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Observedfracturestrengthisalwayslowerthantheoreticalcohesivestrength.

Griffithexplainedthatthediscrepancyisduetotheinherentdefectsinbrittle

materialsleadingtostressconcentrationimplies lowerthefracturestrengthofthematerials.

Crackpropagationcriterion: Considerathroughthicknesscrackoflength2a,

subjectedtoauniformtensilestress ,atinfinity.

Crackpropagationoccurswhenthereleasedelastic

strainenergyisatleastequaltotheenergyrequiredto

generatenewcracksurface.

Griffiththeoryofbrittle

fracture:

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Thestressrequiredtocreatethenewcracksurface isgivenasfollows:

Inplanestraincondition,theequationbecomes:

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TheGriffithequationisstronglydependentonthecracksizea,and

satisfiesonlyideallybrittlematerialslikeglass.

However,metalsarenotideallybrittleandnormallyfailwithcertain

amountsofplasticdeformation,thefracturestressis increaseddueto

bluntingofthecracktip.

IrwinandOrowansuggestedGriffithsequationcanbeappliedtobrittle

materialsundergoneplasticdeformationbeforefracturebyincludingthe

plasticwork, p,intothetotalelasticsurfaceenergyrequiredtoextend

thecrackwall,givingthemodifiedGriffithsequationasfollows:

ModifiedGriffithequation

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InmodeIfailureandplanestraincondition,therelationship

betweenGICan KICcanbeshownbyanexpressionasfollows:

WhereKIC isthecriticalstressintensityfactor

ilure

Stressintensityfactor

Crack deformation

mode.

Fracture modes

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` StressintensityfactorKICcanbedescribedasfracturetoughness

ofmaterials(materialresistancetocrackpropagation)underconditionsof:

1)brittlefracture

2)inthepresenceofasharpcrack

3)undercriticaltensileloading

Where` KIC isthecriticalstressintensityfactorfor planestrainconditionin

mode failure.

` ac isthecriticalcracklengthinaninfiniteplate

` app istheappliedstress

` isaparameterdependentonspecimenandcrackgeometry

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Kvaluesofvariouscrackgeometries:

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FracturetoughnessofmaterialcanbedeterminedaccordingtoLEFManalysis

1)KICfracturetoughness:

workswellforveryhighstrengthmaterials.exhibitingbrittlefracture

2) CracktipopeningdisplacementCTOD:

Usedforlowerstrengthmaterials(o

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` KIC fracturetoughnessofmaterialisobtainedbydeterminingtheabilityof

materialtowithstandtheloadinthepresenceofasharpcrackbefore

failure.

` Fracturetoughnessisrequiredinthesystemofhighstrengthandlight

weight,i.e.,highstrengthsteels,titaniumandaluminium alloys.

KICfracturetoughness

Fracture toughness How longthe existing crack will growuntil the specimen fails

Flaw geometry anddesign of cylindricalpressure vessel

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BCCstructuremetalsexperienceductiletobrittletransitionbehaviour

whensubjectedtodecreasingtemperature,resultingfromastrongyield

stressdependentontemperature.

Ductiletobrittletransition

behaviour

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BCCmetalspossesslimitedslipsystemsavailableatlowtemperature,

minimisingtheplasticdeformationduringthefractureprocess.

Increasingtemperatureallowsmoreslipsystemstooperate,yieldinggeneralplasticdeformationtooccurpriortofailure.

Theoryoftheductiletobrittletransition: Thecriterionforamaterialtochangeitsfracturebehaviourfromductile

tobrittlemodeiswhentheyieldstressattheobservedtemperatureis

largerthanthestressnecessaryforthegrowthofthemicrocrackindicated

intheGriffiththeory.

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Cottrellstudiedtheroleofparameters,whichinfluencetheductileto

brittletransitionasfollows;

i is thelatticeresistancetodislocationmovement

kisaparameterrelatedtothereleaseofdislocationintoapileup Disthegraindiameter(associatedwithsliplength).

Gistheshearmodulus

isaconstantdependingonthestresssystem.