Thermal Aging Effects on the Yield and Tensile Strength of 9Cr-1Mo-V (Grade 91)

The ferritic class of steels typically experience reductions in strength with extended exposure to high temperatures resulting from changes in the material microstructure, essentially long-term tempering. Reliable prediction of the strength reduction is important for design and operational safety of components made of these steels.

For elevated temperature design of ASME pressure boundary equipment, the material time-dependent creep and stress-rupture strength is conventionally predicted by extrapolation of relatively short-term behavior via fitting of laboratory test strength data to a time-temperature parameter (TTP) such as the Larson–Miller parameter, the Manson–Haferd parameter, and the Orr-Sherby–Dorn parameter. These parameters represent some combination of time and temperature associated with the process or exposure conditions. The Larson–Miller parameter (LMP) [1] is the parameter most commonly used to forecast strength for any desired exposure time and temperature. An early example of using the LMP that led to the ASME boiler and piping code allowable stress for 2¼Cr-1Mo steel is the analysis of Smith [2]. A more recent exercise for 9Cr-1Mo-V (Grade 91) is found in the work of Swindeman et al. for ASME [3]. The underlying assumption of an Arrhenius process being operative and related support for application of the LMP is briefly discussed in the next section on use of the TTP parameter.

Prediction of the time-independent yield and tensile strength reductions with elevated temperature aging, on the other hand, has received far less attention mainly because they often do not control lifetime, and therefore have relatively less elevated temperature design relevance. However, the ASME Boiler and Pressure Vessel Code (BPVC), Section III, Division 5 for high temperature reactors, Subsection HB for class A metallic pressure boundary components, Subpart B for elevated temperature service (BPVC III-5, HBB) [4] stipulates specific rules for establishing the effect of thermal aging on the yield and tensile strength (HBB-2160). For the ferritic materials, 2¼Cr-1Mo (Grade 22) and 9Cr-1Mo-V (Grade 91), tabulated time-temperature-varying yield and tensile strength reduction factors are provided to 300,000 h above a specified temperature, except for the yield strength reduction factor for Grade 91 that is listed as 1.0, i.e., no reduction in yield strength prescribed, regardless of temperature or aging time to 300,000 h.

It is important to note that ASME BPVC III-5, HBB-2160, in the 2021 edition, introduced, for the first time, a definition of the strength reduction factor as the ratio of the average strength after aging to the code-tabulated strength at temperature. This new definition, however, is silent on how one may establish the average strength after aging. Since historic background on how the existing factors were developed is not retrievable, the data analysis approach taken for this investigation is consistent with conventional methods and with ASME BPVC practice in estimating the average unaged material strength to determine the average aged material strength. The term “strength” used throughout this paper refers to both yield and ultimate tensile strength, unless specifically stated.

For the ferritic materials, HBB-2160 prescribes a method for a single factor application in case of varying thermal exposure (varying times at differing temperatures) by computing an equivalent time at the maximum temperature of exposure for each temperature of exposure other than the maximum temperature, and adding these computed equivalent time values pegged to the maximum temperature, i.e., providing the time-temperature table cell for the required factor. The LMP TTP formulation is used for the prescribed equivalent time computation.

The BPVC III-5 strength reduction factor, as now defined, requires certain additional aging strength predictions beyond the conventional strength reduction prediction methods, as described below.

where T is the temperature in absolute units, t is time (typically in hours), and C is a constant generally material- and process-specific.

The HJP was developed to characterize and predict the strength response of ferritic-martensitic steel to tempering, as measured by hardness. Since then, there have been numerous studies on tempering using the parameter, e.g., Refs. [6–9], including for Grade 91 [6,9]. The use of the HJP for predicting the effect of (short-term) tempering has been extended to prediction of the effect of long-term thermal aging on the ferritic class of steels, e.g., Refs. [10–14]. Figure 1 is an example of the TTP representation of the thermal aging effect on Grade 91 strength as found in a historical archived report by Oak Ridge National Laboratory (ORNL) [14], normalized strength (aged divided by unaged material strength) versus the HJP. The fit curve, representing the predicted strength reduction ratio, is an exponential function of the HJP in this case.

where Q is the effective activation energy for the process, and R is the universal gas constant.

This property is recognized by the HBB-2160 prescription for computing equivalent time for aging at varying temperatures and times. Use of the normalized strength versus TTP method importantly allows for the collapse of the aging effect curves for a multitude of heats, varying unaged material strength conditions, and varying thermal exposures. This is analogous to the use of the TTP for representing creep rupture strength where a collapsed rupture strength versus LMP curve for various heats of material with varying time-temperature test conditions is the premise.

Key to the normalized strength-TTP application, naturally, is that the normalized strength consists of numerator (aged material) and denominator (unaged material) strengths measured with the same or nearly the same tensile testing parameters, e.g., temperature, strain rate, etc. such that the testing condition is not a significant extraneous influencing or confounding factor on the normalized strength. An analogous normalizing of strength is used in BPVC development of design yield and tensile strength at temperature, where, for a specific heat and product lot, the measured strength at temperature is divided by the strength at room temperature for a normalized strength versus temperature trend curve then used to establish the design strength by multiplying the trend curve with the specified minimum (room temperature) strength for design strength at any desired temperature.

Note the elimination of the subscript “i” referring to heat/lot “I” as long as the numerator and denominator of each R(T, t) ratio are from the same or nearly the same testing condition for the same heat/lot.

where S_C(T, 0) is the ASME BPVC III-5 code-tabulated unaged material strength—yield or tensile at temperature, T, as appropriate.

This study of the thermal aging effect on Grade 91 utilizes the conventional, normalized strength versus HJP representation that would likely have been used in development of the existing strength reduction factors in BPVC III-5. The analysis method follows the development of the master curve, R(T, t), of Eqs. (5) and (6) and average aged material strength, S_avg(T, t), as a function of temperature per Eq. (7), the latter using the BPVC trend curve approach to estimate the (population) average unaged material strength, S_avg(T, 0), to execute Eq. (7). Final reduction factors as a function of aging time and temperature, F(T, t), are computed from Eq. (8). Details on the analysis method are given later. In typical component condition and fitness-for-service assessment practice (e.g., Refs. [10] and [12]), the strength reduction ratio of Eqs. (5) and (6) is directly applied to any initial unaged material strength level—an original specified minimum, as-designed or-constructed, user-estimated, etc. The HBB-2160 new definition, however, requires extending the conventional reduction ratio estimation to the reduction factor per Eqs. (7) and (8). Both, Eqs. (5) and (8) analyses results are presented here. This paper represents a significant expansion on recent work by ORNL [15] with regard to the extent of data compiled and analyzed and application of the HBB-2160 new definition of the strength reduction factor [4].

where σ_fer is the minimum strength of thermally aged 9Cr-1Mo-V represented by fully annealed Fe-9Cr, σ_ss is the strength from Mo solid solution strengthening, σ_sg is the strength from subgrain boundary strengthening, and σ_MX is the strength from MX precipitation hardening.

The model development utilized laboratory data on two control heats, including one ORNL heat, aged at 550, 600, and 650 °C with varying aging durations up to a maximum of about 64,000 h. In addition, the researchers tested and examined material removed from the grip section of specimens from five heats creep-tested by ORNL at 427–538 °C up to 134,000 h and material removed from an ex-service boiler tube reportedly exposed to steam conditions for an extended duration.

The physics-based model is not the subject of this paper and interested readers may refer to Refs. [16–18] and a critique of the model [19] for details.

To provide as much information as possible for the aging effects analysis, the strength data of aged and corresponding unaged Grade 91 heats/lots were garnered in a massive effort from separate collections of ORNL (743 tests) [20–24] and ANL (69 tests) [17,25,26]. The chemical compositions of the heats/lots, as reported in these references, were also reviewed. Reported chemistries of the ORNL crept specimen heats, not detailed here, indicate a few deviations from the current ASME SA-387, Grade 91, Type 1 material specification¹ for all heats except for the fully compliant heat 30383—deviations not considered significant enough to reject use of the strength data. The reported chemical composition of ANL Heat G91-H1 [17] excludes several elements relevant to alloy properties—Al, B, Cu, Ni, Ti. Conformance with the specification for this heat is not evaluated, although the data are used here.

In addition to the ORNL and ANL aged and corresponding unaged material strength data collection, this study leverages the results of a prior analysis for estimating the unaged average material strength as a function of temperature from a separate collection of unaged Grade 91 data (307 tests) [27]. That unaged material collection included much of the unaged material data in the ORNL database, but is significantly larger in the number of heats/lots since its use for the average strength analysis does not require having corresponding aged material strength data. For the ORNL and ANL collections, particular care was taken to include metadata such as details of the material heat/lot, test temperature, and strain rate for subsequent inventory data compilation and critical data screening in order that testing condition effects would not confound the HJP analysis, as previously discussed. These compilation and screening requirements excluded unaged and aged strength data that were unable to pair up under the same heat/lot and nearly the same tensile testing conditions.

Table 1 summarizes the inventory of aged Grade 91 data compiled from the ORNL and ANL collections [17,20–22,25]. The 172 data points are from six heats with seven unique heat-heat treatment combinations (lots). Since most of the data are on plate, and the remainder are also on other wrought product forms, the product form has not been considered in defining lots for the analysis. Aging temperatures ranged up to 704 °C with aging times around or exceeding 100,000 h in a few cases (four data points for material aged at 427–538 °C). The ORNL data were generated mostly at a testing strain rate of 0.4%/min, except for some tests ranging from 0.004 to 8.0%/min. for strain rate effects studies (the ASTM standard stipulates 0.5%/min for yield strength determination). All of the ANL tensile tests were conducted at a strain rate of 6.0%/min. For completeness, the heat treatments listed are as reported, and so identified, although review of the source references indicate heat treatments A and B are very likely the same, and therefore have been treated as such in the analysis.

The compilation of data on unaged Grade 91 identified usable data from heats/lots for which corresponding aged material strength data are available, as summarized in Table 2 [20–26]. The 114 data points are from six heats with seven unique heat–heat treatment combinations (lots) tested at room temperature (20, 25, 38 °C) and elevated temperatures (427–704 °C) for which aged material strength data are available for the same heats/lots. As previously noted for the aged material strength data of Table 1, heat treatments A and B are very likely the same.

The primary screening exercise, in addition to excluding a few collected data obviously in error or duplicated, involved examining the tensile test conditions before computing the aged-to-unaged normalized strength ratio for a given heat/lot to ensure that the ratios for a data point are for the same or similar testing temperature and strain rate.

With respect to the testing temperature, 649 and 650 °C are considered the same testing temperature and 20–38 °C are considered as room temperature. With respect to the test strain rate, analysis as shown in Fig. 2 indicates a significant effect on the strength at temperatures > 482 °C. Thus, for the test data above 482 °C, care was taken to ensure that the ratios were computed for three separate classes of strain rate, i.e., (a) 0.004 and 0.008; (b) 0.4; and (c) 4, 6, and 8 [%/min.], with each class comprising test data from similar testing conditions. In cases where there are no unaged material test data to pair up with aged test data for the class, the aged material data are excluded from the analysis. There were four aged material data points whose testing strain rate was not reported, and the testing strain rate of their counterpart unaged test data was assumed based on the fact that they were from the same data source with the corresponding heat/lot.

There may be a specimen configuration effect in the ANL test data generated via subsize sheet and rod specimens extracted from the ORNL crept specimen grip sections in comparison with the test data on the same heat/lot of unaged material generated on standard specimens. There is, however, little available information to help establish the possible effect, and therefore specimen configuration was ignored in this analysis.

Table 3 summarizes the inventory of the 145 aged material data points used in the analysis following the critical data screening. The inventory includes 47 room temperature test data points and 98 test data generated at the aging temperature. These screened data points are from five heats with six unique heat–heat treatment combinations (lots). A comparison with those before the screening in Table 1 shows that 27 elevated temperature (>482 °C) test data points are now excluded from the analysis. The most significant loss from the screening are two data points, each from heats 5349 and 10148 on the ORNL crept specimen material exposed to 538 °C for approximately 133,000 and 82,000 h, respectively. Both data points were generated by ANL at a strain rate of 6%/min. while the corresponding unaged material test data from historical archives were generated at 0.4%/min.

Figure 3 illustrates an aging time-aging temperature graphic representation of the 98 screened aged material data tested at the aging temperature. The inclusion of the 47 room temperature test data points, not shown here, does not significantly alter the graphic. For aging temperatures > 550 °C and aging time > 50,000 h, there are only six data points (overlap precludes visibility of all points), pertaining to two heats, with a maximum of 75,000 h at 593 and 649 °C for three of those data points from a single heat, heat 30176. The aging exposure conditions of the data have implications with regard to predictive extrapolations to long durations such as 500,000 h for aging temperatures to 650 °C being sought by BPVC III-5, supporting the need for suitable quantification of uncertainties as done by BPVC for creep rupture strength-based design.

The data analysis involved several steps, and each is briefly described along with a presentation of relevant results.

The first step in the analysis is the computation of each yield and tensile strength ratio (normalized strength) data point, R_i(T, t), per Eq. (3). For each aged material strength datum (numerator), S_i(T, t), the corresponding unaged material strength datum (denominator), S_i(T, 0), needs to be established. This involved (a) identification of unaged material strength data pertaining to the same heat/lot as the aged material strength datum and from tests at the same temperature, and also for tests at > 482 °C, the same class of strain rate as for the aged material strength datum; (b) computing an average unaged material strength from the identified data in (a), representing the denominator, S_i(T, 0). In computing the average in (b), a check was conducted in each case to ensure that data points outside of the 90% scatter band about the average are excluded. Only five data points were thus excluded for the strength average computation—three from room temperature tests and two from elevated temperatures.

The resulting normalized yield and tensile strength data points, denoted by R_YS-i(T, t) and R_TS-i(T, t), respectively, are thus prepared for the HJP analysis.

This step of the analysis involves:

• Estimation of the optimal value for the HJP constant, C;

• Polynomial regression curve-fitting of the R_i(T, t)–HJP, specifically R_YS-i(T, t)–HJP and R_TS-i(T, t)–HJP for yield and tensile strength, respectively, both a best-fit relationship and a lower-bound relationship, analogous to the BPVC procedure for developing allowable stresses in the creep regime; and

• Evaluating the room temperature data for inclusion in the analysis, which are aged material strength data generated at room temperature instead of the aging temperature.

The R(T, t)–HJP relationships from the regression curve-fits may be used for component condition and fitness-for-service assessments and are the baseline ratios used to develop the BPVC III-5 strength reduction factors. The relationships were first developed for data from tests at the aging temperature, excluding data from tests at room temperature. However, a statistical analysis was additionally conducted to examine whether the room temperature data belong to the aging temperature dataset, considered for inclusion in the analysis for the general component condition and fitness-for-service application, but not for the BPVC III-5 strength reduction factors estimation.

For each of the yield and the tensile strength datasets for tests at the aging temperature, a second-order R_i(T, t) versus HJP (Eq. (6)) regression relationship was examined for an assumed HJP constant, C, varying from 10 to 30. The C = 10 results in both cases produced the highest regression coefficient, R², and lowest standard error of the estimate (SEE). The C = 10 value was thus chosen for the final regression analysis. This value is notably the same as prescribed by BPVC III-5 for equivalent aging time calculations [4], and is in the range recommended by the ECCC for its second-order fit on rotor steels (7.8–15.82) [12].

Both first and second-order R_i(T, t) versus HJP regression curve-fits were examined. In case of the yield strength data, R_YS-i(T, t) versus HJP, both fits gave comparable R² and SEE. In case of the tensile strength data, R_TS-i(T, t) versus HJP, the second-order fit exhibited a superior fit than did the first-order. For both sets of analyses, the second-order fit was used. Discussed first are curve-fits to data from tests at the aging temperature only.

with HJP = T(°K)[10 + logt(h)], R² = 0.65, and standard error of the estimate, SEE = 5.8018 × 10⁻².

with SEE = 5.8018 × 10⁻².

with HJP = T(°K)[10 + logt(h)], R² = 0.69, and standard error of the estimate, SEE = 5.7263 × 10⁻².

with SEE = 5.7263× 10⁻².

Equations (10)–(13) provide the basis for computing the BPVC III-5 strength reduction factors, as described later.

For the component condition and fitness-for-service application, the inclusion of the room temperature test data in developing the master R(T, t)–HJP curve is explored. The inclusion could enhance the database and make the relationship useful for predicting room temperature strength after aging, provided it can be shown that there is no statistically significant reason to conclude that the room temperature test data do not belong to the population of all test data (room temperature and aging temperature) data. The null hypothesis tested is that the mean of the error or difference between the room temperature normalized strength and the predicted best-fit curve normalized strength for all data is zero; i.e., perfect conformance to the curve-fit. This null hypothesis was tested for the yield and tensile strength using the t-distribution, with the critical region for rejection of the null hypothesis given by t < 2.015 and t > 2.015 for a sample size of 45 data points (for both yield and tensile strength) and a significance level, p = 0.05.

Figure 7 shows the analysis results for tensile strength including the room temperature data, as identified in the graph. The computation for its null hypothesis test produced a t-distribution value of 32.8064, well in the rejection region at p = 0.05, indicating the hypothesis is found easily rejectable, i.e., the room temperature data may not be considered to belong to the overall dataset, and therefore may not be used for elevated temperature predictions. Indeed, the data as seen on the graph generally appear to be above the best-fit line. While the curve-fit results are given in Fig. 7 for completeness, the curve of Fig. 5 along with Eq. (12) is recommended instead for component condition and fitness-for-service applications pertinent to the aging temperature only. The reasons for the room temperature normalized tensile strength data generally exceeding the best-fit prediction are not known, but the observation suggests caution with regard to application of the reduction ratio prediction to temperatures other than the aging temperature.

This part of the analysis seeks to extend the computed strength reduction ratios to the ASME BPVC III-5 strength reduction factors as defined in the 2021 edition of BPVC III-5 HBB-2160:

• Select an appropriate strength reduction ratio prediction curve, R(T, t)-HJP

• Estimate the average aged material strength, S_avg(T, t), at the aging temperature by Eq. (7), i.e., S_avg(T, t) = R(T, t). S_avg(T, 0). This requires first estimating the average unaged material strength at temperature, S_avg(T, 0).

• Compute the strength reduction factor, F(T, t), per Eq. (8) as the ratio of the average aged material strength to the code-tabulated strength, S_C(T, 0); i.e., F(T, t) = S_avg(T, t)/S_C(T, 0)

Figure 8 shows a workflow chart summarizing the various steps taken in the data analysis process. The chart also delineates the relatively straightforward analysis actions associated with the determination of the strength reduction ratio for component condition and fitness-for-service assessment, as described earlier. The workflow is illustrated in terms of the relevant equations associated with each calculation step, with the definition of the symbols and description of the equations given in the preceding and following text.

Selection of the prediction curve for strength reduction factor estimates involves two primary considerations: (a) curves derived from data on aged material tested at the aging temperature, consistent with the manner in which the strength reduction factors are defined and used; and (b) a suitable lower-bound prediction curve to accommodate the limited data and uncertainty associated with extrapolation to long durations.

Equations (10)–(13) and Figs. 4 and 5 represent the available curves for selection. The SEE values provided for the best-fit Eqs. (10) and (12) allow for a user to develop lower-bound predictions for any lower-bound % of choice. Equations 11 and 13 are specifically for the 95% lower-bound and have been selected in this analysis. As noted earlier in the section “Critical Data Screening” regarding Fig. 3, the distribution of data impacts the uncertainty of the extrapolations to long durations such as 500,000 h for aging temperatures to 650 °C being sought by BPVC III-5.

Based on the above considerations, and consistent with the BPVC practice of using a minimum strength defined as the approximate 95% lower-bound of the rupture strength curve to establish time-dependent design allowable stresses, the selected reduction ratio curve for computing the BPVC III-5 strength reduction factor in this analysis is the 95% lower-bound curve, i.e., Eq. (11) for yield strength and Eq. (13) for tensile strength.

As an added driver for use of a lower-bound, the strength reduction factor per the new HBB-2160 definition represented by Eq. (8), which utilizes the average aged strength as the numerator (not a minimum) and the code-tabulated strength as the denominator (close to a minimum), may significantly exceed an expected minimum factor with use of a best-fit strength reduction ratio curve, particularly in long-term exposure. For perspective, this aged material dataset contains 12 aged material yield strength data points less than the BPVC III-5-tabulated yield strength, including three from tests at the aging temperatures of 493 °C for 75,000 h, and 649 °C for 50,000 h and 75,000 h. The aged-to-code strength ratio for the 649 °C data are < 0.80. BPVC III-5 Table HBB-3225-2 currently prescribes a strength reduction factor of 1.0, or no reduction for all aging conditions through to 650 °C and 300,000 h. For the aged material tensile strength data, there are 32 data points less than the BPVC III-5 tabulated tensile strength, including 22 from tests at the aging temperature with some from material aged at 593 °C for as little as 10,000 h. The data also include 6 data points with an aged-to-code strength ratio of < 0.80. The current BPVC III-5 time-temperature tabulated prescription (Table HBB-3225-4) includes just one strength reduction factor value < 0.80, at 650 °C for 300,000 h (0.78).

To apply the HBB-2160 new definition of strength reduction factor, the average aged material strength as a function of temperature, S_avg(T, t), in Eq. (8) needs to be estimated. BPVC III-5, however, does not specify how such an average strength is to be determined, and the procedure used here follows Eq. (7), i.e., application of the strength reduction ratio, R(T, t), to the average unaged strength, S_avg(T, 0). Since BPVC III-5 also does not list average unaged strength, S_avg(T, 0) has been derived in a manner consistent with well-established BPVC practice.

As mentioned earlier in the section, “Data Collection,” the results of a prior analysis conducted for estimating the unaged average material strength as a function of temperature from a separate database of unaged Grade 91 [27] are used here. The compiled unaged material strength dataset analyzed is more extensive with regard to the numbers of heats/lots than the dataset used for the aged strength HJP analysis since it is not constrained by the analysis requirement to have heats/lots of counterpart aged material strength data. The compilation is judged to represent an expansion over that which would have been used decades ago to develop the current BPVC design yield and tensile strength values. For each of yield strength and tensile strength, the analysis covered a total of 27 heats/lots with 307 data points, including 258 points with strength data above room temperature, generally extending to 650 °C and up to 760 °C in some cases. The analysis followed the BPVC trend curve practice for establishing time-independent strength (yield and tensile), in which unitless normalized strength (ratio of strength at temperature to strength at room temperature) is established as a dependent variable of temperature, and the ratio trend curve is then derived via regression of heat/lot-specific data points of the normalized strength. Typically, polynomials of fourth- and fifth-order in temperature are found to be suitable. In this analysis, a fifth-order polynomial was used to represent the best-fit normalized strength trend curve. Figure 9 from Ref. [27] shows the normalized strength data and resulting trend curves, r_Y(T) and r_T(T), for the yield and tensile strength, respectively, applicable to the temperature range as shown.

where R_TS(T, t) is a lower-bound tensile strength reduction ratio given by Eq. (13) and S_avg-TS(T, 0) is the average unaged material tensile strength at temperature given by Eqs. (16) and (18).

where S_avg-TS(T, t), the average aged material tensile strength, is per Eq. (20), and S_C-TS(T, 0) is the BPVC III-5-tabulated tensile strength per Table HBB-3225-1 [4]. The final computed strength reduction factors are constrained to ≤ 1.0 by definition so computed values exceeding 1.0 are set to 1.0.

Tables 4 and 5 for yield and tensile strength aging reduction factors, respectively, summarize the thus computed factors for aging conditions to 650 °C and 500,000 h, applicable to BPVC III-5.

Observations made from the results of Tables 4 and 5 are:

• In comparison with the current BPVC III-5 tabulated yield strength reduction factor of 1.0 for aging temperature and time conditions up to 650 °C and 300,000 h per Table HBB-3225-2 [4], the computed values of this analysis are <1.0 for aging at 650 °C for ≥ 100,000 h, and at 625 °C for 300,000 h.

• In comparison with the current BPVC III-5 tabulated tensile strength reduction factors for aging temperature and time conditions up to 650 °C and 300,000 h per Table HBB-3225-4 [4], the computed values of this analysis are < the BPVC III-5 factor in several instances. Of prime relevance are the computed values for aging at 300,000 h at 600, 625, and 650 °C.

• For the tensile strength reduction factors tabulation, several of the computed factors at <550 °C for aging durations ≤100,000 h appear unexpectedly low. A close examination indicates that the primary reason for these low values lies in the HBB-2160 new definition as shown in Eq. (22), coupled with the fact that the code-tabulated strength or denominator, S_C-TS(T, 0), follows a trend curve (normalized strength based on the specified material minimum vs. temperature) that well exceeds the average strength trend curve or numerator, r_T(T) of Eq. (16), in the temperature range 375–525 °C. To explain, re-writing Eq. (22) with the numerator and denominator broken down

  $FTS(T, t)=Savg−TS(T, t)/SC−TS(T, 0)= [rT(T) · Savg−TS(RT) · RTS(T, t)]/[rT−C(T) · STS−min(RT)]$

  (23)

where r_T-C(T) is the trend curve for developing S_C-TS(T, 0) using the specified minimum (room temperature) material tensile strength, S_TS-min(RT), as anchor.

Ideally, r_T(T) = r_T-C(T), so these cancel out in Eq. (23) and the strength reduction factor follows the trend in the strength reduction ratio, R_TS(T, t). However, in the temperature range < 550 °C, the current BPVC-tabulated strength values indicate a trend curve ratio, r_T-C(T) ≫ r_T(T), i.e., a denominator higher than reflected by the average strength behavior. This relatively elevated code-tabulated design tensile strength effectively suppresses the reduction factor. In case of the yield strength, the two trend curves are comparable, so no such issue arises. Regardless, the computed factors from this comprehensive database reflect the magnitude of the reduction factors, given the existing code-tabulated design tensile strength values.

• In case of the tensile strength factors, there are several computed factors that exceed the current BPVC III-5 tabulated values in the temperature range ≥575 °C in the intermediate aging duration range of 10,000–100,000 h; i.e., current tabulations may be overly conservative.

• These results, along with the detailed description of the analysis provide a basis for updating the current BPVC III-5 tabulated strength reduction factors and assigning factors for aging to 500,000 h.

• The most comprehensive and updated collection of data including data recently generated by ANL in its physics-based model research is employed for this study. The collection includes much of the data generated by ORNL that likely went into the early development of the BPVC III-5 strength reduction factors. As such, the compilation represents a useful database for ongoing review and analysis relating to predicting Grade 91 time-independent strength changes with thermal exposure.

• Except for nondisclosure of the database itself, this paper strives to describe the analysis in sufficient detail for transparency, enabling independent critical review and other analyses going forward.

• For general component condition and fitness-for-service applications, a yield strength reduction ratio prediction given by Eq. (14) is recommended

  $RYS(T, t)=−9.9200×10−2+2.5435×10−4(HJP) – 1.3894×10−8(HJP)2$

  (24)

with HJP = T(°K)[10+logt(h)].

with HJP = T(°K)[10+logt(h)].

In all cases, the temperature, T, associated with the HJP is the aging temperature. The predictions may be applied to aged Grade 91 yield strength at room and at the aging temperature, and to aged Grade 91 tensile strength at the aging temperature only. Application to prediction of aged material strength at other temperatures is not recommended.

• For development of yield strength reduction factors for BPVC III-5, Eqs. (10), (15) (average unaged material yield strength), Eq. (17) (unaged material yield strength trend curve), Eq. (19) (average aged material yield strength), and Eq. (21) (yield strength reduction factor) may be used. Also provided is the SEE associated with the best-fit reduction ratio of Eq. (10), so an appropriate lower-bound % may be selected to accommodate the data distribution and uncertainty with extrapolation.

• For development of tensile strength reduction factors for BPVC III-5, Eq. (12) (reduction ratio), Eq. (16) (average unaged material tensile strength), Eq. (18) (unaged material tensile strength trend curve), Eq. (20) (average aged material tensile strength), and Eq. (21) (tensile strength reduction factor) may be used. Also provided is the SEE associated with the best-fit reduction ratio of Eq. (12), so an appropriate lower-bound % may be selected to accommodate the data distribution and uncertainty with extrapolation.

• Tables 4 and 5 summarize the computed yield strength and tensile strength reduction factors for the BPVC III-5 application, using a 95% lower-bound reduction ratio prediction, consistent with BPVC practice for setting allowable stresses in the time-dependent (creep) regime based on a TTP analysis of relatively short-term data. Computed yield strength reduction factor values are <1.0 (the current BPVC III-5 tabulated factor) for aging at 650 °C for ≥100,000 h and at 625 °C for 300,000 h. Computed tensile strength reduction factor values are < the current BPVC III-5 tabulated factor in several instances, including for aging at 300,000 h at 600, 625, and 650 °C.

Dr. Mark Messner, Argonne National Laboratory, is thanked for providing much of the valuable numeric data pertaining to the ANL physics-based model research.

This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy (DOE). The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.²

• U.S. Department of Energy (Grant No. DE-AC05-00OR22725; Funder ID: 10.13039/100000015).

ANL =

Argonne NationalLaboratory

BPVC =

boiler and pressure vessel code

F(T, t) =

ASME BPVC III-5-computed strength reduction factor applicable to aging temperature T, and time, t

HJP =

Hollomon–Jaffe parameter: T°(K)[constant + logt(h)], T, t are aging temperature and time for this application

LMP =

Larson–Miller parameter

ORNL =

Oak Ridge National Laboratory

R(T, t) =

strength reduction ratio, master curve of R_i (T, t) = f(HJP), heat/lot- and test conditions-independent

R_i(T, t) =

normalized strength datum for heat/lot “I”: strength after aging at temperature, T, for time, t—to-unaged material strength ratio

r_T(T) =

temperature, T-dependent trend curve ratio of tensile strength at temperature normalized for the yield strength at room temperature

r_T-C(T) =

temperature, T-dependent trend curve ratio of tensile strength at temperature normalized for the specified (room temperature) tensile strength, representative of the ASME BPVC design tensile strength at temperature

r_Y(T) =

temperature, T-dependent trend curve ratio of yield strength at temperature normalized for the yield strength at room temperature

S_avg(T, 0) =

average unaged material strength at temperature, T

S_avg(T, t) =

average aged material strength at temperature, T, after aging at temperature, T, for time, t

S_avg-TS(RT) =

average room temperature tensile strength of population, not a variable

S_avg-YS(RT) =

average room temperature yield strength of population, not a variable

S_C(T, 0) =

ASME BPVC III-5 code-tabulated design strength

S_i(T, 0) =

strength datum for heat/lot “I” for unaged material

S_i(T, t) =

strength datum for heat/lot “I” after aging at temperature, T, for time, t

S_TS-min(RT) =

specified material minimum tensile strength, a single value, not a variable

TS =

tensile strength. When shown as a subscript with a variable, it identifies the variable as applying to the tensile strength

TTP =

time-temperature parameter

YS =

yield strength. When shown as a subscript with a variable, it identifies the variable as applying to the yield strength

Conversions

°F =

[(9/5).°C] + 32

°R =

(9/5).°K

ksi =

MPa/6.894757