Damage and fracture mechanism of a nickel-based single crystalsuperalloy during creep at moderate temperature

Sugui Tian n, Xin Ding, Zhongge Guo, Jun Xie, Yongchao Xue, Delong ShuShenyang University of Technology, Shenyang 110870, China

a r t i c l e i n f o

Article history:Received 25 July 2013Received in revised form11 October 2013Accepted 14 November 2013Available online 22 November 2013

Keywords:Nickel-based single crystal superalloyCreepDouble oriented slippingInitiation and propagation of crackFracture mechanism

a b s t r a c t

By means of creep properties measurement, microstructure and fracture morphology observation, aninvestigation has been made into the damage and fracture mechanism of a nickel-based single crystalsuperalloy during creep at intermediate temperature. The results show that the deformation mechanismof the alloy is dislocations slipping in the γ matrix and shearing into γ′ phase, the dislocations shearinginto γ′ phase may be decomposed to form the configuration of the partials plus stacking fault and theK–W locking. While in the latter stage of creep, the primary–secondary slipping systems are alternativelyactivated to shear and twist the cubical γ′/γ phases, which results in the initiation of the micro-crackoccurring in the intersection regions of two slip systems. As creep goes on, the micro-cracks arepropagated on the (001) plane along ⟨110⟩ directions. Because the multi-cracks are formed andpropagated on the different cross-section of the sample during creep, which may result in the tearing edgeor secondary cleavage plane generating at the tip of the cracks along the direction with bigger shearingstress. When the propagating primary cracks on (001) plane intersects with {111} secondary cleavage plane,the propagation of the primary cracks is terminated to form the square-like cleavage plane on the (001)plane. In further, themulti-cracks propagating on the different cross-section are joined by the tearing edge orsecondary cleavage plane until the occurrence of creep fracture, this is thought to be the main reason of thecreep fracture displaying the uneven and multi-level cleavage features.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The microstructure of nickel-based single crystal superalloysconsists of the cubical γ′ phase embedded coherent in γ matrix[1–3], and they have been widely used to make the blade parts ofthe advanced aero-engines for their high volume fraction of γ′strengthening phase which results in the good creep resistance athigh temperature [4–6]. With the increase of service performance,such as the aero-engine power and thermal efficiency, themechanical and creep properties of superalloys at high tempera-tures need to be further improved [7–9]. Adding some refractoryelements, such as W, Ta, or Mo, is expected to improve the creepresistance of single crystal nickel-based superalloys [10] due to thesolution strengthening effects of the elements to slow down thediffusing processes. Although the single crystal nickel basedsuperalloys possess the excellent mechanical and creep propertiesat high temperature, the centrifugal force originated from high-speed rotation in aero-engine in service still may cause the creep

damage of the blade parts, which is thought to be the main modelof aero-engine failure [11–13].

The microstructure and creep feature of the single crystalsuperalloys change with imposed stresses and temperatures.Under the conditions of the applied stress of 552 MPa at 850 1C,the creep of some alloys displays an incubation period, in whichsome dislocations are piled up in matrix channels [14]. In theprimary stage of creep, the activated dislocations overcome theOrowan resistance to slip along the ⟨110⟩ direction on the {111}planes in the γ matrix channel [15]. And the reaction of two setsdislocations slipping in the same channel occurs to form thedislocation networks, which may promote the climbing of disloca-tions during steady state creep of alloy [16]. But with theenhancement of creep temperature, the interfacial dislocation toinduce shearing γ′ phase becomes progressively easier, because ofthe decrease of elastic energy and the increase of diffusivity [17].And the cavities and micro-cracks are formed and propagatedalong the interfaces of γ′/γ phases in the latter stage of creep [18].

When no eutectic and initial melting phenomena occurs in alloy,the micro-void formed during solidification may transform into themicro-cracks during creep at high temperature [19], and thedisordering micro-cracks may initiate and propagate along theγ′/γ interfaces vertical to the stress axis up to the occurrence ofcreep fracture [4,20]. Some investigations on the creep fracture of

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0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.msea.2013.11.049

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Materials Science & Engineering A 594 (2014) 7–16

superalloys at high temperature reported [21–24] that themicro-voidsformed during solidification may be congregated into the cavities ormicro-cracks during creep at high temperature, and the cavities ormicro-cracks are initiated and propagated along the interface of γ′/γphases, as the creep goes on, up to the occurrence of creep fracture.

Due to the work of aero-engines in service undergoing theprocesses from intermediate temperature/higher stress to hightemperature/lower stress, the blade parts in aero-engine had tobear various work conditions from start to stable course. And thesuperalloys with various compositions display different creepproperties at various temperatures. Although some literatureshad reported that the creep and damage behaviors of singlecrystal nickel based superalloys at high temperature [25–28],few literature reported that the damage and deformation mechan-isms of the superalloys during creep at intermediate temperatures,and the effect of the slipping traces on the initiation and propaga-tion of the cracks and the fracture mode of the alloy duringintermediate temperature creep is still not clear. Especially, thesingle crystal blade parts in service at medium temperature/higherstress conditions is easy to failure, and understanding the damageprocess of the blade parts in service has an important guidingsignificance on choosing materials and structure design. Therefore,the damage behaviors of single crystal superalloys during creep atmedium temperature are to be investigated.

Hereby, in the paper, by means of creep properties measure-ment and microstructure observation, the damaged and fracturebehaviors of a single crystal nickel based superalloy during creepat intermediate temperature are investigated.

2. Experimental procedure

The single crystal nickel based superalloy with [001] orienta-tion had been produced by means of selecting crystal method in avacuum directional solidification furnace under the condition of ahigh temperature gradient. The nominal composition of the super-alloy is Ni–6.0Cr–11Co–9W–xMo–6.0Al–7.0Ta (mass fraction, %),and all samples are within 71 deviating from the [001] orientation.The heat treatment regimes of the single crystal nickel basedsuperalloy are given as follows: 1280 1C�2 h, ACþ1315 1C�4 h,ACþ1080 1C�4 h, ACþ870 1C �24 h, AC.

After fully heat treated, the bars of the alloy were machined,along the [001] orientation, into the tensile creep samples with thecross-section of 4.5 mm�2.5 mm and the gauge length of 20 mm,the wider surface of the sample is parallel to the (100) plane. Theuni-axial constant loading tensile tests were conducted, in a creeptesting machine with GWT504 model, under the applied stress of800 MPa at 760 1C, 780 1C and 800 1C and applied stress of 750 MPa,775 MPa an 800 MPa at 800 1C, respectively. The samples after creptup to fracture are grinded and polished, and then themicrostructureand fracture of the alloy are observed by using Scanning electronmicroscope (SEM). The compositions of the eroded solution are 20 gCuSO4þ5 ml H2SO4þ100 ml HCIþ80 ml H2O. The films are pre-pared by twin-jet electro-polishing method for observing themicrostructure under transmission electronmicroscope (TECNAI20model), combined to the contrast analysis of the dislocation config-uration bymeans of the double beams technology, for investigatingthe damage and fracture mechanism of the single crystal nickel-based superalloy during creep at intermediate temperature.

3. Experimental results and analysis

3.1. Creep features of alloy

Under the conditions of the applied higher stress at intermedi-ate temperatures, the creep curves of the free-Re single crystal

nickel-based superalloy are measured, as shown in Fig. 1. Thecreep curves of the alloy under the applied stress of 800 MPa atvarious temperatures are shown in Fig. 1(a), indicating that thestrain rates of the alloy during steady state creep at 760 1C, 780 1Cand 800 1C are measured to be 0.00876%/h, 0.0127%/h and0.0155%/h, respectively, and creep lifetimes of the alloy aremeasured to be 323 h, 165 h and 84 h, respectively. It may beunderstood that when the creep temperature enhances from760 1C to 780 1C, the strain rates of the alloy increase from0.00876%/h to 0.0127%/h, and the lifetimes of the alloy decreasesfrom 323 h to 165 h, the decreasing extent of the lifetime is about96%. The creep curves of the alloy under the applied stress of750 MPa, 775 MPa and 800 MPa at 800 1C are shown in Fig. 1(b),which indicates that the strain rates of alloy during steady statecreep at 750 MPa and 775 MPa are measured to be 0.0067%/h and0.013%/h, respectively, and creep lifetimes of the alloy are mea-sured to be 260 h and 125 h, respectively. When the applied stressenhances from 775 MPa to 800 MPa, the strain rates of the alloyincrease from 0.013%/h to 0.023%/h, and the lifetimes of the alloydecreases from 125 h to 84 h, the decreasing extent of the lifetimeis about 48.8%. This suggests that the alloy possesses an obvioussensibility on the applied temperatures and stresses in the rangesof the applied temperatures and stresses.

The transient strain of the alloy occurs at the moment ofapplying load at high temperatures. And the density of disloca-tions increases as the creep goes on, which results in the strainstrengthening of alloy to decrease the strain rate due to increasingthe dislocations moving resistance [29]. As creep time prolongs,the slipping and climbing of dislocations are activated to promotethe recovery softening of the alloy, which may relax the stressconcentration in local regions. Once the equilibrium of thedeformation strengthening and the recovery softening is obtained,the strain rate of the alloy keeps constant for entering the steadystate stage of creep. Thereinto, the strain rate of the alloy duringsteady-state creep may be described by Dorn's law as follows [30]:

_εss ¼ AsnA exp �Qa

RT

� �ð1Þ

where _ε is the strain rate during steady state creep, A is a constantrelated to the microstructure, sA is the applied stress, n is theapparent stress exponent, R is the gas constant, T is the absolutetemperature, and Q is the apparent creep activation energy.

According to the data in creep curves of Fig. 1, the dependencesof the strain rates during steady state creep on the appliedtemperatures and stresses are shown in Fig. 2(a) and (b). In thefurther, in the ranges of the applied temperatures and stresses, theapparent creep activation energy and apparent stress exponent ofthe superalloy are calculated to be Q¼568.3 kJ/mol and n¼13.8,respectively. This indicates that the single crystal nickel basesuperalloy has a better creep resistance in the ranges of theapplied stresses and temperatures. And it may be deductedaccording to the calculating stress exponent that the dislocationsslipping in the γ matrix and shearing into the γ′ phase are thoughtto be the main deformation mechanisms of the alloys duringsteady state creep at medium temperature.

3.2. Dislocation configuration during creep

The morphologies of the alloy at different states are shown inFig. 3, the normal of the observing sample is [100] orientation, thedirection of the applied stress is marked by the arrows. After fullyheat treated, the microstructure of the alloy consists of the cubicalγ′ phase embedded coherent in the γ matrix, is shown in Fig. 3(a),thereinto, the [001] and [010] directions on (100) plane is markedby the arrows, which indicates that the cubical γ′ phase in the alloyis regularly arranged along 〈100〉 orientation, and the average

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–168

size of the cubical γ′ phase is about 0.45 μm, the width of the γmatrix channel is about 100 nm. The volume fraction of thecuboidal γ′ phase in the alloy at room temperature is about 70%.

After crept for 0.5 h at 775 MPa/800 1C, the morphology ofsome dislocations slipping and cross-slipping in the γ matrix isshown in Fig. 3(b), which indicates that the directions of theslipping traces is about 451 angles relative to the stress axis. Aftercrept for 70 h, the strain value of the alloy is about 2%, themorphology of denser dislocations slipping in the γ matrix isshown in the region A of Fig. 3(c). Thereinto, the dislocationsnetworks are distributed in the interfaces of the cuboidal γ′/γphases, some dislocations shear into the γ′ phase, as marked by the

arrow, the dislocation shearing into the γ′ phase is decomposed asshown in the region B in Fig. 3(c).

After crept for 125 h up to fracture at 800 1C/775 MPa, thedislocations configuration in the alloy is shown in Fig. 4, thenormal of observing sample is [100] orientation, the direction ofapplied stress is marked by the arrows. It may be understood fromFig. 4 that significant amount of dislocations are activated forslipping in the γ matrix, as shown in the regions C and D, only afew dislocations shears into the cubical γ′ phase, as marked bythe arrow.

Another some of the slipping traces display the twistedconfiguration with 901 feature, which is attributed to the

0 50 100 150 200 250 3000

3

6

9

12

15

T -- 800°C1 -- 800MPa2 -- 775MPa3 -- 750MPa

Stra

in, ε

(%)

Time, h

1 2 3

0 50 100 150 200 250 300 3500

3

6

9

12

15

32

σ--800MPa1--800°C2--780°C3--760°C

Time, h

Stra

in ε

, (%

)1

Fig. 1. Creep curves of alloy at different temperatures and stresses. (a) Applied stress of 800 MPa at various temperatures and (b) applied various stresses at 800 1C.

6.62 6.64 6.66 6.68

-5.0

-4.8

-4.6

-4.4

-4.2

-4.0

n = 13.8

9.3 9.4 9.5 9.6 9.7-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

Q = 568.3 kJ/mol

Fig. 2. Dependence of strain rates of alloy during steady state creep on temperatures and stresses. (a) Strain rates and temperatures and (b) strain rates and applied stresses.

[001]

[010]

σ

σ

σ σ B

A

0.4μm 0.4μm 0.3μm

Fig. 3. Morphology of the single crystal nickel based superalloy at different states. (a) After fully heat treatment, cubical γ′ phase embedded coherent in the γ matrix,(b) slipping and cross-slipping of dislocations in the γ matrix, and (c) after crept for 70 h, some dislocations slipping in the γ matrix and shearing into the γ′ phase.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–16 9

cross-slipping of dislocations, as shown in the region E, thereinto,the dislocations shearing into the γ′ phase are decomposed to formthe configuration of partial dislocations plus the stacking fault, asshown in the region F.

The magnification morphology of the dislocations configura-tion in the regions C and D are shown in Fig. 5(a) and (b),respectively. The microstructure of single crystal nickel-basedsuperalloy consists of the cubical γ′ phase embedded coherent in

the γ matrix, compared to the γ′ phase, the γ matrix phasepossesses a lower strength and better plasticity. Therefore, theslipping and cross-slipping of dislocations are firstly activated inthe γ matrix channels when the loading is applied at hightemperature. As the creep time prolongs, the moving dislocationsin the γ matrix are piled up to decrease the strain rate due to therole of the strain strengthening, which results in the creep of thealloy entering the steady state stage. In the latter stage of creep,the denser dislocations with tangles feature slip in the γ matrixchannels, as shown in Fig. 5(a). Thereinto, the (1/2)〈110〉 dis-locations during creep are activated in the γ matrix along thedirection about 451 angles relative to the stress axis, whichindicates that the slipping direction of dislocations is the sameas the maximal shearing stress, as marked by arrow in Fig. 5(a).

Due to the bigger strain occurring during creep of the alloy,significant amount of dislocations with the single and doubleoriented slipping traces are activated in the γ matrix channels inlocal region, as shown in Fig. 5(b), thereinto, the directions of theslipping traces with double oriented feature are marked by thecrossed arrows, and the directions of the slipping traces are about451 angle relative to the stress axis. But another some of theslipping traces display the twisted configuration, and it is thoughtby analysis that the dislocations may cross-slip from {111} plane toanother {111} plane to from the configuration with 901 twistedfeature when the slipping of (1/2)〈110〉 dislocations is hinderedin the front of the cubical γ′ phase, as shown by single arrow inFig. 5(b). As the creep goes on, the density of dislocations in the γmatrix channels increases to produce the stress concentration,

Fig. 4. Dislocation configuration of the alloy crept for 125 h up to fracture at800 1C/775 MPa.

<110>

0.2μm 0.2μm

Fig. 5. Dislocations configuration in the matrix of alloy crept for 125 h up to fracture. (a) Single orientated slipping of dislocations in the matrix and (b) cross-slipping anddouble orientated slipping of dislocations activated in the matrix.

g131

G

H

M

N

g002

H

M

G N

0.2μm

M

N

H

G

g0 ⎯22

Fig. 6. Dislocation configuration of the alloy crept up to fracture at 800 1C/775 MPa. (a) g¼002, B¼[31̄0], (b) g¼131, B¼[31̄0], (c) g¼02̄2, B¼[100].

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–1610

which may promote the initiation and propagation of the cracks inthe interfaces of γ/γ′ phases when the value of the stress con-centration exceeds the yield strength of the interface.

Under the applied stress of 775 MPa at 800 1C, the morpholo-gies of the alloy crept for 125 h up to fracture are shown in Fig. 6,where the normal of the film is parallel to [100] direction. It isindicated that significant amount of dislocations are activated inthe γ matrix channels and piled up the interfaces of γ′/γ phases.Thereinto, the cubical γ′ phase is sheared by 〈110〉 super-dislocation, as marked in the region G, and the super-dislocationshearing into the γ′ phase may be decomposed to form theconfiguration of the Shockley partial dislocations plus the super-lattice intrinsic stacking fault (SISF), as marked in the region H, andthe partial dislocations in the stacking fault sides are marked bythe letters M and N. The directions of the incident beam in theoperating diffraction are B¼[31̄0], B¼[31̄0] and B¼[100], asshown in Fig. 6(a), (b) and (c), respectively.

It may be understood from Fig. 6 that the partial dislocation Hexhibits contrast when the diffraction vectors is g¼131, as shownin Fig. 6(b), while the partial dislocation H disappears contrastwhen the diffraction vectors are g¼002 and g¼02̄2, as shown inFig. 6(a) and (c), respectively. Therefore, it may be determinedaccording to the criteria of the dislocation invisible, b� g¼0, thatthe dislocation N is the super-Shockley partial dislocation withBurgers vector bN¼1/3[211̄]. When the diffraction vectors isg¼002 and g¼131, the partial dislocation M and stacking faultH display contrast, as shown in Fig. 6(a) and (b), when thediffraction vectors is g¼02̄2, the partial dislocation M and stackingfault H disappear contrast, as shown in Fig. 6(c). Therefore, it maybe determined according to the criteria, b� g¼0 and b�g¼7(2/3)that the dislocation M is the Shockley partial dislocation withBurgers vector bM¼1/6[1̄12] due to locating in the interface of γ′/γphases. It is a reasonable consideration that 1/2[011] dislocationshearing into the γ′ phase may be decomposed to form theconfiguration of two super-Shockley partial dislocations withBurgers vector bM¼1/6[1̄12] and bN¼1/3[211̄] plus the stackingfault (SISF). The decomposed reaction formula of the dislocationsmay be expressed in Eq. (2), and the decomposed plane of thereaction may be identified as (11̄1) plane according to bM�bN.

1=2½011�-1=3½112�MþðSISFÞþ1=6 ½211�N=interface ð2ÞOn the other hand, the dislocation E displays contrast when the

diffraction vectors is g¼131 and g¼02̄2, as shown in Fig. 6(b) and(c), but the dislocation G disappears contrast when the diffractionvectors is g¼002 and g¼113̄ (the picture omitted), as shown inFig. 6(a). Therefore, the dislocation G is identified as the super-dislocation with Burgers vector bG¼[1̄10] which is located on the(001) plane. And it is an reasonable consideration that the initialslipping plane of dislocation G is thought to be {111} plane, ascreep goes on, the super-dislocation E shearing into γ′ phase maybe cross-slipped from {111} plane to (001) plane to form the K–Wdislocation locking. This may effectively hinder dislocation slip-ping on {111} plane to improve the creep resistance of alloy.

Moreover, the similar deforming feature displays still in thealloy during creep at 760 1C and 780 1C. The morphology of thealloy crept for 323 h at 760 1C/800 MPa is shown in Fig. 7, includ-ing that the dislocations slip in the γ matrix and shear into the γ′phase. The morphology of dislocations slipping in the γ matrix isshown in the region K, the directions of the double orientationsslipping traces are marked by the cross arrows, the cross-slippingof dislocations for forming the configuration with 901 twistedfeature is marked by the arrow. Dislocations shearing into the γ′phase are decomposed to form the configuration of the partialdislocations plus the stacking fault (SISF), as shown in the regions Jof Fig. 7. Compared to the configuration of Fig. 4, the deformationfeature of the alloy during creep at 760 1C displays the more

configurations of the partials plus the stacking fault (SISF), asshown in Fig. 7, which suggests that a lower stacking fault of thealloy displays during creep at 760 1C.

3.3. Slipping traces in the latter stage of creep

When the alloy is crept for 125 h at 800 1C/775 MPa, theslipping traces appear in the surface of the sample, as shown inFig. 8, the normal direction of the observing sample is [100]orientation, the direction of the applied stress is marked by thedouble arrows. Thereinto, the macroscopic morphology in thelocal region is shown in Fig. 8(a), this displays the morphology ofthe slipping traces with single oriented feature. The direction ofthe slipping traces is about 451 angles relative to the stress axis, asmarked by the arrow, the width of the slipping band is about 1 μm,as marked by two parallel lines. The magnification morphology inlocal region is shown in Fig. 8(b), indicating that the twistedconfiguration of the cubical γ′ phase appear within the slippingbands due to the inverse shearing stresses applying in the sides ofthe slipping band, as shown in the region M of Fig. 8(b).

In another local area of sample, the macroscopic morphology ofthe slipping traces with double oriented feature is shown in Fig. 8(c), the primary slipping trace is marked by the arrow 1, thesecondary slipping trace is marked by the arrow 2. The secondaryslipping traces are activated after the initial slipping traces arefirstly activated, which results in the displacement of the primaryslipping traces, as marked by up and down lines in Fig. 8(c), andthe micro-cracks appear in the intersecting region of two slippingbands, as shown in the region N of Fig. 8(c). The magnifiedmorphology in the region is shown in Fig. 8(d), thereinto, theslipping directions of the primary and secondary slipping bandsare marked by the arrows. The twisted of the γ′/γ phases occurswithin the slipping bands due to the alternate activation of theprimary/secondary slipping systems. And the initiation of thecracks occurs in the interface of γ′/γ phases in the slipping banddue to the alternate activation of the primary/secondary slippingsystems, the fine cracks in the interface of γ′/γ phases are markedby the arrows in Fig. 8(c) and (d).

The interacting features of the slipping traces with differentorientations is shown in Fig. 9, thereinto, the primary slippingsystem is marked by the number 1, the secondary slipping systemis marked by the number 2. During creep, the primary slippingsystem 1 is firstly activated, and then the secondary slippingsystem 2 is activated as the creep goes on, the direction of theslipping trace is marked by the arrow 2. When the slipping system2 is activated to shear the slipping system 1, the traces of the

g020

0.2μm

K

J

J

Fig. 7. Dislocation configuration of the alloy crept for 325 h up to fracture at760 1C/800 MPa.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–16 11

slipping system 1 are displaced toward downside to form theintersected configuration of the slipping traces, the distance of theslipping traces displacement is marked by the dashed and realarrows in Fig. 9.

3.4. Initiation and propagation of crack

After the alloy is crept for 125 h up to fracture at 800 1C/775 MPa, the initiation and propagation of the crack occur alongthe interfaces of γ/γ′ phases, as shown in Fig. 10, in which thedirection of the applied stress is marked by the arrow. In the latterstage of creep, the bigger plastic deformation occurs in the alloy,so that the cavities appear in the intersected region of the primary/secondary slipping traces due to the alternate activation of them.And the quantity of the cavities increases as the creep goes on, inthe further, the cavities are congregated to form the crack in theinterfaces of γ/γ′ phases, as marked by the arrow in Fig. 10(a).

As the creep goes on, the stress concentration occurs in theregion near the cracks initiation, which results in the propagation

of the crack along the direction vertical to stress axis, the tip of thecrack is marked in the region K of Fig. 10(b). It may be understoodfrom Fig. 10(b) that the crack appears in the interface of γ/γ′phases, the inclined and bigger twisted extent of γ′ phase occurs inthe region near the crack, and the γ′ phase with the wavyconfiguration appears in the another regions, which is attributedto the bigger plastic deformation in the regions.

In the latter stage of creep, the propagating morphology of thecracks is shown in Fig. 10(c), the propagation of two parallel cracksoccur contemporary in the interfaces of γ′/γ phases, which isthought to be the congregating region of the cracks. When thecracks are propagated along the γ/γ′ interfaces vertical to the stressaxis, the fine tip of the cracks appears in the region J, but the widersize appears in the middle region of crack, which is attributed tothe propagation of the crack to increase the width along thedirection vertical to the stress axis. In the region far from thecracks, the cubical γ′ phase is regularly arranged along the 〈100〉orientations, but the cubical γ′ phase is disorderedly arranged inthe region near the cracks and cavity, which suggests that thesome defects having an important effect on the configurationevolution of γ′ phase during creep.

After the alloy is crept up to fracture, significant amount ofcracks are piled up in the region near the fracture, the region isdefined as the congregating region of cracks, which displays thevarious configuration and features of the cracks, as shown inFig. 11, the direction of the applied stress is marked by the arrows.This indicates that the cracks in the congregating region areformed in the interfaces of γ/γ′ phases at the different cross-section, and propagated along the direction vertical to stress axis.It is indicated from Fig. 10 that the cracks 1 and 2 are formed in thedifferent cross-section, and propagated at the same time as thecreep goes on, therefore, the effective stress and strain rate of thealloy during creep at the constant loading increases up to occur-rence of the creep fracture due to the decrement of the samplecross-section.

It is considered by analysis that the bigger shearing stressoccurs in the direction being about 451 angles relative to the stressaxis at the moment of the cracks propagation, which results in thecrack 1 tearing along the direction with maximal shearing stress toconnect with the crack 2, as marked by the inclined line in Fig. 11.

σ

σ

3μm 1μm

M

N

3μm

C

1μm1

2

Fig. 8. Deformation features after the alloy crept for 125 h at 800 1C/775 MPa. (a) Morphology of slipping traces with single oriented feature, (b) magnified morphology ofsingle oriented slipping traces, (c) morphology of double oriented slipping traces, (d) magnified morphology of double oriented slipping traces.

2

1

3μm

Fig. 9. Interaction of the double oriented slipping traces during creep.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–1612

3.5. Creep fracture

Under the conditions of the applied stress of 775MPa at 800 1C,the fracture morphology of the alloy crept for 125 h up to rupture isshown in Fig. 12, the macroscopic morphology of the fracture is shownin Fig. 12(a). The normal direction of the photo is [001] orientation, the[100] and [010] orientations in the photo are marked by the arrows inFig. 12(a). It may be understood from Fig. 12(a) that the fracture of the[001] oriented superalloy displays an uneven morphology, the square-like cleavage plane is parallel to (001) one and displays the planar andstraight feature, which is attributed to the cracks propagating alongthe (001) plane. The edge line directions in the square-like cleavageplane are identified as〈110〉 orientations, the inclined walls near thesquare-like cleavage plane are linked by the tearing edges formedfrom the cracks propagation, as marked by the arrows in Fig. 12(a). Theinclined walls being parallel to {111} planes are defined as the {111}secondary cleavage plane. The inclined angle is well agreement withthe inclined line for linking the cracks 1 and 2 in Fig. 11.

The magnified morphology in the local region of fracture is shownin Fig. 12(b), it is indicated from Fig. 12(b) that the square-like cleavageplanes P, Q and R, originating from the cracks propagation along (001)plane during creep, appear in the different height, which suggests thatthe cleavage fracture of the sample occurs in the different cross-sections. The edges length of the square-like cleavage plane is about

30–40 μm, thereinto, the round-like holes locating in the center ofcleavage plane are thought to be the crack source which originatesfrom the alternate activation of the primary/secondary slippingsystems during creep. And the creep fracture of the alloy occurs toform the cleavage steps in the different planes once the cracks in thedifferent height are propagated along the (001) plane for linking eachother by tearing edges or {111} secondary cleavage planes, as markedby the white arrow in Fig. 12(b). Because the slower rate of the crackspropagation occurs during creep at medium temperature, this pro-duces only a smaller affecting zone, so that the quantities of thecleavage planes increases with probability of the crack initiation in thedifferent region.

The morphology in another region of the fracture is shown inFig. 13(a), indicating that the square-like cleavage planes in thefracture is vertical to the stress axis, and linked each other by thetearing edge or {111} secondary cleavage plane. The round-likehole is located in the center of the cleavage plane, as marked bythe arrow in the region S of Fig. 13(a). The magnified morphologyin the region near the hole is shown in Fig. 13(b), the cleavagestripes with radial feature are located in the round of the hole, asmarked by the white arrow, and the hole is thought to be the crackpropagating source of the cleavage plane.

It is thought by analysis on the fracture process that, in thelatter stage of creep, the round-like hole is firstly formed in (001)plane due to the alternate activation of the primary/secondaryslipping systems, As the creep goes on, the round-like hole ispropagated on (001) plane along 〈110〉 directions to form thecleavage stripes with radial feature, as marked by the arrow inFig. 13(b). The bigger shearing stress occurs in the tip of the cracksat different height when the cracks in the different height arepropagated, which promotes the formation and propagation of thesecondary cracks along the direction with the maximal shearingstress to form the tearing edges and {111} secondary cleavageplane. And the creep fracture of the alloy occurs once the cracks onthe different cross-sections are propagated to link each other bythe tearing edges and secondary cleavage planes. Therefore, thefracture of the alloy displays an uneven configuration.

4. Discussion

4.1. Initiation of crack during creep

Based the microstructure observation and analysis of the creepsample, it is thought that, in the latter stage of creep, the slipping

Fig. 10. Initiation and propagation of crack in the region near fracture after the alloy crept for 125 h up to fracture at 800 1C/775 MPa. (a) Initiation of crack, (b) micro-crack,and (c) propagating of crack.

Fig. 11. Initiation and propagation of multi-cracks on various cross-sections in theregion near fracture.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–16 13

traces with double oriented feature are alternately activated topromote the initiation and propagation of the crack along the(001) plane, which is thought to be the damage and fracturemechanisms of alloy during creep at intermediate temperature.

During creep, significant amount of dislocations in the alloy areactivated, and the cubical γ′ phase may hinder the movement ofdislocations to bring the stress concentration. When the value ofthe stress concentration excesses the yield strength of γ′ phase, thecubical γ′ phase may be sheared by the slipping dislocations totwist the regular arranged γ′ phase, as shown in Fig. 9(a) and (b),the process is schematically shown in Fig. 14. The direction of theapplied stress is perpendicular to the (001) plane, the width of theactivated slipping band is marked by the letter W in Fig. 14(a), theregular arranged γ′ phase within the band is twisted to incline anangle relative to the stress axis, as marked by the dashed line.

When the secondary slipping system is activated to shear theprimary slipping band, the primary slipping system is displaced topromote the micro-cracks initiating in the intersecting region oftwo slipping bands, as shown in Fig. 14(b). And then the primaryslipping system is again activated to displace the secondary slippingband, as shown in Fig. 8(c), which is schematically shown in Fig. 14(c), thereinto, the stretching displacement of crack is denoted by theletter a, the length of crack is denoted by the letter 2c.

It is thought by analysis that the stress concentration originat-ing from the dislocations accumulation may be released by powercreep, which is a non-thermal activation process. And the initia-tion of the crack occurs due to the alternate activation of theprimary/secondary slipping systems, the stability of the crack isrelated to the energy change during crack formation. The energychange is expressed as [31]: ΔG¼ΔGWþΔGSþΔGEþΔGP, here,ΔGW being the energy change of the crack displacement (a), ΔGS

being the surface energy change of the crack, ΔGE being thechange of the elastic strain energy, and ΔGP being the change of

the potential energy. Under the plane-strain condition, the free-energy change for forming a crack with 2c in length and thedisplacement (a) is expressed as

ΔG¼ μUa2

4πð1�νÞ ln2Lc

� �þ2ηUc�πð1�νÞs2c2

2μ�sUaUc ð3Þ

where μ is the shear modulus, ν is Poisson's ratio, η is the specificsurface energy, and s is the applied stress. The free-energy in thesystem obtains a minimum value when the crack can stably exist,according to ð∂ΔG=∂cÞ ¼ 0, the length (c) of the crack which maystably exist is calculated to be

c¼ Gηπð1�νÞs2 1�sa

2η

� �7 1�sa

η

� �1=2" #

ð4Þ

According to Eq. (4), it may be concluded that the propagationof the crack may occur when s4η/a, therefore, according to s¼η/a, the critical length (cc) of the crack which may be propagated isdefined as

cc ¼μUa2

2πð1�νÞη¼ Ka2

ηð5Þ

This indicates that the critical length (cc) of the crack forunstable propagating during creep is proportional to the ratio ofthe stretching displacement's square of crack and specific surfaceenergy.

4.2. Propagation of crack

The round-like hole on (001) plane appears firstly in theintersected region of the primary/secondary slipping systemsdue to the alternate activation. Under the action of the appliedstress at high temperature, the quantity and size of the crack

Fig. 13. Magnified morphology of fracture in the alloy after crept up to rupture at 775 MPa/800 1C. (a) Cleavage step on different plane and (b) magnified morphology ofcleavage plane.

Fig. 12. Fracture morphology of the alloy crept up to rupture at 775 MPa/800 1C. (a) Macrostructure of fracture and (b) cleavage planes on fracture.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–1614

increase gradually, as marked by the arrow in Fig. 10. As the creepgoes on, the micro-crack is radially propagated, along the (001)plane vertical to the stress axis, to form the cleavage plane withsquare feature.

It may be understood from Fig. 12(b) that the edge lines in thesquare-like cleavage plane is parallel to 〈110〉 directions, and itis thought by analysis that the 〈110〉 direction in the FCC crystalis the close arranging direction of the atoms, and dislocations iseasily activated along the direction due to the higher elasticmodulus of its than the one of 〈100〉 direction. Therefore, theelastic strain energy may be released when the crack is propagatedalong the direction, which suggests that the 〈110〉 direction inthe FCC crystal possesses the bigger probability of the crackpropagation [32]. The strain value of the alloy increases as thecreep goes on, and significant amount of dislocations are activatedto bring the stress concentration, which may promote the propa-gation of the hole-like crack along the 〈110〉 directions on the(001) plane under the action of the applied loading at hightemperature.

The schematic diagram of the hole-like crack propagating alongthe (001) plane perpendicular to the stress axis to form thesquare-like cleavage plane is shown in Fig. 15. In the latter stageof creep at applied stress along [001] direction, the hole-like crackis gradually propagated along the (001) plane perpendicular to thestress axis to form the square-like plane, as shown in Fig. 12(b),and the edge line in the square-like cleavage plane is parallel to〈110〉 directions, as marked in region F of Fig. 15, which isthought to be the propagated direction of the crack.

On the one hand, the primary crack is propagated on the (001)plane along the〈110〉 directions, and then the secondary crack isactivated to propagate along four {111} planes of symmetrydistribution, in which the dislocations with higher density brings

easily the stress concentration to promote the propagation of thesecondary crack. On the other hand, the primary crack is propa-gated on (001) plane along the 〈110〉 directions which areupright each other, as marked by the thicker arrow in Fig. 15.When the propagation of the primary crack on (001) plane alongthe 〈110〉 directions is intersected with the secondary cleavageplane on {111} planes, the propagation of the primary crack on(001) plane is stopped, therefore, the primary cleavage plane comefrom the crack propagation displays the square-like feature, asshown in Fig. 12(b). The {111} secondary cleavage planes in up anddown sides are encountered on the (001) plane, as schematicallyshown in Fig. 15. The primary cleavage plane with the square-likefeature is perpendicular to the stress axis to bear the normal stressof the applied loading during creep.

It is considered by analysis that the damage process of thesingle crystal nickel-based superalloy during creep at intermediatetemperature may be described as the round-like hole or micro-crack appearing firstly in the (001) interface of γ′/γ phases. As thecreep goes on, the primary crack is gradually propagated on (001)plane along the〈110〉 directions, and then the secondary crack isactivated to propagate along four {111} planes. And the square-likecleavage plane on the (001) plane forms when the propagation ofthe primary crack on (001) plane and secondary cracks on {111}planes is intersected on (001) plane. This is thought to be thefracture mechanism of the alloy during creep. Thereinto, the〈110〉 direction of the alloy has a bigger ability of the crackpropagation, which is thought to be one of reasons for the crackpropagating along 〈110〉 directions on (001) plane to form thecleavage plane with square-like feature. The analysis above state iswell consistent with the experimental results.

5. Conclusion

1) The deformation mechanism of the single crystal nickel-basedalloy during creep at intermediate temperature is dislocationsslipping in the γ matrix and shearing into γ′ phase, the disloca-tions shearing into γ′ phase may be decomposed to form theconfiguration of the partial plus stacking fault or cross-slippedform {111} plane to {100} plane to form the K–W locking.

2) In the latter stage of creep, the deformation mechanism of alloyis the alternate activation of the primary/secondary slippingsystems. The primary slipping system is firstly activated totwist the γ′/γ phases, and then the secondary slipping system isactivated to shear the primary slipping system, which promotesthe initiation of the micro-crack on (001) plane in the inter-sected region of the primary/secondary slipping systems.

3) As the creep goes on, the bigger stress concentration appearing inthe region near the crack tip promotes the initiation and propaga-tion of the secondary cracks on the {111} planes along the direction

Fig. 14. Schematic diagram of the slipping systems activated alternately to bring the crack initiation during creep. (a) Primary slipping system, (b) interaction of the primary/secondary slipping systems, and (c) primary slipping system activated again.

Fig. 15. Schematic diagram of the square-like cleavage plane formed on (001) planeduring creep. (a) Propagating mode of crack and (b) crack propagated along (001)and {111} plane.

S.G. Tian et al. / Materials Science & Engineering A 594 (2014) 7–16 15

with biggest shearing stress. Thereinto, the propagating crackalong 〈110〉 directions on the (001) plane intersects with the{111} secondary cleavage plane to stop the propagation of theprimary crack, which is thought to be the main reason of formingthe square-like primary cleavage plane on (001) plane.

4) As the propagation of the multi-cracks in the different cross-sections goes on, the tearing edges and secondary cracks areformed at the tip of the primary crack along the direction withbiggest shearing stress, which results in the gradual joining ofthe multi-cracks in the different cross-sections, by the tearingedges and secondary cleavage plane, up to the occurrence ofcreep fracture. This is thought to be main reason for the creepfracture of the alloy displaying the uneven cleavage configura-tion with multi-level feature.

Acknowledgments

Sponsorship of this research by the Natural Science Foundationof China under Grant no. 51271125 and the Ministry of EducationFoundation In China under Grant no. 200921020003 is gratefullyacknowledged.

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