Creep deformation, rupture and ductility of Esshete 1250

ARTICLE IN PRESS

International Journal of Pressure Vessels and Piping 85 (2008) 89–98 www.elsevier.com/locate/ijpvp

Creep deformation, rupture and ductility of Esshete 1250$ M.W. Spindler, S.L. Spindler British Energy, Barnett Way, Barnwood, Gloucester GL4 3RS, UK

Abstract Esshete 1250 is an austenitic steel with high creep strength and is used as a superheater boiler tube material in UK power stations. While the rupture strength of Esshete 1250 has previously been characterised, there has been little work on its creep deformation or creep ductility. Hence, the European Creep Collaborative Committee (ECCC) Working Group 3B Austenitic Steels has collated data and performed assessments of the creep deformation and creep ductility of Esshete 1250. In addition, a review of the previous creep rupture assessments identified that there were problems with the fits at temperatures of 550 and 600 1C. Thus, a new rupture assessment has been made, which alleviates these problems. The assessments of the creep ductility and creep rupture are based on the mechanisms of failure and it is shown that there are interactions between the two models. The creep deformation model is shown to give a good prediction of stress relaxation. r 2007 Elsevier Ltd. All rights reserved.

1. Introduction

2. Creep deformation

Esshete 1250 is an austenitic steel with high creep strength [1] and is used as a superheater boiler tube material in UK power stations. In addition, Esshete 1250 is readily welded with either inert gas or metal arc welding and has been used for piping and headers in super critical plants. Furthermore, warm working can increase the tensile and creep properties of Esshete 1250, which enables it to be used for bolting applications [2]. The specification for Esshete 1250 is given in Table 1. While the rupture strength of Esshete 1250 has previously been characterised, there has been little work on its creep deformation or creep ductility. Hence, the European Creep Collaborative Committee (ECCC) Working Group 3B Austenitic Steels has collated and assessed the data on the creep deformation and creep ductility of Esshete 1250. In addition, a review of the previous creep rupture assessments identified that there were problems with the fits at temperatures of 550 and 600 1C. Thus, a new rupture assessment has been made.

The aim of this creep deformation model is to predict stress relaxation in Esshete 1250. For this reason, the plastic loading strains were not modelled and the creep strains were only fitted in the primary and secondary regions of the creep curves. The approach that was used was to fit the deformation model to the constant load data and then to compare the predictions of the model under conditions of strain control with the results of stress relaxation tests on Esshete 1250. The deformation model was then refined and re-fitted to the data until the model gave both a good fit to the constant load data and also a good prediction of the stress relaxation data.

$ This article appeared in its original form in Creep & Fracture in High Temperature Components: Design & Life Assessment Issues, 2005. Lancaster, PA: DEStech Publications, Inc. Corresponding author. E-mail address: [email protected] (M.W. Spindler).

0308-0161/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2007.06.004

2.1. Creep and relaxation data The ECCC Working Group 3B has collated the creep deformation data on seven heats of Esshete 1250. Two of these heats were tested after solution treatment at two different temperatures. There are 60 tests, which cover temperatures between 550 and 700 1C and engineering stresses of 46–420 MPa. Most of the tests (54) had continuous measurement of strain using an extensometer. However, six tests had interrupted strain measurement (ISM) at intervals of typically 1000 or 2000 h. It should be noted that there are many more ISM tests on Esshete 1250.

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Table 1 The composition of Esshete 1250 (X10CrNiMoMn NbVB 15-10-1), in wt%

Min. Max.

C

Si

Mn

P

S

Cr

Mo

Ni

B

Nb

V

Solution treatment (1C)

0.06 0.15

0.2 1

5.5 7

– 0.035

– 0.015

14 16

0.8 1.2

9 11

0.003 0.009

0.75 1.25

0.15 0.4

1050 1150

True Creep Strain (abs.)

0.006 0.005 0.004 0.003 Data Fit to Eq. (1)

0.002 0.001 0 0

50

100

150

200 Time (h)

250

300

350

400

Fig. 1. Example of a creep curve for Esshete 1250.

However, these could not be used, as in most cases only a few points were available for each test and it was difficult to extract parameters such as the strain and time at the end of primary creep or the minimum creep rate. The stress relaxation tests were conducted on doublebeam stress relaxation machines. The specimens were standard creep specimens with 40 mm gauge length and 7.98 mm diameter. Loading was carried out incrementally over 15 steps, until the requisite initial stress was reached. During the creep dwell, the load was manually reduced to maintain the indicated extension to within 70.002 mm. Seven tests were conducted, two at temperatures of 550 and 575 1C each and three at 600 1C. It was noted that initial plastic loading strains of up to 20% were measured in creep and relaxation tests that were above the proof stress. Such levels of plastic strain produce true stresses, which are larger than the engineering stress. Thus, to take the effects of plastic loading into consideration, the ‘engineering’ stress and strain values were converted into ‘true stress’ and ‘true strain’ values using the measured engineering strains and the usual expressions. 2.2. Model fitting The choice of equation for modelling the deformation data was made on the basis of the shape of the creep deformation curve. It was noted that the curves for Esshete 1250 parent material exhibited a sharp change in curvature as the material moved towards the end of the primary creep (see Fig. 1). Such large changes are not easily modelled using a Norton–Bailey type of equation and an exponential form, such as that used by Garofalo [3] for austenitic stainless steel, was used instead. Hence, attempts to model the creep

deformation were made using  ¼ fp ð1  expðrtm ÞÞ þ f_s tg,

(1)

where e is the creep strain (in absolute units), efp the strain at the end of the primary creep (in absolute units), t the time (in h), _s the minimum creep strain rate (1/h) and r and m are the constants. For each test, values of the minimum creep strain rate were derived from the individual creep curves using linear regression. Then, non-linear regression was used to determine the optimum values of efp, r and m in Eq. (1) from the primary and secondary creep strain/time data for each test, using the value of _s that was determined earlier. The values of efp, m, r and _s that were obtained for each test were plotted logarithmically as a function of true stress to observe any trends with stress or temperature, see Figs. 2(a)–(d), respectively. The true stress value plotted for each test was the true stress at the end of the primary creep. This value was used since it is the appropriate stress for modelling the strain at the end of primary creep and the minimum creep strain rate. With regard to m, there were no consistent trends and hence a mean value was determined. This value is given in Table 2 and illustrated graphically in Fig. 2(b). In the case of r, although there was no obvious trend with temperature, there appeared to be an increasing trend with stress, up to about 300 MPa, and thereafter the value of r remained constant as the stress increased. This trend was analysed using non-linear regression and the following equation was derived to describe r: r ¼ exp½minð0:52995; 4:6317 þ 0:01375sTrue Þ,

(2)

where sTrue is the true stress (in MPa). This equation is plotted together with the values of r for each test in Fig. 2(c). With regard to the creep strain at the end of the

ARTICLE IN PRESS M.W. Spindler, S.L. Spindler / International Journal of Pressure Vessels and Piping 85 (2008) 89–98

a

91

b Eq. (4) 550°C Eq. (4) 600°C Eq. (4) 650°C

1.E-01

Eq. (4) 575°C Eq. (4) 625°C Eq. (4) 700°C

10

1 μ

ε fp (abs.)

1.E-02 1.E-03

575°C 625°C 700°C

550°C 600°C 650°C 0.62823

0.1 1.E-04 0.01

1.E-05 0

100

200 300 True Stress (MPa)

400

0

500

c

100

200 300 True Stress (MPa)

400

500

d Eq. (3b) 550°C Eq. (3b) 600°C Eq. (3b) 650°C

Minimum Creep Strain Rate (1/h)

10

r

1 0.1 Eq. (2)

0.01 0.001 0

100

200 300 True Stress (MPa)

400

1.E - 03

Eq. (3b) 575°C Eq. (3b) 625°C Eq. (3b) 700°C

1.E - 04 1.E - 05 1.E - 06 1.E - 07 1.E - 08 1.E - 09

500

0

100

200 300 True Stress (MPa)

400

500

Fig. 2. The effect of stress and temperature on (a) the primary creep strain, efp, (b) the time exponent, m, (c) the time multiplier, r and (d) the minimum creep strain rate, _s .

Table 2 Constants for the creep deformation model m

r

efp

A

si

P

m

_s

B

Q

n

0.62823

Eq. (2)

Eq. (4)

133.89

Eq. (5)

23578

2.873

Eq. (3b)

283613

43359

3.995

primary creep and the minimum creep strain rate, the data were clearly dependent on both stress and temperature (see Figs. 2(a) and (d)). Thus, in order to incorporate stress and temperature dependence within Eq. (1), the strain at the end of the primary creep and the minimum creep rate were substituted by the following power and Norton laws: fp ¼ A expðP=TÞsm True ,

(3a)

_s ¼ B expðQ=TÞsnTrue ,

(3b)

where T is the temperature (in K) and A, B, P, Q, m and n are constants. In the case of the minimum creep strain rate, the optimum values of the constants were determined by taking natural logs in Eq. (3b) and performing multiple linear regression (see Fig. 2(d)). In the case of the creep strain at the end of the primary creep, a similar approach was initially adopted. However, subsequent comparisons of the resulting model with stress relaxation data revealed that the model over-estimated the magnitude of the drop (see Fig. 3(a)), with predicted stress drops being up to 200 MPa

greater than those exhibited by the data. The stress relaxation predictions are made using numerical methods to give a strain-hardening integration of the creep model. Further investigations suggested that the problem was largely due to modelling the primary creep strain and that an improvement in the predictions could be achieved by slowing down the primary creep rate during the stress relaxation predictions, while leaving it unchanged under conditions of constant load. This was achieved by incorporating an internal stress term within Eq. (3a) as follows: fp ¼ A expðP=TÞðsTrue  si Þm ,

(4)

where si is an internal stress. In the present analysis, an internal stress term, which was a function of the initial plastic loading strain and the effective yield stress (190 MPa), was chosen, so that for true stresses 4190 MPa si ¼ 1730:8IPS =1:6 and for stresses less than or equal to 190 MPa

si ¼ 0,

ð5Þ

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a

b 600

Observed Relaxed True Stress (MPa)

Observed Relaxed True Stress (MPa)

600

500

400 Temp., Initial Stress 550°C 523 MPa 550°C 471 MPa 575°C 486 MPa 575°C 444 MPa 600°C 448 MPa 600°C 411 MPa 600°C 182 MPa 1:1

300

200

100 100

200 300 400 500 Predicted Relaxed True Stress (MPa)

600

500

400 Temp., Initial Stress 550°C 523 MPa 550°C 471 MPa 575°C 486 MPa 575°C 444 MPa 600°C 448 MPa 600°C 411 MPa 600°C 182 MPa 1:1

300

200

100 100

200 300 400 500 Predicted Relaxed True Stress (MPa)

600

Fig. 3. Stress relaxation of Esshete 1250 and predictions where: (a) efp is given by Eq. (3a) and (b) efp is given by Eq. (4).

True Stress (MPa)

600

400

200

Data Linear fit to data (>190 MPa)

0 0

0.05

0.1 0.15 Initial Plastic Loading Strain (absolute)

0.2

Fig. 4. Initial plastic loading strains for continuous strain measurement tests.

where eIPS is the initial plastic loading strain (in absolute units). Eq. (5) was largely derived from a plot of true stress versus initial plastic loading strain for all tests (see Fig. 4). It was evident that the yield stress for all tests was about 190 MPa. Below 190 MPa, there was effectively no plastic strain on loading and hence, there was deemed to be no internal stress. Above 190 MPa, the initial plastic loading strain increased linearly with true stress (see Fig. 4), and the effective ‘modulus’ was 1730.8. Through comparisons with the stress relaxation data, a factor of 1/1.6 was found to give a good fit to the data. It should be noted that it is not possible to determine the value of the internal stress from constant load creep tests and it was necessary to do this by comparison with the stress relaxation data. The improvement in fit to the stress relaxation by use of the internal stress is illustrated in Fig. 3(b). Attempts were also made to model the minimum creep strain rate using an internal stress. However, the stress relaxation data show that, at longer durations, tests conducted at the same temperature but at different initial

stresses converged. This suggests that the prior history of the test has no effect on the minimum creep strain rate and that an internal stress, which is a function of prior history, would not be appropriate. Thus, the creep deformation behaviour of Esshete 1250 parent material may be calculated using Eq. (1), where efp is given by Eq. (4) and _s is given by Eq. (3b). The values of all constants used in these equations are given in Table 2. 3. Creep ductility In austenitic stainless steels, the elongation at failure measured after a creep test often contains both initial plastic loading strain and creep strain. This is particularly true for tests at relatively low temperatures such as 550 and 600 1C, which are often conducted above the proof stress. Thus, models have been derived for both the elongation at failure and the creep strain at failure (which excludes plastic loading strains) of Esshete 1250. The main application of these models is in the calculation of creep

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damage during a creep–fatigue cycle. The ISO data set on Esshete 1250 were used. However, since plastic loading strains were measured only in a small number of cases (e.g. the creep tests analysed above), it has been necessary to estimate the plastic loading strains using elevated temperature tensile test data. This means that only those tests that have heat-specific elevated temperature tensile data have been used and thus the available data have been reduced from 1520 (in the whole ISO data set) to 395. Nevertheless, this reduced data set contains most of the longest tests. An examination of the elongation at failure data versus the time at failure, the engineering stress and the temperature identified that there was a strong influence of stress on the elongation at failure (see Fig. 5). The data exhibit three clear regimes: (i) at stresses above 250 MPa the elongation decreases slightly with decreasing stress (particularly for the data at 550 and 600 1C), (ii) at stresses between 100 and 250 MPa the elongation increases with decreasing stress (particularly for the data at 650 and 700 1C) and (iii) below 100 MPa the elongation decreases sharply with decreasing stress (particularly for the data at 750 and 800 1C). These three regimes probably correspond to three different failure mechanisms. At high stresses (and low temperatures), the relatively low sensitivity to stress is consistent with power-law creep cavity growth. At intermediate stresses and temperatures, the increasing elongation is consistent with the ductility being controlled by the effects of cavity nucleation on constrained cavity growth. At low stresses (and high temperatures), the decreasing ductility is consistent with diffusion-controlled cavity growth, although metallurgical changes cannot be ruled out. Each of these mechanisms can be represented by

93

power laws, albeit with different slopes. Thus, the elongation at failure, ef, for each mechanism is given by f ¼ C i expðS i =TÞsl i ,

(6)

where s is the engineering stress in MPa and Ci, li and Si are the material constants in each of the three failure mechanisms: power-law creep cavity growth (Power), constrained cavity growth (Cons.) and diffusion-controlled cavity growth (Diff.). The three mechanisms are combined using logical statements such that the three failure mechanisms can be reproduced. This gives ( f ¼ MIN

MAX½C Power expðS Power =TÞsl Power ; C Cons: expðSCons: =TÞsl Cons: 

)

C Diff: expðS Diff: =TÞsl Diff:

.

(7) Fitting to the above model has been carried out using non-linear regression with loge(ef) as the dependent variable. The values for the constants Ci, li and Si are given in Table 3 and a comparison between the fits and the data is shown in Fig. 5. It can be seen from this figure that Eq. (7) gives a good fit to the data in each of the three regimes. The creep strain at failure has been defined here as the elongation at failure minus the plastic loading strain. The plastic loading strains have been estimated using the Ramberg–Osgood equation: IPS ¼ ðs=K 0 Þ1=b ,

(8)

0

where b and K are the material constants. For tests below the 1% proof stress, the hardening exponent, b, and the constant, K0 , were calculated from the appropriate 0.2% and 1% proof stresses using b ¼ ðLog s1%  Log s0:2% Þ=Log 5 and K 0 ¼ s1% 102b , (9)

1 Elongation at failure (abs.)

550°C 600°C 650°C 700°C 750°C 800°C 850°C Fit 550°C Fit 600°C Fit 650°C Fit 700°C Fit 750°C Fit 800°C Fit 850°C

0.1 0

50

100

150

200 250 300 Stress (MPa)

350

400

450

500

Fig. 5. Elongation at failure versus stress for multiple heat data.

where s0.2% and s1% are the 0.2% and 1% proof stresses, respectively (in MPa). For strains above 1%, b and K0 were obtained from the 1% proof stresses and the ultimate tensile strength using b ¼ ðLog sUTS  Log s1% Þ=1:365

and K 0 ¼ 0:946s1% 102b ,

(10) where sUTS is the ultimate tensile strength (in MPa). The factors 1.365 and 0.946 were determined by comparing the estimated and measured loading strains from continuous strain measurement tests. In the present analysis, where the predicted value of the initial plastic loading strain exceeded the first ISM taken during the test, the first ISM was used

Table 3 Constants for the creep ductility models

Elongation Creep strain Heat specific

CPower

SPower

LPower

CCons.H

SCons.H

lCons.H

CCons.L

SCons.L

lCons.L

CDiff.

SDiff.

lDiff.

3.24 0.084 6.26

4417 0 3930

0.47 0 –

– – 6.4  1023

– – 3000

– – 9.59

143 6883 6136

2526 4536 4536

0.498 0.939 0.939

0.57 5399 1.28 0.162 1708 0.676 As above (assumed)

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as the initial plastic loading strain. The creep strain at failure data were then fitted to Eq. (7) as before. The values for the constants Ci, li and Si are given in Table 3 and a comparison between the fits and the data is shown in Fig. 6. It can be seen from Fig. 6 and Table 3 that although Eq. (7) gives a good fit to the data there are only two significant regimes: the power-law cavity growth regime not being represented by the fit or shown by the data. However, examination of data on two heats shows that at stresses above 100 MPa there may be three different failure mechanisms (at Fig. 7(a)), which become obscured with the heat-to-heat scatter. Thus, in order to analyse the data from these two heats, it is necessary to include a fourth mechanism. It is postulated that there are two regions in which the constrained cavity growth mechanism is operating, one in which the effects of cavity nucleation are modest

and one in which the effects of cavity nucleation are pronounced. This can be modelled by ( f ¼ MIN

) MAX½C Power expðSPower =TÞ; C Cons:H expðSCons:H =TÞsl Cons:H  . C Cons:L expðSCons:L =TÞsl Cons:L ; C Diff: expðSDiff: =TÞsl Diff:

(11) Thus, in Eq. (11) there are two constrained cavity growth regions at low stress (Cons. L) and at high stress where the effects of cavity nucleation are important (Cons. H). In addition, the power-law creep cavity growth region is now assumed to be independent of stress. The values for the constants Ci, li and Si are given in Table 3 and a comparison between the fits and the data is shown in Fig. 7(a). 4. Rupture strength

Creep Strain at Failure (abs.)

1

0.1 600°C 700°C 800°C Fit 550°C Fit 650°C Fit 750°C Fit 850°C

550°C 650°C 750°C 850°C Fit 600°C Fit 700°C Fit 800°C

0.01 0

50

100

150

200

250

300

350

400

450

500

Stress (MPa)

Fig. 6. Creep strain at failure versus stress for multiple heat data.

The creep rupture strength of Esshete 1250 has been analysed previously and is reported in PD6525 [4]. This analysis used the ISO 6303 procedure [5]. In addition, Baker [6] has performed a more recent analysis using the PD6605 procedure [7], which produced an Orr–Sherby–Dorn 4th-order polynomial (OSD4). These assessments used the full ISO data set on Esshete 1250, albeit that the data set assessed using the ISO 6303 procedure contained the data available in 1986, whereas the data set assessed using the PD6605 procedure had been updated in 1994. However, both of these assessments experienced difficulties with fitting the data over the whole temperature range. In the ISO 6303 assessment, only the data at 650, 700, 750 and 800 1C were used. However, the temperatures of interest to British Energy are in the range 550–600 1C; thus, the

Creep Strain at Failure (abs.)

1

550°C Heat A 650°C Heat A 750°C Heat A 600°C Heat B 650°C Heat B Fit 600°C Fit 700°C

0.1

600°C Heat A 700°C Heat A 550°C Heat B 575°C Heat B Fit 550°C Fit 650°C Fit 750°C

0.01 0

100

200

300

400

500

300

400

500

Stress (MPa) Failure Time (hours)

1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 0

100

200

Stress (MPa)

Fig. 7. Creep failure versus stress data on two heats: (a) creep strain at failure versus stress and (b) rupture time versus stress (including a fit to the heatspecific data using Eq. (13)).

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Stress (MPa)

1000

Failed at 550°C Unfailed at 550°C Failed at 600°C Unfailed at 600°C Failed at 650°C Unfailed at 650°C Failed at 700°C Unfailed at 700°C Failed at 750°C Failed at 800°C OSD4 at 550°C OSD4 at 600°C OSD4 at 650°C OSD4 at 700°C OSD4 at 750°C OSD4 at 800°C

100

10 10

100

1000 10000 Failure Time (hours)

100000

1000000

Fig. 8. Creep rupture strength of Esshete 1250 compared with the OSD4 model.

assessment by Baker included all of the data from 550 to 900 1C. Nevertheless, the assessment by Baker also experienced difficulties in fitting the whole data set. In particular, at 550 1C the long-term strength appeared overly optimistic and at 650 1C the model failed to describe the sigmoidal rupture behaviour (see Fig. 8). Following on from the work on the rupture ductility of Esshete 1250, which has shown that changes in failure mechanism control the ductility, it was decided to develop a similar approach for the rupture strength of Esshete 1250. As for the earlier assessments, the ISO data set on Esshete 1250 was used, albeit that the durations of the ongoing tests were updated to the final values (failed or discontinued as none are ongoing at this time). The particular problems with the rupture data for Esshete 1250 that the new approach is intended to address are the following:

 

The data at 550 and 600 1C appear to converge at long times (see Fig. 8). The data at 650 and 700 1C show sigmoidal behaviour, which leads to a reduced strength at times greater than 10,000 and 1000 h, respectively. However, this sigmiodal behaviour is not shown at 550, 600, 750 or 800 1C.

The earlier investigations into the rupture ductility of Esshete 1250 showed that there are three or four different failure mechanisms operating. Below about 250 MPa, grain boundary diffusion-controlled cavity growth and con-

strained cavity growth are dominant, whereas above about 250 MPa power-law creep cavity growth and failure controlled by cavity nucleation are dominant. However, an examination of the rupture data shows that the change from grain boundary diffusion-controlled cavity growth to constrained cavity growth, which occurs at about 100 MPa, does not affect the rupture strength. Therefore, it has been decided to model the rupture strength using only three failure mechanisms, which should be sufficient to describe the sigmoidal rupture behaviour of Esshete 1250. These mechanisms correspond to power-law creep cavity growth (at high stresses and low temperatures), constrained cavity growth (at intermediate stresses and temperatures) and diffusion-controlled cavity growth (at low stresses and high temperatures). Each of the three parts of the model varies with temperature according to an Arrhenius expression and varies with stress according to a power law, in which the power is a function of temperature. Thus, the rupture strength for each mechanism is given by tf ¼ Ai expðQi =TÞsðBi TþC i Þ ,

(12)

where Ai, Bi, Ci and Qi are the material constants in each of the three failure mechanisms: power-law creep cavity growth (Power), constrained cavity growth (Cons.) and diffusion controlled cavity growth (Diff.). The three mechanisms are combined using logical statements such that the sigmoidal rupture behaviour can be reproduced. This gives

(

) MAX½APower expðQPower =TÞsðBPower i TþC Power i Þ ; ACons: expðQCons: =TÞsðBCons: TþC Cons: Þ  tf ¼ MIN . ADiff: expðQDiff: =TÞsðBDiff: TþC Diff: Þ

(13)

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Fitting to the above model has been carried out using non-linear regression with log10(tf) as the dependent variable. One of the main difficulties with non-linear regression is in identifying realistic starting values for the constants. In this work, these have been determined by performing three initial analyses to each of the three mechanisms independently. Thus, judgements were made regarding which of the data failed by each failure mechanism and these three sets of data were fitted independently to give the starting values that were used in the final analysis. The advantage of using the final analysis, Eq. (13), is that it avoids any subjectivity and gives a better fit to the data than the independent fits. The values for the constants Ai, Bi, Ci and Qi are given in Table 4 and a comparison between the fits and the data is shown in Fig. 9. In addition, Eq. (13) has also been fitted to the rupture strength of the two heats that were investigated further regarding their creep ductility (see Fig. 7(b)). It can be seen from Fig. 9 that Eq. (13) gives a good fit, within the range of the data, and that it resolves the two problems with the previous analyses—namely, that the data at 550 and 600 1C appear to converge at long times and that the data at 650 and 700 1C show sigmoidal behaviour, whereas this behaviour is not shown at 550, 600, 750 or 800 1C. In addition, it can be seen in Fig. 9 that Eq. (13) is stable on extrapolation, which contrasts with many polynomial

Table 4 Constants in the new mechanistic model, Eq. (13), for rupture strength Cavity growth

Ai

Qi

Bi

Ci

Power Constrained Diffusion

1.2326  1046 2.0338  1064 6.0714  1024

135554 26567 80045

0.020145 0.019857 0.0066554

25.036 2.2987 10.832

expressions, which turn back or have inflections on extrapolation. It is interesting to note that at 600 1C and above the extrapolated rupture strength is given by the diffusion-controlled cavity growth equation. However, at 550 1C the constrained cavity growth equation is used to predict the extrapolated rupture strength. This is the reason for the difference between the slopes at 550 1C and those at higher temperatures. In order to test the visual realism of the new model, the goodness of fit, within the range of the data, and the repeatability and stability of the model in extrapolation, the ECCC, post assessment tests (PATs) [8] have been used and all of these tests were passed. The key points to note, from the PATs, are that the visual realism of the model and the goodness of fit, within the range of the data, are good (see Fig. 9). In addition, the new model showed very good repeatability and stability on extrapolation (PATs 3.1 and 3.2). Indeed, the differences between the 300,000 rupture strengths for the new model and the fit based on a 50% cull of the longest time data (PAT 3.1) are all less than 1%. Comparison with the previous assessment, made using PD6605 [7], shows that the new model gives a better fit with less scatter over the whole range of the data. In particular, the new model gives a significantly improved fit at 550 and at 650 1C (see Fig. 10), which resolves the two main issues with the PD6605 assessment. Namely, that at 550 1C the long-term strength appeared overly optimistic and at 650 1C the OSD4 model failed to describe the sigmoidal rupture behaviour. Nevertheless, it is interesting to note that the OSD4 model would have passed the ECCC PATs and that the 300,000 rupture strengths for the new model and the OSD4 model are relatively close to one another (4.8%, 0.4%, 0.8% and 6.4% difference at 550, 600, 650 and 700 1C, respectively). Following the ECCC guidelines of performing two independent assessments, which should

Stress (MPa)

1000

Failed at 550°C Unfailed at 550°C Failed at 600°C Unfailed at 600°C Failed at 650°C Unfailed at 650°C Failed at 700°C Unfailed at 700°C Failed at 750°C Failed at 800°C Eq. (13) at 550° C Eq. (13) at 600°C Eq. (13) at 650°C Eq. (13) at 700°C Eq. (13) at 750°C Eq. (13) at 800°C

100

10 10

100

1000 10000 Failure Time (hours)

100000

1000000

Fig. 9. Creep rupture strength of Esshete 1250 compared with the mechanistic model.

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b 1.E+06

Mechanistic Model at 550°C

1.E+05 1.E+04 1.E+03 Data 1:1 ± Log (2) ± 2.5 x S [I-RLT] Power (Data)

1.E+02 1.E+01

y = 2.7951x 0.9015

1.E+00 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Observed Time to Failure (hours)

Observed Time to Failure (hours)

a

1.E+06

Mechanistic Model at 650°C

1.E+05 1.E+04 1.E+03

Data 1:1 ± Log (2) ± 2.5 x S [I-RLT] Power (Data)

1.E+02 1.E+01

y = 0.7094x 1.0499

1.E+00 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Predicted Time to Failure (hours)

Predicted Time to Failure (hours)

1.E+06

OSD4 Model at 550°C

1.E+05 1.E+04 1.E+03 1.E+02 1.E+01

Data 1:1 ± Log (2) ± 2.5 x S [I-RLT] Power (Data)

y = 53.939x 0.5982

1.E+00 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Predicted Time to Failure (hours)

Observed Time to Failure (hours)

d

c Observed Time to Failure (hours)

97

1.E+06

OSD4 Model at 650°C

1.E+05 1.E+04 1.E+03

Data 1:1 ± Log (2) ± 2.5 x S [I-RLT] Power (Data)

1.E+02 1.E+01

y = 0.2233x 1.1772

1.E+00 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Predicted Time to Failure (hours)

Fig. 10. Observed versus predicted plots for Esshete 1250 at (a) 550 1C for the mechanistic model, (b) 650 1C for the mechanistic model, (c) 550 1C for the OSD4 model and (d) 650 1C for the OSD4 model (where S[I-RLT] is the standard deviation at the temperature of interest).

give 300,000 rupture strengths that are within 10%, it can be concluded that the new model, Eq. (13), should be used to calculate the rupture strength of Esshete 1250. The new creep rupture model is applicable over the stress range 509–13.5 MPa and the temperature range 525–925 1C. The durations that are considered to constitute extended time extrapolations are (i) greater than 300 kh at 575–625 1C, (ii) greater than 200 kh at 626–675 1C, (iii) greater than 100 kh at 525–574 1C and 676–725 1C, (iv) greater than 10 kh at 726–825 1C, (v) greater than 3 kh at 826–875 1C and (vi) greater than 1 kh at 876–900 1C. 5. Discussion This paper presents analyses of the creep deformation, creep ductility and creep rupture data for Esshete 1250. In each case, the chosen models are specific to Esshete 1250 in the solution heat treated condition and to the applications that these models are to be used for. In particular, the models have been selected after detailed examination of the data and of how each model predicts the behaviour. Nevertheless, there are some features of the work in this paper which might be of use to other materials and these features are discussed in this section. The creep deformation equation that was chosen for Esshete 1250, Eq. (1), is a modified form of the Garofalo

equation for austenitic stainless steels [3]. The particular modification is to include a time exponent, m, which allows the shape of the primary creep strain–time curves to be modified. The variations of the constants (efp, m, r and _s ) with the independent variables (stress and temperature) were chosen to be stable on extrapolation and to avoid physically incorrect values. For example, efp and _s have power laws in stress and Arrhenius expressions to describe the effect of temperature (Eqs. (3b) and (4)) and the values for m and r are constrained to lie between zero and one. A particular feature of the chosen model for creep deformation has been the use of an internal stress, which is a function of prior plastic strain. The requirement for an internal stress was evident from the stress relaxation predictions (Fig. 3). However, the choice of an internal stress that is a function of the prior plastic strain is based on scientific judgement and has not yet been proven by comparison with data from stress change tests, which could explicitly test whether the correct model has been chosen. Nevertheless, there are clear theoretical justifications for having a reduced creep rate for material hardened by prior plastic strain. The main application of the creep ductility models is in the calculation of creep damage under strain control, such as during a creep–fatigue cycle or the relaxation of a welding residual stress. Thus, the creep ductility models

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that have been developed in this paper are based on those that have been described by the author [9,10] previously. Three models have been developed: (i) for the total inelastic strain at failure (elongation), of multiple heat data, (ii) for the creep strain at failure, of multiple heat data and (iii) for the creep strain at failure, for two specified heats. It should be noted that in applying these models to Esshete 1250 the ductility models have been written in terms of stress and temperature alone. This was done by using the Norton law, Eq. (3b), to remove the creep strain rate, which creep ductility is often found to be a function of, e.g. [9,10]. This was necessary because of the complex behaviour of Esshete 1250, which exhibited three or four different failure mechanisms. Nevertheless, now that this complex behaviour has been identified, it would be possible to to re-write Eqs. (7) and (11) in terms of creep strain rate, stress and temperature. Which of the three models is most useful will only be determined by applying them to the calculation of creep damage under strain control and by showing which gives the best prediction of failure in tests, such as creep–fatigue tests, which could be the subject of a future project. The complex rupture strength of steels is often attributed to their metallurgical activity. However, in the case of Esshete 1250, it can be shown that it is caused by changes in the failure mechanism, which also affect the creep ductility. This can be seen by comparing the stresses at which the rupture strength and the creep ductility mechanisms change and is demonstrated by heat-specific data as shown in Fig. 7. It is interesting to note that two of the changes in failure mechanisms are reflected in both the rupture strength and creep ductility data (see Fig. 7). These are (i) the change from power-law creep cavity growth to constrained cavity growth mechanism, in which the effects of cavity nucleation are pronounced, which occurs at about 260 MPa and (ii) the change from a constrained cavity growth mechanism where the effects of cavity nucleation are pronounced to one where the effects of cavity nucleation are modest (i.e. the slopes become less negative), which occurs at about 210 MPa. However, the change from a constrained cavity growth mechanism, where the effects of cavity nucleation are modest, to grain boundary diffusion-controlled cavity growth, which occurs at about 100 MPa and is clear in the ductility data, does not affect the rupture strength (see Figs. 6 and 9). Nonetheless, the work on creep ductility was influential in identifying the mechanisms that controlled the rupture strength of Esshete 1250. It also provided the data analysis technique, which uses logical statements to allow the rupture data to be fitted to three independent mechanistic equations. This approach was shown to give a better fit to the data than traditional polynomial or parametric equations such as those used in PD6605 [7]. In addition, it prevents short-term rupture data, which often dominate the available test data, from adversely influencing long-term predictions of rupture strength. Furthermore, the long-term predictions of rupture

strength are inherently stable and do not suffer from features such as turn back or points of inflection that afflict polynomials and can lead to overly conservative and overly optimistic predictions of rupture strength, respectively. 6. Conclusions 1. The primary and secondary creep deformation of Esshete 1250 has been fitted to a modified Garofalo equation. The model also gives a good prediction of stress relaxation behaviour, through the use of an internal stress. 2. The elongation at failure and the creep strain at failure of Esshete 1250 have been analysed in terms of models that allow for three or four different failure mechanisms. 3. The rupture strength of Esshete 1250 has also been analysed using a model that allows three different failure mechanisms. This approach gave a better fit to the data than traditional polynomial or parametric equations. In addition, it prevents short-term rupture data, which often dominate the available test data, from adversely influencing long-term predictions of rupture strength, and the long-term predictions of rupture strength are inherently stable and do not suffer from features such as turn-back or points of inflection.

Acknowledgement This paper is published with permission from the British Energy Generation Ltd. References [1] Orr J, McNeely VJ. Esshete 1250—an advanced superheater tube steel for today’s power stations. Special Steels Tech Rev 1975;5:4–11. [2] Orr J, Everson H, Parkin G. Warm worked Esshete 125: a high strength bolting steel. In: Performance of bolting materials in high temperature plant applications. London: IOM; 1995. p. 203–19. [3] Garofalo F. Fundamentals of creep and creep-rupture in metals. New York: Macmillan; 1965. [4] PD6525. Elevated temperature properties for steels for pressure purposes. Part 1: stress rupture properties. British Standards Institute, 1990. [5] ISO 6303. Pressure vessel steels not included in ISO 2604, Parts 1 to 6—derivation of long-time stress rupture properties. 1st ed. 1981. [6] Baker AJ. Creep rupture of Esshete 1250. BEGL Report E/REP/ ATEC/0049/GEN/02, 2002. [7] PD6605. Guidelines on methodology for assessment of stress rupture data. British Standards Institute, 1998. [8] ECCC. Creep data validation and assessment procedures. Pub. European Tech. Develop. Ltd. on behalf of ECCC Management Committee, 2003. [9] Spindler MW. The prediction of creep damage in type 347 weld metal: Part I. The determination of material properties from creep and tensile tests. Int J Pres Ves Pip 2005;82(5):175–84. [10] Spindler MW. The multiaxial creep ductility of austenitic stainless steels. Fatigue Fract Eng Mater Struct 2004;27(4):273–81.