Research ArticleEffects of Grain Orientation on Stress State near GrainBoundary of Austenitic Stainless Steel Bicrystals

Fu-qiang Yang 1 He Xue2 Ling-yan Zhao1 and Xiu-Rong Fang2

1School of Science Xirsquoan University of Science and Technology Xirsquoan 710054 China2School of Mechanical Engineering Xirsquoan University of Science and Technology Xirsquoan 710054 China

Correspondence should be addressed to Fu-qiang Yang yang_afreet163com

Received 1 November 2017 Accepted 22 November 2017 Published 1 February 2018

Academic Editor Pavel Lejcek

Copyright copy 2018 Fu-qiang Yang et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e stress state at the crack tip of structural components in nuclear power plants used in the SCC quantitative predictionmodels is based on the assumption that the polycrystalline material is isotropic and homogeneous at present However thecrystals in polycrystalline materials are anisotropic with different orientations which would induce a nonuniform stress tocause the initiation and propagation of SCC By using a finite element method the elastic responses of anisotropic behaviors ofaustenitic stainless steel bicrystals are studied e results indicate that the stress distribution near GBs depends strongly on thecrystal orientation A larger Mises stress concentration exists on the GB with larger stiffness along the load directioneMisesstress difference is higher in the bicrystal with bigger elastic modulus difference of two neighboring grains along the tensile axisIn the bicrystal with GB perpendicular to the tensile axis the grain orientation has little effects on the Mises stress far from theGB in both grains e strain inconsistency in bicrystals is affected by the mismatch of two neighboring grains e larger theelastic modulus differences between two neighboring grains caused by misorientation the larger the strain inconsistency inthe bicrystal

1 Introduction

Stress corrosion cracking (SCC) of structural componentsis one of the major factors that affect the reliability andintegrity of the nuclear power plants (NPPs) Indeed in-tergranular stress corrosion cracking (IGSCC) has oc-curred in many internal components made up of stainlesssteel nickel alloy and their weld metals [1ndash4] eslipdissolution-oxidation model has been widely acceptedas a reasonable description of SCC in an oxygenatedaqueous system [5ndash7] In this model SCC is regarded as theresult of localized oxidation enhanced by stressstrain andthe crack tip strain rate is expressed as a unique parameterto cause the physical degradation of the interfacial filmMany attempts have been made to acquire the stress state ofthe crack tip due to its importance [6 7] however thestress and strain are obtained macroscopically based on theassumption that the materials are isotropic and homoge-neous in terms of elastic deformation when the materials

have random crystallographic and morphologic texture Infact the crack tip stress state is significantly affected by themicrostructure of materials due to the misorientation andanisotropic of each component crystal and the crack tipwould have a nonuniform stress at the microstructural leveleven under a uniform remote stress condition [8ndash11] einhomogeneity stress distribution caused by anisotropic ofgrains would play an important role in the initiation andpropagation of SCC [12] Researches have shown that theinitiation of IGSCC in nickel alloys in high-temperaturewater greatly depends on inclination of the grain boundary(GB) to the tensile axis [13] the cracks tend to be initiatedeasily at the GB whose inclination is perpendicular to thetensile axis and suggested that the local stress perpendicularto the GB governs the cracking behavior this result seemsto be consistent with the theory However other experi-ments and observations show that cracks could travel indifferent directions such as at an angle perpendicular oreven parallel to the applied load [14ndash16]

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 9409868 10 pageshttpsdoiorg10115520189409868

In order to precisely predict cracking characteristicsresearchers have sought to acquire the local stress state nearan individual GB with random shape and orientation of thecrystal grains and to find the driving force for cracking[17] e test of bicrystals with a single symmetrical 111-tiltGB using the slow strain rate technique (SSRT) shows thatthe susceptibility to IGSCC depends on the misorientationrather than on the GB energy e local stress concen-tration at large-angle GBs could be attributed to a highsusceptibility to the IGSCC [18] Single GBs in real alloyswere also generated and monitored by using cantileversmanufactured by focused ion beam (FIB) and tested bynanoindentation which was expected to provide a moreaccurate method of measuring the crack growth and in-vestigate the dependence of SCC resistance of the single GBon GB character and composition [19ndash22] However it isdifficult to manufacture a specific single GB with respect tothe random orientation of neighboring grains and also toaccurately measure the stress and strain distribution nearthe GB us a three-dimensional anisotropic finite ele-ment method (FEM) is performed in this paper to de-termine how the crystal orientation affects the stress statenear the GB of the bicrystal

2 Finite Element Model

21 Geometry Model Two types of GBs are considered inbicrystals with respect to the relationship between the GBand tensile axis e type-I GB is perpendicular to the tensileaxis as shown in Figure 1 and the type-II GB is parallel to thetensile axis as shown in Figure 2 e average grain size of316L stainless steel varies from 17 μm to 200 μmwith differentaging time temperatures and other factors in literature [2324] the dimension of each component grain in the bicrystalwith type-I GB is assumed to be 20 μmtimes 20 μmtimes 50 μm andeach grain in the bicrystal with type-II GB is of the dimension10 μmtimes 20 μmtimes 50 μm in this study

22 Material Propriety Stainless steel 316L is a poly-crystalline material composed of austenitic crystal which hasthe face-centred cubic (FCC) configuratione single crystalof 316L is orthotropic and the elastic anisotropy is modeledusing the elastic constants d11 2046GPa d12 1377GPaand d44 1262GPa [25] When the crystallographic axialsystem coincides with the global coordinate the elastic stressand strain relationship of the single crystal is described by thegeneralized Hookersquos law

σ Dε (1)

where

ε ε11 ε22 ε33 ε12 ε13 ε231113864 1113865 (2)

σ σ11 σ22 σ33 σ12 σ13 σ231113864 1113865 (3)

D

d11 d12 d13

d21 d22 d23

d31 d32 d33

d44

d55

d66

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

where σ and ε denote the stress tensor and strain tensorrespectively and D is the stiffness matrix dij (i j 1 2 6)is the elastic constant with d11 d22 d33 d44 d55 d66 andd12 d13 d23 d21 d31 d32

In a polycrystalline material the crystal orientation israndom and always differs from the global coordinate estress and strain should be recalculated with the rotationstiffness matrix Dxyz as

Dxyz

ADAT (5)

where A is the rotation matrix which is given as

Fixed surface

Load applied

2

3 1

Grain A

Grain B

1

2

Figure 1 Type-I grain boundary GB perpendicular to the tensile axis

Fixed surface

Load applied

1

2

Grain B2

3 1

11

2

G2

Grain A

Figure 2 Type-II grain boundary GB parallel to the tensile axis

2 Advances in Materials Science and Engineering

A

l21 m21 n2

1 2l1m1 2l1n1 2m1n1

l22 m22 n2

2 2l2m2 2l2n2 2m2n2

l23 m23 n2

3 2l3m3 2l3n3 2m3n3

l1l2 m1m2 n1n2 l1m2 + l2m1 l1n2 + l2n1 m1n2 + m2n1

l1l3 m1m3 n1n3 l1m3 + l3m1 l1n3 + l3n1 m1n3 + m3n1

l2l3 m2m3 n2n3 l2m3 + l3m2 l2n3 + l3n2 m2n3 + m3n2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)where limi and ni (i 1 2 and 3) are the direction cosines ofX Y and Z axes between the global coordinate and crystalcoordinate

e elastic modulus E Poissonrsquos ratio μ and shearmodulus G are equal respectively in the three main axesand they can be calculated by elastic constants

d11 (1minus μ)

(1minus 2μ)(1 + μ)E (7)

d12 μ

(1minus 2μ)(1 + μ)E (8)

d44 G (9)

By substituting d11 d12 and d44 into (7)ndash(9) it can beobtained that E 9406GPa G 1262GPa and μ 0402

e elastic modulus of the single crystal in lt110gt andlt111gt crystal orientations can be described with E G and μin the three main axes as

1G

4

E110minus2minus 2μ

E (10)

1G

3

E111minus1minus 2μ

E (11)

According to (10) and (11) the elastic modulus alonglt110gt and lt111gt orientations is E110 19381GPa and E111

29977GPa respectively e highest elastic stiffness is alongthe lt111gt orientation and the lowest stiffness is along thelt100gt orientation as shown in Figure 3 For differentcrystallographic directions E111gtE110gt E100 E

Considering the relationship between [100] [110] and[111] orientations and the tensile axis three types of grains

3 [001][101]

[1-10]1 [100]

(111) [10-1]

[110]

2 [010]

[111]

(111) [-12-1]

Plane (111)

Figure 3 Selected crystallographic directions for analysis

Table 1 Crystal orientations considered for grains

Grain type xprime yprime zprimeMost compliant (MC) [100] [010] [001]Middle (MID) [1-10] [110] [001]Stiffness (ST) [10-1] [-12-1] [111]

Table 2 Incompatibility bicrystal models with three types of GBs

Incompatibility models Grain A Grain BModel I MC MIDModel II MC STModel III MID ST

S Mises(Avg 75)

0967092708870848080807680729068906490609057005300490

S Mises(Avg 75)

1193113410761017095808990841078207230664060505470488

Grain MC

Grain MID

Model I

Grain MC

Grain ST

Model II

S Mises(Avg 75)

1556149514351374131412531193113310721012095108910830

Grain MID

Grain ST

Model III

Figure 4 Mises stress (GPa) distribution on three incompatibilitybicrystal models

Advances in Materials Science and Engineering 3

with different orientations were modeled to build bicrystalsas listed in Table 1 e most compliant (MC) grain ori-entation is coincided with the global coordinate whichindicates that the crystal orientations [100] [010] and [001]denote the crystal axes xprime yprime and zprime respectively By rotatingthe grain around [001] orientation the middle (MID)stiffness grain has the (001)-[1-10] orientation as the axis xprimethus the (001)-[110] orientation aligns with the global axis xe most stiffness (ST) grain has the [111] orientation whichaligns with the global axis x by defining the (111)-[10-1] and(111)-[-12-1] orientations as the crystal axes xprime and yprime re-spectively In the three different grain types the planesperpendicular to the global coordinate axis x are (100) (110)and (111) planes in MC MID and ST grains respectively

In order to deeply understand the GB characterizationthree types of incompatibility bicrystal models were built bycombining grains with different orientations mentioned

above as listed in Table 2 e orientation of each grain isdefined in the finite element model by rotating the materialcoordinate

23 Boundary Condition and Loading Process e 8-nodelinear brick C3D8R element was used in the finite elementmodel and a fine mesh was carried out at GBs to acquiremore accurate stress and straine surface perpendicular todirection 1 of grain A is fixed initially with U1 U2 U3 0followed by a constant displacement U1 equal to 05 alongdirection 1 applied on the surface of grain B and this causesa total stain of 05 along direction 1 for the whole bicrystal

3 Results and Discussion

31 Bicrystal with Type-I Grain Boundary e Mises stressdistributions in different types of GBs and incompatibility

S Mises(Avg 75)

0967092708870848080807680729068906490609057005300490

MC

MID

01 μm

minus20 μm

minus10 μm

minus5 μm

minus1 μm

minus01 μm

1 μm

5 μm

10 μm

20 μm

1

2

3

Figure 5 Mises stress (GPa) distribution on different cross sections

4 Advances in Materials Science and Engineering

models are shown in Figure 4 which illustrates that theheterogeneity of two adjacent grains will lead to a stressconcentration at the GB and the largest stress exists inthe grain with higher elastic modulus along the tensile axise Mises stress distributions near the GB are differentin the three bicrystals which depend on the crystallo-graphic orientation of the two adjacent grains and GBse maximum Mises stress appears on the GB of model IIIbicrystal

More intuitive stress distribution was shown in Figure 5which illustrates the stress distribution on different crosssections of model I bicrystal On the cross section plusmn1 μmapart from the GB the Mises stress shows a plateau in themiddle of the cross section and a high gradient close to thesurfaces and the Mises stress gradient is higher along axis 3than axis 2 With the cross section away from the GB thehigh-stress area in the cross section reduces accompanied bythe reduction of the Mises stress gradient e stress in-consistency at the GB induced by misorientation disappearswhen the cross section is far from the GB

Let εxA and εxB represent the average strain εxx ofcomponent crystals A and B along axis 1 and let εA and εBrepresent the average strain of all elements in contact withthe GB in component crystals A and B respectively echaracteristic of deformation near the GB of three in-compatibility bicrystal models was evaluated as listed inTable 3 εxAεxB is bigger than 1 which shows that the av-erage strain of grain A is higher than that of grain B and theaverage strain on the GB of grain A is also higher than that ofgrain B as represented by εAεB is indicates that the strainin the softer component (grain A) is higher than that in theharder component (grain B) e values of εAεxA denotethat the strain near the GB is lower than the average strain ofthis grain in the softer component while the strain near theGB is higher than the average strain of this grain in theharder component as denoted by εBεxB e strain in-consistency between two neighboring grains and betweenthe GB and the entire grain is affected by the mismatch oftwo neighboring grains In model II bicrystal the elasticmodulus difference of two grains is the largest thus thestrain inconsistency in this bicrystal is the most serious

To study the stress state caused by misorientation be-tween grain A and grain B a stress concentration factor λ isintroduced to normalize the stress as

λ actual stress

average absolute stress (12)

where the actual stress and average absolute stress are ob-served along two paths as shown in Figure 6 Path 1 pen-etrates the GB from grain A to grain B and path 2 locates onthe GBe average absolute stress is calculated along path 1and path 2 respectively

Figure 7 illustrates the stress concentration factor forpath 1 and the Mises stress concentration factor is ap-proximately flat in the middle and increases or decreasesclose to the edges in the softer and harder componentsrespectively e Mises stress is higher in the harder com-ponent than in the softer component in each model Bydefining the stress difference coefficient κ as

κ σBσA

(13)

where σA and σB are the stress in grain A and grain Brespectively and the Mises stress difference for each modelwas demonstrated in Figure 8 e maximum stress

Table 3 e comparison of strain in each grain of the incompatibilitymodels

Model type εxAεxB εAεB εAεxA εBεxB

Model 1 (MC-MID) 143 204 082 117Model II (MC-ST) 157 265 079 133Model III (MID-ST) 111 130 088 103

05 LPath 1

Path 2

Grain A

Grain B

05 L

05 L

Path 2

Grain B

GB plane

GB plane

Figure 6 Locations of the two paths to determine the stressconcentration factor

Stre

ss co

ncen

trat

ion

fact

or λ

16

14

12

10

08

06minus10 minus5 0 5 10

Distance along path 2 x (μm)

λA Model I λA Model II λA Model IIIλB Model IIIλB Model IIλB Model II

Figure 7 Mises stress concentration factor on the GB along path 1

Advances in Materials Science and Engineering 5

difference appears at the middle of the GB and reducesgradually away from the middle in model II which has thelargest elastic modulus difference along the tensile axis whilethe stress difference coefficient behaves constant in themiddle and reduces slightly close to the edges in the othermodels e minimum stress difference near the GB ofmodel III has the smallest elastic modulus difference be-tween the two adjacent grains along the tensile axis

As shown in Figures 9 and 10 the Mises stress con-centration factor and Mises stress difference coefficient forincompatibility model I and model II have the same ten-dency along path 2 which clearly demonstrates that a stressconcentration exists near the GB and a uniform stressdistribution in the regions is far from the GB in both grainsIn the two harder components the stress concentrationfactors are approximately 16 and 14 respectively and bothreduce to 1 far from the GB In the softer grain near the GBthe stress concentration factor is below 1 and increases to 1far from the GBe stress difference coefficient for both themodels is higher at the GB and reduces to 1 far from the GB

Figure 11 shows a different Mises stress distribution inboth grains along path 2 in model III Stress concentrationexists at the GBs in both grains and it is more significant inthe harder grain e elastic modulus difference in model IIIis the smallest thus the stress difference coefficient at the GBis the lowest and also reduces to 1 far from the GB isindicates that the stress far away from the GB equals eachother and is not affected by the grain orientation and GBus the Mises stress in the middle of grains may be equal ifthe adjacent grain size is larger enough

32 Bicrystal with Type-II Grain Boundary As shown inFigure 12 a big difference of the Mises stress distribution onthe GB of grain B for type-II bicrystal is observed whichintuitively demonstrates the misorientation effects of twoadjacent grains e Mises stress along path 1 increases with

a large gradient initially and then reaches a plateau witha small gradienteMises stress on path 2 seems to be equalin the central region and has a small gradient close to theedgese stress difference coefficient along path 2 in Figure 13shows that a stress concentration exists at the GB and themost serious stress concentration appears in model IIbicrystal which has the largest elastic modulus differencealong the load axise stress concentration is the smallest inmodel III bicrystal with the smallest elastic modulus dif-ference along the load axis

e stress components σ22 σ21 and σ23 on the GB alongpath 2 are further studied e tensile stress component σ22is perpendicular to the GB plane which could lead to thefracture of bicrystal at GB e shear stress components σ21

Stre

ss d

iffer

ence

coeffi

cien

t κ

22

20

18

16

14

12

10

08minus10 minus5 0 5 10

Distance along path 2 x (μm)

Model IModel IIModel III

Figure 8 Mises stress difference coefficient on the GB along path 1

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

20

15

10

05

00

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model I

λAλBκ

Figure 9 Mises stress concentration factor and Mises stress dif-ference coefficient of model I along path 2

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

25

20

15

10

05

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model II

λAλBκ

Figure 10 Mises stress concentration factor and Mises stressdifference coefficient of model II along path 2

6 Advances in Materials Science and Engineering

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

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Hindawiwwwhindawicom Volume 2018

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Advances in Condensed Matter Physics

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High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

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ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

A

l21 m21 n2

1 2l1m1 2l1n1 2m1n1

l22 m22 n2

2 2l2m2 2l2n2 2m2n2

l23 m23 n2

3 2l3m3 2l3n3 2m3n3

l1l2 m1m2 n1n2 l1m2 + l2m1 l1n2 + l2n1 m1n2 + m2n1

l1l3 m1m3 n1n3 l1m3 + l3m1 l1n3 + l3n1 m1n3 + m3n1

l2l3 m2m3 n2n3 l2m3 + l3m2 l2n3 + l3n2 m2n3 + m3n2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)where limi and ni (i 1 2 and 3) are the direction cosines ofX Y and Z axes between the global coordinate and crystalcoordinate

e elastic modulus E Poissonrsquos ratio μ and shearmodulus G are equal respectively in the three main axesand they can be calculated by elastic constants

d11 (1minus μ)

(1minus 2μ)(1 + μ)E (7)

d12 μ

(1minus 2μ)(1 + μ)E (8)

d44 G (9)

By substituting d11 d12 and d44 into (7)ndash(9) it can beobtained that E 9406GPa G 1262GPa and μ 0402

e elastic modulus of the single crystal in lt110gt andlt111gt crystal orientations can be described with E G and μin the three main axes as

1G

4

E110minus2minus 2μ

E (10)

1G

3

E111minus1minus 2μ

E (11)

According to (10) and (11) the elastic modulus alonglt110gt and lt111gt orientations is E110 19381GPa and E111

29977GPa respectively e highest elastic stiffness is alongthe lt111gt orientation and the lowest stiffness is along thelt100gt orientation as shown in Figure 3 For differentcrystallographic directions E111gtE110gt E100 E

Considering the relationship between [100] [110] and[111] orientations and the tensile axis three types of grains

3 [001][101]

[1-10]1 [100]

(111) [10-1]

[110]

2 [010]

[111]

(111) [-12-1]

Plane (111)

Figure 3 Selected crystallographic directions for analysis

Table 1 Crystal orientations considered for grains

Grain type xprime yprime zprimeMost compliant (MC) [100] [010] [001]Middle (MID) [1-10] [110] [001]Stiffness (ST) [10-1] [-12-1] [111]

Table 2 Incompatibility bicrystal models with three types of GBs

Incompatibility models Grain A Grain BModel I MC MIDModel II MC STModel III MID ST

S Mises(Avg 75)

0967092708870848080807680729068906490609057005300490

S Mises(Avg 75)

1193113410761017095808990841078207230664060505470488

Grain MC

Grain MID

Model I

Grain MC

Grain ST

Model II

S Mises(Avg 75)

1556149514351374131412531193113310721012095108910830

Grain MID

Grain ST

Model III

Figure 4 Mises stress (GPa) distribution on three incompatibilitybicrystal models

Advances in Materials Science and Engineering 3

with different orientations were modeled to build bicrystalsas listed in Table 1 e most compliant (MC) grain ori-entation is coincided with the global coordinate whichindicates that the crystal orientations [100] [010] and [001]denote the crystal axes xprime yprime and zprime respectively By rotatingthe grain around [001] orientation the middle (MID)stiffness grain has the (001)-[1-10] orientation as the axis xprimethus the (001)-[110] orientation aligns with the global axis xe most stiffness (ST) grain has the [111] orientation whichaligns with the global axis x by defining the (111)-[10-1] and(111)-[-12-1] orientations as the crystal axes xprime and yprime re-spectively In the three different grain types the planesperpendicular to the global coordinate axis x are (100) (110)and (111) planes in MC MID and ST grains respectively

In order to deeply understand the GB characterizationthree types of incompatibility bicrystal models were built bycombining grains with different orientations mentioned

above as listed in Table 2 e orientation of each grain isdefined in the finite element model by rotating the materialcoordinate

23 Boundary Condition and Loading Process e 8-nodelinear brick C3D8R element was used in the finite elementmodel and a fine mesh was carried out at GBs to acquiremore accurate stress and straine surface perpendicular todirection 1 of grain A is fixed initially with U1 U2 U3 0followed by a constant displacement U1 equal to 05 alongdirection 1 applied on the surface of grain B and this causesa total stain of 05 along direction 1 for the whole bicrystal

3 Results and Discussion

31 Bicrystal with Type-I Grain Boundary e Mises stressdistributions in different types of GBs and incompatibility

S Mises(Avg 75)

0967092708870848080807680729068906490609057005300490

MC

MID

01 μm

minus20 μm

minus10 μm

minus5 μm

minus1 μm

minus01 μm

1 μm

5 μm

10 μm

20 μm

1

2

3

Figure 5 Mises stress (GPa) distribution on different cross sections

4 Advances in Materials Science and Engineering

models are shown in Figure 4 which illustrates that theheterogeneity of two adjacent grains will lead to a stressconcentration at the GB and the largest stress exists inthe grain with higher elastic modulus along the tensile axise Mises stress distributions near the GB are differentin the three bicrystals which depend on the crystallo-graphic orientation of the two adjacent grains and GBse maximum Mises stress appears on the GB of model IIIbicrystal

More intuitive stress distribution was shown in Figure 5which illustrates the stress distribution on different crosssections of model I bicrystal On the cross section plusmn1 μmapart from the GB the Mises stress shows a plateau in themiddle of the cross section and a high gradient close to thesurfaces and the Mises stress gradient is higher along axis 3than axis 2 With the cross section away from the GB thehigh-stress area in the cross section reduces accompanied bythe reduction of the Mises stress gradient e stress in-consistency at the GB induced by misorientation disappearswhen the cross section is far from the GB

Let εxA and εxB represent the average strain εxx ofcomponent crystals A and B along axis 1 and let εA and εBrepresent the average strain of all elements in contact withthe GB in component crystals A and B respectively echaracteristic of deformation near the GB of three in-compatibility bicrystal models was evaluated as listed inTable 3 εxAεxB is bigger than 1 which shows that the av-erage strain of grain A is higher than that of grain B and theaverage strain on the GB of grain A is also higher than that ofgrain B as represented by εAεB is indicates that the strainin the softer component (grain A) is higher than that in theharder component (grain B) e values of εAεxA denotethat the strain near the GB is lower than the average strain ofthis grain in the softer component while the strain near theGB is higher than the average strain of this grain in theharder component as denoted by εBεxB e strain in-consistency between two neighboring grains and betweenthe GB and the entire grain is affected by the mismatch oftwo neighboring grains In model II bicrystal the elasticmodulus difference of two grains is the largest thus thestrain inconsistency in this bicrystal is the most serious

To study the stress state caused by misorientation be-tween grain A and grain B a stress concentration factor λ isintroduced to normalize the stress as

λ actual stress

average absolute stress (12)

where the actual stress and average absolute stress are ob-served along two paths as shown in Figure 6 Path 1 pen-etrates the GB from grain A to grain B and path 2 locates onthe GBe average absolute stress is calculated along path 1and path 2 respectively

Figure 7 illustrates the stress concentration factor forpath 1 and the Mises stress concentration factor is ap-proximately flat in the middle and increases or decreasesclose to the edges in the softer and harder componentsrespectively e Mises stress is higher in the harder com-ponent than in the softer component in each model Bydefining the stress difference coefficient κ as

κ σBσA

(13)

where σA and σB are the stress in grain A and grain Brespectively and the Mises stress difference for each modelwas demonstrated in Figure 8 e maximum stress

Table 3 e comparison of strain in each grain of the incompatibilitymodels

Model type εxAεxB εAεB εAεxA εBεxB

Model 1 (MC-MID) 143 204 082 117Model II (MC-ST) 157 265 079 133Model III (MID-ST) 111 130 088 103

05 LPath 1

Path 2

Grain A

Grain B

05 L

05 L

Path 2

Grain B

GB plane

GB plane

Figure 6 Locations of the two paths to determine the stressconcentration factor

Stre

ss co

ncen

trat

ion

fact

or λ

16

14

12

10

08

06minus10 minus5 0 5 10

Distance along path 2 x (μm)

λA Model I λA Model II λA Model IIIλB Model IIIλB Model IIλB Model II

Figure 7 Mises stress concentration factor on the GB along path 1

Advances in Materials Science and Engineering 5

difference appears at the middle of the GB and reducesgradually away from the middle in model II which has thelargest elastic modulus difference along the tensile axis whilethe stress difference coefficient behaves constant in themiddle and reduces slightly close to the edges in the othermodels e minimum stress difference near the GB ofmodel III has the smallest elastic modulus difference be-tween the two adjacent grains along the tensile axis

As shown in Figures 9 and 10 the Mises stress con-centration factor and Mises stress difference coefficient forincompatibility model I and model II have the same ten-dency along path 2 which clearly demonstrates that a stressconcentration exists near the GB and a uniform stressdistribution in the regions is far from the GB in both grainsIn the two harder components the stress concentrationfactors are approximately 16 and 14 respectively and bothreduce to 1 far from the GB In the softer grain near the GBthe stress concentration factor is below 1 and increases to 1far from the GBe stress difference coefficient for both themodels is higher at the GB and reduces to 1 far from the GB

Figure 11 shows a different Mises stress distribution inboth grains along path 2 in model III Stress concentrationexists at the GBs in both grains and it is more significant inthe harder grain e elastic modulus difference in model IIIis the smallest thus the stress difference coefficient at the GBis the lowest and also reduces to 1 far from the GB isindicates that the stress far away from the GB equals eachother and is not affected by the grain orientation and GBus the Mises stress in the middle of grains may be equal ifthe adjacent grain size is larger enough

32 Bicrystal with Type-II Grain Boundary As shown inFigure 12 a big difference of the Mises stress distribution onthe GB of grain B for type-II bicrystal is observed whichintuitively demonstrates the misorientation effects of twoadjacent grains e Mises stress along path 1 increases with

a large gradient initially and then reaches a plateau witha small gradienteMises stress on path 2 seems to be equalin the central region and has a small gradient close to theedgese stress difference coefficient along path 2 in Figure 13shows that a stress concentration exists at the GB and themost serious stress concentration appears in model IIbicrystal which has the largest elastic modulus differencealong the load axise stress concentration is the smallest inmodel III bicrystal with the smallest elastic modulus dif-ference along the load axis

e stress components σ22 σ21 and σ23 on the GB alongpath 2 are further studied e tensile stress component σ22is perpendicular to the GB plane which could lead to thefracture of bicrystal at GB e shear stress components σ21

Stre

ss d

iffer

ence

coeffi

cien

t κ

22

20

18

16

14

12

10

08minus10 minus5 0 5 10

Distance along path 2 x (μm)

Model IModel IIModel III

Figure 8 Mises stress difference coefficient on the GB along path 1

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

20

15

10

05

00

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model I

λAλBκ

Figure 9 Mises stress concentration factor and Mises stress dif-ference coefficient of model I along path 2

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

25

20

15

10

05

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model II

λAλBκ

Figure 10 Mises stress concentration factor and Mises stressdifference coefficient of model II along path 2

6 Advances in Materials Science and Engineering

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

with different orientations were modeled to build bicrystalsas listed in Table 1 e most compliant (MC) grain ori-entation is coincided with the global coordinate whichindicates that the crystal orientations [100] [010] and [001]denote the crystal axes xprime yprime and zprime respectively By rotatingthe grain around [001] orientation the middle (MID)stiffness grain has the (001)-[1-10] orientation as the axis xprimethus the (001)-[110] orientation aligns with the global axis xe most stiffness (ST) grain has the [111] orientation whichaligns with the global axis x by defining the (111)-[10-1] and(111)-[-12-1] orientations as the crystal axes xprime and yprime re-spectively In the three different grain types the planesperpendicular to the global coordinate axis x are (100) (110)and (111) planes in MC MID and ST grains respectively

In order to deeply understand the GB characterizationthree types of incompatibility bicrystal models were built bycombining grains with different orientations mentioned

above as listed in Table 2 e orientation of each grain isdefined in the finite element model by rotating the materialcoordinate

23 Boundary Condition and Loading Process e 8-nodelinear brick C3D8R element was used in the finite elementmodel and a fine mesh was carried out at GBs to acquiremore accurate stress and straine surface perpendicular todirection 1 of grain A is fixed initially with U1 U2 U3 0followed by a constant displacement U1 equal to 05 alongdirection 1 applied on the surface of grain B and this causesa total stain of 05 along direction 1 for the whole bicrystal

3 Results and Discussion

31 Bicrystal with Type-I Grain Boundary e Mises stressdistributions in different types of GBs and incompatibility

S Mises(Avg 75)

0967092708870848080807680729068906490609057005300490

MC

MID

01 μm

minus20 μm

minus10 μm

minus5 μm

minus1 μm

minus01 μm

1 μm

5 μm

10 μm

20 μm

1

2

3

Figure 5 Mises stress (GPa) distribution on different cross sections

4 Advances in Materials Science and Engineering

models are shown in Figure 4 which illustrates that theheterogeneity of two adjacent grains will lead to a stressconcentration at the GB and the largest stress exists inthe grain with higher elastic modulus along the tensile axise Mises stress distributions near the GB are differentin the three bicrystals which depend on the crystallo-graphic orientation of the two adjacent grains and GBse maximum Mises stress appears on the GB of model IIIbicrystal

More intuitive stress distribution was shown in Figure 5which illustrates the stress distribution on different crosssections of model I bicrystal On the cross section plusmn1 μmapart from the GB the Mises stress shows a plateau in themiddle of the cross section and a high gradient close to thesurfaces and the Mises stress gradient is higher along axis 3than axis 2 With the cross section away from the GB thehigh-stress area in the cross section reduces accompanied bythe reduction of the Mises stress gradient e stress in-consistency at the GB induced by misorientation disappearswhen the cross section is far from the GB

Let εxA and εxB represent the average strain εxx ofcomponent crystals A and B along axis 1 and let εA and εBrepresent the average strain of all elements in contact withthe GB in component crystals A and B respectively echaracteristic of deformation near the GB of three in-compatibility bicrystal models was evaluated as listed inTable 3 εxAεxB is bigger than 1 which shows that the av-erage strain of grain A is higher than that of grain B and theaverage strain on the GB of grain A is also higher than that ofgrain B as represented by εAεB is indicates that the strainin the softer component (grain A) is higher than that in theharder component (grain B) e values of εAεxA denotethat the strain near the GB is lower than the average strain ofthis grain in the softer component while the strain near theGB is higher than the average strain of this grain in theharder component as denoted by εBεxB e strain in-consistency between two neighboring grains and betweenthe GB and the entire grain is affected by the mismatch oftwo neighboring grains In model II bicrystal the elasticmodulus difference of two grains is the largest thus thestrain inconsistency in this bicrystal is the most serious

To study the stress state caused by misorientation be-tween grain A and grain B a stress concentration factor λ isintroduced to normalize the stress as

λ actual stress

average absolute stress (12)

where the actual stress and average absolute stress are ob-served along two paths as shown in Figure 6 Path 1 pen-etrates the GB from grain A to grain B and path 2 locates onthe GBe average absolute stress is calculated along path 1and path 2 respectively

Figure 7 illustrates the stress concentration factor forpath 1 and the Mises stress concentration factor is ap-proximately flat in the middle and increases or decreasesclose to the edges in the softer and harder componentsrespectively e Mises stress is higher in the harder com-ponent than in the softer component in each model Bydefining the stress difference coefficient κ as

κ σBσA

(13)

where σA and σB are the stress in grain A and grain Brespectively and the Mises stress difference for each modelwas demonstrated in Figure 8 e maximum stress

Table 3 e comparison of strain in each grain of the incompatibilitymodels

Model type εxAεxB εAεB εAεxA εBεxB

Model 1 (MC-MID) 143 204 082 117Model II (MC-ST) 157 265 079 133Model III (MID-ST) 111 130 088 103

05 LPath 1

Path 2

Grain A

Grain B

05 L

05 L

Path 2

Grain B

GB plane

GB plane

Figure 6 Locations of the two paths to determine the stressconcentration factor

Stre

ss co

ncen

trat

ion

fact

or λ

16

14

12

10

08

06minus10 minus5 0 5 10

Distance along path 2 x (μm)

λA Model I λA Model II λA Model IIIλB Model IIIλB Model IIλB Model II

Figure 7 Mises stress concentration factor on the GB along path 1

Advances in Materials Science and Engineering 5

difference appears at the middle of the GB and reducesgradually away from the middle in model II which has thelargest elastic modulus difference along the tensile axis whilethe stress difference coefficient behaves constant in themiddle and reduces slightly close to the edges in the othermodels e minimum stress difference near the GB ofmodel III has the smallest elastic modulus difference be-tween the two adjacent grains along the tensile axis

As shown in Figures 9 and 10 the Mises stress con-centration factor and Mises stress difference coefficient forincompatibility model I and model II have the same ten-dency along path 2 which clearly demonstrates that a stressconcentration exists near the GB and a uniform stressdistribution in the regions is far from the GB in both grainsIn the two harder components the stress concentrationfactors are approximately 16 and 14 respectively and bothreduce to 1 far from the GB In the softer grain near the GBthe stress concentration factor is below 1 and increases to 1far from the GBe stress difference coefficient for both themodels is higher at the GB and reduces to 1 far from the GB

Figure 11 shows a different Mises stress distribution inboth grains along path 2 in model III Stress concentrationexists at the GBs in both grains and it is more significant inthe harder grain e elastic modulus difference in model IIIis the smallest thus the stress difference coefficient at the GBis the lowest and also reduces to 1 far from the GB isindicates that the stress far away from the GB equals eachother and is not affected by the grain orientation and GBus the Mises stress in the middle of grains may be equal ifthe adjacent grain size is larger enough

32 Bicrystal with Type-II Grain Boundary As shown inFigure 12 a big difference of the Mises stress distribution onthe GB of grain B for type-II bicrystal is observed whichintuitively demonstrates the misorientation effects of twoadjacent grains e Mises stress along path 1 increases with

a large gradient initially and then reaches a plateau witha small gradienteMises stress on path 2 seems to be equalin the central region and has a small gradient close to theedgese stress difference coefficient along path 2 in Figure 13shows that a stress concentration exists at the GB and themost serious stress concentration appears in model IIbicrystal which has the largest elastic modulus differencealong the load axise stress concentration is the smallest inmodel III bicrystal with the smallest elastic modulus dif-ference along the load axis

e stress components σ22 σ21 and σ23 on the GB alongpath 2 are further studied e tensile stress component σ22is perpendicular to the GB plane which could lead to thefracture of bicrystal at GB e shear stress components σ21

Stre

ss d

iffer

ence

coeffi

cien

t κ

22

20

18

16

14

12

10

08minus10 minus5 0 5 10

Distance along path 2 x (μm)

Model IModel IIModel III

Figure 8 Mises stress difference coefficient on the GB along path 1

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

20

15

10

05

00

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model I

λAλBκ

Figure 9 Mises stress concentration factor and Mises stress dif-ference coefficient of model I along path 2

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

25

20

15

10

05

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model II

λAλBκ

Figure 10 Mises stress concentration factor and Mises stressdifference coefficient of model II along path 2

6 Advances in Materials Science and Engineering

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

models are shown in Figure 4 which illustrates that theheterogeneity of two adjacent grains will lead to a stressconcentration at the GB and the largest stress exists inthe grain with higher elastic modulus along the tensile axise Mises stress distributions near the GB are differentin the three bicrystals which depend on the crystallo-graphic orientation of the two adjacent grains and GBse maximum Mises stress appears on the GB of model IIIbicrystal

More intuitive stress distribution was shown in Figure 5which illustrates the stress distribution on different crosssections of model I bicrystal On the cross section plusmn1 μmapart from the GB the Mises stress shows a plateau in themiddle of the cross section and a high gradient close to thesurfaces and the Mises stress gradient is higher along axis 3than axis 2 With the cross section away from the GB thehigh-stress area in the cross section reduces accompanied bythe reduction of the Mises stress gradient e stress in-consistency at the GB induced by misorientation disappearswhen the cross section is far from the GB

Let εxA and εxB represent the average strain εxx ofcomponent crystals A and B along axis 1 and let εA and εBrepresent the average strain of all elements in contact withthe GB in component crystals A and B respectively echaracteristic of deformation near the GB of three in-compatibility bicrystal models was evaluated as listed inTable 3 εxAεxB is bigger than 1 which shows that the av-erage strain of grain A is higher than that of grain B and theaverage strain on the GB of grain A is also higher than that ofgrain B as represented by εAεB is indicates that the strainin the softer component (grain A) is higher than that in theharder component (grain B) e values of εAεxA denotethat the strain near the GB is lower than the average strain ofthis grain in the softer component while the strain near theGB is higher than the average strain of this grain in theharder component as denoted by εBεxB e strain in-consistency between two neighboring grains and betweenthe GB and the entire grain is affected by the mismatch oftwo neighboring grains In model II bicrystal the elasticmodulus difference of two grains is the largest thus thestrain inconsistency in this bicrystal is the most serious

To study the stress state caused by misorientation be-tween grain A and grain B a stress concentration factor λ isintroduced to normalize the stress as

λ actual stress

average absolute stress (12)

where the actual stress and average absolute stress are ob-served along two paths as shown in Figure 6 Path 1 pen-etrates the GB from grain A to grain B and path 2 locates onthe GBe average absolute stress is calculated along path 1and path 2 respectively

Figure 7 illustrates the stress concentration factor forpath 1 and the Mises stress concentration factor is ap-proximately flat in the middle and increases or decreasesclose to the edges in the softer and harder componentsrespectively e Mises stress is higher in the harder com-ponent than in the softer component in each model Bydefining the stress difference coefficient κ as

κ σBσA

(13)

where σA and σB are the stress in grain A and grain Brespectively and the Mises stress difference for each modelwas demonstrated in Figure 8 e maximum stress

Table 3 e comparison of strain in each grain of the incompatibilitymodels

Model type εxAεxB εAεB εAεxA εBεxB

Model 1 (MC-MID) 143 204 082 117Model II (MC-ST) 157 265 079 133Model III (MID-ST) 111 130 088 103

05 LPath 1

Path 2

Grain A

Grain B

05 L

05 L

Path 2

Grain B

GB plane

GB plane

Figure 6 Locations of the two paths to determine the stressconcentration factor

Stre

ss co

ncen

trat

ion

fact

or λ

16

14

12

10

08

06minus10 minus5 0 5 10

Distance along path 2 x (μm)

λA Model I λA Model II λA Model IIIλB Model IIIλB Model IIλB Model II

Figure 7 Mises stress concentration factor on the GB along path 1

Advances in Materials Science and Engineering 5

difference appears at the middle of the GB and reducesgradually away from the middle in model II which has thelargest elastic modulus difference along the tensile axis whilethe stress difference coefficient behaves constant in themiddle and reduces slightly close to the edges in the othermodels e minimum stress difference near the GB ofmodel III has the smallest elastic modulus difference be-tween the two adjacent grains along the tensile axis

As shown in Figures 9 and 10 the Mises stress con-centration factor and Mises stress difference coefficient forincompatibility model I and model II have the same ten-dency along path 2 which clearly demonstrates that a stressconcentration exists near the GB and a uniform stressdistribution in the regions is far from the GB in both grainsIn the two harder components the stress concentrationfactors are approximately 16 and 14 respectively and bothreduce to 1 far from the GB In the softer grain near the GBthe stress concentration factor is below 1 and increases to 1far from the GBe stress difference coefficient for both themodels is higher at the GB and reduces to 1 far from the GB

Figure 11 shows a different Mises stress distribution inboth grains along path 2 in model III Stress concentrationexists at the GBs in both grains and it is more significant inthe harder grain e elastic modulus difference in model IIIis the smallest thus the stress difference coefficient at the GBis the lowest and also reduces to 1 far from the GB isindicates that the stress far away from the GB equals eachother and is not affected by the grain orientation and GBus the Mises stress in the middle of grains may be equal ifthe adjacent grain size is larger enough

32 Bicrystal with Type-II Grain Boundary As shown inFigure 12 a big difference of the Mises stress distribution onthe GB of grain B for type-II bicrystal is observed whichintuitively demonstrates the misorientation effects of twoadjacent grains e Mises stress along path 1 increases with

a large gradient initially and then reaches a plateau witha small gradienteMises stress on path 2 seems to be equalin the central region and has a small gradient close to theedgese stress difference coefficient along path 2 in Figure 13shows that a stress concentration exists at the GB and themost serious stress concentration appears in model IIbicrystal which has the largest elastic modulus differencealong the load axise stress concentration is the smallest inmodel III bicrystal with the smallest elastic modulus dif-ference along the load axis

e stress components σ22 σ21 and σ23 on the GB alongpath 2 are further studied e tensile stress component σ22is perpendicular to the GB plane which could lead to thefracture of bicrystal at GB e shear stress components σ21

Stre

ss d

iffer

ence

coeffi

cien

t κ

22

20

18

16

14

12

10

08minus10 minus5 0 5 10

Distance along path 2 x (μm)

Model IModel IIModel III

Figure 8 Mises stress difference coefficient on the GB along path 1

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

20

15

10

05

00

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model I

λAλBκ

Figure 9 Mises stress concentration factor and Mises stress dif-ference coefficient of model I along path 2

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

25

20

15

10

05

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model II

λAλBκ

Figure 10 Mises stress concentration factor and Mises stressdifference coefficient of model II along path 2

6 Advances in Materials Science and Engineering

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

difference appears at the middle of the GB and reducesgradually away from the middle in model II which has thelargest elastic modulus difference along the tensile axis whilethe stress difference coefficient behaves constant in themiddle and reduces slightly close to the edges in the othermodels e minimum stress difference near the GB ofmodel III has the smallest elastic modulus difference be-tween the two adjacent grains along the tensile axis

As shown in Figures 9 and 10 the Mises stress con-centration factor and Mises stress difference coefficient forincompatibility model I and model II have the same ten-dency along path 2 which clearly demonstrates that a stressconcentration exists near the GB and a uniform stressdistribution in the regions is far from the GB in both grainsIn the two harder components the stress concentrationfactors are approximately 16 and 14 respectively and bothreduce to 1 far from the GB In the softer grain near the GBthe stress concentration factor is below 1 and increases to 1far from the GBe stress difference coefficient for both themodels is higher at the GB and reduces to 1 far from the GB

Figure 11 shows a different Mises stress distribution inboth grains along path 2 in model III Stress concentrationexists at the GBs in both grains and it is more significant inthe harder grain e elastic modulus difference in model IIIis the smallest thus the stress difference coefficient at the GBis the lowest and also reduces to 1 far from the GB isindicates that the stress far away from the GB equals eachother and is not affected by the grain orientation and GBus the Mises stress in the middle of grains may be equal ifthe adjacent grain size is larger enough

32 Bicrystal with Type-II Grain Boundary As shown inFigure 12 a big difference of the Mises stress distribution onthe GB of grain B for type-II bicrystal is observed whichintuitively demonstrates the misorientation effects of twoadjacent grains e Mises stress along path 1 increases with

a large gradient initially and then reaches a plateau witha small gradienteMises stress on path 2 seems to be equalin the central region and has a small gradient close to theedgese stress difference coefficient along path 2 in Figure 13shows that a stress concentration exists at the GB and themost serious stress concentration appears in model IIbicrystal which has the largest elastic modulus differencealong the load axise stress concentration is the smallest inmodel III bicrystal with the smallest elastic modulus dif-ference along the load axis

e stress components σ22 σ21 and σ23 on the GB alongpath 2 are further studied e tensile stress component σ22is perpendicular to the GB plane which could lead to thefracture of bicrystal at GB e shear stress components σ21

Stre

ss d

iffer

ence

coeffi

cien

t κ

22

20

18

16

14

12

10

08minus10 minus5 0 5 10

Distance along path 2 x (μm)

Model IModel IIModel III

Figure 8 Mises stress difference coefficient on the GB along path 1

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

20

15

10

05

00

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model I

λAλBκ

Figure 9 Mises stress concentration factor and Mises stress dif-ference coefficient of model I along path 2

16

14

12

10

08

06

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

25

20

15

10

05

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model II

λAλBκ

Figure 10 Mises stress concentration factor and Mises stressdifference coefficient of model II along path 2

6 Advances in Materials Science and Engineering

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

and σ23 are tangent to the GB plane which may lead to theshear failure of the GB e shear stress components σ21 andσ23 are considered to be shear stress τ tangent to the GBplane as

τ

σ221 + σ2231113969

(14)

Figure 14 illustrates the stress component distributionon the GB of model I bicrystal As shown in Figure 14(a)the tensile stress in grain A fluctuates in a small rangeof plusmn4MPa and the shear stress also fluctuates slightly

around 13MPa in the central region and increases to85MPa rapidly close to the edges e shear stress is largerthan the tensile stress in grain A especially close to theedges e angle between shear stress and load directionvaries from minus135deg to +135deg at different positions e angleis about plusmn135deg close to the edges which indicates that theshear stress is almost parallel to the [101] and [10-1] di-rections on the slip plane 111 e angle equal to 0deg orplusmn180deg indicates that the stress component σ23 is zero whilethe angle equal to plusmn90deg indicates that the stress componentσ21 is zero As shown in Figure 14(b) the tensile stress is

λAλBκ

120

115

110

105

100

095

Stre

ss co

ncen

trat

ion

fact

or λ

0 10 20 30 40 50Distance from interface along path 1 x (μm)

12

11

10

09

08

Stre

ss d

iffer

ence

coeffi

cien

t κ

Model III

Figure 11 Mises stress concentration factor and Mises stress difference coefficient of model III along path 2

Grain A

Grain B

Path 1Path 2

Grainboundary

2

3 1

3

1

S Mises(Avg 75)

249213001200115011001000090008000663

S Mises(Avg 75)

211915001450140013501300120010000842

S Mises(Avg 75)

250016801600152014401360128012000740

Model I

Model IIIModel II

Figure 12 Mises stress distribution on the GB of grain B for type-II bicrystal

Advances in Materials Science and Engineering 7

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

larger than the shear stress in the central region and thenthey all reduce gradually from the central region to edges andresult in a larger shear stress at edges e stress componentsare much higher in grain B than in grain A which dem-onstrates the stress concentration in grain B e anglebetween shear stress and load direction is in a narrow rangeof [minus1deg 6deg] which indicates that the stress component σ21dominates the shear stress τ and the shear stress is almostparallel to the [110] directione symmetrical characteristicof stress components in grain A and grain B could be in-duced by the physical property symmetry of two grains withrespect to tensile direction

As shown in Figure 15(a) the tensile stress and shear stressalong path 2 in grain A of model II are similar to those of

model I due to the same grain orientation of grain A inmodelII and model I e tensile stress is flat with small values andthe shear stress is a little bigger than tensile stress in the centralregion and increases rapidly close to the edges Due to thesymmetry of grain A and the asymmetry of grain B the stresscomponents are approximately symmetry in grain A Asshown in Figure 15(b) the shear stress is about 2 times thetensile stress along path 2 thus the shear failure appears eangle between shear stress and tensile direction is in the rangeof [minus150deg minus135deg] which is close to the angle between [012]direction and tensile direction on planes 1ndash3 or (-12-1)

A bigger difference between tensile stress and shearstress in grain A and grain B is observed in Figures 14 and 15which indicates that a high stress concentration exists on the

30

25

20

15

10

Stre

ss d

iffer

ence

coeffi

cien

t κ

0 5 10 15 20 25 30 35 40 45 50Distance along path 2 x (μm)

Model IModel IIModel III

Figure 13 Mises stress difference coefficient along path 2

100

80

60

40

20

0Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

135

90

45

0

minus45

minus90

minus135 Ang

le b

etw

een

τ and

axes

1 θ

(ordm)

σ23

σ21

τθ

σ22τθ

Model I grain A

(a)

650

600

550

500

450

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

0 10 20 30 40 50Distance along path 2 x (μm)

2

0

minus2

minus4

minus6

Ang

le b

etw

een τ a

nd ax

es 1

θ (ordm

)

Model I grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 14 Stress components on model I GB (a) grain A and (b) grain B

8 Advances in Materials Science and Engineering

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

GB of grain B which has greater stiffness along the loaddirection in model I and model II However the situation isdifferent in model III as shown in Figure 16 even the Misesstress is higher in grain B with greater stiffness and theaverage tensile stress and shear stress in grain A are about 38and 11 times than those in grain B respectively

4 Conclusions

A constitutive model has been presented to assess the elasticresponse of anisotropic behaviors of the austenitic stainlesssteel crystale FE method has been proposed to determinehow the crystal orientation affects the stress state near theGB e results indicate that the stress distribution near theGB depends strongly on the crystal orientation

For bicrystals with the GB perpendicular or parallel tothe tensile axis elastic anisotropy causes additional stress ingrain boundary regions and leads to the stress concentrationon the GB of grains with larger stiffness along the loaddirection e larger the elastic modulus difference of twoneighboring grains along the tensile axis the bigger theMises stress difference appears at the GB

With a GB perpendicular to tensile axes a uniformMisesstress distribution in the region far from the GB in bothgrains is observed which indicates that the grain orientationhas little effects on the Mises stress distribution in this re-gion e Mises stress in the middle of adjacent grains maybe equal if the grain size is larger enough

e strain in the softer component is higher than that inthe harder component the strain near the GB is lower than

750

700

650

600

550

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

Distance along path 2 x (μm)0 10 20 30 40 50

20

15

10

5

0

minus5

minus10

minus15

minus20

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

200

00 10 20 30 40 50

Distance along path 2 x (μm)

minus135

minus140

minus145

minus150

minus155

minus160

minus165

minus170

Ang

le b

etw

een τ a

nd ax

es 1

θ (deg

)

Model III grain B

σ23

σ21

σ22

τ

τθ

θ

(b)

Figure 16 Stress components on model III GB (a) grain A and (b) grain B

160

120

80

40

0Stre

ss co

mpo

nent

s στ (

MPa

)

0 10 20 30 40 50Distance along path 2 x (μm)

180

135

90

45

0

minus45

minus90

minus135

minus180

Ang

le b

etw

een τ a

nd ax

es 1

θ (

deg)

Model II grain A

σ22

σ23

σ21

τ

τ

θ

θ

(a)

Stre

ss co

mpo

nent

s σ

τ (M

Pa)

600

400

500

200

100

300

Distance along path 2 x (μm)0 10 20 30 40 50

minus135

minus140

minus145

minus150

Ang

le b

etw

een τ a

md

axes

1 θ

(deg)

Model II grain B

σ23

σ21

σ22

τ

τ

θ

θ

(b)

Figure 15 Stress components on model II GB (a) grain A and (b) grain B

Advances in Materials Science and Engineering 9

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

the average strain of this grain in the softer componentwhile the strain near the GB is higher than the average strainof this grain in the harder component e strain in-consistency between two neighboring grains and between theGB and the entire grain is affected by the mismatch of twoneighboring grains e larger the elastic modulus differencesbetween two neighboring grains caused bymisorientation thelarger the strain inconsistency in the bicrystals

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper e authors confirmthat the mentioned funding in the ldquoAcknowledgmentsrdquosection did not lead to any conflicts of interest regarding thepublication of this manuscript

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51475362 11502195 and51775427) the Scientific Research Program Funded by ShaanxiProvincial Education Department (Grant no 16JK1492) andthe Start-up Foundation for Doctors of Xirsquoan University ofScience and Technology (Grant no 2016QDJ010)

References

[1] P M Scott and C Benhamou ldquoAn overview of recent ob-servation and interpretation of IGSCC in nickel base alloys inPWR primary waterrdquo NACE International Lake Tahoe NVUSA 2001

[2] P M Scott and P Combrade ldquoOn the mechanism of stresscorrosion crack initiation and growth in alloy 600 exposed toPWR primary waterrdquo pp 29ndash38 ANS Stevenson WA USA2003

[3] USNRC Crack in Weld Area of Reactor Coolant System HotLeg Piping at VC Summer NRC Information Notice USNuclear Regulatory Commission Washington DC USA2000

[4] R M Horn G M Gordon F P Ford and R L CowanldquoExperience and assessment of stress corrosion cracking inL-grade stainless steel BWR internalsrdquo Nuclear Engineeringand Design vol 174 no 3 pp 313ndash325 1997

[5] P L Andresen and F P Ford ldquoFundamental modeling ofenvironmental cracking for improved design and lifetimeevaluation in BWRsrdquo International Journal of Pressure Vesselsand Piping vol 59 no 1ndash3 pp 61ndash70 1994

[6] T Shoji Z Lu and H Murakami ldquoFormulating stress cor-rosion cracking growth rates by combination of crack tipmechanics and crack tip oxidation kineticsrdquo Corrosion Sci-ence vol 52 no 3 pp 769ndash779 2010

[7] F Q Yang H Xue L Y Zhao and X R Fang ldquoA quantitativeprediction model of SCC rate for nuclear structure materials inhigh temperature water based on crack tip creep strain raterdquoNuclear Engineering and Design vol 278 pp 686ndash692 2014

[8] K Hashimoto and H Margolin ldquoe role of elastic in-teraction stresses on the onset of slip in polycrystalline alphabrass-II Rationalization of slip behaviourrdquo Acta Metallurgicavol 31 no 5 pp 787ndash800 1983

[9] C S Nichols R F Cook D R Clarke and D A SmithldquoAlternative length scales for polycrystalline materials-I

Microstructure evolutionrdquo Acta Metallurgica et Materialiavol 39 no 7 pp 1657ndash1665 1991

[10] B M Schroeter and D L McDowell ldquoMeasurement of de-formation fields in polycrystalline OFHC copperrdquo InternationalJournal of Plasticity vol 19 no 9 pp 1355ndash1376 2003

[11] M Kamaya and T Kitamura ldquoStress intensity factors ofmicrostructurally small crackrdquo International Journal ofFracture vol 124 no 3-4 pp 201ndash213 2003

[12] M Kamaya and T Kitamura ldquoA simulation on growth ofmultiple small cracks under stress corrosionrdquo InternationalJournal of Fracture vol 130 no 4 pp 787ndash801 2004

[13] M Kamaya ldquoInfluence of grain boundaries on short crackgrowth behaviour of IGSCCrdquo Fatigue and Fracture of Engi-neeringMaterials and Structures vol 27 no 6 pp 513ndash521 2004

[14] Z Lu T Shoji F Meng Y Qiu T Dan and H Xue ldquoEffectsof water chemistry and loading conditions on stress corrosioncracking of cold-rolled 316NG stainless steel in high tem-perature waterrdquo Corrosion Science vol 53 no 1 pp 247ndash2622011

[15] Z Lu T Shoji F Meng et al ldquoCharacterization of micro-structure and local deformation in 316NG weld heat-affectedzone and stress corrosion cracking in high temperature wa-terrdquo Corrosion Science vol 53 no 5 pp 1916ndash1932 2011

[16] T Terachi T Yamada T Miyamoto and K Arioka ldquoSCCgrowth behaviors of austenitic stainless steels in simulatedPWR primary waterrdquo Journal of Nuclear Materials vol 426no 1ndash3 pp 59ndash70 2012

[17] B Alexandreanu and G S Was ldquoe role of stress in theefficacy of coincident site lattice boundaries in improvingcreep and stress corrosion crackingrdquo Scripta Materialiavol 54 no 6 pp 1047ndash1052 2006

[18] H Miyamoto H Koga T Mimaki and S Hashimoto ldquoIn-tergranular stress corrosion cracking of pure copper lt111gt tiltbicrystalsrdquo Interface Science vol 9 no 3ndash4 pp 281ndash286 2001

[19] D E J Armstrong M E Rogers and S G RobertsldquoMicromechanical testing of stress corrosion cracking ofindividual grain boundariesrdquo Scripta Materialia vol 61 no 7pp 741ndash743 2009

[20] H Dugdale D E J Armstrong E Tarleton S G Roberts andS Lozano-Perez ldquoHow oxidized grain boundaries failrdquo ActaMaterialia vol 61 no 13 pp 4707ndash4713 2013

[21] A Stratulat D E J Armstrong and S G Roberts ldquoMicro-mechanical measurement of fracture behaviour of individualgrain boundaries in Ni alloy 600 exposed to a pressurized waterreactor environmentrdquo Corrosion Science vol 104 pp 9ndash16 2016

[22] D E J Armstrong A JWilkinson and S G Roberts ldquoMicro-mechanical measurements of fracture toughness of bismuthembrittled copper grain boundariesrdquo Philosophical MagazineLetters vol 91 no 6 pp 394ndash400 2011

[23] S Kobayashi R Kobayashi and T Watanabe ldquoControl ofgrain boundary connectivity based on fractal analysis forimprovement of intergranular corrosion resistance inSUS316L austenitic stainless steel random boundariesrdquo ActaMaterialia vol 102 no 1 pp 397ndash405 2016

[24] C Y Jeong K J Kim H U Hong and S W Nam ldquoEffects ofaging temperature and grain size on the formation of serratedgrain boundaries in an AISI 316 stainless steelrdquo MaterialsChemistry and Physics vol 139 no 1 pp 27ndash33 2013

[25] H M Ledbetter ldquoMonocrystal-polycrystal elastic constants ofa stainless steelrdquo Physica Status Solidi A Applications andMaterials Science vol 85 no 1 pp 89ndash96 1984

10 Advances in Materials Science and Engineering

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom