ALL 12 CHAPTERS COVERED
o o o
SOLUTIONS MANUAL
o
,Table of Contents o o
Chapter 1. Elastic Response of Solids Chapter
o o o o o o
2. Yielding and Plastic Flow Chapter 3. Contr
o o o o o o o o
olling Strength o
Chapter 4. Time- o o
Dependent Deformation Chapter 5. Fractur o o o o
e: An Overview
o o
Chapter 6. Elements of Fracture Mechanics C
o o o o o o
hapter 7. Fracture Toughnesso o o
Chapter 8. Environment- o o
Assisted Cracking Chapter 9. Cyclic Stress and St
o o o o o o o
rain Fatigue Chapter 10. Fatigue Crack Propagat
o o o o o o
ion Chapter 11. Analyses of Engineering Failure
o o o o o o
s Chapter 12. Consequences of Product Failure
o o o o o o
,DeformationoandoFractureoMechanicsoofoEngineeringoMaterials,o5thoed. ProblemoSolutionsop.o1/162
Draftodocument,oCopyrightoR.oHertzberg,oR.oVinci,oJ.oHertzbergo2009
CHAPTER 1 o
Review
1.1 Ino youro owno words,o whato areo twoo differenceso betweeno producto testingo ando materialo
testing?
Possibleoanswersoinclude:o(a)oTheogoaloofotheotwooproceduresoisodifferent.oWhereasoproductotes
tingoisodesignotoodetermineotheolifetimeoofoaocomponentounderoconditionsothatomimicoreal-
oworldouse,omaterialotestingoisointendedotooextractofundamentalomaterialopropertiesothatoareoind
ependentoofotheomaterial’souse.o(b)oTheospecimenoshapeoisodifferent.oProductotestingomustouseoth
eomaterialoinotheoshapeoinowhichoitowillobeousedoinotheorealoproduct.oMaterialotestingousesoidealiz
edospecimenoshapesodesignedotoounambiguouslyodetermineooneooromoreopropertiesoofo theomater
ialowithotheosimplestoanalysisopossible.
1.2 Whatoareotheodistinguishingodifferencesobetweenoelasticity,oplasticity,oandofracture?
Elasticityoinvolvesoonlyodeformationothatoisofullyoreversibleowhenotheoappliedoloadoisoremovedo(
evenoifoitotakesotimeotoooccur).oPlasticityoisopermanentoshapeochangeowithoutocracking,oevenowh
enonooloadoexists.oFractureoinherentlyoinvolvesobreakingoofobondsoandotheocreationoofonewosurfa
ces.oOftenotwoooromoreoofotheseoprocessesotakeoplaceosimultaneously,obutotheocontributionoofoea
chocanobeoseparatedofromotheoothers.
1.3 Writeo theo definitionso foro engineeringo stress,o trueo stress,o engineeringo strain,o ando trueo
strainoforoloadingoalongoaosingleoaxis.
load P
eng oengineeringostresso o (1-1a)
initialo cross-sectionalo area A0
load P
true otrueostresso o (1-2a)
instantaneouso cross-sectionalo area Ai
changeoinolengtho lofo ol0
oengineeringostrainoo o (1-1b)
eng
initialolength l0
finalolength lof
true otrueostrainoolno olno (1-2b)
initialolength l0
1.4 Undero whato conditionso iso Eq.o 1-
4o valid?o Whato makeso ito noo longero usefulo ifo thoseoconditionsoareonotomet?
Excerptsofromothisoworkomayobeoreproducedobyoinstructorsoforodistributionoonoaonot-for-
profitobasisoforotestingooroinstructionalo purposesoonlyotoostudentsoenrolledoinocoursesoforowhichotheotextbookohasobeenoadopted.
o Anyootheroreproductionoorotranslationoofo thiso workobeyondo thatopermittedo byo Sectionso107o oro108o ofotheo 1976o Unitedo States
oCopyrighto Actowithoutotheo permissiono ofothe
copyrightoowneroisounlawful.
, DeformationoandoFractureoMechanicsoofoEngineeringoMaterials,o5thoed. ProblemoSolutionsop.o1/162
Draftodocument,oCopyrightoR.oHertzberg,oR.oVinci,oJ.oHertzbergo2009
Po
o (lo /olo )oo (lo /olo )oo (1oo o ) (1-4)
true i 0 engo o i 0 eng eng
A0
Thisoexpressionoisotrueowhenovolumeoisoconserved.oHowever,oitoisoonlyousefuloifotheocross-
osectionaloareaoisotheosameoeveryoneoonotheotestospecimen.oIfothisoisn’totheocaseothenotheostressoa
ndostrainowillovaryofromooneopartoofotheospecimenotooanother.
1.5 SketchoFigureo1.3,ocurveo‘b’o(aoductileometal).oLabeloitowithotheofollowingoterms,oindicati
ngofromowhicholocationoonotheocurveoeachoquantityocanobeoidentifiedooro extracted:oelastico
region,oelastic-
plasticoregion,oproportionalolimit,otensileostrength,oonsetoofonecking,ofractureostress.
onsetoofonecking
tensileostrength
fractureostress
proportionalolimit
elastic-plasticoregion
elasticoregion
stress
strain
1.6 Onoaosingleosetoofoaxes,osketchoapproximateoatomicoforceovs.oatom-
separationocurvesolikeotheooneoshownoinoFig.o1.4boforotungstenoatotemperaturesoofo200,o60
0,oando1000oK.oPayocloseoattentionotootheopointox0oandotheoslopeodF/dxoforoeachoofotheocur
vesoyouodraw.
Theokeyofeaturesoofotheoplotoareotheoincreasingox0ospacingowithoincreasingotemperatureo(i.e.,owit
hothermaloexpansion)oandotheodecreasingoslopeoassociatedowithodecreasedoelasticomodulus.oThe
oplotoisoexaggeratedobutotheotrendsoareoreasonable.
F
dF
od
x 200o K
600o K
1000o K
x
x0o(1000oK)
x0o(600oK)
Excerptsofrom
x
0o (200
othisooK)
workomayobeoreproducedobyoinstructorsoforodistributionoonoaonot-for-
profitobasisoforotestingooroinstructionalo purposesoonlyotoostudentsoenrolledoinocoursesoforowhichotheotextbookohasobeenoadopted.
o Anyootheroreproductionoorotranslationoofo thiso workobeyondo thatopermittedo byo Sectionso107o oro108o ofotheo 1976o Unitedo States
oCopyrighto Actowithoutotheo permissiono ofothe
copyrightoowneroisounlawful.
o o o
SOLUTIONS MANUAL
o
,Table of Contents o o
Chapter 1. Elastic Response of Solids Chapter
o o o o o o
2. Yielding and Plastic Flow Chapter 3. Contr
o o o o o o o o
olling Strength o
Chapter 4. Time- o o
Dependent Deformation Chapter 5. Fractur o o o o
e: An Overview
o o
Chapter 6. Elements of Fracture Mechanics C
o o o o o o
hapter 7. Fracture Toughnesso o o
Chapter 8. Environment- o o
Assisted Cracking Chapter 9. Cyclic Stress and St
o o o o o o o
rain Fatigue Chapter 10. Fatigue Crack Propagat
o o o o o o
ion Chapter 11. Analyses of Engineering Failure
o o o o o o
s Chapter 12. Consequences of Product Failure
o o o o o o
,DeformationoandoFractureoMechanicsoofoEngineeringoMaterials,o5thoed. ProblemoSolutionsop.o1/162
Draftodocument,oCopyrightoR.oHertzberg,oR.oVinci,oJ.oHertzbergo2009
CHAPTER 1 o
Review
1.1 Ino youro owno words,o whato areo twoo differenceso betweeno producto testingo ando materialo
testing?
Possibleoanswersoinclude:o(a)oTheogoaloofotheotwooproceduresoisodifferent.oWhereasoproductotes
tingoisodesignotoodetermineotheolifetimeoofoaocomponentounderoconditionsothatomimicoreal-
oworldouse,omaterialotestingoisointendedotooextractofundamentalomaterialopropertiesothatoareoind
ependentoofotheomaterial’souse.o(b)oTheospecimenoshapeoisodifferent.oProductotestingomustouseoth
eomaterialoinotheoshapeoinowhichoitowillobeousedoinotheorealoproduct.oMaterialotestingousesoidealiz
edospecimenoshapesodesignedotoounambiguouslyodetermineooneooromoreopropertiesoofo theomater
ialowithotheosimplestoanalysisopossible.
1.2 Whatoareotheodistinguishingodifferencesobetweenoelasticity,oplasticity,oandofracture?
Elasticityoinvolvesoonlyodeformationothatoisofullyoreversibleowhenotheoappliedoloadoisoremovedo(
evenoifoitotakesotimeotoooccur).oPlasticityoisopermanentoshapeochangeowithoutocracking,oevenowh
enonooloadoexists.oFractureoinherentlyoinvolvesobreakingoofobondsoandotheocreationoofonewosurfa
ces.oOftenotwoooromoreoofotheseoprocessesotakeoplaceosimultaneously,obutotheocontributionoofoea
chocanobeoseparatedofromotheoothers.
1.3 Writeo theo definitionso foro engineeringo stress,o trueo stress,o engineeringo strain,o ando trueo
strainoforoloadingoalongoaosingleoaxis.
load P
eng oengineeringostresso o (1-1a)
initialo cross-sectionalo area A0
load P
true otrueostresso o (1-2a)
instantaneouso cross-sectionalo area Ai
changeoinolengtho lofo ol0
oengineeringostrainoo o (1-1b)
eng
initialolength l0
finalolength lof
true otrueostrainoolno olno (1-2b)
initialolength l0
1.4 Undero whato conditionso iso Eq.o 1-
4o valid?o Whato makeso ito noo longero usefulo ifo thoseoconditionsoareonotomet?
Excerptsofromothisoworkomayobeoreproducedobyoinstructorsoforodistributionoonoaonot-for-
profitobasisoforotestingooroinstructionalo purposesoonlyotoostudentsoenrolledoinocoursesoforowhichotheotextbookohasobeenoadopted.
o Anyootheroreproductionoorotranslationoofo thiso workobeyondo thatopermittedo byo Sectionso107o oro108o ofotheo 1976o Unitedo States
oCopyrighto Actowithoutotheo permissiono ofothe
copyrightoowneroisounlawful.
, DeformationoandoFractureoMechanicsoofoEngineeringoMaterials,o5thoed. ProblemoSolutionsop.o1/162
Draftodocument,oCopyrightoR.oHertzberg,oR.oVinci,oJ.oHertzbergo2009
Po
o (lo /olo )oo (lo /olo )oo (1oo o ) (1-4)
true i 0 engo o i 0 eng eng
A0
Thisoexpressionoisotrueowhenovolumeoisoconserved.oHowever,oitoisoonlyousefuloifotheocross-
osectionaloareaoisotheosameoeveryoneoonotheotestospecimen.oIfothisoisn’totheocaseothenotheostressoa
ndostrainowillovaryofromooneopartoofotheospecimenotooanother.
1.5 SketchoFigureo1.3,ocurveo‘b’o(aoductileometal).oLabeloitowithotheofollowingoterms,oindicati
ngofromowhicholocationoonotheocurveoeachoquantityocanobeoidentifiedooro extracted:oelastico
region,oelastic-
plasticoregion,oproportionalolimit,otensileostrength,oonsetoofonecking,ofractureostress.
onsetoofonecking
tensileostrength
fractureostress
proportionalolimit
elastic-plasticoregion
elasticoregion
stress
strain
1.6 Onoaosingleosetoofoaxes,osketchoapproximateoatomicoforceovs.oatom-
separationocurvesolikeotheooneoshownoinoFig.o1.4boforotungstenoatotemperaturesoofo200,o60
0,oando1000oK.oPayocloseoattentionotootheopointox0oandotheoslopeodF/dxoforoeachoofotheocur
vesoyouodraw.
Theokeyofeaturesoofotheoplotoareotheoincreasingox0ospacingowithoincreasingotemperatureo(i.e.,owit
hothermaloexpansion)oandotheodecreasingoslopeoassociatedowithodecreasedoelasticomodulus.oThe
oplotoisoexaggeratedobutotheotrendsoareoreasonable.
F
dF
od
x 200o K
600o K
1000o K
x
x0o(1000oK)
x0o(600oK)
Excerptsofrom
x
0o (200
othisooK)
workomayobeoreproducedobyoinstructorsoforodistributionoonoaonot-for-
profitobasisoforotestingooroinstructionalo purposesoonlyotoostudentsoenrolledoinocoursesoforowhichotheotextbookohasobeenoadopted.
o Anyootheroreproductionoorotranslationoofo thiso workobeyondo thatopermittedo byo Sectionso107o oro108o ofotheo 1976o Unitedo States
oCopyrighto Actowithoutotheo permissiono ofothe
copyrightoowneroisounlawful.
