effectofcoldworkingonthedrivingforceofthecrackgrowth ... · 2020. 8. 25. · mechanical parameters...

Research ArticleEffect of Cold Working on the Driving Force of the Crack Growthand Crack Growth Rate of Welded Joints under One Overload

Hongliang Yang 1 He Xue 2 Fuqiang Yang 2 and Shuai Wang 23

1Center of Engineering Training Xirsquoan University of Science and Technology Xirsquoan 710054 China2School of Mechanical Engineering Xirsquoan University of Science and Technology Xirsquoan 710054 China3College of Engineering Design and Physical Sciences Brunel University London Uxbridge UB8 3PH UK

Correspondence should be addressed to Hongliang Yang yanghongliangxusteducn and He Xue xue_hehotmailcom

Received 26 June 2020 Accepted 4 August 2020 Published 25 August 2020

Guest Editor Guian Qian

Copyright copy 2020 Hongliang Yang et al )is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

To understand the effect of cold working of welding heat-affected zone on the driving force of the crack growth and crack growthrate of stress corrosion cracking (SCC) near the welding fusion line the finite element simulation method was used to analyze theeffect of cold working on the tensile stress of the crack tip at different locations near the fusion line On this basis the strain rate ofthe crack tip in the Ford-Andresen model is replaced by the creep rate of the crack tip and the creep rate of the crack tip is used asdriving force for the crack growth of SCC )e effect of the cold working level at the heat-affected zone on the driving force of thecrack growth and crack growth rate of SCC are analyzed and driving force of the crack growth and crack growth rate of SCC afterone overload was compared

1 Introduction

)ere are significant differences in mechanical properties ofmaterials on the two sides of the fusion line of welded joints innuclear power plants )e material composition and orga-nization of the weld area after welding are extremely complexAt the same time in the process of welding cooling due torapid decrease in the temperature of the weld zone whichcauses cold shrinkage it will have a tensile effect on materialsin the heat-affected area and thematerials in the heat-affectedarea will have plastic deformation in different levels under thetensile effect leading to different levels of cold working in theheat-affected zone [1 2] Changes of mechanical properties inthe heat-affected zone will affect distribution of stress andstrain fields at the crack tip in different areas of welded jointswhich can affect the driving force of the crack growth andcrack growth rate )e SCC crack of welded joints in nuclearpower plants is mainly in the weld and heat-affected zone nearthe fusion line [3] In the service of material the phenomenonthat load suddenly increases in a short time and exceeds yieldstress of the material and then falls back to normal load is

called one overload One overload will occur due to a suddenincrease of load when nuclear power pipelines and pressurevessels in service for example sudden increase of load causedby earthquake Although duration of the one overload processis short one overload also occurs occasionally in nuclearpower plants One overload will cause mechanical parametersof the microzone at the crack tip of SCC to change andhardening of the crack tip will occur One overload will causemechanical parameters of the microregion at the SCC cracktip to change and hardening of the crack tip will occur SCCexperiments have found that when loading amplitude changessuddenly or experiment is interrupted and restarted the SCCcrack growth is different [4 5] )erefore it is of practicalengineering significance to study cold working on the SCCdriving force of the crack growth and crack growth rate ofwelded joints in nuclear power plants under one overload

2 Theory of EAC Driving Force

Ford and Andresen put forward the theory of slip disso-lutionfilm fracture and on the basis the FordndashAndresen

HindawiAdvances in Materials Science and EngineeringVolume 2020 Article ID 4972589 9 pageshttpsdoiorg10115520204972589

model [6] was proposed to predict the crack growth rate ofSCC which is also widely accepted and applied in theprediction model of SCC crack growth in a nuclear powerhigh temperature water environment)e SCC crack growthrate dadt can be expressed by

da

dt

M

ρ middot z middot Fmiddot

i0

1 minus m

t0 middot _εctεf

1113888 1113889

m

minus m middott0 middot _εctεf

1113888 11138891113888 11138891113890 1113891

(1)

where M is the atomic weight ρ is the density z is thenumber of equivalents exchanged F is Faradayrsquos constantmis the current attenuation curve exponent i0 is the oxi-dization current density t0 is the duration of constant εf isthe fracture strain of the oxide film at the crack tip and _εct isthe strain rate

If m≪1 and tf≫ t0 (1) can be simplified to

da

dt

M


i01 minus m

t0εf

1113888 1113889

m

middot _εct( 1113857m

(2)

From (2) it can be seen that the strain rate of the crack tipas a single mechanical influencing factor the strain rate of thecrack tip can be regarded as driving force of crack growth thestrain rate of crack tip is large the driving force of crackgrowth is large and the crack growth rate is also large

SCC crack growth behavior can be regarded as a slowprocess of oxide film rupture and regeneration under theinteraction of mechanics materials and corrosive environ-ment at the crack tip)is process is consistent with the creepprocess At the same time the stress at the crack tip is constantfor a long period of time which meets the creep condition ofmetal Studies have shown that creep has an important effecton the grain boundary slip at the crack tip It can be con-sidered that during crack growth of SCC rupture of the oxidefilm is due to grain boundary slippage caused by creep ex-ceeding the rupture strength of the oxide film )erefore thecreep rate of the crack tip instead of the strain rate of the cracktip is used as the driving force for crack growth

_εcr _εct (3)

Nuclear power structural materials work at high tem-perature and high pressure the microregion of the crack tipis a high stress area and the creep rate usually changesexponentially with stress )erefore the creep rate of thecrack tip is described by the Norton model which is ex-ponential to the stress as shown in the following equation

_εcr AσR (4)

where _εcr is the creep rate at the crack tip σ is the stress R isthe creep stress exponent ofmaterialA is the Norton constantof material R 398 and A 1153times10minus15MPaminus1middothminus1

According to the FordndashAndresenmodel the quantitativeprediction model of the SCC crack growth rate can beexpressed as

_a ka M


i01 minus m

t0εf

1113888 1113889

m

middot AσR1113872 1113873

m (5)

κa can be calculated by the values of standard electro-chemical and material parameters [7] and κa 8643times10minus4

3 Finite Element Modeling

31GeometricModel Taking welded joints in nuclear powerplants as the research object in finite element analysis of thedriving force of the crack growth and crack growth rate ofstress corrosion cracking (SCC) compact tensile specimen(1T-CT) is used and the geometric dimension of thespecimen is shown in Figure 1 )e initial precrack lengtha 2mm During the SCC process a dense oxide film isformed at the crack tip of 316L SS)e thickness of the oxidefilm varies according to the corrosion environment )ethickness of the oxide film is generally 01 μmsim2 μm [8] Inthe study the geometric model of the oxide film at the cracktip of SCC is simplified as shown in Figure 1 and thethickness of the oxide film is 05 μm

According to the location of the SCC crack in weldedjoints in nuclear power plants SCC cracks are easily gen-erated in the heat-affected zone and the fusion line and coldworking at heat effects can occur due to the welding process

)e distribution of cracks in different positions of weldedjoint is shown in Figure 1 When a crack initiates at theinterface the crack coincided with fusion line and two sidesof the crack are nickel-based 600 and 316L SS When a crackinitiates in the heat-affected zone the distance d between thecrack and fusion line is 5 μm and 15 μm respectively

32 Mechanical Model )e structure material for nuclearpower pipelines is 316L SS and material for welds is nickel-based 600 Both are power hardening materials )ereforethe RambergndashOsgood (RndashO) relationship is selected as theconstitutive equation

εεy

σσy

+ ασσy

1113888 1113889

n

(6)

)e heat-affected zone of the welded joint has a differentlevel of cold working due to cold shrinkage of the weld Tosimulate the different level of cold working in the heat-affectedzone tensile experiments were used to 316L SS by 10 and20 respectively to obtain mechanical parameters of materialwith a different level of cold working Youngrsquos modulus of theoxide film is about 70 of metal materialrsquos [9] )ereforeYoungrsquos modulus of the oxide film at the crack tip is 140GPaand the Poisson ratio of the oxide film is 03 In experimentstress intensity factor KI 30MPamiddotm12 [10] It is assumed thatnickel-based 600 and 316L SS have the same creep parameters)e mechanical parameters of materials are shown in Table 1

33 Finite Element Model Using the numerical simulationmethod the finite element model is as shown in Figure 2)e plane strain model is adopted in finite element analysisbecause the crack in the nuclear power pipeline conforms tothe plane strain model )e crack tip adopts a circular arcshape )e submodel technology is used to refine the cracktip to obtain more accurate simulation data Both the global

2 Advances in Materials Science and Engineering

model and submodel use an 8-node quadratic plane strainelement (CPE8) )e discrepancy of material properties inthe finite element model is marked in Figure 1

4 Analysis of Tensile Stress at the Crack Tip

One overload occurs in service and the microregion at thecrack tip will harden)e hardening of the microregion at thecrack tip will affect the distribution of stress field at the cracktip )e tensile stress direction is consistent with the externalload direction and it is perpendicular to the crack openingdirection which can truly reflect stress at the crack tip)erefore distribution of tensile stress at the crack tip is

mainly analyzedWhen SCC crack is on the fusion line tensilestress at the crack tip with and without hardening is as shownin Figure 3 It can be seen from the figure that tensile stress atthe crack tip with hardening is greater Because thematerial inthe microregion at the crack tip is hardened and plasticitybecomes worse it is not easy to deform and release stress)emechanical properties of the two sides of the crack are dif-ferent and the distribution of tensile stress is also asymmetric

Cold working is generated due to cold shrinkage of theheat-affected zone )e effect of cold working of 316L SS inthe heat-affected zone on tensile stress at the crack tip on thefusion line is shown in Figure 4 It can be seen from thefigure that the higher the cold working level of 316L SS in the

06W

06W

027

5W0

275W

2-Oslash 025W

Fusion line

a

d

c

W125W

316L

600 alloy

a

b Path

0deg

180degOxide film

Figure 1 Sample geometry and schematic diagram at the crack tip (W 50mm c 05W a 2mm and b 1 μm)

Table 1 Mechanical parameters of materials

Mechanical parameters 600 alloy 316L-CW0 316L-CW10 316L-CW20 Oxide filmYield strength (MPa) 436 [11] 238 416 589 mdashYoungrsquos modulus (GPa) 1895 195 193 189 140 [9]Poissonrsquos ratio 0286 03 03 03 03Hardening exponent 6495 46 69 97 mdashHardening coefficient 3075 168 096 067 mdash

(a) (b)

Figure 2 Finite element model

Advances in Materials Science and Engineering 3

heat-affected zone the greater the tensile stress at the cracktip and tensile stress is more and more biased to the 316L SSside as the cold working level of 316L SS increases Tensilestress is more andmore concentrated on the side with higherlevel of cold working because the metal with higher level ofcold working is less plastic and less prone to deformation

When the crack is in the heat-affected zone the effect ofcold working of material in the heat-affected zone on tensilestress is as shown in Figure 5 It can be seen that when d 5μmand d 15μm and there is no cold working in the heat-affectedzone the yield strength and hardening exponent of 600 alloy arehigher than that of 316L SS and so tensile stress shifts towardthe 600 alloy As the level of cold working in the heat-affectedzone increases the tensile stress at the crack tip shifts toward316L SS Because the level of cold working of 316L SS is higherthan that of nickel-based alloys it can be seen that tensile stress

will shift to the side where the material is at high level of coldworking When the level of cold working is higher tensile stressis also relatively greater Comparing the distribution tensilestress at the crack tip with d 5μmand d 15μm it can be seenthat when the crack tip is closer to the weld the tensile stress atthe crack tip is greatly affected by mechanical parameters of 600alloy As d increases the crack tip gradually moves away fromweld and tensile stress at the crack tip is greatly affected by themechanical properties of 316L SS in the heat-affected zone

5 EffectofColdWorkingontheDrivingForceofCrack Growth

51 Effect of Cold Working on the Driving Force of CrackGrowth on the Fusion Line On the one hand hardening atthe crack tip will improve mechanical properties of the crack

2000 600 alloy

316L

S S22 (MPa)

175017001650160015500

(a)

2000S S22 (MPa)

175017001650160015500

600 alloy

316L

(b)

Figure 3 Comparison of tensile stress between the crack tip with and without hardening (a) Without hardening (b) With hardening

600 alloy2000175017001650160015500

316L

S S22(MPa)

(a)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(b)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(c)

Figure 4 Effect of cold working on tensile stress (a) CW 0 (b) CW 10 (c) CW 20


tip When external load is constant and the crack tip ishardened the plasticity of the crack tip decreases and thestress of the crack tip increases On the other hand due tothe restraint of the crack tip hardening of the crack tip willgenerate residual compressive stress at the crack tip)erefore only considering hardening of the crack tipwithout considering the residual stress when the crack tip ishardened the tensile stress is greater When the hardening atthe crack tip and residual stress are considered at the sametime the effective stress at the crack tip should be thecombination of tensile stress and residual stress )e ef-fective stress is used in the calculation of the driving forceand crack growth rate When the crack occurs on the fusionline the 0degndash90deg area of the crack tip belongs to the weld areaand the material is nickel-based 600 and the 90degndash180deg areabelongs to the heat-affected area and material is 316L SS Tostudy the distribution of the creep rate at different distancesfrom crack tips three paths from the crack tip r 0 μmr 02 μm and r 04 μm were chosen and analyzed

When the crack tip is not hardened and the heat-affectedzone is not cold-worked the creep rate at the crack tip is asshown in Figure 6 It can be seen from the figure that thecloser to the crack tip the greater the creep rate of crack tipand the greater the driving force for crack growth )e valueand distribution of the creep rate at the crack tip are affectedby mechanical properties of the weld and heat-affected zone)e yield strength and hardening exponent of the nickel-based 600 in the weld zone are higher than those of 316L SSin the heat-affected zone and the maximum value of thecreep rate at the crack tip is biased toward the weld material

When the crack tip is hardened and the heat-affectedzone is not cold-worked the distribution of the creep rate at

the crack tip is as shown in Figure 7 It can be seen from thefigure that the closer to the crack tip the higher the creeprate )e maximum value of the creep rate at the crack tipdid not appear at 90deg in front of the crack tip but was biasedtowards the weld zone

)e distribution of the creep rate at the crack tip with andwithout hardening is shown in Figure 8 It can be seen that thecreep rate at the crack tip with hardening is smaller )is isbecause although the hardening at the crack tip increases tensilestress it also generates residual compressive stress )e residualcompressive stress needs to be overcomewhen reloading whichwill temporarily reduce the stress at the crack tip

)e effect of cold working on the creep rate at the cracktip is shown in Figure 9 It can be seen from the figure thatthe value of the maximum creep rate appears in weld whenthere is no cold working in the heat-affected zone As thelevel of cold working in the heat-affected zone increases themaximum value of the creep rate will shift When themechanical properties of material in the heat-affected zoneare higher than those of the material in the weld zone themaximum value of the creep rate appears in the heat-affectedzone and the maximum value of creep rate increases As thelevel of cold working in the heat-affected zone further in-creases the maximum value of the creep rate also increasesrapidly and the maximum value of the creep rate is still inthe heat-affected zone )erefore the creep rate tends to beon the side of the material with higher level of cold working

52 Effect of Cold Working on the Driving Force of CrackGrowth in theHeat-AffectedZone )e creep rate at the cracktip of cold working 316L SS in the heat-affected zone is

600 alloy

2000175017001650160015500

316LS S22(MPa)

(a)

600 alloy

2000175017001650160015500

316LS S22(MPa)

(b)

2000175017001650160015500

S S22(MPa)

(c)

2000175017001650160015500

S S22(MPa)

(d)

Figure 5 Effect of cold working on tensile stress at different distances from the fusion line (a) d 5 μm 316L-CW0 (b) d 5 μm 316L-CW10 (c) d 15 μm 316L-CW0 (d) d 15 μm 316L-CW10


shown in Figure 10 when the crack is in the heat-affectedzone It can be seen that the higher the level of cold workingthe greater the creep rate and the greater the driving force forcrack growth )e maximum value of the creep rate isgradually away from the weld zone and the maximum valueof the creep rate increases rapidly )at is the higher thelevel of cold working the greater the driving force for crackgrowth

)e distribution of the creep rate at the crack tip isshown in Figure 11 when the distance between the fusionline and crack tip is different It can be seen from the figurethat the crack is closer to the weld fusion line the creep rateis greatly affected by the weld material and the maximumvalue of the creep rate is also biased toward the weld zoneWhen the crack is far away from the weld the creep rate ismainly affected by mechanical parameters of 316L SS in the

heat-affected zone and the effect of mechanical properties inweld gradually decreases

6 Effect of Cold Working on the CrackGrowth Rate

)e effect of cold working of 316L SS in the heat-affectedzone on the crack growth rate is shown in Figure 12 whenthe crack is on the fusion line of the weld It can be seenfrom the figure that with the higher level of cold working of316L SS in the heat-affected zone the maximum value ofthe crack growth rate is gradually transferred from the weldto the heat-affected zone )e maximum value of the crackgrowth rate is biased toward the side of metal with higherlevels of cold working )e higher level of cold working in

0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)

r = 0micromr = 02micromr = 04microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

Figure 7 Creep rate of the crack tip with hardening

0 30 60 90 120 150 180

Without hard coreWith hard core

600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

Figure 8 Comparison of the creep rate of the crack tip with andwithout hardening

0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

Figure 9 Effect of cold working of the heat-affected zone on thecreep rate

0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

Figure 6 Creep rate of the crack tip without hardening


the heat-affected zone the greater the crack growth rateand the crack growth rate increases rapidly with the in-crease of the level of cold working )e cold working ofmaterial increases the crack growth rate of SCC which is anunfavorable factor

Figure 13 shows the comparison of the crack growth rateat the crack tip with hardening and without hardening whenthe crack is on the fusion line It can be seen from the figurethat the crack growth rate is smaller when the crack tip ishardened and the hardening at the crack tip has a greatereffect on the crack growth rate )e crack tip with hardeningreduces the crack growth rate within a certain range whichmay be a favorable factor

When crack appears in the heat-affected zone at a dis-tance d 5 μm from the fusion line the effect of coldworking in the heat-affected zone on the crack growth rate is

as shown in Figure 14 It can be seen that as the level of coldworking of 316L SS in heat-affected zone increases themaximum value of the crack growth rate gradually movesaway from the weld zone )e higher the level of coldworking of 316L SS the greater the crack growth rate It canbe seen that cold working of material increases the crackgrowth rate

Figure 15 compares the crack growth rate in the heat-affected zone when the distance between the crack andfusion line is different It can be seen from the figure that thegreater the distance between the crack tip and fusion line thegreater the crack growth rate )is is because mechanicalproperties of the metal in the heat-affected zone are higherthan those of the weld metal At this time the crack growthrate is greatly affected by the mechanical properties of themetal in the heat-affected zone

0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

Figure 10 Effect of cold working on the creep rate

0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12

d = 5micromd = 15microm

Angle θ (deg)

Figure 11 Effect of distance of the crack from the fusion line on thecreep rate

0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)

Figure 12 Effect of cold working on the crack growth rate on thefusion line

00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)

a = 2mmKI = 30MPamiddotm12

r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)

Figure 13 Comparison of the crack growth rate between the cracktip with and without hardening


7 Conclusions

(1) Using the creep rate of the crack tip to replace thestrain rate of the crack tip in the FordndashAndresenmodel the driving force of the crack growth andcrack growth rate calculation models are optimizedwhich is more convenient for practical application

(2) )e mechanical properties of the metal on both sidesof the fusion line are different and the tensile stress isdifferent )e tensile stress will be biased toward theside of metal with a higher level of cold working Asthe level of cold working in the heat-affected zoneincreases tensile stress is obviously biased towardsthe heat-affected zone and the tensile stress increasesas the level of cold working increases

(3) Both the driving force of the crack growth and crackgrowth rate increase with the level of cold working ofmaterial in the heat-affected zone and the maximumvalue of the crack growth driving force and crackgrowth rate are biased toward the side of the metalwith a high level of cold working )e farther thecrack tip is from the fusion line the smaller the effectof the crack growth driving force and crack growthrate on mechanical properties of weld metal and thegreater the effect on mechanical properties of metalin the heat-affected zone

(4) One overload will cause the crack tip of SCC toharden )e hardening of the crack tip not onlyincreases the tensile stress to a certain extent but alsogenerates residual compressive stress )erefore thedriving force of the crack growth and crack growthrate is reduced to a certain extent

Data Availability

1 Previously reported Youngrsquos modulus and Poissonrsquos ratioof the oxide film were used to support this study and areavailable at httpsdoiorg101016S00406090(01)01464-X)ese prior studies (and datasets) are cited at relevant placeswithin the text as references [9] 2 Mechanical parameters ofnickel-based alloy 600 were used to support this study andare available at httpsdoiorg101016jijpvp201904005)ese prior studies (and datasets) are cited at relevantplaces within the text as references [11] 3 )e data ofmechanical parameters of 316L SS with a different level ofcold working are obtained by the research group through thetensile test 4 )e numerical simulation data at the crack tipof 316L stainless steel used to support the findings of thisstudy are included in the article

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is work was financially supported by the InternationalExchanges Programme Scheme project by the NationalNatural Science Foundation of China and the Royal Society(51811530311) and National Natural Science Foundation ofChina (51475362)

References

[1] K Chen D Du W Gao et al ldquoEffect of cold work on thestress corrosion cracking behavior of Alloy 690 in supercriticalwater environmentrdquo Journal of Nuclear Materials vol 498pp 117ndash128 2018

[2] J Chen Z Lu Q Xiao et al ldquo)e effects of cold rollingorientation and water chemistry on stress corrosion crackingbehavior of 316L stainless steel in simulated PWR waterenvironmentsrdquo Journal of Nuclear Materials vol 472 pp 1ndash12 2016

[3] G J Li Research on Performance of Dissimilar Metal WeldedParts SA508-52M-316L in Simulated PWR Primary Water

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

Figure 14 Effect of cold working on the crack growth rate of theheat-affected zone

316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

Figure 15 Comparison of the crack growth rate at differentdistances from the fusion line


Environment Shanghai Institute of Materials ShanghaiChina 2011

[4] H Xue Z Li Z Lu and T Shoji ldquo)e effect of a single tensileoverload on stress corrosion cracking growth of stainless steelin a light water reactor environmentrdquo Nuclear Engineeringand Design vol 241 no 3 pp 731ndash738 2011

[5] C Bichler and R Pippan ldquoEffect of single overloads in ductilemetals a reconsiderationrdquo Engineering Fracture Mechanicsvol 74 no 8 pp 1344ndash1359 2007

[6] P L Andresen and F Peter Ford ldquoLife prediction bymechanistic modeling and system monitoring of environ-mental cracking of iron and nickel alloys in aqueous systemsrdquoMaterials Science and Engineering A vol 103 no 1pp 167ndash184 1988

[7] Q J Peng J Kwon and T Shoji ldquoDevelopment of a fun-damental crack tip strain rate equation and its application toquantitative prediction of stress corrosion cracking of stainlesssteels in high temperature oxygenated waterrdquo Journal ofNuclear Materials vol 324 no 1 pp 52ndash61 2004

[8] Z Wang and Y Takeda ldquoAmorphization and structuralmodification of the oxide film of Ni-based alloy by in-situ Hcharging in high temperature high pressure water environ-mentrdquo Corrosion Science vol 166 2020

[9] P Goudeau P O Renault P Villain et al ldquoCharacterizationof thin film elastic properties using X-ray diffraction andmechanical methods application to polycrystalline stainlesssteelrdquo Bin Solid Films vol 398-399 pp 496ndash500 2001

[10] K Chen J Wang D Du P L Andresen and L Zhang ldquodKda effects on the SCC growth rates of nickel base alloys inhigh-temperature waterrdquo Journal of Nuclear Materialsvol 503 pp 13ndash21 2018

[11] K Zhao H Xue F Yang and L Zhao ldquoProbability predictionof crack growth rate of environmentally assisted cracks ofnickel-based alloys based on Latin hypercube samplingrdquoInternational Journal of Pressure Vessels and Piping vol 172pp 391ndash396 2019


model [6] was proposed to predict the crack growth rate ofSCC which is also widely accepted and applied in theprediction model of SCC crack growth in a nuclear powerhigh temperature water environment)e SCC crack growthrate dadt can be expressed by

da

dt

M


i0

1 minus m

t0 middot _εctεf

1113888 1113889

m

minus m middott0 middot _εctεf

1113888 11138891113888 11138891113890 1113891

(1)

where M is the atomic weight ρ is the density z is thenumber of equivalents exchanged F is Faradayrsquos constantmis the current attenuation curve exponent i0 is the oxi-dization current density t0 is the duration of constant εf isthe fracture strain of the oxide film at the crack tip and _εct isthe strain rate

If m≪1 and tf≫ t0 (1) can be simplified to

da

dt

M


i01 minus m

t0εf

1113888 1113889

m

middot _εct( 1113857m

(2)

From (2) it can be seen that the strain rate of the crack tipas a single mechanical influencing factor the strain rate of thecrack tip can be regarded as driving force of crack growth thestrain rate of crack tip is large the driving force of crackgrowth is large and the crack growth rate is also large

SCC crack growth behavior can be regarded as a slowprocess of oxide film rupture and regeneration under theinteraction of mechanics materials and corrosive environ-ment at the crack tip)is process is consistent with the creepprocess At the same time the stress at the crack tip is constantfor a long period of time which meets the creep condition ofmetal Studies have shown that creep has an important effecton the grain boundary slip at the crack tip It can be con-sidered that during crack growth of SCC rupture of the oxidefilm is due to grain boundary slippage caused by creep ex-ceeding the rupture strength of the oxide film )erefore thecreep rate of the crack tip instead of the strain rate of the cracktip is used as the driving force for crack growth

_εcr _εct (3)

Nuclear power structural materials work at high tem-perature and high pressure the microregion of the crack tipis a high stress area and the creep rate usually changesexponentially with stress )erefore the creep rate of thecrack tip is described by the Norton model which is ex-ponential to the stress as shown in the following equation

_εcr AσR (4)

where _εcr is the creep rate at the crack tip σ is the stress R isthe creep stress exponent ofmaterialA is the Norton constantof material R 398 and A 1153times10minus15MPaminus1middothminus1

According to the FordndashAndresenmodel the quantitativeprediction model of the SCC crack growth rate can beexpressed as

_a ka M


i01 minus m

t0εf

1113888 1113889

m

middot AσR1113872 1113873

m (5)

κa can be calculated by the values of standard electro-chemical and material parameters [7] and κa 8643times10minus4

3 Finite Element Modeling

31GeometricModel Taking welded joints in nuclear powerplants as the research object in finite element analysis of thedriving force of the crack growth and crack growth rate ofstress corrosion cracking (SCC) compact tensile specimen(1T-CT) is used and the geometric dimension of thespecimen is shown in Figure 1 )e initial precrack lengtha 2mm During the SCC process a dense oxide film isformed at the crack tip of 316L SS)e thickness of the oxidefilm varies according to the corrosion environment )ethickness of the oxide film is generally 01 μmsim2 μm [8] Inthe study the geometric model of the oxide film at the cracktip of SCC is simplified as shown in Figure 1 and thethickness of the oxide film is 05 μm

According to the location of the SCC crack in weldedjoints in nuclear power plants SCC cracks are easily gen-erated in the heat-affected zone and the fusion line and coldworking at heat effects can occur due to the welding process

)e distribution of cracks in different positions of weldedjoint is shown in Figure 1 When a crack initiates at theinterface the crack coincided with fusion line and two sidesof the crack are nickel-based 600 and 316L SS When a crackinitiates in the heat-affected zone the distance d between thecrack and fusion line is 5 μm and 15 μm respectively

32 Mechanical Model )e structure material for nuclearpower pipelines is 316L SS and material for welds is nickel-based 600 Both are power hardening materials )ereforethe RambergndashOsgood (RndashO) relationship is selected as theconstitutive equation

εεy

σσy

+ ασσy

1113888 1113889

n

(6)

)e heat-affected zone of the welded joint has a differentlevel of cold working due to cold shrinkage of the weld Tosimulate the different level of cold working in the heat-affectedzone tensile experiments were used to 316L SS by 10 and20 respectively to obtain mechanical parameters of materialwith a different level of cold working Youngrsquos modulus of theoxide film is about 70 of metal materialrsquos [9] )ereforeYoungrsquos modulus of the oxide film at the crack tip is 140GPaand the Poisson ratio of the oxide film is 03 In experimentstress intensity factor KI 30MPamiddotm12 [10] It is assumed thatnickel-based 600 and 316L SS have the same creep parameters)e mechanical parameters of materials are shown in Table 1

33 Finite Element Model Using the numerical simulationmethod the finite element model is as shown in Figure 2)e plane strain model is adopted in finite element analysisbecause the crack in the nuclear power pipeline conforms tothe plane strain model )e crack tip adopts a circular arcshape )e submodel technology is used to refine the cracktip to obtain more accurate simulation data Both the global







06W

06W

027

5W0

275W

2-Oslash 025W

Fusion line

a

d

c

W125W

316L

600 alloy

a

b Path

0deg

180degOxide film




(a) (b)








2000 600 alloy

316L

S S22 (MPa)

175017001650160015500

(a)

2000S S22 (MPa)

175017001650160015500

600 alloy

316L

(b)


600 alloy2000175017001650160015500

316L

S S22(MPa)

(a)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(b)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(c)










600 alloy

2000175017001650160015500

316LS S22(MPa)

(a)

600 alloy

2000175017001650160015500

316LS S22(MPa)

(b)

2000175017001650160015500

S S22(MPa)

(c)

2000175017001650160015500

S S22(MPa)

(d)








0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)


Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180


600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot








0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8


















06W

06W

027

5W0

275W

2-Oslash 025W

Fusion line

a

d

c

W125W

316L

600 alloy

a

b Path

0deg

180degOxide film




(a) (b)








2000 600 alloy

316L

S S22 (MPa)

175017001650160015500

(a)

2000S S22 (MPa)

175017001650160015500

600 alloy

316L

(b)


600 alloy2000175017001650160015500

316L

S S22(MPa)

(a)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(b)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(c)










600 alloy

2000175017001650160015500

316LS S22(MPa)

(a)

600 alloy

2000175017001650160015500

316LS S22(MPa)

(b)

2000175017001650160015500

S S22(MPa)

(c)

2000175017001650160015500

S S22(MPa)

(d)








0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)


Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180


600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot








0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8


















2000 600 alloy

316L

S S22 (MPa)

175017001650160015500

(a)

2000S S22 (MPa)

175017001650160015500

600 alloy

316L

(b)


600 alloy2000175017001650160015500

316L

S S22(MPa)

(a)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(b)

600 alloy2000175017001650160015500

316L

S S22(MPa)

(c)










600 alloy

2000175017001650160015500

316LS S22(MPa)

(a)

600 alloy

2000175017001650160015500

316LS S22(MPa)

(b)

2000175017001650160015500

S S22(MPa)

(c)

2000175017001650160015500

S S22(MPa)

(d)








0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)


Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180


600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot








0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8




















600 alloy

2000175017001650160015500

316LS S22(MPa)

(a)

600 alloy

2000175017001650160015500

316LS S22(MPa)

(b)

2000175017001650160015500

S S22(MPa)

(c)

2000175017001650160015500

S S22(MPa)

(d)








0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)


Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180


600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot








0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8


















0 30 60 90 120 150 180000

001

002

003

600 alloy 316L

Angle θ (deg)


Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180


600 alloy 316L

000

001

002

003

Angle θ (deg)

r = 0microm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

002

004

006

008

316L-CW0316L-CW10316L-CW20

600 alloy 316L

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 180000

001

002

003


Angle θ (deg)

600 alloy 316LCrac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot








0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8


















0 30 60 90 120 150 180000

002

004

006

008

KI = 30MPamiddotm12

316L-CW0316L-CW10316L-CW20

600 alloy 316L

a = 2mmd = 5microm

Angle θ (deg)

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot


0 30 60 90 120 150 1800004

0008

0012

0016

0020

316L600 alloy

a = 2mm

Crac

k tip

cree

p str

ain

rate

ε cr (

hndash1 )

middot

KI = 30MPamiddotm12


Angle θ (deg)


0 30 60 90 120 150 18000

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

Crac

k gr

owth

rate

da

dt (m

ms

)

316L600 alloy

r = 0μm

a = 2mm

KI = 30MPamiddotm12

Angle θ (deg)


00

20 times 10ndash9

40 times 10ndash9

60 times 10ndash9

80 times 10ndash9

316L600 alloy


0 30 60 90 120 150 180Angle θ (deg)


r = 0μm

Crac

k gr

owth

rate

da

dt (m

ms

)



7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8













7 Conclusions





Data Availability




Acknowledgments


References




00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8

316L-CW0316L-CW10316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mmd = 5μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)


316L-CW20

600 alloy 316L

KI = 30MPamiddotm12

a = 2mm

d = 5μmd = 15μm

r = 0μm

0 30 60 90 120 150 180Angle θ (deg)

Crac

k gr

owth

rate

da

dt (m

ms

)

00

50 times 10ndash9

10 times 10ndash8

15 times 10ndash8

20 times 10ndash8













effectofcoldworkingonthedrivingforceofthecrackgrowth ... · 2020. 8. 25. · mechanical parameters...

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