatonehasacubiccrystalandthedirectionindicesforthesethreedirectionsareknown,onecaneasilycomputethesecosineswiththeaidofthefollowingequation:

Whereh1,k1,andl1arethedirectionindicesofoneofthedirectionsandh2,k2,andl2arethedirectionindicesoftheotherdirection.

Thus,toillustratetheuseoftheEq.,supposethatonewishestofindthecosineoftheanglebetweenthe[121]and[

]directions.Inthiscasewehave

orcosф=0.258andф=75.04˚.

Ithasbeenexperimentallyverifiedthatthecriticalresolvedshearstressforagivencrystallographicplaneisindependentoftheorientationofthecrystalforsomemetals.Thus,ifanumberofcrystals,differingonlyintheorientationoftheslipplanetotheaxisoftensilestress,arepulledintension,andtheshearstressatwhichtheyyieldiscomputedwiththeaboveequation,itwillbefoundthattheyieldstressisaconstant.

Insomemetalsthecriticalresolvedshearstressforsliponagiventypeofplaneisremarkablyconstantforcrystalsofthesamecompositionandprevioustreatment.However,thecriticalresolvedshearstressissensitivetochangesincompositionandhandling.

Thecriticalresolvedshearst