弹塑性断裂力学讲义(ABAQUS).docx

Elastic-PlasticFractureMechanics

ProfessorS.Suresh

ElasticPlastic

Fracture

Previously,wehaveanalyzedproblemsinwhichtheplasticzone

wassmallcomparedtothespecimendimensions(smallscale

yielding).Intoday’slecturewepresenttechniquesforanalyzing

situationsinwhichtherecanbelargescaleyielding,and

determineexpressionsforthestresscomponentsinsidethe

plasticzone.Wewillbeginwithadiscussionoftheintegral.

FatigueandFracture1

Derivation

Integral

Theintegralisalineintegral(path-independent)aroundthe

cracktip.Ithasenormoussigni?canceinelastic-plasticfracture

mechanics.KeyReference:J.R.Rice,JournalofApplied

Mechanics,1968.

(Relatedworks:Eshelby,ProgressinSolidStatePhysics1956;

Sanders,JournalofAppliedMechanics,1960;Cherepanov,

InternationalJournalofSolidsandStructures,1969)

FatigueandFracture2

Integral

Derivation

Continued

Considerthepatharoundthecracktipshownbelow:

FatigueandFracture3

Integral

Derivation

Continued

Wewillusethefollowingvariables:

=cracklength.

=acurvelinkingtheloweranduppercracksurfaces.

=anelementofarconthiscurve.

=tractionvectoronthiscurvede?nedinrelationtoanoutward

normalunitvector,i.e..

=correspondingdisplacementvector.

Weconsiderasmallstrainanalysis;weneglectany

deformation-inducedbluntingofcracktip.

FatigueandFracture4

Integral

Derivation

Continued

Weusethedeformationtheoryofplasticity(equivalentto

non-linearelasticity).The(reversible)stress-strainresponseis

depictedschematicallybelow:

FatigueandFracture5

Integral

Derivation

Continued

Forproportionalloadingdeformationtheoryand?ow

theory(incrementaltheoryofplasticity)giveresultsthatare

comparable(i.e.formonotonicloading,stationarycracks).

Notappropriateforsituationswheresigni?cantunloadingoccurs.

Thetotalmechanicalpotentialenergyofthecrackedbodyis

Thisrepresentsthesumofthest