influence of strain and stress triaxiality on the fracture

Research ArticleInfluence of Strain and Stress Triaxiality on the FractureBehavior of GB 35CrMo Steel during Hot Tensile Testing

Zheng Li Yajun Zhou and Sanxing Wang

College of Mechanical and Electrical Engineering Central South University Changsha 410083 China

Correspondence should be addressed to Yajun Zhou zhouyjuncsueducn

Received 4 June 2018 Revised 27 August 2018 Accepted 4 September 2018 Published 1 November 2018

Academic Editor Davide Palumbo

Copyright copy 2018 Zheng Li et alis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To better understand cavitation nucleation and crack initiation in 35CrMo steel during high-temperature tensile processing andthe effect of stress triaxiality on its fracture behaviors uniaxial and notch high-temperature tensile tests were performed emicrostructure fracture morphology fracture strain and stress triaxiality of the tested 35CrMo steel were then characterized anddiscussed e results showed that crack formation in 35CrMo steel included stages of nucleation growth and microcavityaggregation Scanning electron microscopy and energy-dispersive X-ray spectroscopy demonstrated that crack formation wasclosely related to the presence of steel inclusions High-temperature tensile testing of samples with different notch radii showedthat the fracture strain of 35CrMo steel was decreased with increasing stress triaxiality that is increased stress levels correspondedto decreased material plasticity In addition the recrystallization degree was decreased with increased stress triaxiality and thegrain size growth was slowed e failure of 35CrMo steel occurred via ductile fracture and low stress triaxiality and hightemperature conditions induced large and deep dimples on the fracture surface

1 Introduction

Because it offers excellent comprehensive mechanical prop-erties 35CrMo steel is often used to manufacture importantstructural parts such as the rotors of turbo generatorsspindles transmission shafts with heavy loads and large-section parts [1ndash4] To manufacture these key components itis necessary to consider the complexity of the forging processCrack initiation can occur in materials when the forgingdeformation process parameters are incompatible with thematerial properties To avoid cracks and holes it is importantto study the factors affecting the properties and fracturemechanism of 35CrMo steel during hot working [5 6]

e study of the effects of crack initiation and stress stateon ductile fractures began with Ludwik and Scheu [7] whoassumed that ductile metal fracture was controlled by thestress-strain curve Correlative studies have shown thatcrack formation during thermoforming always occurred bythe nucleation growth and coalescence of microcavities asshown in Figure 1 [8 9] From the perspective of mesoscopicdamage mechanics studies have confirmed a correlationbetween the presence of cracks and second-phase particle

inclusions [10] Recently Pardoen and Hutchinson [9]Benzerga [11] and Gao and Kim [12] demonstrated that theGologanundashLeblondndashDevaux model showed significantlyimproved accuracy in its description of void growth and thecorresponding material behavior during ductile fracture Inaddition similar relationships betweenmaterial fracture andthermal processing parameters have been reported for EH36alloys [13] Ni-based superalloys [14] Al-70Si-03Mgfoundry Al alloys [15] and other alloys [16 17] esesuccessful studies have demonstrated that thermotensiletests are important in understanding metal thermoformingand are powerful tools that can guide thermal processingZhang et al [18] and Duan and Liu [19] also used the theoryof mesoscopic damage mechanics to study the ductilefracture behavior of 316LN stainless steel

Stress triaxiality is the most commonly used stress-stateparameter for ductile metals Several scholars have con-firmed that it can reflect complex material stress statesMcClintock [20] and Rice and Tracey [21] studied the mi-crostructural growth and identified strong relationshipsbetween stress triaxiality and ductile metal fracture strainand behavior Hancock and Mackenzie [22] also found via

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 5124524 11 pageshttpsdoiorg10115520185124524

a series of notched-sample tensile tests that metal duc-tility was affected by the triaxiality state of the sampleRecent experimental and numerical studies by Mirza et al[23] on pure Fe mild steel and the BS1474 Al alloy ina wide range of strain rates and by Bao and Wierzbicki[24 25] and Bao [26 27] on 2024 Al alloy during qua-sistatic loading reaffirmed the strong relationship amongequivalent strain stress triaxiality and crack formationIn these studies stress triaxiality was used to define thefailure function of the material e hot tensile tests of35CrMo steel are only found in Xiaorsquos study Xiao et al[28] studied the hot tensile and fracture behaviors of35CrMo steel at high temperatures and strain ratesHowever the initiation and propagation of cracks underdifferent strain and stress states have not been reportederefore the effect of strain and stress triaxiality on thefracture behavior of 35CrMo steel under hot tensile de-formation requires further study

Hence in this paper the effects of strain temperatureand stress triaxiality on the fracture behavior of 35CrMosteel were investigated by uniaxial and notched high-temperature tensile testing e microstructure evolutionand fracture behavior of 35CrMo steel under different tensileconditions were studied after stretching by means of me-tallographic structure and fracture scanning analysis

2 Experimental Materials and Procedures

21 High-Temperature Tensile Test A commercial 35CrMoalloy with the composition 034C-021Si-056Mn-095Cr-019Mo-00051S-0019Si-(bal) Fe (wt) was used in thisinvestigation e shape and size of the high-temperaturetensile samples are shown in Figure 2

Tensile tests were performed using a Gleeble 3500 testingmachine (Huazhong University of Science and TechnologyWuhan China) Hot tensile tests of the samples shown inFigure 2(a) were performed at 1000degC and the strain rate of05 sminus1 to the tensile strain values of 02 04 054 06 08 and097 Hot tensile tests of the samples shown in Figure 2(b) wereperformed at temperatures of 850degC 950degC 1050degC and1150degC with the strain rate of 05 sminus1 and notch radii of 1mm2mm 4mm and 6mm All samples were heated to 1150degCat 10degCs soaked for 120 s to eliminate thermal gradientsand then cooled to the set deformation temperature at10degCs Before tensile testing samples were maintained atthe deformation temperature for 120 s en the tensiletests were performed as shown in Figure 3 Immediately

after the tensile tests each sample was quenched in Ar toretain the deformed microstructure e deformed sam-ples were cut in the axial direction polished and etched ina solution consisting of picric acid (5 g) H2O (100mL)and HCl (1mL) at 60ndash80degC for 3ndash8min to perform bothoptical microscopy (OM Olympus Tokyo Japan) andSEM (EVO MA10 EISS Jena Germany) observations

22 Initial Stress Triaxiality e necking phenomenon ofstretched materials is complicated In this case thecomplex stress can be simplified to the three-dimensionalstress state shown in Figure 4 When the stress states of thematerial changes the plastic deformation and fracturestrain of the materials will also change To further un-derstand the three-dimensional stress and its relationshipto void initiation the parameter Rσ known as the stresstriaxiality is introduced and the following expression isgiven [29]

Rσ 13

+ lna2 + 2aRminus r2

2aR1113888 1113889 (1)

where a is the radius of the minimum cross section of thepart undergoing necking r is the radial value from the axis ofthe smallest cross section of the neck to the edge and R is thecurvature radius of the minimum cross section of thenecking zone When r 0 the maximum Rσ value isobtained

Rσ 13

+ ln 1 +a

2R1113874 1113875 (2)

During high-temperature tensile testing the stress tri-axiality Rσ is the highest in the center part (r 0) of thenecking region and the holes form in the center for themaximum stress triaxiality and then connection grows andthen diffuse to the surface of the sample eventually leadingto fracture of the sample ere is a strong correlation be-tween stress triaxiality and crack initiation in sample frac-ture As shown in Figure 5(e) large and deep interconnectedcracks appear in the center of the necking region When thecrack occurs the axial tensile stress plays a leading role in thecrack propagation and the crack propagates along the di-rection of the maximum tensile stress

e initial central stress triaxiality Rσ can be calculatedby inserting the initial radius r and the initial notch radiusR of the minimum section into formula (1) e initialminimum radius r of all notched samples is equal to 3mm

(a) (b) (c) (d) (e)

Figure 1 Process of crack formation (a) inclusions (b) cavity nucleation (c) cavity growth (d) cavity necking and (e) cavity coalescence

2 Advances in Materials Science and Engineering

M10 oslash8 oslash10

16

R1

4896 4527

1415

(a)

oslash10

oslash6M10

16

1415

R1 R2 R4 R6

(b)

Figure 2 Scheme of the tensile sample (all dimensions are in mm) (a) uniaxial high-temperature tensile (b) notch high-temperature tensile

Time t

1150degC2min holding 1000degC

2min holding

Heating rate 10degCsArgon

quenching

Tensile deformationStrain rate 05sndash1

Deformation degree02 04 054 06 08 097Te

mpe

ratu

re T

Coolingrate 10degCs

(a)

Time t

1150degC2min holding 1150degC 1050degC 950degC 850degC

2min holding

Heating rate 10degCs Argonquenching


Notched radius1mm 2mm 4mm 6mmTe

mpe

ratu

re T

Coolingrate 10degCs

(b)

Figure 3 Experimental procedure used for hot tensile tests (a) uniaxial high-temperature tensile (b) notch high-temperature tensile

Three-dimensionalstress

One-way tension

Z

2a

rθ

R

Figure 4 ree-dimensional stress of a part that undergoes necking during tensile testing

Advances in Materials Science and Engineering 3

and the initial notch radii R are 6mm 4mm 2mm and1mm respectively According to formula (2) the corre-sponding initial stress triaxiality values are 055 065 089and 130 respectively In other words the initial stresstriaxiality increases with the decrease of the notch radius ofthe sample

3 Results and Discussion

31 Cavity Nucleation and Crack Initiation Figure 6 showsthe tensile curves at various strain levels In the initial stageof deformation the stress increases rapidly until it hasreached 40MPa and then the increase gradually becomes

200μm

(a)

200μm

(b)

50μm

Recrystallizedgrain

(c)

50μm

Microscopic void

(d)

50μm

Crack initiation

(e)

50μm

Split of the grains

(f )

FIGURE 5 Microstructure transformation during the hot tensile process (a) ε 02 (b) ε 04 (c) ε 054 (d) ε 06 (e) ε 08 and (f)ε 097


gentlee stress reaches its maximum value when the strainreaches 054 Beyond this level the stress decreases sharply asthe strain increases Figure 6 shows an experimental fracturestrain of εf 097

e necking phenomenon is the signicant contractionoccurring in a local region of a sample when the applied loadis maximized As shown in Figure 7 necking becomes in-creasingly obvious as the strain increases A stress peakappears in the tensile sample when the strain reaches 054Research has shown that the material begins to fail after thisstress peak appears in tensile testing Microcracks areformed in the sample and necking is observed macro-scopically Once microcrack formation begins additionalexternal stress causes the development of macroscopiccracks and eventual material fracture and failuree surfaceof the sample begins to show obvious macroscopic crackswhen the strain reaches 06 When the strain reaches 08necking is very serious Although there are no obvious cracksformed in the sample at this time the crack propagationwithin the sample is severe as proven by the observation ofthe microstructure As the strain continues to increasefracture occurs at the value of 097

e microstructures of the hot deformation zones wereobserved after axial wire cutting of the 35CrMo steel samplesto further understand the high-temperature plastic de-formation crack initiation and propagation mechanismse results are shown in Figure 5

When the strain reaches 02 and high-temperatureplastic deformation begins some austenite grains begin togrow However the strain is not yet sucient to producelarge microcracks When the strain reaches 04 the grainsgrow more than they do at the strain of 02 and some tinyvoids emerge in the microstructure e stress peak appearswhen the strain reaches 054 e grains are elongated inthe axial direction and many grains grow signicantlyBecause the amount of deformation is small the number ofrecrystallized nuclei formed is small and minute voids beginto form Figure 5 shows that recrystallization occurs duringvoid nucleation and growth In addition signicant re-crystallization nucleation initiation occurs at the grainboundaries when the strain increases to 06 At the same

time voids nucleate and form primarily in the axial di-rection e voids grow further when the strain is increasedto 08 and all recrystallization occurs in the heat-aectedzone When the voids grow and converge the strain reaches097 and the samples undergo axial tensile stress fracture

32 Eect of Heterogeneous Phases on Voids InitiationVia the high-temperature thermal stretching and neckingprocess organization analysis can be determined Asshown in Figure 5(c) crack nucleation and initiation donot occur at the grain boundaries in 35CrMo steel butrather in the grain interiors High dislocation densitiesoccur near the heterophases of the grains because of thehigh temperature and strain rate is causes the dislo-cation density to increase where its product can accu-mulate easily Voids are nucleated as the dislocationaccumulation increases and cracks form at the grainboundaries as the strain and stress concentration caused bycavity growth increases

e fracture was observed using SEM to survey andevaluate the void nucleation mechanism e resultingimages are shown in Figure 8 e inclusions in molten steelare primarily composed of various deoxidizers such as FeSiAl and SiMn and rening agents such as CaF2 and NaClwhich are oxidized to Al2O3 SiO2 MnO Al2O3ndashSiO2ndashMnOand Ca compounds during smelting ese endogenousinclusions can also form secondary deoxidization productsduring the latter solidication stages ese deoxidizedoxides may not be able to precipitate from the ingot duringsubsequent cooling thus forming inclusions An inclusionparticle was analyzed via energy-dispersive X-ray spec-troscopy (EDS) As shown in Figure 8 the inclusions in35CrMo steel are primarily endogenous e alloying ele-ments of Ca and Al are oxidized to form inclusions such asCa compounds and Al2O3 eir eects on the mechanicalproperties plasticity toughness and fatigue limit of theingot are signicant during thermal processing and heattreatment ese inclusions can cause stress concentrationand microcrack formation resulting in ingot failureerefore the use of Al-containing deoxidizers and relatedCa-containing rening agents should be strictly limitedduring the 35CrMo steel ingot melting process

33 Rheological Behavior and Fracture Strain of DierentStress Triaxiality Figure 9 shows the true stress-strain

ε = 02ε = 04

ε = 054

ε = 06

ε = 08

ε = 097

Figure 7 Samples after hot deformation ε 02 ε 04 ε 054ε 06 ε 08 and ε 097

02

04

Temperature 1000degCStrain rate 05sndash1

05406

08

097ndash20

0

20

40

60

80

100

120

140

160

True

stre

ss (M

pa)

01 02 03 04 05 06 07 08 09 10 11 1200True strain

Figure 6 e true stress-strain curve at high temperatures


le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N

0261266 counts in 60 seconds

1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S

Atomic percentageO 4753

Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion

Figure 8 Chemical compositions of the inclusion particles

0

00 01 02 03True strain

04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280

Notched radius 4mmNotched radius 6mm


(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)

Figure 9 e true stress-strain curve of 35CrMo steel under dierent strain conditions (a) 850degC (b) notched radius 2mm


curves of 35CrMo steel at dierent temperatures and notchradii at the strain rate of 05 sminus1 At the beginning of tensiledeformation the stress growth is very rapid When the strainis reached the rheological stress increases slowly As thetensile curves reach a certain strain the initiation and ac-cumulation of voids in the material rapidly weakens thematerialrsquos resistance to deformation and the rheologicalstress shows sharp decrease until material fracture occurs

Figure 9(a) shows the true stress-true strain curves at850degC for specimens with dierent notch radii As shown inFigure 9(a) the stress reaches its peak value more quicklyand the peak stress is increased as the notch radius is de-creased in other words samples with higher stress triaxialityreach the maximum stress earlier and the peak stress valuesare higher than those of samples with lower stress triaxialityAdditionally when the peak strain is reached the stress-strain curve decreases rapidly under the condition of highstress triaxiality and fracture occurs under the condition oflower strain levels is phenomenon relates not only to thestress state of the material during the tensile process but alsoto the degree of recrystallization in the matrix and the degreeof dislocation annihilation As shown in Figure 9(b) there islittle dierence in the overall strain range of the curve withincreasing tensile temperature Furthermore the peak stressgradually decreases e analysis indicates that under thecondition of low stress triaxiality sample deformation isuniform and the accumulated energy in the deformation ismore fully used for microstructure transformation Forexample the nucleation and growth of recrystallized grainsand the enhancement of high-energy boundary activity athigh tensile temperatures provide favorable conditions fordislocation elimination erefore low stress triaxiality andhigh tensile temperatures are benecial to decrease rheo-logical resistance and increase the fracture strain

e fracture strain value at high temperature is animportant index reiexclecting the plastic deformation of thematerial e eects of the notch radius and temperature onthe fracture strain are shown in Figure 10 With the decreaseof notch radius at the same tensile deformation temperaturethe fracture strain decreases that is increased stress levelscorrespond to decreased material plasticity and easier ma-terial fracture under the same stress condition In the samestress state with the increase of the tensile deformationtemperature the fracture strain of the 35CrMo steel in-creases the plasticity increases and the fracture deformationresistance is strengthened

34 Microstructural Observation and Analysis Figure 11shows the metallographic structure near the fracture sur-face of a notched tensile sample after testing at a strain rate of05 sminus1 and a tensile temperature of 850degC e notch radiiare 6mm 4mm 2mm and 1mm respectively Dynamicrecrystallization occurs in all four notched radii regionsAs the notch radius decreases the recrystallization degreedecreases with increasing stress triaxiality and the grainsize growth is slowed At the notch radius of 6mm re-crystallization occurs more fully but the dynamic re-crystallization of the sample with the notch radius of 1mm

remains in the starting stage e analysis shows thatwhen the notch radius is 1mm the stress triaxiality andstrain concentration are both large Strong deformationdistortion can drive recrystallization nucleation but becauseof the strong strain concentration the recrystallization oc-curs before the material deforms As a result the grainstructure after the nal fracture is obviously ner than that ofother samples but with increased notch radius the strain inthe heat-aected zone becomes uniform the fracture re-sistance is strengthened and the fracture strain increasese dynamic recrystallization becomes increasingly com-plete with increased deformation as shown in Figure 11(a)the recrystallization of the sample with the notch radius of6mm is completed more fully

35 Fracture Scanning and Analysis e samples fromwhich the rheological curves in Figure 9 were obtained at thetemperature of 850degC and the notch radius of 2mm wereobserved using SEM e resulting images are shown inFigures 12 and 13 Under the selected reference conditionsthe fracture mechanism and iniexcluence law of dierent stressstates and deformation temperatures on the samples can befurther explained

As shown in Figure 12 when the deformation tempera-ture is 850degC the sections in dierent stress states are occupiedby dimples of dierent sizes e dimples are macroscopicfeatures reiexclecting the growth and convergence of internalvoids in the plastic deformation of materials is demon-strates once again that the tensile failure of 35CrMo steeloccurs by typical ductile fracture Ductile fracture occurs indierent forms after considering the factors of void rotationand changes in void shape but the basic process is similarey all occur in the normal stress state with normal stresstriaxiality and rough dimples on the fracture surface estress-strain curves show that the fracture strains are de-creased with increasing stress triaxiality which is obvious and

038

850 950TemperaturedegC

Frac

ture

stra

in

1050 1150

042

046

050

054

058



Figure 10 e fracture strain of the sample at dierent temper-atures and notched radius is obtained when the deformation rateis 05 sminus1


reiexclected by the microscopic void growth As shown in Fig-ure 12 as the radius of the notch decreases that is as the stresstriaxiality increases the diameters and depths of the dimplesare decreased is is because higher degrees of stress tri-axiality produce greater stress concentrations in the materialand fracture occurs at smaller strainse voids in thematerialinitiated under tensile stress do not accumulate and grow nordo they extend along the tensile direction Instead as the stresstriaxiality decreases the fracture strain of the material in-creases the time of deformation increases for the same strainrate and the voids in the material grow and accumulateusthe dimples are large and deep in the cross section

Figure 13 shows the fracture-scanning morphology ofsamples strained at temperatures from 850degC to 1150degC withthe notch radius of 2mm Under the same stress state thedeformation temperature has a signicant eect on theshrinkage of the cross section of the material It is shown thatthe shrinkage rate of the section is increased sharply withincreasing temperature and the necking ability of 35CrMosteel is obviously improved with increasing temperature

When the deformation temperature is 850degC the dim-ples are shallow and dierent in size At this lower

temperature the combined deformation ability and neckingability of adjacent dimples is decreased which decreases thedamage tolerance of the material With increased de-formation temperature the wall of dimples between adjacentdimples is torn and the number of dimples is graduallydecreased Because of the increase of temperature thefracture strain of the materials is increased thereby allowingsucient time for the growth and accumulation of micro-voids especially in the tensile direction where the dimplesgradually deepen Finally the dimples merge into onedimple thus allowing the individual dimples to grow Asshown in Figure 13 when the temperature reaches 1050degCand 1150degC the number of dimples on the fracture sectiondecreases sharply and the dimples obviously increase anddeepen demonstrating the good plasticity of 35CrMo steel athigh temperatures e dimple wall under high-temperaturedeformation shows obvious slip characteristics which isa signicant feature of large plastic strain which also ex-plains the phenomenon of the increased fracture strain valuein the rheological stress curve with increased temperaturethat is the damage capacity limit of the material is enhancedat higher temperatures

50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)

Figure 11 e metallographic structure near the fracture surface of notched tensile samples at a strain rate of 05 sminus1 and a tensiletemperature of 850degC (a) 6mm (b) 4mm (c) 2mm and (d) 1mm


(a) (b)

(c) (d)

Figure 13 e fracture morphology of samples with notch radius of 2mm at different temperatures (a) 850degC (b) 950degC (c) 1050degCand (d) 1150degC

(a) (b)

(c) (d)

Figure 12 e fracture morphology of different notched samples at a tensile temperature of 850degC (a) 6mm (b) 4mm (c) 2mm and (d)1mm


4 Conclusions

Tensile tests and tensile unloading experiments wereconducted to investigate the crack initiation and fracturebehavior of 35CrMo steel e main conclusions are asfollows

(1) Crack formation in 35CrMo steel proceeds by thenucleation growth and coalescence of microcavitiesduring high-temperature tensile processing Withthe superposition of the dislocation density stressconcentrations are produced by grain heterogeneityand cavity nucleation occurs first e process ofvoid growth and coalescence leads to the fracture ofthe material Inclusions such as compounds of Caand Al2O3 are the main heterogeneous phases thatcause cavity nucleation

(2) e effect of stress triaxiality on the rheologicalbehavior of 35CrMo steel is very significant esample with higher stress triaxiality reaches the peakstress first and the peak stress is higher than that ofthe sample with lower stress triaxiality and thefracture strain is lower e temperature has littleeffect on the fracture strain range of 35CrMo steelbut the fracture strain increases slightly with in-creasing tensile temperature

(3) At the same tensile deformation temperature therecrystallization degree of the steel decreases withthe increase of stress triaxiality the dynamic re-crystallization grain size is large while the dimples inthe fracture surface are small and shallow Howeverthe temperature is mainly reflected in the shrinkagerate of the section the 35CrMo steel exhibits goodplasticity at high temperature and the fracturedimple is large and deep

Data Availability

e data in the manuscript are all from experiments epicture data used to support the findings of this study areincluded within the article Finally the curve data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

e authors declare no conflicts of interest

Authorsrsquo Contributions

Zheng Li and Sanxing Wang conceived and designed theexperiments Sanxing Wang carried out the experimentsZheng Li and Sanxing Wang analyzed the data Yajun Zhoucontributed reagents materials and analysis tools andZheng Li wrote the paper

Acknowledgments

e authors are grateful for financial support by the Fun-damental Research Funds for the Central Universities of

Central South University (2018zzts477) and the NationalProgram on Key Basic Research Project of China (No2014CB046702)

References

[1] Y Lv ldquoInfluence of laser surface melting on the micropittingperformance of 35CrMo structural steel gearsrdquo MaterialsScience and Engineering A vol 564 pp 1ndash7 2013

[2] J W Zhang L T Lu P B Wu J J Ma G G Wang andW H Zhang ldquoInclusion size evaluation and fatigue strengthanalysis of 35CrMo alloy railway axle steelrdquoMaterials Scienceand Engineering A vol 562 pp 211ndash217 2013

[3] G Liang C Shi Y Zhou and D Mao ldquoEffect of ultrasonictreatment on the solidification microstructure of die-cast35CrMo steelrdquo Metals vol 6 no 11 p 260 2016

[4] J Chen Y Zhou C Shi and D Mao ldquoMicroscopic analysisand electrochemical behavior of Fe-based coating producedby laser claddingrdquo Metals vol 7 no 10 p 435 2017

[5] Z Xiao Y Huang and Y Liu ldquoEvolution of dynamic re-crystallization in 35CrMo steel during hot deformationrdquoJournal of Materials Engineering and Performance vol 27no 3 pp 924ndash932 2018

[6] A Y Churyumov M G Khomutov A N SoloninA V Pozdniakov T A Churyumova and B F MinyayloldquoHot deformation behaviour and fracture of 10CrMoWNbferritic-martensitic steelrdquo Materials and Design vol 74pp 44ndash54 2015

[7] P Ludwik and R Scheu ldquoUeber kerbwirkungen bei flus-seisenrdquo Stahl und Eisen vol 43 pp 999ndash1001 1923

[8] P K Liaw C Y Yang S S Palusamy and W Ren ldquoFatiguecrack initiation and propagation behavior of pressure vesselsteelsrdquo Engineering Fracture Mechanics vol 57 no 1pp 85ndash104 1997

[9] T Pardoen and J W Hutchinson ldquoAn extended model forvoid growth and coalescencerdquo Journal of the Mechanics andPhysics of Solids vol 48 no 12 pp 2467ndash2512 2000

[10] Y Zhang ldquoMagnetic relaxation behavior in Tb-doped pe-rovskite manganiterdquo Journal of Magnetism and MagneticMaterials vol 323 no 1 pp 1ndash3 2011

[11] A A Benzerga ldquoMicromechanics of coalescence in ductilefracturerdquo Journal of the Mechanics and Physics of Solidsvol 50 no 6 pp 1331ndash1362 2002

[12] X Gao and J Kim ldquoModeling of ductile fracture significanceof void coalescencerdquo International Journal of Solids andStructures vol 43 no 20 pp 6277ndash6293 2006

[13] J Choung C S Shim and H C Song ldquoEstimation of failurestrain of EH36 high strength marine structural steel usingaverage stress triaxialityrdquo Marine Structures vol 29 no 1pp 1ndash21 2012

[14] Y C Lin J Deng Y Q Jiang D X Wen and G Liu ldquoHottensile deformation behaviors and fracture characteristics ofa typical Ni-based superalloyrdquo Materials amp Design vol 55pp 949ndash957 2014

[15] Z Man Z Jian L Yao C Liu G Yang and Y Zhou ldquoEffectof mischmetal modification treatment on the microstructuretensile properties and fracture behavior of Al-70Si-03Mgfoundry aluminum alloysrdquo Journal of Materials Sciencevol 46 no 8 pp 2685ndash2694 2011

[16] LWang H Yu and Y S Lee ldquoEffect of microstructure on hottensile deformation behavior of 7075 alloy sheet fabricated bytwin roll castingrdquo Materials Science and Engineering Avol 652 pp 221ndash230 2016


[17] M Zhou Y C Lin J Deng and Y Q Jiang ldquoHot tensiledeformation behaviors and constitutive model of an AlndashZnndashMgndashCu alloyrdquo Materials amp Design vol 59 pp 141ndash150 2014

[18] X Zhang Y Zhang Y Li and J Liu ldquoCracking initiationmechanism of 316LN stainless steel in the process of the hotdeformationrdquo Materials Science and Engineering A vol 559pp 301ndash306 2013

[19] X W Duan and J S Liu ldquoResearch on damage evolution anddamage model of 316LN steel during forgingrdquo MaterialsScience and Engineering A vol 588 pp 265ndash271 2013

[20] F A Mcclintock ldquoA criterion for ductile fracture by thegrowth of holesrdquo Journal of Applied Mechanics vol 35 no 2pp 363ndash371 1968

[21] J R Rice and D M Tracey ldquoOn the ductile enlargement ofvoids in triaxial stress fieldslowastrdquo Journal of the Mechanics andPhysics of Solids vol 17 no 3 pp 201ndash217 1969

[22] J W Hancock and A C Mackenzie ldquoOn the mechanisms ofductile failure in high-strength steels subjected to multi-axialstress-statesrdquo Journal of the Mechanics and Physics of Solidsvol 24 no 2-3 pp 147ndash160 1976

[23] M S Mirza D C Barton and P Church ldquoe effect of stresstriaxiality and strain-rate on the fracture characteristics ofductile metalsrdquo Journal of Materials Science vol 31 no 2pp 453ndash461 1996

[24] Y Bao and R Treitler ldquoDuctile crack formation on notchedAl2024-T351 bars under compressionndashtension loadingrdquoMaterials Science and Engineering A vol 384 no 1-2pp 385ndash394 2004

[25] Y Bao and TWierzbicki ldquoOn fracture locus in the equivalentstrain and stress triaxiality spacerdquo International Journal ofMechanical Sciences vol 46 no 1 pp 81ndash98 2004

[26] Y Bao ldquoDependence of ductile crack formation in tensile testson stress triaxiality stress and strain ratiosrdquo EngineeringFracture Mechanics vol 72 no 4 pp 505ndash522 2005

[27] Y Bao and T Wierzbicki ldquoOn the cut-off value of negativetriaxiality for fracturerdquo Engineering Fracture Mechanicsvol 72 no 7 pp 1049ndash1069 2005

[28] Z Xiao Y Huang H Liu and S Wang ldquoHot tensile andfracture behavior of 35CrMo steel at elevated temperature andstrain raterdquo Metals vol 6 no 9 p 210 2016

[29] P W Bridgman Studies in Large Plastic Flow and Fracturewith Special Emphasis on the Effects of Hydrostatic PressureHarvard University Press Cambridge MA USA 1964


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Journal ofNanomaterials

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a series of notched-sample tensile tests that metal duc-tility was affected by the triaxiality state of the sampleRecent experimental and numerical studies by Mirza et al[23] on pure Fe mild steel and the BS1474 Al alloy ina wide range of strain rates and by Bao and Wierzbicki[24 25] and Bao [26 27] on 2024 Al alloy during qua-sistatic loading reaffirmed the strong relationship amongequivalent strain stress triaxiality and crack formationIn these studies stress triaxiality was used to define thefailure function of the material e hot tensile tests of35CrMo steel are only found in Xiaorsquos study Xiao et al[28] studied the hot tensile and fracture behaviors of35CrMo steel at high temperatures and strain ratesHowever the initiation and propagation of cracks underdifferent strain and stress states have not been reportederefore the effect of strain and stress triaxiality on thefracture behavior of 35CrMo steel under hot tensile de-formation requires further study

Hence in this paper the effects of strain temperatureand stress triaxiality on the fracture behavior of 35CrMosteel were investigated by uniaxial and notched high-temperature tensile testing e microstructure evolutionand fracture behavior of 35CrMo steel under different tensileconditions were studied after stretching by means of me-tallographic structure and fracture scanning analysis

2 Experimental Materials and Procedures

21 High-Temperature Tensile Test A commercial 35CrMoalloy with the composition 034C-021Si-056Mn-095Cr-019Mo-00051S-0019Si-(bal) Fe (wt) was used in thisinvestigation e shape and size of the high-temperaturetensile samples are shown in Figure 2

Tensile tests were performed using a Gleeble 3500 testingmachine (Huazhong University of Science and TechnologyWuhan China) Hot tensile tests of the samples shown inFigure 2(a) were performed at 1000degC and the strain rate of05 sminus1 to the tensile strain values of 02 04 054 06 08 and097 Hot tensile tests of the samples shown in Figure 2(b) wereperformed at temperatures of 850degC 950degC 1050degC and1150degC with the strain rate of 05 sminus1 and notch radii of 1mm2mm 4mm and 6mm All samples were heated to 1150degCat 10degCs soaked for 120 s to eliminate thermal gradientsand then cooled to the set deformation temperature at10degCs Before tensile testing samples were maintained atthe deformation temperature for 120 s en the tensiletests were performed as shown in Figure 3 Immediately

after the tensile tests each sample was quenched in Ar toretain the deformed microstructure e deformed sam-ples were cut in the axial direction polished and etched ina solution consisting of picric acid (5 g) H2O (100mL)and HCl (1mL) at 60ndash80degC for 3ndash8min to perform bothoptical microscopy (OM Olympus Tokyo Japan) andSEM (EVO MA10 EISS Jena Germany) observations

22 Initial Stress Triaxiality e necking phenomenon ofstretched materials is complicated In this case thecomplex stress can be simplified to the three-dimensionalstress state shown in Figure 4 When the stress states of thematerial changes the plastic deformation and fracturestrain of the materials will also change To further un-derstand the three-dimensional stress and its relationshipto void initiation the parameter Rσ known as the stresstriaxiality is introduced and the following expression isgiven [29]

Rσ 13

+ lna2 + 2aRminus r2

2aR1113888 1113889 (1)

where a is the radius of the minimum cross section of thepart undergoing necking r is the radial value from the axis ofthe smallest cross section of the neck to the edge and R is thecurvature radius of the minimum cross section of thenecking zone When r 0 the maximum Rσ value isobtained

Rσ 13

+ ln 1 +a

2R1113874 1113875 (2)

During high-temperature tensile testing the stress tri-axiality Rσ is the highest in the center part (r 0) of thenecking region and the holes form in the center for themaximum stress triaxiality and then connection grows andthen diffuse to the surface of the sample eventually leadingto fracture of the sample ere is a strong correlation be-tween stress triaxiality and crack initiation in sample frac-ture As shown in Figure 5(e) large and deep interconnectedcracks appear in the center of the necking region When thecrack occurs the axial tensile stress plays a leading role in thecrack propagation and the crack propagates along the di-rection of the maximum tensile stress

e initial central stress triaxiality Rσ can be calculatedby inserting the initial radius r and the initial notch radiusR of the minimum section into formula (1) e initialminimum radius r of all notched samples is equal to 3mm

(a) (b) (c) (d) (e)

Figure 1 Process of crack formation (a) inclusions (b) cavity nucleation (c) cavity growth (d) cavity necking and (e) cavity coalescence



16

R1

4896 4527

1415

(a)

oslash10

oslash6M10

16

1415

R1 R2 R4 R6

(b)


Time t


2min holding


quenching



mpe

ratu

re T

Coolingrate 10degCs

(a)

Time t


2min holding




mpe

ratu

re T

Coolingrate 10degCs

(b)



One-way tension

Z

2a

rθ

R






200μm

(a)

200μm

(b)

50μm

Recrystallizedgrain

(c)

50μm

Microscopic void

(d)

50μm

Crack initiation

(e)

50μm

Split of the grains

(f )











ε = 02ε = 04

ε = 054

ε = 06

ε = 08

ε = 097


02

04


05406

08

097ndash20

0

20

40

60

80

100

120

140

160

True

stre

ss (M

pa)

01 02 03 04 05 06 07 08 09 10 11 1200True strain



le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N


1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S


Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion


0


04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280



(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)










038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





16

R1

4896 4527

1415

(a)

oslash10

oslash6M10

16

1415

R1 R2 R4 R6

(b)


Time t


2min holding


quenching



mpe

ratu

re T

Coolingrate 10degCs

(a)

Time t


2min holding




mpe

ratu

re T

Coolingrate 10degCs

(b)



One-way tension

Z

2a

rθ

R






200μm

(a)

200μm

(b)

50μm

Recrystallizedgrain

(c)

50μm

Microscopic void

(d)

50μm

Crack initiation

(e)

50μm

Split of the grains

(f )











ε = 02ε = 04

ε = 054

ε = 06

ε = 08

ε = 097


02

04


05406

08

097ndash20

0

20

40

60

80

100

120

140

160

True

stre

ss (M

pa)

01 02 03 04 05 06 07 08 09 10 11 1200True strain



le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N


1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S


Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion


0


04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280



(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)










038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







200μm

(a)

200μm

(b)

50μm

Recrystallizedgrain

(c)

50μm

Microscopic void

(d)

50μm

Crack initiation

(e)

50μm

Split of the grains

(f )











ε = 02ε = 04

ε = 054

ε = 06

ε = 08

ε = 097


02

04


05406

08

097ndash20

0

20

40

60

80

100

120

140

160

True

stre

ss (M

pa)

01 02 03 04 05 06 07 08 09 10 11 1200True strain



le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N


1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S


Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion


0


04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280



(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)










038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls












ε = 02ε = 04

ε = 054

ε = 06

ε = 08

ε = 097


02

04


05406

08

097ndash20

0

20

40

60

80

100

120

140

160

True

stre

ss (M

pa)

01 02 03 04 05 06 07 08 09 10 11 1200True strain



le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N


1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S


Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion


0


04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280



(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)










038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




le

CAtomic percentage

OCS

NFeCaNaMgAl

52292963

685560

186171105076025

Ca

O

N


1 2 3 4 5 6 7

Na Al S

S

CaCa Fe Fe

Inclusion


1 2 3 4 5 6 87

S


Ca 2893Fe 967C 869S 470

Al 049

Fe

Fe

Fe

O

Ca

C

AlAlCa

Ca

S

Inclusion


0


04 05

40

80True

stre

ss (M

Pa)

120

160

200

240

280



(a)

True strain00 01 02 03 04 05

850degC950degC

1050degC1150degC

0

40

80

120

160

200

240

280

True

stre

ss (M

Pa)

(b)










038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls











038


Frac

ture

stra

in

1050 1150

042

046

050

054

058









50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








50μm

(a)

50μm

(b)

50μm

(c)

50μm

(d)



(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




(a) (b)

(c) (d)


(a) (b)

(c) (d)



4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




4 Conclusions





Data Availability






Acknowledgments



References


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




influence of strain and stress triaxiality on the fracture

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