m m m
SOLUTIONS MANUAL
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,Table of Contents m m
Chapter 1. Elastic Response of Solids Chapt
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er 2. Yielding and Plastic Flow Chapter 3. Co
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ntrolling Strengthm
Chapter 4. Time- m m
Dependent Deformation Chapter 5. Fractur
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e: An Overview
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Chapter 6. Elements of Fracture Mechanics
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Chapter 7. Fracture Toughness
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Chapter 8. Environment-
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Assisted Cracking Chapter 9. Cyclic Stress and
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Strain Fatigue Chapter 10. Fatigue Crack Propa
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gation Chapter 11. Analyses of Engineering Fai
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lures Chapter 12. Consequences of Product Fail
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ure
,DeformationmandmFracturemMechanicsmofmEngineeringmMaterials,m5thmed.
ProblemmSolutionsmp.m1/16
2
Draftmdocument,mCopyrightmR.mHertzberg,mR.mVinci,mJ.mHertzbergm2009
CHAPTER 1 m
Review
1.1 Inm yourm ownm words,m whatm arem twom differencesm betweenm productm testingm andm mate
rialmtesting?
Possiblemanswersminclude:m(a)mThemgoalmofmthemtwomproceduresmismdifferent.mWhereasmproduct
mtestingmismdesignmtomdeterminemthemlifetimemofmamcomponentmundermconditionsmthatmmimicmreal
-
mworldmuse,mmaterialmtestingmismintendedmtomextractmfundamentalmmaterialmpropertiesmthatmarem
independentmofmthemmaterial’smuse.m(b)mThemspecimenmshapemismdifferent.mProductmtestingmmust
musemthemmaterialminmthemshapeminmwhichmitmwillmbemusedminmthemrealmproduct.mMaterialmtestingm
usesmidealizedmspecimenmshapesmdesignedmtomunambiguouslymdeterminemonemormmoremproperti
esmofm themmaterialmwithmthemsimplestmanalysismpossible.
1.2 Whatmaremthemdistinguishingmdifferencesmbetweenmelasticity,mplasticity,mandmfracture?
Elasticityminvolvesmonlymdeformationmthatmismfullymreversiblemwhenmthemappliedmloadmismremove
dm(evenmifmitmtakesmtimemtomoccur).mPlasticitymismpermanentmshapemchangemwithoutmcracking,mev
enmwhenmnomloadmexists.mFractureminherentlyminvolvesmbreakingmofmbondsmandmthemcreationmofm
newmsurfaces.mOftenmtwomormmoremofmthesemprocessesmtakemplacemsimultaneously,mbutmthemcontr
ibutionmofmeachmcanmbemseparatedmfrommthemothers.
1.3 Writem them definitionsm form engineeringm stress,m truem stress,m engineeringm strain,m andm tr
uemstrainmformloadingmalongmamsinglemaxis.
load P
eng mengineeringmstressm m (1-1a)
initialm cross-sectionalm area A0
load P
true mtruemstressm m (1-2a)
instantaneousm cross-sectionalm area Ai
changeminmlengthm lmfm ml0
mengineeringmstrainmm m (1-1b)
eng
initialmlength l0
finalmlengt lm
true mtruemstrainmmlnm mlnm (1-2b)
h f
initialmlength l0
1.4 Underm whatm conditionsm ism Eq.m 1-
Excerptsmfrommthismworkmmaymbemreproducedmbyminstructorsmformdistributionmonmamnot-for-
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Unitedm StatesmCopyrightm Actmwithoutmthem permissionm ofmthe
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, 4m valid?m Whatm makesm itm nom longerm usefulm ifm thosemconditionsmaremnotmmet?
DeformationmandmFracturemMechanicsmofmEngineeringmMaterials,m5thmed.
ProblemmSolutionsmp.m1/16
2
Draftmdocument,mCopyrightmR.mHertzberg,mR.mVinci,mJ.mHertzbergm2009
Excerptsmfrommthismworkmmaymbemreproducedmbyminstructorsmformdistributionmonmamnot-for-
profitmbasismformtestingmorminstructionalm purposesmonlymtomstudentsmenrolledminmcoursesmformwhichmthemtextbookmhasmbeenma
dopted.m Anymothermreproductionmormtranslationmofm thism workmbeyondm thatmpermittedm bym Sectionsm107m orm108m ofmthem 1976m
Unitedm StatesmCopyrightm Actmwithoutmthem permissionm ofmthe
copyrightmownermismunlawful.