1 Introduction

The application of thin metallic sheets and foils for structural components operating at high-temperatures in the time-dependent deformation regime is of engineering importance to a number of technologies including heat exchangers, micro-turbine recuperators (Ref 1), solid oxide fuel cells (Ref 2), and micro-electronics (Ref 3). Creep behavior (typically resistance to creep deformation) is one of the most challenging of the design parameters which limits the performance, reliability, and lifetime of the components. Recently, there has been a move to apply diffusion bonded compact heat exchangers (CHX) for high-temperature advanced nuclear systems such as gas cooled reactors, supercritical CO2 (sCO2) power cycles for heat-to-power conversion or for transformative fossil fuel power systems, and the next generation of high efficiency concentrated solar power (CSP) systems (Ref 4,5,6). The heat-transfer surfaces for the diffusion bonded CHX are essentially chemically etched or machined metallic sheets which are stacked and diffusion bonded using various proprietary techniques under an applied load to form the primary structural pressure boundary for the CHX. To date, creep-testing on these diffusion bonded stacks has generally shown inferior performance of the bonds to base (wrought) metal expectations due to failure at bond lines (Ref 7, 8). However, in all of these studies, the creep performance of the starting sheet material was not considered or independently measured to determine its contribution to the observed creep strength and ductility in the bonded structure. Furthermore, the spacing between the small channels (which hold the pressure) in a myriad of diffusion bonded CHX designs is often on the order of about a millimeter which is similar in thickness to the starting sheets. The typical alloys being used or considered for all of these applications (with the exception of the micro-electronics) are austenitic stainless steels and nickel-based alloys due to their good combination of oxidation resistance, favorable corrosion properties depending on the specific environment, and high-temperature mechanical properties including creep.

2 Background

It is well recognized that many metallurgical factors influence creep behavior of engineering alloys with grain size being one of the more important considerations in many alloy systems. The typical processing routes for metallic sheets and foils can differ from traditional wrought processing, such as the use of continuous annealing furnaces, with heat-treatment times on the order of a few minutes instead of hours. This may result in important differences in grain size and size, type, and distribution of precipitates which can in-turn effect creep-behavior. Additionally, as test sample thickness approaches the grain size of the material being tested, the creep behavior may not be governed by bulk creep deformation and failure but by local microstructural and geometric considerations. The testing of thin sheets, foils, and wire have long taken advantage of this approach to understand fundamental creep mechanisms using pure metals, binary alloys, and other solid solution strengthened materials where physical proof of grain boundary sliding and/or deformation can be observed and changes in creep rates and mechanisms explained due to the interactions of free surfaces and grain size (Ref 9, 10). Auer and Sagues performed some of the earliest experiments on the creep of foils made from alloys and showed (only 5 tests) an ~ 6X increase in creep rate for a ‘pure’ alloy 316 with an average grain size of 7.5 microns when foil thickness was approximately only 4X the average grain size (Ref 11). More extensive room temperature tensile testing for the same materials suggested foil tensile properties were independent of thickness if the thickness was larger than 2-3 grains. Similar room temperature tensile studies by Miyazaki on Cu, Al, Cu + Al, and Fe (Ref 12) and Igata on commercially produced 304 stainless steels suggest a critical sample thickness to average grain size ratio of 4-5 is required to achieve bulk tensile flow behavior in thin samples (Ref 13). However, the limited creep work in some of these studies did not make definitive conclusions based on creep behavior and in general only steady-state creep rates were studied. Thus, these studies have limited application for creep performance in engineering alloy sheets.

A number of researchers have explored the creep performance of metallic sheets and foils both commercially produced as well as developed in the laboratory. Maziasz and co-worked studied creep, oxidation, and microstructural development for a number of commercial austenitic stainless steels and nickel-based sheets and foils for advanced micro-turbine recuperators (Ref 14,15,16). Their testing at 704-750 °C showed some alloys had equivalent creep behavior in foil and wrought forms, but the foils had reduced creep ductility (HR120); while other sheets and foils had inferior creep resistance and almost a 10X reduction in rupture strength and life to equivalent wrought materials (Haynes® Alloy 230®); others showed similar creep behavior for sheets and wrought products with only minor loss of rupture life (Alloy 625); and yet others showed variable foil behavior due to changes in foil processing (AL20/25 + Nb). General trends showed for the same material, larger average grain size improved creep resistance and rupture life (Ref 17) and that alloys which showed good creep strength showed more stable precipitate structures (Ref 18) but due to the limited number of tests and large number of materials no conclusive optimum grain size or other precipitate measure was identified as a function of foil and sheet thickness. Jung et al. evaluated creep behavior of 316 and a similar austenitic stainless steel alloy cold-worked foils and found no systematic dependence of creep rate on foil thickness (Ref 19). Sharma studied the short-term creep behavior of nickel-based alloy 617 foil at 800 to 1000 °C in the as-received, cold-rolled, and cold-rolled and solution treated conditions and found increasing grain size increased the creep strength at 800 to 900 °C for solution annealed materials, but no effect of thickness at 1000 °C and for cold-rolled materials dynamic recrystallization reduced creep strength (Ref 20, 21). Testing times were short (generally < 100 h) so the applicability of such short-term results to long-term behavior cannot be made. Dryepondt studied the long-term (> 10,000 h) creep behavior of FeCrAl foils at 875 and 1050 °C and found the oxide scale which grew during testing had a stronger influence in longer-term lower stress tests on the creep results independent of the applied stress (Ref 22).

To address the gap in knowledge specific to the creep performance of grain size and sample thickness for engineering alloys, the material selected for this study was INCONEL®alloy 740H® (herein referred to as alloy 740H). Alloy 740H is an age hardenable nickel-based alloy which is a candidate for application up to 800 °C in pressure boundary applications for many of the advanced energy systems previously mentioned (Ref 23,24,25). The alloy is advantageous because in addition to being commercially relevant its creep-rupture behavior has been well characterized which shows moderate and quantifiable dependence on grain size for a range of wrought products (Ref 26, 27) and for testing times between ~ 300 and  ~ 20,000 h at 750 °C no systematic change in creep damage mechanism with rupture ductility showing a nearly constant value for a range of product forms and heat chemistries (Ref 28). This work extends, using multiple sheet thicknesses, prior research by the authors to understand how different solutioning annealing (SA) heat-treatments of mill annealed (MA) 740H sheet effected grain size distributions, room temperature hardness, and short-term rupture life on a single sheet thickness of alloy 740H (Ref 29).

3 Experimental Procedure

The sheet material used for this study came from a single heat of alloy 740H with a composition shown in Table 1. Three sheet thicknesses of nominally 1.65, 0.94, and 0.46 mm were supplied in the Mill Annealed (MA) condition. The manufacturing route was Vacuum Induction Melting followed by Electroslag Remelting (VIM/ESR), forging into a slab and rolling to 6.4 mm (0.25″) thick hotband, and then successive rolling reductions and anneals to the desired thickness. The final continuous anneal was 1107 °C for approximately 5 min followed by a spray quench and stretcher leveled in coil as an outwork step. Materials were prepared for testing in either the MA, MA + Age, Solution Annealed (SA), or SA + Age condition. For solution annealing (SA) sheet sections were placed within stainless steel bags to minimize oxidation and heat-treated in a pre-warmed box furnace at 1150 °C for 30 min or 1190 °C for 840 min followed by still air cooling. Aging was conducted in air at 800 °C for 4 h followed by still air cooling. Pin-loaded sheet-type creep specimens with a 31.8 mm gauge length were extracted from the sheets using wire electro-discharge machining (EDM); see (Ref 29) for additional sample details. Creep testing was conducted in accordance with ASTM E139 at constant load in dead weight or lever-arm creep machines with continuous strain monitoring attached to the specimen shoulders outside the gauge at 750 °C. It is important to note that per the ASTM standard all samples received a minimum 1 h soak at the testing temperature prior to starting the test so the MA test condition has some prior aging in the creep frame before testing.

Table 1 Composition (wt.%) of Alloy 740H (Sheets) used in this study (Heat-Lot: HT6306JK) compared to the UNS N07740 Specification (Spec) requirements
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Samples from sheets and tested specimens were mounted in cross-section parallel to the rolling and creep testing direction (so the through thickness microstructure could be observed) and prepared using standard metallographic procedures with a final polish of 0.4 μm colloidal silica with additional vibratory methods employed for advanced characterization on selected samples. Light optical microscopy was performed using a high resolution digital microscope (Keyence VHX-7000) and images were stitched together using the accompanying microscope software. Creep cavitation analysis was completed on 1000X magnification images of unetched samples. Each stitched image was cropped into a standard sized square (approximately 15,000 pixels wide) and analyzed using a common image analysis software (Fiji ImageJ). Images were scaled using the “set scale” feature with a calibration of 9.585 pixels per micron, as determined by the amount of pixels in the micron bar. Images were then converted into grayscale, and further into binary for cavitation analysis. The images were then analyzed using the “analyze particles” feature which automatically averaged the amount of white (representing a value of 0) and black (representing a value of 1) within each column of the image, resulting in a gray value number. The gray value number was converted to a count of black pixels which was used to calculate the void density within each column of the image and was used in plotting of the data.

Electron backscatter diffraction (EBSD) was conducted on an FEI Teneo FEG-SEM equipped with Hikari Pro high-speed EBSD detector. Individual scans at 500X magnification were collected using an accelerating voltage of 25 kv, spot size of 13, working distance of 18 mm with the sample tilted to 70°. The EBSD camera was set up to collect data with at a 0.9 um step size on the ultra fast setting, which resulted in data collection at approximately 400 points per second equating to an 8 min scan time. Using the accompanying EDAX Teams analysis software, individual scans were stitched together manually for final analysis.

Two grain size analysis methods required the sample to be etched. Etching was performed with electrolytic nital (2% Nital@6V for 20-30 s). Manual grain size measurements were conducted on stitched images using traditional lineal intercept procedures in accordance with ASTM E112 for equiaxed grains. Automated image analysis for grain size was conducted using MIPAR Version 3.0.4 (Ref 30) with a custom recipe tailored to equiaxed grains with twins present. Due to surface etching effects and some fine carbides being identified as fine grains, the final analysis only included measured grains greater than 10 micros for mill annealed samples, 30 microns for samples solution annealed at 1150 °C, and 50 microns for samples solution annealed at 1190 °C.

4 Results

4.1 Initial Microstructures

Figure 1 shows typical through-thickness optical microstructures for the starting sheets comparing the MA versus the SA + Age condition and the defined grains from the automated grain size analysis. It should be noted that these images have been truncated and the automated analysis area was approximately 2.5 times larger than what is shown in the image. Significant grain growth is observed in the SA condition compared to the MA condition. Additionally, carbide ‘stringers’ are observed along the rolling direction. Etching was deeper at the sample edges and as can be seen the automated analysis does not select grains for analysis which intersect the sample edges. Figure 2 show the EBSD maps for all the starting microstructures at the same scale. The grain size is equiaxed and no clear orientation or texture is observed. Most grains show twinning typical of nickel-based austenitic materials. The MA materials appear to show a small increase in larger grains with decreasing thickness, and both SA conditions show significant increase in overall grain size. It should also be noted that the 0.46 mm EBSD images do not fill the box because the sheet thickness is less than the height of the box. It can be seen in the case of the 0.46 mm thick 1150 °C-SA sheet that there are only a few grains on average through the thickness of the sheet in this specific location. Table 2 summarizes the grain size measurements and Fig. 3 provides the statistic box plot of the individual grains measured by the automated image analysis routine. Overall, the data show increasing grain size with solution annealing at 1150 °C and further grain coarsening with the long-term 1190 °C-SA. While the average grain sizes are all reasonable for typical wrought structures, Fig. 3 identifies outlier grains (beyond the 95th percentile) generally > 200 microns in some cases approaching 1 mm in size.

Fig. 1
figure 1

Typical optical image and corresponding automated grain size analysis for the MA (a, b) and SA (c, d) 0.94 mm sheet. Rolling direction is in the horizontal plane

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Fig. 2
figure 2

EBSD maps for all starting sheets, rolling direction is in the horizontal plane, through thickness in the vertical plane

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Table 2 Measured grain sizes
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Fig. 3
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Results of the automated grain size analysis including outlier measurements beyond the 95th percentile

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4.2 Creep-Rupture Testing

Creep-rupture tests were all conducted at 750 °C at stresses from 200 to 320 MPa resulting in rupture times of ~ 100 to ~ 7000 h. The tabular results for all tests are shown in Table 3. All MA material was tested without aging since this is a likely use condition in some CHX designs based on brazing of thin fins. As noted previously, the standard creep testing practice followed in this research requires a minimum 1 h soak time at the testing temperature prior to initiating the creep test which effectively provides an aging heat-treatment at this test condition. To ensure that testing in the non-aged condition would produce equivalent results to the standard alloy 740H aging heat-treatment and thus valid comparisons, one 1.65 mm MA sample was aged prior to testing and a duplicate test was run at 220 MPa. The rupture lives were nearly identical with the MA sample having a life of 1192.2 h and the MA + Age of 1238.6 h. Rupture ductility (elongation and reduction of area) and minimum creep rates were all similar. This finding of no effect of aging on the creep behavior 740H when tested at temperatures of 700 °C and above is consistent with the findings of other researchers (Ref 31, 32).

Table 3 Creep-rupture test results
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Figure 4 provides a comparison of the creep-strain versus time curve and creep-rate versus time curves for the 1.65 mm sheets tested at 265 MPa. Inspection of the MA material in the figure shows a typical alloy 740H creep curve with a minimal primary regime followed by a modest secondary creep regime and most of the alloy’s deformation taking place in the tertiary regime. The 1150 °C-SA + Age results in a lowering of the minimum creep rate by a factor of about 7 and a corresponding rupture life improvement of 4.2X. The 1190 °C-SA + Age sample showed a similar minimum creep rate to the 1150 °C-SA sample, but the rupture life was only slightly longer than the MA material. Additionally, a large reduction in rupture elongation is observed. Inspection of the table shows this change in rupture ductility (both reduction of area and elongation) is consistent for all the test conditions for this sheet thickness where the MA material had the highest ductility at ~ 15-22%, the 1150°SA was slightly lower at ~ 9-12%, and the 1190 °C-SA was significantly lower at only ~ 1-4%.

Fig. 4
figure 4

Creep-curves for 1.65 mm sheets with different heat-treatments at 750 °C-265 MPa

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Figure 5 shows the creep curves for all three thicknesses of MA sheet at 265 MPa. The creep deformation and rupture times are similar for the 1.65 mm and 0.94 mm sheet, but a modest reduction in creep rate of 2-3X and corresponding rupture life increase is observed in the thinnest (0.46 mm) sheet. Rupture ductility was lower in the thinnest sheet but was similar to the 1150 °C-SA sample in Fig. 4. Figure 6 compares the SA + Aged samples tested at 200 MPa for all three sheet thicknesses. These were the longest durations tested with the 1.65 mm sheet with the 1150 °C-SA sample having the longest rupture life of 6,901.5 h. All other conditions, despite the different SA temperatures and times sample had similar creep rates, but the final strains at rupture were about 4% and the life was about ½ of that of the 1.65 mm 1150 °C-SA. An additional observation of all the creep curves is that although the the time spent in primary creep (decreasing creep rate) and the magnitude of the minimum creep rate can vary significantly, in most cases for the same stress level the time to onset of tertiary creep is reasonably similar.

Fig. 5
figure 5

Creep-curves for MA sheets of varying thicknesses at 750 °C-265 MPa

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Fig. 6
figure 6

Creep-curves for SA + Aged sheets of varying thickness and heat-treatment conditions tested at 750 °C-200 MPa

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All creep samples were sectioned for metallographic analysis after testing. Figure 7 shows the characteristics of the creep damage in the gauge of all the 1.65 mm thick sheets. The MA material appears to show the highest propensity for cavitation and grain boundary decohesion and some bias towards increased damage at the surface of sheets. Longer-test durations appear to result in increased density of creep damage with extensive micro-cracking throughout the sample. Similarily, the 1150 °C-SA samples showed a mix of individual cavitation and grain boundary decohesion which was uniform throughout the gauge, but the overall amount of damage was much less than the MA materials. For the 1190 °C-SA sample, few cavities were observed, but the coarse grain size (relative to the sheet thickness) is visible and most damage is entire grain boundary decohesion for grain boundaries oriented normal to the applied stress. Since all samples were tested until failure it is not possible to create a full description of the evolution of damage, but by comparing the different locations within the samples (near and far away from the failure) and multiple testing times, it appears the large amount of micro-cracking in the longer-term tests indicates the growth and coalescence of creep voids over time which is most prevalent in the MA material and the thicker SA materials. While oxide filled cracks surface were observed in some samples, these did not appear to lead to creep failure. This is shown in Fig. 8 on the 0.94 mm thick sheet which shows the failure location for the MA and 1150 °C-SA conditions. Figure 8 shows clear evidence of fine grain boundary creep voids forming in the SA condition but minimal microcracking with a low ductility failure via a few large grains. Conversely, the finer grains in the MA material allow for a large number of microcracks to form before they link up and eventually cause failure. To minimize bias in image selection and interpretation, Fig. 9 compares the through-thickness area distribution of creep damage in the MA and 1150 °C-SA 1.65 mm samples. The 1150 °C-SA samples all showed essentially equivalent area fractions of creep damage with no change in thickness confirming optical observations of relatively uniform isolated cavity formation and grain boundary decohesion. In contrast, the finner grain MA samples show higher propensity for creep damage to occur near the sample surfaces which persisted for all test conditions with lower stress longer-term tests having increased damage.

Fig. 7
figure 7

Cross-sectional optical metallography (unetched) in the gauge section of all the 1.65 mm thick sheets after creep testing

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Fig. 8
figure 8

Creep failure location for the 0.94 mm thick sheets after creep testing at 200 MPa. Applied stress was in the horizontal direction

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Fig. 9
figure 9

Through thickness cavity analysis for 1.65 mm sheets

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5 Discussion

Review of the data in Table 2 and the more detailed creep curves presented in Fig. 4, 5, and 6 suggest a more complex relationship exists to describe creep behavior which includes both grain size and/or grain size distribution and sample thickness. Furthermore, the observations of post-test creep samples (Fig. 7, 8) and the damage analysis in Fig. 9 clearly shows that the amount of damage depends on heat-treatment, test conditions, and thickness. To explore the relationship between the traditionally measured ASTM lineal intercept grain size and the automated analysis, Fig. 10 plots the measured equivalent grain diameters to the ASTM size in (Figure Table 2). Overall the trends are consistent, but a direct relationship does not exist between the average grain diameter and the ASTM grain size. Understanding that grain size is not an exact number but a distribution and appreciating that there are numerous challenges in digital image capturing and processing to produce accurate and repeatable results (Ref 33, 34), it appears that for finer grain sizes the two methods are in agreement in part due to a relatively normal distribution (see box plots in Fig. 3), but for the samples with the larger grain sizes and large outlier grains, the average grain size (via automated analysis) is not the best methodology for capturing the influence of these large grains. In these cases, the ASTM method falls between the 75th and 90th percentile of the distribution.

Fig. 10
figure 10

Comparison of ASTM grain size to grain size measurements from the automated analysis (see Fig. 3)

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To compare the creep test results for the sheets in this study to typical wrought alloy 740H, the time-to-rupture, minimum creep rate, and rupture ductility (elongation and reduction of area) were plotted against the range of data for the existing alloy 740H database at 750 °C (Ref 27, 32, 35) in Fig. 11. Only one condition, the 1.65 mm sheet 1150 °C-SA fell within the typical alloy 740H range for rupture life, minimum creep rate, and rupture ductility. All of the MA sheets showed below scatter band rupture life creep resistance but good (in most cases above average) ductility. The 0.94 and 0.46 mm SA sheets showed creep resistance at the bottom of the expected scatter band but due to lower creep ductility resulted in rupture lives slightly below the typical 740H behavior. The long-term 1190 °C-SA 1.65 mm sample had good creep resistance but very low rupture ductility (< 5% in all tests) resulting in shortened rupture life. Since many materials show a direct relationship between rupture life (tr) and minimum creep rate (\({\dot{\varepsilon }}_{\mathrm{min}}\)) per the monkman–grant (M–G) or modified M–G relationship (Ref 36):

$$\frac{{\dot{\varepsilon }_{{{\text{min}}}}^{m\prime } }}{{\varepsilon_{{\text{r}}} }} \times t_{{\text{r}}} = {\text{C}}\prime$$
(1)

where m’ is a material parameter, C’ is the modified M–G constant and εr is the elongation at failure, the data were plotted in Fig. 12. Significant variation is observed between tests which is comparable to the distributions of creep rates in the wrought database. No satisfactory M–G fits could be made to the database or the sheet data even when accounting for rupture ductility. The global data suggest that the characteristic creep curves for this alloy, which only shows a limited region of secondary creep with most of the creep behavior dominated by tertiary creep (see Fig. 4, 5, 6), leads to challenges in applying the traditional M–G relationships. Similar challenges have been found in creep analysis of other nickel-based alloys (Ref 37). The lack of convergence for the tests in this study, which was conducted within a limited stress range and only at one temperature, indicates the sample thickness and grain size may both be affecting creep-rupture behavior.

Fig. 11
figure 11

Time to rupture, minimum creep rate, and rupture ductility as a function of stress for all tests compared to the alloy 740H wrought database

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Fig. 12
figure 12

Relationship between rupture life and minimum creep rate

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To clarify the effects of grain size and sheet thickness, the sheet thickness was dived by the average ASTM grain size (ST:GS ratio). These ratios were then compared in Fig. 13, to the following:

  • The ratio of the applied test stress to the stress required to produce the same rupture time for average alloy 740H behavior based on the rupture life equations in ref (Ref 26), i.e. a ratio of 1 would equal average alloy 740H rupture predictions and a ratio of 0.8 equals a 20% reduction in creep performance on the basis of stress.

  • The creep damage tolerance factor (λ) which is the reciprocal of the modified M–G constant (C’) assuming m’ = 1 as follows:

    $$\lambda = \frac{1}{{{\text{C}}\prime }} = \frac{{\varepsilon_{r} }}{{\dot{\varepsilon }_{{{\text{min}}}} \times t_{r} }}$$
    (2)

  • The measured rupture ductility (elongation and reduction of area)

Fig. 13
figure 13

Analysis of ratio of rupture life, lambda, and rupture ductility as a function of Sheet Thickness to Grain Size (ST:GS)

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Additionally, the average, minimum, and maximum values from the alloy 740H database are indicated on the y-axis. It should be noted that individual datapoints could not be plotted since the alloy 740H database, where reported, utilizes standard sample geometries typically 6.35 mm diameter and greater and only some heats have reported grain sizes.

Inspection of the figure and analysis of the data show that no clear trend is observed in rupture life as a function of ST:GS and, as indicated previously, only one combination of grain size and thickness met average rupture life with all datapoints falling within expectations. Similarly, the Lamda parameter does not show a clear trend which is likely due to the same reasons discussed earlier for lack of obtaining an acceptable M-G relationship. Some researchers have suggested a minimum Lambda of 5 is needed for a material to have sufficient ‘intrinsic ductility’ to redistribute stresses when subjected to multiaxial creep which may be an important consideration for the design of engineering structures operating at high-temperature (Ref 38). On this basis, about \({1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}\) the datapoints at a ST:GS ratio < 10 do not meet the 5% criteria. When comparing the ST:GS ratio to all the rupture ductility data, a clear trend to increasing ductility with increasing ratio is observed. Based on comparison to the alloy 740H wrought database, nearly all the rupture ductility data falls below the scatter band when the ST:GS ratio is < 10 and the effect saturates at a ratio > 20.

Ali and co-workers (Ref 39) conducted creep tests on 0.25 mm thick stainless steel foils and found significant differences in rupture life and creep rate when comparing their data to wrought databases which they proposed was due in part to differences in creep mechanisms in the foils at lower stresses. Furthermore, they had to significantly alter the M–G relationships in order to fit the data, but no data were provided on grain size, and ductilities were all reasonably high (> 10%). Based on the data generated in this study, it does not appear a difference in creep mechanism is responsible for the variation in creep-rupture life and ductility. Figure 7 shows that minimum creep rates are similar at larger grain sizes but increases at finer grain sizes which is consistent with a grain boundary sliding mechanism in the power law regime (Ref 40). Detailed characterization including transmission electron microscopy analysis of dislocation-precipitate interactions was conducted by Unocic et al. on alloy 740 indicating ‘grain interiors are more resistant to deformation than the grain boundaries’ (Ref 41) which supports a grain boundary sliding mechanism and thus a grain size dependence on creep performance. Although most of the samples did not meet the wrought scatterband for rupture life, all samples with grain size > 50 μm did fall within the base metal scatterband for creep rate. Inspection of the creep-rate versus time curves (Fig. 4, 6) show that while the magnitude of the minimum creep rate is dependent on sheet thermal history and thickness, the time to the start of tertiary creep is reasonably similar for all samples. Thus, when grain size is sufficiently larger, > 50 μm for this study, the differences in rupture life is related to the rupture ductility. The physical evidence supports a similar creep damage process for all samples as follows:

  1. 1.

    For the finer grain materials, < 50 μm, with ST:GS ratio > 20, the creep rate is high but failure of one grain boundary (via cavitation and grain boundary decohesion) results in a small local stress increase which is accommodated through stress redistribution throughout the sample. The result is a high fraction of cavitated grain boundaries throughout the sample (Fig. 7, 8) which is shown to be much higher in cavity density than the other samples (Fig. 9).

  2. 2.

    For coarser grain materials, > 50 μm, with a ST:GS ratio < 20, creep rates are generally comparable but a clear decrease in rupture ductility is observed with decreasing ST:GS falling from ~ 10 to 4% leading to a corresponding decrease in rupture life.

Thus for ‘optimum’ performance to ensure in-scatterband wrought creep behavior, a sheet should have a grain size > 50 μm and a ST:GS ratio > 10 which equates to an ~ 1 mm thick sheet based on these creep test results at 750 °C. The result is the 1.65 mm 1150 °C-SA sheet, which is the only combination to meet this criterion, had the highest Lamda parameter.

Considering the variability of large creep-rupture data sets from multiple sources representing multiple product forms, in order to ensure in-scatterband rupture ductility, it appears the ST:GS ratio should be about 10 which is greater than the typical ‘rule-of-thumb’ for 3-5 grains to ensure homogenous behavior often cited in the literature. In reality, grain size is not a single number but a distribution (see Fig. 3) and examination of the data in Table 2 and Fig. 10 show that the 95% confidence interval and largest maximum outlier for the best performing samples was about 200 and 300 μm, respectively, which translates into a minimum of ~ 3 to ~ 8 grains for the ‘worst-case’ location.

6 Conclusions

A comprehensive study was conducted on thin metallic sheets of nickel-based alloy 740H subject to various heat-treatments to examine the role of grain size and sheet thickness on long-term creep performance at 750 °C. The results showed that when grain size was fine, < 50 μm, and the sheet thickness to grain size (ST:GS) ratio was large, > 20, the alloy had good creep ductility but reduced creep performance, likely due to enhanced grain boundary sliding, resulted in a reduction in creep-rupture life. Conversely, when grain size was coarser, > 50 μm, creep ductility was found to be a function of ST:GS ratio and when ST:GS < 10, low-rupture ductility resulted in poor creep-rupture life. An optimum combination of grain size > 50 μm and ST:GS > 10 appears necessary to achieve typical wrought behavior. These findings are in contrast to most literature which presume only 3-5 grains are needed to ensure bulk material behavior. Considering the statistical distribution of grains within these samples, the minimum number of grains likely to occur in samples with wrought scatterband creep strength and ductility was between 3 and 8 grains. For practical engineering application, if designing components and heat-treatments to meet the > 50 mm and ST:GS > 10 ratio is not possible, finer grain sizes are likely preferred as they show acceptable levels of damage tolerance even if rupture life is moderately reduced.