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Predicting weld creep strength reduction for 9% Cr steels
ARTICLE IN PRESS
International Journal of Pressure Vessels and Piping 83 (2006) 803–808 www.elsevier.com/locate/ijpvp
Predicting weld creep strength reduction for 9% Cr steels Stefan Holmstro¨m, Pertti Auerkari VTT, Espoo, Finland
Abstract In design standards and in post-service life assessment, the cross-weld (CW) creep strength of ferritic steels is nearly universally assumed to be 80% of the corresponding value for the parent material (PH). However, CW data assessment of some 9% Cr steels such as E911 and P91 suggests that this would not hold at least at the high temperature end of the testing range. The resulting weld creep strength factor (WSF) is then attaining values well below 0.8 when extrapolated to typical design life of 100 000 h or more. Under such conditions the conventional value of 0.8 would result in non-conservative (too long) predicted life for structures subjected to CW loading in the creep regime. To accommodate the CW strength data for realistic values of WSF requires appropriate correction based on actual data. For this purpose, an alternative assessment approach, rigidity parameter correction (RPC), is proposed. This approach can be used to predict CW rupture strength from the PM master curves, with any PM rupture model optimized to correspond to the welded materials data. r 2006 Elsevier Ltd. All rights reserved. Keywords: Creep; Welds; Modeling; Extrapolation; 9% Cr; Ferritic steel; ECCC
1. Introduction Cross-weld (CW) creep rupture data typically span over shorter durations in time and the data sets are usually much smaller than those for the corresponding parent material (PM). The drawback of short-term weld creep testing is that for the lower temperatures the fracture location is seldom found in the heat affected zone (HAZ) but rather in the parent or weld metal, which may not represent the expected long term failure mode. As failures in PM, weld metal and HAZ reflect properties of different materials (or their combinations), modelling for creep life prediction should only consider the relevant failure modes for the selected purpose, typically cases of long term life. Fitting the weld rupture data, including all fracture modes (parent, weld metal and HAZ) easily leads to a situation where the selected creep rupture model cannot accommodate the change of fracture location. On the other hand, CW data sets on HAZ failures can be small and very limited in the range of typical service temperatures (p600 1C). Corresponding author. Fax: +358 20 722 7002.
E-mail address: stefan.holmstrom@vtt.fi (S. Holmstro¨m). 0308-0161/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2006.08.007
Welds of ferritic steels are known to be weaker than the corresponding PM, and traditionally a universal 20% reduction in rupture strength has been assumed. This reduction can be however more pronounced in the 9% Cr steels, and in general the weld creep strength factor (WSF) is defined according to ECCC recommendations as WSF ¼
RuðW Þ=t=T , Ru=t=T
(1)
where RuðW Þ=t=T is the predicted strength of the weld at specified time and temperature and the Ru=t=T is the corresponding strength of the PM. Fitting the CW rupture data in a routine manner to a range of different models and then selecting the ‘‘best’’ model according to these fitting results may also lead to problems in terms of WSF. If the resulting model is different from that for the PM, any differences in the extrapolated predictions may well accumulate because of differences in the mathematical expressions, rendering predicted values of WSF even more uncertain than the predictions on rupture strength. Therefore it would be best to apply similar models for welds and PM, and this also could be otherwise justified when the welds fail in the HAZ, i.e. in the PM with only microstructural deviation from the
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
804
unaffected PM. Furthermore, when CW data sets usually are much smaller than that for the PM, it seems reasonable to apply the PM model also for the welded joints. Applying this principle, a method called rigidity parameter correction (RPC) has been used for predicting creep strength values welded 9% Cr steels. This principle is here demonstrated for the steels E911 (X11CrMoWVNb9-1-1) and P91 (X10CrMoVNb9-1). The method was originally developed for countering the pivoting effect evident in most classical creep rupture models caused by ‘‘overrepresented’’ short term data [1]. Here the RPC tool is used for modifying the master curve of the PM to represent the weld creep rupture data. 2. Methods, applied models and test data The RPC approach applies a similar non-linearity formulation as the master curve equation of the Manson’s [2] minimum commitment method (MCM): logðtr Þ ¼
GðsÞ PðTÞ , 1 þ APðTÞ
(2)
R-corrected prediction [log(trR)]
6 R-corrected model No correction (x=y) Factor of 2 in time
5
4
3
where tr is the predicted time to rupture, P(T) and G(s) are respectively temperature and stress functions of the expression, and A is a constant called instability parameter. Increasing negative value of the instability parameter A will reduce the predicted life (and creep strength) in extrapolation. MCM is not included in standard PD6605 [3] models for creep rupture data fitting, except as a simplified linear MC model with A ¼ 0. Somewhat analogous to Eq. (2), a rigidity parameter R can be defined to transform the predicted rupture time of the PM to the corresponding CW rupture time by bending it over a pivot point in time as shown in Fig. 1. Since the RPC is a transformation of the PM time to rupture the R-parameter will naturally affect the master curve both in stress and temperature. The time transformation is defined as logðtrR Þ ¼
logðtrm Þ logðtp Þ þ logðtp Þ, 1 þ Rðlogðtrm Þ logðtp ÞÞ
(3)
where trR is the corrected (RPC) time to rupture (here the welded material prediction), trm the uncorrected (PM master curve) time to rupture and tp the pivot point in time. The correction is zero at the pivot point and reduces the predicted life elsewhere. The term log(tp) can be fitted as a temperature-dependent function or used (as here) as a constant. Any PM creep model can be then modified for the CW data by minimising the root mean square error (RMS) and optimising the values of R and log (tp). The ECCC recommendations [4] further define a convenient fitting efficiency parameter or scatter factor as Z ¼ 102:5 RMS .
2
1
0 0
1
2
3
4
5
6
Model prediction [log(tr∗)] Fig. 1. Example of R-parameter corrected rupture life (in h). A value of R ¼ 0.089 halves the rupture time at predicted 100 000 h when the pivot point is set at 1000 h. For CW data fitting purposes the pivoting point is however usually located at times shorter than 1 h (negative in log scale).
(4)
In RPC, log(tp) and R are optimised in the fitting procedure. To find the lower bound (time) limits where the RPC fitted values would be applicable, the minimum times to rupture for HAZ failures and the maximum times to rupture for PM failure are listed as a function of temperature in Table 1 for the E911 data. Fitting the CW data by non-linear regression to Eq. (3), replacing trm with the PM master curve predictions for the temperature and stress of the available weld data and trR with the recorded CW failure times transforms the PM values as close to the CW values as possible (see Fig. 2).
Table 1 Maximum time to parent material (PM) failure and minimum time to HAZ failure for welded E911; the corresponding stress level is given in brackets (in MPa) Failure in
PM HAZ
Temperature (1C) 550
575
600
625
650
10 605 h (195) [40 000]
16 025 h (160) [10 000]
3082 h (148) 2694 h (155)
473 h (140) 1479 h (135)
275 h (117) 262 h (120)
Note that there are no recorded HAZ failures at 550 and 575 1C, where the shown values are predicted times by log–linear extrapolation.
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
3. Performance of RPC approach for Cross-Welded 9% Cr steels
5.5 5.0 4.5 4.0 3.5 3.0 PM master curve vs. CW data RPC transformed PM master curve CW master curve Perfect fit
2.0 2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Recorded rupture log time (CW data set) Fig. 2. Predicted rupture times of the parent material (PM), CW master curve and RPC transformed rupture times versus recorded HAZ failure times for steel E911.
To characterise relative shortening of weld life, the weld time factor (WTF) is defined as WTF ¼
tuðW Þ=s=T , tu=s=T
(5)
where tuðW Þ=s=T is the predicted rupture time of the weld at specified stress and temperature, and tu=s=T is the corresponding predicted rupture time of the PM. To show the potential of RPC, two ECCC data sets of Cross-Welded 9% Cr material (E911, P91) are fitted to their PM master curve models for creep rupture. The RPC predictions and fitting efficiency parameters are compared to those of a traditional full data assessment, i.e. independently obtained master curves for the welded data. For the majority of the assessed data the test specifics such as used testing standard and specimen details were not known. Possible increased data scatter due to differing testing procedures and used specimen dimensions can therefore not be ruled out. The full E911 CW data set was provided by ECCC and consists of 159 data points including specimens ruptured in the PM, weld metal and in the HAZ. The data covers a temperature range of 550–690 1C and stress range of 26–230 MPa, with the longest ruptured test about 32 000 h. Only HAZ data (with WSFo0.9) were RPC fitted to avoid data in the transition zone of fracture location change. The full P91 CW data set was also provided by ECCC and consists of 257 data points including specimens ruptured in the parent material, weld metal and in the heat affected zone (HAZ). The data covers a temperature range of 550–695 1C and stress range of 40–250 MPa, with the longest ruptured test about 30 000 h. Also here only HAZ data (WSFo0.9) were RPC fitted to avoid data in the transition zone of fracture location change.
200
Stress (MPa)
2.5
The two data sets on welded 9% Cr steels were assessed by using a full creep rupture assessment on HAZ failures data and by the RPC method. The traditionally acquired master curves are plotted with the HAZ data in Fig. 3 for P91 steel and in Fig. 4 for steel E911. The corresponding RPC fits are presented in Fig. 5 for P91 and Fig. 6 for E911. The calculated WSF as a function of test stress (of the CW data set) for P91 and E911 are presented in Figs. 7 and 8. The calculated WSF as a function of time is presented in Fig. 9 (P91) and Fig. 10 (E911) for the RPC fit and in Fig. 11 (P91) and Fig. 12 (E911) for the traditional creep rupture modelling. The fitting efficiency calculated on the HAZ data is presented in Table 2 together with predicted WSF at 600 1C/100 000 h for both P91 and E911 (Fig. 4). The optimised RPC parameters are presented in Table 3. The RPC modification seems to fit the data remarkably well and the calculated WSF curves behave well at all test temperatures.
150 575 100
600 625
50
650
1
2
3
4 log(time[h])
5
6
7
Fig. 3. Best fit (pre-assessed) Cross-Welded master curve (dashed), parent material master curve (solid) and HAZ failures data (points) for steel P91.
200 550 Stress (MPa)
Predicted rupture log time (models for PM, CW and RPC-PM)
805
150
575 600
100
625 50
650
100
1·103
1·104
1·105
Time (h) Fig. 4. CW master curve (dashed line), PM master curve (solid) and HAZ failure data (points) for E911.
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
806
1 200
650
150
600
0.8 WSF
Stress (MPa)
0.9
575 100 600
0.7 600
625
0.6
625
625
50
650
650
Linear (600)
0.5
Linear (625) Linear (650)
1
2
3
4 log(time[h])
5
6
7
0.4 20
Fig. 5. PM master curve (solid lines), RPC-modified curve (dashed) and HAZ failure data points for P91.
40
60
80
100
120
140
160
180
Stress (MPa) Fig. 8. WSF as a function of test stress for CW E911 data (showing values below 0.9).
P91 200 150
0.9
575 600
100
WSF
Stress (MPa)
550
625 50
650
1·103
100
1·104
0.8
0.7 1·105 0.6
Time (h) Fig. 6. RPC curve (dashed), PM master curve (solid) and HAZ fracture data (points) for E911.
1·103
RPC 575°C RPC 600°C RPC 625°C RPC 650°C data 600°C
1·104
1·105
Time(h) Fig. 9. WSF calculated on RPC modified master curve for welded P91. The WSF values from actual Cross-Welded data points and PM master curve are shown for 600 1C (boxes) to demonstrate the scatter.
1 650
0.9
625
600 575
WSF
0.8
0.7 575 600 625
0.6
650 Linear (575) Linear (600)
0.5
Linear (625) Linear (650)
0.4 20
40
60
80
100
120
140
160
180
Stress (MPa) Fig. 7. WSF as a function of test stress for cross-welded P91 data (showing values of WSFo0.9).
In case of E911, the 600 1C RPC fitted curve is located on the lower bound of HAZ failure data (Fig. 9). Estimates of the WSF can also be calculated from the standard listed values [5,6] and Eq. (3) without knowing the actual master curves for welds or PM. For example, for P91 (Table 4) the mean failure time of the parent P91 would be at 10 000 h at 600 1C and 123 MPa. This failure time approximately coincides with the predicted CW failure time (9650 h) at 600 1C and 86 MPa, where the mean life for the PM would be 200 000 h. Then for the 600 1C isotherm and 10 000 h WSF ¼ 86 MPa/ 123 MPa ¼ 0.7. This is in fact quite close to the value represented in Fig. 9, as the value calculated with RPC using the P91 master curve gave WSF ¼ 0.69.
ARTICLE IN PRESS
1
1
0.9
0.9
0.8
0.8
807
WSF
WSF
S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
0.7 0.6 0.5
0.7 (550°C) (575°C) 600°C 625°C 650°C data 600°C
1·103
(550°C) (575°C) 600°C 625°C 650°C data 600°C
0.6 0.5 1·104 Time (h)
1·105
1·103
1·105
1·104 Time (h)
Fig. 10. WSF calculated on RPC modified master curve for E911. The isotherms where there is no HAZ data are dotted. The WSF values calculated from the CW data points and PM master curve for 600 1C (boxes) are also shown.
Fig. 12. WSF from an independently obtained CW master curve for E911. The isotherms where there is no HAZ data are dotted. The WSF values from the CW data points and PM master curve for 600 1C (boxes) are also shown.
Table 2 Calculated Z-values for RPC and cross-weld (CW) preferred model predicting failure in the HAZ
P91
0.9 Model
E911
P91
WSF
ZRMS WSF (600 1C, 100 kh) ZRMS WSF (600 1C, 100 kh)
0.8 PM-RPC 2.46 CW-master 2.20
1·103
3.29 3.18
0.48 0.471
The data is restricted to HAZ failures with calculated WSFo0.9. 1 Pre-assessment curve (Manson–Brown) shown in Fig. 3.
0.7
0.6
0.62 0.67
master 575°C master 600°C master 625°C master 650°C data 600°C
1·104
1·105
Time(h) Fig. 11. WSF from independently obtained CW master curve for P91. The WSF values from the CW data points and PM master curve at 600 1C (boxes) are shown for comparison.
Table 3 Optimised values of log(tp) and R in Eq. (3) for P91 and E911 Model
P91 E911
RPC parameters Log(tp)
R
5.64132 1.58723
0.0125 0.02224
4. Discussion and conclusive remarks The CW data sets available for assessment are often smaller in both test numbers and tested heats and the data scatter is inherently larger than for corresponding PM data sets. The increased data scatter is on the other hand to be expected due to several added uncertainty factors of the tested ‘‘material’’ such as the applied welding procedures, post-weld heat treatments, filler materials and even specimen dimensions used. Furthermore the fracture location change from PM fracture towards HAZ fracture complicates long-term WSF predictions. Weld strength factor calculation from independent CW master curves are therefore more prone to problems such as cross-over and turn-backs (see Figs. 9 and 10 vs.
Table 4 Calculated WTF at 600 1C using RPC and Eq. (3), with parent material prediction using EN 10216-2 for P91 and the ECCC data sheet for E911 Time (PM)(h)
P91 welded WTF/time (h)/RuðW Þ=t=600 C (MPa)
E911 welded WTF/ time (h)/RuðW Þ=t=600 C (MPa)
10 000 30 000 100 000 200 000
0.092/920/123 NA 0.056/5650/94 0.048/9650/86
0.241/2400/139 0.190/5700/119 0.144/14400/98 0.122/24320/86
The corresponding predicted cross-weld time to failure times and rupture strength values are also shown.
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808
Table 5 Predicted WSF at 600 1C using RPC approach and independent crossweld data assessment for P91 and E911 HAZ failure time (h)
P91 WSF RPC/ independent
E911 WSF RPC/ independent
30 000 100 000
0.60/0.56 0.48/0.47
0.72/0.76 0.62/0.56
Figs. 11–12). To counter these draw-backs the RPC approach was developed, that can be used on any PM creep rupture model, to obtain a conservative predictive model for CW data with the same mathematical behaviour as the corresponding PM. The RPC modification will force the curvature of the PM master curve to fit the weld data by finding a pivoting point and reducing life outside this point. In the example cases of Cross-Welded 9% Cr steels, the data fits were nearly as good as for a traditionally assessed master curves. The method has good potential in reducing the mismatching effect of different selected models for predicting WSF. Examples of obtained WSF values for the steels P91 and E911 at 600 1C are shown in Table 5, using both the RPC approach and independently evaluated models (master curves) for the CW data (Fig. 8). For this isotherm the differences are not very large, but as is seen from Figs. 9–12, the RPC approach will avoid obvious inconsistencies from the differences in the models for parent and CW data. The principal benefits of the RPC approach can be listed as follows:
No independently tested CW master curve is required to obtain conservative values of weld failure times and WSF Weld time factors (WTF) can be calculated from listed standard values Short duration (10–30 kh) WSF can be calculated from listed standard values
Only two fitting parameters are used for RPC approach All obtained WSF isotherms are smooth and well behaving without cross-over The method requires less CW data than traditional assessments to guarantee conservative predictions of creep rupture life of welds.
References [1] Holmstro¨m S, Auerkari P. Effect of short-term data on predicted creep rupture life, pivoting effect and optimized censoring. In: Proceedings of the international conference on creep and fracture in high temperature components—design and life assessment issues. London, 2005. [2] Manson SS, Ensign CR. Interpolation and extrapolation of creep rupture data by the minimum commitment method. Part I, focal point convergence. In: Proceedings of the pressure vessel and piping conference. Montreal, 1978. p. 299–398. [3] PD 6605. Guidance on methodology for assessment of stress rupture data, Part 1 and 2. London:BSI;1998. 51+27pp. [4] ECCC recommendations. Generic recommendations and guidance for the assessment of full size creep rupture data sets. Vol. 5. Part 1a. Issue 5. 2003; ECCC recommendations. Recommendations and guidance for the assessment of creep strain and creep strength data. Vol. 5. Part 1b. Issue 2. 2003. [5] EN 10216-2. Non-alloy and alloy steel tubes with specified elevated temperature properties. Seamless steel tubes for pressure purposes. Technical delivery conditions. Part 2. Brussels:CEN;2002. 59pp.+app. [6] X11CrMoWVNb9-1-1. ECCC data sheet. 2005. 2pp.
International Journal of Pressure Vessels and Piping 83 (2006) 803–808 www.elsevier.com/locate/ijpvp
Predicting weld creep strength reduction for 9% Cr steels Stefan Holmstro¨m, Pertti Auerkari VTT, Espoo, Finland
Abstract In design standards and in post-service life assessment, the cross-weld (CW) creep strength of ferritic steels is nearly universally assumed to be 80% of the corresponding value for the parent material (PH). However, CW data assessment of some 9% Cr steels such as E911 and P91 suggests that this would not hold at least at the high temperature end of the testing range. The resulting weld creep strength factor (WSF) is then attaining values well below 0.8 when extrapolated to typical design life of 100 000 h or more. Under such conditions the conventional value of 0.8 would result in non-conservative (too long) predicted life for structures subjected to CW loading in the creep regime. To accommodate the CW strength data for realistic values of WSF requires appropriate correction based on actual data. For this purpose, an alternative assessment approach, rigidity parameter correction (RPC), is proposed. This approach can be used to predict CW rupture strength from the PM master curves, with any PM rupture model optimized to correspond to the welded materials data. r 2006 Elsevier Ltd. All rights reserved. Keywords: Creep; Welds; Modeling; Extrapolation; 9% Cr; Ferritic steel; ECCC
1. Introduction Cross-weld (CW) creep rupture data typically span over shorter durations in time and the data sets are usually much smaller than those for the corresponding parent material (PM). The drawback of short-term weld creep testing is that for the lower temperatures the fracture location is seldom found in the heat affected zone (HAZ) but rather in the parent or weld metal, which may not represent the expected long term failure mode. As failures in PM, weld metal and HAZ reflect properties of different materials (or their combinations), modelling for creep life prediction should only consider the relevant failure modes for the selected purpose, typically cases of long term life. Fitting the weld rupture data, including all fracture modes (parent, weld metal and HAZ) easily leads to a situation where the selected creep rupture model cannot accommodate the change of fracture location. On the other hand, CW data sets on HAZ failures can be small and very limited in the range of typical service temperatures (p600 1C). Corresponding author. Fax: +358 20 722 7002.
E-mail address: stefan.holmstrom@vtt.fi (S. Holmstro¨m). 0308-0161/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2006.08.007
Welds of ferritic steels are known to be weaker than the corresponding PM, and traditionally a universal 20% reduction in rupture strength has been assumed. This reduction can be however more pronounced in the 9% Cr steels, and in general the weld creep strength factor (WSF) is defined according to ECCC recommendations as WSF ¼
RuðW Þ=t=T , Ru=t=T
(1)
where RuðW Þ=t=T is the predicted strength of the weld at specified time and temperature and the Ru=t=T is the corresponding strength of the PM. Fitting the CW rupture data in a routine manner to a range of different models and then selecting the ‘‘best’’ model according to these fitting results may also lead to problems in terms of WSF. If the resulting model is different from that for the PM, any differences in the extrapolated predictions may well accumulate because of differences in the mathematical expressions, rendering predicted values of WSF even more uncertain than the predictions on rupture strength. Therefore it would be best to apply similar models for welds and PM, and this also could be otherwise justified when the welds fail in the HAZ, i.e. in the PM with only microstructural deviation from the
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
804
unaffected PM. Furthermore, when CW data sets usually are much smaller than that for the PM, it seems reasonable to apply the PM model also for the welded joints. Applying this principle, a method called rigidity parameter correction (RPC) has been used for predicting creep strength values welded 9% Cr steels. This principle is here demonstrated for the steels E911 (X11CrMoWVNb9-1-1) and P91 (X10CrMoVNb9-1). The method was originally developed for countering the pivoting effect evident in most classical creep rupture models caused by ‘‘overrepresented’’ short term data [1]. Here the RPC tool is used for modifying the master curve of the PM to represent the weld creep rupture data. 2. Methods, applied models and test data The RPC approach applies a similar non-linearity formulation as the master curve equation of the Manson’s [2] minimum commitment method (MCM): logðtr Þ ¼
GðsÞ PðTÞ , 1 þ APðTÞ
(2)
R-corrected prediction [log(trR)]
6 R-corrected model No correction (x=y) Factor of 2 in time
5
4
3
where tr is the predicted time to rupture, P(T) and G(s) are respectively temperature and stress functions of the expression, and A is a constant called instability parameter. Increasing negative value of the instability parameter A will reduce the predicted life (and creep strength) in extrapolation. MCM is not included in standard PD6605 [3] models for creep rupture data fitting, except as a simplified linear MC model with A ¼ 0. Somewhat analogous to Eq. (2), a rigidity parameter R can be defined to transform the predicted rupture time of the PM to the corresponding CW rupture time by bending it over a pivot point in time as shown in Fig. 1. Since the RPC is a transformation of the PM time to rupture the R-parameter will naturally affect the master curve both in stress and temperature. The time transformation is defined as logðtrR Þ ¼
logðtrm Þ logðtp Þ þ logðtp Þ, 1 þ Rðlogðtrm Þ logðtp ÞÞ
(3)
where trR is the corrected (RPC) time to rupture (here the welded material prediction), trm the uncorrected (PM master curve) time to rupture and tp the pivot point in time. The correction is zero at the pivot point and reduces the predicted life elsewhere. The term log(tp) can be fitted as a temperature-dependent function or used (as here) as a constant. Any PM creep model can be then modified for the CW data by minimising the root mean square error (RMS) and optimising the values of R and log (tp). The ECCC recommendations [4] further define a convenient fitting efficiency parameter or scatter factor as Z ¼ 102:5 RMS .
2
1
0 0
1
2
3
4
5
6
Model prediction [log(tr∗)] Fig. 1. Example of R-parameter corrected rupture life (in h). A value of R ¼ 0.089 halves the rupture time at predicted 100 000 h when the pivot point is set at 1000 h. For CW data fitting purposes the pivoting point is however usually located at times shorter than 1 h (negative in log scale).
(4)
In RPC, log(tp) and R are optimised in the fitting procedure. To find the lower bound (time) limits where the RPC fitted values would be applicable, the minimum times to rupture for HAZ failures and the maximum times to rupture for PM failure are listed as a function of temperature in Table 1 for the E911 data. Fitting the CW data by non-linear regression to Eq. (3), replacing trm with the PM master curve predictions for the temperature and stress of the available weld data and trR with the recorded CW failure times transforms the PM values as close to the CW values as possible (see Fig. 2).
Table 1 Maximum time to parent material (PM) failure and minimum time to HAZ failure for welded E911; the corresponding stress level is given in brackets (in MPa) Failure in
PM HAZ
Temperature (1C) 550
575
600
625
650
10 605 h (195) [40 000]
16 025 h (160) [10 000]
3082 h (148) 2694 h (155)
473 h (140) 1479 h (135)
275 h (117) 262 h (120)
Note that there are no recorded HAZ failures at 550 and 575 1C, where the shown values are predicted times by log–linear extrapolation.
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
3. Performance of RPC approach for Cross-Welded 9% Cr steels
5.5 5.0 4.5 4.0 3.5 3.0 PM master curve vs. CW data RPC transformed PM master curve CW master curve Perfect fit
2.0 2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Recorded rupture log time (CW data set) Fig. 2. Predicted rupture times of the parent material (PM), CW master curve and RPC transformed rupture times versus recorded HAZ failure times for steel E911.
To characterise relative shortening of weld life, the weld time factor (WTF) is defined as WTF ¼
tuðW Þ=s=T , tu=s=T
(5)
where tuðW Þ=s=T is the predicted rupture time of the weld at specified stress and temperature, and tu=s=T is the corresponding predicted rupture time of the PM. To show the potential of RPC, two ECCC data sets of Cross-Welded 9% Cr material (E911, P91) are fitted to their PM master curve models for creep rupture. The RPC predictions and fitting efficiency parameters are compared to those of a traditional full data assessment, i.e. independently obtained master curves for the welded data. For the majority of the assessed data the test specifics such as used testing standard and specimen details were not known. Possible increased data scatter due to differing testing procedures and used specimen dimensions can therefore not be ruled out. The full E911 CW data set was provided by ECCC and consists of 159 data points including specimens ruptured in the PM, weld metal and in the HAZ. The data covers a temperature range of 550–690 1C and stress range of 26–230 MPa, with the longest ruptured test about 32 000 h. Only HAZ data (with WSFo0.9) were RPC fitted to avoid data in the transition zone of fracture location change. The full P91 CW data set was also provided by ECCC and consists of 257 data points including specimens ruptured in the parent material, weld metal and in the heat affected zone (HAZ). The data covers a temperature range of 550–695 1C and stress range of 40–250 MPa, with the longest ruptured test about 30 000 h. Also here only HAZ data (WSFo0.9) were RPC fitted to avoid data in the transition zone of fracture location change.
200
Stress (MPa)
2.5
The two data sets on welded 9% Cr steels were assessed by using a full creep rupture assessment on HAZ failures data and by the RPC method. The traditionally acquired master curves are plotted with the HAZ data in Fig. 3 for P91 steel and in Fig. 4 for steel E911. The corresponding RPC fits are presented in Fig. 5 for P91 and Fig. 6 for E911. The calculated WSF as a function of test stress (of the CW data set) for P91 and E911 are presented in Figs. 7 and 8. The calculated WSF as a function of time is presented in Fig. 9 (P91) and Fig. 10 (E911) for the RPC fit and in Fig. 11 (P91) and Fig. 12 (E911) for the traditional creep rupture modelling. The fitting efficiency calculated on the HAZ data is presented in Table 2 together with predicted WSF at 600 1C/100 000 h for both P91 and E911 (Fig. 4). The optimised RPC parameters are presented in Table 3. The RPC modification seems to fit the data remarkably well and the calculated WSF curves behave well at all test temperatures.
150 575 100
600 625
50
650
1
2
3
4 log(time[h])
5
6
7
Fig. 3. Best fit (pre-assessed) Cross-Welded master curve (dashed), parent material master curve (solid) and HAZ failures data (points) for steel P91.
200 550 Stress (MPa)
Predicted rupture log time (models for PM, CW and RPC-PM)
805
150
575 600
100
625 50
650
100
1·103
1·104
1·105
Time (h) Fig. 4. CW master curve (dashed line), PM master curve (solid) and HAZ failure data (points) for E911.
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
806
1 200
650
150
600
0.8 WSF
Stress (MPa)
0.9
575 100 600
0.7 600
625
0.6
625
625
50
650
650
Linear (600)
0.5
Linear (625) Linear (650)
1
2
3
4 log(time[h])
5
6
7
0.4 20
Fig. 5. PM master curve (solid lines), RPC-modified curve (dashed) and HAZ failure data points for P91.
40
60
80
100
120
140
160
180
Stress (MPa) Fig. 8. WSF as a function of test stress for CW E911 data (showing values below 0.9).
P91 200 150
0.9
575 600
100
WSF
Stress (MPa)
550
625 50
650
1·103
100
1·104
0.8
0.7 1·105 0.6
Time (h) Fig. 6. RPC curve (dashed), PM master curve (solid) and HAZ fracture data (points) for E911.
1·103
RPC 575°C RPC 600°C RPC 625°C RPC 650°C data 600°C
1·104
1·105
Time(h) Fig. 9. WSF calculated on RPC modified master curve for welded P91. The WSF values from actual Cross-Welded data points and PM master curve are shown for 600 1C (boxes) to demonstrate the scatter.
1 650
0.9
625
600 575
WSF
0.8
0.7 575 600 625
0.6
650 Linear (575) Linear (600)
0.5
Linear (625) Linear (650)
0.4 20
40
60
80
100
120
140
160
180
Stress (MPa) Fig. 7. WSF as a function of test stress for cross-welded P91 data (showing values of WSFo0.9).
In case of E911, the 600 1C RPC fitted curve is located on the lower bound of HAZ failure data (Fig. 9). Estimates of the WSF can also be calculated from the standard listed values [5,6] and Eq. (3) without knowing the actual master curves for welds or PM. For example, for P91 (Table 4) the mean failure time of the parent P91 would be at 10 000 h at 600 1C and 123 MPa. This failure time approximately coincides with the predicted CW failure time (9650 h) at 600 1C and 86 MPa, where the mean life for the PM would be 200 000 h. Then for the 600 1C isotherm and 10 000 h WSF ¼ 86 MPa/ 123 MPa ¼ 0.7. This is in fact quite close to the value represented in Fig. 9, as the value calculated with RPC using the P91 master curve gave WSF ¼ 0.69.
ARTICLE IN PRESS
1
1
0.9
0.9
0.8
0.8
807
WSF
WSF
S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
0.7 0.6 0.5
0.7 (550°C) (575°C) 600°C 625°C 650°C data 600°C
1·103
(550°C) (575°C) 600°C 625°C 650°C data 600°C
0.6 0.5 1·104 Time (h)
1·105
1·103
1·105
1·104 Time (h)
Fig. 10. WSF calculated on RPC modified master curve for E911. The isotherms where there is no HAZ data are dotted. The WSF values calculated from the CW data points and PM master curve for 600 1C (boxes) are also shown.
Fig. 12. WSF from an independently obtained CW master curve for E911. The isotherms where there is no HAZ data are dotted. The WSF values from the CW data points and PM master curve for 600 1C (boxes) are also shown.
Table 2 Calculated Z-values for RPC and cross-weld (CW) preferred model predicting failure in the HAZ
P91
0.9 Model
E911
P91
WSF
ZRMS WSF (600 1C, 100 kh) ZRMS WSF (600 1C, 100 kh)
0.8 PM-RPC 2.46 CW-master 2.20
1·103
3.29 3.18
0.48 0.471
The data is restricted to HAZ failures with calculated WSFo0.9. 1 Pre-assessment curve (Manson–Brown) shown in Fig. 3.
0.7
0.6
0.62 0.67
master 575°C master 600°C master 625°C master 650°C data 600°C
1·104
1·105
Time(h) Fig. 11. WSF from independently obtained CW master curve for P91. The WSF values from the CW data points and PM master curve at 600 1C (boxes) are shown for comparison.
Table 3 Optimised values of log(tp) and R in Eq. (3) for P91 and E911 Model
P91 E911
RPC parameters Log(tp)
R
5.64132 1.58723
0.0125 0.02224
4. Discussion and conclusive remarks The CW data sets available for assessment are often smaller in both test numbers and tested heats and the data scatter is inherently larger than for corresponding PM data sets. The increased data scatter is on the other hand to be expected due to several added uncertainty factors of the tested ‘‘material’’ such as the applied welding procedures, post-weld heat treatments, filler materials and even specimen dimensions used. Furthermore the fracture location change from PM fracture towards HAZ fracture complicates long-term WSF predictions. Weld strength factor calculation from independent CW master curves are therefore more prone to problems such as cross-over and turn-backs (see Figs. 9 and 10 vs.
Table 4 Calculated WTF at 600 1C using RPC and Eq. (3), with parent material prediction using EN 10216-2 for P91 and the ECCC data sheet for E911 Time (PM)(h)
P91 welded WTF/time (h)/RuðW Þ=t=600 C (MPa)
E911 welded WTF/ time (h)/RuðW Þ=t=600 C (MPa)
10 000 30 000 100 000 200 000
0.092/920/123 NA 0.056/5650/94 0.048/9650/86
0.241/2400/139 0.190/5700/119 0.144/14400/98 0.122/24320/86
The corresponding predicted cross-weld time to failure times and rupture strength values are also shown.
ARTICLE IN PRESS S. Holmstro¨m, P. Auerkari / International Journal of Pressure Vessels and Piping 83 (2006) 803–808
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Table 5 Predicted WSF at 600 1C using RPC approach and independent crossweld data assessment for P91 and E911 HAZ failure time (h)
P91 WSF RPC/ independent
E911 WSF RPC/ independent
30 000 100 000
0.60/0.56 0.48/0.47
0.72/0.76 0.62/0.56
Figs. 11–12). To counter these draw-backs the RPC approach was developed, that can be used on any PM creep rupture model, to obtain a conservative predictive model for CW data with the same mathematical behaviour as the corresponding PM. The RPC modification will force the curvature of the PM master curve to fit the weld data by finding a pivoting point and reducing life outside this point. In the example cases of Cross-Welded 9% Cr steels, the data fits were nearly as good as for a traditionally assessed master curves. The method has good potential in reducing the mismatching effect of different selected models for predicting WSF. Examples of obtained WSF values for the steels P91 and E911 at 600 1C are shown in Table 5, using both the RPC approach and independently evaluated models (master curves) for the CW data (Fig. 8). For this isotherm the differences are not very large, but as is seen from Figs. 9–12, the RPC approach will avoid obvious inconsistencies from the differences in the models for parent and CW data. The principal benefits of the RPC approach can be listed as follows:
No independently tested CW master curve is required to obtain conservative values of weld failure times and WSF Weld time factors (WTF) can be calculated from listed standard values Short duration (10–30 kh) WSF can be calculated from listed standard values
Only two fitting parameters are used for RPC approach All obtained WSF isotherms are smooth and well behaving without cross-over The method requires less CW data than traditional assessments to guarantee conservative predictions of creep rupture life of welds.
References [1] Holmstro¨m S, Auerkari P. Effect of short-term data on predicted creep rupture life, pivoting effect and optimized censoring. In: Proceedings of the international conference on creep and fracture in high temperature components—design and life assessment issues. London, 2005. [2] Manson SS, Ensign CR. Interpolation and extrapolation of creep rupture data by the minimum commitment method. Part I, focal point convergence. In: Proceedings of the pressure vessel and piping conference. Montreal, 1978. p. 299–398. [3] PD 6605. Guidance on methodology for assessment of stress rupture data, Part 1 and 2. London:BSI;1998. 51+27pp. [4] ECCC recommendations. Generic recommendations and guidance for the assessment of full size creep rupture data sets. Vol. 5. Part 1a. Issue 5. 2003; ECCC recommendations. Recommendations and guidance for the assessment of creep strain and creep strength data. Vol. 5. Part 1b. Issue 2. 2003. [5] EN 10216-2. Non-alloy and alloy steel tubes with specified elevated temperature properties. Seamless steel tubes for pressure purposes. Technical delivery conditions. Part 2. Brussels:CEN;2002. 59pp.+app. [6] X11CrMoWVNb9-1-1. ECCC data sheet. 2005. 2pp.