On the Rapid Assessment of Mechanical Behavior of a Prototype Nickel-Based Superalloy using Small-Scale Testing

On the Rapid Assessment of Mechanical Behavior of a Prototype Nickel-Based Superalloy using... TOPICAL COLLECTION: SUPERALLOYS AND THEIR APPLICATIONS On the Rapid Assessment of Mechanical Behavior of a Prototype Nickel-Based Superalloy using Small-Scale Testing ´ ´ SABIN SULZER, ENRIQUE ALABORT, ANDRE NEMETH, BRYAN ROEBUCK, and ROGER REED An electro-thermal mechanical testing (ETMT) system is used to assess the mechanical behavior of a prototype single-crystal superalloy suitable for industrial gas turbine applications. Miniaturized testpieces of a few mm cross section are used, allowing relatively small volumes to be tested. Novel methods involving temperature ramping and stress relaxation are employed, with the quantitative data measured and then compared to conventional methods. Advantages and limitations of the ETMT system are identified; particularly for the rapid assessment of prototype alloys prior to scale-up to pilot-scale quantities, it is concluded that some significant benefits emerge. https://doi.org/10.1007/s11661-018-4673-5 The Author(s) 2018 I. INTRODUCTION conditions for which mechanical tests are needed can quickly become very significant. The difficulties identi- NEW alloy grades are never deployed without fied above are then exacerbated. Moreover, there is a careful testing of their properties and performance traditional emphasis—even today—on the use of stan- under conditions close to those experienced in service. dard testpieces of traditional design, which can mean Such so-called qualification activities can be difficult and that substantial volumes of material are needed. Might costly; this explains why the time needed to insert them there be better ways of approaching this problem? [1–3] into new applications can be notoriously long. The research reported in this paper was carried out Furthermore, processing costs for the production of with these ideas in mind. Miniaturized testpieces are pilot-scale material quantities can be excessively lar- used within a novel electro-thermal mechanical testing ge—often too great to justify—thus leading to conser- [4] (ETMT) system to assess relatively small volumes of vatism and undue emphasis on maintaining the status material, with nonetheless representative materials quo. Without a doubt, such challenges lead to a behavior being shown to arise. But we have aimed to slackening in the pace of technological change. go further. First, a novel temperature ramping test is Consider, for example, the assessment of the mechan- devised to allow the rapid assessment of the athermal ical response of a material destined for high-temperature yielding behavior of a new material, from just a single applications. The yield stress depends upon tempera- non-isothermal test. Second, a stress relaxation test is ture, but also on the strain rate. The creep resistance used to quickly deduce the time-dependent response. In depends upon temperature once again, but also on the this way, materials behavior is extracted rapidly from a stress level. Even before the cyclic loading needed to small number of tests. To garner confidence in our assess fatigue behavior or the effects of a biaxial or approaches, comparisons are made with more tradi- triaxial stress state are considered, the number of tional techniques. II. EXPERIMENTAL METHOD ´ ´ SABIN SULZER and ANDRE NEMETH are with the Department of Materials, University of Oxford, Parks Road, A. Material Oxford, OX1 3PH, UK. Contact e-mail: sabin.sulzer@materials.ox.ac.uk ENRIQUE ALABORT is with the A single-crystal superalloy developed by Siemens Department of Engineering Science, University of Oxford. BRYAN Industrial Turbomachinery (SIT) was chosen for the ROEBUCK is with the National Physical Laboratory, Hampton present study. Its nominal composition in order of Road, Teddington TW1 0LW, UK. ROGER REED is with decreasing wt pct is Ni-Cr-Ta-Co-Al-W-Mo-Si-Hf-C-Ce, Department of Materials, University of Oxford and also with the [5] Department of Engineering Science, University of Oxford. and is similar to that reported previously by Reed et al. Manuscript submitted January 18, 2018. This alloy is a candidate for future industrial gas turbine Article published online May 30, 2018 4214—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A (IGT) applications and was designed to combine good The orientations of the six bars used to manufacture oxidation, corrosion, creep, and thermal-mechanical the test specimens for the present study were checked [5–7] fatigue (TMF) resistance. Single-crystal test bars of again using a Zeiss EVO MA10 SEM fitted with a 16 mm diameter and 165 mm length were cast with near high-speed Bruker Quantax e Flash EBSD detec- h001i, h011i, and h111i crystal growth directions. tor. Areas of 3 9 2.5 mm were scanned at 20 keV with Chemical analysis using XRF, GDMS, OES, and LECO a5-lm step size. Average misorientations calculated showed very good agreement between the measured and using the EBSD results and standard deviations for each nominal values. Impurity levels were confirmed to be far data set are given in Table I. EBSD orientations are also lower than the maximum values allowed by the shown in the simplified inverse pole figure map in specification. Figure 1. All the bars were macro-etched to check for the Miniaturized ETMT blanks with a nominal size of absence of grain boundaries and were then subjected to either 40 9 3 9 1or40 9 4 9 2mm were manufac- X-ray analysis using the Laue back-reflection technique tured along longitudinal bar directions by wire-guided to ensure their orientation differed by less than 15 deg electro-discharge machining (EDM). These blanks were from the specified direction. Heat treatment consisted further waisted via EDM to give nominal widths in the of solutioning at 1280 C for 5 hours, followed by center of the testpiece of 1.1 and 2 mm, respectively, as primary aging at 1100 C for 4 hours, and secondary shown in Figure 2. The main advantage of the waisted aging at 850 C for 20 hours, in each case concluding geometry is that it enables using customized grips, which with gas fan cooling in argon. SEM images of test bar precisely fit the waist radius and which ensure correct cross sections were obtained using a JEOL alignment during testing. JSM-6500F SEM operating at 20 keV and are shown A further benefit is that this geometry gives rise to a in Figure 1. The microstructure is characteristic of IGT concentration of stress and temperature within the superalloys, and is composed of cuboidal, secondary c central region. This limits the influence of the anoma- precipitates with side lengths of  400 nm and spher- lous yielding effect observed in nickel-based superal- ical, tertiary c particles with diameters on the order of loys—i.e., an increase in yield strength with 10 nm, embedded in the c matrix. Particle size distri- temperature—which could otherwise lead to higher butions were analyzed using the image processing levels of plastic deformation in cooler regions closer to [8] 0 software package MIPAR. The estimated c volume the grips. The latter point is of particular importance in fraction after heat treatment is 53 pct, close to the the context of the present work and is discussed in 58 pct predicted by Thermo-Calc and the TTNi8 further detail in Section IV–A. Nonetheless, a paral- Ni-alloy database. lel-sided section is maintained in the center of the Fig. 1—SEM images of alloy microstructures and IPF map of test bar orientations. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4215 Table I. Results of Crystal Orientation Measurements with EBSD Test Bar Average Misorientation (Deg) Standard Deviation (Deg) h001i 1 2.39 0.56 h001i 2 4.59 0.45 h011i 1 2.86 2.40 h011i 2 11.82 3.44 h111i 1 0.90 0.92 h111i 2 1.99 1.88 Fig. 2—ETMT specimen geometries used in the present study for (a) verification tensile and stepped-temperature tests and (b) stress relaxation tests (all measurements in mm). specimen to ensure a constant stress level and a uniform the case of nickel-based superalloys, which must be temperature distribution. qualified at very high temperatures, often close to their Surfaces were ground to a 4000-grit mirror finish melting point. This makes the design and implementa- using silicon carbide grinding paper. Besides ensuring a tion of the load string, and of small-scale specimens, constant, repeatable finish, this step is crucial for grips, and extensometers, difficult. The ETMT system removing the recast layer caused by EDM and for was developed at the National Physical Laboratory minimizing residual stresses in the sample prior to (NPL) with these concerns in mind and has been used [9] testing. The actual cross section dimensions were successfully for the characterization of c precipitate [14] [15] measured with a micrometer gauge for each specimen volume fraction, recrystallization kinetics, [16,17] [4,18–20] and were used to compute engineering stress. Lastly, TMF, flow stress, and creep strain evolu- [21,22] each specimen was cleaned in an ultrasonic bath with tion in nickel-based superalloys. ethanol, after which a high-temperature paint pattern The Instron ETMT system used in the present work for direct image correlation (DIC) was applied. is illustrated in Figure 3. It uses a mechanical loading assembly capable of testing in both tension and com- pression up to a maximum load of 5 kN. Load cell B. The ETMT System readings are based on a strain gauge element with Interest in high-temperature miniaturized testing has integrated automatic calibration. A versatile gripping grown over time and has led to a multitude of system allows the use of customized grips for each [10–13] approaches. However, ensuring accurate and specimen geometry, in order to ensure correct align- reproducible results remains challenging, especially for ment. Displacement of the top, moving grip can be 4216—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 3—(a) Overview of the testing system used for miniaturized testing of superalloys; images courtesy of Instron and Imetrum Ltd.(b) Schematic illustration of ETMT components. readily measured with an LVDT, and strain at room where R and R are resistances before and during s t temperature can be calculated after considering the deformation. initial grip separation. The second approach measures strain by DIC. A fine speckle pattern is produced on one of the sample Specimens are heated using a 400-A DC power supply surfaces using high-temperature paint. The resulting via the Joule effect. An advantage—for example over pattern with many light, dark, and gray areas offers an furnace-based apparatus—is that a wide range of ideal target for tracking. During testing, the specimen is heating and cooling rates can be achieved and accurately illuminated by a bright, diffuse LED light source controlled. The testing temperature is measured and positioned behind an Allied Vision Technologies controlled with a type K thermocouple composed of Manta G-146 camera which records the test. The thin, 0.1-mm-diameter wires of chromel and alumel, camera has a resolution of 1.4 megapixels and offers a fusion-welded under argon gas to form a small bead. nominal frame rate of 17.8 fps when the full field of view This bead is carefully positioned and spot-welded under (FOV) of 1388 9 1038 pixels is monitored. Higher argon at the center of the specimen. frame rates of up to around 50 fps can be achieved As the grips are water-cooled, a parabolic tempera- when the full FOV is reduced to a smaller region of ture distribution will develop along the specimen. [17,19] interest (ROI), which for the case of present tests Previous studies have shown that the peak temper- ature remains reasonably uniform (T = ± 5 C) in the measures around 250 9 1000 pixels. However, such high central 2 to 3 mm of the sample at high temperatures frame rates have been found to produce unnecessarily between 500 C and 1000 C, with the size of this region large amounts of data and offer little additional infor- decreasing with increasing temperature. A consequence mation at typical strain rates; hence, frame rates is that the majority of plastic deformation is localized in between 1 and 10 fps were chosen. this central region. The Imetrum Ltd Video Gauge software tool Two different strain measurement techniques were analyses images captured by the camera and applies used to account for this effect. The first is the method proprietary sub-pixel pattern recognition algorithms to [4] proposed by Roebuck, in which resistance is measured detect any changes occurring during testing in compar- over the central 2 to 3 mm using two thin, spot-welded ison to a reference state. Displacement and strain are Pt-13 pctRh wires. Changes in cross sectional area measured and calculated in real time between user-de- fined target areas, in this case set 3 mm apart around the during testing lead to changes in resistance and in the center of the specimen, with a strain resolution of voltage drop measured over the two wires. Roebuck around 20 microstrain. The target areas were chosen to showed that, assuming the test volume remains constant be quadratic, with the side length corresponding to the and neglecting elastic changes, plastic strain can be width of the specimen. This choice was made as a calculated as: compromise between improved strain accuracy provided pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e ¼ ln ðÞ R =R ; ½1 p t s by larger windows and increased spacial resolution METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4217 [23] provided by smaller ones. Finally, analogue signals to a total strain of around 3.25 pct during ramping. This for load, LVDT, or temperature channels are transmit- value was chosen to be significantly lower than the total ted from the ETMT to the Video Gauge software elongation observed in standard tensile tests. This through a Signal Interface Unit, thus allowing all implies that specimen necking can be disregarded and relevant data to be collected and saved in one location, that the apparent flow stress can be calculated as and averting potential issues of synchronizing data. engineering stress. The reason for repeating tests over two different temperature ranges, of 650 C and 400 C, was to check whether the level of plastic C. Stepped-Temperature Testing (STT) hardening affects deformation behavior at higher Non-isothermal tensile tests—with the temperature temperatures. being ramped at a constant rate after reaching the As it is intended that the specimen continues to plastic regime—were carried out to deduce information deform plastically at the prescribed strain rate during regarding the variation of flow stress with temperature. temperature ramping, crosshead speed must be com- A schematic illustration of the method is given in pensated to also account for thermal expansion effects in Figure 4(a). Samples are first deformed isothermally at a accordance with: constant initial temperature T of 500 C or 750 Cand 5 4 e_ ¼ e_ þ e_ : ½2 t mechanical thermal constant initial strain rates e_ close to 2 9 10 ,10 , and 5 9 10 /s. After reaching an initial plastic strain Here e_ is the total strain rate measured for the value e of 0.2, 0.5, or 1 pct, the temperature is ramped, p;i specimen, e_ is the strain rate component result- mechanical at a constant rate T of 0.4, 2, and 10 C/s, respectively, ing from the constant crosshead displacement, and up to 1150 C. The values of these temperature ramps e_ is the additional strain rate due to thermal thermal were chosen in accordance with the three different strain expansion and changes in c volume fraction. e_ was thermal rates to yield similar total levels of plastic deformation. measured for each testing condition in a separate In the case of tests between 500 C and 1150 C, the stepped-temperature test at zero load and e_ mechanical durations of temperature ramps were 1625, 325, and was adjusted accordingly to yield the desired total strain 65 seconds, respectively. In each case, this corresponds rate. All testing conditions for STT are summarized in Table II. D. Stress Relaxation Testing (SRT) Isothermal stress relaxation tests were performed between 650 C and 1050 C at intervals of 100 C using the method shown in Figure 4(b) to deduce information on creep performance. Specimens are deformed at a constant initial strain rate of approxi- mately 10 /s until a predefined plastic strain level of [24] 0.2 pct was reached. This value was chosen following in order to achieve steady-state stress behavior and to provide a measure of the current creep strength of the alloy. Crosshead displacement is then stopped and held in that exact position under LVDT control. Load relaxation is measured over a period t of 20 hours, [24] again following. Considering the much longer test durations compared to tensile tests or stepped-temper- ature tests, a larger specimen cross section of 2 9 2mm was chosen to ensure that oxidation would not affect mechanical properties. Values for specimen width/thick- ness were chosen based on the extensive experimental and modeling work on creep and oxidation damage in [25–27] thin-walled specimens. Comparison tests were carried out for the h001i direction on cylindrical specimens of 6 mm gauge length and 3 mm diameter using an Instron Electropuls E10000 linear-torsion all-electric system. This testing rig is equipped with a split furnace controlled using a type K thermocouple positioned close to the specimen gauge. For both systems, the DIC method was used to measure strain. Testing conditions employed for SRT are summarized Fig. 4—Schematic ETMT test methodology for (a) in Table III. stepped-temperature testing and (b) stress relaxation testing. 4218—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Table II. Summary of Stepped-Temperature Tests Carried Out on the ETMT System DT (C) T (C/s) e_ (s ) e (Pct) p;i Test Specimen Heating Strain Measure- 500 to 750 to 5 4 4 System Cross Section Method ment Method 1150 1150 0.4 2 10 2 9 10 10 5 9 10 0.2 0.5 1 Instron 1 9 1.1 mm Joule DIC x x x x ETMT heating xx x x xx x x xx x x xx x x xx x x xx x x xx x x E. Verification Testing and h111i directions are slightly higher in the NPL tests. This could be related to the higher strain rate of around A limited number of tensile tests was carried out on 10 /s corresponding to the chosen constant loading each crystallographic orientation for verification pur- rate of 2 N/s, as opposed to a strain rate of 10 /s in poses and to prove the reliability of the new testing Instron ETMT tests. However, similar experiments on system, as summarized in Table IV. Benchmark tests on alloy CMSX-4 showed that the influence of strain rate the Instron ETMT were performed on samples of 2 only becomes significant above 700 C and justified 1 9 1.1 mm cross section at 500 C and an initial strain 5 differences in flow stress with changes in the off-axis rate close to 10 /s, and at 750 C and initial strain rates [31] 5 4 2 deviation of the test specimens. Considering that of 10 ,10 ,and 10 /s. LVDT control was used at specimens in the present study were manufactured from constant crosshead displacement rates. distinct bars and that cross section measurements were Comparison tests were performed under similar carried out independently, discrepancies caused by conditions at NPL using an in-house ETMT system. crystal orientation and sample dimensions cannot be As this system lacks an LVDT sensor for displacement ruled out. control, tests were carried out at constant loading rates Similarly good agreement is found in tests at 750 C of 0.4, 2, and 10 N/s, which came close to replicating the across all testing conditions, as illustrated in Figure 6(a) constant displacement rate conditions. through (f). Agreement is best at intermediate strain Finally, further comparison tests at 750 C were rates of 10 /s, regardless of crystal orientation. At carried out using regular, cylindrical testpieces of 10 /s, tests on the Instron ETMT exhibit lower 6 mm gauge length and 3 mm diameter using an engineering stress values, likely due to effects of oxida- Instron 8862 servo-electric system. In this case, high tion over longer testing periods. Oxidation damage in temperature was achieved with a split furnace arrange- thin-walled specimens is characterized by both (1) a ment and was controlled with a type K thermocouple reduction in load-bearing cross section through the positioned close to the specimen gauge. With regards to formation of a continuous oxide scale and a c denuded strain measurement, the DIC method was used for all zone near the surface, and (2) changes in c volume tests on the Instron ETMT and the 8862 servo-electric fraction and chemical concentration profiles within the systems. For tests on the NPL ETMT, plastic strain was [26] substrate. On the one hand, this highlights the calculated from resistance measurements, as described in importance of taking into account environmental dam- Eq. [1]. The elastic strain component was added sepa- age and of carrying out small-scale tests at low strain rately using temperature-dependent values for the elastic rates in a protective argon atmosphere if they are to be moduli, E(T), calculated from high-temperature [19] compared directly with standard tests. On the other dynamic resonance measurements carried out for each hand, this also proves the usefulness of miniaturized individual orientation at NPL. For further details ETMT testing for replicating service conditions experi- regarding this procedure, the interested reader is enced by thin-walled turbine blade sections. For rapid directed to References 28 through 30. tests at 10 /s, verification tests on the 8862 servo-elec- tric system yield higher stress values than ETMT tests in the h001i and h111i directions. III. RESULTS A. Verification Tests B. Stepped-Temperature Tests Tensile curves at 500 C are shown in Figure 5; The variation of proof stress with temperature is comparison is made with duplicate tests on the NPL illustrated as a function of orientation in Figure 7(a) ETMT system. Results from both ETMT systems are in through (f) and as a function of deformation rate in good agreement for all orientations, but values of Figure 8(a) through (f). The ramping step was started engineering stress in the plastic regime for the h011i after reaching an initial plastic strain of 0.2 pct at (1) METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4219 Table III. Summary of Stress Relaxation Tests Carried Out on the ETMT and the E10000 Systems Specimen Strain T (C) e_ (s ) e (Pct) t (h) Cross Section Meas. p;i R 2 4 Test System (mm ) Heating Method Method 650 750 850 950 1050 10 0.2 20 Instron ETMT 2 9 2 Joule heating DIC x x x x x x x x Instron E10000 7.1 Furnace DIC x x x x x Table IV. Summary of Tensile Tests Carried Out on the NPL and the Instron ETMT Systems as well as on the 8862 Servo-Electric System Specimen Strain T (C) e_ (s ) Cross Section Measurement 2 5 4 3 Test System (mm ) Heating Method Method 500 750 10 10 10 Instron ETMT 1 9 1.1 Joule heating DIC x x xx x x NPL ETMT 1 9 1 Joule heating Resistance x x xx x x Instron 8862 7.1 Furnace DIC x x x x Fig. 5—Tensile test results at 500 C from the Instron ETMT and the NPL ETMT. Results are plotted up to (a) 5 pct engineering strain to provide an overview of the test and (b) 2 pct engineering strain to provide a more detailed view of the elastic regime and initial yielding. [39,40] 500 C and (2) 750 C, in order to compare the effects of locks or large Kear–Wilsdorf locks —is operative. prior deformation at lower temperatures on the anoma- Such cross-slip events are promoted by the anisotropy of lous yielding effect. One can see that, for all orientations, both APB energy and elastic properties along the f111g a peak in the proof stress occurs in the range of 750 C and f001g planes. to 800 C. This is in accordance with the results of Shah Second, once material strength decreases above [32] [33,34] and Duhl for PWA1480, of Miner et al. for Rene´ 750 C, higher strength at larger strain rates is consis- [35] [31] N4, and of Allan and Bullough et al. for CMSX-4. tently observed, in accordance with time-dependent Several points emerge from the results presented in plasticity. The initial decline in proof stress has been Figures 7 and 8. First, the proof stress is not influenced commonly related to slip activation on the cube plane by by strain rate by strain rate and/or temperature ramping a=2h110i pairs and, at higher temperatures, by perfect [40] rate until a peak stress has been reached, in agreement a[100] single dislocations. Recent studies have iden- [31,36–38] with previous experimental and modeling work. tified diffusion-activated plasticity as an additional In this anomalous yielding regime, cross-slip of short operating mechanism which could explain the decreas- [41,42] dislocation segments from f111g to f001g glide ing strength in this temperature regime. A further planes—leading to either small Paidar–Pope–Vitek significant weakening effect at higher temperatures is a 4220—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 6—Tensile test results at 750 C from the Instron ETMT and 8862 servo-electric systems presented for the (a and b) h001i direction, (c and d) h011i direction, and (e and f) h111i direction. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4221 Fig. 7—STT results for single-crystal specimens with (a and d) h001i orientation, (b and e) h011i orientation, and (c and f) h111i orientation. 5 5 4 Fig. 8—STT results for tests carried out at initial strain rates of (a and b)2 9 10 /s, (c and d)10 /s, and (e and f)5 9 10 /s. 4222—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 9—STT results from tests in which the temperature-ramping step was started after varying initial plastic strain levels of 0.2, 0.5, and 1 pct. Results are shown separately for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. decrease in c volume fraction, / . Calculations using above 800 C, but, at lower temperatures, the h111i direction is much stronger than h011i and even surpasses Thermo-Calc and the TTNi8 Ni-alloy database predict a h001i below 600 C. decrease from 58 pct at 600 C to nearly 0 pct at Third, the results are nearly identical regardless of 1150 C (see Figure 13(d)). Maximum precipitate whether temperature ramping was initiated at 500 Cor strength is approximated to scale with the square root [43] at 750 C, thus suggesting that the degree of strain of / , thus explaining this pronounced drop. hardening imposed at lower temperatures does not For all tests—and regardless of strain rate—the substantially alter the estimate of the flow stress. strength on the h011i direction is much lower until However, to study the influence of the magnitude of temperatures of 1000 C and above are reached, at pre-straining on the measured proof stress in greater which point all orientations exhibit similar proof stress detail, tests at an initial constant temperature of 500 C values. This observation is of particular interest, as [31,32,35] were repeated while varying the plastic strain level previous studies reported that yield strength before ramping to 0.5 and 1 pct. As shown in above 750 C consistently increases from the h111i to Figure 9(a) through (c), very little effect on proof stress the h011i, and finally to the h001i orientation. While was observed in the plateau region, in agreement with h001i remains the direction with highest strength for the [31,36–38] previous reports. In the high-temperature SIT superalloy, there is now a discrepancy between the regime, the influence of initial plastic strain and of the h011i and h111i directions. Proof stress values converge METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4223 Fig. 10—Apparent activation energies extracted from STT between 500 C and 1150 C for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. Estimates were extracted by fitting the dashed lines to experimental data from lower strain rate tests. accumulated total strain level is unclear and there are Finally, it has been found that the STT curves can differences in the responses of the three orientations. be analyzed at temperatures beyond those associated While for h001i and h111i the strength decreases with with a maximum in the flow stress to extract an increasing initial strain, for h011i the results are almost estimate of apparent activation energy, as shown identical for initial plastic strain levels of 0.2 and 0.5 pct, schematically in Figure 4(a). For this, it is assumed 5 4 and the strength is higher above 800 C in the specimen that deformation rates of 2 9 10 and 10 /s are slow pre-strained up to 1 pct. It can be concluded that, if a enough for a steady-state condition to be approached fair comparison is to be made, the level of pre-straining at each temperature level during the ramping segment. must be carefully controlled and maintained constant Estimates of the steady-state creep rate, e_ , can then be across all tests. expressed as: 4224—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 11—Double-logarithmic plots of strain rate over applied stress extracted from SRT between 650 and 1050 C. A comparison of all results is shown in (a). SRT data are then presented separately for the (b) h001i direction, (c) h011i direction, and (d) h111i direction. Arrows indicate testing temperatures in cases in which lines are overlapping. Quantitative values are obtained assuming a constant app n stress exponent of 8 for this range of strain rates and e_ ¼ Ar exp  ; ½3 app RT temperatures, chosen based on the SRT results pre- sented in Figure 12. This leads to apparent activation where A is a material-specific constant, n is the stress energies of 1028, 620, and 631 kJ/mol. In normalized exponent, R is the gas constant, r is the measured app terms, these figures correspond to 75.9RT , 45.8RT , m m apparent proof stress, and Q is the apparent activa- app and 46.5RT , with the melting temperature T of 1630 m m tion energy. Equation [3] can be rearranged to yield a K predicted by Thermo-Calc. Activation energies must plot of lnðr Þ vs 1/ T, in which the slope will be equal app be considered carefully, as they are directly influenced to Q =Rn. Results of this analysis are shown for the app by the chosen stress exponent, which in turn corre- three crystal directions in Figures 10(a) through (c). The sponds to an apparent, extrapolated value rather than [44,45] dashed lines used to extract estimates for Q were app an effective, phenomenological one. Nonetheless, fitted to experimental data from lower strain rate tests. these figures are in fair agreement with values of 41RT , [46] Qualitative results confirm that resistance to reported by Carey and Sargent for IN738LC, and of [47] high-temperature creep deformation increases from the 53.3RT , obtained by Sajjadi and Nategh for h011i to the h111i, and finally to the h001i direction. GTD-111 in this regime. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4225 Fig. 12—Contour maps of the apparent stress exponent as a function of temperature and strain rate for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. Quantitative values are shown next to the color bars. Minimum and maximum values were manually set to 4 and 300, and 16 linearly distributed major levels were generated in between. Dark gray lines mark the limits of individual major levels. C. Stress Relaxation Tests where e_ , e_ , and e_ are the total, the plastic, and the t p e elastic strain rates of the specimen, and e_ is the elastic Stress relaxation testing has been used to rapidly strain rate of the testing apparatus. Plastic strain rate assess creep performance, building on efforts made [48–51] can then be expressed following Reference 55 as: elsewhere. This method aims to quantify remaining creep resistance—before or after service exposure—and r _ Ar _ r _ e_ ¼  ¼ ; ½5 represents a paradigm shift away from attempting to E Lk E m app re-create microstructural damage evolution, as is carried [24] out in a regular creep test. Several recent studies have where r _ is the change in stress with time during load made use of SRT for the mechanical characterization of relaxation and E is the apparent modulus of the app superalloys and have shown results consistent with material. The latter can be calculated using E as the conventional creep data from the literature, thus elastic modulus, A as the sample cross section, k as the enabling accelerated testing campaigns of new stiffness of the machine, and L as the specimen gauge [52–54] alloys. Here, in common with such approaches, it length. While k is unknown, it can be estimated by is assumed that the total strain rate of the system analyzing elastic data obtained during loading and/or [24,55] remains in equilibrium as crosshead displacement is unloading. fixed, consistent with: As load relaxation occurs across the ETMT specimen, and not only in the central high-temperature region, e_ ¼ e_ þ e_ þ e_ ¼ 0; ½4 t p e m slight changes in total strain cannot be avoided. Here, 4226—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 13—Stress/temperature deformation mechanism maps for material deformed along the (a) h001i direction, (b) h011i direction, and (c) h111i 1 [58] direction. Contours of shear strain rate are given in s . Field boundaries reported by Frost and Ashby for conventionally cast Mar-M200 material are added for comparison. The plot in (d) shows changes in c, c , and liquid phase fractions for the SIT superalloy predicted by Thermo-Calc using the Ni-alloy database TTNi8. these have been measured with DIC in the central 3 mm By using the approach depicted in Figure 4(a), the of the specimen to provide a correction for Eq. [5], apparent stress exponent, n, can be obtained as a yielding e_ ¼ e_  r _ =E . Application of this correction function of the logarithmic values of stress, r, and strain p t app rate, e_ , consistent with: has been found to be especially important for the first minutes of relaxation, during which the ETMT appara- @ log e_ tus contracts elastically as the applied load decreases. n ¼ ½6 @ log r Longer-term SRT results are not affected by the finite e;T stiffness of the load frame and corrections to Eq. [5] are [55] for given values of total strain and temperature. minimal. Application of this equation locally to segments of the Curves of applied stress over plastic strain rate are stress–strain rate curves allows contour maps to be presented on double logarithmic plots in Figure 11(a) derived for the apparent stress exponent at strain rates through (d). Noticeable changes in gradient occur at 5 9 between 10 and 10 /s and temperatures between 650 intermediate strain rates, giving the curves a character- C and 1050 C, as shown in Figure 12(a) through (c). istically sigmoidal shape. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4227 These can be regarded as Ashby-type high-temperature apparent stress exponents show a significant rise, with deformation mechanism maps and can be derived rather values that can no longer be rationalized by any type of rapidly with the ETMT approach. high-temperature deformation mechanisms. As opposed An initial decrease in the apparent stress exponent has to a standard creep test, the driving force for directional been observed for tests performed above 750 Cat coarsening and creep strain accumulation decreases with 6 8 strain rates between 10 and 10 /s. This occurs earlier time during SRT and exceedingly tends towards zero. [53] in the test, i.e. at higher strain rates, as the temperature Nathal et al. observed no further microstructural increases. Similar behavior has been reported by Nathal changes when comparing specimens relaxed at 982 C [53] et al. for the first-, second-, and fourth-generation for 100 and 370 hours. As such, once a steady-state single-crystal superalloys, NASAIR 100, CMSX-4, and stress value has been reached, the results from SRT are EPM-102. These authors showed that the effect disap- increasingly affected by mechanical noise and provide pears if the specimens are crept prior to stress relaxation, little further insight into high-temperature damage as the pre-rafted microstructure offers higher resistance accumulation mechanisms. to primary creep. As such, this transition can be related SRT data can also be presented in the form of stress/ to a shift from primary creep deformation, dominated temperature deformation mechanism maps, following [58] by APB shearing of c precipitates, to tertiary creep, Frost and Ashby. The resulting maps shown in dominated by dislocation climb bypass. Transition Figure 13(a) through (c) provide a means of visualizing stress values at different temperatures are in accordance material performance in different deformation regimes with the deformation mechanism maps for nickel-based and of comparing normalized results to data from the [56] [46,47] superalloys proposed by Smith et al. and Barba literature. [22] [58] et al. No transition is clear at 650 C, probably As discussed by Frost and Ashby, any deformation because this temperature is too low to enable diffusional mechanism can be described by a rate equation of the climb around the precipitates. form: Values of apparent stress exponents associated with c_ ¼ f s; T; S ; P ½7 i j primary and tertiary creep, respectively, decrease with increasing temperature. This reduction has been shown to be related to directional coarsening of precipitates at This relates shear strain rate, c_, to shear stress, s, [53] higher temperatures. It should be noted that these temperature, T, a set of i state variables, S , describing figures cannot be readily related to effective stress the current microstructural state of the material, and a exponents used in creep models, as explained by Carry set of j material properties, P , which are inherent to the [44] [45] and Strudel for both primary and tertiary creep. material. Key simplifying assumptions are that stea- Discrepancies between apparent and effective exponents dy-state conditions are reached during deformation and were also confirmed by the experimental results of that material properties and state variables either remain [55] Dupeux et al. from stress relaxation and conventional constant or are directly determined by s and/or T. This [57] creep tests on CMSX-2. At strain rates below 10 8/s, leads to a reduction of Eq. [7]to c_ ¼ fðs; TÞ. Fig. 14—(a) CAD-derived drawing of a gripped ETMT specimen. (b) Schematic representation of heat conduction in an ETMT specimen with heat generation from Joule heating. 4228—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A In order to construct maps following Frost and moduli, G(T), were obtained for each individual orien- Ashby, the tensile stress/strain data from Figure 11 are tation from high-temperature dynamic resonance mea- first converted to shear stress/strain. Geometrical trans- surements at NPL. These are the same assessments formation factors were chosen following the work of mentioned in Section II–E with regards to obtaining [59] Ghosh et al., who modeled the crystallographic temperature-dependent elastic moduli, E(T), for each anisotropy of tensile creep deformation in single-crystal orientation. superalloys. These authors assumed that macroscopic As suggested by Frost and Ashby, data points in creep deformation results from glide on both the Figure 13 are labeled with the value of the third macroscopic variable, in this case logðc_Þ. The red dashed f111gh101i and f001gh110i systems, while neglecting lines represent contours of constant shear strain rate macroscopic contributions from f111gh112i slip vectors. based on data between 750 C and 1050 C. The solid Their work contains an in-depth discussion on the green lines divide fields dominated by power law creep, predicted number of active slip systems and their diffusion creep, and low-temperature plasticity con- respective Schmid factors, leading to geometrical con- [59] trolled by dislocation glide. These boundaries were versions for each orientation. reported for Mar-M200 material with a large grain size In a second step, shear stress and temperature values of around 1 cm, which can be taken as an estimate of are normalized with respect to shear modulus and directionally solidified or single-crystal material behav- melting temperature. The aforementioned value of 1630 [58] ior and offer a benchmark for the SIT superalloy. A K predicted by Thermo-Calc and TTNi8 for T is used further power law breakdown regime dominated by to calculate the homologous temperature (see APB shearing of c precipitates can be inferred in the Figure 13(d)). Values for temperature-dependent shear [61] Fig. 15—(a) Cubic and linear fits for electrical resistivity and thermal conductivity data obtained by Mills et al. for CMSX-4. Modeling results for the distribution of (b) temperature, (c) electrical resistivity, and (d) thermal conductivity along a heated ETMT specimen. The dotted lines in the temperature distribution graph mark regions predicted to remain, respectively, at T  5 C and T  15 C. max max METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4229 upper left corner of the maps and would include data at the sample and the accuracy of DIC strain measure- 650 C. The lower limit of this area is estimated at ments are discussed in the following. Here, accumulated 2 [58] around 10 G. errors in load are not considered, as the 5-kN load cell was calibrated against a reference before the testing campaign. IV. DISCUSSION 1. Modeling of the temperature distribution in ETMT A. Validity and Limitations of the ETMT System specimens [4,19,23] Previous ETMT studies have reported a uni- In this work, it has been demonstrated that the ETMT form temperature distribution in the central 2 to 4 mm offers substantial practical advantages associated with of the specimen. However, these observations are based testpiece miniaturization. Nevertheless, a critical issue on limited experimental results and lack validation by concerns whether or not results are comparable to those modeling. This issue is considered in greater detail here. obtained from established techniques which are For a given material volume containing a heat source, regarded as more standardized. In particular, one the temperature distribution T(x, y, z, t)—depending on should be concerned with (1) real size effects—such as three spatial variables (x, y, z) and the time variable the effect of oxidation damage at low strain rates—and t—can be expressed by the heat equation: (2) potential errors and increased data scatter arising from sub-scale testing. 2 2 2 @T @ T @ T @ T c q  k þ þ ¼ q_ : ½8 In this context, several generic issues have been p V 2 2 2 @t @x @y @z [11,12] identified. First, a minimum representative material volume must be sampled. This may be less of an issue Here, c is the specific heat capacity, q is the mass for the case of single-crystal specimens; however, it density of the material, k is the thermal conductivity, poses a significant challenge for testing polycrystalline and q represents the volumetric heat source. Three materials with grain sizes of the order of testpiece width/ assumptions are made at this point to simplify the thickness. Second, there is an increased probability that integration of Eq. [8]. small defects or heterogeneities will affect bulk material First, a steady-state case is considered, in which the response. Considering the good quality of the cast- heat equation is not dependent on time, so that ings—which exhibit low levels of porosity and reduced @T=@t ¼ 0. For temperature or current control, the segregation after heat treatment—this point may not be Instron ETMT system uses a high bandwidth 8800 so vital to consider. Third, test specimens must be servo-hydraulic controller with a maximum internal carefully manufactured and mechanically finished to acquisition and control loop sampling rate of 10 kHz. reduce the possibility of surface residual stresses or This high bandwidth enables fast and accurate control [23] re-cast layers influencing the results. Preparation steps even when large heating or cooling rates are required. taken to avoid this are described in Section II–A. Last, With well-tuned PID control parameters, the system uncertainties associated with measurements of load shows an immediate response to changes in the com- (stress), temperature, and strain must be critically mand channel, as well as very good long-term stability. assessed. The effect of temperature heterogeneity along As such, steady-state conditions are a reasonable Fig. 16—Effects of selected virtual gauge length for DIC strain measurements on experimental results. A test on the h001i direction at 750 C and 10 /s was chosen for this analysis. Results are plotted up to (a) 10 pct engineering strain to provide an overview of the test, and (b) 5 pct engineering strain to provide a more detailed view of the elastic regime and initial yielding. 4230—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A 3 Fig. 17—2D color maps of strain distribution in a h001i specimen tested at 750 C and 10 /s. Results are shown for total strain levels of (a) 5 pct, (b) 10 pct, and (c) 15 pct. assumption, even in the case of stepped-temperature where P is the power converted from electrical to tests. thermal energy in a volume element DV, I is the current Second, the heat equation is treated as a one-dimen- traveling through the testpiece, R is the electrical sional problem, in which the temperature only varies resistance, q is the electrical resistivity, and A is the along the tensile axis of the specimen, chosen here as the specimen cross section. x spatial coordinate, as shown in Figure 14. While the The boundary conditions necessary to solve Eq. [9] temperature will also vary across the width and thick- uniquely are that temperature at the gripped ends, ness of the testpiece, relative differences are much TðLÞ¼ T , remains constant during testing. This grip smaller than along the tensile axis. Equation [8] can yields the one-dimensional temperature distribution: now be simplified to: 2 2 L x TðxÞ¼ q_ 1  þ T V grip @ T 2k L k ¼ q_ ½9 V 2 2 2 2 @x I L x q ¼ 1  þ T : ½11 grip A 2 L k Third, an additional negative term of the form lT can be added to Eq. [9] to account for radiative heat loss It can be seen that temperature scales with the square to the immediate environment. However, it is assumed of applied current over the specimen cross section. The here that cooling rates are primarily determined by the term T has been measured during testing at high grip thermal diffusivity of the specimen and by heat loss to temperatures and remains constant at around 40 C. the water-cooled grips, and that radiation can be For the case of the larger ETMT testpiece geometry neglected. While this final assumption is incorrect at chosen for stress relaxation tests, A is equal to 4 mm very high temperatures, it should not have a significant and L to 7.5 mm. impact on modeling results for temperatures below The two remaining material parameters—electrical [23] 1100 C. resistivity, q, and thermal conductivity, k—both depend The volumetric heat source q_ for a certain portion of on chemical composition and on temperature, thus the testpiece volume can be described using Joule’s first requiring a discrete solution of Eq. [11]. Considering law and Ohm’s law as: that the same master heat was used to cast all the bars, it is anticipated that temperature distribution will not 2 2 P I R I q depend on orientation. Several extensive studies have q_ ¼ ¼ ¼ ; ½10 DV DxA A discussed the measurement and calculation of METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4231 4 Fig. 18—2D color maps of strain distribution in a h001i specimen tested at 750 C and 10 /s. Results are shown for total strain levels of (a) 5 pct, (b) 10 pct, and (c) 15 pct. [60–62] thermophysical properties of superalloys. In the results are in good agreement with previous find- [4,19] present work, results obtained for the second-generation ings. The section of the testpiece at T  5 C max single-crystal superalloy CMSX-4 at temperatures decreases with increasing temperature. It is predicted to between 298 and 1550 K are used as estimates for the be 1.67 mm at 700 C and 1.54 mm at 900 C, close to [61] SIT superalloy. Data for qðTÞ and k(T) are fitted the experimentally determined values of 2.4 mm and [19] using a cubic and a linear equation, respectively, as 2.2 mm, respectively, for the disc superalloy RR1000. shown in Figure 15(a): Modeling predicts that the central 3-mm region observed for DIC strain measurements remains at a qðTÞ¼ 9:06032  10 þ 1:88864 reasonably uniform temperature of ± 15 C. These 9 12 2 results are an important validation of temperature 10 T  1:55977  10 T þ 3:53139 ½12 distribution in ETMT specimens, and they furthermore 16 3 10 T ½ Xm highlight the importance of precise, localized strain measurements in the hot zone. kðTÞ¼ 3:50617 þ 0:01909T ½WmK 2. Non-contact strain measurements via DIC The applied current, I , is registered during testing. app A recent review on miniaturized testing critically However, due to previous imprecise assumptions and assessed a number of strain measurement techniques estimates, the temperature calculated for the center of including LVDT, line scan cameras, capacitance gauges, the specimen using I in Eq. [11] does not exactly app electrical resistance measurements, interferometry tech- [12] match T . As such, a current correction parameter, max niques, and DIC. It was concluded that, despite the I , is introduced to ensure that Tð0Þ¼ T . corr max modest strain resolution obtained for usual camera/lens/ Modeling results for the distribution of temperature, FOV combinations, DIC provides substantial advan- electrical resistivity, and thermal conductivity in ETMT tages as a full field non-contact method, especially specimens between 500 C and 1200 C are shown in considering ongoing developments in higher-resolution Figure 15(b) through (d). Qualitative and quantitative cameras and increased computing power. 4232—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A [2,63] A convenient feature is that, once a test video has (ICME). Several promising approaches toward been recorded and stored, it can be readily post-pro- alloy design have been proposed and applied to the [64–68] cessed using different window sizes, gauge lengths, and development of new grades of superalloys. Fur- processing accuracy/speed parameters. An analysis of thermore, laboratory-scale process chains for rapid this type, exploring the effects of different gauge lengths production of single-crystal superalloy trial castings [69–71] between virtual target windows, is shown in Figure 16. have been successfully established. However, test- An ETMT tensile test on the h001i direction at 750 C ing methods continue to be dominated by standard and an initial strain rate of 10 /s was chosen as an approaches. It can be concluded that, within the example. The importance of selecting a correct reduced design–make–test cycle, the last segment currently offers gauge length is evident. As this value increases, it most potential for improvement in the context of ICME encompasses more of the cooler regions of the specimen, goals. in which less plastic deformation takes place. This leads The ETMT testing methods presented here offer a to large discrepancies between analysis results at higher viable and convenient contribution to this overarching plastic strain values. While the impact on 0.2 pct proof goal of more efficient and rapid materials development. stress—and on initial conditions for stepped-tempera- Acquired data can be used to extract estimates of key ture testing—is limited, choosing an incorrect gauge material properties and to make critical decisions length will have a strong impact on stress relaxation regarding screening and/or ranking of trial alloys during results through Eq. [5]. The analysis below confirms the the development stage. Based on the reported dimen- [71] validity of DIC strain measurements in the central 3 mm sions of small-scale single-crystal rods, and using of the specimen. testpiece dimensions shown in Figure 2, a sufficient Another useful feature of DIC—and in particular of number of ETMT samples for STT and SRT can be the Video Gauge software package—is the ability to produced from each trial casting. output 2D strain maps. These provide a simple way of Stepped-temperature testing enables a rapid assess- locating strain concentrations and a direct proof that ment of changes in athermal material strength with anomalous yielding is not affecting test results. In order temperature at a certain deformation rate. Data to generate a strain map, the ROI is first divided into a obtained from STT is valuable for informing TMF [72,73] grid of targets. Displacements between these targets are and cyclic fatigue lifing models. In our experience, then continuously analyzed and used to calculate the several trial alloys can be compared in only a few hours Lagrangian strain tensor at each node of the grid. For and optimal compositions can be identified. Further- the present calculations, the side length of the quadratic more, it should be noted that STT can be readily applied targets and their grid spacing were chosen to be 15 pixels to other classes of high-temperature materials. For as a compromise between spacial resolution and com- example, tests on titanium alloys for aerospace applica- puting time. A filter size of 30 pixels was used to tions have shown that STT results capture the smoothen displacements around each node and to microstructural changes introduced by different heat reduce image noise. Finally, changes in 2D strain treatments, and indicate a composition-dependent tran- distribution over time are exported as a .avi video file. sition in the operating deformation mechanisms between [74] Figures 17 and 18 show the development of strain low and high temperatures. distribution within ETMT specimens with h001i orien- Stress relaxation tests over a temperature range of tation tested at 750 C and initial strain rates of 10 interest can rapidly yield Ashby-type deformation and 10 /s, respectively. Individual video frames were mechanism maps. Plotting data in this fashion offers a selected for comparison at total strain levels of 5, 10, direct comparison with other materials for different and 15 pct. The variable E plotted in the color maps is operating conditions. For any particular application, a xx the calculated strain in the tensile direction. The color target region can be added using the range of temper- range is scaled between the minimum and maximum atures and stresses encountered in service. Contours of strain values detected up to that point during the test. constant strain rate provide a first estimate for screening Some artefacts appear due to discontinuities in the ROI, alloys that surpass the maximum acceptable strain rate commonly specimen edges or areas where the high-tem- and for ranking the remaining ones. The SRT results perature paint layer was damaged. The 2D strain maps can be readily exported as inputs for commercial FEM confirm that deformation is localized in the center of the software packages like ABAQUS. This ensures that specimen. Furthermore, they show that anomalous FEM simulations—increasingly applied to modeling yielding does not impact test results. Particularly in high-temperature deformation in superalloy compo- 4 [75–77] the test at 10 /s, it is also clear that macroscopic nents —provide reliable quantitative results. deformation is concentrated along f111g slip planes at a 45 deg angle to tensile loading. V. SUMMARY AND CONCLUSIONS B. On the Potential of the ETMT for Rapid Alloy Miniaturized testing using an electro-thermal Development mechanical testing system has been carried out on a The importance of accelerated material development prototype single-crystal superalloy along the h001i, cycles has led to large-scale enterprises like the Materials h011i, and h111i loading axes. Compared with full-scale Genome Initiative (MGI), part of the broader field of testing methods on testpieces of more standard geom- Integrated Computational Materials Engineering etry, the approach is advantageous owing to its METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4233 increased speed, degree of simplicity, and the use of REFERENCES smaller quantities of material. The following specific 1. R.E. Schafrik and S. Walston: in Superalloys 2008: Proceedings of conclusions can be drawn from the present study: the Eleventh International Symposium on Superalloys, R.C. Reed, K.A. Green, P. Caron, T. Gabb, M.G. Fahrmann, E.S. Huron, 1. The ETMT has been shown to be a viable tool for and S.A. Woodward, eds., TMS, Warrendale, 2008, pp. 3–9. assessing material properties of single-crystal nick- 2. W. Xiong and G.B. Olson: NPJ Comput. Mater., 2016, vol. 2, p. 15009. el-based superalloys. Mechanical properties derived 3. T.M. Pollock: Nat. Mater., 2016, vol. 15, pp. 809–15. from miniaturized testing are found to be compa- 4. B. Roebuck, D.C. Cox, and R.C. Reed: in Superalloys 2004: rable to those obtained from conventional tensile Proceedings of the Tenth International Symposium on Superalloys, tests over a range of temperatures and strain rates. K. Green, H. Harada, and T.M. Pollock, eds., TMS, Warrendale, 2004, pp. 523–28. 2. Stress relaxation tests and stepped-temperature tests 5. R.C. Reed, J. Moverare, A. Sato, F. Karlsson, and M. Hasselqvist: have been used as a rapid means of extracting creep in Superalloys 2012: Proceedings of the Twelfth International and tensile strength estimates and parameters. Symposium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, 3. It has been demonstrated that changes in athermal M.J. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., plastic deformation with temperature can be deter- Wiley, New York, 2012, pp. 197–204. 6. A. Sato, Y.-L. Chiu, and R.C. Reed: Acta Mater., 2011, vol. 59, mined with a single test by ramping up the pp. 225–40. temperature during deformation at a constant strain 7. A. Sato, J.J. Moverare, M. Hasselqvist, and R.C. Reed: Metall. rate. This has allowed for an estimate of the Mater. Trans. A, 2012, vol. 43A, pp. 2302–15. variation of flow stress with temperature. 8. J.M. Sosa, D.E. Huber, B. Welk, and H.L. Fraser: Integr. Mater. Manuf. Innov., 2014, vol. 3, p. 5. 4. Stress relaxation tests with the ETMT enable a 9. D.A. LaVan and W.N. Sharpe: Exp. Mech., 1999, vol. 39, rapid assessment of time-dependent deformation at pp. 210–16. high temperatures. Changes in operating mecha- 10. K.J. Hemker and W.N. Sharpe: Annu. Rev. Mater. Res., 2007, nisms are revealed through deformation mechanism vol. 37, pp. 93–126. maps, generated using data measured at different 11. T.H. Hyde, W. Sun, and J.A. Williams: Int. Mater. Rev., 2007, vol. 52, pp. 213–55. temperatures. The results show a transition from 12. J.D. Lord, B. Roebuck, R. Morrell, and T. Lube: Mater. Sci. precipitate shearing to dislocation climb bypass at Technol., 2010, vol. 26, pp. 127–48. higher temperatures and lower plastic strain rates. 13. C.C. Dyson, W. Sun, C.J. Hyde, S.J. Brett, and T.H. Hyde: Mater. 5. Such rapid testing methodologies can be applied in Sci. Technol. 2015, pp. 1–15. 14. B. Roebuck, D. Cox, and R.C. Reed: Scr. Mater., 2001, vol. 44, studies of small-scale superalloy castings to deter- pp. 917–21. mine both athermal and time-dependent plastic 15. D.C. Cox, B. Roebuck, C.M.F. Rae, and R.C. Reed: Mater. Sci. responses. This accelerated design–make–test cycle Technol., 2003, vol. 19, pp. 440–46. has the potential to significantly reduce the time for 16. S. Pahlavanyali, A. Rayment, B. Roebuck, G. Drew, and C. Rae: qualification and insertion of new grades of Int. J. Fatigue, 2008, vol. 30, pp. 397–403. 17. B. Roebuck, M. Loveday, and M. Brooks: Int. J. Fatigue, 2008, superalloys. vol. 30, pp. 345–51. 18. S. Kuhr, G. Viswanathan, J. Tiley, and H. Fraser: in Superalloys 2012: Proceedings of the Twelfth International Symposium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, M.J. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., Wiley, New York, ACKNOWLEDGMENTS 2012, pp. 103–10. 19. A.A.N. Nemeth, D.J. Crudden, D.M. Collins, D.E.J. Armstrong, Financial support and material provision from Sie- and R.C. Reed: in Superalloys 2016: Proceedings of the 13th mens Industrial Turbomachinery AB (Finspa˚ ng, Swe- International Symposium on Superalloys, M.C. Hardy, E.S. Huron, den) is gratefully acknowledged. The provision of the U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. Seetharaman, and S. Tin, eds., Wiley, Hoboken, 2016, pp. 801–10. ETMT was facilitated by funding from the Engineer- 20. A. Ne´ meth, D.J. Crudden, D. Armstrong, D.M. Collins, K. Li, ing and Physical Sciences Research Council (EPSRC) A.J. Wilkinson, C. Grovenor, and R.C. Reed: Acta Mater., 2017, under grant number EP/M50659X/1. RR acknowl- vol. 126, pp. 361–71. edges additional support from the EPSRC under grant 21. D. Barba, S. Pedrazzini, A. Vilalta-Clemente, A.J. Wilkinson, number EP/M005607/01. Roger Morrell at NPL is M.P. Moody, P. Bagot, A. Jerusalem, and R.C. Reed: Scr. Mater., 2017, vol. 127, pp. 37–40. acknowledged for his support on high-temperature 22. D. Barba, E. Alabort, S. Pedrazzini, D.M. Collins, A.J. Wilkinson, measurements of elastic constants. P. Bagot, M.P. Moody, C. Atkinson, A. Jerusalem, and R.C. Reed: Acta Mater., 2017, vol. 135, pp. 314–29. 23. B. Roebuck, M. Brooks, and A. Pearce: Good Practice Guide for Miniature ETMT Tests: Measurement Good Practice Guide No. 137: PDB: 7798; Technical Report, National Physical Laboratory OPEN ACCESS Division of Materials Applications, 2016. 24. D.A. Woodford: Mater. Res. Innov., 2016, vol. 20, pp. 379–89. This article is distributed under the terms of the 25. M. Bensch, J. Preusner, R. Huttner, G. Obigodi, S. Virtanen, J. Creative Commons Attribution 4.0 International Gabel, and U. Glatzel: Acta Mater., 2010, vol. 58, pp. 1607–17. License (http://creativecommons.org/licenses/by/4.0/), 26. M. Bensch, A. Sato, N. Warnken, E. Affeldt, R.C. Reed, and U. Glatzel: Acta Mater., 2012, vol. 60, pp. 5468–80. which permits unrestricted use, distribution, and 27. M. Bensch, C.H. Konrad, E. Fleischmann, C. Rae, and U. Glatzel: reproduction in any medium, provided you give Mater. Sci. Eng. A, 2013, vol. 577, pp. 179–88. appropriate credit to the original author(s) and the 28. W. Hermann, H.G. Sockel, J. Han, and A. Bertram: in Superalloys source, provide a link to the Creative Commons 1996: Proceedings of the Eighth International Symposium on license, and indicate if changes were made. Superalloys, R.D. Kissinger, D.J. Deye, D.L. Anton, A.D. Cetel, 4234—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A M.V. Nathal, and T.M. Pollock, eds., TMS, Warrendale, 1996, pp. 53. M.V. Nathal, J. Bierer, L. Evans, E.A. Pogue, F. Ritzert, and T.P. 229–38. Gabb: Mater. Sci. Eng. A, 2015, vol. 640, pp. 295–304. 29. M. Fahrmann, W. Hermann, E. Fahrmann, A. Boegli, T.M. 54. S.L. Semiatin, P.N. Fagin, R.L. Goetz, D.U. Furrer, and R.E. Pollock, and H.G. Sockel: Mater. Sci. Eng. A, 1999, vol. 260, Dutton: Metall. Mater. Trans. A, 2015, vol. 46A, pp. 3943–59. pp. 212–21. 55. M. Dupeux, J. Henriet, and M. Ignat: Acta Metall., 1987, vol. 35, 30. R. Morrell, D.A. Ford, and K. Harris: Calculations of Modulus in pp. 2203–12. Different Directions for Single-Crystal Alloys, NPL Report 56. T.M. Smith, R.R. Unocic, H. Deutchman, and M.J. Mills: Mater. DEPC-MN 004; Technical Report, NPL, 2004. High Temp., 2016, vol. 33, pp. 372–83. 31. C.K. Bullough, M. Toulios, M. Oehl, and P. Luka´ sˇ:in Materials 57. H. Rouault-Rogez, M. Dupeux, and M. Ignat: Acta Metall. for Advanced Power Engineering 1998: Proceedings of the 6th Liege Mater., 1994, vol. 42, pp. 3137–48. Conference/Jacqueline Lecomte-Beckers, F. Schubert and P.J. 58. H.J. Frost and M.F. Ashby: Deformation-mechanism maps, 1st ed., Ennis, J. Lecomte-Beckers, F. Schubert, and P.J. Ennis, eds., Pergamon Press, Oxford Oxfordshire and New York, 1982. Schriften des Forschungszentrums Julich. Reihe Energietechnik/ 59. R.N. Ghosh, R.V. Curtis, and M. McLean: Acta Metall. Mater., Energy technology, 1433–5522, Vol. 5, 2; Forschungszentrum 1990, vol. 38, pp. 1977–92. Julich: Julich, Germany, 1998, pp. 861–78. 60. K.C. Mills: Recommended values of thermophysical properties for 32. D.M. Shah and D.N. Duhl: in Superalloys 1984: Proceedings of the selected commercial alloys, Woodhead, Cambridge, 2002. Fifth International Symposium on Superalloys, M. Gell, 61. K.C. Mills, Y.M. Youssef, Z. Li, and Y. Su: ISIJ Int., 2006, C.S. Kortovich, R.H. Bricknell, eds., TMS, Warrendale, 1984, pp. vol. 46, pp. 623–32. 105–14. 62. P.N. Quested, R.F. Brooks, L. Chapman, R. Morrell, Y. Youssef, 33. R.V. Miner, T.P. Gabb, J. Gayda, and K.J. Hemker: Metall. and K.C. Mills: Mater. Sci. Technol., 2009, vol. 25, pp. 154–62. Trans. A, 1986, vol. 17, pp. 507–12. 63. G.B. Olson and C.J. Kuehmann: Scr. Mater., 2014, vol. 70 (25), 34. R.V. Miner, R.C. Voigt, J. Gayda, and T.P. Gabb: Metall. Trans. p. 30. A, 1986, vol. 17, pp. 491–96. 64. R.C. Reed, T. Tao, and N. Warnken: Acta Mater., 2009, vol. 57 35. C.D. Allan: PhD Thesis, Massachusetts Institute of Technology, (5898), p. 5913. 1995. 65. R. Rettig, N.C. Ritter, H.E. Helmer, S. Neumeier, and R.F. 36. G.R. Leverant and D.N. Duhl: Metall. Trans., 1971, vol. 2, Singer: Modell. Simul. Mater. Sci. Eng., 2015, vol. 23, p. 35004. pp. 907–08. 66. R. Rettig, K. Matuszewski, A. Muller, H.E. Helmer, N.C. Ritter, 37. B.H. Kear and J.M. Le Oblak: J. Phys. Colloq., 1974, vol. 35, and R.F. Singer: in Superalloys 2016: Proceedings of the 13th pp. 35–45. International Symposium on Superalloys, M.C. Hardy, E.S. Huron, 38. L12 Ordered Alloys: Nabarro, F.R.N., Duesbery, M.S., Eds., U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. Seetharaman, S. Tin, Dislocations in Solids, Vol. 10; Elsevier, Amsterdam, 1996. eds., Wiley, Hoboken, 2016, pp. 35–44. 39. A. Nitz, U. Lagerpusch, and E. Nembach: Acta Mater., 1998, 67. R.C. Reed, Z. Zhu, A. Sato, and D.J. Crudden: Mater. Sci. Eng. vol. 46, pp. 4769–79. A, 2016, vol. 729 (667), pp. 261–78. 40. R.C. Reed and C.M.F. Rae: in Physical Metallurgy, 68. R.C. Reed, A. Mottura, and D.J. Crudden: in Superalloys 2016: D.E. Laughlin and K. Hono, eds., Elsevier, Amsterdam, 2014, pp. Proceedings of the 13th International Symposium on Superalloys, 2215–90. M.C. Hardy, E.S. Huron, U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. 41. T.M. Smith, Y. Rao, Y. Wang, M. Ghazisaeidi, and M.J. Mills: Seetharaman, and S. Tin, eds., Wiley, Hoboken, 2016, pp. 13–23. Acta Mater., 2017, vol. 141, pp. 261–72. 69. R. Vo¨ lkl, E. Fleischmann, R. Rettig, E. Affeldt, and U. Glatzel: in 42. D. Barba, T.M. Smith, J. Miao, M.J. Mills, and R.C. Reed: Metall. Superalloys 2016: Proceedings of the 13th International Symposium Mater. Trans. A, 2018, https://doi.org/10.1007/s11661-018-4567-6. on Superalloys, M.C. Hardy, E.S. Huron, U. Glatzel, B. Griffin, B. 43. D.J. Crudden, A. Mottura, N. Warnken, B. Raeisinia, and R.C. Lewis, C. Rae, V. Seetharaman, and S. Tin, eds., Wiley, Hoboken, Reed: Acta Mater., 2014, vol. 75, pp. 356–70. 2016, pp. 75–81. 44. C. Carry and J. Strudel: Acta Metall., 1977, vol. 25, pp. 767–77. 70. M. Probstle, S. Neumeier, P. Feldner, R. Rettig, H.E. Helmer, 45. C. Carry and J. Strudel: Acta Metall., 1978, vol. 26, pp. 859–70. R.F. Singer, and M. Goken: Mater. Sci. Eng. A, 2016, vol. 676, 46. J.A. Carey, P.M. Sargent, and D.R.H. Jones: J. Mater. Sci. Lett., pp. 411–20. 1990, vol. 9, pp. 572–75. 71. N.C. Ritter, E. Schesler, A. Muller, R. Rettig, C. Korner, and R.F. 47. S.A. Sajjadi and S. Nategh: Mater. Sci. Eng., 2001, vol. 307, Singer: Adv. Eng. Mater., 2017, vol. 19, p. 1700150. pp. 158–64. 72. M. Segersa¨ ll, J. Moverare, K. Simonsson, and S. Johansson: in 48. D.A. Woodford, D.R. van Steele, K. Amberge, and D. Stiles, in Superalloys 2012: Proceedings of the Twelfth International Sym- Superalloys 1992: Proceedings of the Seventh International Sym- posium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, M.J. posium on Superalloys, R.A. MacKay, S.D. Antolovich, R.W. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., Wiley, Stusrud, D.L. Anton, T. Khan, R.D. Kissinger, and New York, 2012, pp. 215–23. D.L. Klarstrom, eds., TMS, Warrendale, 1992, pp. 657–64. 73. M. Segersa¨ ll, D. Leidermark, and J.J. Moverare: Mater. Sci. Eng. 49. D.A. Woodford: Mater. Des., 1993, vol. 14, pp. 231–42. A, 2015, vol. 623, pp. 68–77. 50. Woodford, D.A.: in Superalloys 1996: Proceedings of the Eighth 74. Alabort, E.: PhD thesis, University of Oxford, Oxford, 2015. International Symposium on Superalloys, R.D. Kissinger, D.J. 75. S. Keshavarz and S. Ghosh: Acta Mater., 2013, vol. 61, Deye, D.L. Anton, A.D. Cetel, M.V. Nathal, and T.M. Pollock, pp. 6549–61. eds., TMS, Warrendale, 1996, pp. 353–57. 76. Y.S. Choi, M.A. Groeber, P.A. Shade, T.J. Turner, J.C. Schuren, 51. J.A. Daleo, K.A. Ellison, and D.A. Woodford: J. Eng. Gas Tur- D.M. Dimiduk, M.D. Uchic, and A.D. Rollett: Metall. Mater. bines Power, 1999, vol. 121, p. 129. Trans. A, 2014, vol. 45A, pp. 6352–59. 52. J. Beddoes and T. Mohammadi: J. Strain Anal. Eng. Des., 2010, 77. S. Keshavarz, S. Ghosh, A.C. Reid, and S.A. Langer: Acta Mater., vol. 45, pp. 587–92. 2016, vol. 114, pp. 106–15. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4235 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Metallurgical and Materials Transactions A Springer Journals

On the Rapid Assessment of Mechanical Behavior of a Prototype Nickel-Based Superalloy using Small-Scale Testing

Free
22 pages

Loading next page...
 
/lp/springer_journal/on-the-rapid-assessment-of-mechanical-behavior-of-a-prototype-nickel-WNVw30Km6b
Publisher
Springer Journals
Copyright
Copyright © 2018 by The Author(s)
Subject
Materials Science; Metallic Materials; Characterization and Evaluation of Materials; Structural Materials; Surfaces and Interfaces, Thin Films; Nanotechnology
ISSN
1073-5623
eISSN
1543-1940
D.O.I.
10.1007/s11661-018-4673-5
Publisher site
See Article on Publisher Site

Abstract

TOPICAL COLLECTION: SUPERALLOYS AND THEIR APPLICATIONS On the Rapid Assessment of Mechanical Behavior of a Prototype Nickel-Based Superalloy using Small-Scale Testing ´ ´ SABIN SULZER, ENRIQUE ALABORT, ANDRE NEMETH, BRYAN ROEBUCK, and ROGER REED An electro-thermal mechanical testing (ETMT) system is used to assess the mechanical behavior of a prototype single-crystal superalloy suitable for industrial gas turbine applications. Miniaturized testpieces of a few mm cross section are used, allowing relatively small volumes to be tested. Novel methods involving temperature ramping and stress relaxation are employed, with the quantitative data measured and then compared to conventional methods. Advantages and limitations of the ETMT system are identified; particularly for the rapid assessment of prototype alloys prior to scale-up to pilot-scale quantities, it is concluded that some significant benefits emerge. https://doi.org/10.1007/s11661-018-4673-5 The Author(s) 2018 I. INTRODUCTION conditions for which mechanical tests are needed can quickly become very significant. The difficulties identi- NEW alloy grades are never deployed without fied above are then exacerbated. Moreover, there is a careful testing of their properties and performance traditional emphasis—even today—on the use of stan- under conditions close to those experienced in service. dard testpieces of traditional design, which can mean Such so-called qualification activities can be difficult and that substantial volumes of material are needed. Might costly; this explains why the time needed to insert them there be better ways of approaching this problem? [1–3] into new applications can be notoriously long. The research reported in this paper was carried out Furthermore, processing costs for the production of with these ideas in mind. Miniaturized testpieces are pilot-scale material quantities can be excessively lar- used within a novel electro-thermal mechanical testing ge—often too great to justify—thus leading to conser- [4] (ETMT) system to assess relatively small volumes of vatism and undue emphasis on maintaining the status material, with nonetheless representative materials quo. Without a doubt, such challenges lead to a behavior being shown to arise. But we have aimed to slackening in the pace of technological change. go further. First, a novel temperature ramping test is Consider, for example, the assessment of the mechan- devised to allow the rapid assessment of the athermal ical response of a material destined for high-temperature yielding behavior of a new material, from just a single applications. The yield stress depends upon tempera- non-isothermal test. Second, a stress relaxation test is ture, but also on the strain rate. The creep resistance used to quickly deduce the time-dependent response. In depends upon temperature once again, but also on the this way, materials behavior is extracted rapidly from a stress level. Even before the cyclic loading needed to small number of tests. To garner confidence in our assess fatigue behavior or the effects of a biaxial or approaches, comparisons are made with more tradi- triaxial stress state are considered, the number of tional techniques. II. EXPERIMENTAL METHOD ´ ´ SABIN SULZER and ANDRE NEMETH are with the Department of Materials, University of Oxford, Parks Road, A. Material Oxford, OX1 3PH, UK. Contact e-mail: sabin.sulzer@materials.ox.ac.uk ENRIQUE ALABORT is with the A single-crystal superalloy developed by Siemens Department of Engineering Science, University of Oxford. BRYAN Industrial Turbomachinery (SIT) was chosen for the ROEBUCK is with the National Physical Laboratory, Hampton present study. Its nominal composition in order of Road, Teddington TW1 0LW, UK. ROGER REED is with decreasing wt pct is Ni-Cr-Ta-Co-Al-W-Mo-Si-Hf-C-Ce, Department of Materials, University of Oxford and also with the [5] Department of Engineering Science, University of Oxford. and is similar to that reported previously by Reed et al. Manuscript submitted January 18, 2018. This alloy is a candidate for future industrial gas turbine Article published online May 30, 2018 4214—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A (IGT) applications and was designed to combine good The orientations of the six bars used to manufacture oxidation, corrosion, creep, and thermal-mechanical the test specimens for the present study were checked [5–7] fatigue (TMF) resistance. Single-crystal test bars of again using a Zeiss EVO MA10 SEM fitted with a 16 mm diameter and 165 mm length were cast with near high-speed Bruker Quantax e Flash EBSD detec- h001i, h011i, and h111i crystal growth directions. tor. Areas of 3 9 2.5 mm were scanned at 20 keV with Chemical analysis using XRF, GDMS, OES, and LECO a5-lm step size. Average misorientations calculated showed very good agreement between the measured and using the EBSD results and standard deviations for each nominal values. Impurity levels were confirmed to be far data set are given in Table I. EBSD orientations are also lower than the maximum values allowed by the shown in the simplified inverse pole figure map in specification. Figure 1. All the bars were macro-etched to check for the Miniaturized ETMT blanks with a nominal size of absence of grain boundaries and were then subjected to either 40 9 3 9 1or40 9 4 9 2mm were manufac- X-ray analysis using the Laue back-reflection technique tured along longitudinal bar directions by wire-guided to ensure their orientation differed by less than 15 deg electro-discharge machining (EDM). These blanks were from the specified direction. Heat treatment consisted further waisted via EDM to give nominal widths in the of solutioning at 1280 C for 5 hours, followed by center of the testpiece of 1.1 and 2 mm, respectively, as primary aging at 1100 C for 4 hours, and secondary shown in Figure 2. The main advantage of the waisted aging at 850 C for 20 hours, in each case concluding geometry is that it enables using customized grips, which with gas fan cooling in argon. SEM images of test bar precisely fit the waist radius and which ensure correct cross sections were obtained using a JEOL alignment during testing. JSM-6500F SEM operating at 20 keV and are shown A further benefit is that this geometry gives rise to a in Figure 1. The microstructure is characteristic of IGT concentration of stress and temperature within the superalloys, and is composed of cuboidal, secondary c central region. This limits the influence of the anoma- precipitates with side lengths of  400 nm and spher- lous yielding effect observed in nickel-based superal- ical, tertiary c particles with diameters on the order of loys—i.e., an increase in yield strength with 10 nm, embedded in the c matrix. Particle size distri- temperature—which could otherwise lead to higher butions were analyzed using the image processing levels of plastic deformation in cooler regions closer to [8] 0 software package MIPAR. The estimated c volume the grips. The latter point is of particular importance in fraction after heat treatment is 53 pct, close to the the context of the present work and is discussed in 58 pct predicted by Thermo-Calc and the TTNi8 further detail in Section IV–A. Nonetheless, a paral- Ni-alloy database. lel-sided section is maintained in the center of the Fig. 1—SEM images of alloy microstructures and IPF map of test bar orientations. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4215 Table I. Results of Crystal Orientation Measurements with EBSD Test Bar Average Misorientation (Deg) Standard Deviation (Deg) h001i 1 2.39 0.56 h001i 2 4.59 0.45 h011i 1 2.86 2.40 h011i 2 11.82 3.44 h111i 1 0.90 0.92 h111i 2 1.99 1.88 Fig. 2—ETMT specimen geometries used in the present study for (a) verification tensile and stepped-temperature tests and (b) stress relaxation tests (all measurements in mm). specimen to ensure a constant stress level and a uniform the case of nickel-based superalloys, which must be temperature distribution. qualified at very high temperatures, often close to their Surfaces were ground to a 4000-grit mirror finish melting point. This makes the design and implementa- using silicon carbide grinding paper. Besides ensuring a tion of the load string, and of small-scale specimens, constant, repeatable finish, this step is crucial for grips, and extensometers, difficult. The ETMT system removing the recast layer caused by EDM and for was developed at the National Physical Laboratory minimizing residual stresses in the sample prior to (NPL) with these concerns in mind and has been used [9] testing. The actual cross section dimensions were successfully for the characterization of c precipitate [14] [15] measured with a micrometer gauge for each specimen volume fraction, recrystallization kinetics, [16,17] [4,18–20] and were used to compute engineering stress. Lastly, TMF, flow stress, and creep strain evolu- [21,22] each specimen was cleaned in an ultrasonic bath with tion in nickel-based superalloys. ethanol, after which a high-temperature paint pattern The Instron ETMT system used in the present work for direct image correlation (DIC) was applied. is illustrated in Figure 3. It uses a mechanical loading assembly capable of testing in both tension and com- pression up to a maximum load of 5 kN. Load cell B. The ETMT System readings are based on a strain gauge element with Interest in high-temperature miniaturized testing has integrated automatic calibration. A versatile gripping grown over time and has led to a multitude of system allows the use of customized grips for each [10–13] approaches. However, ensuring accurate and specimen geometry, in order to ensure correct align- reproducible results remains challenging, especially for ment. Displacement of the top, moving grip can be 4216—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 3—(a) Overview of the testing system used for miniaturized testing of superalloys; images courtesy of Instron and Imetrum Ltd.(b) Schematic illustration of ETMT components. readily measured with an LVDT, and strain at room where R and R are resistances before and during s t temperature can be calculated after considering the deformation. initial grip separation. The second approach measures strain by DIC. A fine speckle pattern is produced on one of the sample Specimens are heated using a 400-A DC power supply surfaces using high-temperature paint. The resulting via the Joule effect. An advantage—for example over pattern with many light, dark, and gray areas offers an furnace-based apparatus—is that a wide range of ideal target for tracking. During testing, the specimen is heating and cooling rates can be achieved and accurately illuminated by a bright, diffuse LED light source controlled. The testing temperature is measured and positioned behind an Allied Vision Technologies controlled with a type K thermocouple composed of Manta G-146 camera which records the test. The thin, 0.1-mm-diameter wires of chromel and alumel, camera has a resolution of 1.4 megapixels and offers a fusion-welded under argon gas to form a small bead. nominal frame rate of 17.8 fps when the full field of view This bead is carefully positioned and spot-welded under (FOV) of 1388 9 1038 pixels is monitored. Higher argon at the center of the specimen. frame rates of up to around 50 fps can be achieved As the grips are water-cooled, a parabolic tempera- when the full FOV is reduced to a smaller region of ture distribution will develop along the specimen. [17,19] interest (ROI), which for the case of present tests Previous studies have shown that the peak temper- ature remains reasonably uniform (T = ± 5 C) in the measures around 250 9 1000 pixels. However, such high central 2 to 3 mm of the sample at high temperatures frame rates have been found to produce unnecessarily between 500 C and 1000 C, with the size of this region large amounts of data and offer little additional infor- decreasing with increasing temperature. A consequence mation at typical strain rates; hence, frame rates is that the majority of plastic deformation is localized in between 1 and 10 fps were chosen. this central region. The Imetrum Ltd Video Gauge software tool Two different strain measurement techniques were analyses images captured by the camera and applies used to account for this effect. The first is the method proprietary sub-pixel pattern recognition algorithms to [4] proposed by Roebuck, in which resistance is measured detect any changes occurring during testing in compar- over the central 2 to 3 mm using two thin, spot-welded ison to a reference state. Displacement and strain are Pt-13 pctRh wires. Changes in cross sectional area measured and calculated in real time between user-de- fined target areas, in this case set 3 mm apart around the during testing lead to changes in resistance and in the center of the specimen, with a strain resolution of voltage drop measured over the two wires. Roebuck around 20 microstrain. The target areas were chosen to showed that, assuming the test volume remains constant be quadratic, with the side length corresponding to the and neglecting elastic changes, plastic strain can be width of the specimen. This choice was made as a calculated as: compromise between improved strain accuracy provided pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e ¼ ln ðÞ R =R ; ½1 p t s by larger windows and increased spacial resolution METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4217 [23] provided by smaller ones. Finally, analogue signals to a total strain of around 3.25 pct during ramping. This for load, LVDT, or temperature channels are transmit- value was chosen to be significantly lower than the total ted from the ETMT to the Video Gauge software elongation observed in standard tensile tests. This through a Signal Interface Unit, thus allowing all implies that specimen necking can be disregarded and relevant data to be collected and saved in one location, that the apparent flow stress can be calculated as and averting potential issues of synchronizing data. engineering stress. The reason for repeating tests over two different temperature ranges, of 650 C and 400 C, was to check whether the level of plastic C. Stepped-Temperature Testing (STT) hardening affects deformation behavior at higher Non-isothermal tensile tests—with the temperature temperatures. being ramped at a constant rate after reaching the As it is intended that the specimen continues to plastic regime—were carried out to deduce information deform plastically at the prescribed strain rate during regarding the variation of flow stress with temperature. temperature ramping, crosshead speed must be com- A schematic illustration of the method is given in pensated to also account for thermal expansion effects in Figure 4(a). Samples are first deformed isothermally at a accordance with: constant initial temperature T of 500 C or 750 Cand 5 4 e_ ¼ e_ þ e_ : ½2 t mechanical thermal constant initial strain rates e_ close to 2 9 10 ,10 , and 5 9 10 /s. After reaching an initial plastic strain Here e_ is the total strain rate measured for the value e of 0.2, 0.5, or 1 pct, the temperature is ramped, p;i specimen, e_ is the strain rate component result- mechanical at a constant rate T of 0.4, 2, and 10 C/s, respectively, ing from the constant crosshead displacement, and up to 1150 C. The values of these temperature ramps e_ is the additional strain rate due to thermal thermal were chosen in accordance with the three different strain expansion and changes in c volume fraction. e_ was thermal rates to yield similar total levels of plastic deformation. measured for each testing condition in a separate In the case of tests between 500 C and 1150 C, the stepped-temperature test at zero load and e_ mechanical durations of temperature ramps were 1625, 325, and was adjusted accordingly to yield the desired total strain 65 seconds, respectively. In each case, this corresponds rate. All testing conditions for STT are summarized in Table II. D. Stress Relaxation Testing (SRT) Isothermal stress relaxation tests were performed between 650 C and 1050 C at intervals of 100 C using the method shown in Figure 4(b) to deduce information on creep performance. Specimens are deformed at a constant initial strain rate of approxi- mately 10 /s until a predefined plastic strain level of [24] 0.2 pct was reached. This value was chosen following in order to achieve steady-state stress behavior and to provide a measure of the current creep strength of the alloy. Crosshead displacement is then stopped and held in that exact position under LVDT control. Load relaxation is measured over a period t of 20 hours, [24] again following. Considering the much longer test durations compared to tensile tests or stepped-temper- ature tests, a larger specimen cross section of 2 9 2mm was chosen to ensure that oxidation would not affect mechanical properties. Values for specimen width/thick- ness were chosen based on the extensive experimental and modeling work on creep and oxidation damage in [25–27] thin-walled specimens. Comparison tests were carried out for the h001i direction on cylindrical specimens of 6 mm gauge length and 3 mm diameter using an Instron Electropuls E10000 linear-torsion all-electric system. This testing rig is equipped with a split furnace controlled using a type K thermocouple positioned close to the specimen gauge. For both systems, the DIC method was used to measure strain. Testing conditions employed for SRT are summarized Fig. 4—Schematic ETMT test methodology for (a) in Table III. stepped-temperature testing and (b) stress relaxation testing. 4218—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Table II. Summary of Stepped-Temperature Tests Carried Out on the ETMT System DT (C) T (C/s) e_ (s ) e (Pct) p;i Test Specimen Heating Strain Measure- 500 to 750 to 5 4 4 System Cross Section Method ment Method 1150 1150 0.4 2 10 2 9 10 10 5 9 10 0.2 0.5 1 Instron 1 9 1.1 mm Joule DIC x x x x ETMT heating xx x x xx x x xx x x xx x x xx x x xx x x xx x x E. Verification Testing and h111i directions are slightly higher in the NPL tests. This could be related to the higher strain rate of around A limited number of tensile tests was carried out on 10 /s corresponding to the chosen constant loading each crystallographic orientation for verification pur- rate of 2 N/s, as opposed to a strain rate of 10 /s in poses and to prove the reliability of the new testing Instron ETMT tests. However, similar experiments on system, as summarized in Table IV. Benchmark tests on alloy CMSX-4 showed that the influence of strain rate the Instron ETMT were performed on samples of 2 only becomes significant above 700 C and justified 1 9 1.1 mm cross section at 500 C and an initial strain 5 differences in flow stress with changes in the off-axis rate close to 10 /s, and at 750 C and initial strain rates [31] 5 4 2 deviation of the test specimens. Considering that of 10 ,10 ,and 10 /s. LVDT control was used at specimens in the present study were manufactured from constant crosshead displacement rates. distinct bars and that cross section measurements were Comparison tests were performed under similar carried out independently, discrepancies caused by conditions at NPL using an in-house ETMT system. crystal orientation and sample dimensions cannot be As this system lacks an LVDT sensor for displacement ruled out. control, tests were carried out at constant loading rates Similarly good agreement is found in tests at 750 C of 0.4, 2, and 10 N/s, which came close to replicating the across all testing conditions, as illustrated in Figure 6(a) constant displacement rate conditions. through (f). Agreement is best at intermediate strain Finally, further comparison tests at 750 C were rates of 10 /s, regardless of crystal orientation. At carried out using regular, cylindrical testpieces of 10 /s, tests on the Instron ETMT exhibit lower 6 mm gauge length and 3 mm diameter using an engineering stress values, likely due to effects of oxida- Instron 8862 servo-electric system. In this case, high tion over longer testing periods. Oxidation damage in temperature was achieved with a split furnace arrange- thin-walled specimens is characterized by both (1) a ment and was controlled with a type K thermocouple reduction in load-bearing cross section through the positioned close to the specimen gauge. With regards to formation of a continuous oxide scale and a c denuded strain measurement, the DIC method was used for all zone near the surface, and (2) changes in c volume tests on the Instron ETMT and the 8862 servo-electric fraction and chemical concentration profiles within the systems. For tests on the NPL ETMT, plastic strain was [26] substrate. On the one hand, this highlights the calculated from resistance measurements, as described in importance of taking into account environmental dam- Eq. [1]. The elastic strain component was added sepa- age and of carrying out small-scale tests at low strain rately using temperature-dependent values for the elastic rates in a protective argon atmosphere if they are to be moduli, E(T), calculated from high-temperature [19] compared directly with standard tests. On the other dynamic resonance measurements carried out for each hand, this also proves the usefulness of miniaturized individual orientation at NPL. For further details ETMT testing for replicating service conditions experi- regarding this procedure, the interested reader is enced by thin-walled turbine blade sections. For rapid directed to References 28 through 30. tests at 10 /s, verification tests on the 8862 servo-elec- tric system yield higher stress values than ETMT tests in the h001i and h111i directions. III. RESULTS A. Verification Tests B. Stepped-Temperature Tests Tensile curves at 500 C are shown in Figure 5; The variation of proof stress with temperature is comparison is made with duplicate tests on the NPL illustrated as a function of orientation in Figure 7(a) ETMT system. Results from both ETMT systems are in through (f) and as a function of deformation rate in good agreement for all orientations, but values of Figure 8(a) through (f). The ramping step was started engineering stress in the plastic regime for the h011i after reaching an initial plastic strain of 0.2 pct at (1) METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4219 Table III. Summary of Stress Relaxation Tests Carried Out on the ETMT and the E10000 Systems Specimen Strain T (C) e_ (s ) e (Pct) t (h) Cross Section Meas. p;i R 2 4 Test System (mm ) Heating Method Method 650 750 850 950 1050 10 0.2 20 Instron ETMT 2 9 2 Joule heating DIC x x x x x x x x Instron E10000 7.1 Furnace DIC x x x x x Table IV. Summary of Tensile Tests Carried Out on the NPL and the Instron ETMT Systems as well as on the 8862 Servo-Electric System Specimen Strain T (C) e_ (s ) Cross Section Measurement 2 5 4 3 Test System (mm ) Heating Method Method 500 750 10 10 10 Instron ETMT 1 9 1.1 Joule heating DIC x x xx x x NPL ETMT 1 9 1 Joule heating Resistance x x xx x x Instron 8862 7.1 Furnace DIC x x x x Fig. 5—Tensile test results at 500 C from the Instron ETMT and the NPL ETMT. Results are plotted up to (a) 5 pct engineering strain to provide an overview of the test and (b) 2 pct engineering strain to provide a more detailed view of the elastic regime and initial yielding. [39,40] 500 C and (2) 750 C, in order to compare the effects of locks or large Kear–Wilsdorf locks —is operative. prior deformation at lower temperatures on the anoma- Such cross-slip events are promoted by the anisotropy of lous yielding effect. One can see that, for all orientations, both APB energy and elastic properties along the f111g a peak in the proof stress occurs in the range of 750 C and f001g planes. to 800 C. This is in accordance with the results of Shah Second, once material strength decreases above [32] [33,34] and Duhl for PWA1480, of Miner et al. for Rene´ 750 C, higher strength at larger strain rates is consis- [35] [31] N4, and of Allan and Bullough et al. for CMSX-4. tently observed, in accordance with time-dependent Several points emerge from the results presented in plasticity. The initial decline in proof stress has been Figures 7 and 8. First, the proof stress is not influenced commonly related to slip activation on the cube plane by by strain rate by strain rate and/or temperature ramping a=2h110i pairs and, at higher temperatures, by perfect [40] rate until a peak stress has been reached, in agreement a[100] single dislocations. Recent studies have iden- [31,36–38] with previous experimental and modeling work. tified diffusion-activated plasticity as an additional In this anomalous yielding regime, cross-slip of short operating mechanism which could explain the decreas- [41,42] dislocation segments from f111g to f001g glide ing strength in this temperature regime. A further planes—leading to either small Paidar–Pope–Vitek significant weakening effect at higher temperatures is a 4220—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 6—Tensile test results at 750 C from the Instron ETMT and 8862 servo-electric systems presented for the (a and b) h001i direction, (c and d) h011i direction, and (e and f) h111i direction. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4221 Fig. 7—STT results for single-crystal specimens with (a and d) h001i orientation, (b and e) h011i orientation, and (c and f) h111i orientation. 5 5 4 Fig. 8—STT results for tests carried out at initial strain rates of (a and b)2 9 10 /s, (c and d)10 /s, and (e and f)5 9 10 /s. 4222—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 9—STT results from tests in which the temperature-ramping step was started after varying initial plastic strain levels of 0.2, 0.5, and 1 pct. Results are shown separately for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. decrease in c volume fraction, / . Calculations using above 800 C, but, at lower temperatures, the h111i direction is much stronger than h011i and even surpasses Thermo-Calc and the TTNi8 Ni-alloy database predict a h001i below 600 C. decrease from 58 pct at 600 C to nearly 0 pct at Third, the results are nearly identical regardless of 1150 C (see Figure 13(d)). Maximum precipitate whether temperature ramping was initiated at 500 Cor strength is approximated to scale with the square root [43] at 750 C, thus suggesting that the degree of strain of / , thus explaining this pronounced drop. hardening imposed at lower temperatures does not For all tests—and regardless of strain rate—the substantially alter the estimate of the flow stress. strength on the h011i direction is much lower until However, to study the influence of the magnitude of temperatures of 1000 C and above are reached, at pre-straining on the measured proof stress in greater which point all orientations exhibit similar proof stress detail, tests at an initial constant temperature of 500 C values. This observation is of particular interest, as [31,32,35] were repeated while varying the plastic strain level previous studies reported that yield strength before ramping to 0.5 and 1 pct. As shown in above 750 C consistently increases from the h111i to Figure 9(a) through (c), very little effect on proof stress the h011i, and finally to the h001i orientation. While was observed in the plateau region, in agreement with h001i remains the direction with highest strength for the [31,36–38] previous reports. In the high-temperature SIT superalloy, there is now a discrepancy between the regime, the influence of initial plastic strain and of the h011i and h111i directions. Proof stress values converge METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4223 Fig. 10—Apparent activation energies extracted from STT between 500 C and 1150 C for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. Estimates were extracted by fitting the dashed lines to experimental data from lower strain rate tests. accumulated total strain level is unclear and there are Finally, it has been found that the STT curves can differences in the responses of the three orientations. be analyzed at temperatures beyond those associated While for h001i and h111i the strength decreases with with a maximum in the flow stress to extract an increasing initial strain, for h011i the results are almost estimate of apparent activation energy, as shown identical for initial plastic strain levels of 0.2 and 0.5 pct, schematically in Figure 4(a). For this, it is assumed 5 4 and the strength is higher above 800 C in the specimen that deformation rates of 2 9 10 and 10 /s are slow pre-strained up to 1 pct. It can be concluded that, if a enough for a steady-state condition to be approached fair comparison is to be made, the level of pre-straining at each temperature level during the ramping segment. must be carefully controlled and maintained constant Estimates of the steady-state creep rate, e_ , can then be across all tests. expressed as: 4224—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 11—Double-logarithmic plots of strain rate over applied stress extracted from SRT between 650 and 1050 C. A comparison of all results is shown in (a). SRT data are then presented separately for the (b) h001i direction, (c) h011i direction, and (d) h111i direction. Arrows indicate testing temperatures in cases in which lines are overlapping. Quantitative values are obtained assuming a constant app n stress exponent of 8 for this range of strain rates and e_ ¼ Ar exp  ; ½3 app RT temperatures, chosen based on the SRT results pre- sented in Figure 12. This leads to apparent activation where A is a material-specific constant, n is the stress energies of 1028, 620, and 631 kJ/mol. In normalized exponent, R is the gas constant, r is the measured app terms, these figures correspond to 75.9RT , 45.8RT , m m apparent proof stress, and Q is the apparent activa- app and 46.5RT , with the melting temperature T of 1630 m m tion energy. Equation [3] can be rearranged to yield a K predicted by Thermo-Calc. Activation energies must plot of lnðr Þ vs 1/ T, in which the slope will be equal app be considered carefully, as they are directly influenced to Q =Rn. Results of this analysis are shown for the app by the chosen stress exponent, which in turn corre- three crystal directions in Figures 10(a) through (c). The sponds to an apparent, extrapolated value rather than [44,45] dashed lines used to extract estimates for Q were app an effective, phenomenological one. Nonetheless, fitted to experimental data from lower strain rate tests. these figures are in fair agreement with values of 41RT , [46] Qualitative results confirm that resistance to reported by Carey and Sargent for IN738LC, and of [47] high-temperature creep deformation increases from the 53.3RT , obtained by Sajjadi and Nategh for h011i to the h111i, and finally to the h001i direction. GTD-111 in this regime. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4225 Fig. 12—Contour maps of the apparent stress exponent as a function of temperature and strain rate for the (a) h001i direction, (b) h011i direction, and (c) h111i direction. Quantitative values are shown next to the color bars. Minimum and maximum values were manually set to 4 and 300, and 16 linearly distributed major levels were generated in between. Dark gray lines mark the limits of individual major levels. C. Stress Relaxation Tests where e_ , e_ , and e_ are the total, the plastic, and the t p e elastic strain rates of the specimen, and e_ is the elastic Stress relaxation testing has been used to rapidly strain rate of the testing apparatus. Plastic strain rate assess creep performance, building on efforts made [48–51] can then be expressed following Reference 55 as: elsewhere. This method aims to quantify remaining creep resistance—before or after service exposure—and r _ Ar _ r _ e_ ¼  ¼ ; ½5 represents a paradigm shift away from attempting to E Lk E m app re-create microstructural damage evolution, as is carried [24] out in a regular creep test. Several recent studies have where r _ is the change in stress with time during load made use of SRT for the mechanical characterization of relaxation and E is the apparent modulus of the app superalloys and have shown results consistent with material. The latter can be calculated using E as the conventional creep data from the literature, thus elastic modulus, A as the sample cross section, k as the enabling accelerated testing campaigns of new stiffness of the machine, and L as the specimen gauge [52–54] alloys. Here, in common with such approaches, it length. While k is unknown, it can be estimated by is assumed that the total strain rate of the system analyzing elastic data obtained during loading and/or [24,55] remains in equilibrium as crosshead displacement is unloading. fixed, consistent with: As load relaxation occurs across the ETMT specimen, and not only in the central high-temperature region, e_ ¼ e_ þ e_ þ e_ ¼ 0; ½4 t p e m slight changes in total strain cannot be avoided. Here, 4226—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 13—Stress/temperature deformation mechanism maps for material deformed along the (a) h001i direction, (b) h011i direction, and (c) h111i 1 [58] direction. Contours of shear strain rate are given in s . Field boundaries reported by Frost and Ashby for conventionally cast Mar-M200 material are added for comparison. The plot in (d) shows changes in c, c , and liquid phase fractions for the SIT superalloy predicted by Thermo-Calc using the Ni-alloy database TTNi8. these have been measured with DIC in the central 3 mm By using the approach depicted in Figure 4(a), the of the specimen to provide a correction for Eq. [5], apparent stress exponent, n, can be obtained as a yielding e_ ¼ e_  r _ =E . Application of this correction function of the logarithmic values of stress, r, and strain p t app rate, e_ , consistent with: has been found to be especially important for the first minutes of relaxation, during which the ETMT appara- @ log e_ tus contracts elastically as the applied load decreases. n ¼ ½6 @ log r Longer-term SRT results are not affected by the finite e;T stiffness of the load frame and corrections to Eq. [5] are [55] for given values of total strain and temperature. minimal. Application of this equation locally to segments of the Curves of applied stress over plastic strain rate are stress–strain rate curves allows contour maps to be presented on double logarithmic plots in Figure 11(a) derived for the apparent stress exponent at strain rates through (d). Noticeable changes in gradient occur at 5 9 between 10 and 10 /s and temperatures between 650 intermediate strain rates, giving the curves a character- C and 1050 C, as shown in Figure 12(a) through (c). istically sigmoidal shape. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4227 These can be regarded as Ashby-type high-temperature apparent stress exponents show a significant rise, with deformation mechanism maps and can be derived rather values that can no longer be rationalized by any type of rapidly with the ETMT approach. high-temperature deformation mechanisms. As opposed An initial decrease in the apparent stress exponent has to a standard creep test, the driving force for directional been observed for tests performed above 750 Cat coarsening and creep strain accumulation decreases with 6 8 strain rates between 10 and 10 /s. This occurs earlier time during SRT and exceedingly tends towards zero. [53] in the test, i.e. at higher strain rates, as the temperature Nathal et al. observed no further microstructural increases. Similar behavior has been reported by Nathal changes when comparing specimens relaxed at 982 C [53] et al. for the first-, second-, and fourth-generation for 100 and 370 hours. As such, once a steady-state single-crystal superalloys, NASAIR 100, CMSX-4, and stress value has been reached, the results from SRT are EPM-102. These authors showed that the effect disap- increasingly affected by mechanical noise and provide pears if the specimens are crept prior to stress relaxation, little further insight into high-temperature damage as the pre-rafted microstructure offers higher resistance accumulation mechanisms. to primary creep. As such, this transition can be related SRT data can also be presented in the form of stress/ to a shift from primary creep deformation, dominated temperature deformation mechanism maps, following [58] by APB shearing of c precipitates, to tertiary creep, Frost and Ashby. The resulting maps shown in dominated by dislocation climb bypass. Transition Figure 13(a) through (c) provide a means of visualizing stress values at different temperatures are in accordance material performance in different deformation regimes with the deformation mechanism maps for nickel-based and of comparing normalized results to data from the [56] [46,47] superalloys proposed by Smith et al. and Barba literature. [22] [58] et al. No transition is clear at 650 C, probably As discussed by Frost and Ashby, any deformation because this temperature is too low to enable diffusional mechanism can be described by a rate equation of the climb around the precipitates. form: Values of apparent stress exponents associated with c_ ¼ f s; T; S ; P ½7 i j primary and tertiary creep, respectively, decrease with increasing temperature. This reduction has been shown to be related to directional coarsening of precipitates at This relates shear strain rate, c_, to shear stress, s, [53] higher temperatures. It should be noted that these temperature, T, a set of i state variables, S , describing figures cannot be readily related to effective stress the current microstructural state of the material, and a exponents used in creep models, as explained by Carry set of j material properties, P , which are inherent to the [44] [45] and Strudel for both primary and tertiary creep. material. Key simplifying assumptions are that stea- Discrepancies between apparent and effective exponents dy-state conditions are reached during deformation and were also confirmed by the experimental results of that material properties and state variables either remain [55] Dupeux et al. from stress relaxation and conventional constant or are directly determined by s and/or T. This [57] creep tests on CMSX-2. At strain rates below 10 8/s, leads to a reduction of Eq. [7]to c_ ¼ fðs; TÞ. Fig. 14—(a) CAD-derived drawing of a gripped ETMT specimen. (b) Schematic representation of heat conduction in an ETMT specimen with heat generation from Joule heating. 4228—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A In order to construct maps following Frost and moduli, G(T), were obtained for each individual orien- Ashby, the tensile stress/strain data from Figure 11 are tation from high-temperature dynamic resonance mea- first converted to shear stress/strain. Geometrical trans- surements at NPL. These are the same assessments formation factors were chosen following the work of mentioned in Section II–E with regards to obtaining [59] Ghosh et al., who modeled the crystallographic temperature-dependent elastic moduli, E(T), for each anisotropy of tensile creep deformation in single-crystal orientation. superalloys. These authors assumed that macroscopic As suggested by Frost and Ashby, data points in creep deformation results from glide on both the Figure 13 are labeled with the value of the third macroscopic variable, in this case logðc_Þ. The red dashed f111gh101i and f001gh110i systems, while neglecting lines represent contours of constant shear strain rate macroscopic contributions from f111gh112i slip vectors. based on data between 750 C and 1050 C. The solid Their work contains an in-depth discussion on the green lines divide fields dominated by power law creep, predicted number of active slip systems and their diffusion creep, and low-temperature plasticity con- respective Schmid factors, leading to geometrical con- [59] trolled by dislocation glide. These boundaries were versions for each orientation. reported for Mar-M200 material with a large grain size In a second step, shear stress and temperature values of around 1 cm, which can be taken as an estimate of are normalized with respect to shear modulus and directionally solidified or single-crystal material behav- melting temperature. The aforementioned value of 1630 [58] ior and offer a benchmark for the SIT superalloy. A K predicted by Thermo-Calc and TTNi8 for T is used further power law breakdown regime dominated by to calculate the homologous temperature (see APB shearing of c precipitates can be inferred in the Figure 13(d)). Values for temperature-dependent shear [61] Fig. 15—(a) Cubic and linear fits for electrical resistivity and thermal conductivity data obtained by Mills et al. for CMSX-4. Modeling results for the distribution of (b) temperature, (c) electrical resistivity, and (d) thermal conductivity along a heated ETMT specimen. The dotted lines in the temperature distribution graph mark regions predicted to remain, respectively, at T  5 C and T  15 C. max max METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4229 upper left corner of the maps and would include data at the sample and the accuracy of DIC strain measure- 650 C. The lower limit of this area is estimated at ments are discussed in the following. Here, accumulated 2 [58] around 10 G. errors in load are not considered, as the 5-kN load cell was calibrated against a reference before the testing campaign. IV. DISCUSSION 1. Modeling of the temperature distribution in ETMT A. Validity and Limitations of the ETMT System specimens [4,19,23] Previous ETMT studies have reported a uni- In this work, it has been demonstrated that the ETMT form temperature distribution in the central 2 to 4 mm offers substantial practical advantages associated with of the specimen. However, these observations are based testpiece miniaturization. Nevertheless, a critical issue on limited experimental results and lack validation by concerns whether or not results are comparable to those modeling. This issue is considered in greater detail here. obtained from established techniques which are For a given material volume containing a heat source, regarded as more standardized. In particular, one the temperature distribution T(x, y, z, t)—depending on should be concerned with (1) real size effects—such as three spatial variables (x, y, z) and the time variable the effect of oxidation damage at low strain rates—and t—can be expressed by the heat equation: (2) potential errors and increased data scatter arising from sub-scale testing. 2 2 2 @T @ T @ T @ T c q  k þ þ ¼ q_ : ½8 In this context, several generic issues have been p V 2 2 2 @t @x @y @z [11,12] identified. First, a minimum representative material volume must be sampled. This may be less of an issue Here, c is the specific heat capacity, q is the mass for the case of single-crystal specimens; however, it density of the material, k is the thermal conductivity, poses a significant challenge for testing polycrystalline and q represents the volumetric heat source. Three materials with grain sizes of the order of testpiece width/ assumptions are made at this point to simplify the thickness. Second, there is an increased probability that integration of Eq. [8]. small defects or heterogeneities will affect bulk material First, a steady-state case is considered, in which the response. Considering the good quality of the cast- heat equation is not dependent on time, so that ings—which exhibit low levels of porosity and reduced @T=@t ¼ 0. For temperature or current control, the segregation after heat treatment—this point may not be Instron ETMT system uses a high bandwidth 8800 so vital to consider. Third, test specimens must be servo-hydraulic controller with a maximum internal carefully manufactured and mechanically finished to acquisition and control loop sampling rate of 10 kHz. reduce the possibility of surface residual stresses or This high bandwidth enables fast and accurate control [23] re-cast layers influencing the results. Preparation steps even when large heating or cooling rates are required. taken to avoid this are described in Section II–A. Last, With well-tuned PID control parameters, the system uncertainties associated with measurements of load shows an immediate response to changes in the com- (stress), temperature, and strain must be critically mand channel, as well as very good long-term stability. assessed. The effect of temperature heterogeneity along As such, steady-state conditions are a reasonable Fig. 16—Effects of selected virtual gauge length for DIC strain measurements on experimental results. A test on the h001i direction at 750 C and 10 /s was chosen for this analysis. Results are plotted up to (a) 10 pct engineering strain to provide an overview of the test, and (b) 5 pct engineering strain to provide a more detailed view of the elastic regime and initial yielding. 4230—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A 3 Fig. 17—2D color maps of strain distribution in a h001i specimen tested at 750 C and 10 /s. Results are shown for total strain levels of (a) 5 pct, (b) 10 pct, and (c) 15 pct. assumption, even in the case of stepped-temperature where P is the power converted from electrical to tests. thermal energy in a volume element DV, I is the current Second, the heat equation is treated as a one-dimen- traveling through the testpiece, R is the electrical sional problem, in which the temperature only varies resistance, q is the electrical resistivity, and A is the along the tensile axis of the specimen, chosen here as the specimen cross section. x spatial coordinate, as shown in Figure 14. While the The boundary conditions necessary to solve Eq. [9] temperature will also vary across the width and thick- uniquely are that temperature at the gripped ends, ness of the testpiece, relative differences are much TðLÞ¼ T , remains constant during testing. This grip smaller than along the tensile axis. Equation [8] can yields the one-dimensional temperature distribution: now be simplified to: 2 2 L x TðxÞ¼ q_ 1  þ T V grip @ T 2k L k ¼ q_ ½9 V 2 2 2 2 @x I L x q ¼ 1  þ T : ½11 grip A 2 L k Third, an additional negative term of the form lT can be added to Eq. [9] to account for radiative heat loss It can be seen that temperature scales with the square to the immediate environment. However, it is assumed of applied current over the specimen cross section. The here that cooling rates are primarily determined by the term T has been measured during testing at high grip thermal diffusivity of the specimen and by heat loss to temperatures and remains constant at around 40 C. the water-cooled grips, and that radiation can be For the case of the larger ETMT testpiece geometry neglected. While this final assumption is incorrect at chosen for stress relaxation tests, A is equal to 4 mm very high temperatures, it should not have a significant and L to 7.5 mm. impact on modeling results for temperatures below The two remaining material parameters—electrical [23] 1100 C. resistivity, q, and thermal conductivity, k—both depend The volumetric heat source q_ for a certain portion of on chemical composition and on temperature, thus the testpiece volume can be described using Joule’s first requiring a discrete solution of Eq. [11]. Considering law and Ohm’s law as: that the same master heat was used to cast all the bars, it is anticipated that temperature distribution will not 2 2 P I R I q depend on orientation. Several extensive studies have q_ ¼ ¼ ¼ ; ½10 DV DxA A discussed the measurement and calculation of METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4231 4 Fig. 18—2D color maps of strain distribution in a h001i specimen tested at 750 C and 10 /s. Results are shown for total strain levels of (a) 5 pct, (b) 10 pct, and (c) 15 pct. [60–62] thermophysical properties of superalloys. In the results are in good agreement with previous find- [4,19] present work, results obtained for the second-generation ings. The section of the testpiece at T  5 C max single-crystal superalloy CMSX-4 at temperatures decreases with increasing temperature. It is predicted to between 298 and 1550 K are used as estimates for the be 1.67 mm at 700 C and 1.54 mm at 900 C, close to [61] SIT superalloy. Data for qðTÞ and k(T) are fitted the experimentally determined values of 2.4 mm and [19] using a cubic and a linear equation, respectively, as 2.2 mm, respectively, for the disc superalloy RR1000. shown in Figure 15(a): Modeling predicts that the central 3-mm region observed for DIC strain measurements remains at a qðTÞ¼ 9:06032  10 þ 1:88864 reasonably uniform temperature of ± 15 C. These 9 12 2 results are an important validation of temperature 10 T  1:55977  10 T þ 3:53139 ½12 distribution in ETMT specimens, and they furthermore 16 3 10 T ½ Xm highlight the importance of precise, localized strain measurements in the hot zone. kðTÞ¼ 3:50617 þ 0:01909T ½WmK 2. Non-contact strain measurements via DIC The applied current, I , is registered during testing. app A recent review on miniaturized testing critically However, due to previous imprecise assumptions and assessed a number of strain measurement techniques estimates, the temperature calculated for the center of including LVDT, line scan cameras, capacitance gauges, the specimen using I in Eq. [11] does not exactly app electrical resistance measurements, interferometry tech- [12] match T . As such, a current correction parameter, max niques, and DIC. It was concluded that, despite the I , is introduced to ensure that Tð0Þ¼ T . corr max modest strain resolution obtained for usual camera/lens/ Modeling results for the distribution of temperature, FOV combinations, DIC provides substantial advan- electrical resistivity, and thermal conductivity in ETMT tages as a full field non-contact method, especially specimens between 500 C and 1200 C are shown in considering ongoing developments in higher-resolution Figure 15(b) through (d). Qualitative and quantitative cameras and increased computing power. 4232—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A [2,63] A convenient feature is that, once a test video has (ICME). Several promising approaches toward been recorded and stored, it can be readily post-pro- alloy design have been proposed and applied to the [64–68] cessed using different window sizes, gauge lengths, and development of new grades of superalloys. Fur- processing accuracy/speed parameters. An analysis of thermore, laboratory-scale process chains for rapid this type, exploring the effects of different gauge lengths production of single-crystal superalloy trial castings [69–71] between virtual target windows, is shown in Figure 16. have been successfully established. However, test- An ETMT tensile test on the h001i direction at 750 C ing methods continue to be dominated by standard and an initial strain rate of 10 /s was chosen as an approaches. It can be concluded that, within the example. The importance of selecting a correct reduced design–make–test cycle, the last segment currently offers gauge length is evident. As this value increases, it most potential for improvement in the context of ICME encompasses more of the cooler regions of the specimen, goals. in which less plastic deformation takes place. This leads The ETMT testing methods presented here offer a to large discrepancies between analysis results at higher viable and convenient contribution to this overarching plastic strain values. While the impact on 0.2 pct proof goal of more efficient and rapid materials development. stress—and on initial conditions for stepped-tempera- Acquired data can be used to extract estimates of key ture testing—is limited, choosing an incorrect gauge material properties and to make critical decisions length will have a strong impact on stress relaxation regarding screening and/or ranking of trial alloys during results through Eq. [5]. The analysis below confirms the the development stage. Based on the reported dimen- [71] validity of DIC strain measurements in the central 3 mm sions of small-scale single-crystal rods, and using of the specimen. testpiece dimensions shown in Figure 2, a sufficient Another useful feature of DIC—and in particular of number of ETMT samples for STT and SRT can be the Video Gauge software package—is the ability to produced from each trial casting. output 2D strain maps. These provide a simple way of Stepped-temperature testing enables a rapid assess- locating strain concentrations and a direct proof that ment of changes in athermal material strength with anomalous yielding is not affecting test results. In order temperature at a certain deformation rate. Data to generate a strain map, the ROI is first divided into a obtained from STT is valuable for informing TMF [72,73] grid of targets. Displacements between these targets are and cyclic fatigue lifing models. In our experience, then continuously analyzed and used to calculate the several trial alloys can be compared in only a few hours Lagrangian strain tensor at each node of the grid. For and optimal compositions can be identified. Further- the present calculations, the side length of the quadratic more, it should be noted that STT can be readily applied targets and their grid spacing were chosen to be 15 pixels to other classes of high-temperature materials. For as a compromise between spacial resolution and com- example, tests on titanium alloys for aerospace applica- puting time. A filter size of 30 pixels was used to tions have shown that STT results capture the smoothen displacements around each node and to microstructural changes introduced by different heat reduce image noise. Finally, changes in 2D strain treatments, and indicate a composition-dependent tran- distribution over time are exported as a .avi video file. sition in the operating deformation mechanisms between [74] Figures 17 and 18 show the development of strain low and high temperatures. distribution within ETMT specimens with h001i orien- Stress relaxation tests over a temperature range of tation tested at 750 C and initial strain rates of 10 interest can rapidly yield Ashby-type deformation and 10 /s, respectively. Individual video frames were mechanism maps. Plotting data in this fashion offers a selected for comparison at total strain levels of 5, 10, direct comparison with other materials for different and 15 pct. The variable E plotted in the color maps is operating conditions. For any particular application, a xx the calculated strain in the tensile direction. The color target region can be added using the range of temper- range is scaled between the minimum and maximum atures and stresses encountered in service. Contours of strain values detected up to that point during the test. constant strain rate provide a first estimate for screening Some artefacts appear due to discontinuities in the ROI, alloys that surpass the maximum acceptable strain rate commonly specimen edges or areas where the high-tem- and for ranking the remaining ones. The SRT results perature paint layer was damaged. The 2D strain maps can be readily exported as inputs for commercial FEM confirm that deformation is localized in the center of the software packages like ABAQUS. This ensures that specimen. Furthermore, they show that anomalous FEM simulations—increasingly applied to modeling yielding does not impact test results. Particularly in high-temperature deformation in superalloy compo- 4 [75–77] the test at 10 /s, it is also clear that macroscopic nents —provide reliable quantitative results. deformation is concentrated along f111g slip planes at a 45 deg angle to tensile loading. V. SUMMARY AND CONCLUSIONS B. On the Potential of the ETMT for Rapid Alloy Miniaturized testing using an electro-thermal Development mechanical testing system has been carried out on a The importance of accelerated material development prototype single-crystal superalloy along the h001i, cycles has led to large-scale enterprises like the Materials h011i, and h111i loading axes. Compared with full-scale Genome Initiative (MGI), part of the broader field of testing methods on testpieces of more standard geom- Integrated Computational Materials Engineering etry, the approach is advantageous owing to its METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4233 increased speed, degree of simplicity, and the use of REFERENCES smaller quantities of material. The following specific 1. R.E. Schafrik and S. Walston: in Superalloys 2008: Proceedings of conclusions can be drawn from the present study: the Eleventh International Symposium on Superalloys, R.C. Reed, K.A. Green, P. Caron, T. Gabb, M.G. Fahrmann, E.S. Huron, 1. The ETMT has been shown to be a viable tool for and S.A. Woodward, eds., TMS, Warrendale, 2008, pp. 3–9. assessing material properties of single-crystal nick- 2. W. Xiong and G.B. Olson: NPJ Comput. Mater., 2016, vol. 2, p. 15009. el-based superalloys. Mechanical properties derived 3. T.M. Pollock: Nat. Mater., 2016, vol. 15, pp. 809–15. from miniaturized testing are found to be compa- 4. B. Roebuck, D.C. Cox, and R.C. Reed: in Superalloys 2004: rable to those obtained from conventional tensile Proceedings of the Tenth International Symposium on Superalloys, tests over a range of temperatures and strain rates. K. Green, H. Harada, and T.M. Pollock, eds., TMS, Warrendale, 2004, pp. 523–28. 2. Stress relaxation tests and stepped-temperature tests 5. R.C. Reed, J. Moverare, A. Sato, F. Karlsson, and M. Hasselqvist: have been used as a rapid means of extracting creep in Superalloys 2012: Proceedings of the Twelfth International and tensile strength estimates and parameters. Symposium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, 3. It has been demonstrated that changes in athermal M.J. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., plastic deformation with temperature can be deter- Wiley, New York, 2012, pp. 197–204. 6. A. Sato, Y.-L. Chiu, and R.C. Reed: Acta Mater., 2011, vol. 59, mined with a single test by ramping up the pp. 225–40. temperature during deformation at a constant strain 7. A. Sato, J.J. Moverare, M. Hasselqvist, and R.C. Reed: Metall. rate. This has allowed for an estimate of the Mater. Trans. A, 2012, vol. 43A, pp. 2302–15. variation of flow stress with temperature. 8. J.M. Sosa, D.E. Huber, B. Welk, and H.L. Fraser: Integr. Mater. Manuf. Innov., 2014, vol. 3, p. 5. 4. Stress relaxation tests with the ETMT enable a 9. D.A. LaVan and W.N. Sharpe: Exp. Mech., 1999, vol. 39, rapid assessment of time-dependent deformation at pp. 210–16. high temperatures. Changes in operating mecha- 10. K.J. Hemker and W.N. Sharpe: Annu. Rev. Mater. Res., 2007, nisms are revealed through deformation mechanism vol. 37, pp. 93–126. maps, generated using data measured at different 11. T.H. Hyde, W. Sun, and J.A. Williams: Int. Mater. Rev., 2007, vol. 52, pp. 213–55. temperatures. The results show a transition from 12. J.D. Lord, B. Roebuck, R. Morrell, and T. Lube: Mater. Sci. precipitate shearing to dislocation climb bypass at Technol., 2010, vol. 26, pp. 127–48. higher temperatures and lower plastic strain rates. 13. C.C. Dyson, W. Sun, C.J. Hyde, S.J. Brett, and T.H. Hyde: Mater. 5. Such rapid testing methodologies can be applied in Sci. Technol. 2015, pp. 1–15. 14. B. Roebuck, D. Cox, and R.C. Reed: Scr. Mater., 2001, vol. 44, studies of small-scale superalloy castings to deter- pp. 917–21. mine both athermal and time-dependent plastic 15. D.C. Cox, B. Roebuck, C.M.F. Rae, and R.C. Reed: Mater. Sci. responses. This accelerated design–make–test cycle Technol., 2003, vol. 19, pp. 440–46. has the potential to significantly reduce the time for 16. S. Pahlavanyali, A. Rayment, B. Roebuck, G. Drew, and C. Rae: qualification and insertion of new grades of Int. J. Fatigue, 2008, vol. 30, pp. 397–403. 17. B. Roebuck, M. Loveday, and M. Brooks: Int. J. Fatigue, 2008, superalloys. vol. 30, pp. 345–51. 18. S. Kuhr, G. Viswanathan, J. Tiley, and H. Fraser: in Superalloys 2012: Proceedings of the Twelfth International Symposium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, M.J. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., Wiley, New York, ACKNOWLEDGMENTS 2012, pp. 103–10. 19. A.A.N. Nemeth, D.J. Crudden, D.M. Collins, D.E.J. Armstrong, Financial support and material provision from Sie- and R.C. Reed: in Superalloys 2016: Proceedings of the 13th mens Industrial Turbomachinery AB (Finspa˚ ng, Swe- International Symposium on Superalloys, M.C. Hardy, E.S. Huron, den) is gratefully acknowledged. The provision of the U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. Seetharaman, and S. Tin, eds., Wiley, Hoboken, 2016, pp. 801–10. ETMT was facilitated by funding from the Engineer- 20. A. Ne´ meth, D.J. Crudden, D. Armstrong, D.M. Collins, K. Li, ing and Physical Sciences Research Council (EPSRC) A.J. Wilkinson, C. Grovenor, and R.C. Reed: Acta Mater., 2017, under grant number EP/M50659X/1. RR acknowl- vol. 126, pp. 361–71. edges additional support from the EPSRC under grant 21. D. Barba, S. Pedrazzini, A. Vilalta-Clemente, A.J. Wilkinson, number EP/M005607/01. Roger Morrell at NPL is M.P. Moody, P. Bagot, A. Jerusalem, and R.C. Reed: Scr. Mater., 2017, vol. 127, pp. 37–40. acknowledged for his support on high-temperature 22. D. Barba, E. Alabort, S. Pedrazzini, D.M. Collins, A.J. Wilkinson, measurements of elastic constants. P. Bagot, M.P. Moody, C. Atkinson, A. Jerusalem, and R.C. Reed: Acta Mater., 2017, vol. 135, pp. 314–29. 23. B. Roebuck, M. Brooks, and A. Pearce: Good Practice Guide for Miniature ETMT Tests: Measurement Good Practice Guide No. 137: PDB: 7798; Technical Report, National Physical Laboratory OPEN ACCESS Division of Materials Applications, 2016. 24. D.A. Woodford: Mater. Res. Innov., 2016, vol. 20, pp. 379–89. This article is distributed under the terms of the 25. M. Bensch, J. Preusner, R. Huttner, G. Obigodi, S. Virtanen, J. Creative Commons Attribution 4.0 International Gabel, and U. Glatzel: Acta Mater., 2010, vol. 58, pp. 1607–17. License (http://creativecommons.org/licenses/by/4.0/), 26. M. Bensch, A. Sato, N. Warnken, E. Affeldt, R.C. Reed, and U. Glatzel: Acta Mater., 2012, vol. 60, pp. 5468–80. which permits unrestricted use, distribution, and 27. M. Bensch, C.H. Konrad, E. Fleischmann, C. Rae, and U. Glatzel: reproduction in any medium, provided you give Mater. Sci. Eng. A, 2013, vol. 577, pp. 179–88. appropriate credit to the original author(s) and the 28. W. Hermann, H.G. Sockel, J. Han, and A. Bertram: in Superalloys source, provide a link to the Creative Commons 1996: Proceedings of the Eighth International Symposium on license, and indicate if changes were made. Superalloys, R.D. Kissinger, D.J. Deye, D.L. Anton, A.D. Cetel, 4234—VOLUME 49A, SEPTEMBER 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A M.V. Nathal, and T.M. Pollock, eds., TMS, Warrendale, 1996, pp. 53. M.V. Nathal, J. Bierer, L. Evans, E.A. Pogue, F. Ritzert, and T.P. 229–38. Gabb: Mater. Sci. Eng. A, 2015, vol. 640, pp. 295–304. 29. M. Fahrmann, W. Hermann, E. Fahrmann, A. Boegli, T.M. 54. S.L. Semiatin, P.N. Fagin, R.L. Goetz, D.U. Furrer, and R.E. Pollock, and H.G. Sockel: Mater. Sci. Eng. A, 1999, vol. 260, Dutton: Metall. Mater. Trans. A, 2015, vol. 46A, pp. 3943–59. pp. 212–21. 55. M. Dupeux, J. Henriet, and M. Ignat: Acta Metall., 1987, vol. 35, 30. R. Morrell, D.A. Ford, and K. Harris: Calculations of Modulus in pp. 2203–12. Different Directions for Single-Crystal Alloys, NPL Report 56. T.M. Smith, R.R. Unocic, H. Deutchman, and M.J. Mills: Mater. DEPC-MN 004; Technical Report, NPL, 2004. High Temp., 2016, vol. 33, pp. 372–83. 31. C.K. Bullough, M. Toulios, M. Oehl, and P. Luka´ sˇ:in Materials 57. H. Rouault-Rogez, M. Dupeux, and M. Ignat: Acta Metall. for Advanced Power Engineering 1998: Proceedings of the 6th Liege Mater., 1994, vol. 42, pp. 3137–48. Conference/Jacqueline Lecomte-Beckers, F. Schubert and P.J. 58. H.J. Frost and M.F. Ashby: Deformation-mechanism maps, 1st ed., Ennis, J. Lecomte-Beckers, F. Schubert, and P.J. Ennis, eds., Pergamon Press, Oxford Oxfordshire and New York, 1982. Schriften des Forschungszentrums Julich. Reihe Energietechnik/ 59. R.N. Ghosh, R.V. Curtis, and M. McLean: Acta Metall. Mater., Energy technology, 1433–5522, Vol. 5, 2; Forschungszentrum 1990, vol. 38, pp. 1977–92. Julich: Julich, Germany, 1998, pp. 861–78. 60. K.C. Mills: Recommended values of thermophysical properties for 32. D.M. Shah and D.N. Duhl: in Superalloys 1984: Proceedings of the selected commercial alloys, Woodhead, Cambridge, 2002. Fifth International Symposium on Superalloys, M. Gell, 61. K.C. Mills, Y.M. Youssef, Z. Li, and Y. Su: ISIJ Int., 2006, C.S. Kortovich, R.H. Bricknell, eds., TMS, Warrendale, 1984, pp. vol. 46, pp. 623–32. 105–14. 62. P.N. Quested, R.F. Brooks, L. Chapman, R. Morrell, Y. Youssef, 33. R.V. Miner, T.P. Gabb, J. Gayda, and K.J. Hemker: Metall. and K.C. Mills: Mater. Sci. Technol., 2009, vol. 25, pp. 154–62. Trans. A, 1986, vol. 17, pp. 507–12. 63. G.B. Olson and C.J. Kuehmann: Scr. Mater., 2014, vol. 70 (25), 34. R.V. Miner, R.C. Voigt, J. Gayda, and T.P. Gabb: Metall. Trans. p. 30. A, 1986, vol. 17, pp. 491–96. 64. R.C. Reed, T. Tao, and N. Warnken: Acta Mater., 2009, vol. 57 35. C.D. Allan: PhD Thesis, Massachusetts Institute of Technology, (5898), p. 5913. 1995. 65. R. Rettig, N.C. Ritter, H.E. Helmer, S. Neumeier, and R.F. 36. G.R. Leverant and D.N. Duhl: Metall. Trans., 1971, vol. 2, Singer: Modell. Simul. Mater. Sci. Eng., 2015, vol. 23, p. 35004. pp. 907–08. 66. R. Rettig, K. Matuszewski, A. Muller, H.E. Helmer, N.C. Ritter, 37. B.H. Kear and J.M. Le Oblak: J. Phys. Colloq., 1974, vol. 35, and R.F. Singer: in Superalloys 2016: Proceedings of the 13th pp. 35–45. International Symposium on Superalloys, M.C. Hardy, E.S. Huron, 38. L12 Ordered Alloys: Nabarro, F.R.N., Duesbery, M.S., Eds., U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. Seetharaman, S. Tin, Dislocations in Solids, Vol. 10; Elsevier, Amsterdam, 1996. eds., Wiley, Hoboken, 2016, pp. 35–44. 39. A. Nitz, U. Lagerpusch, and E. Nembach: Acta Mater., 1998, 67. R.C. Reed, Z. Zhu, A. Sato, and D.J. Crudden: Mater. Sci. Eng. vol. 46, pp. 4769–79. A, 2016, vol. 729 (667), pp. 261–78. 40. R.C. Reed and C.M.F. Rae: in Physical Metallurgy, 68. R.C. Reed, A. Mottura, and D.J. Crudden: in Superalloys 2016: D.E. Laughlin and K. Hono, eds., Elsevier, Amsterdam, 2014, pp. Proceedings of the 13th International Symposium on Superalloys, 2215–90. M.C. Hardy, E.S. Huron, U. Glatzel, B. Griffin, B. Lewis, C. Rae, V. 41. T.M. Smith, Y. Rao, Y. Wang, M. Ghazisaeidi, and M.J. Mills: Seetharaman, and S. Tin, eds., Wiley, Hoboken, 2016, pp. 13–23. Acta Mater., 2017, vol. 141, pp. 261–72. 69. R. Vo¨ lkl, E. Fleischmann, R. Rettig, E. Affeldt, and U. Glatzel: in 42. D. Barba, T.M. Smith, J. Miao, M.J. Mills, and R.C. Reed: Metall. Superalloys 2016: Proceedings of the 13th International Symposium Mater. Trans. A, 2018, https://doi.org/10.1007/s11661-018-4567-6. on Superalloys, M.C. Hardy, E.S. Huron, U. Glatzel, B. Griffin, B. 43. D.J. Crudden, A. Mottura, N. Warnken, B. Raeisinia, and R.C. Lewis, C. Rae, V. Seetharaman, and S. Tin, eds., Wiley, Hoboken, Reed: Acta Mater., 2014, vol. 75, pp. 356–70. 2016, pp. 75–81. 44. C. Carry and J. Strudel: Acta Metall., 1977, vol. 25, pp. 767–77. 70. M. Probstle, S. Neumeier, P. Feldner, R. Rettig, H.E. Helmer, 45. C. Carry and J. Strudel: Acta Metall., 1978, vol. 26, pp. 859–70. R.F. Singer, and M. Goken: Mater. Sci. Eng. A, 2016, vol. 676, 46. J.A. Carey, P.M. Sargent, and D.R.H. Jones: J. Mater. Sci. Lett., pp. 411–20. 1990, vol. 9, pp. 572–75. 71. N.C. Ritter, E. Schesler, A. Muller, R. Rettig, C. Korner, and R.F. 47. S.A. Sajjadi and S. Nategh: Mater. Sci. Eng., 2001, vol. 307, Singer: Adv. Eng. Mater., 2017, vol. 19, p. 1700150. pp. 158–64. 72. M. Segersa¨ ll, J. Moverare, K. Simonsson, and S. Johansson: in 48. D.A. Woodford, D.R. van Steele, K. Amberge, and D. Stiles, in Superalloys 2012: Proceedings of the Twelfth International Sym- Superalloys 1992: Proceedings of the Seventh International Sym- posium on Superalloys, E.S. Huron, R.C. Reed, M.C. Hardy, M.J. posium on Superalloys, R.A. MacKay, S.D. Antolovich, R.W. Mills, R.E. Montero, P.D. Portella, and J. Telesman, eds., Wiley, Stusrud, D.L. Anton, T. Khan, R.D. Kissinger, and New York, 2012, pp. 215–23. D.L. Klarstrom, eds., TMS, Warrendale, 1992, pp. 657–64. 73. M. Segersa¨ ll, D. Leidermark, and J.J. Moverare: Mater. Sci. Eng. 49. D.A. Woodford: Mater. Des., 1993, vol. 14, pp. 231–42. A, 2015, vol. 623, pp. 68–77. 50. Woodford, D.A.: in Superalloys 1996: Proceedings of the Eighth 74. Alabort, E.: PhD thesis, University of Oxford, Oxford, 2015. International Symposium on Superalloys, R.D. Kissinger, D.J. 75. S. Keshavarz and S. Ghosh: Acta Mater., 2013, vol. 61, Deye, D.L. Anton, A.D. Cetel, M.V. Nathal, and T.M. Pollock, pp. 6549–61. eds., TMS, Warrendale, 1996, pp. 353–57. 76. Y.S. Choi, M.A. Groeber, P.A. Shade, T.J. Turner, J.C. Schuren, 51. J.A. Daleo, K.A. Ellison, and D.A. Woodford: J. Eng. Gas Tur- D.M. Dimiduk, M.D. Uchic, and A.D. Rollett: Metall. Mater. bines Power, 1999, vol. 121, p. 129. Trans. A, 2014, vol. 45A, pp. 6352–59. 52. J. Beddoes and T. Mohammadi: J. Strain Anal. Eng. Des., 2010, 77. S. Keshavarz, S. Ghosh, A.C. Reid, and S.A. Langer: Acta Mater., vol. 45, pp. 587–92. 2016, vol. 114, pp. 106–15. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, SEPTEMBER 2018—4235

Journal

Metallurgical and Materials Transactions ASpringer Journals

Published: May 30, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off