A universal fracture criterion for high-strength materials.

0.55 MB·English

by  Qu, Rui Tao

A universal fracture criterion for
high-strength materials
SUBJECTAREAS:
RuiTaoQu&ZheFengZhang
GLASSES
METALSANDALLOYS
ShenyangNationalLaboratoryforMaterialsScience,InstituteofMetalResearch,ChineseAcademyofSciences,72WenhuaRoad,
APPLIEDPHYSICS
Shenyang,110016,P.R.China.
MECHANICALPROPERTIES
Recentlydevelopedadvancedhigh-strengthmaterialslikemetallicglasses,nanocrystallinemetallic
Received materials,andadvancedceramicsusuallyfractureinacatastrophicbrittlemanner,whichmakesitquite
15November2012 essentialtofindareasonablefracturecriteriontopredicttheirbrittlefailurebehaviors.Basedontheanalysis
ofsubstantialexperimentalobservationsoffracturebehaviorsofmetallicglassesandotherhigh-strength
Accepted materials,herewedevelopedanewfracturecriterionandprovediteffectiveinpredictingthecriticalfracture
19December2012 conditionsundercomplexstressstates.Thenewcriterionisnotonlyaunifiedonewhichunifiesthethree
classicalfailurecriteria,i.e.,themaximumnormalstresscriterion,theTrescacriterionandthe
Published Mohr-Coulombcriterion,butalsoauniversalcriterionwhichhastheabilitytodescribethefracture
23January2013 mechanismsofavarietyofdifferenthigh-strengthmaterialsundervariousexternalloadingconditions.
Correspondenceand Inthe17thcentury,GalileoGalileiproposedthatthefractureofmaterialsoftenhappensattheconditionoflocal
normal stress equals to a critical value1,2. Now we know that this critical stress condition describes the
requestsformaterials
maximumnormalstresscriterion,afamousfracturecriterionforpredictingthebrittlefractureofmaterials3.
shouldbeaddressedto
Sincethen,theeffortstoseekforareasonableanduniversalfracturecriterionhaveneverbeenstoppedbecause
Z.F.Z.(zhfzhang@imr.
brittlefracturesofengineeringcomponentsareusuallydisasterscausinggreatlosstohumanlifeandproperty1–3.
ac.cn)
Drivingbytheurgentrequirementofmodernindustryforhigh-strengthmaterials,manyadvancedmaterialslike
metallicglasses(MGs),nanocrystalline(NC)metallicmaterialsandadvancedceramics,etc.havebeensuccess-
fullydevelopedandextensivelyinvestigatedinthepastthreedecades4–7.However,onecommonshortageofthese
new materials is their brittle fracture behavior or low tensile ductility, which limits their structural applica-
tions5,6,8,9.Thefracturecriteriaforthesehigh-strengthbutbrittlematerialsthusbecomequiteessential.Dueto
theamorphousstructure,MGsexhibitnotonlyhighstrengthbutalsosuperiorformabilityinthesupercooled
liquidregion,showingpromisingpotentialforengineeringstructuralapplication8,10.Thehighstrength,nearly
zerotensileductility,andhomogeneousisotropicstructurealsoendowMGsnaturalmodelmaterialstorevealthe
fracturecriterionforthosehigh-strengthmaterials.
ThefractureofMGmaterialsusuallyhappensinashearmodealongaverynarrowshearbandinwhichsevere
plasticdeformationlocalizes11,12.Besidestheshearstresswhichisthedrivingforceofshearplasticdeformation,
thenormalstressontheshearbandplanealsoinfluencesthefracturebehaviors11–16.Thisnormalstresseffectcan
befoundmainlyinthreeexperimentalfacts11,12,14,17:(1)thefracturestrengthunderuniaxialcompressionsF is
C
moreorlesshigherthanthatundertensionsF,showingatension-compression(T-C)strengthasymmetry;(2)
T
thetensileshearbandanglesh areoftenmuchlargerthan45u,whichistheangleofthemaximumresolvedshear
T
stressplane;whilethecompressiveshearbandangleshCareslightlysmallerthan45u;(3)thefracturemorphol-
ogiesarealsostronglyinfluencedbythenormalstress.Therefore,thefracturecriterionofMGsshouldbecapable
ofdescribingthisnormalstresseffect.Forexample,theMohr-Coulomb(M-C)criterion14,15,whichassumesa
linearnormalstressdependentshearfracturecondition,hasbeenusedtoexplaintheshearfracturebehaviorsof
MGs.However,thereareseveralinevitablecontradictionsbetweenthepredictionsbytheM-Ccriterionandthe
experimental results, as elaborated in detail in supplementary materials online (Fig. S1, Table S1). Another
fracture criterion, the Ellipse criterion18, has been also proposed to interpret the tensile fracture behaviors of
MGmaterials19–21.TheEllipsecriterioncanbeexpressedas,
t2 s2
z ~1, ð1Þ
t2 s2
0 0
wheret isthecriticalshearfailurestress,ands isthecriticalnormalfracturestress,andtheratioa~t =s is
0 0 0 0
definedastheintrinsicfracturemodefactor18,20.
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In order to quantitatively examine the validation of the Ellipse a~t =s 18,20, but also influenced by the extrinsic conditions like
0 0
criterion,werecentlydesignedsometensiletestsontheMGspeci- temperature, strain rate, etc3,11. Hence, in order to describe such
mens with a series of inclined notches20. A wide range of normal fracturebehaviorsdependentonbothintrinsicparametersofmate-
stresses acting on the fracture plane was successfully obtained, as rialsandextrinsicconditions,hereweproposeamoregeneralfrac-
shown in Fig. 1. The results show that the critical fracture locus turecriterionwhichcanbewrittenasbelow,
predictedbytheEllipse criteriongives aprecise description ofthe t2za2bs2~t2: ð2Þ
critical stress states of tensile fracture of the studied MG. 0
Furthermore, we found that the Ellipse criterion is capable to a~t =s istheintrinsicparameter,whilebisanextrinsicparameter
0 0
describe all the different contributions of normal stress effect on describing the effect of external conditions. At room temperature
the tensile fracture behavior of a large number of compositionally and quasi-static strain rate, b should be different between tensile
differentMGs20.ThissuggeststhattheEllipsecriterionmaybesuit- and compressivestress states because ofthefollowingreasons. (1)
ableasaunifiedtensilefracturecriterionforallMGs. The directions of normal stresses on the shear fracture plane for
However,theEllipsecriteriononlyconcernsthecasesoftensile tension and compression are always opposite; (2) the compressive
stressstates,i.e.,s1zs3w0,wheres1ands3arethemaximumand normalstressonthefracturebehaviorsalwaysplaysaweakerrolein
minimumprincipalstresses,respectively.Toexplainallthefracture thefailurebehaviorsofmaterialsthanthetensilenormalstress;one
behaviorsofMGsundervariousstressconditions,itisnecessaryto of direct evidences can be found in the experimental fact of the
findmoregeneralfracturecriterion.Accordingtotheexperimental smallerdeviationfrom45uofthecompressiveshearfractureangle
facts of most MGs as described above, a more general fracture thanthetensileone14;(3)thetensilenormalstresshasmuchmore
criterion should have the ability to predict: (I) the T-C strength pronounced effect onthe evolution offree volume orshear trans-
asymmetry, i.e., sF(cid:2)sF§1; (II) the shear fracture angles: formation zone (STZ) and structural defects of MG than the
C T
0ƒhCƒ450ƒhTƒ900; and (III) the critical fracture under pure compressive stress13,15,22,23. Therefore, for tensile stress states
shear occurring along the plane with the maximum shear stress, (s zs §0), we suggest that b~b ~1 so that the new criterion
dt 1 3 T
i.e., dsjs~0~0.IfusingtheTrescacriteriontopredictthecompress- hFoasrthceosmampreefsosirvmewsitthretshseosrtaigtiensal(Esllizpsescvrite0r)i,onbo~febquvati0ona(n1)d.
ivefracturebehaviorswhileusingtheEllipsecriteriontodescribethe jb jvb ~1, which means the comp1ressiv3e normal strCess plays a
tensilesituations21,theconditions(I)and(III)aresatisfiedbutthe C T
less important role than the tensile one in influencing the critical
predictedcompressiveshearfractureangleh willbealwaysequalto
C shear fracture stress. By applying the new criterion to predict the
45u. If the fracture behaviors under compressive stress states are
fracture properties under uniaxial tension like tensile fracture
describedbytheM-Ccriterion19,thenthepureshearfracturecannot
strengthsF andtensilefractureangleh ,theintrinsicfactoraand
bewellpredictedalthoughtheconditions(I)and(II)canbefulfilled. T T
thecriticalshearfracturestrengtht canbederivedasbelow:
Therefore,thisgivesrisetoasignificantscientificquestion:whether 0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
themoregeneralfracturecriterionexistsornotanditcansoundly 1
a~ ð1{cot2h Þ, ð3Þ
describeallthefracturebehaviors(I)–(III)above? 2 T
Results t ~ psFT : ð4Þ
SincetheEllipsecriterionwasexperimentallyfoundtobethereas- 0 2 ffi1ffiffi{ffiffiffiffiffiaffiffi2ffiffi
onable expression of the normal stress dependent tensile fracture
behaviors,thefracturecriteriontodescribethefracturebehaviorof By applying the new criterion to predict the compressive fracture
MGs under compressive stress states should possess a similar sec- anglehC,theextrinsicparameterundercompressivetypeloadingcan
ond-orderdependenceofshearfracturestressonthenormalstress befurtherderivedas:
(equation(1)).Notethatthefracturebehaviorsofmaterialsnotonly 1{cot2h
b ~ C: ð5Þ
dependontheintrinsicfactorssuchascompositionandmicrostruc- C 1{cot2h
T
ture which can be identified by the intrinsic parameter of
According to equations (3)–(5), the three parameters of the new
criterioncanbeachievedthroughuniaxialtensionandcompression.
InTable1,welistedtheexperimentalresultsofthepresentstudyand
otherinvestigators20,24–28forseveralZr-,Ti-,Pd-andNi-basedMGs
andalsothecalculatedthreeparametersofthenewcriterion.Inthe
present study, the shear fracture angle, which is important for the
calculation of a and b , were carefully measured and accurately
C
adjusted by considering both the spatial shear plane and elastic
recovery20 (More details and discussions about the experimental
resultsareshowninsupplementarymaterials).Itcanbeseenfrom
Table1thattheextrinsicparameterb forthelistedMGsatroom
C
temperature seemsto bealwaysaround 20.5, independent onthe
compositionormicrostructureofmaterials.Thisconclusionismore
affirmativeforthepresentandpreviousresults20inwhichboththe
tensile and compressive shear fracture angles were carefully mea-
sured.Inamicroscopicview,thesimilarvalueofb forMGsmay
C
reflectthesimilaratomicmechanismofcooperativeshearingofSTZs
forshearingplasticflow13,29.Thenormalstressactingontheshearing
plane of STZ influences the behavior of individual STZ and even-
tually affects the yield and fracture behavior of MGs. The normal
Figure1|QuantitativelyexperimentalverificationoftheEllipse stresseffectcanbespecificallydescribedbythenewcriterionwiththe
criterion. TheexperimentaldataindicatestheEllipsecriterioncanwell intrinsicfactoraandtheextrinsicparameterb .Accordingtothe
C
predictthetensilefracturebehaviorsoftheZr Cu Ni Al Ti MG20. presentcriterion,areflectsthedegreesofnormalstresseffect,while
52.5 17.9 14.6 10 5
Insetisthesketchofthedesignedsample. b describes the differences between the effects by tensile normal
C
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Table1|Experimentallymeasuredfracturestrengths(sF andsF),shearfractureangles(h andh )ofdifferentMGmaterialsatroom
C T C T
temperature,andthecalculatedparameters(a,t andb )ofthenewcriterion
0 C
Investigators Alloys sFC (GPa) sFT (GPa) hC (deg.) hT (deg.) t0(GPa) a bC
Presentstudy Zr Fe Al Cu 1.66 1.62 42.1 53.3 0.92 0.47 20.51
65 5 10 20
Presentstudy Zr Cu Ni Al 1.58 1.48 42.3 53.0 0.84 0.47 20.48
50.7 28 9 12.3
Presentstudy Ti Zr Ni Cu Be 1.84 1.68 42.6 51.8 0.93 0.44 20.47
40 25 3 12 20
Presentstudy Ti Zr Ni Cu Be annealed 1.87 1.72 41.4 56.8 1.02 0.54 20.50
40 25 3 12 20,
Quetal.20 Zr Ni Al Cu Ti 1.84 1.66 43 50.7 0.91 0.41 20.46
52.5 14.6 10 17.9 5
Zengetal.24 Ni Pd P 1.80 1.40 41.5 55.5 0.82 0.51 20.53
50 30 20
Carisand Zr Ti Ni Cu Be 2.05 1.95 42 53 1.10 0.46 20.55
41.25 13.75 10 12.5 22.5
Lewandowski25
Mukaietal.26,27 Pd Ni P 1.74 1.6 42 56 0.94 0.52 20.43
40 40 20
Zhangetal.28 Zr Ni Al Cu Ti 1.76 1.66 42 56 0.97 0.52 20.43
52.5 14.6 10 17.9 5
stressandbycompressivenormalstress.Withvaryingthecomposi- fracturestrengths (sF,sF) and shearfractureangles (h ,h )under
T C T C
tion or microstructure, the local properties of STZ (like volume, tensionandcompressioncanbepredictedintermsofthefollowing
activationenergyetc.)arechangedandfinallytheMGshowdifferent equations,respectively,
p
tensileyieldorfracturebehavior29,30,whichcanbewelldescribedby sF~2t ffi1ffiffi{ffiffiffiffiffiaffiffi2ffiffi, ð6Þ
theEllipsecriterionwiththedominantfactora,indicatingthatais T 0
composition-andmicrostructure-dependent. However,thesimilar sF~2t pffi1ffiffizffiffiffiffiffiaffiffi2ffiffi=ffiffi2ffiffiffi, ð7Þ
b forcompositionallyorstructurallydifferentMGsindicatesthatit C 0
C
shouldbemainlydominatedbyextrinsicconditionsratherthanthe h ~arccotpffi1ffiffi{ffiffiffiffiffi2ffiffiaffiffi2ffiffi, ð8Þ
intrinsicnatureofthematerials. T
Figure 2 illustrates the graphical representation of the new cri- h ~arccotpffi1ffiffizffiffiffiffiffiaffiffi2ffiffi: ð9Þ
terionwhenapplyingtoatypicalMG.Acontinuouscriticalfracture C
locus covers the whole range of normal stress, which allows the
ThiswillleadtoaT-Cstrengthasymmetrywitharatioasbelow,
pstrreedssictsitoanteso.fOthbeviocruistliyca,lthsetrenseswcocnridteitriioonnscfaonr wfrealcltuexrepluainndearllatnhye sFC~r1ffiffiffizffiffiffiffiffiaffiffi2ffiffi=ffiffi2ffiffiffiƒpffi1ffiffi0ffiffi: ð10Þ
three characteristic fracture behaviors of MGs, i.e. (I) the T-C sF 1{a2 2
T
strengthasymmetry,(II)theshearfractureanglesand(III)thepure
Whenthematerialsfailinthenormalfracturemodeundertensionas
stehreiaornfsraatcitsufireestbheehathvrioeer.nTehceisssianrdyiccoatnedsittihoantstfhoerparforapcotsuerdecnreiwterciorin- awpffi2ffiffi.2,thetensilefracturestrengthsF thenbecomesthecritical
T
ofMGs.
cleavagestrengths ofthematerials,i.e.,
0
Inordertofurtherexaminetherationalityofthenewcriterionand
sF~s ~t =a: ð11Þ
toachieveanoverallunderstandingofthenormalstresseffectonthe T 0 0
fracture behaviors of various MG materials, experimentally mea-
Andthecompression-tensionstrengthratiobecomes,
suredstrengthsofmorethan30differentcompositionsofMGswere
collected from literatures and listed in Table S3 in supplementary sFC~2apffi1ffiffizffiffiffiffiffiaffiffi2ffiffi=ffiffi2ffiffiffi: ð12Þ
sF
materials.Sincetherarenessofaccuratelymeasuredshearfracture T
angle,thefurtherquantitativelyexaminationofthenewcriterionwill
Ifthetensileandcompressivefracturestrengthsortheirratiosare
be accomplished by comparing the measured and predicted T-C available,theparametera~t =s canbeeasilycalculatedintermsof
strength asymmetry. If assuming b 5 20.5 as obtained in 0 0
C equation (10) or (12). Accordingly, the compression-tension
Tocacbulers1i,nacacosrhdeianrgmtoodthee(0nƒewaƒcripteffi2rffiffii.on2,)wlihkeeninthme otesntsMileGfsr1a4c,tuthree strengthratiosFC(cid:2)sFT vs.theintrinsicparametera~t0=s0 ofmore
than30differentcompositionaldifferentMGmaterialswerecom-
paredinTableS3andplottedinFig.S2insupplementarymaterials.
ItisfoundthatmostMGshavetheT-Cstrengthasymmetrywitha
strengthratiosF(cid:2)sF rangingfrom1.01to1.30;andtheparameter
C T
a~t =s isthusintherangeof0:1ƒaƒ0:6.Accordingtoequations
0 0
(8)and(9),thetensileandcompressiveshearfractureanglesh and
T
h should be in the ranges of 450vh ƒ620, and 400ƒh v450,
C T C
respectively.Thesepredictionsoftheshearfractureanglesagreewell
withthereportedvaluesintheliteratures(e.g.,seeTable1inRef.14),
furtherindicatingthatitisreasonabletoquantitativelydescribethe
fracture behaviors of the MG materials with the new fracture cri-
terion.
Figure2|Graphicalrepresentationofthenewfracturecriterion. The
greenlinerepresentsthecriticalfracturelocusofthenewcriterionof Discussion
equation(2)whiletheMohr’sstresscirclesareunderuniaxialtension, Accordingtothenewcriterion,thepredictionsstronglydependon
uniaxialcompressionandpureshear,respectively.Allthethreeconditions theintrinsicparametera~t0=s0.AsillustratedinFig.3,withvary-
forthefracturecriteriondescribingthefracturebehaviorsofMGsare ing a~t0=s0, three different cases can be classified. When
obviouslyfulfilledforthenewcriterion.Thecriticalfracturelocusofthe a~t0=s0?0 or s0??, the differences in strengths and shear
newcriterionclarifiesthatonlythosestressstatesenvelopedbythefracture fracture angles under tension and compression can be neglected
locusaresafe. and both the tensile and compressive shear angles are quite close
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Ttore4s5cua(cFriitge.ri3oan),1,3w.Whichhenar0evraat~hetr s=ismivlarptffi2offiffi.th2e,apsrsehdoicwtnioinnsFbigy.t3hbe, ionrtoMsGubmmaictreorimalestewriothrnamanoormphetoeursscsatrleusctluikree,UtFhGe forracNtuCremsatrteernigatlsh,
0 0
thecompressivefracturestrengthbecomesgraduallylargerthanthe increasesandtheT-Cstrengthasymmetrybecomesgraduallyobvi-
tensileonewithincreasinga;meanwhilethecompressiveshearfrac- ous(regionBinFig.4).Thehighstrengthlevelandtheshearfracture
tureanglehCissmallerthan45uandthetensileshearfractureangle nature of these materials make the normal stress effect hard to be
h islargerthan45u;theseapproximatelyagreewiththeM-Ccri- neglected12,13,31,32. In addition, different from the metallic materials
teTrion. When a~t =s §pffi2ffiffi.2, the T-C strength asymmetry withmetallicbonding,ceramicswitheitherionicbondingorcova-
becomesmuchlarger0and0thetensilefracturewillalwaysoccuralong lent bonding often display very high strength ratio sFC(cid:2)sFT even
the plane perpendicular to the loading axis, showing the fracture greater than 10 (see supplementary Table S4 online). The strong
behavior controlled by the maximum normal stress criterion1,18. ionic or covalent bonding greatly increases the resistance to shear
Therefore, the new criterion inherits the unified characteristic of deformationand thecriticalshearfailurestresst0,whiletheinev-
theEllipsecriterionandcanberegardedasacriterionunifyingthe itableinternaldefectslikeporesdecreasethecriticalnormalfracture
aboveclassicalfailurecriteria. stresss0,leadingtotheintrinsicfactora~t0=s0verylargeforcera-
Theaboveresultsindicatethattheproposednewcriterioncannot mics.Inthiscase,besidesthehighT-Cstrengthasymmetry,normal
onlywellpredictthefractureconditionsofMGmaterials,butalso fracture with hT~900 under tension and shear fracture within
havetheunifiedcharacteristictounifytheclassicalfailurecriteria. 0vhCv450 orevensplittingfailure14undercompressionareoften
BsterseindgetshthmeaMteGriamlsatienrcilaulsd,itnhgeufrlatrcatufirneeb-gerhaaivnieodrs(oUfFmGa)n,yNoCthmerehtaigllhic- pobresseernvetdc3r3i;tetrhioesnewfritahctau§repbffi2effiffi.ha2v,ioasrsillcuasntrabteedwienllFciga.p3tuc.red by the
materialsandadvancedceramicsetc.areinfluencedmoreorlessby From the analysis above, it is known that the definition of
the normal stress acting on the fracture or yield plane14,31,32. For a~t =s endows a the materials constant reflecting the intrinsic
0 0
isotropicmaterials,theT-Cstrengthasymmetryisoneofkeyindi- competition between shear failure and cleavage fracture. Usually
cators showing the normal stress effect. A summary of the T-C low a materials are easy to fail by plastic deformation but hard to
strengthasymmetryforvariousmaterialsarelistedinsupplementary cleavage fracture. This is why cleavage fracture is difficult to be
TablesS3,S4andS5online.Asaunifiedfracturecriterion,thenew observedinductileFCCcrystalslikeCuorAl3.Highamaterialslike
criterionmayhavetheabilitytodescribethefracturebehaviorsofa ceramics, however, are very easy to cleavage fracture but hard to
varietyofdifferentmaterials.Althoughthephysicalmechanismof deformplastically.FormaterialssuchasUFG,NCorMGmaterials,
theextrinsicparameterb isnotveryclearformaterialsotherthan theyhavemoderatea(Fig.4)andthusoftendeformandfractureina
C
MGmaterials,thefracturebehaviorsincludingT-Cstrengthasym- shearmode,exhibitinghighstrengthbutmoderateductility.Besides
metry and fracture mode of various materials can be generally thecompositionandmicrostructurewhichidentifiedbytheintrinsic
describedbythenewcriterionifassumingb atroomtemperature factora,theexternalloadingconditions,whichcanbecharacterized
C
andquasi-static strain rateis aconstantof20.5. Accordingly, the bytheextrinsicparameterb,alsoinfluencethefracturebehaviorsof
relationship of the material constant a~t =s versus the T-C materials3. For instance, as increasing the testing temperature of
0 0
strengthasymmetryofvariousdifferentmaterialscanbeplottedin nanocrystallineAl Fe Cr Ti alloy,theT-Cstrengthasymmetryis
93 3 2 2
Fig.4,andthreeregionsareclassified.Fortheconventionalductile foundtodecrease34.Moreevidencesofthefracturebehaviorsinflu-
metallicmaterialslikeAl-alloys,Ti-alloysorsteels,nearlynodiffer- encedbytheexternalfactorsandtheinterpretationsbythepresent
encebetweentensileandcompressivestrengthscanbeobserved.The criterion were discussed in supplementary materials. The new cri-
normal stress should only have little influence and the Tresca cri- terionsuggeststhatthefracturebehaviorsarewellcontrolledbyboth
terioncanbeused.Thefactora~t =s isnearlyzeroandthenew theintrinsicfactoraandextrinsicfactorb,whichmeansthateven
0 0
criterioninthiscaseisconsistentwiththeTrescacriterion(Fig.3a). ductilematerialswithverysmallacouldpossiblyfractureinabrittle
When aR0, the normalized strength sF(cid:2)t or sF(cid:2)t is approxi- modeundercertainexternalconditionswithlargebandviceversa.
T 0 C 0
mately equal to 2, which is also the same as the prediction by the These unique characteristics enable the new criterion becoming a
Trescacriterion1,3.Asthegrainsizeofmetallicmaterialsdecreases fracturecriterionnotonlyunifyingtheclassicalfailurecriteriabut
Figure3|Representativecriticalfracturelocipredictedbythenewfracturecriterionindifferentcasesasvaryingtheintrinsicfactora~t =s .
(a)aR0,h <450<h andsF(cid:2)sF<1;(b)0vavpffi2ffiffi.2,0vh v450vh v900andsF(cid:2)sFw1;(c)a§pffi2ffiffi.2,0vh v450,h ~900andsF0(cid:2)sF0?1.
C T C T C T C T C T C T
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Figure4|NormalizedtensilestrengthsF(cid:2)t andnormalizedcompressivestrengthsF(cid:2)t ofvariousdifferentmaterials(withdifferenta). Thesolid
T 0 C 0
linesweredrawnaccordingtothenewcriterion(equation(2))withb5b 51fortension(blue)andb5b 520.5forcompression(red).
T C
Experimentalandsimulationdataofconventionalmetallicmaterials,ultrafine-grained(UFG)andnanocrystalline(NC)materials,MGs,MGcomposites
(MGCs)andceramicswerefilledbasedonthedatalistedinsupplementaryTablesS3,S4andS5online.
alsoauniversalcriteriontopredictthefracturebehaviorsofavariety withdimensionsof23234mm3werecutbyelectricsparkcuttingandsubsequently
ofcompositionaldifferentmaterialsundervariousexternalloading grindedandpolishedby2.5mmabrasivepaste.Uniaxialtensionandcompression
wereconductedbyusinganInstron5982testingmachineatanominalstrainrateof
conditions.
531024s21atroomtemperatureinair.Thedeformationandfracturefeatureswere
In summary, the experimental results of inclined notch tension observedwithaLeoSupra35scanningelectronmicroscope.
indicatethattheEllipsecriterioncanquantitativelypredictthetens-
ilefracturebehaviorsofMGs.Inordertocoverthewholerangeof
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