Mechanical Properties of Engineered Materials 2008 Part 1 pps

... Inc.Bibliography 11 FundamentalsofFractureMechanics 11 .1Introduction 11 .2FundamentalsofFractureMechanics 11 .3NotchConcentrationFactors 11 .4GriffithFractureAnalysis 11 .5EnergyReleaseRateandCompliance 11 .6LinearElasticFractureMechanics 11 .7Elastic–PlasticFractureMechanics 11 .8FractureInitiationandResistance 11 .9InterfacialFractureMechanics 11 .10 DynamicFractureMechanics 11 .11 SummaryBibliography 12 MechanismsofFracture 12 .1Introduction 12 .2FractographicAnalysis 12 .3ToughnessandFractureProcessZones 12 .4MechanismsofFractureinMetalsandTheirAlloys 12 .5FractureofIntermetallics 12 .6FractureofCeramics 12 .7FractureofPolymers 12 .8FractureofComposites 12 .9QuantitativeFractography 12 .10 ThermalShockResponse 12 .11 SummaryBibliography 13 TougheningMechanisms 13 .1Introduction 13 .2TougheningandTensileStrength 13 .3ReviewofCompositeMaterials 13 .4TransformationToughening 13 .5CrackBridgingCopyright ... Inc.Bibliography 11 FundamentalsofFractureMechanics 11 .1Introduction 11 .2FundamentalsofFractureMechanics 11 .3NotchConcentrationFactors 11 .4GriffithFractureAnalysis 11 .5EnergyReleaseRateandCompliance 11 .6LinearElasticFractureMechanics 11 .7Elastic–PlasticFractureMechanics 11 .8FractureInitiationandResistance 11 .9InterfacialFractureMechanics 11 .10 DynamicFractureMechanics 11 .11 SummaryBibliography 12 MechanismsofFracture 12 .1Introduction 12 .2FractographicAnalysis 12 .3ToughnessandFractureProcessZones 12 .4MechanismsofFractureinMetalsandTheirAlloys 12 .5FractureofIntermetallics 12 .6FractureofCeramics 12 .7FractureofPolymers 12 .8FractureofComposites 12 .9QuantitativeFractography 12 .10 ThermalShockResponse 12 .11 SummaryBibliography 13 TougheningMechanisms 13 .1Introduction 13 .2TougheningandTensileStrength 13 .3ReviewofCompositeMaterials 13 .4TransformationToughening 13 .5CrackBridgingCopyright ... Dekker, Inc. 15 .9CreepLifePrediction 15 .10 CreepDesignApproaches 15 .11 ThresholdStressEffects 15 .12 CreepinCompositeMaterials 15 .13 ThermostructuralMaterials 15 .14 IntroductiontoSuperplasticity 15 .15 IntroductiontoCreepDamageandTime-DependentFractureMechanics 15 .16 SummaryBibliographyCopyright...

... Dekker, Inc. 1 Overview of Crystal/Defect Structureand Mechanical Properties andBehavior 1. 1 INTRODUCTIONThe mechanical behavior of materials describes the response of materials to mechanical ... fundamen-tals of the mechanical behavior of materials. The text provides a rigorousreview of the fundamental mechanics aspects of the mechanical behavior of materials. Shackleford, J. F. (19 96) Introduction ... macroscopic level of understanding of structure [Figs 16 (a)–(d)]. They are often unaware of the atomic and micro-structural constituents that can affect the mechanical behavior of materials and of the...

... Inc.3BasicDefinitionsofStressandStrain3.1INTRODUCTIONThemechanicalpropertiesofmaterialsdescribetheircharacteristicresponsestoappliedloadsanddisplacements.However,mosttextsrelatethemechanicalpropertiesofmaterialstostressesandstrains.Itis,therefore,importantforthereadertobecomefamiliarwiththebasicdefinitionsofstressandstrainbeforeproceedingontotheremainingchaptersofthisbook.However,thewell-preparedreadermaychoosetoskip/skimthischapter,andthenmoveontoChap.4inwhichthefundamentalsofelas-ticityareintroduced.Thebasicdefinitionsofstressandstrainarepresentedinthischapteralongwithexperimentalmethodsforthemeasurementandapplicationofstrainandstress.Thechapterstartswiththerelationshipsbetweenappliedloads/displacementsandgeometrythatgiverisetothebasicdefinitionsofstrainandstress.Simpleexperimentalmethodsforthemeasurementofstrainandstressarethenpresentedbeforedescribingthetestmachinesthatareoftenusedfortheapplicationofstrainandstressinthelaboratory.3.2BASICDEFINITIONSOFSTRESSTheforcesappliedtothesurfaceofabodymayberesolvedintocompo-nentsthatareperpendicularorparalleltothesurface,Figs3 .1( a)–3 .1( c).InCopyright ... T. H. (19 90) Mechanical Behavior of Materials, McGraw-Hill, New York.Dieter, G. E. (19 86) Mechanical Metallurgy. 3rd ed. McGraw-Hill, New York.Dowling, N. (19 93) Mechanical Behavior of Materials, ... invariant of the stress tensor can be obtainedfrom the algebraic sum of the cofactors of the three terms in any of the threerows or columns of the stress tensor. This gives the same value of I2,...

... Inc.expressionsforstresses,strains,anddisplacementsaheadofthenear-tip,whichexhibit,r 1= ðn 1 ,rn=nðn 1 ,andr 1= ðn 1 singularity,asshowninthefollowing,respectively,ij¼yJy"yInr 1= ðn 1 ~ijð;nÞ 11 :85aÞ"ij¼"yJy"yInrn=ðn 1 ~""ijð;nÞ 11 :85bÞui¼"yJy"yInn=ðn 1 r 1= ðn 1 ~uuið;nÞ 11 :85cÞwherenisthehardeningexponentintheRamberg–Osgoodequation:"="y¼=yþ=yÞn 11 :85dÞandyistheyieldstress,"yistheyieldstrain,ristheradialdistancefromthecrack-tip,isadimensionlessconstant,Inisanintegrationconstant(Fig .11 .19 ),and~ijð;nÞ,~""ijð;nÞ,and~uuið;nÞcanbefoundinmoststandardtextsonfracturemechanics(Broek ,19 78;EwaldsandWanhill ,19 84;KanninenandPopelar ,19 85).Plotsof~ijð;nÞarepresentedinFig .11 .19 .FIGURE 11. 18SchematicofthecomponentsofthepathindependentJinte-gral. (Adapted from Suresh, 19 99—reprinted ... Inc.@r@rþ 1 r@@þ2rr¼0 11 :21bÞThein-planestraincomponentsaregivenby"rr¼@ur@r 11 :21cÞ"¼urrþ 1 r@u@ 11 :21dÞ"r¼ 1 2 1 r@ur@þ@u@rur 11 :21eÞFinally,forstraincompatibilitywemustsatisfy@2"@r2þ2r@"@r 1 r@2"r@r@ 1 r2@"r@rþ 1 r2@"2rr@2 1 r@"rr@r¼0 11 :22ÞForthein-planeproblem(ModesIandII),thecrack-tipstrainsareonlyfunctionsofrand.Also,fortheplanestressproblemzz¼0.TherelationshipbetweenstressandstrainisgivenbyHooke’slaw:E"rr¼rr 11 :23aÞE"¼rr 11 :23bÞ2"r¼r¼r 11 :23cÞAsdiscussedinChap.4,thesolutionstotheaboveequationsaresatisfied ... second moment of area, I, is given byI ¼Bb3 12 11 :72ÞHence, substituting Eq. (11 .72) into Eq. (11 . 71) givesÁ2¼4Pa3EBb3 11 :73ÞBy definition, the energy release rate [from Eq. (11 .20)] is...

... components ðu 1 v 1 w 1 Þ, the unit vector,^nn 1 , is given by^nn 1 ¼u 1 ^ii þ v 1 ^jj þ w 1 ^kkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 1 þ v2 1 þ w2 1 qð2:3ÞFIGURE 2.2 Examples of crystal planes. ... Shackleford, 19 96.Reprinted with permission from Prentice-Hall.)FIGURE 2.3 Determination of crystal directions: (a) single [11 1] directions; (b)family of h 111 i directions. (Adapted from Shackleford, 19 96. ... forthe a 1 direction as ½ 211 0. Note that the unit vector along the a 1 direction is 1/ 3½2 11 0. Similarly, we may show that the unit vectors along the a2and a3directions are given by 1/ 3 12 10...

... 415 505 11 — 717 8 -T6 540 605 11 —PlasticsACBS Medium impact — 46 6 14 —Acetal Homopolymer — 69 25–75 —Poly(tetrafluorethylene) — — 14 –48 10 0–450 —Poly(vinylidenefluoride) — — 35–48 10 0–300 ... (8)Transformationtoughened zirconia 17 60 (255) 350 ( 51) 635 (92) 200 (29)Partially stabilizedzirconia þ9% MgO 18 60 (270) — 690 (10 0) 205 (30)Cast Si3N4 13 8 (20) 24 (3.5) 69 (10 ) 11 5 (17 )Hot-pressed Si3N43450 ... (19 48) Fracturing of Metals. ASM International, Materials Park,OH, p 246.Brindley and Worthington (19 70) Metall Rev. vol. 15 , p 10 1.Bu¨lfinger, G. B. (17 35) Common Acad Petrop. vol. 4, p 16 4.Cottrell,...

... structure. Note that since [" 11 01] direction is common toboth the (11 1) and (1 " 11 1Þ closed packed planes, the screw dislocation can glideon either of these planes: (a,b) before cross-slip; ... Inc.Cottrell, A.H. (19 57) The Properties of Materials at High Rates of Strain. Institute of Mechanical Engineering, London, UK.Courtney, T.H. (19 90) Mechanical Behavior of Materials, John Wiley, ... Inc.levels.Furthermore,dislocationloopstendtodevelopsemiellipticalshapesinanattempttominimizetheirstrainenergies.Thiswillbecomeapparentlateraftertheconceptofthedislocationline/strainenergyisintroduced.Finally,itisimportanttonotethatdislocationscannotterminateinsideacrystal.Theymust,therefore,eitherformloopsorterminateatotherdislocations,grainboundaries,orfreesurfaces.Thisconceptisillu-stratedinFig.6 .14 usingaschematicoftheso-calledFranknet.Notethatwhenthreedislocationsmeetatapoint(oftencalledadislocationnode),thealgebraicsumoftheBurgersvectors,b 1 ,b2,andb3(Fig.6 .14 )iszero.Hence,X3i 1 b 1 þb2þb3¼0ð6:9ÞWhenthesensevectorsofthedislocationsareasshowninFig.6 .14 ,thenEq.(6.9)maybeexpressedasb 1 ¼b2þb3ð6 :10 ÞFIGURE6 .13 Schematicillustrationofthecross-slipofascrewdislocationinaface-centered...

... 2003 Marcel Dekker, Inc.b 1 ¼ b2þ b3ð7 :12 aÞor 1 2½ 11 0¼ 1 6½ 211 þ 1 6½ 12 1ð7 :12 bÞThe partial dislocations, b2and b3, are generally referred to as Shockleypartials. They are formed ... energies of the ordinary dis-locations of type b 1 are greater than the sum of the line energies of theShockley partials. Hence,Gðb 1 Þ2> Gðb2Þ2þ Gðb3Þ2ð7 :13 aÞorG4ð 1 2þ 1 2þð0Þ2hi>G36ð 1 2þð2Þ2þð 1 2hiþG36ðÀ2Þ2þ 1 2þ 1 2hið7 :13 bÞorG2>G3ð7 :13 cÞThe ... Inc.sourceisinitiated.Theaboveprocessmaycontinuebysubsequentcross-slipandFrank–Readsourcecreation,givingrisetoalargeincreaseinthedis-locationdensityondifferentslipplanes.Thehighdislocationdensity (10 15 10 18 m/m3)thatgenerallyresultsfromtheplasticdeformationofannealedcrystals(withinitialdislocationdensitiesof $10 8 10 10 m/m3)may,therefore,beexplainedbythebreedingofdislocationsatsingleFrank–Readsources(Fig.7 .12 ),ormultipleFrank–Readsourcesproducedbycross-slipprocesses(Fig.7 .15 ).7.7...

... F.R.N. (19 51) The equilibrium of lineararrays of dislocations. Phil Mag. vol. 42, p 3 51. Fleischer, R.L. (19 61) Solution hardening. Acta Metall. vol. 9, pp 996 10 00.Fleischer, R.L. (19 62) Solution ... (Taylor, 19 34):Ád¼ mGb 1= 2¼ kd 1= 2ð8 :11 Þwhere kd¼ m  Gb and the other variables have their usual meaning.Equations (8 .10 ) and (8 .11 ) have been shown to apply to a large number of metallic ... 8 .14 .It should be clear from Fig. 8 .14 that the stresses required for particleshearing are lower than those required for particle looping when the particleFIGURE 8 .14 Schematic of the role of...

... 325 18 25 11 5Brass (Cu-30%Zn) 8.50 10 0 550 70 12 65Nickel–20%Cr 15 %Co 8 .18 204 12 00 26 25 14 7Mild steel 7.86 210 460 35 27 59Titanium–2.5% Sn 4.56 11 2 792 20 24 17 4PolymersEpoxy 1. 12 4 ... 4 1. 5 4 36Melamine formaldehyde 1. 50 9 70 6 47Nylon 6.6 1. 14 2 70 60 18 61 Poly(ether ether ketone) 1. 30 4 70 3 54Poly(methyl methacrylate) 1. 19 3 50 3 1. 5 3 42Polystyrene 1. 05 3 50 2 1. 0 ... fiber 1. 34 22 246 1. 7 413 16 18 4Epoxide + 70% glass fibersunidirectional—longitudinal 19 0 42 750 12 00 22 395unidirectional—transverse 1. 90 12 50 6 26Epoxy +60% Aramid 1. 40 77 18 00 55 12 86Poly(ether...