材料力学专业英语课件

Chapter1TensionandCompression第一章拉伸与压缩Chapter1第一章1AxiallyLoadedBar

Thesimplestcasetoconsideratthestartisthatofaninitiallystraightmetalbarofconstantcrosssection,loadedatitsendsbyapairofoppositelydirectedcollinearforcescoincidingwiththelongitudinalaxisofthebarandactingthroughthecentroidofeachcrosssection.Forstaticequilibriumthemagnitudesoftheforcesmustbeequal.Iftheforcesaredirectedawayfromthebar,thebarissaidtobeintension;iftheyaredirectedtowardthebar,astateofcompressionexists.ThesetwoconditionsareillustratedinFig.1-1.

轴向受载杆件同线的质心平衡大小不变的AxiallyLoadedBarThes2

首先我们研究最简单情况：一等截面金属直杆在其两端承受一对共线、反向力的作用。这两个力的作用线与各截面形心组成的纵向轴线重合，为了满足静力学平衡条件，这两个力的数值必须相等。如果这两个力的方向是离开此杆的，杆将承受拉伸；如果这两个力是指向此杆的，杆将承受压缩，如图1-1所示。Fig.1-1图1-1首先我们研究最简单情况：一等截面金属直杆在其两3

Undertheactionofthispairofappliedforces,internalresistingforcesaresetupwithinthebarandtheircharacteristicsmaybestudiedbyimaginingaplanetobepassedthroughthebaranywherealongitslengthandorientedperpendiculartothelongitudinalaxisofthebar.Suchaplaneisdesignatedasa-ainFig.1-2(a).Fig.1-2图1-2垂直的，正交的

在这样两个力的作用之下，杆的内部将产生抗力。我们可以用位于杆轴某处、且与杆轴垂直的假想截面来研究杆的内部抗力，这样的截面如图1-2（a）中的a-a所示。Undertheactionoft4Ifforpurposesofanalysistheportionofthebartotherightofthisplaneisconsideredtoberemoved,asinFig.1-2(b),thenitmustbereplacedbywhatevereffectitexertsupontheleftportion.Bythistechniqueofintroducingacuttingplane,theoriginallyinternalforcesnowbecomeexternalwithrespecttotheremainingportionofthebody.Forequilibriumoftheportiontotheleftthis“effect”mustbeahorizontalforceofmagnitudeP.However,thisforcePactingnormaltothecross-sectiona-aisactuallytheresultantofdistributedforcesactingoverthiscrosssectioninadirectionnormaltoit.施加（力）水平的法线合力分布式的Ifforpurposesofanalysisth5为了分析计算，可考虑将此截面右侧的杆段除去，如图1-2（b）所示。因而，必须补充右侧杆段对左侧杆段的作用。用此处引入的截面法，初始的内力便成为保留杆段的外力。为使左侧杆段平衡，这种效应在数值上等于水平力P。然而，沿截面a-a法向作用的力P实际上是截面上法向分布力合成的结果。Fig.1-2图1-2为了分析计算，可考虑将此截面右侧的杆段除去，如图1-2（b）6

Insteadofspeakingoftheinternalforceactingonsomesmallelementofarea,itisbetterforcomparativepurposestotreatthenormalforceactingoveraunitareaofthecrosssection.Theintensityofnormalforceperunitareaistermedthenormalstressandisexpressedinunitsofforceperunitarea,e,g.,1N/m2.NormalStress法应力把…称作比较的应力Insteadofspeak7替代讨论作用在某处小面积上内力，最好转为处理单位面积上法向力。单位面积上法向力的强度称为法应力，它是用单位面积上的作用力单位表示的，亦即1替代讨论作用在某处小面积上内力，最好转为处理单位面积上法向力8Iftheforcesappliedtotheendsofthebararesuchthatthebarisintension,thentensilestressesaresetupinthebar;ifthebarisincompressionwehavecompressivestresses.Itisessentialthatthelineofactionoftheappliedendforcespassthroughthecentroidofeachcrosssectionofthebar.如果杆端的力使杆拉伸，杆内就产生拉应力，如果杆是受压缩的，杆内产生压应力。施加在杆端的力作用线必须通过每一个截面形心。Iftheforcesappliedtothee9

TheaxialloadingshowninFig.1-2(a)occursfrequentlyinstructuralandmachinedesignproblems.Tosimulatethisloadinginthelaboratory,atestspecimenisheldinthegripsofeitheranelectricallydrivengear-typetestingmachineorahydraulicmachine.Bothofthesemachinesarecommonlyusedinmaterialstestinglaboratoriesforapplyingaxialtension.TestSpecimens试样样品夹具电力地液压的应用，施加Theaxialloadingsho10

图1-2（a）所示的轴向载荷经常出现在结构和机械设计中，为了在实验室中模拟这种轴向载荷，试件应夹持在电子或液压万能试验机的夹头中。这两种试验机通常在材料实验室用做施加轴向载荷。图1-2（a）所示的轴向载荷经常出现在结构11InanefforttostandardizematerialstestingtechniquestheAmericanSocietyforTestingMaterials(ASTM)hasissuedspecificationsthatareincommonuse.Onlytwoofthesewillbementionedhere,oneformetalplatesthickerthanin(4.76mm)andappearingasinFig.1-3,theotherformetalsover1.5in(38mm)thickandhavingtheappearanceshowninFig.1-4.在材料实验技术规范标准中，美国材料实验协会颁布了详细的使用说明。此处只讲其中两种试件。一种厚度超过3/16in（4.76mm）的金属板试件如图1-3所示，另外一种直径为1.5in（38mm）的金属圆棒状试件如图1-4所示。标准化Inanefforttosta12Asmaybeseenfromthesefigures,thecentralportionofthespecimenissomewhatsmallerthantheendregionssothatfailurewillnottakeplaceinthegrippedportion.Theroundedfilletsshownareprovidedsothatnostressconcentrationswillariseatthetransitionbetweenthetwolateraldimensions.Thestandardgagelengthoverwhichelongationsaremeasuredis8in(203mm)forthespecimenshowninFig.1-3and2in(57mm)forthatshowninFig.1-4.正如图中所看到的，试件的中部区域尺寸略小于两端尺寸。因而，破环不会发生在两端的夹持段，过度圆角保证试件两种尺寸的过渡部位不会发生应力集中。供测量伸长的标距长度为8in（203mm，图1-3试件）和2in（51mm，图1-4试件）。稍微，有些失效，破坏过渡区伸长标距Asmaybeseenfromthesefigu13Theelongationsaremeasuredbyeithermechanicaloropticalextensometersorbycementinganelectricresistance-typestraingagetothesurfaceofthematerial.Thisresistancestraingageconsistsofanumberofveryfinewiresorientedintheaxialdirectionofthebar.Asthebarelongates,theelectricalresistanceofthewireschangesandthischangeofresistanceisdetectedonaWheatstonebridgeandinterpretedaselongation.伸长计粘贴电阻应变片细的转换Theelongationsare14试件的伸长既可以使用机械的、光学的伸长计，也可以使用粘贴在试件表面的电阻应变片来测量，这种电阻应变片由若干个沿试件轴向的、很细的电阻丝组成。当试件伸长时，电阻丝的电阻就会发生改变，电阻的改变由惠斯通电桥测量并转换为伸长量。试件的伸长既可以使用机械的、光学的伸长计，也可15

Letussupposethatoneofthesetensionspecimenshasbeenplacedinatension-compressiontestingmachineandtensileforcesgraduallyappliedtotheends.

Theelongationoverthegagelengthmaybemeasuredasindicatedaboveforanypredeterminedincrementsoftheaxialload.Fromthesevaluestheelongationperunitlength,whichistermednormalstrainanddenotedbyε,maybefoundbydividingthetotalelongationΔbythegagelengthL,thatis,ε=Δ/L.

Thestrainisusuallyexpressedinunitsofinchesperinchormeterspermeterandconsequentlyisdimensionless.NormalStrain法应变应变增量Letussuppose16对于每一个事先指定的轴向载荷增量都要测量相应的标距的伸长。由这些数值得到单位长度的伸长，并将之定义为法应变，用ε来表示，可以用标距长度L去除总伸长Δ来得到法应变。对于每一个事先指定的轴向载荷增量都要测量相应17

Astheaxialloadisgraduallyincreasedinincrements,thetotalelongationoverthegagelengthismeasuredateachincrementofloadandthisiscontinueduntilfractureofthespecimentakesplace.Knowingtheoriginalcross-sectionalareaofthetestspecimenthenormalstress,denotedbyσ,maybeobtainedforanyvalueofaxialloadbytheuseoftherelationStress-StrainCurve应力—应变曲线Astheaxialloadi18wherePdenotestheaxialloadinpoundsorNewtonsandAtheoriginalcross-sectionalarea.Havingobtainednumerouspairsofvaluesofnormalstressσandnormalstrainε,theexperimentaldatamaybeplottedwiththesequantitiesconsideredasordinateandabscissa,respectively.Thisisthestress-straincurveordiagramofthematerialforthistypeofloading.Stress-straindiagramsassumewidelydifferingformsforvariousmaterials.Figure1-5isthestress-straindiagramforamedium-carbonstructuralsteel,Fig.1-6isforanalloysteel,andFig.1-7isforhardsteelsandcertainnonferrousalloys.FornonferrousalloysandcastironthediagramhastheformindicatedinFig.1-8,whileforrubbertheplotofFig.1-9istypical.

量，数量纵坐标横坐标碳素结构钢有色金属合金铸铁wherePdenotestheaxialload19P是轴向载荷，A是初始截面积。于是，得到由法应力σ和法应变ε组成的很对数据对，然后分别以法应力为纵轴，法应变为横轴，用上述实验数据作图，这就是材料的应力—应变曲线或拉伸图。图1-5是碳素结构钢的应力—应变图，图1-6是合金钢，图1-7是硬质刚或某些有色金属合金的应力—应变图，有色金属合金或铸铁的应力—应变图如图1-8所示，而对于橡胶，图1-9是典型的应力—应变图。P是轴向载荷，A是初始截面积。于是，得到由法应力σ和法应变ε20材料力学专业英语课件211.Theconceptsofstressandstraincanbeillustratedinanelementarywaybyconsideringtheextensionofaprismaticbar.Asshowninfig.1,aprismaticbarisonethathasconstantcrosssectionthroughoutitslengthandastraightaxis,inthisillustrationthebarisassumedtobeloadedatitsendsbyaxialforcesPthatproduceauniformstretching,ortension,orthebar.Atthelefthandthetensileforce1.Theconceptsofstressand222.Bymakinganartificialcut(sectionmm)throughthebaratrightanglestoitsaxis,weanisolatepartofthebarasafreebody[seeFig.1(b)].AtthelefthandthetensileforcePisapplied,andattheotherendthereareforcesrepresentingtheactionoftheremovedportionofthebaruponthepartthatremains.Theseforceswillbecontinuouslydistributedoverthecrosssection,analogoustothecontinuousdistributionofhydrostaticpressureoverasubmergedsurface.Atthelefthandthetensileforce2.Bymakinganartificialcut23Chapter1TensionandCompression第一章拉伸与压缩Chapter1第一章24AxiallyLoadedBar

Thesimplestcasetoconsideratthestartisthatofaninitiallystraightmetalbarofconstantcrosssection,loadedatitsendsbyapairofoppositelydirectedcollinearforcescoincidingwiththelongitudinalaxisofthebarandactingthroughthecentroidofeachcrosssection.Forstaticequilibriumthemagnitudesoftheforcesmustbeequal.Iftheforcesaredirectedawayfromthebar,thebarissaidtobeintension;iftheyaredirectedtowardthebar,astateofcompressionexists.ThesetwoconditionsareillustratedinFig.1-1.

轴向受载杆件同线的质心平衡大小不变的AxiallyLoadedBarThes25

首先我们研究最简单情况：一等截面金属直杆在其两端承受一对共线、反向力的作用。这两个力的作用线与各截面形心组成的纵向轴线重合，为了满足静力学平衡条件，这两个力的数值必须相等。如果这两个力的方向是离开此杆的，杆将承受拉伸；如果这两个力是指向此杆的，杆将承受压缩，如图1-1所示。Fig.1-1图1-1首先我们研究最简单情况：一等截面金属直杆在其两26

Undertheactionofthispairofappliedforces,internalresistingforcesaresetupwithinthebarandtheircharacteristicsmaybestudiedbyimaginingaplanetobepassedthroughthebaranywherealongitslengthandorientedperpendiculartothelongitudinalaxisofthebar.Suchaplaneisdesignatedasa-ainFig.1-2(a).Fig.1-2图1-2垂直的，正交的

在这样两个力的作用之下，杆的内部将产生抗力。我们可以用位于杆轴某处、且与杆轴垂直的假想截面来研究杆的内部抗力，这样的截面如图1-2（a）中的a-a所示。Undertheactionoft27Ifforpurposesofanalysistheportionofthebartotherightofthisplaneisconsideredtoberemoved,asinFig.1-2(b),thenitmustbereplacedbywhatevereffectitexertsupontheleftportion.Bythistechniqueofintroducingacuttingplane,theoriginallyinternalforcesnowbecomeexternalwithrespecttotheremainingportionofthebody.Forequilibriumoftheportiontotheleftthis“effect”mustbeahorizontalforceofmagnitudeP.However,thisforcePactingnormaltothecross-sectiona-aisactuallytheresultantofdistributedforcesactingoverthiscrosssectioninadirectionnormaltoit.施加（力）水平的法线合力分布式的Ifforpurposesofanalysisth28为了分析计算，可考虑将此截面右侧的杆段除去，如图1-2（b）所示。因而，必须补充右侧杆段对左侧杆段的作用。用此处引入的截面法，初始的内力便成为保留杆段的外力。为使左侧杆段平衡，这种效应在数值上等于水平力P。然而，沿截面a-a法向作用的力P实际上是截面上法向分布力合成的结果。Fig.1-2图1-2为了分析计算，可考虑将此截面右侧的杆段除去，如图1-2（b）29

Insteadofspeakingoftheinternalforceactingonsomesmallelementofarea,itisbetterforcomparativepurposestotreatthenormalforceactingoveraunitareaofthecrosssection.Theintensityofnormalforceperunitareaistermedthenormalstressandisexpressedinunitsofforceperunitarea,e,g.,1N/m2.NormalStress法应力把…称作比较的应力Insteadofspeak30替代讨论作用在某处小面积上内力，最好转为处理单位面积上法向力。单位面积上法向力的强度称为法应力，它是用单位面积上的作用力单位表示的，亦即1替代讨论作用在某处小面积上内力，最好转为处理单位面积上法向力31Iftheforcesappliedtotheendsofthebararesuchthatthebarisintension,thentensilestressesaresetupinthebar;ifthebarisincompressionwehavecompressivestresses.Itisessentialthatthelineofactionoftheappliedendforcespassthroughthecentroidofeachcrosssectionofthebar.如果杆端的力使杆拉伸，杆内就产生拉应力，如果杆是受压缩的，杆内产生压应力。施加在杆端的力作用线必须通过每一个截面形心。Iftheforcesappliedtothee32

TheaxialloadingshowninFig.1-2(a)occursfrequentlyinstructuralandmachinedesignproblems.Tosimulatethisloadinginthelaboratory,atestspecimenisheldinthegripsofeitheranelectricallydrivengear-typetestingmachineorahydraulicmachine.Bothofthesemachinesarecommonlyusedinmaterialstestinglaboratoriesforapplyingaxialtension.TestSpecimens试样样品夹具电力地液压的应用，施加Theaxialloadingsho33

图1-2（a）所示的轴向载荷经常出现在结构和机械设计中，为了在实验室中模拟这种轴向载荷，试件应夹持在电子或液压万能试验机的夹头中。这两种试验机通常在材料实验室用做施加轴向载荷。图1-2（a）所示的轴向载荷经常出现在结构34InanefforttostandardizematerialstestingtechniquestheAmericanSocietyforTestingMaterials(ASTM)hasissuedspecificationsthatareincommonuse.Onlytwoofthesewillbementionedhere,oneformetalplatesthickerthanin(4.76mm)andappearingasinFig.1-3,theotherformetalsover1.5in(38mm)thickandhavingtheappearanceshowninFig.1-4.在材料实验技术规范标准中，美国材料实验协会颁布了详细的使用说明。此处只讲其中两种试件。一种厚度超过3/16in（4.76mm）的金属板试件如图1-3所示，另外一种直径为1.5in（38mm）的金属圆棒状试件如图1-4所示。标准化Inanefforttosta35Asmaybeseenfromthesefigures,thecentralportionofthespecimenissomewhatsmallerthantheendregionssothatfailurewillnottakeplaceinthegrippedportion.Theroundedfilletsshownareprovidedsothatnostressconcentrationswillariseatthetransitionbetweenthetwolateraldimensions.Thestandardgagelengthoverwhichelongationsaremeasuredis8in(203mm)forthespecimenshowninFig.1-3and2in(57mm)forthatshowninFig.1-4.正如图中所看到的，试件的中部区域尺寸略小于两端尺寸。因而，破环不会发生在两端的夹持段，过度圆角保证试件两种尺寸的过渡部位不会发生应力集中。供测量伸长的标距长度为8in（203mm，图1-3试件）和2in（51mm，图1-4试件）。稍微，有些失效，破坏过渡区伸长标距Asmaybeseenfromthesefigu36Theelongationsaremeasuredbyeithermechanicaloropticalextensometersorbycementinganelectricresistance-typestraingagetothesurfaceofthematerial.Thisresistancestraingageconsistsofanumberofveryfinewiresorientedintheaxialdirectionofthebar.Asthebarelongates,theelectricalresistanceofthewireschangesandthischangeofresistanceisdetectedonaWheatstonebridgeandinterpretedaselongation.伸长计粘贴电阻应变片细的转换Theelongationsare37试件的伸长既可以使用机械的、光学的伸长计，也可以使用粘贴在试件表面的电阻应变片来测量，这种电阻应变片由若干个沿试件轴向的、很细的电阻丝组成。当试件伸长时，电阻丝的电阻就会发生改变，电阻的改变由惠斯通电桥测量并转换为伸长量。试件的伸长既可以使用机械的、光学的伸长计，也可38

Letussupposethatoneofthesetensionspecimenshasbeenplacedinatension-compressiontestingmachineandtensileforcesgraduallyappliedtotheends.

Theelongationoverthegagelengthmaybemeasuredasindicatedaboveforanypredeterminedincrementsoftheaxialload.Fromthesevaluestheelongationperunitlength,whichistermednormalstrainanddenotedbyε,maybefoundbydividingthetotalelongationΔbythegagelengthL,thatis,ε=Δ/L.

Thestrainisusuallyexpressedinunitsofinchesperinchormeterspermeterandconsequentlyisdimensionless.NormalStrain法应变应变增量Letussuppose39对于每一个事先指定的轴向载荷增量都要测量相应的标距的伸长。由这些数值得到单位长度的伸长，并将之定义为法应变，用ε来表示，可以用标距长度L去除总伸长Δ来得到法应变。对于每一个事先指定的轴向载荷增量都要测量相应40

Astheaxialloadisgraduallyincreasedinincrements,thetotalelongationoverthegagelengthismeasuredateachincrementofloadandthisiscontinueduntilfractureofthespecimentakesplace.Knowingtheoriginalcross-sectionalareaofthetestspecimenthenormalstress,denotedbyσ,maybeobtainedforanyvalueofaxialloadbytheuseoftherelationStress-StrainCurve应力—应变曲线Astheaxialloadi41wherePdenotestheaxialloadinpoundsorNewtonsandAtheoriginalcross-sectionalarea.Havingobtainednumerouspairsofvaluesofnormalstressσandnormalstrainε,theexperimentaldatamaybeplottedwiththesequantitiesconsideredasordinateandabscissa,respectively.Thisisthest