Chapter 10: Failure. Titanic on April 15, 1912 ISSUES TO ADDRESS. Failure Modes:

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1 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. ( 2 LECTURER: PROF. SEUNGTAE CHOI

2 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

3 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

4 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 b a x 2 MAX a yy (A) b a a a 2 0 a 0 b A a x Theaboveequationshowthatasb 0(theellipsebecomesacrack)astress singularity( ~1/r) developsatthecracktip. 8 LECTURER: PROF. SEUNGTAE CHOI

5 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 K I 22 cos 2 1 sin 2 sin 3 2 2r 12 sin 2 cos 3 2 sin 2 2 cos 2 cos K II 22 sin 2 cos 2 cos 3 2 2r 12 cos 2 1 sin 2 sin 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

6 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

7 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

8 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 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

9 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= atx= atx=0.55 x=a/w,(0.45<x<0.55) K IC B, a 2.5 yield 2 18 LECTURER: PROF. SEUNGTAE CHOI

10 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

11 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

12 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

13 LibertyShipduringWorldWarII 25 LECTURER: PROF. SEUNGTAE CHOI LibertyShipduringWorldWarII JohnP.Gaines EmpireDuke 26 LECTURER: PROF. SEUNGTAE CHOI

14 Patterning by Controlled Cracking K. H. Nam, I. H. Park, & S. H. Ko, Patterning by controlled cracking, Nature, Vol. 485, pp , LECTURER: PROF. SEUNGTAE CHOI Fragmentation of Ice in the Arctic Ocean 28 LECTURER: PROF. SEUNGTAE CHOI

15 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

16 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

17 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

18 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) n Q c s K2 exp RT Steadystatecreeprate(%/1000hr) e s 427C 538 C 649 C Callister&Rethwisch 4e. Metals Handbook:PropertiesandSelection: StainlessSteels,ToolMaterials,and SpecialPurposeMetals 36 LECTURER: PROF. SEUNGTAE CHOI

19 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

20 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

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