m-虎克定律-强度理论.ppt

3.广义虎克定律,GeneralizedHookeslaw,(1)广义虎克定律(GeneralizedHookeslawforthegeneralstateofstress),正应力与正应变之间的关系,切应力与切应变之间的关系,在小变形情况下，切应力不影响正应变，正应力不影响切应变。,(2)GeneralizedHookeslawforthetwo-dimensionalstressstate,Fortheplanestateofstress,itsstrainstateisthree-dimensional.,平面应力状态的虎克定律,(3)平面应力状态斜方位的广义虎克定律(GeneralizedHookeslawfortheplanestressstatealongtheslopedirection),Example:AbarwasactedbyanaxialforcePshownfollows,knownEandvofthematerial,determinethetensionoflineAB.,Solve:,Whereiswrong?,Solve:,SupposeCisanabtrarypointonthelineAB,itsstateofstresscanbeshowninthefollowsfigure.,Acoordingtotheformulaof,wecanget:,Example:AbarwasactedbyanaxialforcePshownfollows,knownEandvofthematerial,determinethetensionoflineAB.,AcoorgingtothegeneralizedHookslaw,followsresultcanbeattained.,BecauseCisanabtrarypointonthelineAB,sothenormalstrainalongthelineABisuniform.Acoorgingtothedifinitionofnormalstrainwecanget:,ThetensionoflineABis:,例对如图均匀变形的板，求：厚度的改变量；板面积的改变量；体积的改变量。,板中各方向上的应变,厚度的改变量,板面积的改变量,体积的改变量,4.强度理论,StrengthCriteria,4.1强度理论的概念,Conceptofstrengthcriteria,SupposepointAisthemostdangerouspointinastructure,ordinarilybarswereconsideredinMechanicsofMaterials.Forthispointofthematerials,itsstressstateperhapsissimpleorcomplexstressstate.Isitinsafetyornot?Howtodetermineitsstrength?,Question:,Themostimportantthingisthatthereisonlyonestressonthesurfaceofelement!ThestrengthofpointAisdecidedjustonlybyonestressparameteror,anditslimitvaluecanbeeasilydeterminedbytensiontest.Soforthesimplestateofstresswecangetthestrengthcriteriaofmaterialsatonepointveryeasy.,对简单应力状态来说,其单元体的微分面上只有一个应力,也即该点的强度控制参数只有唯一的一个,所以可以很容易根据实验建立起其强度准则来.,Forthecomplexstressstate:,When:,PerhapspointAisnotinsafety.,Forthecomplexstressstate,wecannotusethestrengthcriteriashownbeforetodeterminethesafetyofthepoint.,Howtodeterminethesafetyofthepoint?,对处于复杂应力状态的点来说,不能应用前述简单应力状态的强度条件判别其安全性.,-calledequivalentstress,Howtodeterminethefunction?,称为等效应力,Becausetherearethreecontrolparametersofstrengthatonepoint,thefunctionfcannotbeattainedbyexperimentofmaterials.,Ifthebrokenreasonofmaterialscanbefined,thefunctionfwillbedetermined.SothestrengthcriterionofmaterialsatpointAcanbeattainedbyfollowingsteps:,因为一点处的强度控制参数有三个,所以无法根据材料实验得到函数,如果知道材料的破坏原因,那么函数就可以找到.所以根据下述步骤可以建立材料的强度准则:,(1)假设材料的破坏机理;而且无论材料各点处于何种应力状态,其破坏原因都是一样的.,Attainethestrengthcriterionofmaterialsatonepoint.,Supposeabrokenreasonforthematerials.Dontconsiderthepointofmateralsisornotsimpleandcomplexstateofstress,thebrokenreasonsarejustsame.,(2)根据材料的破坏机理得到材料的强度准则.,Examinethestrengthcriterioniscorrectorwronginengenering.Ifitiscorrect,recordit.Ifitiswrong,abandonedit.,(3)在工程实际中检验该强度准则是否正确,如果是正确的,保留它;如果是错误的,抛弃它.,特别注意:1)在工程中任何强度准则都有一定的适用范围,即到目前为止还不存在适用于所有材料的强度准则.2)目前广泛使用的强度准则都是经过长期的实践检验证明在一定范围内是符合工程实际的.,(a)破坏原因:对任何应力状态，第一主应力超过了许用应力,(1)第一强度理论(最大拉应力理论）,4.2四个常用的强度理论,Fourkindsofstrengthcriteriaoftenused,Thefirststrengthcriterion,Foranystateofstress,brokenreasonisthefirstprincipalstressoveritslimit.,(b)Thestrengthcriterion,(2)第二强度理论(最大线应变理论）,(a)破坏原因:对任何应力状态，第一主应变超过了许用应变,第一、第二强度理论属于脆性断裂强度准则,(b)Thestrengthcriterion,Foranystateofstress,brokenreasonisthefirstprincipalstrainoveritslimit.,(3)第三强度理论(最大切应力理论）,(a)破坏原因:对任何应力状态，最大切应力超过许用切应力,Foranystateofstress,brokenreasonisthemaximumshearingstressoveritslimit.,(b)Thestrengthcriterion,(4)第四强度理论(最大形状改变比能理论）,第三、第四强度理论属于塑性屈服强度准则,(b)Thestrengthcriterion,(a)破坏原因:对任何应力状态，形状改变比能超过许用值,4.3强度理论的应用,Applicationsofstrengthcriteria,(1)在材料力学中的应用(ApplicationsinMechanicsofMaterials),InMecahnicsofMaterialsthestateofstressofpointsinthebarsoftenisaspecialplanestateofstress.,AcoordingtotheopinionofstrengthinMechanicsofMaterials,thestructuresdesignedbythirdst