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.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
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