Chapter10:Failure ISSUESTOADDRESS FailureModes: 1 LECTURER: PROF. SEUNGTAE CHOI TitaniconApril15, 1912 RMS Titanic was a British passenger liner that sank in the North Atlantic Ocean on 15 April 1912 after colliding with an iceberg during her maiden voyage from Southampton, UK to New York City, US. The sinking of Titanic caused the deaths of 1,502 people in one of the deadliest peacetime maritime disasters in history. (http://en.wikipedia.org/wiki/rms_titanic) 2 LECTURER: PROF. SEUNGTAE CHOI
10.3DuctileFracture(Rupture) Classificationoffracturebehavior Callister &Rethwisch 9e. AR EL 3 LECTURER: PROF. SEUNGTAE CHOI ModeratelyDuctileFracture(Rupture) Stagesinthecupandconefracture Callister &Rethwisch 9e. Analysisof MetallurgicalFailures 4 LECTURER: PROF. SEUNGTAE CHOI
10.4 Brittle Fracture Brittle Fracture I. Transgranular Fracture (Cleavage Fracture) 5 Ǥ ͳͳǥ ǡ Callister & Rethwisch 9e. LECTURER: PROF. SEUNGTAE CHOI II. Intergranular Fracture II. Intergranular Fracture: Ǥ Ǥ ͳǥ ʹǤ Ǥ Ǥ ͳͳǥ ǡ Callister & Rethwisch 9e. 6 LECTURER: PROF. SEUNGTAE CHOI
10.5PrincipleofFractureMechanics AnAtomicViewofFracture Bonding energy: E b Pdx x0 Interatomic force-displacement relation: x P Pc sin For small displacements, forcedisplacement relationship is linear: x Pc cx0 PPc kx, where k= E= E c Surface energy: 1 x sin dx 2 0 Es c x s c c 7 LECTURER: PROF. SEUNGTAE CHOI 0 StressConcentrationEffectofFlows StressconcentrationaroundanellipticholebyC.E.Inglis (1913) x a y b 2 2 2 2 1 0 2 b a x 2 MAX a yy (A) 0 2 1 b a a 02 1 0 2 1 a 2 0 a 0 b A a x 1 0 0 Theaboveequationshowthatasb 0(theellipsebecomesacrack)astress singularity( ~1/r) developsatthecracktip. 8 LECTURER: PROF. SEUNGTAE CHOI
StressAnalysisofCracks ThreeModesofFracture Stressfieldsnearacracktip K m I I KII II KIII III 2 (m) f( ) f( ) f ( ) Amr g ( ) 2r 2r 2r m0 I I II III : stress tensor K : Mode I stress intensity factor K : Mode II stress intensity factor K : Mode III stress intensity factor II III f,f, and f : dimensionless functions of 9 LECTURER: PROF. SEUNGTAE CHOI StressFieldsnearaCrackTip Stressfieldsnearacracktip 1sin 2 sin 3 2 11 K I 22 cos 2 1 sin 2 sin 3 2 2r 12 sin 2 cos 3 2 sin 2 2 cos 2 cos 3 2 11 K II 22 sin 2 cos 2 cos 3 2 2r 12 cos 2 1 sin 2 sin 3 2 31 K sin 2 III 32 2r cos 2 K I: Mode I stress intensity factor K II: Mode II stress intensity factor K III: Mode III stress intensity factor 10 LECTURER: PROF. SEUNGTAE CHOI
DesignCriteria Stressapproach : applied stress : ultimate stregth u u Fracturemechanics approach K I K IC KI: stress intensity factor (SIF) calculated value due to loading KIC: fracture toughness material property yy KI 2r r 11 LECTURER: PROF. SEUNGTAE CHOI ExamplesofStressIntensityFactors Acenteredcrackinaninfiniteplate: underuniformuniaxialstress Apennyshapedcrackinaninfinite domain KI a a KI 2 12 LECTURER: PROF. SEUNGTAE CHOI
ElasticEnergy Strainenergydensity: u d 0 Internalenergyofadeformablebody: U udv d dv V V 0 Linearelasticmaterials(Hooke slaw): 1 kk or 2 kk E E ( and:lamé constant) Strainenergydensityoflinearelasticmaterials: 1 u d 0 2 Internalenergyoflinearelasticmaterials: V 1 U d dv dv 0 2 V 13 LECTURER: PROF. SEUNGTAE CHOI ConservationofEnergy 14 LECTURER: PROF. SEUNGTAE CHOI
EnergyBalanceDuringCrackGrowth Thefirstlawofthermodynamics(Lawofconservationofenergy) W U U E P E P W : Work done by the applied load U : Elastic energy U : Plastic energy : Surface energy Applied traction A A t A t A a 2a a U A A A P E where =U W Thereductionofpotentialenergyisequaltotheenergydissipatedinplastic workandsurfacecreation. Forbrittlematerials,U P 0. 2 A A S 15 LECTURER: PROF. SEUNGTAE CHOI GriffithEnergyBalance Griffith(1920)usedthestressanalysisofInglis (1913)toshow 2 2 2 ab a 0 E A E 4aBS 2S A Griffithfracturestress a 2a a f 2E S a 12 B ModifiedGriffithfracturestress f 2E( P S) a 12 P : plastic work per unit area of surface 16 LECTURER: PROF. SEUNGTAE CHOI
EnergyReleaseRate Energyreleaserate,G:Ameasureofthe energyavailableforanincrementofcrack extension(irwin,1948) A Itisalsocalledthecrackextensionforceor thecrackdrivingforce. FromtheGriffithenergybalance,thecrack extensionoccurswheng reachesacritical value,i.e., 2 a c 2 S, A E A whereg c isameasureofthefracture toughnessofthematerial. 17 LECTURER: PROF. SEUNGTAE CHOI 10.6FractureToughnessTesting Standard:ASTME399,D5045 Specimen:CompactTension(CT) Calculation K PQ fx BW IC 1/ 2 K IC :Fracturetoughness P Q :Criticalload f(x)= 8.34 atx=0.45 9.66 atx=0.50 11.35 atx=0.55 x=a/w,(0.45<x<0.55) K IC B, a 2.5 yield 2 18 LECTURER: PROF. SEUNGTAE CHOI
PlasticEffectonCrackTip Yielding zone size: r y 1 K I 2 y 2 Plastic zone size ry rp r 2 1 K I rp 2r y for plane stress y 2 1 K I rp 2r y for plane strain 3 y Ductile fracture : sufficient plastic deformation before fracture Brittle fracture : small plastic deformation before fracture 19 LECTURER: PROF. SEUNGTAE CHOI 3DAspectsofPlasticZone 20 LECTURER: PROF. SEUNGTAE CHOI
VariationofK C withspecimenthickness K C Plane stress Transition region Plane strain K IC Specimen thickness 21 LECTURER: PROF. SEUNGTAE CHOI FractureToughnessRanges K IC (MPam 0.5 ) Callister&Rethwisch 9e. ASMHandbook FractureMechanics ofceramics Ceram.Eng.Sci.Proc. 22 LECTURER: PROF. SEUNGTAE CHOI
ImpactTesting Impactloading: final height Callister&Rethwisch 9e. TheStructureandPropertiesof MaterialsMechanicalBehavior initial height 23 LECTURER: PROF. SEUNGTAE CHOI InfluenceofTemperatureonImpactEnergy DuctiletoBrittleTransitionTemperature(DBTT)... T y E Callister&Rethwisch 9e. 24 LECTURER: PROF. SEUNGTAE CHOI
LibertyShipduringWorldWarII 25 LECTURER: PROF. SEUNGTAE CHOI LibertyShipduringWorldWarII JohnP.Gaines EmpireDuke 26 LECTURER: PROF. SEUNGTAE CHOI
Patterning by Controlled Cracking K. H. Nam, I. H. Park, & S. H. Ko, Patterning by controlled cracking, Nature, Vol. 485, pp. 221-224, 2012. 27 LECTURER: PROF. SEUNGTAE CHOI Fragmentation of Ice in the Arctic Ocean 28 LECTURER: PROF. SEUNGTAE CHOI
10.7CyclicStressesFatigue Fatigue=failureunderappliedcyclicstress. Callister&Rethwisch 9e. Stressvarieswithtime. Keypoints:Fatigue... Callister&Rethwisch 9e. 29 LECTURER: PROF. SEUNGTAE CHOI 10.8TheSNCurve Fatiguelimit,S fat : Forsomematerials, S fat Callister&Rethwisch 9e. Callister&Rethwisch 9e. 30 LECTURER: PROF. SEUNGTAE CHOI
10.9CrackInitiationandPropagation RateofFatigueCrackGrowth:Crackgrowsincrementally da dn ( K ) m ~ a Failedrotatingshaft Callister&Rethwisch 9e. UnderstandingHowComponentsFail 31 LECTURER: PROF. SEUNGTAE CHOI 10.10FactorsThatAffectFatigueLife 1.Imposecompressivesurfacestresses (tosuppresssurfacecracksfromgrowing) Callister&Rethwisch 9e. m m m bad bad better better Callister &Rethwisch 9e. 32 LECTURER: PROF. SEUNGTAE CHOI
10.12GeneralizedCreepBehavior Creepphenomenon:Time dependentandpermanent deformationofmaterialswhen subjectedtoconstantloador stress. e t et) 33 LECTURER: PROF. SEUNGTAE CHOI CreepFractureMechanism Schematicdrawingofthreefracturemechanismsinahightemperaturecreep regime [Abe et al., Creep-Resistant Steels, 2008] 34 LECTURER: PROF. SEUNGTAE CHOI
10.13StressandTemperatureEffects Occursatelevatedtemperature,T>0.4T m (ink) tertiary secondary primary elastic Callister&Rethwisch 9e. 35 LECTURER: PROF. SEUNGTAE CHOI SecondaryCreep Strainrateisconstantatagiven(T,s) StrainrateincreaseswithincreasingT, Stress(MPa) 200 100 40 20 10 n Q c s K2 exp RT 10 2 10 1 1 Steadystatecreeprate(%/1000hr) e s 427C 538 C 649 C Callister&Rethwisch 4e. Metals Handbook:PropertiesandSelection: StainlessSteels,ToolMaterials,and SpecialPurposeMetals 36 LECTURER: PROF. SEUNGTAE CHOI
ArrheniusEquation TheArrheniusequation(SvanteArrhenius,1889) E a k Aexp RT or E B k Aexp kbt k T A E a R E B k B 37 LECTURER: PROF. SEUNGTAE CHOI 10.14DataExtrapolationMethods TheLarson Millerparameterisameansofpredictingthelifetimeofmaterial vs.timeandtemperatureusingacorrelativeapproachbasedonthearrhenius rateequation. LarsenMillerparameterP LM isusedtorepresentcreepstressrupturedata. n Qc s K2 exp RT l Qc A exp t RT l Qc ln lna t RT Qc TB lnt where R A B ln l P LM T C log t r 38 LECTURER: PROF. SEUNGTAE CHOI
PredictionofCreepRuptureLifetime T s t r T (20 logt r ) P LM Tt r Callister&Rethwisch 9e. Trans.ASME74 ( 1073K)(20 logt ) t r r 3 24x10 39 LECTURER: PROF. SEUNGTAE CHOI SUMMARY Engineeringmaterialsnotasstrongaspredictedbytheory Flawsactasstressconcentratorsthatcausefailureatstresseslowerthan theoreticalvalues. Sharpcornersproducelargestressconcentrationsandprematurefailure. FailuretypedependsonTand: 40 LECTURER: PROF. SEUNGTAE CHOI