Optimisation of sample geometry for thermo‐mechanical testing of precipitation hardenable nickel‐based superalloys with an ETMT machine

Accurate determination of thermo‐mechanical properties in precipitation hardenable materials using an electro‐thermal mechanical testing (ETMT) system is a well‐established challenge. The non‐uniform distribution of temperature resulting from heating based on the joule effect (i.e., resistivity heating) leads to heterogeneous deformation along the gauge length, owing to the temperature dependency of mechanical properties, which makes their direct measurements complicated. This study presents an evaluation of four different miniaturised sample geometries that were tested to achieve an optimised sample with acceptable uniform strain and temperature distributions in the gauge volume. In‐situ displacement mapping, using digital image correlation (DIC), was utilised to calibrate the optimised sample dimensions with the aim of forcing the deformation to the hottest region of the gauge lengths during the tests. Tests were carried out on Inconel 718 (IN718) at 720°C, an optimal temperature for the precipitation of γ″, the primary strengthening particle in this alloy. The results showed that only in the case of the geometry proposed in this study (i.e., a sample with a short gauge length [~2 mm]) did the deformation acceptably localise at the centre, compared to other geometries. A correction methodology is developed that equates the strain measured using DIC over the 2 mm gauge length of the modified sample geometry with the strain measured using the linear variable differential transformer (LVDT) integrated to the ETMT, making future tests on IN718, and other precipitation hardenable materials, possible without the need for the use of a DIC system.

Understanding materials' thermo-mechanical properties is vital for the optimisation of manufacturing process parameters (e.g., during forging) and for the prediction of their behaviour in service.Determination of these properties can be difficult, time-consuming and costly, especially at elevated temperatures and under high strain rates; this makes the introduction of new alloys qualified for applications extremely difficult. [1,2]In particular, the cost for the production of enough material for testing can be excessive, as can the facilities required for the determination of thermo-mechanical properties, often beyond justification.This becomes even more problematic when testing high-value components such as those made from a single crystal (e.g., gas turbine aerofoils).
The mechanical properties of materials vary with temperature, and as such, mechanical testing at elevated temperatures is often required to gain a clearer understanding of materials' behaviour.Conventional testing rigs, typically equipped with convection and/or induction furnaces for heating the test piece to the target temperature, are often used as the means for testing materials' thermo-mechanical behaviours.The time taken for these furnaces to reach and stabilise at the test temperature varies depending on the target temperature, the size of the specimen and the type of furnace used.This is usually no quicker than 20 min for testing medium-scale samples. [3]Within this period, before the commencement of the mechanical test and whilst the sample is reaching the target temperature and stabilising, there are often microstructural changes taking place that affect the mechanical properties and are not captured in the test results.This is because the sample is in such a dynamic state whilst heating for a prolonged period of time.The inability of the conventional test rigs to capture these microstructural changes that take place during heat-up and the long heat-up time themselves are, of course, disadvantages.However, these are not the only challenges; for instance, adhering to ASTM standards E8/E8M-21 [4] and E21-20, [5] which require fairly large-sized samples used for tensile testing, can be disadvantageous for manufacturing samples from costly materials such as aerospace-grade nickel-based superalloys and titanium alloys.Furthermore, if the sample is to be manufactured from a part, as is often the case, and the part is small or complicated, it can be impossible to cut out a full-sized specimen.Undoubtedly, such challenges lead to prolonged experimental approaches using alternative methods to optimise forging conditions and to certify materials for service conditions.
To combat some of these challenges, the National Physical Laboratory (NPL), in conjunction with Instron, developed the electro-thermal mechanical testing (ETMT) system capable of performing tests to assess both the thermomechanical and the thermo-physical properties of materials. [6]One of the major advantages of the ETMT system is its swift heating that is based on a material's electrical resistivity.It maintains temperature control through the use of water-cooled grips at the top and bottom of a sample.Despite its advantages in heating up samples to the target temperature at very fast rates, as well as the capability of very fast cooling rates, the very physical nature of the assembly (i.e., cooling grips) leads to a parabolic distribution of temperature along the length of the sample, with the hottest part being in the middle of the gauge length. [7,8]This leads to two distinct challenges.Firstly, this non-uniform distribution of temperature leads to a heterogeneous deformation (i.e., strain) along the gauge length due to the dependency of materials' mechanical properties on temperature and the development of an effective gauge length, which makes the direct measurement of these properties complicated.The effective gauge length is a shorter region within the gauge length of a sample where the peak of the parabolic temperature distribution normally causes all of the strain to localise. [6]This can be seen in Figure 1a.Linear engineering strain (ε) is defined as where ΔL is the change in length of a sample and L 0 is the initial gauge length, in this case, the effective gauge length.Figure 1b shows three example stress-strain curves that all derive from the same data (meaning the crosshead displacement [ΔL] is the same in all tests) but with different effective gauge lengths selected.Selecting a smaller effective gauge length (L 0 ) than appropriate will have the effect of increasing the engineering strain, which will subsequently make the material appear to have a lower stiffness and a greater elongation.Equally, selecting an unduly large effective gauge length will have the opposite effect and, critically, can lead to the appearance of premature failure in the material.If the strain value is calculated over a gauge length of 6 mm, but the effective gauge length is actually 2 mm, then the localised strain magnitude at the effective gauge length is far higher than the calculated value, meaning it will appear to fail sooner.It can therefore be seen that an accurate determination of the effective gauge length is crucial for determining the material's mechanical properties.The NPL good practice guide recommends determining this effective gauge length using finite element methods or by experimentation.Both of these methods have significant challenges.A finite element approach requires a material model that may not be available, and performing several exploratory tests to determine the effective gauge length experimentally can be time-consuming and costly, especially if the material being investigated itself is expensive, as is often the case for tests carried out with the ETMT.
The second distinct challenge created by the parabolic temperature distribution relates to the class of material being tested.For most materials, the hottest region typically becomes the weakest and undergoes deformation under comparatively lower loads.This is however not the case for precipitation hardenable materials such as different grades of nickel-based superalloys for aerospace applications (e.g., turbine discs), where the hottest part of the specimen can become the strongest depending on temperature. [3]This can lead to a drift in plastic deformation away from the hot mid-gauge section of the sample, where the temperature is known, out towards the end of the gauge length, where the temperature is significantly lower and unknown.It is possible to estimate the temperature at the outer gauge length by using numerical approaches, but this often leads to erroneous results. [9]In this instance, if the crosshead displacement is used as the basis for the evaluation of strain, then the determination of the materials' mechanical properties and the level of plastic deformation become compromised as the displacement is coming from regions at the edge of the gauge length where the temperature is unknown and not in the middle of the gauge length where the temperature is recorded.This very phenomenon is mentioned in the NPL good practice guide, [6] especially for precipitation hardened nickel-based superalloys over a temperature range (i.e., aging temperatures) where different strengthening particles are stable. [3,10,11] recent study [12] has attempted to address this issue by using digital image correlation (DIC) to measure the displacement map in-situ, from which the strain has then been evaluated.However, this study has only used a scaleddown sample geometry on a single crystal, which may not be applicable to all nickel-based superalloys.In the present study, the existing sample geometry recommended by NPL's good practice guide [6] and also a number of other geometries, including both modified and adopted from previous reports, [6,12,13] have been tested with an ETMT in-situ, using DIC to track the spread of deformations, to find a geometry most suitable to satisfy three critical conditions.Firstly, the deformation (and hence strain) must be centred at the middle of the gauge length with no measurable drift.This will give confidence that the plastic strain and mechanical properties are for the recorded temperature and not an unknown, cooler temperature closer to the grips.Secondly, the size of the effective gauge length must be known, preferably prior to test commencement.This means there would be homogenous deformation across the effective gauge length, allowing for a far easier determination of the material's plastic strain and mechanical properties.Thirdly, and finally, the temperature distribution across the effective gauge length must be within 1% of the recorded temperature at the centre of the sample.ASTM E21-20 states that the temperature must not exceed ±3 C for test temperatures of 1000 C and ±6 C for test temperatures above 1000 C when heated with a convection furnace.The parabolic temperature distribution present in the case of the ETMT makes these limits very challenging, so a more achievable target of 1% of the recorded temperature at the centre of the sample was selected.Only when all three of these criteria are satisfied will a geometry be classified as suitable.These tests are conducted on IN718, a nickel-based superalloy, over a range of temperatures that are used in industry for forging processes and subsequent aging heat treatments.A thermal imaging camera was used on the sample that satisfied the above criteria best, as well as on the rectangular geometry recommended in the NPL's good practice guide, [5] to investigate the temperature distributions.Finally, a set of interrupted mechanical tests was carried out using the best-performing sample geometry for the determination of mechanical properties to compare with existing data on IN718 in the literature.1. Specimens were cut out using an electrical discharge machine (EDM) and tested in the as-received condition.All samples were cut in the same direction to avoid any potential impact of mechanical anisotropy on the test results.
Four different sample geometries were tested, including (i) rectangular sample, recommended by the NPL good practice guide for testing with the ETMT system [6] ; (ii) standard tensile sample (hereby referred to as the dog-bone sample), which is a scaled-down classic dog-bone shape slightly modified from the NPL good practice for testing with the ETMT system for nickel-based superalloys [6] ; (iii) winged sample, adopted from a methodology developed for thermo-mechanical testing with increased uniform temperature distribution using a Gleeble thermal-mechanical physical simulation system which is similar to the ETMT system in principal [13] ; and (iv) modified dog-bone sample, developed during the course of this study and hereby referred to as the short gauge length sample.The optimisation criteria for the development of the short gauge length sample were to force the deformation to the hottest area of the sample (i.e., the centre of the gauge length).This was (i) to equate the gauge length and the effective gauge length to the same size, that is, homogenous deformation across the gauge length for far easier determination of the materials' plastic strain and mechanical properties, and (ii) to have a temperature distribution across the effective gauge length of no more than ±1% of the recorded temperature at the centre of the sample.There were three key design variables that were taken into consideration to meet the optimisation criteria.The gauge length of the sample was reduced from 6 mm for the winged sample and 5 mm for the dog-bone sample to 2 mm to make the gauge length and effective gauge length the same size.Having sharper fillets of 1.5 mm radius as opposed to 20 mm radius in an attempt to prevent strain migration from the centre and the deformation encroaching on the cross-sectional area at the fillets, which is unknown and larger than the cross-sectional area at the gauge length, hence it would impact the stress values and be undesirable.Finally, the maximum width of the sample could be no more than 6 mm in order to fit between the screws in the grips.A value of 5 mm was selected to allow 1 mm for clearance.Figure 2 shows schematic sketches for these geometries with all the relevant dimensions provided.

| Equipment and methodology
The experiments were carried out using an Instron™ ETMT 8800© system equipped with a mechanical assembly capable of testing in tension and compression up to a maximum load of 5 kN.A customised gripping system was designed in-house to accommodate samples of different geometries with high accuracy and repeatable alignment.The grips were sand-blasted to increase the friction coefficient and reduce the potential for slip in the samples without pinholes.The sample gripping assembly was water cooled during operation for temperature control.The samples were heated with the aid of a 400 A DC power supply based on electrical resistivity (i.e., the Joule effect).For each test, the temperature was measured and controlled through an R-type thermocouple, composed of 0.1-mm-diameter wires consisting of platinum and platinum-13% rhodium, spot-welded to the sample at the centre of the gauge length under a condition where a bead was formed as a result of melting both wires.Figure 3 shows the basic ETMT assembly, and Figure 4 shows an image of a typical bead formed during spot welding.
During each mechanical test, displacement of the top moving grip was measured with a built-in linear variable differential transformer (LVDT).Concurrently, the surface strain along and across the gauge length for each sample was measured during the test using a 3D DIC system, which was capable of mapping in-plane and out-of-plane displacements.Ten images were captured at 1 s intervals, and the displacements in the x and y directions (denoted u and v, respectively) were measured.Consequently, the strain in the x, y, and xy directions (denoted ε xx , ε yy and ε xy , respectively) was calculated using the same settings as for the actual tests whilst at temperature.Both the spatial and temporal standard deviations (STDs) were computed to understand the level of uncertainty associated with the DIC measurements, as can be seen in Table 2.The values for displacement and strain are an order of magnitude higher than what has been reported in the literature for noise values calculated at room temperature, but are in line with noise values calculated at elevated temperatures, as was the case in these tests. [14,15]I G U R E 2 Four sample geometries were investigated in this study for testing with the electro-thermal mechanical testing ( For the measurement of surface displacement with DIC, a fine speckle pattern was produced on the surface in the area of interest using a white high-temperature paint as a background with an overspray of a black paint of the same type.This method has been shown to produce a consistent pattern with high contrast between features at elevated temperatures, which makes it ideal for this application.[12,16] The resulting pattern with random distributions of fine objects with light, dark and grey contrast offered an appropriate number of features for tracking.It is important to note that the speckle pattern deteriorated when held at room temperature, though the contrast was good enough for tracking displacements by DIC.An example of a surface with speckle patterns at room and elevated temperatures is provided in Figure 5.As the spatial and temporal standard deviations were calculated at elevated temperatures when the speckle pattern had deteriorated, the impact of the texture evolution of the paint has been mitigated as much as possible. Consecutive images of the sample surface were recorded using LaVision's MX4M digital cameras installed on a Zeiss Discovery V12 3D stereo microscope.To eliminate any possible black body radiation emitting from the sample whilst at room temperature, blue LED lights and a filter were used during image acquisition.For each test, images were recorded from the beginning of the test to the end at a frequency of 10 Hz using an incremental correlation mode, meaning each image is correlated to the previous image and each incremental deformation is summed.This increases the amount of error in the correlation compared to a correlation with a single reference image; however, for large displacements where the DIC pattern is likely to change substantially, this is the preferred method.Analogue signals for load, LVDT, and temperature transmitted from the ETMT were connected to the DIC system through a signal interface unit.This enabled the relevant data to be collected and recorded in real-time and used for synchronising the mechanical test data measured by the ETMT with those of the DIC.The images obtained during the tests were analysed by the LaVision DaVis image correlation software (version 8.3.0) to evaluate the strain maps.The International Digital Image Correlation Society's good practice guide recommends a practical subset size of 21 Â 21 pixel 2 for correlation [17] ; however, as these tests had features that were larger and more sparse, the strain maps were obtained using a 41 Â 41 pixel 2 subset size.The same good practice guide recommends that the step size be between one-third and one-half of the subset  size, [17] so a step size of 20 was selected.A second-order polynomial smoothing filter with 3 Â 3 pixel 2 was used to smooth the results and reduce noise.Comparison with unfiltered results showed no significant bias.In these tests, one pixel was equivalent to 5.2 μm, except for the case of the short gauge length sample, where field of view was less of a priority, so the magnification was increased slightly so that one pixel was 3.65 μm.The fast Fourier transform algorithm was used to correlate the images.

| Effect of sample geometry on deformation
For the evaluation of a suitable sample geometry, the thermo-mechanical test procedure started with heating the sample to 980 C at a 10 C/s heating rate and dwelled at this temperature for 10 min to annihilate any pre-existing residual stress and to dissolve the γ 0 and γ 00 precipitates present.This heat treatment resembles the final closed die forging operation that is typically done at 980 C for IN718, and it normalises the microstructure of all samples relative to one another in the gauge length.The sample was then cooled at a rate of 50 C/s (i.e., to resemble the quenching condition) to the target test temperature of 720 C and soaked for 2 min to allow the temperature to homogenise throughout the gauge length.The aging temperature of 720 C is an optimised temperature for effective precipitation of γ 00 and hence was selected for these analyses.The rationale was to understand the effect of the onset of precipitation at aging temperatures on the evolution of residual stress generated following the fast cooling from the forging temperature.The mechanical loading was then commenced and continued until either the sample failed or was deemed to have slipped.These measurements were controlled by the LDVT to ensure that the level of localised deformation to be measured by the DIC was in excess of 2% as a minimum.All tests were carried out at a constant crosshead speed of 4 Â 10 À3 mm/s and a starting engineering strain rate of 2 Â 10 À3 /s.The effective gauge length was assumed to be 2 mm for all geometries.The size of the effective gauge lengths is central to this study, and before the tests were performed, it was acknowledged that they may differ from the original assumption of 2 mm in size.An accurate determination would be made by using the in-situ DIC results obtained later.Therefore, the decision was taken to keep the crosshead speed constant for all tests, acknowledging that if the effective gauge lengths were greater or smaller than the assumed 2 mm, this would mean differing engineering strain rates for each sample.
A typical displacement and temperature versus time plot is shown in Figure 6, outlining the test procedure.

| Analysis of temperature distribution by thermal imaging
For the short gauge lengths and rectangular geometries (Figure 2), in addition to the temperature measurement using R-type thermocouples, an arc-thermal imaging camera manufactured by Ametek Land Instruments was also used to measure the temperature distribution over the gauge lengths.The camera had a spectral response of 8-14 μm and a field of view of 22 .It had a focus range of 0.3 m to infinity, a maximum recording frequency rate of 30 Hz, and a thermal image resolution of 384 Â 288 pixel 2 .The camera has an accuracy of ±2% or ±2 C (whichever is greater) of reading for a blackbody target (i.e., an emissivity value of 1).

| Determination of mechanical properties at different temperatures using the optimised sample geometry
Following the selection of an optimised sample geometry, additional tests were carried out on the short gauge length sample at various aging temperatures to further ascertain this geometry's suitability in the testing of nickel-based superalloys by the ETMT system.Similarly to the test procedure implemented for samples of different geometries, for these tests the samples were initially heated to 980 C at a 10 C/s heating rate and maintained at this temperature for 10 min for the annihilation of residual stress and dissolution of existing γ 0 and γ 00 precipitates.The samples were then cooled down to the target aging temperature at a rate of 50 C/s (see Figure 6).Four tensile tests were carried out at different final aging temperatures, including 620, 670, 720 and 770 C. The Young's modulus was calculated for each test via the strain output from the DIC system and the stress calculated from the ETMT system's load cell.The equipment and setup used were the same as those used for the geometry evaluation tests.Meanwhile, for the evaluation of the surface displacement with the DIC system, the strain maps were obtained using a 41 Â 41 pixel 2 subset size with a step size of 20.
In these tests, one pixel was equivalent to 3.65 μm, and the image capture rate remained at 10 Hz.Information was only gathered up until the 0.2% yield point, as the purpose of these tests was to determine the Young's modulus at the precipitation hardening temperatures and compare them to the existing data, particularly those measured by conventional tensile test rigs, where considerable time ($20-30 min) is needed for the sample to reach and stabilise at the target temperature. [3]| RESULTS

| Effect of sample geometry
Figure 7 shows the stress-strain curves plotted using the data recorded by the LVDT and load cell of the ETMT.Firstly, it is important to note that both the dog-bone sample and the rectangular sample showed signs of slip as the tests progressed at 23% and 36% of strain, respectively, but the data is still suitable for the majority of the test for comparison with other samples.Secondly, there is a high degree of variation in the stress-strain curves.A reasonable conclusion would be that the only variable in these tests was the sample geometry, thus demonstrating the significant impact that this has Typical plot of nominal temperature and displacement profiles against time, applied during a test.
on the resultant curves.Without the use of DIC, that would have been the conclusion drawn.The reason for this variation was further investigated by using DIC to plot strain maps to better understand the strain distribution in the ε yy direction.Figures 8, 9, 10 and 11 show the strain distribution maps for each of the four different sample geometries.In each case, a target of 40% strain of the original 2 mm effective gauge length (i.e., 0.8 mm grip-to-grip separation) was applied via the ETMT system.Only the data up to 155 s is presented for the winged geometry, after which significant amounts of slip began to take place, which impacted the results.Critically, these strain localisations did not take place in the centre of the sample for most geometries, where the temperature was at its maximum, as demonstrated in the strain maps.For a clearer demonstration, the midsection of each sample was divided into three areas of 2 mm gauge length each with no overlap, and the strain evolution as a function of time was evaluated from the DIC data to explore the magnitude of strain localisation.This was to show that the majority of the deformation occurred in the region where the temperature was the highest.
The strain distribution measured for the rectangular geometry (Figure 8a) shows the strain localisation 1 mm below the centre point.Figure 8b shows that despite a small majority of the strain still coming from the centre of the sample, a significant portion of the deformation takes place away from the midsection of the sample, in particular in the 2 mm section immediately below the middle 2 mm midsection of the sample.
The strain distribution map for the dog-bone geometry shown in Figure 9a reveals that a significant strain localisation has taken place within the 5 mm gauge length.However, closer inspection shows that the strain F I G U R E 9 (a) Strain map obtained in the ε yy direction by digital image correlation (DIC) for the dog-bone geometry at 40% strain readout on the electro-thermal mechanical testing (ETMT) (i.e., measured by the linear variable differential transformer [LVDT]) after 200 s, and (b) plots of strain evolution measured in the ε yy direction by DIC as a function of time for the dog-bone geometry over three different areas with a 2 mm gauge length each at the middle, above the middle and below the middle section of the sample.Note that the maximum temperature was reached in the centre of the sample.
F I G U R E 1 0 (a) Strain map obtained in the ε yy direction by digital image correlation (DIC) for the winged geometry at 30% strain readout on the electro-thermal mechanical testing (ETMT) (i.e., measured by the linear variable differential transformer [LVDT]) after 155 s, and (b) plots of strain evolution measured in the ε yy direction by DIC as a function of time for the winged geometry over three different areas with a 2 mm gauge length each at the middle, above the middle and below the middle section of the sample.Note that the maximum temperature was reached in the centre of the sample.concentration was 2.5 mm below the centre of the gauge length.Figure 9b confirms that the majority of the measured deformation did not occur at the middle of the sample but rather at the area with a 2 mm gauge immediately below the midsection.Figure 9b also shows serration in the strain versus time plots, which is believed to be quantisation from the virtual strian gauge; this could be due to the size of the virtual strain gauge.
As for the winged geometry, the strain localisation has drifted away from the mid-gauge area to regions between 2 and 2.5 mm above and below the centre, as can be seen in Figure 10a.After 60 s, the rate of strain in the midsection can be seen to drop as the sample hardens in that area (marker 1) and then continues to deform at a lower rate compared to the 2 mm areas immediately above and below.Figure 10b shows serration in the strain versus time plots, suggesting that this sample is showing quantisation because of the use of a virtual strain gauge.
Meanwhile, for the short gauge length geometry, the strain concentration occurred nicely in the central 2 mm gauge length area of the sample, satisfying the first condition of no strain drift.For this sample, it appeared (Figure 11a) that the strain concentration encroaches out-with the 2 mm gauge length where the cross-sectional area increases due to the fillets, and as Figure 11b shows, the strain out-with the central 2 mm section of the sample is not negligible.This means the second condition of having the gauge length and effective gauge length be the same value is not entirely satisfied; however, this geometry does show a clear majority of strain at the centre.The impact that the strain encroaching into the fillet section has on the strain calculated from the LVDT sensor is analysed more in the discussion section.These measurements and observations suggest that the only sample geometry that satisfies the necessary criteria for appropriate deformation (i.e., localised at the centre-point of the sample), where the target temperature is reached, is the optimised geometry with short gauge length developed in this study.The short gauge length sample partially meets the second criteria of having the gauge length and the effective gauge length be the same size.

| Temperature distribution
Figures 12 and 13 show the temperature distributions measured by a thermal camera for the rectangular and short gauge length samples.The temperature at a position 1 mm above the centre line and 1 mm below the centre line was measured for both samples and gives an indication of the temperature stability across the 2 mm total gauge length.In the case of the rectangular sample, the largest temperature drop was 1.89 C over the 2 mm gauge length, and for the short gauge length sample, the largest temperature drop was 1.97 C.This represents a 0.263% and 0.274% difference from the edge of the 2 mm gauge length to the centre for the rectangular and short gauge length samples, respectively.The NPL's good practice guide indicates that for a rectangular geometry, the temperature difference across a 2-4 mm gauge length is ±3 C at a temperature of 1250 C and less than ±3 C at lower temperatures. [6]The results of these tests carried out using a thermal camera are in good agreement with those from the NPL's good practice guide.It can therefore reasonably be said that the short gauge length sample likely satisfies the necessary criteria of the temperature remaining as consistent across a 2 mm gauge length with a difference of <0.28% at 720 C.

| Temperature dependant mechanical properties
It can be seen in Figure 14 that the results produced from the LVDT sensor of the ETMT are fairly consistent with one another for temperatures between 670 and 770 C. The curve produced for the test carried out at 620 C shows a less severe slope in the elastic portion of the test, meaning that the Young's modulus is noticeably less than for the other tests (see Table 3).It has been shown for this material and at these temperatures that as the aging temperature decreases, the Young's modulus increases. [3,18]The Young's modulus values calculated from the LVDT sensor of the ETMT do not exhibit this trend, as Table 3 shows.The results of the tests carried out at 620 and 770 C give values that are much smaller and much larger, respectively, when compared with similar tests in the literature and shown in Table 3.
Table 3 also shows the measured Young's modulus values at five different temperatures on the optimised short gauge length sample geometry calculated by DIC.At all temperatures, the determined Young's modulus values calculated using the DIC are smaller than those from the two other comparable reports.The difference between the Young's modulus at room temperature is relatively small and could be due to differences in the thermal or mechanical processing histories of the materials or in their chemical compositions.Meanwhile, for the tests carried out at the aging temperature range, there is a general trend of decreasing Young's modulus as temperature increases for the data calculated using DIC, matching the other two studies.However, at lower aging temperatures, the data measured by the DIC were significantly lower than those reported in the literature.This is due to the fact that the data reported in the literature, including a previous study by the authors, [10] were all obtained using conventional testing rigs equipped with F I G U R E 1 4 Plot of stress-strain curves evaluated from the data measured by linear variable differential transformer (LVDT) on the short gauge length sample for the temperature dependant mechanical properties tests carried out at different temperatures.All tests were done within the elastic limit.

Temperature ( C)
Young's modulus calculated from the ETMT LVDT (GPa) Young's modulus calculated from the ETMT and DIC tests (GPa) Young's modulus calculated from Rahimi et al. [3] (GPa) ASM Specialty Handbook values [18] (GPa) furnaces, whereby a significant time ($20-30 min) was required to reach the target temperature, which is long enough for the precipitation of a considerable amount of γ 00 , [11] leading to a material with higher stiffness.Whereas for the tests conducted with the ETMT, the sample was heated to the target temperature almost instantly (i.e., within a few seconds) with little time for γ 00 precipitation to occur, resulting in a material with lower stiffness.Meanwhile, by increasing the temperature towards the ideal temperature for γ 00 precipitation (i.e., 720 C), the difference in the measured Young's modulus by ETMT with those reported in the literature reduces.This can be due to the higher kinetics of γ 00 precipitation at higher temperatures, meaning that a sufficient volume of strengthening precipitate could become present in the material despite being heated quickly by the ETMT.Note that the materials used for these analyses were all solutionannealed prior to the test.Overall, there is good agreement in the values, emphasising that the short gauge length sample satisfies both the thermal and mechanical criteria needed for a successful mechanical properties (e.g., Young's modulus) determination at elevated temperatures where heavy γ 00 precipitation is likely to occur for IN718.

| DISCUSSION
The material investigated in this study, IN718, is a precipitation hardenable nickel-iron-based superalloy containing considerable fractions of Nb and Mo and small fractions of Ti and Al (see Table 1).This grade of superalloy achieves its superior mechanical strength for high temperature applications from precipitation phases, predominantly made of Ni 3 Nb, with varying fractions of Ti and Al substituting for Nb in the form of Ni 3 (Al, Ti). [11,19,20]The δ-phase is the most stable form of Ni 3 Nb precipitates (≈700-1000 C) that usually nucleates intergranularly (i.e., at grain boundaries), with a possibility of intragranular nucleation (i.e., within grains) in the presence of γ 00 precipitate.γ 00 is the main strengthening phase in IN718 with thermodynamic stability over the 620-900 C temperature range and has the same chemical stoichiometry (i.e., Ni 3 Nb) as that of the δ-phase.[21][22][23][24] The test plan implemented in this study included a 10-min annealing at 980 C, followed by cooling to the aging temperature at a 50 C/s rate, and then mechanical testing at this temperature after a 2-min dwell time.The initial annealing temperature leads to the dissolution of all γ 0 and γ 00 precipitates and also a minor dissolution of the δ-phase (i.e., less than 10% dissolved) over the majority of the gauge length since 980 C is approaching the upper limit stability of the δ-phase. [3,11]Due to the parabolic distribution of temperature in the middle section of the sample, the dissolution rate of the δ-phase over the gauge length may differ.However, considering the <2 C difference in the temperature between the extreme ends of the gauge length and the centre of the sample (see Figures 12 and 13), the local temperatures are still well beyond γ 0 and γ 00 stability, and hence these precipitates are all dissolved throughout.When the sample is cooled to the aging temperature range, which is an ideal temperature for γ 00 precipitation, [11] an onset of precipitation starts to occur at the centre of the gauge length, with reduced precipitation kinetics towards either end due to the <2 C difference caused by the parabolic distribution of temperature.This heterogeneity in the precipitation kinetics results in γ 00 with different size and distribution throughout the gauge length, which has implications for the mechanical properties.This is manifested clearly in the flat rectangular geometry proposed by NPL's good practice guide [6] for testing with ETMT after mechanical testing at 720 C (see Figure 8).As can be seen from the strain map in Figure 8a, localised deformation occurs in a zone that is slightly below the central part of the specimen, where the temperature is highest for the rectangular geometry.Figure 8b shows that the information recorded during the test is not dominated by the deformation behaviour of the central region and that the regions outwith the area of interest with a known temperature (i.e., where the thermocouple was installed) show significant levels of strain.
In an attempt to address this problem, a dog-bone geometry (see Figure 2b) recommended by NPL's good practice guide, which was also used in a previous study, [12] was slightly modified and selected as an alternative geometry.As can be seen in Figure 9a, strain localisation was still observed to consistently occur in a region below the central zone of the sample.Similarly, this indicates that the hardening effect caused by γ 00 precipitation was strong enough to shift the strain localisation away from the middle of the sample, where the temperature was the highest and the crosssectional area was the least.
To resolve this problem, the winged geometry was adapted from literature. [13]This geometry was originally designed for testing on a Gleeble 3800, an apparatus that works based on similar principals as those of the ETMT; that is, both systems use electrical resistivity to heat the samples to the target temperature.However, unlike the ETMT, the sample used for testing with the Gleeble was not miniaturised.Nevertheless, the problem arising from the parabolic temperature distribution across the gauge length was shared by both systems.It was shown in reference [13] that by manufacturing samples with wings extending out from both sides of the sample, above and below the gauge length area (Figure 2c), and then connecting each side from top to bottom with copper wires, it is possible to make the temperature distribution at the gauge length more homogeneous.This is to create a parallel circuit that would heat the sample and extend the hot zone out from the gauge length.It was thought that a similar design might be deployed for testing with the ETMT using a smaller sample.The geometry manufactured (Figure 2c) was a refinement of the flat specimen recommended by NPL's good practice guide, with additional wings.
Based on the results of a previous study, [13] the winged sample was expected to have a uniform temperature distribution across the gauge length, which would in turn lead to a uniform distribution of precipitation and hence deformation.However, Figure 10a shows that the strain was not evenly distributed throughout the gauge length, where a clear shift in strain was observed away from the centre towards the top and the bottom.Therefore, the winged sample, despite its success in testing using the Gleeble 3,800, [13] was observed to be unsuitable for testing IN718 at 720 C using the ETMT.The combination of a miniaturised sample and having a lower current output from the ETMT, which means a sharper parabolic temperature distribution across the gauge length, was likely the cause of this problem.
In all the rectangular, dog-bone and winged sample geometries, deformation occurred outside the area of interest (i.e., the centre of the gauge length) where the temperature was measured to be highest.It was thought that this was predominantly because the gauge length of these geometries were too long, that is, 16, 5 and 6 mm for the rectangular, dog-bone and winged samples, respectively.Therefore, it was decided to reduce the gauge length to 2 mm in the short gauge length geometry to force the deformation into the centre of the sample.As such, the radii of the fillets for the standard dog-bone sample were 20 mm to avoid any stress localisation that leads to fracture in this area.This was possible when the fillets were too sharp and is likely to happen when the material is brittle.However, a radius of 1.5 mm was considered for the optimised geometry.As can be seen in Figure 11a, the strain map obtained for the short-gauge length sample with sharp fillets shows deformation centred in the middle of the sample, indicating that it successfully satisfied the first criteria.The third criteria, having a temperature distribution across the gauge length of less than 1%, can be seen to have been satisfied, as shown in Figures 12 and 13.The second criteria of having the effective gauge length equal to that of the actual gauge length is only partially satisfied.The majority of deformation does indeed come from the middle of the sample, far more so than in the case of any other geometry tested; however, there is still a small but significant proportion that does not and comes from areas just outside the central 2 mm region.This still means that the sharper fillets combined with the reduced gauge length enabled successful tests of IN718 nickel-based superalloy at the aging temperature range (i.e., 620-720 C) to take place; however, care must be taken when interpreting strain results from the LVDT sensor.
The Young's modulus is a difficult quantity to measure using DIC due to the small level of displacements to be measured, which can often be smaller than the noise of the DIC. [25]It is however an excellent quantity to measure for the sake of comparison with other reports in literature. [3,18,26]As such, this was selected as the final qualifying criteria in a bid to find a sample geometry suitable for the determination of thermo-mechanical properties in superalloys.The work carried out by Rahimi et al. [3] was used for comparative purposes, as were the results published in the ASM Specialty Handbook. [18]To extract data for the temperatures examined in this study, a linear interpolation was applied to the results from the ASM Specialty Handbook, as the exact temperatures did not match up with the test temperatures carried out in these tests.
Finally, an approach has been suggested to equate the strain measured using the DIC system over the 2 mm gauge length of the short gauge length sample with the strain measured by the LVDT.This was done by correcting the strain measured by the LVDT to the strain measured using the DIC using a generalised reduced gradient solver built into Microsoft Excel.The average absolute relative error (AARE) seen in Equation (2), where E i is the experimental stress values, P i is the predicted stress values and N is the number of data points, was used as an objective function, and the strain measured using the LVDT was corrected to two different equations and then compared.The first equation was the standard equation of a straight line (y = mx + c), and the second equation was the power law (y = mx b ).The only constraint applied was for the value of c in the equation of a straight line to equal zero, as would have to be the case.

AARE
Figure 15a,b shows the plots of strain versus time measured by both the DIC system and the LVDT for both equations.The values for m and b in the power law were 0.740 and 1.289, respectively.The value of m for the equation of a straight line was 0.460.The AARE for the power law equation was 15.15%, and the AARE for the equation of a straight line was 28.43%, meaning the power law is a better fit at correcting the strain measured from the LVDT sensor of the ETMT to the data from the DIC.This can be seen in Figure 15a,b, where the power law shows a much closer fit than the straight line.Polynomial equations were not selected for comparison as the power law showed good accuracy and was simpler than a polynomial equation for prediction.The reason for the divergence of the uncorrected LVDT strain from the DIC strain, especially at the beginning of a test, is because the LVDT sensor is attached to the grips of the ETMT machine and therefore not sensitive enough to detect the impact of machine compliance and/or that of sample straightening during testing in cases where they have not been aligned perfectly.The LVDT sensor reads displacement along the sample, even if the sample has yet to fully settle into the grips and align with the direction of tension.DIC is more astute at detecting this phenomenon, which is thought to be the reason behind the early divergence in the curves.Thereafter, the difference in strain continues to grow between the uncorrected LVDT strain value and the DIC measured strain.Figure 11 shows that the majority of the strain comes from the 2 mm gauge length in the middle of the sample, but there was still some strain measured out with this gauge length.The strain out with this gauge length is thought to be the reason behind the difference in the uncorrected strain measured from the LVDT and the strain measured using the DIC.Therefore, it can be seen that the correction applied is predominantly to address the strain outside the 2 mm gauge length in the centre of the sample.Constitutive models have been used to predict the flow stress at elevated temperatures [27][28][29][30][31] ; however, it is well known that a constitutive model is heavily dependent on the material characteristics (i.e., microstructure), the strain rate and the temperature at which the tests were carried out.Therefore, it is assumed that further work would need to be carried out to determine the robustness of Equation ( 3), to see if it is representative of all precipitation hardened materials, and for what temperature and strain rate regimes.
where ε ETMTcorrected is the strain measured from the LVDT sensor of the ETMT after correction to the strain measured by the DIC system, and ε ETMTuncorrected is the strain measured directly from the LVDT sensor on the ETMT.This approach enables one to confidently rely on the strain measured by the LVDT without the need for a DIC system.The authors recommend further work to understand the impact that temperature and strain rate have on this equation, as well as its applicability to other precipitation hardened materials.Furthermore, the development of this empirical equation, though rooted in practicality, could potentially be better strengthened if it were to be rooted in a physical-based model.This would require additional data at different temperatures and strain rates, which were beyond the scope of this work.Although additional data is needed to verify this approach for other materials as the coefficients can vary, the F I G U R E 1 5 Plots of strain versus time at 720 C for the uncorrected linear variable differential transformer (LVDT) strain, the strain measured by digital image correlation (DIC) and (a) strain data collected from the LVDT sensor of the electro-thermal mechanical testing (ETMT) and corrected using a power law equation and (b) strain data collected from the LVDT sensor of the ETMT and corrected using the equation of a straight line.
proposed methodology works for the IN718 nickel-based superalloy at a temperature of 720 C for a starting engineering strain rate of 2 Â 10 À3 /s.Nevertheless, the sample geometry is essential in obtaining the correct data for this class of materials (i.e., precipitation hardenable) with the aid of ETMT, and this study has demonstrated the appropriate sample geometry.

| CONCLUSION
Four different sample geometries were examined to determine their suitability for thermo-mechanical testing of a precipitation hardenable material, IN718 nickel-based superalloy, using an ETMT system.The following conclusions can be drawn: • The results of surface displacement and strain mapping with the aid of digital image correlation showed that in all geometries, strain localisation occurred away from the centre of the gauge lengths of the samples, where the deformation is expected to be, with the exception of a modified geometry with a short gauge length.This sample showed strain localisation perfectly at the centre of the sample.• The short gauge length sample showed a 0.274% difference in temperature between the centre of the gauge length and its 2 mm outer edge at a temperature of 720 C. In comparison, this value was 0.263% for the standard rectangular sample over a matching 2 mm gauge length and at the same temperature.• The short gauge length sample is suitable for determining arguably the most difficult of mechanical properties, the Young's modulus, for the precipitation hardenable material IN718 at room temperature as well as at aging temperatures in the region of 620-770 C, where significant γ 0 and γ 00 precipitation takes place, making the material stronger, by making use of digital image correlation.• These results suggest that the modified geometry designed, tested and verified in this study is in fact suitable for mechanical testing of precipitation hardenable materials, such as nickel-based superalloys, at elevated temperatures.• A methodology is proposed to facilitate the use of the short gauge length sample in accurately determining the strain from the ETMT's LVDT sensor for IN718 nickel-based superalloy.

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I G U R E 1 (a) Dog-bone sample showing the difference between the gauge length and the effective gauge length and (b) example stress-strain curves showing the impact of three different effective gauge lengths of 2, 4 and 6 mm.
ETMT) system, (a) rectangular, (b) dog-bone, (c) winged and (d) short gauge length.All dimensions are in mm.Note: in (c) the coloured lines connecting the wings are schematic representations of the copper wires used to create an electric short-cut.F I G U R E 3 Sketch of the experimental set-up demonstrating the basic electro-thermal mechanical testing (ETMT) grips and the area explored by digital image correlation (DIC).[Correction added on 16 August 2023, after first online publication: Figures 3 and 4 have been interchanged in this version.]

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I G U R E 4 Photograph of a short gauge length sample with a thermocouple bead spot-welded onto the middle of the gauge length.[Correction added on 16 August 2023, after first online publication: Figures 3 and 4 have been interchanged in this version.]T A B L E 2 Noise floor given by spatial and temporal standard deviations for each test.

F I G U R E 5
Examples of surfaces with speckle patterns (a) at room temperature and (b) at 770 C, prepared for displacement mapping during thermo-mechanical testing with the electro-thermal mechanical testing (ETMT) system.

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I G U R E 7 Plots of stress-strain curves measured by the linear variable differential transformer (LVDT) interfaced to the electrothermal mechanical testing (ETMT) for all sample geometries.F I G U R E 8 (a) Strain map obtained in the ε yy direction by digital image correlation (DIC) for the rectangular geometry at 40% strain read-out on the electro-thermal mechanical testing (ETMT) (i.e., measured by the linear variable differential transformer [LVDT]) after 200 s, and (b) plots of strain evolution measured in the ε yy direction by DIC as a function of time for the rectangular geometry over three different areas with a 2 mm gauge length each at the middle, above the middle and below the middle section of the sample.Note that the maximum temperature was reached in the centre of the sample.

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I G U R E 1 1 (a) Strain map obtained in the ε yy direction by digital image correlation (DIC) for the short gauge length geometry at 40% strain read-out on the electro-thermal mechanical testing (ETMT) (i.e., measured by the linear variable differential transformer [LVDT]) after 200 s, and (b) plots of strain evolution measured in the ε yy direction by DIC as a function of time for the short gauge length geometry over three different areas with a 2 mm gauge length each at the middle, above the middle and below the middle section of the sample.Note that the maximum temperature was reached in the centre of the sample.

F I G U R E 1 2
Temperature distribution maps measured by a thermal camera at 720 C after a 2-min dwell across the sample length for (a) a rectangular sample and (b) a short gauge length sample.F I G U R E 1 3 Temperature distribution plot measured by a thermal camera at 720 C after a 2-min dwell across the gauge length of the rectangular sample and the short gauge length sample.

T A B L E 3
Summary of the Young's modulus values measured by the ETMT for Inconel 718 (IN718) nickel-based superalloy in comparison to the data in the literature.
Nominal chemical composition of the Inconel 718 (IN718) material used in this study, provided by the manufacturer.
T A B L E 1