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NATIONAL RESEARCH COUNCIL2101CONSTITUTION AVENUE, WASHINGTON 25,D.C.
COIVHVIITTEEON SHIP STEELOF TEE
131VISION OF ENGINKSRING AND INDUSTRIAL RESEARCH
December20, 1950
Chief,Bureauof Shipscode 343Navy DepartmentWashingtm 25, D. G.
War Sir:
Attachedis ReportSerialNo. SW-38 entitled“A Studyof PlasticDeformationand Fracturingby st~ai~EnergyDistribution.”This reporthas been submittedbythe contractoras a ProgressReportof the work done onResearchProjectSR-98underContractNObs-45521betweenthe Bureauof Ships,Navy Departmentand SwarthmoreCollege.
TIM reporthas been reviewedand acceptancerecom-mendedby representativesof the Committe=on.Ship Steel,Division-ofEngineeringand IndustrialResearch,NRC,accordsmcewith the terms of the contractbetw~entheof Ships,Navy Depa~tmentand the NationalAcademyof
Very trulyyours,
in
BureauSciences.
RFM:mhR. l?,Mehl, ChairmanCommitteeon Ship 5tael
.--
Aohisorgtothe SHIP STRUCTURE COMMITTEE ucommitieerepresentingthecombinedshipbuildingresearchnativitiesof thememberagencies- U. S. Navy, U.S. coast Guard, U.S. Maritime Commission,American Bureau of Shipping and the Military SeaTransportation Service.
~ PREFACE
. The XavyDepartmentthroughthe Bureauof Shipsis distributingthis reportfar the SHIF STRIJdTURE!XNMITYEEto thoseagenciesand individualswho weresztj.velyassociatedwith the researchwork- This reportrepresentsresultsofPart of the researchprogramconductedunderthe Ship StructureCommitteetsdirectiveto llinvestigatethe designand methodsof construction of we~dedsteelmerchantvesselse’f
The distributionof thisreportis as follows:
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Chief,Bureau of Ships,Navy D~partruentDr. DouglasWhitaker,NationalResearchCouncil
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,-,.,U. S. MaritimsAdministration ,
VitaAdm. E, L. Cochrane,USN (Ret.)E. E. hlart~nslq ,.
Rep~eS@ntatives of Atierica~ Iron and Steel Irstitqte’Committeeon manufacturingProblems’ ,
C. M, Parker,Secretary,GeneralTechnicalCommittee,AmericanIronand Steel Institute
L. C.C. H.E. C.
C. A.Harry
C. R.R. F.
Bibber,Carnegie-IllinoisSteelCdrp.Herty,Smith,
Adams
Jr., BethlehemSteelCompanyRepublicSteel Corp.
WeldingResearchCouncil
Copy}To.9$ * LellotteGroverBoardman copy No. 2&- Wrn.Spraragen
Soderberg,Chairman,Div. of Engineering~ lndmRe~earch~~CMehl.Chairman.Committeeon Ship Steel
Finn Jonas~en,TechnicalDirectoryComhitteeon ShipSteelC+y lb. 100 - S. I. Liui InvestigatoryResearchPraj.ectSR-98copy No. 101 - S.”T.‘CarpeiiterJIUvestigator~ResearchProjecfSR+@ and SR-118Copy No. 27 - Hm,,II.13aldwInyJr;, InvestigatorsResea-~hProjectSR-99and 111CopyNo. 102 = L. J+-Ebert~‘!hxvestigatorjResearchPioj6ctSR-99
,“ .-. —. .’
-iv-Klfmg3er,Investigator,Research@ject SR-99Voldrich,Invsstige,tor,ResearchProjectSR-1OOEieppel,Imvestj.gatar,”ResearchProject,SR-100Williams,Irwestiga.tot,ResearchProjectSR-106Mehl,InvestigatorgRessarchProjectS,&l,08 7Brtck,Investigator,ResearchProject&&109 ‘Lorig,Investigator,ResearchProject5&l10~uppiger,Investigator,ResearchProjectSR-113W5rd, InvestIgator,Researcfi’Preject S&l13Riparbel’li,Investigator,ResearchProjectSR-113Wallace,Investiga.tor~ResearchProjectSRPPl14Russo,InvestigatoY~’”ResearchProjectSRW117Hechtman,Investigator,ResearchProjectSR+li9Mikhalapov,Investigator,R@~a$ch ProjactSR-120
.
copy No. 114 - ClarenceAltenburger,GreatLakesSte@ Cofipa~Ycopy No. 115 - T. N. Armstrong,International@~&L Co.g IPe.Copy No. 116 - A. B. Eagsar,Sun Cil Company ““ ‘i”‘,,.,.copyNo. 117 - BritishShimbuildhgResearchAsso&ia~ic$,Attn*J. C. Asher,sec.CopyNoi,118 + GeorgeElli~ger,National’Bureauof”Standardscopy No. 119 - A. E. Flanigan,Universityof Californiacopy No. 120 - 0. J. Horger3TimkenRollerBeaii~ Gompany .,copy NO. 121 - E. P. Klier,UniversityoPMa~land : “..Copyl$o=nz - RobertC. MaddenjKaiserSteel Compa~ +copy No. 123 - N. & Newmark,lhive~sityof IllinoisCopies124 thruu~ - E. G- HillJBritishJointSetivicesMlssIon(NavyStaff) ‘CopyNo. I-49- E. Orowan$MassachusettsInstituteof TechnologyCopyNo= i50 -
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I
.— .- .—.
PROGRESSREPORT
NAVY BUSHIF’ScQNTRACTNObs-45521
p~~c~ sR.9g
~SiudY of PlasticDefamation and Fracturingby StrainEnemzvDistrfb@iQ
n-itemal&-Notched SteelPlatesunderTension
wS. 1. Liu
SamuelT. Carpenter
StructuralLaboratorySwarthmoreCollege
IMvisionof EngineeringSwa@unore, Pa.
,-,
.. _
I ‘1
.
,.
ABSTRACT
LIST OF ‘1’ABLES
LIST OF FIGURES
INTRODUCTION
MATERIALAND SPEKllUfJi3
PRCICEDUREAND EQUIPMENT
THEORYAND NETHODOF EVALUATION
RESULTSAND DISCUSSION
Stress-Strainand Energy-Strai~~Relationsafthe ltiaterial
Nlacro-Propagationof plasticDeformation~.ndthe Crack
, Theoryand ExperbentalFacts
Correlationwith Specimenof Va~ing width andConstantThickness
CONCLUSIONS
SIGGESTEDFUTUREWORK
ACKNCIITLFJIGEIIENTS
Pare No.
i
ii
ii
3-
2
4
4
8
8
#
10
11
15
-.
*i-
,,’.,.
This investigation
fracturingof 12” wide$3/411
was conductadto
thick.int~ally
studythe plasticdeformationand
nctohedsteelpla,tes~der ~al
tensionby determiningthe strainenergydistributionon the surfaceof the
deformedregionsof the plates. Severalstagesin the processof deformation.. ,- ,
and fracturingat TO” F and ’10°F were in~~tigatedto maximumload,?OO F being
akovethe transitiontemperatureand 10° F beingbelow
temperature,Surfacestrainenergydistributionacrms
determinedfor a spectienfracturedductile~yat70° F.
the transition
the crackwa~ also
By suingthe octahedraltheoryin connectionwith liaeassumptionof,., :.
incompressibilityand the assumptionthat thepr~ncipalcoordinatesystemis
parallalto the threedimensionsof the’plate,“theunit etiergieson the surface.,:. ,,!,,of the platewere obtainedYrom gridmeasurements.By assumtigthat the energy
distributionis independentof tbe’thidcnebsdimension;+@xd energyis obtained>.....”
for comparisonwith the totalenergyinput.nl~asuredfrom the Mad-elongatfin
ctmve.
The results
octahedraltheo~ and
totalobsemmd energy
of this Mmstigation show that the totalenergybasedon
the above-statedassumpt~ansagreesverywell wfth the,.
input;that the rate of propagationof plasticdeformation
with respectto energyinputdecreaseswitihdecreasing,,,
specimenswith two dimensionalsimilarityand ~onstant
ener~ of individualspecimansof inwying.widt??oem be,,
temperature;that,for
thickness,the total
predictedby the strain
energydistributionof a @inglespecimenof:proparwidth;and that$at room
temperature,the unit strainenergyat the cra~ &S fo~dto @ aPProx~ately
in the orderof 30,000in-lbsper cubicinch in.aductilespech=.
— — —.,
.- *i-
2
3’
4’
5
:, , ‘,..
6 .\
:7,
,,,’”
9
,.,
10a
.,
10b
“!- .’
LIST OF TABLES——
.:Title ‘,,, .,.
ChemicalAnalysisof ~~~~!Steel
Surma=of EnergyComputations
,. :~, ‘“’
,,.LIST OE FIGURES.. ....“.
“’~itie “
,.Te’stSpe&nen for StrainEner~
.,
...>j...,., Pa~e No..,,,,, .!—
., ,, , 3.;.“,“,
.,.
. .
TestSpecimenfor Un~4%ial Tension
Tme Str6ss_Str~inC&es in Un~&ia,l’Tension
“Utive~sai’Stii&s-5j5afi~ctions for’3/411WS,teelShipPlate,“-4.,:”’-=<*.:“;’; : ,’ ,. “.
,-
,,. , +,,, ,
Pa~e No.’ : “
,UnitStra,inEnm~ of 3/41f.,~l+pPlateas Functionsof OctahedralShear’”Straihas Deterr&nedbyUrJ-.Axi&lTest,at~Oo F and 10° F
.-.:, ,,.;.
Unit StrainEnergyDistributionon the Surfaceof,. A 121(X3/411~Tot&hedSpecimen”:W-29-4,Loadedto
277~000lbs (VisibleCrack)at 70° F
,UnitStrain.Ener~Diptrib@ion,o~7,,the..SwfaoeofA 12’1x ?f~nNotchedSpecimefi’W-29-4~Loah’edto295,0001bE ~t 7~~~ +., ~,/, ,,,
Unit StraipEnergyDistributionon the SurfaceofA 12’1x 3/411NotchsdSpeck&i W-29-4;Lc&dadto325,000lbs at700F ,,,,, j ., ,..,,.“, ,,, .,)
Unit StrainEnergyDistributionon the SurfaceofA 12tii’~/@ &’tchedS&ctieti”~i~~+&,Ldad&d’”to”352,000lb~,ll~$,Load.at+700F.,,. ,1:...........-!‘.,!,1.,,.-.
21““’””’-”’’”
22 “’”’””’
23
23 “’”3..., ~... -<,
24” .,.,, “
. .
24
,.
,?5
., -.. .. .. .....,! ,-
25-+’’!..‘ ,“::..“
.,, ,-,.,.,
2’43,, ,,.
Unit Stra@,EnergyQZstri@@on,,onthe Wrf:+q of ,,.V,,,A 12’~x 3/411lTotefied’Sp6cti6tiW-29-~, Tested ‘j ‘
--
.. to Fgacture,a}.,70°F .,;.,., ,,:‘+.:,+::...,...,,.. ,( .’.“-, ,.
——.
. . .- 111 -
LIST OF FIGURES(continued)
F~gureRo. Title -b
13
14
u UnitStrainEnergyDistributionon the Surfaceofa 12ttx 3/4’1NotchedSg?ecimenW-29-3,Loadedto277,740lbs (VisibleCrack)at 10° F
i2 Unit StrainEnergyDistributionon the Surfaceofa,12tJx 3/411NotchedSpecimenW-29-3,Loadedto295,00:0lbs at 10~ F ~
,,,Unit StrainEnergyDistributicmon the Surfaceofa 12!’x 3/411NotchedSpecimenW-29-3?Loadedti325$000lbs (Fracture)at 10°F
,.Unit StrainEnergy~istributionIn the.DiagonalandTransverseDirectionof “121ix 3/4t*l~otcheti”SpecimensLoadedto VisibleCrack at 70° F and.lO”F.
19
I ~ ‘-.
.,
20
21
22
23
Distributionon the Differenceof Unit StrainEnergiesfrom 277~T40’lbs(VisibleCr~.ck)to 325,000lbs(Fracture)for the 1211x 3/.4’~NotchedSpecimenW-29-3at ~0° F
LongitudinalDistributionof Unit Str=inlhergyonlineSurfaceof a 1211x 3/4tlNotchedSpecimenW-29-14,Testedto Fractureat 70° F -Quadrants2 and 3
LongitudinalDistributionof Unit Str3.inEnergyonthe Surfaceof a 1211x 3/411I~otchedSpecimenW-29-14Testedto Fractureat 70° F -Quadrants1 and 4
Mncm-Propagationof PlasticDeformationW~.thin1211x ~/~~1N~tclledSpectiensunderL~ndttudinalTensionat 70° F and 10°F
Macro-Propagationof Crackacross12’1x 3/AIINctchedSpecimensof SteelsS.9-11at 92° F and S-9-8 at57°F Correspondingto Ductileand BrittleFractures
Error in StrainEnergyIntegraland its Correction
Effectof StrainAgingon Load-DeformationCurve,(SpecimenW-29==4)
Effectof StrainAgingon Load-DeformationCmve,(Specimenw-29-3)
ContinuousLoad-ElongationCurvefor specimenT-29-14at 70° F
—..— — ..-.-
-iv-
LIST OF FIGURES(aontinued) ,.
25
26
27
..,-,,
.Compatiisonof TotalStmin EnergyBasedonSurfaceStrainsand OctahedrKL~heo~ against
“36.ActualTotalEnergyInput
QuarterViewjShowingOutltnesof Specimenwith “.36Two-Dimensional&mIlari~ Suptm%nposed.onthe Surfaceof a 12i1Spedimem,with all NotchEnds Coincidingwith Each Other., .“
Cor~e3ationbetweenthe UnitStrainEnergy ’37Distributionin a 1211x 3/4ttNotchedSpecimenand the AverageUnit Energyof 3/4*tNotchedSpecimensva.ry3ng,inWidth: ,“..
,..,.,.CorrelationbetweentheUnit StrainEner~ *..
DistribuWo~lin a Fractured1211x 3/41~:UotchadSpecimenand the AverageUnit,Energyof Fractured3/41’NotchedSpectienv&ying.in Width ,!: ,.
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— —. .-.
.
PROGRESSREPORTNAVY 13USHll%CONTRACTilUbs-45521
PROJECTSR-9$
~tudy of P~ttc Defamation and Fracturing.by Straz~~er D Distribution
Internall?-NotchedSteelPlatesunderTension—,—-—l—..,by
. .“S. I. Liu ‘
., ,,,Samuel,,T,,,.c~ente~:.}.,
!, St~chral Laboratory ,,1 ,.SwarthmoreCollege
Divisionof Engineering .,Swarthmore,Pa.
,,.‘!., ,,., ,.,
H--- ---- ----- ---- ---- -+--
. ~ .,. .,
INTRODUCTION
,,.. Two of the most importantfactorswhichdictatethe behaviorof ship
. .stru&ure underservicecondition~’are’geom&y and temperature.Many investi-
gaticns”havebeenundertaken’inan dffoit’’ti’determinethe effectof theset~
variables’upon the flow and fracturing”behaviorof shippla”te~Becau9eof
I.lsuPficientinformationon the physicnlinsightof flowand fFaoturingphenomena
generally,”and in particularthe transitionphenomenoti”insteel,the problems-’”
,,
involvedare stillfar from a completewhfion.’ ~~wever~the =l~e of the,.
mechanicaland phefiomenologicalapproachto +u’ch’”problemshas been dem~n’~~rated
by the valuableapplicationsin PracticeO”’ ““/, ,:
The effectof geometryope~tes throtigh’’s%ressstate. .Inmost cases,
experimentaldeterminationof plasti~stressstateis impossible.On the other~.,. ...,,. ..... .,.,.
hand, in many casesstrainenergylendsitse~ to measurement=.Becauseof the!,,.,”” !.,1.:
possibilityof measurementand becauseof the functionaldependencebetweenstress.* ;,,, ., ,.
stateand strainenergy?one way to approachthisproblemis to dealwith the ,,
effectof geometryin termsof !’Qtrainenergydistributionlt~
—— ..——. .—— -. ., .,
.,2-1 ,~,j::,*.,(.l$.r.,.f:’,,,,., ,’.,,’,.!’! .,
Accordingly,this investigationwas.en@mt&d to “analyzethe relation
betweenthe behaviorbf internallymt,ch~~platesat various~mp~rat+uresand., ...,!,. ,,..,, $.,,, ;. .,1.,,, ,,
the strainenergydistributiond&loped”&d&r differentstagesof longitudinal~“’”.,,, ,,.. .,.
tensileloading,by employingthe octahedral’theb~’”~~”~a~~le:ctiuhwith grid,.
measurements.By thismeans it may be ultimatelypossibleto explainthe effact$
of size and geometryon the basis”.:ofstrain’energy@istribution-This preliminary
investigationcoversone platesize(12~-@de ky 24!1long by 3/4’1thickpl~te)~“~, !’ :..,
one notohcondition(a 311internalslotwith 0S023!1end radius),two temperatures,.,
70° and 10° F, corre,spoadingrespectively”’tothe ductileand cleavagefracture. .
of thismaterial, The gridanalysiswas studiedfor threespeeimen~.,,
The resultsof thispreltiinary.~~yes:~gationare as follows. For ‘
identicq~specimensof consta~t,,thiclmessand two dimensionalsimilarityunder.. ,,.’, : ,. ‘i.7::,’,.!.’:,.’‘tensi9%.it,app@ars~%Qat ,th~,totalstrainenergyabsorbedat ‘atitageof’’deformtion ‘-,, ,. “, ~,J,.:...’after.tJne.,.~@l+c~ackJand afterfracturecan be predictedby consideringthb’strain,’ .? ‘: ..
,., , ,A ;
=-w dWr$Fp$ipp o,f#,siug!~sw~imen of: properVlidth.It was also‘fbund:’th&t”’.“ II ..:,,.,,,....!J,,.I .’; ,.
as temperaturedeorq~ses,z,the rate of propagationof deformationappearsto ““,, , .,-.,,,,”:,, ..?,.decreasewith respeo$,t~ tot@strain ener~ tnputm For a ductilefracture,’the
“.. . . .,,.:..! ,.. ,!unit strq~ enery~,atthe,,~~e.cturemaybe in the order‘of“>QV600in-lbsp& cubic’
,1 ,.%+: ,-’~..,.,,,, . . ..
inch.br,greatero Underthe georn~tricconditions”&estigatedy the’e~erimen~~,“? :, !,, .fl,,+,,,;..,.,,h,,,, .,resultsin termsof strainenergywere foundto be in good agreemeht:with’” ‘
.: . .,
*.>::. .>,.,,,,..:,..comp,@ations.,based up,qnthe oc~ahp,draltheo~o
!- ,.*; ,......!-’ >,,,,. , r)‘;:.;,,’1,-’)!,.:‘,1,;.., .,,;,,,
# - ,,; ,..;,,
.
., , #UITERIALANDSPECINEUS - :,;+’,., .:,,,,.,., ,.....‘,..-,:,.,..
.,
plates:~ffully~k~l~dd‘lWTIste~l;werd.’tisedmThe:.ana3+ysisGf,,this..mterial.is,,,- ,,
givenin Table”T. “’ ‘“’~ ‘ ‘ ,,.,,,.,. ...-’.,.,..:;:,,..!.P,,“? *.1,,..
,J. >.,.:.,:’ ‘. 4,..i,. ~,..,~ , ,:, ,. .,.,,-, .-, ,, ,., .’ ., ,.
.; !’,...’ ! ., ,.‘A!
.- .
—. . . ..—- ..—- .——-
..
-3-
,. TABLE T
ChemicalAnalysis- lrWnStael
c Mn ““ Si Al “N “:,
.~~: ‘“ ‘& .23 “.006 ‘ .00$ ‘.. .... . . .,-
Figure1 showsthe internally-notchedspecimenwith lightlyscmtched.,,,.,’.!,1/4’1gridlinesover a gage lengthof 9tton one SUrfaCeOf the Plate* ‘he 3“ ‘:d*
,“internalnotchterminatesin two’holesof 0*04611diameterat the end of the jemeier%
,, ,,saw cut*“ YO determinethe unit energynear the “cracks1/16’1grid lineswere used
. ,. ,,,’for a singlespec:men’’testedto fractureat 70°F,
..,-the 1/16’tgridli~esextendj-ng
.- .,. ,.to a longitudinaldistancaof l~r from the transversecenterline of the plate~
The threespec?.mensused,with testingand loadingschedule,were as follows:.,,.,.
Specimenlr;-29-4:Testedat 7~OF.,.
Gridmeasurementsmade afterthe
SpecimenW-29-3:
Specimen?~-29-14:
loadsproducing,’anobservablecrackat,0.046t!.,d$~~, ::, -.hole (277,000lbs)j295,000lbsl 325~oo~lbss andat a meximumload of 352~70~lbs= Approximatelyone meek,iqtervals-be.twesnlo~dingsafteriniti~loa~.
i, ,..,,.,Testedat 10°F~ Grid ~easurernentsmade afterloadsp~oduci~gan observable@ack atO~04611dia+ hole,,~ ~ :“’(27?~740lbs),295,~’Olbs, and at the fract~~eload of 325,000lbsa Approxf~at~ly”w@~e~k -’ “’ “ Vintervalsbetweenloadingsafterinitialload-:, .,,,. ...:’:
Testedcontinuouslyto fractureat a temperatureof‘,
70° F, and gridmeaswed. See Figure?3,for,load-.,,
.-
elongationdiagram,.
Figure2 showsthe cylindricalspecimencut from the
.,, . .. .. 3.’
samematerialfor
functionx The
211radiusand
the determinationof the octahedralstress- octahedralS-k~i-n
+ ,001”.df~meteris ~650- For measurementcontrol,a notchof.,.
approximately●005ttdepthwas machinedon the cylindricalcontour.,,
fromunl-axialitycausedby sucha very shallownotched-contowis
be negligilnle,
The deviation
assumedto
-4-
PROCEDUREAND EQUm.N~
Both typesof specimenware meldedto adapters. All testingwas done
in a 600,000.lb testingmachine. Ths atiangernefitsfor matitainingtempenture
and for elongationmeasurementsbya clip.gtigetisingSR-,4mire strai~rgageswere
l+ The te~e~describedin detailin a previotis:pti~eri tui=e’tif10Q’F:As ““;’ ‘
maintainedby circulatingair chil&d’.~ dky~icein & insulated”’t~ans’parent‘;”
chambersurrouidimgthe specimen. TliGgr”i~def&tiatio&at d&f&k~ ~tag~~ “’L
hf loadingwere m“eksumdon a milling’machihe’’&&rateto _OOl~a &l g“rid ‘“
layoutswers alsomeasuredbeforetestingta providea referencesystem. A
time intervalof about.,a”
for gridmeasurements.:,
The changesin
a mechanicalstraingage
@eek elap8edbetm~en&loading and reloadingto &’l~ow
,.:,,
diameterof.
accurateto
.’ ,,.+ ,, . .
.,,!.,,,
the cylindricalsp@mens weremeasuredby,,
,000111.,.,
THEORYAND hOl?THODOFEVALUATIOIi”:: ‘;“- ‘~:~’”’,., ,.,.:‘, !,, ,
directions
tne plate.
systemwas
.’.
coincidewith longitudinal,‘15ansvsrseand thicknessdimensionsof
For convenienceof fieatmrementjtheorigik,,ofthe chostinc6&d&te....“
put at th~ pointO insteadof’the’’tienter”ofthe’platet
stateis
..
givenby the,fo,l~owi~gintegrals,,,,.: ,.~~ ,. .-.?-. ..,:.’‘,. ,
..’
;,.; ,,
,( .. .,,. ,,., ,, I*..
,1 “ ..,, ... ,.
,. .’, ..” - .,..(l)”;!,
,. . ., .,,: . ...4.,.;
-.“.
‘,, , .,, -,,1,..;.“,
.,’ +
~ Superscriptsreferto references-inBibliography,,,,., .:
L-where
“-5-
.>
L!~ unit straipenergyin in-lbs/in3
z’ ~ octahedralshearstressin
]= octahedralshearstrain
The localvalueof unit strainenergyand,) ,. ~r ...;<.,..,,
lb~/in2
the totalstrainenergyfor
the griddedportionof the plateca~’%ededucedfmm surfacegridmeawremen~s
“byusingEquation(1) and,.the,followingthreeassumptions:
,. ,,!<
(a)
(c)!,.
.,,
, ,- ,.
Constancyof volume(usedin computing&it energy)
The chosenx-y-zsystemis the principalsystem’(used‘;.. ,,, .,
in compuiitigunit en&y)
The unit strainenergyis independentof z (usedin - :
computingtotalstrainenergy)”’” ‘ “
By the firsttwo assumptions,the expressionsfor octahedralsh~arstresb’;and,“ .,, ,, . ,,
octahedralshearstrainare reducedto the followingforms:,.,,..-
.,~ For uniaxialstressstate:’ ,....! .,..
(,
For triaxialstressstate:
,:-
where
(3)
(5)
EX)ZY= prZncipalstrainsas givenby:
(6)
-6-
where
u: displnceme~tok P ~gridpointin the x direction,..,!.. . ,,‘:.; .., .. ..
v ,-.-, :“ Msplacementof a grid pointin the y dirqct@
mm pocfalms for Col!,putingthe wm.faceunit strainenergyfrom grid,.,:;>,...,
measurementare as follows$,. ,, . ,, ,.
(1)Establishingthe IIoctahedralshear“stress-octahedralshea~:straiuw,,...,,,,. ..,.
law by uniexialtest:‘i;:”~:l,f
The true stress-strainrelationsbeforeneckingwere obtainedby tensile....,.,. ., .:,.440.:,.,.,...,,,:,..- .+,,,,.!
testsof the cylindricalspecimensat 7CP F and 10° F corres&ndi~gto ductileend,,. 4,. t ,,.
. .. . . . .. . :. ::
cleavagefractureof the materialin 121~wide internallynotchedplates,as”’shown‘“. . ...
,..,.,#ifiFigure3. I& Equatian(2) and Eq&ion (3}’y’thesetrue stress+~raindata ‘“ 7
,.
were expressedin
with the quantity
in Figure4* The
energy. ;
termsof octahedralshearstrqppand.,gp@hedr&lshaarstrain,
3/2 (octahedralshearstress}as a,,dependentvariable,as shown
areaundereach curvein Fi~~ra4 givesdirectlythe unit strain
[2)Establishingthe relationbetweenunit strainenergyand octahedral.....-.,,.,, .,,’.,).:-~.:.,,.,,“.,:,.;’shearstrain: .,..,.,. ,...
By graphicalintegrationof the two curvesin.Figure4, the unit strain
energ was plottedas functions”’ofoctah+ral shearstrain,as shownin Figure5*,,1.,(. ,,Theserelationsholdfor any stressstateaccordingto octahedraltheory. For
..,..-
Iargestrainsat 7G0Fy the unit stratienergieswere obtd,madfrom the eqerbqtal.,
equationof the correspondingcurve~.’
-.
=-7”
(3) Determiningthe Iota.1valuesof octahedralshearstrainon the,, ‘,
surfaceof the notchedplate:
,’ The gridmea.s’u~ementsgiv~ the v.duesof displacements(U and V)
of the grid p~int~ in the x and y directions.The slopeof the experimental,’ ,.’.
curves,U ~ f (x) and ?,~,fl,(y)givascorrespondingconventionalstrains,which$,.,!”,.4,
by Equation,(6),give the prin~ipalstr~in$t By Equation(5),the PrinciPal,.
strainswere conve:ted.intooctahedralshearstrains~.,“., ,’
(4) T~, ~~rfa~euqit straine~ergieswere obtainedby the universal
relations(seeequations2 and 3) betweenunit strainenergyand octakedrd
shearstrainin Figure5 and the octahedralshearstrainsdeterminedin step (3).
?3ecauseOS the secondiassumptionthat the shearstraincomp~ents an
vanish,the valuesof unit energ ( ~e ) in a smallregionin the vicinityof,.
the notchand the crackaresubjetiedto certainerrtm~ For this smallregion>
the values”of unit enefgy( (JO’)shouldbe multipl~edby a factorto give the
correctvalues( ‘“U’”):
where(-i. ; “unitenergy based‘onali
,-U4?= unit energybased”on %
,,x-y-z systemused is the
8 = shearstraincomponents
.,
six straincomponents,.
assumptionthat the
principalsystem ‘“
. .w= strain-hardenfigexponentin:uniaxialtension
As far as the totalstrainenergyis ‘concerned$neithertfiesecondnor the
thirdassmp-tionintrodl~cesany ser~ouserroryas has been cotiirmedbY
nume~icalevaluations.l?
-.
●
✍✘✍
Becauseof the preliminarydata.of the threeplatesinvestigatedare not
suffic~.entto c+o,~rect..the
in th% reportare values
between \),,-jand !..1,,,is,,
,.:RESULTSAND DISCUSSION“ ‘“‘“ ‘“
&tress-Strainand En&i& %dmainRelations of the~~$er$al: “’‘:‘————
are
Was
The-truestrtis$-straincurvesin’unbdal tensionat 70°’FAd 10° F 4’
shownin Figure3. In Figure4 the quantity~~2i:(octahedralshearstress) ““”~.
plottedagainstoctahedralstiainSQ that the areaunde~ eachcurvegives,. ~
directlythe un?.tstraineneigy~ Figure5 showsthe uni~ st&ri ’etieigy’Piotted”i“,.,, ,.,.$::,.1....:;,:i.,. r.,,-.
as functionsof the octah&d&l shearstrain. All r&I&tio&’in’thkie’thee’”””“’ “’‘
figuresehow a slighteffec%’:ofthe temperaturediffere~cd~h.,~T,~.’
-t;:,- .,,.“., -’.!,.1,‘‘Iiv ,;::?;,rf:~’
M+cro-ProPa~ationof PlasticDefmmat~on and StrainEn.e~Distributi.on: ,——,—!—.*
,,~. J’:r: :,..;L ,.,.,+‘,J,, ,,,“
Figures6 to 13 show~y ggqtqursthe unit straiqener~ d~s,tr~bu+i~nson.>,!:..,. ,.. ‘ ., ,, ,
the surfaceof the tlnreespectiensat variousstagesof loadingt Figure15+ShIWS,.,
the distributionof unit energyabsorbedbetweenthe firstvisiblecrackand
fracturefor sp@cimenW-29-3tested,,at10° F. Exceptin ~.gures10a and lobs,.,, ,., ,. ,’representingtineresultsfor the fractl~edspecimenat 70° F> the energy. 1
distributionis appvximatelysymnet+icalwith respectto the axesof symmet~ tif”“’,J.,,.
the specimen;howe~r, the valuesof.unitenergyare averagevaluesof four
quadrants,reportedhere as unit energycontoursin one ql~adrant.Figure14 shows;.., ,,,
the unit strainenergydistributionI:,the diagonaland tr~qsversedirectionsat.,
loadsproducingthe vi~~blecrackfor specime~~VJ-29-4and ~-29-3~ Figures16
arid17 showthe longitu~~aldistributionof,~it strainenergyacrossthe cr+ .,.,’ > ,>,,
afterfractureat 70° F fo~ sp~cimenW-2%14. .,:;<.-“-..,f:“:
>,.!..,4..
—...- .
-9-
Under the geometricconditionsof the specimen~the primarydirectionof
~ nlasticdeformationfollowsP~’onfi@v~:Qn0’ .
the no-tch,as shownin Figures6, 7* $J 93
directionof propagationof deformatj.onis
advam,cingcr~ck,when the crackpropagates
the diagonalextendtiigfromthe eqd of4,
11~ 12 and13. Howeverga secondary
developedin the d.irecti~o: the
adrossthe width qf the specimen~
This is more clearlyrevealedby the orientationsof the unit energycontm~s,, ,; ,
representingthe part of unit ener~ absorbedbetweenthe firstvisiblecraokand.’
the fractureat 10° F as shownin Figure15* Thesecontoursare primarilyariented
in two directions;one followsthe diagonal,and the otherfollowsthe widthof the
specimen. The formeris ,dueto th~ notchconditionand probablyhas alreadybeen
developedat the very earlystageof the.propagationof the crack;the latter .
resultsfrom the motionof the crackt As the crackproceeds,the propagation,of,’
,. plasticdeformationmainlyfollowst@ dirqctiou,,ofpropagati~~of the c~a~; as
a ~es~t, the orientationof the enerb~contoms tendsto becomeparallelto the
caseinvestigateddoesthe plasticz~ne covertheentire regionwithin
lines*
At the loadingproducingthe firstvisiblecrack,the energy
Figure6, for spenimenT?-29-4testedat 70° F,andthe energycontours9,..-,
the gage
contours!
Figure,113..
for specimenY-2%3 te~tedat 10° F may be compareda ThiE comparisonindicates:,,,
thatthe spec-immtestedat 10°,Fhad @rimarilya preferencefor deformationin,,
the diagonaldirection. A graphical,,compaisonof uyit energyvariation,in two .,..!
directionsalonga 45°,diagonalline extendingfrom the ,notch,.towardtheedge> ~d
a transverseline extendingfrom the notchoutmardlis givenin Figure14. At the.,,
next loadingY295$000lbs.3this preferentialdirectionof defo~ation for 5Pec~en
W-29=3as defiiedby Unit ~t~ain energyis largel~’,sliminated~Figure15 is a,.
graphicalrepresentationof the way fn wblchenergydistributionis changedin the
..-. -.
-1o”
specimen:~estedat 10° F duringthe loadibgi’ntervalbetweenvisiblecrack and,.,.. :: .: ,,.~’, 9jr,-,
tlze pqxirpn load- The”gain& ener~ a~orptiah tsprimarilyalongtwo diagor~l
. -,: .j-....~., .,4.
.,.~pecim:g,::29-~mste$tedtintinuoislyto fracture.. ..~,.,
a temperatq~eof 70° F. Fi&~es 10R”and’10bShow+thecomputed,... ~..:,.:.L ,..,“ , ,.
wkELemai@aining
energycontours
at fra~tura.for thfs specimen. It is tobe noted’thatastigleridge of high., ,.....-.,:,,..,~...,.,..energy.:ak@orptionexistsau alongthe’f&&e line.,whilea steepenergy , ,....:,,!+ ,,..,.,., :F~-:., .:.,gradi+t ~~ists,,asthe crackis ap&oa&d’alomg.kll -linesparallelto the,,.... ~,,>,.:,:.-;;,:,.:,,:,i,.-,7,A....<,-,7.,:vertical.de, of the specimen. A plot b$’t~fisener~”mriation is givenin.7....!, .,!,..,.::”‘,,~,.,l,,~..,,,.,,;.,,r,;.F:+qr@s;l$,,,,,and17,
~.,Althoughextrapolationof the energydata gi~n in Figures,. ‘.!!,‘“’,J-,..’,,”.. ,.l>L,,f,. ,;
26 and.17,,is,undoubtedlly& u&ci&Mfic @ocedure, suoh extrapdationtiwsre; ,, ,,“,.~’.,,..,+,1:, ;,made ,qnd.a,valueof unit ener&:””~f’”’about+’30,00Cindbs per cutin.was obtained.. .., .,.. .,., ... . ...”’., .+.. ,. ... ,, -.,.,
at.ithe.,crack..This co~ares very poorlywith vaiuasin the orderof 90~000to..”’:.>-.,1,. ., ,..
;. ..; 1; ,-,.“:”,,!,100,.OOOin;+ per cuqin.whichmay be
,.” .,,,, ,, .,,.,n@y be said?howeverlthat~any of the.. ..,,,. ,,~, .,.crack,did s~ow computedvalue~of the., ,- ,*
expectedat .thel,crackm*. T:n,paSsiggit.,. ,,,.,,,
gii~’~intslwherq.$ntweectedby the,’
orderof 30,000b-lb. per,cu.in. These..-.
resultshencepointout the ~ifficu~tlesof the gridmethodin making,such.,
~qedictianseven if extrapolationis carriedout over sucha shortdistance,. ,.
,.qs,adZstanceof l/I_6*.,. ,.
The energycontoursfor 600 in-lbper cuzin.were salectedto studythe
relationbetmeentotalenerbginputand the extentof plasticzone. The value
.6OOfn-lbsper cu. in. correspondsapproxtitelyto the valueof octahed@ shear, ,,
strainat the end of ‘tyieldingjog~t~see Figure41 in unicd.altension. In ,
Figure18 the area sweptby the 600 in-lbscontourwas plottedas a functionof
- .——
++Calculationsbasedon theoreticalstrainenergyconditionsfor fracturegivea valueof w~OGO in-lbsper cu.in~ The Universityof Californiahas reported
unit energyvaluesin the orderof 250,000in-lbsper OU. in? basedon hardnesssurvep of the frficturezone.5
.— -.
the total
- “u -
energyinput. This:figurereveals‘thefollowing:
(l.)
(2)
(3)
The relatiohbetweenthe‘areasweptIy this contourand the total
ensrgyinputappearsto be linear.
Extrapolationof the s’traightllnes~Figure185 apparentlyshows
that the @O in-lbcontourmay appearat the notchat the value
of total.energyInputof approximately
temperatures.
The mhme of
decreasewith
To .illu.stratethe
been pretiaus~yobtninedmn
metielundergoing.plastic
decreasing+empemturet
macro-propagation‘ofthe3
10,000in-lbs~or Both
..’.
deformationappearsto
crackitself,data thathad
steelS-9Jispresented,in F%gure19* Two partic~-~ar
1,211wide specirnen~of this steel~pecimen,S-9-lJ.testedat 9Z0,Fwith a ductile
failureand specimenS-9-18testedat 5@ F ~~ith a Cleavage failurewere used
in plottingFigure19~ The positionof,theend of the advancingtirackmeasured
fromthe notchhas beenplottedagainst”thesimultaneousenergyinputas measu~ed
by the areaunderthe appropri~,te”laad~~elo~at~-ondiagrem~ The rate of prol%ation
of the crackwith respectto total‘energyinputincreaseswith decreasing
., ,
temperature. !, ,,,.
Theom and Experimental.Factns ‘,,,
.—
In computingthe unit and totalenergyfrom gridmeasurement,the “’
octahedraltheoryhas beenused in conjunctionwith certainassumptions.It i~
not possibleto experimentallycheckthe degreebf “walidityaf eachof the
assumptionsthroughunit’energy. However,a comparism”betweanthe directly
meawired~lues of totalenergyinputand the valuesof totalenergyobtained
by.integratingthe localvalue’s from the gridmeasurementover the whole volume
wouldgive same indic’atdonastotha owrall validityof the assumptions.In so
doimg~the fo~lowingtwo aspectsshouldbe oonsidereds
“12-
(1) The lirqitof integ&~,on for unit ,stgainen$rgy:, ,,.,.,,.,
As shownin Figure20, the valueof unit energyat a valueof
octahedralshearstrain( ~~1), meas~~ after@Oadi~,,, isactuallycomputed
to be al, whereasthe unit ener~ inpbtduringthe test lowdingcyclewas
al / a2g The energycalculatedon the basisof experimetitallydetemined
strainsis thereforelessthan the ‘actual e~e~gy @ut by an amounta2m
Individualcorrectionfor a2 is im~oossiblejhoweverfthe totaldifference,
<:.:..a2for”the”’”ehtireplatecan be dorr~ctedby the relation~ ~. a2 equalsA2~
whereA2 equalsthe indicatedpart of -totalener~ Xnputfrom the load-deforma~
tlontitiin Figure20. A2 is termedthe errorin strdinenergyintegral,and
representsthe energywhichmust be addedto the totalenergycalculatedby the
&rid&a~ysis to enablecheckcomparisons”tolx+madeo . .- R
“’(2) -Strainaglngg., !:,,:.~,,-,
“’~Iti~he”&~lbrato~procedureof thisinvestigation;it:was ~~
nece’ssh~to A-now’’:abotita:’weekfor gnidmeasurementbetween@Oad,3ng ~d .
“~+elhadi~’. This a~pamtlycaused strain.aging.asshownimtFfmreg 21~d Z2
wherethe load-alohgktioncurvesfez-,tha”specimensW-2%4 and W-29-3a~pr:-
comparedwith the load-elongationcurms for similarspecimeusof ‘lW:lsteel
testedcontinuously.The load-deformationc~mvesin these.~wo.fi~es show. :.. . ,}, . .,,.,. -,.:
the two~~mponantsof the effeet.of,,straih-agingz,i: !,.Ji,: : ~
. (a) Increasein strehgths:.+or,a:.gi,vpneloqgatto~,,t,heload i$
,’ Jxigherin the:Strain-a@d.,con~t~,onfithemfore,,:th~enerm ,
,~’ ,: Is”higherbyim amountyeamred by the area boundedbytwo
!.‘,.* .:‘load-deformation’oum@stith and withoutstrainaging. But
.~...:,., ‘..“‘ $he unit strainenergieswere’com~ted-from:thes,tresq-stnin
‘:law in tkie’ab~erice’bf”ktrainagingas ShO~ in Eigure 3,
,- ,, .,
-13-
(b) Decreasein ductility;As shownkathese f@m=$,
specimenre~ehedthe mexi.mumloadat an elongation
the strain-aged
smallerthan
+.M elongationat the maximumloadwithoutstrain-aging-Bec~~e
of thesetwo effects,the total=n~r~ computedfrom gridmeasure-
ment understrain-agedcordittanscan mi13~be comparedto the total
energyat the same elongationobtainedfrom the load-elongation
curvesin the absenceof strain-agingas for specimensw-32+7 and
~ (SeeFi~esW-32-n reportedh a pretiousProgressReport.
21 and 22). Theselaterspecimenswere run priortO the gridstudy
and were deemedsatisfactoryfor purposesof comparj.son.The reason
for takingequalelo~gatio~ for comparisonis thatfor the same
amountof eloagationzthe totelamountof strainproducedwithin
the gagelinesshouldbe the same>no matterwhetherthe specimen
I Is strain-agedor riot.
In case of tine~pecimen
fracture,’thestrain-agingeffectdoes
w29p14 testedcOntlnmuslyto complete
not
by grid measurementshouldbe, and in fact
measuredvalues.
Table 11 listsa summaryof
appear;thus the valueof totalenergy
is, WIT closeto the directly
energywmnputationsfor the three
recallthat two of the gridspecimensW-29-?and %29-4 were
agingdur~ngthe processof the investigation.It must also
summaryit is well to
subjectedto strain-
be recalledthat the
errorA2 in the strainener~ integralmust be takenintoaccountwhen makfig
comparisonsbetweencomputedenergie~W the grid analysisand measuredenergy,.
input* These ccmbinedeffectsmake it impossibleto directlycomparethe,.
totalenergyinputfor the specimenswhichwere strai~-agedwith the strain
ener@ correctedfor the errm AZ. As a consequencess~ectienW-32*1Ihas been
. . .,. ,.,.
,. ,. TABLE11 “’. ..—— ., ‘1
,. !.=
,. S~aW of Enerw Commutations,,..,...,” .,
‘J!ot~EnergyInput@ Load-ElongationCurve - in-lbs-
:,, .
TotalGrid EnergyB&ed onOctdwiral Theory- in-lbs~.—
., ‘“DuctileFracture
GO1* 1 Col.2 ““; cd. 3 Cd. 4With Strain-aging Withoutstrain-ag~ngBeforecorrectionfor error
.ippli.edLoadqlbs }~snecg W-29-Lntvo~) Spec.W-32-7at gl ) in strainenergy irrte~al,,..;
277,000 ‘“ 23;56& 23,700* 21,356(visible,mqck)-: ,’ (no stra@-aging)
.:.Zyj$ooo “ : ; 2@Q 24,A8CI* : ::+ 239%4 -32pjOQo” ‘, 52*5&l 5~,.3@ “ AL,792352,700(Kk&load), 78>500 73,340? :, .
70,48$.. ,...,. e Fracture ‘ ‘“ ,“...,,,,
fi~ec.W-2$-9at 10°~ (S~ec.W-32-11at-21°~,, ,.
277,740 . “ 1+,920* “14,888(tisible-crack) ., (n: s~a~waging) ‘-
295,000 “, 21@o* ‘ “’ 19,234325t~ (~%load),’ 35;320 34,460* 31,251
,...,. ,. (Spec.W-29-14tested
.:. continuouslyat 70°)..,. - 265,000* 256,785
CO1* 5 “,
Correctedfor errorin strainener~
integral.,
23, 966**
2~j031#w36,3.51?
260,085M
(*, *)’+ ~igu& with,(*)~&e ~omp~rablewith’co~espondingfigureswith (*)*.. i
used for comparingthe resu~tsof W-2%3J and,.
comparingthe resultsof ~r-29-& Accordingly.l’
specimenW-32+ has been used for
the valuesof energyshownin
cohmn :.andcolumn5 of Table11 are corqxwmble.Note thatno
specimenwas neededto comparethe resultsof specime~sW-29-U
agifigwas not present, In additiq the energyshownin’’colw..
additional
sincestraw
2 for the vis~ble
crackloadingsis also comparablewith columr” 5 sinceduringthe firstloading,-
of the specimensto the visiblecrackload no strain--e.gimgeffectsappear; The,,:.
degre~of correlationbetweenthe valuesin column3 and’c&inn 5 of TableII
is clearly,shownin Figure24~ wherethe directlymeasured’’valuesor total,,
energyinputagreecloselywith the valuesof totalenergyby gridmeasurements,,
when properlycorrectedfor strain-agingand the errorin the strainenergy
integral- This agreement indicatesthat the amumptions are substantially
correct. Near,thenotqhexceptionswouldneed to be made,as no elementary,’. ‘~
considerationswouldprobablyhold in thisregimt,. ,.,., ‘ ,,.
M~~elat$Q~wi~~&e4ti-%m0k2M“”W@&JfiNi&Qnd C9ns4xmtTh@mess:—.—-— ..
For the followingEsted,reasons$.,it s-m pyf.b~~ that the e~e%Yfi’., -, , ,.,,. ,.
absorptionof individualspecimensof variouswidthbut of the same thickness,/, ... /,.....,- ,.
can,be.predictedby usingthe ener~ distributionfound in the”12°wide
specinens:,, ,-.
(1) The uzcitenargyat the crackis the sameregardlessof width of,.
specimenafterfailureby ductilebehaviour.,,
(~)At the end of tineadvancing&@sP the mtcb acuity(azkltherefore:.,, ..+the stressstate)is essentiallytinesameregardlessof the ““
,.~
.’. ... . ‘-, ,,,,. ,, ‘,widthof the specimen.
!. ,’ ...It followsfromthe firstreamn that at giventemperatureand a given. .. ,,,,
stegeof atralning,the energy
widthhave an equalmaxim-mat
,.,.surfaces,u R f (xjy)for spectiensof mm~g
the crack;and it followsfrom the secondreason
-16-
that the energysurfacesfor specimensof vazyingwidth fall off from,~n equal
maximumvalueat approximatelyequalslopes. This leadsto the deduc?fiionthat
eachhalf of a narrowspecimenmightbehaveas if it wefe a part of a wide,;
specimen~if the notch-endsof both speuimenswere made coincident.
The first step in examiningthi$”deductio’hwas
as follows:
Upon the
has been
surfaceof the 12’fwide fullyductile
drawnthe outlinesof one quadrantof
notchedplates,eachof differentaspectratio-
to constmct FigurB25,.
.,.,
specimenlI&9-4Jthere,.
3/41’thick~ternally
Aspect nrtio, .
designatedby IIARI!,is equalto widthdivided~ thickness.~@
ends of the notcheswere
shownin Figure25* “’:Tti&’
to one ha~~ the’ti’dthof
all made coincidentwith eachotheras
“quadrantreferredto has d.im@ions equal ,,,
the plate~”’anda lengthequalto one,hslf,T ...’’.”.}
the gage lengthwherethe gagelengthis threefourthsthe width
of a givenspecimenq.“ ,.,,,:,
The next’’~%epin comparingthe.platesas showr,iqF@re Z5 was to.,..
computeavetiageunit strminenergiesat maximumload-terme,d,,(ui).mAverage.~t ,,
strainener& (u’]w& obtatiedby firstcalculattigthe ~q~l.stmin energy
withinthe boundariesof one quadrantof a platefor a given (AR)and dividing..,,.: :;,
this totalenergy&-the voltieof ~etal’in’onequadrantof the,plate~vThe
totalstrainenergywas d&e&&ned by’utilizingthe:mit.s.t~jqfi.ene~gydistri-
butionas givenin Fig&e’9 for the
load. Thiswas separatelydonefor
the 12’twide specixento anAR of 1
derivedvaluesof the &it ‘enekgies.... ..J.
ftily-ductilespeci’mefiV?-2,9-4”,~,tmaximum
variktisvalues bf AR _ng from 16 for
for the narrowestplateconsiderede The
(~’)~~ plottedin Figure2.6,
,,... ,,, .,,.,.,
.— .-
-17-Iitdependentlyof the foregoingprocedure,the averageuntt energies(u)
at meximumload of individual3/411thickductilespecimensof 3~61and 121’widths
of WTt steel(previouslytested,but not reported
Theseunitenerg:es(u) are plottedin Figure26.
maximumloadfor greaterwidth,data givenin the
in deta~lhere)were ddmmlined~
To obtainvalussof (u) at
final report~of’the University
of Illinoisfor W’ steel,fullykilled,and chemicallysimilarto W’ steel?
have alsobeen plotted. Universityof Illinoisspecimens,19B-3of 24H width
(AW32) S@ 17A-7 of 72’) width (AR+6) were the only two complyingwith the,,
requirementneededhereYnamely~fullyductileaction. The dottedextension&
the (u) curveshouldonlybe consi~ereilas tentativeand indicativethat grid...>.
analysisfor l_2t1wide specimensmightpossiblybe of use in predicting{a{al ‘
energyor
neededto
.,
unit enerkgyfor widerplates- Furthe~testsat
confirmthis statement
Figure26 showstwo curves,one marked(U1)and
The differencein unit energybetweenthesetwo curves‘“
effectof strain-aging(seepaga 12). The (uf)values
specimenW-29-4whichhad ur.dergonestrain-agingwhile
largeraspectratio are
the ithermarked(u).
may be attributedto second
were obtainedfrom the 12”
the (u) valueswere
obtainedfrom specimenscontinuouslytested; For a 12~’wide specimen(AR=16),4. ..
contl.nuouslytested,datawas availableto comparetotalenergiesat equal
elongeticmover the gagelengthof 91~~The valueof (u)for AR 16 was raducedto
a valuecomparableto (uf)by usingthe areaunderthe load-elongationcurveat
the elongation reachedby specimenW-29-4at maximumload. This redticedvaluei$
-plottedas a hollowsquareand agreeswith the valueof (u’;}obtainedfor W-29-.4
in the presenceof strain-&ging.,.,
for gridmeasurementbe loadedto
curvewouldtend to coincidewith.-,
This indicatesthat, shouldthe specimenused
maximumload withoutstrain-aging,the [ut)
the (u) curve.
The same procedurewas also extendedto the fuilyductilespecimen
W-29-14whichwas testedcontinuouslyto fracture. The strainenergydistribution
afterfracture,ehownin Figure10a, thenfompsthe basisfor computingaverage
— —. .
-“ 18-
unit energywithinthe gagelengthvolume● The outlinesof platesof va~ing,..
Theunit energyvaluesderivedfromFigure10a are plottedin Figure27, giving,,
the uppercurve. For comparisonwith the uppercurve,two pointshave been plotted..
representingactualtestresultsfor aspectratiosof 4 and 8, in additionto the
experimentallydeterminedvalueat AR 16* The derivedcurveand the test-results.-”\
agreeclo~ely, The lowercurveof Figure27 is ths (U1)curveofF&u~e 26
representingunit energyto maximumload. It appearsthatthe upperand lawer
curvsstend to intersectat low aspectratios. This is perhapsexplainedby the
fact that?once the crackgoesthrougha part of the spectien,thatpart Is
subjectedto veryltttleadditionalplasticdpfomation as the crackadvances,,, ,.
further.,.)
The correlationsnotedin Figures26 and 27 stronglysuggestthat the..,. ,;,, ., . .,, ‘..,.,,,, .,strainenergydistributionof a singlespecimenof properwidthand thicknesscan.. .?7,,,., .,,,.-, -“.’” .. ”,’ :....’,,
be used to predictthe ener~ absorptionof individualplatesof varyingwidth,“, .“. ,!. ,., ,’---
and thickness,. ,, ,.“.,. ., ..~oNGIEsIoNS‘. ‘,
Analysisof the experimentaldata of thesespecimensat this. ,...
exploratorystageshowprimarily:
.: (1)
(?)).
(3)
.. , ., ,.
thatthe use of octahedraltheoryis confirmedin te~ of strain‘,” .,.4:......,.= ,,..
energyby the resultsof this investigation.,..-.‘. ,. ... .,, ,.
that the strainenergydistributionof a,singlespecimenof propr.,. .,,‘.
widthappearsuseful
specimensof va~ing
that,as temperature
in predictingthe totale~ergyof individual
width and constantthickness.,. .- .’deoreases~the rate of propagationof deformation
withrespectto totalstrainenergyinputdecrea~es,and
propagationof crackw~th re,spect@ totalstrai~energy
,,. -4, .,
the rate of
inputincreases
—— —
C919.
(=4.) that~ for ductileaction,the unit strainenergyat the crack is
foundto be approxtiatelyin the orderof 30,000in-ibsper cu. in.;
hcwever,this valuemay be questionablein tiem of extrapolation
methodsused-
SVGGESTEDFUTIJREWORK.-!——
The experimentalresultsdescribedsuggestfuturework in the follofig,.
directional
(1)
(2)
(3)
(4)
Changingthe expertmeatal~rocedureto eliminatestrain-agingand to
obtainmore completedata, To this end> a methodof photographingthe
gridsat intermediateloadsis preferable,so as to permitGontinuom
loadingto fracture.
Investigatingtinestraine,nergydistributionin the entirerangefrom
yieldingto fracture,fox’both shearand cleavagefailures,to reveal
the macro-mechanismof the wholeprocess.
investigatingspecimen~of differentsize at d?~fiferenttemperatures~,..
The materialfor investigationshould
will be availableto comparewith the
Experimentaland theoreticalanalysis
be chosenso thatpretiausdata
resultsof gridanalyses.
for
&iiNOIULEDGEW.NTS
The detailwark of this investigationwas
ResearchAssociate3in collaborationwith and uader
ProfessorSamuslT. Carpenter,Chairm+ Department
thE wnallregion aroiind.,
of CivilEngineering-The
helpfuladviceof V?.P* Roop (Captain,USN,Retired)5s also acknowledged.
Mrm EmaldKastencontributedgreatlytO
measuring the gridsand the testswere made under
Zen. Drawingswere made by ErwinNewmanand Roy
the instrumentationfor
the supervisionof Mr. A- W.
Bosshardt-
.
-20-
BIBLIOGRAYHY
.,. .,
(1) S. T, Carpenter,W. P. Roop7 et al$ SwarthmoreCollege,Swartbmore3...
Pa. rlProgressReport an””Twelve~Itioh’FlatPlateTestsn,Ship Structure
CommitteeReport,Serj.alNo. SSC-213April 15, 1949. “.,
(2) A. Nadai,‘lEnergyof D~stortionabsorbedby PlasticDeformation”of
Thi~ Steel Platesn. ResearchReportSR-182,WestinghouseResearch,..,
Laboratories,April1943.,,.’
(3) St T. Carpenter,W. P. Roop,E. Kastenand A. Zen, Swarthore College,,,.
Stmrthmore,Pa., ‘iProgressReportsPart I TwelveInchFlat PlateTestsz.,.. .
Part 11 AspectRatioProgram~l,Ship”StructureCommitteeReport
SerialNo. SSC-35,December15, 1949. ‘“.,,
[4) W, M. Wilson$R. A. ll~chtmanand W* H* B~&er, Universityo~ Illinois,
‘~FinalReporton CleavageFractureof ShipP1’atks“asInfluence-dby Size.,...
Effectft$Ship StructureCommitteeReport,SerialNom SSCrn~O$June 12~,“:,
194.7.,.
,.
(5) H. E. Da&, G. E. Troxeli,A. BoodbergfiE.’”R~ParkerandMti P* OfBrtin,
university of California ProgressReportOn’FCausesof CleavageFracture“..,.
,,:in Ship Plate: Flat PlateTestkfi,’ShipStructureComnrltteeReport,
,.SerialNo. SSC-2,August235 ~946p
,: >.,,
,..’
..,,.. ,.:,”
,.,,:. . ‘,,
..,. , ,.~
—. . ———. .— —
-21-
1I
TI
Id
1
/> 10>
I
i
I
,,21
z
-22-
FIG. 2 TEST SP:#M51& FOR UNI-AXIAL
-.
— —
W-
m“WIIda1-U-)
Ld3a●
-2?. -
90,000
80,000
; 70,000n
2- 60,000
50,000
4oGa
r30,000
>z 20,CQ02z4~ 10,000
00 0.05 0.10 0.15 0.20 T
MAXIMUM NATURAL sTRAIN, &
FIG. 3 TRUE STRESS-STRAIN CURVES IN UN I-AXIAL TENSION
m 50,0d.IdzWI
140,00
A= UNIT STRAIN ENERGY AT 70 F. CORRESPONDINGTO ~, , IN INCH- LBS. PER CUBIC INCH
Im.
,0 0 Q05 0.10 0.15 0.20
oCTAHEDRAL SHEAR STRAIN. 8
FIG. 4 UNIVERSAL STRESS-STRAIN3/49w-sTEEL SHIP
FUNCTIOM FORPLATE
.—
-2L -
/
./”10” F --
,/
./”,*’\,..E
/
/
/“/
/,
1
ok-’o 0.05 0.10
OCTAHEDRAL SHEA; 15 STRAIN, ~0.20 0,25
F.IG. 5 UNIT STRAIN ENERGY OFFUNCTIONS 3/4” SHIP PLATE AS
O& OCTAHEDRAL SHEAR STRAIN AS DETERMINEDUNI - AXIAL TEST AT 70”E AND 10-E
o _J~
tI 2
I
3 4 5
. ..-— -..
‘EF”R””%WBOUNDARY OF MEASURABLE
//
.“ ~
! 4
‘END OF NOTCH
FIG. 6 UNIT STRAIN ENERGY DISTRIBUTION ON THESURFACE OF A 12” X 34”
dNOTCHED SPECIMEN, W-29-4,
LOADED TO 277,000 L S. (VISIBLE CRACK) AT 70” F.
,.,,
DIRECTION OF ROLLING ~_ ~
I
GI
-26-
rd.
—
I
—
..
.-
-—. _ _ —.— . ..____
--
.-
o
I
2
Yo
6 5 4 3 2 I Tx
+00,000
Isacl@o boo
&\cq~
2.00
?“QQ 0
+00
\
DuADRANT 2
‘\ \\’\
3
1
4
3
2
-YI 2 3 4 5 6
0
I
2
3
4
I \\ \ \ ! ,—
4
0 13 2 i 0 I .2 4 5 6
6 5 43
FRALTURE
I
2I
3
2
I
0
~“NoTcH~D spEc IMEN, w-29 -14, TESTEDFIG. IOA UNiT STRAIN ENERGY DISTRIBUTION ON THE SURFACE OF A 12”X4
TO FRACTURE AT 70” F. (X, Y IN INCHES).
CRACK
--- ---- ---- --,----- .-J ---- -------- —--- ___ __
---- ----
------
6 3 ~F
~2 4 5 ~ ~
4~
2 4 4 ~ ~4
J2 4 3 3 ~
Ti
z z 2 3 J-Y— z 2
,:
FIG. IOB UNIT STRAIN ENERGY DISTRIBUTION NEAR THE CRACK ON THE SURFACE OF A f2’’x3/4” NoTc HED
SPECIMEN, W-29 -14, TESTED TO FRACTURE AT 70aF, (X,Y, IN INCHES) — QUADRANT 2AND3.
., , , i!
-2y -
0 —Y--+ I 2. 3 4 5 6
~“ -.
wziJoa
ILozoF
ii!,
.0>
/#
BOUNDARY OF MEASURABLE DEFORMATION1,’”
/’
0 _Y_+ I 2 3 4 5 f
J.
.’0 ,z .-> ,’A .0 /E
.BOUNDARY OF MEASURABLE
~ I --
0 \
DEFORMATION ,“
,’.
z ,0 ,
1=/
g/
/
a? /
~z -. /
.’/
.—
. .
-30-
— y- I z 3 4
I
1’/,,
BOUNDARY OF MEASURABLE .“
/
DEFORMATION ~,.’,
,’.
.’,
,
5
/’
FIG.13 UNIT - STRAjN-” ENERGY DISTRIBUTION ON THESURFACE OF A 12” X 3~” NOTCHED SPECIMEN,I ~~}29 -3,
LOADED TO 325,000 LBS. ( FRACTURE) AT
.,.
■
o——
D—
■ \ U.= F(DII AT 10” F
\
P\ U.: F(DI) AT 70” F
UO=F(D1 AT IOF. L
~= F<E71 AT 70’F — ●.m
%.,
1 7 2 A .0D15TANCE TROM THi NOTCH IN ~hICHES “
FIG. 14 UNIT STRAIN ENERGY DISTRIBUTION IN THEDIAGONAL (D ) AND TRANSVERSE CD) DIRECTION OF12” X3/4° NO+CHED SPECIMENS LoADED TO VISIBLECRACK AT 70” E AND 10-F
- .,
.— .-
* 4 5 0o— ~-41 3
I i
._
—
FIG, 16
12,’1
L+J-—
3!4
. Y=2
. Y=3
. y=4
. y=s
. Y=6
@ FRACTURE
4 3 2 I 0 I 2 3 4
uPPEti PARTP —LOWER PART
LONGITUDINAL DISTANCE FROMFnACTURE~ INCHES
LONGITUDINAL DISTRIBUTION OF UNIT STRAIN ENERGY ON THE SURFACE
OF A 12’’x3A4” NoTCHED SPECIMEN, W-29 -14, TESTED TO
FRACTURE AT 70” F. QUADRANTS 2 AND 3.
-32-
I
QUADRANTS
D
2
+—,
3’4
P
-Y.3
_Y,5
–Y.4-Y.2
*.
!
.O
,b.
y.ze Y=3A y,4A y=5
@ FRAC iUR E
LONGITUDINAL DIsTANc Es FROM THE CMCK — INCHES
FIG !7 LONGITUDINAL DISTRIBUTION OF UNIT STRAIN ENERGY ON THE SURFACE OF A
12”X 3/4 NOTCHED SPECIMEN, W-29 -14, TESTED TO FRACTURE AT 70” E
QUADRANTS I AND 4
MAXIMUM LOAD
7
,@,- ~v[$lBLE~RA~K
oIo,om Zo,m aaoca 404m3 m,ca oo,m rn~m BO
MEASURED ENERGY INPUT WITHIN THE GAGE LINE IN IN, - L
..
~lG, l& MACRO - PROPAGATION OF PLASTICDEFORMATION WITHIN 12M X ~4m NOTCHEDSPECIMENS UNDER LONGITUDINAL TENSIONAT 70-K AND 10* F,
LV:&l:&L&
o0
z04
EDGE OF SPECIMEN . a
/
/
-57% (NO. 18 - O~o SHEAR)
/ CRACK
/’
./
g/@ END OF NOTCH/9
\
.0’sw@-Ioomlo~
30GOO0—
TOTAL ENERGY INPUT IN IN. - L8S.
/;
$/j\///\l/#k
FIG. 19 MACRO - PROPAGATION OF CRACK ACROSS 12” X 3/4m NOTCHED p “
SPECIMENS OF STEELS s-9 -NO.J~, H: L:2’E AND S-Q ‘No. la AT @R~CORRESPONDING TO DUCTILE AND FRACTURES
ToTAL UNIT EMERGY INPUT = al + 42
UNIT ENERGY COMPUTED ❑ U{ ~1) . a,
02 Is UNKW3WN
II
VALUE OF v, AS-MEASURED ON GRID
AFTER UMLOADIHG
-i-—
TOTAL ENERGY INPUT ❑ A, + A2
1
AZ
Al/ /
1--- h~l~
( I ) Z~t FOR THE ENTfRE PLATE LI.E., THE TOTAL GRIDCOMPUTED ) DOES NOT CORRESPOND TO THE ENERGY ASINPuT, AI+A3 TOTAL ENERGY
G?) coRREcT’lo~~ ZC?> (FOR WHOLE PLATE) =A.FIG.20 ERROR IN SiRAIN ENERGY tNTiGRAL AND ITS
CORRECTION
350,04
300,0(
g 200,00z2g
z
n
;J
100,00
4
?-8
\
LEGEND : &
~ VV-32-7, CONTINUOUSLY TESTED AT 8?F.
~ W-29-4, TEsTED IN 4 STEPS AT 70*E , WITHA TIME INTERVAL BETWEEt.J EACH STEP OFAT LEAsT A WEEK
0.2 0.4ELONGATION lN””?NCHES
o.b /.0
FIG.21 EFFECT OF STRAIN AGING ONLOAD - DEFORMATION CURVE
!,,
., ;,,
-35-
—
Id>lx3u
IL
I Inz
za1-m 200000
a-WzL-
100000 -
LEGEND’~ 70” F,a IO” F.
FRACTURE AT
70” F.
/
/
/’~—FRACTURE ATIO”F,
no*5
o I Omoo 2WOO0ACTUAL TOTAL ENERGY INPUT BY LOAO- DEFORMATION
CURVE IN IN.-LBs
FIG.24 COMPARISON OF TOTAL STRAIN ENERGY BASED ON SURFACE STRAIFJS
AND OCTAHEDRAL THEORY AGAINSTACTUAL TOTAL ENERGY INPUT
GAGE LltESCJF
S43EC!MENS
o L 12”x
J
I*G
Ilx Afl 13./,
m OA
Ii’ ‘, AR !0.7
Gw% Y
o—IL
I
0 1x
u)w mz z
u
—-
FIG.25 QUARTER VIEW) SHOWING OUTLINES OF
SPECIMEN WITH TWO-DIMENSIONAL SIMILARITY
SUPERIMPOSED ON THE SuRFAcE oF A 12”
SPECIMEN, WITH ALL NOTCH ENDS COINCIDING
WITH EACH OTHER.
/
I
um1
—
SWARTHMORE COLLEGEA->cl-cn
,i
-m~- CQUEGEI-13-SO
-37-
8 aoc
7000
6000
o
-1
\
./”UlllDIFFERENCE ATTRIBUTED
TO STRAIN AGING
LEGEND:
● . INDICATES VALUES DERIvED FROM
SPECIMEN W-2 R-4.
o TEST VALUES FOR W-STEEL
WITHOUT STRAIN AGING.
n VALUE AT AR 16,0BTAINE0 BY CORRECTING
A CONTINUOUSLY TESTED SPECIMEN FOR
STRAIN AGING,
A DATA FOR “D” STEEL, UNIV, OF ILLINOIS
FINAL REPORT Ssc-lo
L\ -----—--—..—-——______———____A -A
I I I 1 I I 1 i I I I I I I I 1
) 46810121620 30 40 5032
60 70 80 90 98
ASPECT RATIO
FIG. 26 CORRELATION BETWEEN THE UNIT STRAIN ENERGY DISTRIBUTION
IN A 12; 3/4” NOTCHED SPECIMEN AND THE AVERAGE UNIT ENERGY
OF 3/4” THlCK NOTCHED SPECIMENS, VARYING IN WIDTH .
.“—. .—_...._._. —
40
DERIvED FROM A
SINGLE SPECIMEN
FROM INDIVIDUAL
SpECIMENS OF DIFFERENTASPECT RATIO.
\ ‘-
\
\ AFTER FRACTURE,<,
—n ---— --
L
‘-T MAX. LOAD
‘~..A—4 —---- _.
0:2 4 6 8 10 12 14 16 16 2
ASPECT RATIO
FIG. 27 CORRELATION (UPPER CURVE) BETWEEN THE UNIT STRAIN
ENERGY DISTRIBUTION IN A FR,4CTURED 12’’X3/4’ NOTCHED
SPECIMEN AND THE AVERAGE UNIT ENERGY OF FRACTURED
3/4” NOTCHED SPECIMEN VARYING IN WIDTH,
