复合型裂纹的断裂准则Word格式文档下载.doc
- 文档编号:15435682
- 上传时间:2022-10-31
- 格式:DOC
- 页数:11
- 大小:372.50KB
复合型裂纹的断裂准则Word格式文档下载.doc
《复合型裂纹的断裂准则Word格式文档下载.doc》由会员分享,可在线阅读,更多相关《复合型裂纹的断裂准则Word格式文档下载.doc(11页珍藏版)》请在冰豆网上搜索。
MaximumstresscriterioncanbeappliedtothemixedmodecrackofmodeIandmodeII.
Theasymptoticstresssolutionis
Byapplicationofthecoordinatetransformationformulas,wecanobtaintheexpressionsofthreestresscomponentsinthepolarcoordinates(r,q).Thecircumferentialnormalstressis
Thecircumferentialnormalstressintensityfactorisdefinedas
Hence,canbewrittenas
Assumptions:
(1)Crackinitiationdirectionisthedirectionofthemaximum;
(2)Whenreachesitscriticalvalue,breakoccurs.isamaterialconstant.
Thecrackinitiationanglecanbedeterminedfrom
Theresultis
Thecriticalconditionis
Determinationof:
FormodeIcrack,,,,thecriticalconditionreducesto
Notethatisamaterialconstant.When,and,therestillprevails.Themaximumstresscriterionisexpressedas
ApplicationtomodeIIcrack:
ForamodeIIcrack,and.Thecrackinitiationanglecanbesolved,.From
onecanobtainthat
,
ThefracturecriterionforModeIIcrackcanbederivedfromthemaximumstresscriterionthat
Itisconvenientfortheengineeringapplication.However,thereisnodifferencebetweentheplanestressandplanestrain.
5-2Maximumnormalstraincriterion
Nearthecracktip,thecircumferentialnormalstrainis
,forplanestress;
,forplanestrain.
Thecircumferentialnormalstrainintensityfactorisdefinedas
Then,
Thecrackinganglesatisfies
Thecriticalvaluecanbedeterminedby.ForModeI,,.Itcanbeobtainedthat
Themaximumnormalstraincriterionis
Nowtheplanestressandplanestraincanbedistinguished.
5-3Strainenergydensityfactortheory
StrainenergydensityfactortheorywasproposedbyProf.G.C.Sihthatcanbeappliedtothethreedimensionalproblem.
When,,,,theasymptoticstresssolutionis
Thestrainenergydensitywis
Thestrainenergydensitywcanbeexpressedintheformof
where
strainenergydensityfactor
itisphysics,notmathematics.
(1)CrackinitiationdirectionisthedirectionoftheminimumS;
Thecrackinganglecanbesolvedfrom
DeterminationofSc:
FormodeI,itcanbederivedthat
Theminimumstrainenergydensityfactorcriterioncanbeexpressedas
S£
Sc,i.e.,.
ModeIIcrack:
,
Take.Thereis
Recallthatforthemaximumnormalstresscriterion,thereis
Tworesultshavelittledifference.
5-4Modifiedmaximumnormalstresscriterion
Sometimethemaximumnormalstresscriterionisnotsogood.Amodifiedmaximumnormalstresscriterionhasbeenproposed.
Ithasbeenknownthatinviewof
astrainenergydensityfactorSisdefined.ForthemixedmodeofmodeIandII,Scanbewrittenas
Let.
FordifferentvaluesofC,wecanobtainagroupofcurvescalledasisolinesofstrainenergydensity.
Thecircumferentialnormalstressis
Let,.
Let.Thisgives
Ontheisolinesofthestrainenergydensity,,thecircumferentialnormalstressis
Thecircumferentialnormalstressintensityfactorisidenticalwith§
5-1.
(1)Crackinitiationdirectionisthedirectionofthemaximumontheisolineofthestrainenergydensity.Thecrackinitiationanglecanbedeterminedfrom
(2)Whenreachesitscriticalvalue,breakoccurs.
ItcanbederivedfromModeIproblemthat
Thefracturecriterionis
5-5Energyreleaseratetheory
Nearthecracktip,thestressesinthepolarcoordinatesare
Let
Thereresults
Energyreleaseratealongtheangleq:
Gdenotestheenergyreleaseratealongthedirectionq=0.Nowweneedtoknowtheenergyreleaseratealongthedirectionq.
Itisknownthat
Recallthedefinitionsofand.Itisknownthat
Comparingtwocases,weknowthatandarethestressintensityfactorsofthevirtualcrack.Thestressfieldsfortwocracksarecompletelysam
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 复合型 裂纹 断裂 准则