Lattice Strain Evolution During Creep in Single Crystal Superalloys

James Coakleya, Roger C Reedb, Jonnathan LW Warwickc, Khandaker M Rahmanc, David Dyec

aNeutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USAbDepartment of Metallurgy and Materials, The University of Birmingham, Edgbaston, Birmingham B15 2TT, England

cDepartment of Materials, Imperial College, South Kensington, London SW7 2AZ, England

Abstract

In-situ neutron diffraction studies are carried out to characterise the micro-mechanical deformation occurring duringtensile creep of a typical single crystal nickel-based superalloy, CMSX-4. The loading responses of the matrix γ phaseand the precipitate γ′ are distinct. Moreover, the behaviour in the tertiary creep regime (in which the γ′ phase remainsintact) is qualitatively different from that in the primary creep regime (when γ′ is sheared). In tertiary creep, initialdeformation of the matrix leads to a release of misfit between the phases in the (100), resulting in elastic compressionof the γ in the loading direction. The load state then remains fairly constant during creep. During the initial stagesof primary creep, elastic compression of the γ phase is observed until at around 2-4% creep strain this compressionstabilises as the (100) misfit is released. This is the point at which γ′ shearing is thought to begin. Subsequently, theload in the γ increases by around 200 MPa until a maximum is reached at around 8% creep strain. This load is thensuddenly released, which may be due to the release of back stress.

Key words: neutron diffraction, nickel alloys, creep, dislocations, creep

1. Introduction

Certain questions remain unanswered about the mi-cromechanics of deformation of the single crystal super-alloys. For example, to what extent is deformation onthe microscale restricted to the face-centered cubic γ ma-trix which resides between the strengthening, ordered γ′

precipitates? Or alternatively, under what conditions arethe γ′ particles sheared by dislocation activity? More-over, how do the different modes of deformation on themicroscale depend upon the temperature T and the ap-plied stress level σ? And from an engineering perspective,how does the underlying micromechanical mode of defor-mation influence the macroscopic response? Answers tothese questions would allow a greater understanding of thedeformation characteristics of these materials, and wouldallow more physically-faithful constitutive models to beconstructed [1, 2]. In turn, such understanding would en-able more accurate estimates to be made of the deforma-tion induced under engine operating conditions.

To answer these questions unequivocally, novel andhigh resolution characterisation techniques are needed. Un-fortunately, the micromechanics of deformation are mostusually studied by post-mortem characterisation of themicrostructure and dislocation activity, often under con-ditions very different from those at which deformationwas induced in the first place. For example, in the caseof creep in nickel-based superalloys, the regimes of tem-perature and stress relevant to practical applications are700 − 1100 ◦C and 100 − 850 MPa, as experienced in gasturbine applications. Yet is is probably true to state that

transmission electron microscopy (TEM) has been, untilnow, the most viable and widely used tool for studyingthe modes of dislocation activity [3, 4]. However, a weak-ness of this approach is that one is unable to probe thekinematics of deformation. Moreover, it is necessary tomake sometimes rather subjective interpretations basedupon the dislocation configurations, which are often re-laxed because of the necessity to examine thin foils at roomtemperature. Finally, it is necessary to be sure that onesamples a volume of material whose deformation charac-teristics are representative of the bulk behaviour, whichmight not always be the case.

In superalloys, conventionally creep is studied in threeregimes [2–4]. At low temperatures and high stresses,dislocation shear of the γ′ precipitates is observed andthe creep rate initially decreases in a conventional man-ner. This is followed by a so-called steady state regimeand finally, acceleration of the creep rate associated withvoid formation. Low temperature and high stress creep istermed the primary creep regime due to the large primarycreep strains observed. At intermediate temperatures andstresses shear of the precipitates does not occur and littleinitial primary creep is observed. Instead the creep rateincreases continuously with time; this is termed the ter-tiary regime since only the final accelerating creep rate isobserved. Morphological changes of the γ′ occur at thehighest temperatures. This change is termed rafting andtherefore this regime is called the rafting creep regime.

In this paper, neutron diffractometry is used to directlystudy the micromechanisms occurring during the creep de-

Preprint submitted to Acta Materialia December 19, 2011

formation of a typical single crystal superalloy. Whilstneutron diffractometry is now a widely used method forcharacterising engineering alloys [5–18], it is still rare forthe measurements to be made in-situ at temperatures andloading conditions beyond simple tensile or compressiontesting, as is attempted here. Moreover, the nature ofspecimens which are monocrystalline in form means thatthe experimental setup is more complicated than that usedconventionally for polycrystalline materials [7, 9–11, 19,20]. Here, it is demonstrated that neutron diffractome-try can be used to elucidate the micromechanisms of creepdeformation in these materials; moreover some of the firstin-situ measurements made on this class of material arepresented. This is done by making phase-specific determi-nations of the load-strain response during creep deforma-tion.

2. Experimental Details

Tensile-creep bars of the single crystal nickel superalloyCMSX-4 were machined from homogenized, heat treatedand aged castings provided by Rolls-Royce Plc., Derby,UK. The orientation of the three bars were with the load-ing axis within θ < 5.8 ◦ of the [100] direction. The mo-saic spread of the crystals was ∼ 1◦ in the casting [100]direction and around ∼ 7◦ in the secondary [010] and [001]orientations, as is typical for industrial Bridgman castings.

In time-of-flight diffraction, the measurement is radialin reciprocal space. For this reason the sample mosaiccontributions to the peak d-spacing width are observedonly indirectly. The samples were tested on the Engin-Xtime-of-flight (TOF) neutron diffractometer at ISIS, Did-cot, UK [21, 22]. The samples were mounted such that thestress was applied along the nominal [100] direction eachtime. The loading axis was horizontal and the rig waspositioned to give the longitudinal lattice displacement inone detector and the transverse lattice displacement in theother. The detectors were fixed at 90 ◦ to the incidentbeam (Figure 1), and data obtained from the full ±15 ◦

radial detector bank.In general, if more than one Bragg peak is required, a

TOF source outperforms a constant-wavelength (reactor)source, as a TOF pulse contains a wide range of wave-lengths and thus can obtain a complete diffraction pat-tern. The variable in TOF is the wavelength, and themeasurements are radial in reciprocal space in a single de-tector within a bank. The set-up of a single crystal sam-ple for neutron diffraction experimentation is more com-plicated than that for a polycrystal. For a single crystalto be correctly aligned, measurements need to be takenand the sample subsequently rotated until the desired lat-tice planes are found in each detector. An example of thediffraction spectra obtained is shown in Figure 2.

Three creep tests were performed; a tertiary creep testat 900 ◦C 460 MPa (sample c), and two primary creep testsat 650 ◦C 825MPa (samples a, b). Following sample align-ment, the temperature T was increased to the test tem-

Figure 1: Schematic of the experimental arrangement used to per-form neutron diffraction measurements at Engin-X, ISIS, Didcot,England.

Figure 2: Diffraction spectrum obtained by time-of-flight (TOF) neu-tron diffraction for CMSX-4 single crystal nickel superalloy. The(100) and (300) are γ′ reflections while the (200) doublet is a com-pound peak of γ and γ′ phases.

perature. The stress was stepped in order to measure theelastic constants, and then ramped to the creep stress.The elastic data generated serves to improve confidencein the experimental methodology and diffraction-spectrumfitting routine performed, by providing a reference casefor comparison with measurements made using other tech-niques in other nickel alloys [23–29]. This provides someconfidence in the measurements, as the elastic propertiesare relatively well known, and the d-spacing must be lin-ear with stress. In addition, the thermal expansion coef-ficients and constrained misfit of the phases were found.The results from the elastic analysis have been presentedelsewhere [22].

The first primary creep test (sample b) was commencedat 700 ◦C 825 MPa. However, the initial creep rate wasfound to be rather high and therefore after ∼ 0.2 h thetemperature was dropped to 650 ◦C. To remove any am-biguity, the test was repeated at 650 ◦C on a subsequentvisit to ISIS, sample (a). Unfortunately, the sample pro-vided in this test (sample a) had not been subjected tothe final ageing heat treatment, while samples (b) and (c)

2

Mac

rosc

op

ic C

reep

Str

ain

(%

)

Figure 3: Macroscopic creep curves obtained during the threetests; (a) 650 ◦C and d825 MPa, (b) 700 ◦C dropping to 650 ◦C and825 MPa and (c) 900 ◦C and 460 MPa.

3.643.623.603.583.56

80

60

40

20

0

1.841.821.801.78

-4-2024

Figure 4: (200) composite peak obtained by time-of-flight diffraction.The (200) γ′ peak fit was constrained by the location of the (100)reflection.

had the final ageing heat treatment. This was noticed af-ter the experiments had been performed, and should be aconsideration when comparing the experimental results.

The macroscopic creep curves are shown in Figure 3,with an inset to show the early stages of creep and thetemperature drop in sample (b). It can be observed thatthe creep rate accelerated continuously in (c) with no pri-mary creep, and that there was a small incubation periodin samples (a-b), as noted by [2].

A pseudo-Voigt peak shape was used to fit the (h00)(h = 1,3) γ′ peaks. Often, TOF neutron diffraction peakscan be asymmetric, leading to the use of a leading or trail-ing exponential convoluted with the pseudo-Voigt, and theasymmetry can be wavelength-dependent. In the presentcase, both the {100} and {300} single phase peaks could beadequately described without resorting to such measures,and so were not used. The (200) composite peak, Figure 4,was fitted in a similar manner to that performed by Stoneet al. [10], by assuming i) the instrumental peak widths ofboth phases are equal, ii) the Voigt shape function of bothpeaks are equal and iii) that the (200) γ′ position is fixed

from the dγ′

(100), dγ′

(200) = 0.5× dγ′

(100).

The intensity ratio was found by testing the fit of dif-ferent ratios to measurements which contained widely sep-arated γ′ and γ (200) peaks. It was found that Iγ(200) =

0.25 × Iγ′

(200). The final fitting parameters for the (200)

doublet were therefore the width, shape function, overallintensity and the location of the γ peak. The {100} and{300} peak widths were found to be the same, ruling out awavelength dependence of peak width. The primary con-tributions to the peak widths were felt to be (i) strain,i.e. dislocations, (ii) the initial sample mosaic spread and(iii) instrumental broadening. Given that the γ′ precip-itated from the γ matrix, the assumption that the peakwidths were similar therefore seems reasonable, and wasconsistent with the data observed (Figure 4).

The individual detectors used in ENGIN-X are 196 mmhigh and and 3 mm wide, providing a horizontal angularresolution of around 0.12◦. Hence the (x00) peaks cov-ered around 10 detector elements horizontally but was con-tained within a single element vertically; the (0x0) peakscovered more elements owing to their higher mosaic. Eachelement was calibrated by reference to a standard powdersample to provide a composite detector response. Dur-ing straining, the peaks rotate as the crystal rotates, butsince the d-spacing measurement is in time-of-flight (wave-length), such movements are not of concern. The compa-rability of this approach to that obtained at a constantwavelength source has previously been examined in [22].

In the case of the (200) peak, at times the d-spacing ofthe two phases was very similar, giving rise to difficulty inaccurately fitting the doublet. Several different peaks thatarose in this experimentation are shown in Figure 5. Whenthe γ and γ′ components of the (200) were widely spreadapart (case (a) and (e)), the fitting routine could readilydetermine the position of the smaller γ peak. Similarlyfor cases (b) and (d), with a small separation between thepeaks, the methodology employed was satisfactory, withthe exception of some early measurements in the tertiarycreep test. Where the two overlap, the solution for the γposition becomes increasingly indeterminate (as measuredby stability of the fitting routine solution to the initial triallocation of the γ peak). Therefore care must be taken wheninterpreting the γ d-spacing output when both phases havesimilar d-spacing values (case (c) of Figure 5).

3. Results

The macroscopic creep behaviour observed during creepin the primary regime, at 650 ◦C and 825 MPa, is quite dif-ferent to that observed during tertiary creep at 900 ◦C and460 MPa, Figure 3. The macroscopic strain is defined bythe standard formula ε = (l− l0)/l0, where l is the instan-taneous length of the sample and l0 is the original samplelength at 0MPa. The macroscopic creep strain is definedas εcreep = (l − lx)/lx where lx is the sample length fol-lowing initial elastic loading when the applied creep stressis applied. Thus any subsequent strain is, to first order,plastic deformation due to creep. Of course, elastic soft-ening due to rotation of the crystal may occur and there-fore this experimental decomposition is not quite the same

3

Re

sid

ua

lIn

ten

sity

(A

rb. u

nit

s)

d-spacing (Å)

Diffraction Raw Data Deconvoluted γ ' peak Deconvoluted γ peak Calculated Total Profile

1.861.841.821.801.78 1.861.841.821.801.78

80

60

40

20

0

1.861.841.821.801.78

-4-2024

1.861.841.821.801.78 1.861.841.821.801.78

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

γ '

γ

γ '

γ

γ '

γ

γ '

γ

γ '

γ

Figure 5: The different (200) peaks observed from experimentation. From left (a) to right (e), different situations with the γ peak movingfrom the left of the γ′ to the right of the γ′. The example in (c) is the most challenging for peak fitting analysis, and illustrates the necessity ofthe fitting assumptions made. (a) T = 650 ◦C σ = 825 MPa ε = 11.74% (200) (b) T = 650 ◦C σ = 825 MPa ε = 10.14% (200) (c) T = 650 ◦Cσ = 825 MPa ε = 9.34% (200) (d) T = 650 ◦C σ = 825 MPa ε = 0.29% (020) (e) T = 650 ◦C σ = 825 MPa ε = 11.74% (020).

d-s

paci

ng (

Å)

macroscopic strain ε (%)

(020

) (2

00)

a) Primary Creep, 650oC 825MPa c) Tertiary Creep, 900oC 460MPa

γ

γ '

γ '

γ

γ '

γ

γ

γ '

b) Primary Creep, 650oC 825MPa

γ '

γ

γ '

γ1.836

1.832

1.828

1.824

1.820

1.816

1.820

1.816

1.812

1.808

1.804

1.800

12 10 8 6 4 2 0 12 10 8 6 4 2 0 12 10 8 6 4 2 0

Figure 6: The d-spacing response during elastic loading and creep under two different operating conditions; top row, longitudinal (200) data,bottom row, transverse (020) data. γ d-spacing data from peaks which proved difficult to fit accurately are highlighted in grey in (a) and (c).

as that classically used in micromechanical models wherethe total strain is decomposed into its elastic and inelastic(creep) components. The tertiary creep test was run tofailure, while the first primary creep test finished at ap-proximately 4% macroscopic strain due to failure of thegrips. The second primary creep test was run for 24 h.

The evolution of measured d-spacing during the test,after sample heating is shown in Figure 6. The errorbars have been removed from the d -spacing graphs (Fig-ure 6), corrected lattice strain graphs (Figure 7), and mis-fit graphs (Figure 8). Their inclusion obscures the data,making it difficult to distinguish the γ from the γ′ datapoints. Error bars have been included on two γ and twoγ′ data points in the (200), Figure 6 (a), to give a represen-tion of the small calculated error from the fitting routine,ranging from ∼ ±2 × 10−5 → 3 × 10−4 A. Of course, theactual uncertainty in peak location has additional contri-butions; typically an uncertainty of ±5×10−5 A is achiev-

able on polycrystal samples at this instrument [21] whenperforming strain measurement. One would expect a simi-lar accuaracy to be achievable for CMSX-4 measurements,given the similarity in experimental procedure and thehigh intensity of the peaks measured, Figure 2. Thereexists an additional error associated from the furnace con-trol (±1 ◦C) [30]. A fluctuation of ±1 ◦C will give a cor-responding change in d -spacing of ±2.8 × 10−5 A in theγ and ±5.4 × 10−5 A in the γ′, from the calculation ofthermal expansion coefficients in the longitudinal direc-tion [22]. Thus the associated error in d -spacing from fur-nace control is of a similar value to the error from thepeak fitting routine, and both will contribute to the over-all total error in d -spacing measurement. Observing thed -spacing results, there is very little observable scatter ofthe γ′ in any of the graphs, due to the clean data and suit-able single-peak fitting routine. Thus it is fair to assumethat the γ′ d -spacing error is of the order of 10−4 A when

4

the contributions of peak location, peak fit, and thermalinstability are accounted for. The use of a doublet peak fitin order to deconvolute the γ from the (200) and (020) dou-blet peaks introduces additional uncertainty for this phase,particularly when the γ and γ′ d -spacing are not widelyspread. This is clearly seen in the range of scatter in γ inFigure 6. The (020) transverse measurements have morewidely spread γ and γ′ peaks compared with the longitudi-nal (200), giving less scatter for the transverse γ d -spacingfrom the fitting routine. The scatter in the transverse γd -spacing results is estimated to be ∼ 14 × 10−4 A, fromFigure 6b, which to an approximation is ∼ ±7 × 10−4 Aabout an averaged free-hand fit to the data. The γ d -spacing scatter is worse in the longitudinal direction, asthe (200) γ and γ′ contributions are not as widely spreadmaking the deconvolution from the doublet more difficult.The scatter in this data in the worst case approximately∼ ±3 × 10−3 A about a free-hand graphical fit to the γdata in Figure 6(b). This is much greater than the er-ror calculated from the fitting routine and a more realisticestimate for the error in achieving the γ d -spacing results.

The γ d-spacing measurements are an average of con-tributions from both the horizontal and vertical channels.Considering the three dimensional cubic precipitate sys-tem dispersed amongst the γ matrix, there are twice asmany vertical channels than horizontal. Unfortunately it isnot possible to separate the contributions from each chan-nel type, further complicating analysis. This is discussedfurther in the data analysis.

Initially, the d-spacing of both phases in each test in-creases in the (200) loading direction as the stress is rampedthrough the elastic loading regime, Figure 6(a - c). This isfollowed by an evolution during creep at elevated stress,Figure 6(a - c). The d-spacing is temperature depen-dent, and at zero stress, the (200) and (020) measure-ments should be equal. However, this is not observed inFigure 6(a - c). The authors can only attribute this to apossible offset in experimental set-up and recognise thatabsolute d-spacing measurements in two detectors are in-herently difficult.

Following the elastic loading regime, the (200) γ′ d-spacing increases quite linearly during tertiary creep, Fig-ure 6(c). The γ data points shaded grey between ε ∼0.5→ 1.0%, are due to unsatisfactory fits of the (200) dou-blet peak. By minimisation of errors the γ peak fits to theleft of the fixed γ′ peak position in the (200) doublet. How-ever by visual inspection of the data it is seen that the γ isclearly to the right of the γ′, thus the outputted d-spacing

incorrectly gives dγ(200) < dγ′

(200). The only good fit between

ε ∼ 0.5 → 1.0% occurred at ε = 0.6%, dγ(200) = 1.829 A.

Following this region the fits were all good.Neglecting the poor fits in the (200) tertiary creep d-

spacing data, there is a sudden decrease in (200) γ d-spacing following the elastic loading, Figure 6(c). Afterthis sudden decrease, the γ d -spacing increases almost lin-early. This is in contrast to the (020) data for each creep

test. The elastic loading leads to a decrease in d-spacingof both phases in the transverse direction (due to Poissoncontraction). Once the load is stabilized in the tertiaryregime, the d-spacing of the (020) γ initially increases,Figure 6(c). The rate at which the γ d-spacing is increas-ing declines during early creep, after which the d-spacingincreases slowly at a constant rate. The γ′ lattice param-eter continuously decreases during tertiary creep, almostthe exact reverse of the behaviour observed in the (020) γ.

In the primary creep test, Figure 6(b), the tempera-ture drop from 700 → 650 ◦C is seen in both phases as adecrease in d -spacing, at ε ∼ 1.4%. Following the elas-tic region, the (020) d-spacing is constant in the γ phaseand decreases in the γ′, Figure 6(b). The second primarycreep test performed without the temperature drop, Fig-ure 6(a), agrees with the first in the (020). In the (200),the γ′ d-spacing increases during creep after the first ∼ 1%strain, Figure 6(a and b). dγ(200) is initially greater than

dγ′

(200), seen clearly in Figure 6(b). Unfortunately it was

not possible to accurately fit the first three γ creep mea-surements of the second primary creep test, shaded greyin Figure 6(a). On visual inspection of these three fits itwas observed that the γ fit was too far to the right, givinglarger γ d -spacing values.

Between 2 and 3% strain in Figure 6(b), there is a dropin (200) γ lattice parameter. From Figure 6(b), this dropin γ lattice parameter is equivalent to a lattice strain ofapproximately (1.830−1.824)/1.830 = 3×10−3, or roughly320 MPa, where the elastic constant for γ at 650 ◦C is106 ± 7GPa, Table 1. The γ d-spacing of both primarycreep tests steadily increases from ∼ 3% strain in the lon-gitudinal direction. At a macroscopic strain of ∼ 9% amaximum γ d -spacing is reached in Figure 6(a). The firstprimary creep test ended due to grip failure before thismaximum was observed, Figure 6(b). Following the maxi-mum γ d -spacing value in Figure 6(a), there is a quite sud-den drop in the γ (200) lattice parameter, and hence av-erage elastic lattice strain, over the course of around 1.5%macroscopic creep strain. This is followed by a slightlyincreasing γ d -spacing.

In order to relate the d-spacing measurements to strain,conventionally, we define the (elastic) lattice strain as fol-lows

εxh00 =∆d

d0(1)

where εxh00 is the lattice strain of phase x in the (h00)lattice plane. d0 is the d -spacing at the creep temperatureand zero stress. The strain was then corrected to accountfor true stress and temperature changes

εx,corrh00 = εxh00 −σ

Exh00(1 + ε)− αx 4 T (2)

where σ is the applied macroscopic nominal stress, Exh00is the apparent or effective stiffness of the (h00) plane, εis the macroscopic engineering strain, x denotes the phaseand α the thermal expansion coefficient. The strain εx,corrh00

5

is therefore the measured elastic strain due to creep, af-ter correcting for the strain due to elastic loading, changesin section area due to plasticity and thermal expansion.This allows for the the test which began at 700 ◦C to becorrected for the drop in temperature using the measuredlattice thermal expansion coefficients, published in [22].The modulus Eh00 is the diffraction elastic constant mea-sured for each phase, given in Table 1. This should bedistinguished from the < h00 > moduli of the isolatedphases. The diffraction elastic constants are the measuredapparent moduli and differ from the isolated moduli bythe constraint between the two phases.

The evolution of this corrected lattice strain duringeach creep test is shown in Figure 7. Pollock and Argon [3]discuss their TEM observations and finite element study ofcreep in CMSX-3 in terms of misfit. This suggests anotherway to view the diffraction measurements presented withinthis paper. Defining the apparent misfit δapp as follows

δapp = 2× dγ′ − dγdγ′ + dγ

(3)

we obtain Figure 8. It should be emphasized that mis-fits measured always include a degree of stress accommo-dation between the phases at the temperature and stressconditions that pertain to the measurement made, whetherthis is in TEM or in a bulk diffraction measurement.

Examining the apparent lattice misfit of the (100) and(010) in the tertiary regime (900 ◦C 460 MPa), Figure 8(c),there is some agreement with conclusions made from thefinite element model for CMSX-3 of Pollock and Argonin the (100) direction, but not the (010) [3]. The finiteelement model of CMSX-3 suggests that at 850 ◦C andan applied stress of 552 MPa (a tertiary creep regime), allmisfit stresses are totally relieved after t = 1170 s, i.e. 19.5minutes. Figure 8(c) shows that the (100) misfit is nearlytotally released at a macroscopic strain of 0.62%. Thisdata point corresponds to the earliest (100) γ data pointin Figure 7(c) that came from a good peak fit (i.e. thefirst data point not shaded grey), at 0.14% macroscopiccreep strain. From Figure 3(c), a macroscopic creep strainof 0.14% was reached at t = 0.85 h, i.e. ∼ 50 minutes.Unfortunately the earlier data points were poor fits so wecannot say for certain at what point in time before 50minutes this release occurred.

The misfit derived from the tertiary creep transversestrain data also decreases slightly in magnitude from −4×

Table 1: Measured diffraction elastic constants in the loading andtransverse directions of each phase [22].

T Eγ′,eff[100] Eγ,eff

[100] Eγ′,eff[010] Eγ,eff

[010]◦C GPa GPa GPa GPa

20 128 ± 3 109 ± 7 −192 ± 3 −208 ± 16650 105 ± 4 106 ± 7 −198 ± 12 −211 ± 12700 102 ± 2 108 ± 6 −227 ± 5 −196 ± 12900 87 ± 2 89 ± 3 −217 ± 7 −171 ± 17

10−3 to −3× 10−3 on initial elastic loading, and then in-creases in magnitude continuously during creep to nearly−5×10−3, Figure 8(c). This shows that the (010) misfit isnever fully released, in contradiction of Pollock and Argon[3].

The misfit analysis aids the explanation of the cor-rected strain evolution of both phases during tertiary creep,Figure 7(c). In the tertiary regime, the release of misfitstress in the (100) direction during the first 1% of creepcauses the observed compressive strain in the (100) γ,Figures 8(c) and 7(c) respectively. The corrected strainsof both phases then increase in tandem, Figure 7(c).Thismight be taken to imply that co-deformation of both phaseswas occurring, as both phases would strain harden result-ing in an increase in observed elastic strains in the (100).However it is generally agreed that tertiary creep is con-fined to the γ matrix [3, 31–33]. The effect of changingcross section during deformation, which increases the truestress, has been removed from the lattice strain data toobtain the corrected lattice strains. Thus the increase ofcorrected lattice strain in both phases cannot be attributedsolely to an increasing true stress.

We suggest that this change, which is a strain of around1.0 × 10−3 in the γ (200) between creep strains of 1 and8% is due to lattice rotation. A lattice rotation towardsthe less stiff (100) would give an increase in observed lat-tice strain. In order to measure the degree of lattice ro-tation, the post-crept sample was cut along the tensileaxis and electron backscattered diffraction (EBSD) analy-sis was performed at the fracture region and at the threadsof the sample (where no deformation occurs during test-ing). From analyses of the pole figures and by calculatingthe degree of relative rotation from the Euler angles [34],the crystal rotated ∼ 10.5◦, with a rotation of (100) ∼ 6◦

towards the tensile axis. The consequent change in mod-ulus could be responsible for at least some of the increasein corrected lattice strain observed in Fig 7(c); approxi-mate calculations yield a value of order 1 × 10−3 for themagnitude of this effect.

It is unclear how the matrix (200) compresses to releasemisfit, with no apparent effect on the γ′. It may be possiblethat plastic flow of the matrix around the precipitate actsin such a way as to release the (200) misfit strain.

The longitudinal lattice strain measurements measuredby Ma et al. [19] for CM247LC differ quite markedly tothose presented here. This is not surprising as single crys-tal creep lifetimes are much greater than those of polycrys-tals, indicating differences in the creep mechanics. Forexample, the creep lifetime of a first generation single-crystal, MAR-M200, when tested at 982 ◦C and 206 MPaincreases from approximately 36 h with a failure strain of4% when cast as a polycrystal, to 110 h with a failure strainof 28% when cast as a single crystal [35]. The final stressof a multiple stress creep test performed by Ma et al. was425 MPa at a temperature of 900 ◦C i.e. a tertiary creepregime. The (100) γ′ lattice strain increased by approxi-mately 1.3×10−3 while the (100) γ lattice strain decreased

6

a) Primary Creep, 650oC 825MPa c) Tertiary Creep, 900

oC 460MPa b) Primary Creep, 650

oC 825MPa

γ '

2.0x10

Co

rrec

ted

Lat

tice

Str

ain

εco

rr

macroscopic creep strain εcreep (%)

-3

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

10 8 6 4 2 0

-6x10 -3

-4

-2

0

2

γγγ

γγ

γ ' γ '

10 8 6 4 2 0

γ

γ '

γ ' γ '

10 8 6 4 2 0

(020)

(200)

Figure 7: The corrected lattice strains of phase x, εx,corrh00 , against the macroscopic creep strain, εcreep. The temperature drop from 700 ◦C to

650 ◦C in the primary creep test (b), has been corrected. As in Figure 6, the poor fits in test (a) and (c) are highlighted in grey.

Ap

par

ent

Mis

fit δ

macroscopic strain ε (%)

a) Primary Creep, 650oC 825MPa b) Primary Creep, 650

oC 825MPa

-6x10 -3

-4

-2

0

2

4

12 10 8 6 4 2 0

c) Tertiary Creep, 900oC 460MPa

(100)

(010)

12 10 8 6 4 2 0 12 10 8 6 4 2 0

(100)

(010)

(100)

(010)

Figure 8: The apparent misfit during elastic and creep deformation for the primary and tertiary creep tests. The data from the poor fits intest (a) and (c) have been removed for clarity.

by 0.8×10−3 over 8% macroscopic creep strain. The latticestrain response of (100) γ′ is similar in this work, howeverthe [100] lattice strain of γ increases in CMSX-4, Figure2. Ma et al. believed that the observed tertiary stage be-haviour of CM247LC is due to a build up of dislocationsin the vertical γ channel [19]. It is difficult to compare thelattice strain responses of a polycrystal and single crystalalloy without noting more than they differ markedly, asthe lattice strain response of a grain within a polycrystalis dependent upon the deformation of surrounding grainsof different orientations. That is to say the lattice strainresponse of a (100) grain will be dependent on the defor-mation of surrounding grains of (110), (111) etc. This isnot a consideration when studying the response of a singlecrystal as there is only one grain. Ma et al. did not presentthe transverse data, so it is not possible to compare the(010) lattice strain response. Furthermore grain boundarysliding is not a consideration of single crystals, which inturn allows the single crystal to be alloyed very differentlyto polycrystals as grain boundary strengthening elements

are not required.In the tertiary creep transverse measurements, the (020)

γ lattice strain increases rapidly during the first 1% macro-scopic creep strain after which the rate decreases, presum-ably due to strain hardening, Figure 7(c). Following aninitial compression in the (020) γ′ during early tertiarycreep, the γ′ strain slightly decreases. Focusing solely onthe (020) data, this could be interpreted as a load trans-fer from the γ to the γ′. Considering the (020) data inlight of what was suggested as the interpretation of the(200) data, if the lattice is rotating towards (020) in thetransverse direction, this would result in increasing com-pressive lattice strains of both phases. Pollock and Argon[3] showed that under a similar temperature and stresscondition in CMSX-3 there is much greater stress in thematrix (020) than (200). Thus the authors hypothesizethat in the (020) the creeping matrix continues to trans-fer compressive load into the stronger γ′ phase, with thechange in strain being far greater in the γ phase due to theeffect of volume fraction. It is clear from this analysis that

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the interpretation of the transverse data is extremely diffi-cult and is sometimes omitted from papers for this reason,see for example Ma et al. [19].

In conclusion of the tertiary creep analysis, the mea-surements taken can be interpreted to be somewhat consis-tent with the tertiary creep analysis of Pollock and Argon[3]: The γ initially yields to relieve the misfit stresses inthe (100), and then dislocation motion is confined to theγ channels without precipitate shear. The lattice is rotat-ing and true stress is increasing, seen clearly in the (200).There appears to be a lot of stress transfer from γ to γ′

in the (020) direction which could be indicative of a lotof creep occurring in the (020) γ, as suggested by Pollockand Argon [3].

Analysing the macroscopic creep curves of the two pri-mary creep tests, it is seen that the creep responses dif-fer quite markedly, despite being performed on bars thathave very similar orientations, Figure 3. The initial pri-mary creep strain before a steady-state regime is exhibitedis almost three times greater in test (a) than (b). A pos-sible explanation for this ambiguity is the sample in test(b) had been subjected to the final aging heat treatment,but the sample in (a) had not. The post-crept sampleswere tested for ovalisation; the ratio of the minor to majordiameters was 0.99 for test (b), and 0.79 for test (a), i.e.test (b) showed no ellipticity. The degree of ellipticity hasbeen shown to be a function of macroscopic primary creepstrain [31]. The thinning along the < 110 > during pri-mary creep has proved controversial. Pan et al. [36] pro-posed that slip occurs along the 6 cube {100}<110> and12 normal {111}<110> slip systems, while others empha-size the importance of the {111}<112> slip system [37–43]. There is strong evidence that suggests the dominantslip mode is temperature and stress dependent. Matanet. al [31] showed that macroscopic shape deformation at750 ◦C and 750 MPa is due to {111}<112>, but at 950 ◦Cand 185 MPa slip is due to {111}<110>. The primarycreep test conditions employed here are similar to 750 ◦C750 MPa, so one would expect the {111}<112> slip modeto dominate. The ovalisation that occurs during test (a)is a first indication that {111}<112> ribbon shear has oc-curred, however the lack of ovalisation in test (b) indicatesthat, if particle cutting has occurred, it has not occurredto a degree where it is evident by optical analysis, i.e. theprimary creep strain was not large enough. The diffractiondata allows us to probe further into the micro-mechanicsof primary creep.

During both primary creep tests, the initial misfit isrelaxed by elastic compression of the γ phase in the (200).This occurs within the first 2% of creep, seen clearly inFigure 7(b). The release of misfit corresponds to compres-sion of the (200) γ in the horizontal channel, however arelaxation of misfit will also cause expansion of the (200)γ in the vertical channels. Although these vertical chan-nels are twice as numerous, the net effect is still a com-pression of the (200) γ matrix, as the contribution fromthe direct compression in the (200) horizontal channels

outweighs the expansion due to Poisson’s effect in the ver-tical channels. As the initial period of rapid (primary)creep begins to slow, the (200) γ corrected lattice straingradually increases from a minimum of −4.5 × 10−3 toaround −2 × 10−3 at a creep strain of ∼ 8% and a to-tal strain of ∼ 9%, Figure 7(a). The γ′ phase graduallyincreases from 1 × 10−3 to 2 × 10−3 during the same pe-riod of creep. This would be interpreted, in the light ofRae et al. [4, 37, 38, 44], to correspond to the shearing ofboth phases. Plastic deformation of both phases causes anincrease in hardness due to the increase in dislocation den-sity, which would be seen as an increase in lattice strain inboth phases. However one can’t ignore that lattice rota-tion towards (100) could also cause an increase in latticestrain in both phases due to the change in sample modulusas it rotates.

Then, quite suddenly, there is a large change in misfitand decrease in the longitudinal (200) strain in the γ phasein test (a) between 8 and 9% creep strain, followed by aplateau (test (b) did not run to a large enough strain forthis to be observed), Figure 7a. There is a correspondingdrop of ∼ 1× 10−3 lattice strain in the γ′. The rapid de-crease of γ lattice strain could be indicative of a release ofaccomodation stress (sometimes termed back stress) be-tween the phases, however this would be accompanied bya corresponding increase in γ′ lattice strain. A decrease of4.5 × 10−3 corresponds to to a stress of around 450 MPa,Table 1, i.e. relaxation of approximately 55% of the ap-plied stress of 825 MPa. Notably, there is no correspond-ing change in the macroscopic creep curve, suggesting thatcompression of the γ is balanced by a decrease in the γ′

shear rate during a period of stress release. A decreasein γ′ shear results in a lower γ′ lattice strain rate. Oneexplanation might be that a recovery mechanism may beoperating, allowing the (200) γ′ lattice strain to also de-crease.

Similarly to the tertiary creep test, although the ther-mal misfit is relieved in the (200) during primary creepby compression of the γ matrix (Figures 6b and 8b), themisfit in the (020) is never relieved, even up to 12% macro-scopic strain, Figure 8(a). The stress transfer from γ toγ′ observed in the transverse data during tertiary creepalso occurs in the (020) for the duration of the first pri-mary creep test, Figure 7(b), and up to 9% of the secondcreep test, Figure 7(a). As the lattice rotates towards the(100) in the longitudinal direction, one would expect thelattice strain of both phases to decrease in the (020), how-ever the γ phase lattice strain is approximately constantin Figure 7(b) and increases to a maximum at 9% macro-scopic strain in Figure 7(a), while the γ′ lattice strain de-creases in both. This is indicative of a stress transfer from(020) γ to (020) γ′. At 9% macroscopic strain a changein the creep mechanics is observed in the (020). This isthe same macroscopic strain at which the (100) creep me-chanics change. Thus the data, although very difficult tointerpret, is real. At this macroscopic strain the (020) γlattice strain decreases while the γ′ increases, Figure 7(a).

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This is consistent with the hypothesis put forward for the(100) primary creep data. A release of back stress from γ′

to γ results in an increase in the (020) γ′ lattice strain anda reduction in the (020) γ lattice strain. This results inan increase of the creep rate in the γ phase, however thereis no dramatic change in macroscopic creep rate at thisstrain (Figure 3). The authors propose that dislocationshear of the γ′ was occurring to this strain and then stopsso there is no observed overall increase in the creep rate,as a possible interpretation. Certain works suggest thatshearing of the γ′ ceases after the end of primary creep[45], while others have concluded that shearing of the γ′

continues through secondary creep [4, 46, 47].In summary, then, primary creep proceeds in three

phases. 1, An increase in misfit towards zero in the (100).There is stress transfer from γ to γ′ in the (020). 2, Thestress gradually increases in both phases in the (200) un-til 3, there is an increase of the creep rate in the γ phasewhen a stress is released from the γ′. The macroscopicstrain rate is fairly constant when this increase of creeprate in the γ occurs, and the authors take this to be in-dicative that shearing of γ′ was occurring to this point,at which point it halts, effectively keeping the net macro-scopic creep rate steady.

Finally, the samples were examined after testing, Fig-ure 9. The γ′ of the primary creep samples still possessed acubic morphology, while the tertiary creep samples possessa partially rafted structure in the (010) plane. Therefore,even at a temperature below that traditionally recognisedas causing rafting in CMSX-4, some rafting can be ob-served. If tertiary creep is confined to the γ, presumably apoint would eventually be reached where rafting would beso extensive as to require either glissile sliding of the γ/γ′

interfaces to accommodate creep of the γ, or shearing ofboth phases would be required. However, there is no indi-cation in the diffraction data that such a point was reachedin the present testing, which was performed to failure.

4. Summary and Conclusions

The elastic lattice strain evolution during the tertiaryand primary creep of single crystals of the nickel-base su-peralloy CMSX-4 has been examined using in-situ neu-tron diffraction and analysed in light of our current un-derstanding of the dislocation mechanisms operative dur-ing creep from TEM studies. The following conclusionscan be drawn from this work.

1. In-situ neutron diffractometry can be used to exam-ine the evolution of loading state in the two phases ina single crystal superalloy during creep deformationusing the peak positions as an internal elastic straingauge.

2. The lattice strain response observed in the two regimesis quite distinct, indicating a difference in the oper-ative micromechanisms of deformation during pri-mary and tertiary creep.

Figure 9: Observed post-creep microstructures (etched sample, sec-ondary electron imaging), viewed transverse to the loading direction[(010) plane]; (a) the primary creep test at 650 ◦C and (b) the ter-tiary creep test at 900 ◦C.

3. During the initial stages of tertiary creep deforma-tion of the matrix phase leads to a release of mis-fit between the two phases in the (100), resultingin elastic compression of the γ phase in the loadingdirection. The load state in the two phases then re-mains fairly constant during creep in the (100), witha gradual increase observed that is thought to be dueto lattice rotation. There is no unequivocal evidenceof shearing of the γ′ phase. There is load transferfrom γ to γ′ in the (020).

4. In primary creep, during the initial stages elasticcompression of the γ phase is also observed in the(100) until at a creep strain of around 2-4% this com-pression stabilises as the misfit is released. This isexpected to be the point at which shearing of theγ′ begins. Subsequently, the load in the γ increasesby around 200 MPa until a maximum is reached ataround 8% creep strain. A large fraction of the loadin the γ′ is then suddenly released into the γ be-tween 8 and 9% creep strain. This is thought to bethe point where shearing of the γ′ halts.

5. Limited rafting is observed to occur during tertiarycreep testing at 900◦C and 460 MPa.

5. Acknowledgements

JC would like to acknowledge funding from EPSRC andQinetiQ plc. of a CASE studentship. DD and RCR gratefullyacknowledge funding from EPSRC and Rolls-Royce Plc. for

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this work, and for the provision of the test bars and useful dis-cussions by Drs. DW MacLachlan and N Jones at Rolls-Royceplc. Beamtime at ISIS was generously provided by STFC, as-sistance in performing the experiments by Dr EC Oliver andwith profile fitting by Dr HJ Stone.

References

[1] Basoalto SK, Sondhi BF, Dyson M, McLean. A genericmicrostructure-explicit model of creep in nickel-base superal-loys. In: Superalloys 2004. Champion, PA, United States: TheMinerals, Metals and Materials Society, Proceedings of the In-ternational Symposium on Superalloys, 897–906

[2] Ma A, Dye D, Reed RC. A model for the creep deformation be-haviour of single-crystal superalloy CMSX-4. Acta Mater 2008;58:1657

[3] Pollock TM. Acta Metall Mater 1992;40:1[4] Rae CMF, Zhang L. Mater Sci and Technol 2009;25:228[5] Hutchings HT, Withers PJ, Holden TM, Lorentzen T. Intro-

duction to the characterization of residual stress by neutrondiffraction. Boca Raton, Fl : CRC Press 2005

[6] Dye D, Conlon K, Reed RC. Metall Mater Trans A 2004;48:4191[7] Daymond MR, Preuss M, Clausen B. Acta Mater 2007;55:3089[8] Neil CJ, Wollmershauser JA, Clausen B, Tome CN, Agnew SR.

Int J Plasticity 2010;26:1772[9] Preuss M, da Fonesca JQ, Grant B, Knoche E, Moat R, Day-

mond M. The effect of γ′ particle size on the deformation mech-anism in an advanced polycrystalline nickel-base superalloy. In:Reed RC, Green KA, Caron P, Gabb TP, Fahrmann MG, HuronES, Woodard SA, editors, Superalloys 2008. Pennsylvania: Min-erals, Metals and Materials Soc, 405–414

[10] Stone HJ, Holden TM, Reed RC. Acta Metall 1999;47:4435[11] Ma S, Rangaswamy P, Majumdar BS. Scr Mater 2003;48:525[12] Agnew SR, Tome CN, Brown DW, Holden TM, Vogel SC. Scr

Mater 2003;48:1003[13] Brown DW, Agnew SR, Bourke MAM, Holden TM, Vogel SC,

Tom’e CN. Mater Sci Eng A 2005;399:1[14] Clausen B, Bourke MAM. Metall Trans A 2001;32:691[15] Daymond MR, Tome CN, Bourke MAM. Acta Mater 2000;

48:553[16] Holden TM, Holt RA, Tome CN. Physica B 1997;:1246[17] Holden TM, Holt RA, Tome CN. Mater Sci Eng A 1997;282:131[18] Lorentzen T, Daymond MR, Clausen B, Tom’e CN. Acta Mater

2002;50:1627[19] Ma S, Brown D, Bourke MAM, Daymond MR, Majumdar BS.

Mater Sci and Eng A 2005;399:141[20] Dye D, Stone HJ, Reed RC. Acta Mater 2000;49:1271[21] Santisteban JR, Daymond MR, James JA, Edwards L. J Appl

Crystallogr 2006;39:812[22] Dye D, Coakley J, Vorontsov VA, Stone HJ, Rogge RB. Scri

Mater 2009;61:109[23] Alers GA, Neighbours JR, Sato H. J Phys Chem Solids 1960;

13:40[24] Wallow F, Neite G, Schroer W, Nembach E. Phys Stat Solidi

A 1987;99:483[25] Pottebohm H, Neite G, Nembach E. Mater Sci and Eng 1983;

60:189[26] Sieborger D, Brehm H, Wunderlich F, Moller D, Glatzel U. Z

MetaIlkd 2001;92:58[27] Prikhodko SV, Carnes JD, Isaak DG, Yang H, Ardell AJ. Metall

Mater Trans A 1999;30:2403[28] Kayser FX, Stassis C. Phys Stat Solidi A 1981;64:335[29] Yasuda H, Takasugi T, Koiwa M. Acta Metall Mater 1992;

40:381[30] Xu P, Tomota Y, Oliver EC. ISIJ Int 2008;48(11):1618[31] Matan N. Acta mater 1999;47:1549[32] Caron P, Ohta Y, Nakagawa YG, Khan T. Creep deformation

anisotropy in single crystal superalloys. In: Reichman S, DuhlD, Maurer G, Antolovich S, Lund C, editors, Superalloys 1988.Pennsylvania: Minerals, Metals and Materials Soc, 215–224

[33] Sass V, Glatzel U, Feller-Kniepmeier M. Creep anisotropy in themonocrystalline nickel-base superalloy CMSX-4. In: KissingerR, et al., editors, Superalloys 1996. Pennsylvania: Minerals,Metals and Materials Soc, 283–90

[34] Kocks U.F, Tome C.N, Wenk H.-R. Texture and Anisotropy.Cambridge, UK : Cambridge University Press 1998

[35] Kear BH, Piearcey BJ. Trans of the Metall Soc of AIME 1967;239:1209

[36] Pan LM, Shollock BA, McLean M. Proc R Soc Lond A 1997;453:1689

[37] Rae CMF, Matan N, Cox DC, Rist MA, Reed RC. Metall MaterTrans A 2000;31:2219

[38] Rae CMF, Reed RC. Acta Mater 2007;55:1067[39] Leverant GR, Kear BH. Metall Trans 1970;1:491[40] MacKay RA, Maier RD. Metall Trans A 1982;13:1747[41] Kear BH, Oblak JM, Giamei AF. Met Trans 1970;1:2477[42] Hopgood AA, Martin JW. Mater Sci and Eng 1986;82:27[43] Leverant GR, Kear BH, Oblak JM. Metall Trans A 1973;4:355[44] Rae CMF, Matan N, Reed R. Mater Sci and Eng A 2001;300:125[45] Link T, Feller-Kniepmeier M. Metall Trans A 1992;23:99[46] Drew GL, Reed RC, Kakehi K, Rae CMF. Single crystal su-

peralloys: the transition from primary to secondary creep. In:Superalloys 2004. Champion, PA, United States: The Minerals,Metals and Materials Society, Proceedings of the InternationalSymposium on Superalloys, 127–136

[47] Preußner J, Rudnik Y, Volkl R, Glatzel U. Z Metalkd 2005;96:595

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