Creep Deformation by Dislocation Movement in Waspaloy - MDPI

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Creep Deformation by Dislocation Movement in Waspaloy Mark Whittaker 1, *, Will Harrison 1 , Christopher Deen 1 , Cathie Rae 2 and Steve Williams 3 1 2 3

*

Institute of Materials, Bay Campus, Swansea University, Swansea SA1 8EN, UK; [email protected] (W.H.); [email protected] (C.D.) Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, UK; [email protected] Rolls-Royce plc, Elton Road, Derby DE24 8BJ, UK; [email protected] Correspondence: [email protected]

Academic Editor: Richard Thackray Received: 25 October 2016; Accepted: 5 January 2017; Published: 12 January 2017

Abstract: Creep tests of the polycrystalline nickel alloy Waspaloy have been conducted at Swansea University, for varying stress conditions at 700 ◦ C. Investigation through use of Transmission Electron Microscopy at Cambridge University has examined the dislocation networks formed under these conditions, with particular attention paid to comparing tests performed above and below the yield stress. This paper highlights how the dislocation structures vary throughout creep and proposes a dislocation mechanism theory for creep in Waspaloy. Activation energies are calculated through approaches developed in the use of the recently formulated Wilshire Equations, and are found to differ above and below the yield stress. Low activation energies are found to be related to dislocation interaction with γ0 precipitates below the yield stress. However, significantly increased dislocation densities at stresses above yield cause an increase in the activation energy values as forest hardening becomes the primary mechanism controlling dislocation movement. It is proposed that the activation energy change is related to the stress increment provided by work hardening, as can be observed from Ti, Ni and steel results. Keywords: creep; dislocations; Wilshire equations; forest hardening

1. Introduction The prediction of long-term creep properties based on short timescale experiments is rated as the most important challenge to the UK Energy Sector in the recent UK Energy Materials Review [1]. However, despite extensive research performed over more than half a century, no single approach linking micro-mechanical behaviour to macroscopic properties and material behaviour has gained widespread support [2–9]. It is clearly desirable that the framework of any successful theory derive from, and be consistent with, microstructural observations. Furthermore, any successful theory should be able to predict a range of properties, such as time to fracture, minimum creep rate, applied stress and creep strain evolution. In many approaches, the importance of creep strain evolution is overlooked since only total service life (normally time to fracture) is the critical parameter. Typically, static components, such as steam generation and transport plant found in the power generation sector, fall into this category, however, other applications of rotating components require more detailed information on the evolution of creep strain as deformation can lead to contact and therefore material damage. In gas turbines, rotating components operating in a high temperature gas stream have blade clearances minimised in order to promote higher efficiency. Creep deformation of both discs or blades will lead to contact with casings and promote wear fatigue and/or tip cracking.

Materials 2017, 10, 61; doi:10.3390/ma10010061

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Materials 2017, 10, 61

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Traditional methods of creep lifing have been based on power law type equations, in which the . minimum creep rate (εm ) and the rupture time (tf ) vary with stress (σ) and temperature (T) according to the relationship . M/tf = εm = A·σn · exp(Qc /RT) (1) where Qc is the activation energy for creep, R is the gas constant and M is the Monkman Grant constant. The description of the equation in terms of minimum creep rate, rather than secondary creep rate is important, since recent research [10–12] has questioned the existence of a true steady-state (secondary) creep rate, as the decaying primary stage is immediately offset by the accelerating tertiary phase, resulting only in a minimum, and not a steady state, creep rate. This smooth transition from primary to tertiary creep is consistent with models proposed by Evans [13], Dyson [14] and Wu [15]. In Equation (1) [16], the parameters (A and M), the stress exponent (n) and the activation energy for creep (Qc ) vary depending on the stress and temperature imposed, despite being initially proposed as constants. The dominant creep mechanism is identified by comparing experimentally measured and theoretically predicted values of n and Qc . With pure metals, a decrease from n ∼ = 4 to n ∼ =1 with decreasing stress has been widely attributed to a change from diffusion-controlled dislocation processes to diffusional creep mechanisms not involving dislocation movement. Clearly, the variation in n and Qc values offers significant difficulties in producing a comprehensive lifing methodology capable of holistic predictions over a range of temperatures and stresses, but this approach has also encountered a number of more specific difficulties. Firstly, the contribution of non-dislocation based diffusional creep mechanisms has recently been questioned [17]; Secondly, at high stresses with alloys strengthened by dispersions of fine precipitates or insoluble particles, n can take values substantially in excess of 4 and the value for Qc significantly exceeds that of the activation energy for lattice diffusion, QSD . No generally accepted physical interpretation of these anomalously large n and Qc values has been agreed [5]. Several modern approaches to creep lifing normalise the stress by the Ultimate Tensile Strength (UTS) [14,15], and a recent approach that has been particularly successful is the use of the Wilshire equations [16–20]. The Wilshire equations acknowledge that tf → 0 as σ → σTS , and tf → ∞ as σ → 0; as a result, the equations produce more appropriate curve shapes. Temperature is accounted for by use of an activation energy, Qc *, that takes account of the variability embodied in the UTS and is thus slightly lower than a conventional activation energy fitted to the same data. Indeed, approaches to creep lifing utilising the Wilshire equations have been extremely successful [18–20]. Initial investigations involving aluminium alloys and pure copper have more recently been supplemented by predictions of long-term creep behaviour in key power generation steels as P22/T22, P23/T23 [21], P91, P92, Grade 122 [22], HK40, HP40 [23] and Type 316 stainless steel [24]. Significant features have consistently arisen in fitting the constants for the Wilshire equations to the data sets of these alloys. Datasets can be fitted more accurately to two distinct sets of parameters in terms of minimum creep rate or rupture time with the ‘break points’ being a function of stress. A break point is commonly found to occur at stresses approximately equal to the yield stress of the material, and this is assumed to be related to a change in the dislocation behaviour at this point. More recently, application of the Wilshire Equations to engineering materials has indicated that not only should the material fitting constants k1 and u vary either side of a break point, approximately equal to the yield stress, but that the apparent activation energy (Qc *) should also differ. A wide range of materials [24–27] have now been studied for which optimised fits are obtained when the value of the apparent activation energy (Qc *) is allowed to vary either side of the break point. Interestingly, the most significant changes in the apparent activation energy observed have been in stainless steel grade 316, with values of 250 kJ/mol observed above the yield stress, decreasing to 150 kJ/mol below. It is useful to compare these values with Titanium-6-4, where no change in activation energy was observed, and Udimet 720 where only a small change (40 kJ/mol) was observed. When considering however, that 316 stainless steel shows an extremely high rate of strain hardening under monotonic loading,


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and Ti-6-4 shows extremely low rates of strain hardening, it becomes clear that dislocation interactions must play a significant role in the determination of this value, and hence the behaviour of the material. This paper examines the deformation structures observed above and below the threshold in order to rationalise this apparent change in behaviour. 2. Experimental Methods The material selected for the programme was Waspaloy. It is a precipitation hardened alloy which was developed from the Nimonic series of alloys. It has considerable strength and corrosion resistance at temperatures up to 870 ◦ C above which intergranular oxidation compromises performance. The nominal chemical composition of Waspaloy is shown in Table 1. Table 1. Chemical Composition of Waspaloy (in wt %) [28]. Cr

Co

Mo

Al

Ti

C

B

Ni

19.5

13.5

4.3

1.3

3

0.08

0.006

Bal

The material selected for this programme had undergone a forging heat treatment, which would typically involve 995 to 1040 ◦ C (sub-solvus) for 4 h, air cooled, stabilisation at 845 ◦ C for 4 h, air cooled and aging at 760 ◦ C for 16 h, air cooled [29]. Creep testing during the programme was completed in air on a Mayes constant stress creep machine with a loading lever ratio of 15:1 for stresses above 10 MPa (discounting the onset of tertiary failure and necking). Specimen strains were monitored using extensometers incorporating a pair of differential capacitance transducers capable of resolving changes in gauge length to 10 nm. Testing was carried out at temperatures ranging from 550 to 800 ◦ C (823–1073 K) measured using 2 R-type thermocouples, to an accuracy of ±3 ◦ C between thermocouples. All loading, temperature and strain monitoring systems are calibrated annually, in line with BS EN ISO 7500-2 [30] and BS EN ISO 9513 [31]. For one set of experiments, tests were stopped at the minimum strain rate condition, frequently recalculated during test progression using the secant method, then air cooled under reduced load. For a second set of experiments, tests were stopped at 1% creep strain accumulation and furnace cooled with the load removed. For minimum strain rate experiments, test specimens were machined down to 3 mm gauge diameter from the standard specimen design shown in Figure 1, to avoid excess machining post testing. No effect of environment would be expected from the different gauge diameters, due to the short timescales of these tests, at only intermediate temperatures. For 1% strain experiments, test specimens utilised a standard specimen shown in Figure 1. These discs were then spark eroded to produce a 3 mm diameter disc. In preparation for TEM analysis, thin discs were cut from within the gauge length of the crept specimen, to an approximate thickness of 500 microns to 1 mm, using a high precision cutting wheel. These discs were then mounted using MWH135 mounting wax and ground to a thickness of 150–200 microns. The thin discs were subjected to twin-jet electropolishing using a solution of 10 vol % perchloric acid in methanol at −5 ◦ C and 20.5 V.


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Figure 1. Creep specimen design.

Figure 1. Creep specimen design.

3. Results

3. Results

High precision extensometry allowed for the recording of creep curves in the experiments High precision extensometry allowed the recording of for creep insimilar the experiments undertaken and it is clear from Figure 2 that for the creep curve shape testscurves showing rupture times canand vary temperature stress. Curves lower temperatures undertaken it significantly is clear fromwith Figure 2 that theand creep curve shapegenerated for tests at showing similar rupture such 550significantly °C generallywith are undertaken at and stresses in excess the yield at stress of temperatures the material tosuch times canas vary temperature stress. Curvesofgenerated lower ◦ produce appropriate rupture times, and therefore a significant amount of primary creep strain is as 550 C generally are undertaken at stresses in excess of the yield stress of the material to produce evident as dislocations are continually generated under this high stress. At higher temperatures and appropriate rupture times, and therefore a significant amount of primary creep strain is evident as lower stresses, creep deformation occurs more readily belowtemperatures the yield stress, dislocations are continually generated under this high under stress.stresses At higher andand lower deformation is accommodated by the movement of pre-existing dislocations subject to processes such stresses, creep deformation occurs more readily under stresses below the yield stress, and deformation as climb and cross slip, with most deformation accommodated in grain boundary zones. This results is accommodated by the movement of pre-existing dislocations subject to processes such as climb and in a reduced primary stage, but extended tertiary creep. The difference in the shape of the curves is crosssignificant, slip, withasmost deformation grain boundary zones. This in acurve reduced shown in Figure 2,accommodated and illustrates theinrequirement for prediction of theresults full creep primary stage, but extended tertiary creep. The difference in the shape of the curves is significant, where possible, so that creep strain is well defined under all conditions. With appropriate models in as shown in Figure 2, andwhere illustrates thea requirement for prediction of thethan full total creeprupture curve where possible, place, applications time to predefined strain is more critical time can be so that creepaccommodated. strain is well defined under all conditions. With appropriate models in place, applications suitably where time a predefinedbetween strain isstress more and critical than total rupture can be suitably accommodated. Thetorelationship minimum creep rate time is displayed in Figure 3. Linear relationships can be derived allowing for the calculation of n values according to Equation by The relationship between stress and minimum creep rate is displayed in Figure 3.(1) Linear plotting ln(ε m ·exp(Q c /RT)) against lnσ where the n value is represented by the gradient of the graph relationships can be derived allowing for the calculation of n values according to Equation (1) by . (Figure is clear that a significant change in gradient occurs at higher stresses as the n value varies plotting ln(4). εm It ·exp(Q c /RT)) against lnσ where the n value is represented by the gradient of the graph from ~5 to ~18. This region, historically known ‘poweroccurs law breakdown’, has beenas widely (Figure 4). It is clear that a significant change in as gradient at higher stresses the nobserved value varies for a range of precipitation hardened alloys, and provides a significant challenge to designers as from ~5 to ~18. This region, historically known as ‘power law breakdown’, has been widely observed power law based equations fail to accommodate the rapidly changing gradient of the graph. The for a range of precipitation hardened alloys, and provides a significant challenge to designers as power situation is further complicated when Equation (1) is used to derive an activation energy for the law material based equations fail to accommodate the rapidly changing gradient of the graph. The situation by plotting lnεm vs. 1/Temperature as shown in Figure 5. When high stresses are used for the is further complicated when is derived, used to derive anthis activation the material calculation, values of Qc = Equation 350 kJ/mol(1)are whereas increasesenergy to 700for kJ/mol for low by . plotting lnεmfurther vs. 1/Temperature shownof inso-called Figure 5.‘variable When high stresses are used (1) forupon the calculation, stresses, illustrating theas problem constants’ in Equation which values of Q kJ/mol are arebased. derived, whereas this increases to 700 kJ/mol for low stresses, further c = 350 many lifing approaches

illustrating the problem of so-called ‘variable constants’ in Equation (1) upon which many lifing approaches are based.

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Figure 2. Creep curves may take significantly different shapes dependent on applied stress and Figure 2. curves may take different shapes on applied and Figure 2. Creep Creep curves maysignificantly take significantly significantly different shapes dependent dependent onstress applied stress and Figure 2. Creep curves may take different shapes dependent on applied andstress temperature. temperature. temperature. temperature.

Figure 3. The relationship between stress and minimum strain rate rate in Waspaloy. Waspaloy. Figure in Figure 3. 3. The The relationship relationship between between stress stress and and minimum minimum strain strain ratein in Waspaloy. Waspaloy.

Figure 4. The relationship between ln(stress) and ln(ε m·exp(Qc/RT)) in Waspaloy. Qc* = 500 KJ/mol. . Figure The relationship between ln(stress) and ln(ε ·exp(Q in Waspaloy. Q == 500 Figure 4.The Therelationship relationship between ln(stress) and ln(ε ·exp(Qc/RT)) c/RT)) /RT)) in in Waspaloy. Waspaloy.Q Qcc*** = 500 KJ/mol. KJ/mol. Figure 4.4. between ln(stress) and ln( εmm·mexp(Q 500 KJ/mol. c c

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. Figure 5. The The relationship between between lnε m vs. Figure εm vs. 1/Temperature 1/Temperaturein inWaspaloy. Waspaloy. Figure 5. 5. The relationship relationship between ln lnε m vs. 1/Temperature in Waspaloy.

One approach to overcome these difficulties has been to normalise each temperature dataset by One approach approach to to overcome overcomethese thesedifficulties difficultieshas hasbeen beentoto normalise each temperature dataset normalise each temperature dataset by the UTS of the material, obtained from high-strain-rate tests at each temperature, as shown in Figure 6. the the UTSUTS of the obtained from high-strain-rate tests attests each at temperature, as shownasinshown Figure in 6. by of material, the material, obtained from high-strain-rate each temperature, It can be seen that the data produced over a range of temperatures now can be collapsed to a single It can be the data over a range temperatures now cannow be collapsed to a single Figure 6. seen It canthat be seen that produced the data produced overof a range of temperatures can be collapsed to curve defining a single modified activation energy. Whilst it is recognized that normalization by other defining a single modified activation energy. Whilst is recognized that normalization by other acurve single curve defining a single modified activation energy.itWhilst it is recognized that normalization temperature dependent parameters (i.e., yield stress) may also be utilized, normalization by the UTS temperature dependent parameters (i.e., yield(i.e., stress) may alsomay be utilized, normalization by the UTS by other temperature dependent parameters yield stress) also be utilized, normalization by offers a parameter which is easily measurable and encompasses all possible values of stress offers parameter which which is easily measurable and and encompasses all all possible the UTSa offers a parameter is easily measurable encompasses possiblevalues valuesof of stress conveniently between 0 and 1. conveniently between 0 and 1.

Figure 6. The relationship between σ/σTS and (ε. m·exp(Qc/RT)) in Waspaloy. Figure6.6.The Therelationship relationshipbetween betweenσ/σ σ/σTS TS and ininWaspaloy. Figure and (ε (εmm·exp(Q ·exp(Qc/RT)) Waspaloy. c /RT))

4. Discussion 4. Discussion 4. Discussion The unknown curvature of Figure 6 provides a problem for designers should data The unknown unknowncurvature curvature of Figure 6 provides a problem for should designers should data The of Figure 6 provides a problem designers extrapolation outside of the original dataset be required and itfor soon becomes clear data that aextrapolation more robust extrapolation outside ofdataset the original dataset and be required and it soon becomes clear that a more robust outside of the original be required it soon becomes clear that a more robust approach approach should be attempted. The Wilshire equations are a natural (though not the only) choice approach should be attempted. The Wilshire equations are a natural (though not the only) choice should be attempted. The Wilshire equations are a natural (though only)been choice since they since they are based around normalisation through the UTS which not has the already shown to be since they around are based around normalisation through the UTS which hasbeen already been shown to be are based normalisation through the UTS which has already shown to be effective, effective, Equation (2). effective, (2). Equation (2). Equation v  n   .  vv o  *∗   = exp − k ε exp Q /RT (2)  ) ( )    exp k exp Q / RT   m * 2 (2)   //(σ/σ  TS c  TS c 2  m  (2) TS   exp   k2  m exp Qc / RT  









 

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In attempting to derive the Wilshire equation fits for the Waspaloy tests described here, a break Indata attempting to derive Wilshire fits for with the Waspaloy tests described a break in the provides a morethe accurate fitequation in conjunction the parameters derivedhere, in Figure 7. in A the data provides a more accurate fit in conjunction with the parameters derived in Figure 7. A linear linear relationship for ‘high stress’ data can be observed for which v = −0.24, k2 = 434 and Qc* = 400 −1 relationship fora ‘high stress’ can be fitting observed for stress which data v = −where 0.24, k2v == 434 Qc * = and 400 kJ kJ·mol−1, with second line data accurately lower 72, kand 2 = −0.14 Q·c*mol = 340, with a −1 second lineof accurately datascatter where in v =the 72, data k2 = − 0.14allows and Qfor 340 kJ ·mol−1 . c * =more kJ·mol . The use differingfitting valueslower of Qcstress * reduces and accurate The differing values of Q scatter scatter in the data and allows for more and c * reduces fits, use and of should be compared with the increased which occurs when usingaccurate a single fits, value in should beClearly compared the increased scatter occurs when using single value in[11,16,18– Figure 6. Figure 6. fromwith previous experience and which numerous examples in theaopen literature Clearly from and numerous examples open literature [11,16,18–20,24,25], 20,24,25], the previous transitionexperience point between the two lines would in bethe expected to approximate the onset of the transition between the individual two lines would be expected to approximate the onset yielding in yielding in thepoint material at each temperature, and simple calculations show of that to be the the at eachmaterial. individual temperature, and simple calculations show that toprovided be the case the casematerial in the current (Values for the yield stress and 0.2% proof stress are in in Table current (Values forincluded the yielddue stress 0.2%monitoring proof stressissue are provided intest.) TableFurthermore, 2, values for 2, valuesmaterial. for 650 °C are not to and a strain during the ◦ 650 arevalue not included due to aactivation strain monitoring during the test.) Furthermore, since the value sinceCthe of the apparent energy, Qissue c*, is derived from each individual linear segment, of the apparent activation energy, Q *, is derived from each individual linear segment, a change in c a change in activation energy was observed above (420 kJ/mol) and below (340 kJ/mol) the yield activation energy was observed above (420 kJ/mol) and below (340 kJ/mol) the yield stress, as has stress, as has been found for previous materials [24,27]. The fits for stress vs. minimum strain rate been previous materials fits for8.stress vs. minimum strain rate based on the basedfound on thefor Wilshire equations can[24,27]. be seenThe in Figure Wilshire equations can be seen in Figure 8. To investigate whether there is an underlying physical mechanism change driving the variation To investigate whether is antests underlying physical at mechanism change driving theabove variation in activation energy, a seriesthere of creep was undertaken graded levels of stress both and in activation energy, of creep tests was graded of stress both above below the yield stressaatseries a temperature of 700 °C.undertaken Figure 9a,b at shows the levels dislocation structure of the ◦ C. Figure 9a,b shows the dislocation structure and below the yield under stress transmission at a temperature of 700 as-received material electron microscope (TEM) imaging. In Figure 9a, a bimodal of the as-received material under transmission microscope (TEM) imaging. In 200 Figure distribution of γ′ precipitates is visible with theelectron secondary precipitates approximately nm 9a, in 0 precipitates is visible with the secondary precipitates approximately adiameter bimodaland distribution of γ the tertiary of the order of 50 nm diameter. Dislocations are visible in the γ matrix at 200 nm in diameter andthey the tertiary of the order of 50 nm diameter. are visible in the γ moderate density but generally avoid passing through the Dislocations larger secondary precipitates, matrix at moderate density they generally avoid passingisthrough the with largerthe secondary precipitates, wrapping around in loose but networks. The microstructure consistent thermo-mechanical wrapping in loose is consistent with thearea thermo-mechanical processingaround route. Figure 9bnetworks. shows an The areamicrostructure straddling a grain boundary. In an 1–2 µm around processing route.there Figure shows an area straddling a grain In an area 1–2 µm recovery around the the boundaries, is 9b evidence of additional strain whichboundary. has undergone significant to boundaries, thereof is sub-grains evidence ofseparated additionalby strain undergone significant produce produce a series lowwhich angle has boundaries. Carbides are recovery visible ontothe grain aboundary. series of sub-grains separated by low angle boundaries. Carbides are visible on the grain boundary.

Figure 7. Deriving Wilshire equations. equations. Figure 7. Deriving the the constants constants for for the the Wilshire Table values for for Waspaloy. Waspaloy. Table 2. 2. Yield Yield stress stress values

Temperature (°C) 550 550600 600 700700 800800

Temperature (◦ C)

Yield Stress (MPa) 0.2% Proof Stress (MPa) Yield Stress (MPa) 0.2% Proof Stress (MPa) 745 912 745 750 920 912 750 920 735735 874 874 520520 675 675

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Figure 8. 8. Predictions of minimum minimum creep creep rate rate as as aa function function of of stress. stress. Figure Predictions of Figure 8. Predictions of minimum creep rate as a function of stress.

(a) (a)

(b) (b)

Figure 9. Dislocation structure in as-received Waspaloy material (a) within the grains (b) in the grain Figure 9. Dislocation structure in as-received Waspaloy material (a) within the grains (b) in the grain boundary zone. Figure 9. Dislocation structure in as-received Waspaloy material (a) within the grains (b) in the grain boundary zone. boundary zone.

In order to identify the separate effects of creep and plasticity, a monotonic tensile test was In order to identify the separate effects of creep and plasticity, a monotonic tensile test was performed where the test the wasseparate halted ateffects the approximate 0.2% proof stress (740 MPa)tensile of Waspaloy at In order to identify of creep and plasticity, a monotonic test was performed whereand the test was halted at the approximate 0.2% proof stress (740 MPa) of Waspaloy at 700 °C, unloaded removed from the test machine. The dislocation structure mid-grain and at the performed where and the test was halted at the approximate 0.2% proof stress (740 MPa) of Waspaloy at 700 °C, unloaded removed from the test machine. The dislocation structure mid-grain and at the boundaries can beand seen in Figure 10a,b. Mid-grain there an increasestructure in the dislocation as ◦ C, unloaded 700 removed from the test machine. Theis dislocation mid-graindensity, and at the boundaries can be seen in Figure 10a,b. Mid-grain there is an increase in the dislocation density, as appropriatecan sources areinactivated at the yield point. The dislocations aredislocation looping around the boundaries be seen Figure 10a,b. Mid-grain there is an increase in the density, as appropriateprecipitates, sources are at the point. through The dislocations are looping around the secondary butactivated for the part,yield are cutting the tertiary γ′ around as single dislocations appropriate sources are activated atmost the yield point. The dislocations are looping the secondary secondary precipitates, but for the most part, are cutting through the tertiary γ′ as single dislocations with the exception of some of the larger precipitates: an example of this is evident in the top rightthe of 0 precipitates, but forofthe most part, are cutting through the tertiaryofγthis as is single dislocations with with the exception some of the larger precipitates: an example evident in the top right of Figure 10a. Thereofisthe nolarger evidence of stacking faults in anyispart of the microstructure and it10a. is exception of some precipitates: an example of this evident in the top right of Figure Figure 10a. There is no evidence of stacking faults in any part of the microstructure and it is interesting to note that the dislocation does not appear to be moving in pairs. Figure 10b shows the There is no to evidence of the stacking faults does in any part of thetomicrostructure and itFigure is interesting to note interesting note that dislocation not appear be moving in pairs. 10b shows the grainthe boundary areadoes of the The low as ingrain the virgin material. that dislocation notyielded appearsample. to be moving in angle pairs.sub-grains Figure 10bremain shows the boundary area grainCreep boundary area of the yielded sample. The low angle sub-grains remain as in the virgin material. tests were performed at 500, 600, 700 remain and 800asMPa in virgin which material. the material was loaded and of theCreep yielded sample. The low angle sub-grains in the tests were performed at 500, 600,rate 700was and reached; 800 MPa Table in which the material was loaded and allowed to creep until the minimum creep 3 marks the end of the primary Creep tests were performed at 500, 600,rate 700 was and reached; 800 MPa Table in which the material was loaded and allowed to creep until the minimum creep 3 marks the end of the primary phase. As material does not show sustained steady state Table creep,3as shown Figure 2, primary this also allowed tothis creep until the minimum creep rate was reached; marks thein end of the phase. the As this material does not show sustained steady state creep, as shown in Figure 2, this also marks onset of tertiary creep, where damage begins to accumulate leading to an acceleration in phase. As this material does not show steady to state creep, as leading shown in 2, this also marksrate the onset of tertiary creep, wheresustained damage begins accumulate to Figure an acceleration in creep and final failure. marks the onset of tertiary creep, where damage begins to accumulate leading to an acceleration in creep rate and final failure. creep rate and final failure.


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(a)

(b)

Figure 10. Dislocation structure in Waspaloy subjected to loading to 0.2% proof stress in the (a) grains; Figure 10. Dislocation structure in Waspaloy subjected to loading to 0.2% proof stress in the (a) grains; (b) grain boundary boundary zones zones (bright (bright field field images). images). (b) grain Table 3. Time to minimum creep rate and associated strain for the range of stress conditions. Table 3. Time to minimum creep rate and associated strain for the range of stress conditions.

Applied Stress (MPa) Time to Minimum Creep Rate (h) Strain at Minimum Creep Rate (%) Applied Time to Minimum Creep Rate (h) Strain at Minimum 500Stress (MPa) 21 0.25 Creep Rate (%) 0.25 600 500 22 21 1.02 1.02 700 600 3 22 2 700 3 2 800 800 2 2 4.4 4.4 Following the attainment of the minimum creep rate, specimens were air cooled immediately Following attainment of the minimum creep rate, For specimens were cooled immediately under a reducedthe load to preserve the dislocation structure. the creep testair performed at 500 MPa, under a reduced load to preserve the dislocation structure. For the creep test performed 500 MPa, the test was interrupted at 21 h (0.25% creep strain), the time associated with the minimumatstrain rate the test was interrupted at 21 h (0.25% creep strain), the time associated with the minimum strain rate from a similar test to rupture. At this point, the dislocation structures should be fully evolved but the from testbehaviour to rupture.avoided. At this point, the dislocation structures should be fully evolved but the effectsa similar of tertiary effects of tertiary behaviour avoided. Figure 11a,b shows the TEM images for the dislocation structure at this creep condition. In the Figure 11a,b the TEM images for the dislocation structure atimage) this creep condition. Inand the grain centres, theshows dislocation density (bright lines in this weak-beam is relatively low grain centres, the dislocation density (bright lines in this weak-beam image) is relatively low and those those present are hindered by the γ′. There are frequent instances of Orowan looping around not only present are hindered γ0 .the There are frequent instances of Orowan loopingofaround notfaults only all all the secondary γ′, by butthe also larger tertiary γ′ and occasional instances stacking in the the 0 0 secondary γ , but also the larger tertiary γ and occasional instances of stacking faults in the tertiary γ0 . tertiary γ′.

(a)

(b)

Figure 11. Dislocation structure in Waspaloy subjected to creep loading at 500 MPa in the (a) weak Figure 11. Dislocation structure in Waspaloy subjected to creep loading at 500 MPa in the (a) weak beam image of the interior of a grain; (b) bright field image of the grain boundary zone. beam image of the interior of a grain; (b) bright field image of the grain boundary zone.

The grain boundary zones at this condition retain the sub-grain structure of the virgin material, but also show similar creep dislocation structures within the sub-grains. It is unclear the extent to


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The grain boundary zones at this condition retain the sub-grain structure of the virgin material, 10 of 14 but also show similar creep dislocation structures within the sub-grains. It is unclear the extent to which evolution of the sub-grain structure in this area is contributing significantly to the creep strain. which evolution of the sub-grain structure in this area is contributing significantly to the creep strain. As the overall creep strain remains low at about 1%, it would require a detailed study to establish As the overall creep strain remains low at about 1%, it would require a detailed study to establish whether any enhanced grain boundary activity was in addition to that required to accommodate whether any enhanced grain boundary activity was in addition to that required to accommodate different strains in adjacent grains. different strains in adjacent grains. At 600 MPa and 700 MPa, the specimens were crept to the minimum strain rate in 22 and 3 h At 600 MPa and 700 MPa, the specimens were crept to the minimum strain rate in 22 and 3 h (1.02% and 2% creep strain) respectively. In comparison to the 500 MPa condition, dislocation density (1.02% and 2% creep strain) respectively. In comparison to the 500 MPa condition, dislocation density has increased with stress. Figure 12a,b shows the dislocation structures formed during the 600 MPa has increased with stress. Figure 12a,b shows the dislocation structures formed during the 600 MPa test, below the 0.2% proof stress (740 MPa). Stacking faults have become much more widely distributed test, below the 0.2% proof stress 0 (740 MPa). Stacking faults have become much more widely in both the secondary and tertiary γ as the precipitates are cut by superlattice partial dislocations, and distributed in both the secondary and tertiary γ′ as the precipitates are cut by superlattice partial Orowan looping is consequently reduced, as shown in Figure 12a. In some grains, slip is occurring dislocations, and Orowan looping is consequently reduced, as shown in Figure 12a. In some grains, on more than one slip system as evidenced by the stacking faults on a second plane. The dislocation slip is occurring on more than one slip system as evidenced by the stacking faults on a second plane. spacing in between the secondary precipitates, although increased over that at the 500 MPa interrupted The dislocation spacing in between the secondary precipitates, although increased over that at the test, remains below the tertiary precipitate spacing, indicating that the principal barrier to slip is still 500 MPa interrupted test, remains below the tertiary precipitate spacing, indicating that the principal the tertiary precipitates. barrier to slip is still the tertiary precipitates. Grain boundary boundary zones zones are are populated populated by by the the low low angle angle sub-grains sub-grains with with dislocation dislocation banding banding still still Grain present at the sub-grain boundaries, as visible in Figure 12b. The overall dislocation structure is now present at the sub-grain boundaries, as visible in Figure 12b. The overall dislocation structure is now seemingly aacombination of dislocation recovery and strain processes, showing considerable seemingly combination of dislocation recovery andhardening strain hardening processes, showing changes when compared to the 500 MPa test specimen. considerable changes when compared to the 500 MPa test specimen. The specimens specimens crept crept at at 700 700 MPa MPa and and 800 800 MPa MPa reached reached the the minimum minimum strain strain rate rate in in very very similar similar The times of 3 and 2 h (2% and 4.4% creep strain) respectively. In contrast, the stress conditions below the times of 3 and 2 h (2% and 4.4% creep strain) respectively. In contrast, the stress conditions below the yield point at 500 and 600 MPa required 21 and 22 h respectively. yield point at 500 and 600 MPa required 21 and 22 h respectively. Figure 13a,b 13a,b highlights highlights the the dislocation dislocation structure structure present present above above the the yield yield stress stress at at 800 800 MPa, MPa, crept crept Figure until the minimum strain rate was reached. In the bulk of the material, the dislocation density is so so until the minimum strain rate was reached. In the bulk of the material, the dislocation density is great that individual dislocations become increasingly difficult to resolve. A second creep test was great that individual dislocations become increasingly difficult to resolve. A second creep test was performed to min) to to help resolve thethe dislocation behaviour but was performed to only only 1% 1%strain strain(attained (attainedwithin within2020 min) help resolve dislocation behaviour but substantially similar. was substantially similar. Dislocations are are extremely extremely dense dense but but mostly mostly confined confined to to the the γ γ and and the the tertiary tertiary γ′ γ0 with with occasional occasional Dislocations 0 stacking faults in the secondary γ . These larger precipitates continue to resist cutting by lattice lattice stacking faults in the secondary γ′. These larger precipitates continue to resist cutting by dislocations as observed in the tensile test to yield, as shown in Figure 10a. dislocations as observed in the tensile test to yield, as shown in Figure 10a. Materials 2017, 10, 61

(a)

(b)

Figure 12. Dislocation structure in Waspaloy subjected to creep loading at 600 MPa (below the yield Figure 12. Dislocation structure in Waspaloy subjected to creep loading at 600 MPa (below the yield stress) in the (a) grains (b) grain boundary zones. stress) in the (a) grains (b) grain boundary zones.


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(a)

(b)

Figure 13. Dislocation structure in Waspaloy subjected to creep loading at 800 MPa (above the yield Figure 13. Dislocation structure in Waspaloy subjected to creep loading at 800 MPa (above the yield stress) in the (a) grains (b) grain boundary zones. stress) in the (a) grains (b) grain boundary zones.

The best fit of the creep rupture data to the Wilshire equations for Waspaloy (and many other The fit of by thedefining creep rupture data to linear the Wilshire equations for Waspaloy (and other alloys) is best obtained two separate relationships describing the high andmany low stress alloys) is obtained by defining two separate linear relationships describing the high and low stress behaviour. The stress transition point giving the best fit falls naturally at the approximate yield stress behaviour. The stress transition point giving thein best fit falls naturally at the approximate yield stress of the material, 735 MPa. This implies a change creep behaviour associated with the yield stress as of the material, 735 MPa. This implies a change in creep behaviour associated with the yield stress as evidenced by the change in activation energy. The dislocation structures after creep above and below evidenced the change in activation energy. The dislocation structures after creep above and below the originalbyyield stress do indeed show a distinct difference. Below the yield stress, densities are the original yield stress do indeed show a distinct difference. Below the yield stress, densities relatively low, increasing slightly with stress, and the time to minimum creep strain is of the orderare of relatively increasing slightlystructure with stress, andvicinity the timeoftothe minimum creep strain of the order of 20 h. The low, pre-existing subgrain in the grain boundaries is is retained. Above 20 The point, pre-existing subgrain structure in the vicinity the grain is retained. Above the theh.yield the dislocation density increases to theof point whereboundaries the dislocation spacing is closer yield point, the dislocation density increases to the point where the dislocation spacing is closer than than that of the precipitates and the sub-grain structure around the grain boundaries is obliterated that of the precipitates and throughout. the sub-grainMinimum structure around the grain is obliterated byThe the by the increased density creep rates are boundaries achieved after about 3 h. increased throughout. Minimum creep rates achieved after about secondarydensity precipitates alone remain clear of all but theare occasional stacking fault.3 h. The secondary precipitates alone remain clear of all but the occasional stacking fault. These observations can be rationalised as follows. During creep below the yield stress, the These canvery be rationalised follows. During creep below the is yield stress, the dislocation observations densities remain low and the as main resistance to dislocation motion the interaction dislocation densities remain very low and the main resistance to dislocation motion is the interaction with the tertiary precipitates. The secondary precipitates alone are too widely spaced to offer much with the tertiary precipitates. secondary precipitates alonetoare to offer of much additional hardening. Indeed,The at 500 MPa the stress appears betoo toowidely low tospaced allow cutting the additional hardening. Indeed, at 500 MPa the stress appears to be too low to allow cutting of the tertiary tertiary precipitates, even by partial dislocations trailing low energy superlattice stacking faults, let precipitates, evenenergy by partial dislocations trailing(APB) low energy faults, let alone the alone the higher Anti Phase Boundary faults.superlattice Dislocationstacking motion is therefore limited higher energy Anti Phase Boundary (APB) faults. Dislocation motion is therefore limited by the climb by the climb of these dislocations over and around all but the smallest tertiary precipitates. Densities of these dislocations and around all but the smallest tertiary Densities increase with increase with stress over but nevertheless remain low as sources of precipitates. new dislocations cannot readily be stress but nevertheless remain low as sources of new dislocations cannot readily be activated by stress activated by stress below yield. As the stress rises to 600 MPa, the precipitates are increasingly below below yield. As the for stress rises to MPa, the precipitates are increasingly below the size threshold the size threshold cutting by600 superlattice partial dislocations and the microstructure shows for cutting by superlattice partial dislocations and the microstructure shows numerous faults numerous stacking faults in the precipitates as during creep there is sufficient timestacking to allow the in the precipitates as during creep there is sufficient time to allow the reordering necessary for this to reordering necessary for this to happen [32]. happen [32].yield, the stress is sufficient for the dislocations to cut through the tertiary precipitates as Above Above yield, the test stress sufficient for the to cut through shown in the tensile to is yield, as shown in dislocations Figure 10. This reveals thatthe thetertiary processprecipitates of yield is as shown in the tensile test to yield, as shown in Figure 10. This reveals that the process yield is associated with the ability of dislocations to cut the tertiary precipitates which provide theofprincipal associated the ability to cut the tertiary precipitates which provide thesecondary principal increment with of strength in ofa dislocations bimodal distribution of ordered precipitates [33]. The increment of strength in a bimodal distribution of ordered precipitates [33]. The secondary precipitates precipitates are too large to cut and dislocations loop around them leaving them dislocation free. At are too large cutin and dislocations around them leaving them dislocationisfree. At the high the high straintorate a tensile test, theloop activated movement of partial dislocations not possible, and strain rate in a tensile test, the activated movement of partial dislocations is not possible, and the the dislocations cut through the tertiary precipitates as single dislocations producing APB faults dislocations cut through the tertiary precipitates as single dislocations producing APB faults which are which are rectified by subsequent dislocations, i.e., ‘weak coupling’ [34]. In the creep tests above rectified subsequent dislocations, i.e., ‘weak coupling’ In the creep of tests yield, the yield, thebyrapid multiplication of dislocations, triggered [34]. by the freedom theabove dislocations to rapid glide multiplication of dislocations, triggered by the freedom of the dislocations to glide through the tertiary through the tertiary precipitate structure, leads to a greatly increased dislocation density. This, in turn, leads to the increase in flow strength associated with forest hardening due to the exceptionally high dislocation densities between the tertiary precipitates adding to the precipitate hardening of the


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precipitate structure, leads to a greatly increased dislocation density. This, in turn, leads to the increase in flow strength associated with forest hardening due to the exceptionally high dislocation densities between the tertiary precipitates adding to the precipitate hardening of the virgin material. Note that the stress is still insufficient for the dislocations to pass through the secondary precipitates leaving these relatively dislocation free. At these higher stresses, the minimum strain rate will occur when the dislocation multiplication rate is balanced by the recovery rate. Initially, the flow rate increases due to higher mobile dislocation density, but eventually the density becomes so high that dislocations become locked in tangles lowering the creep rate. The closer spacing of the dislocations facilitates recovery until equilibrium is reached. Based on this interpretation, the critical activation event below the original yield stress is associated with the climb of the dislocations around the tertiary γ0 precipitates: above the original yield point with the climb and recovery of dislocation tangles. The extent of dislocation interaction during the high stress regime of any material in creep is reflected in the rate of strain hardening of a material observed during monotonic tensile tests. There is a qualitative relationship between the apparent activation energy and the amount of strain hardening a material undergoes after yield, as evidenced by three model materials; 316 stainless steel has a very high rate of strain hardening and shows Qc * values of 250/150 kJ/mol [24]; Waspaloy has a medium rate of strain hardening with Qc * values of 400/340 kJ/mol; and Titanium 6-4 has a very low rate of strain hardening with negligible activation energy change, having Qc * values of 250/250 kJ/mol [26]. This supports the proposal that activation energy change in creep is a direct result of the onset of strain hardening: an alloy with no potential for strain hardening would not be expected to show a change in activation energy. 5. Conclusions The following conclusions can be drawn from this programme of work:

• • • • •

Creep deformation in Waspaloy is dominated by diffusion controlled dislocation movement. The best fit of the creep rupture data to the Wilshire equations for Waspaloy is obtained by two separate linear relationships separated at the yield point. Below yield creep takes place through the movement of dislocations controlled by diffusive climb around precipitates, whereas above yield dislocation movement is limited by forest hardening. The change in apparent activation energy, Qc *, is directly related to the amount of strain hardening in an alloy brought about by high dislocation densities generated at stresses above yield. The change in activation energy, and the concomitant breaks in the Wilshire equations, are brought about by a change the mechanism controlling dislocation movement, not a complete change of mechanism.

Acknowledgments: The authors would like to thank Harshal Mathur of Cambridge University for his help and guidance using the Transmission Electron Microscope to capture some of the images seen in this paper. We also acknowledge the Rolls-Royce EPSRC Strategic Partnership (EP/H500375/1 and EP/H022309/1) for support of this work and provision of materials. Author Contributions: The manuscript was mainly authored by Mark Whittaker with assistance from Cathie Rae, who also provided interpretation of the TEM work. The research was conducted as part of the EngD of Christopher Deen, who conducted the experiments in conjunction with Will Harrison. Will Harrison and Steve Williams undertook data analysis and interpretation of the Waspaloy database. Conflicts of Interest: The authors declare no conflict of interest.

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