Creep–Fatigue Life Estimation of Gr.91 Steel and Its Welded Joints

: A series of creep–fatigue tests of Gr.91 steel were performed at 600 ◦ C. Fatigue life was reduced by tensile strain holding. The minimum life reduction factor was approximately 0.3. The creep–fatigue life could not be estimated properly via the conventional linear summation rule of the fatigue damage and creep damage. Since this material is considered to have a large creep–fatigue interaction, it was proposed that the creep–fatigue life should be estimated using the improved linear summation rule of the fatigue damage, the creep damage and the creep–fatigue interaction damage. In the future, it will be necessary to clarify the creep–fatigue interaction mechanism and deﬁne its damage value. On the other hand, a series of creep–fatigue tests for Gr.91 steel welded joints were also performed in the strain range of 0.5% at 600 ◦ C. Again, the fatigue life was shortened by the tensile strain holding. The minimum fatigue life reduction factor was approximately 0.2. All the test pieces fractured in the ﬁne-grained HAZ of the welded joints. The creep–fatigue life could not be estimated properly using the linear summation rule of the fatigue damage and creep damage in the HAZ. One possible reason was thought to be the effects of the elastic follow-up phenomena peculiar to welded joints. The creep strain of the HAZ might increase due to the transfer of the elastic strain from both the base metal and the weld metal, according to the elastic follow-up phenomena during strain holding. In the future, it will be important to quantitatively estimate the effects of the elastic follow-up phenomena.


Introduction
Most components operating at elevated temperatures are subjected to cyclic loading (fatigue) due to their startup-shutdown operations and constant loading (creep) due to their steady operations.This is true not only for large equipment such as power plants, but also small devices such as personal computers.Therefore, it seems to be reasonable to apply creep-fatigue life estimation methods to those apparatuses and devices.In Japan, many creep-fatigue studies were actively conducted from the 1970s to the 1980s.They were mainly aimed at establishing the strength design method for fast breeder reactor (FBR) components.Low-pressure sodium was planned to flow through the pipes at approximately 500 • C. Thermal stress was expected to be dominant in FBR components, as shown in Figure 1 [1].It was divided into steady thermal stress via thermal expansion in the piping system and transient thermal stress via the temperature gradient in the reactor vessel.Both are strain-controlled stresses.The main fracture mode was thought to be strain-controlled creep-fatigue due to thermal stress, while it was creep due to load-controlled hoop stress under high-pressure steam in thermal power plants.A large amount of creep-fatigue data were obtained, and a creep-fatigue life estimation method was established.However, the concept of a creep-fatigue life estimation has not spread well in industry.Alternatively, it is common to estimate only the fatigue life or creep life for components operated at elevated temperatures.A possible reason is that the creep-fatigue life estimation method is complex and has not yet been satisfactorily verified, but a more important reason may be that the necessity of a creep-fatigue life estimation is not fully recognized.Without clarification of the mechanism of the creep-fatigue interaction, the necessity of a creep-fatigue life estimation is obscured.and turbine inlet, the thermal expansion is restrained, and then thermal stress is generated.Therefore, circumferential welded joints are subjected to creep-fatigue loading due to thermal expansion stress and internal pressure during plant operation.Recently, thermal power plants have come to be used as regulated power sources, so creep-fatigue estimation is becoming an important issue as the number of plants starts and stops increases.In this paper, a series of creep-fatigue tests for Gr.91 steel welded joints were also performed at 600 °C to investigate their creep-fatigue properties.The creep-fatigue lives were also estimated using the linear damage summation rules of the fatigue damage and creep damage.Simultaneously, the elastic follow-up phenomena were discussed, where the creep strain in the heat-affected zone (HAZ) of welded joints increases during the strain holding.Gr.91 (9Cr-1Mo-V-Nb) steel is an excellent material with high-temperature strength properties and oxidation resistance around 600 • C, so it is widely used in thermal power plants and petrochemical plants.Recently, there have been several reports regarding the creep-fatigue properties of Gr.91 steel or Gr.92 (9Cr-1.8W-0.5Mo-V-Nb)steel [2][3][4][5].In this paper, a series of creep-fatigue tests of Gr.91 steel were performed at 600 • C to investigate its creep-fatigue properties.Furthermore, the creep-fatigue lives were estimated using the linear damage summation rules of the fatigue damage, the creep damage and the creep-fatigue interaction damage.On the other hand, Gr.91 steel welded joints are key structures for life estimation in thermal power plants.Figure 2 shows an example of the routing and elements in a high-energy piping system [6].There is a straight pipe, an elbow, a T-piece, a Y-piece and so on, that are connected via circumferential welding.A high-energy piping system is more than 100 m long, and it thermally expands by about 1 m when heated to operating temperatures.However, since it is fixed at the boiler outlet and turbine inlet, the thermal expansion is restrained, and then thermal stress is generated.Therefore, circumferential welded joints are subjected to creep-fatigue loading due to thermal expansion stress and internal pressure during plant operation.Recently, thermal power plants have come to be used as regulated power sources, so creep-fatigue estimation is becoming an important issue as the number of plants starts and stops increases.In this paper, a series of creep-fatigue tests for Gr.91 steel welded joints were also performed at 600 • C to investigate their creep-fatigue properties.The creep-fatigue lives were also estimated using the linear damage summation rules of the fatigue damage and creep damage.Simultaneously, the elastic follow-up phenomena were discussed, where the creep strain in the heat-affected zone (HAZ) of welded joints increases during the strain holding.

Creep-Fatigue Test Results
To investigate the creep-fatigue properties of Gr.91 steel, a series of cree tests were performed [7].The test material was an ASME A387 Gr.91 Cl.2 steel it was normalized and tempered.The test was performed on a hydraulic servofatigue test machine with a load capacity of 100 kN, and the test piece was hea high-frequency induction device.The test piece was a round bar with a diam mm.The test temperature was 600 °C, and the axial strain was controlled at a gau of 25 mm. Figure 3 shows the loading waveform.It was strain-controlled fati stress ratio −1 with strain holding at the tensile peak.Several loading waveform considered, but a strain-controlled trapezoidal wave with tensile strain holdin lected, which simulates the loading patterns during actual component opera reason for the selection is that the thermal stress in the actual components is s trolled, and the other reason is that rachet deformation is likely to occur with loa The strain range was 0.4% to 1.5%, and the strain hold time was 1 to 60 min shows the relationship between the strain range and the cycles to failure.The failure were defined as when the peak stress decreased by 25% of the steady v fatigue lives were shortened by strain holding within all strain ranges.Figure 5 relationship between the fatigue life reduction factor and the strain hold time.T life reduction factor was defined as the ratio of the creep-fatigue life to pure f without strain holding.The minimum life reduction factor was approximatel there was a tendency showing that the smaller the strain range, the smaller the tion factor.In addition, the longer the strain hold time, the smaller the fatigue tion factor, but the fatigue life reduction factor tended to saturate at the strain about 30 min in all the strain ranges.Figure 6 compares the fatigue life reducti among Gr.91 steel at 600 °C, HR6W steel at 750 °C [8] and Alloy 617 at 700 ° fatigue life reduction factor of Alloy 617 was much smaller than that of Gr.9 HR6W steel.In Alloy 617, the cause of the fatigue life reduction seems to be Routing and elements in the high-energy piping system of a thermal power plant.

Creep-Fatigue Test Results
To investigate the creep-fatigue properties of Gr.91 steel, a series of creep-fatigue tests were performed [7].The test material was an ASME A387 Gr.91 Cl.2 steel plate, and it was normalized and tempered.The test was performed on a hydraulic servo-controlled fatigue test machine with a load capacity of 100 kN, and the test piece was heated with a high-frequency induction device.The test piece was a round bar with a diameter of 10 mm.The test temperature was 600 • C, and the axial strain was controlled at a gauge length of 25 mm. Figure 3 shows the loading waveform.It was strain-controlled fatigue of the stress ratio −1 with strain holding at the tensile peak.Several loading waveforms could be considered, but a strain-controlled trapezoidal wave with tensile strain holding was selected, which simulates the loading patterns during actual component operations.One reason for the selection is that the thermal stress in the actual components is straincontrolled, and the other reason is that rachet deformation is likely to occur with load control.The strain range was 0.4% to 1.5%, and the strain hold time was 1 to 60 min.Figure 4 shows the relationship between the strain range and the cycles to failure.The cycles to failure were defined as when the peak stress decreased by 25% of the steady value.The fatigue lives were shortened by strain holding within all strain ranges.Figure 5 shows the relationship between the fatigue life reduction factor and the strain hold time.The fatigue life reduction factor was defined as the ratio of the creep-fatigue life to pure fatigue life without strain holding.The minimum life reduction factor was approximately 0.3, and there was a tendency showing that the smaller the strain range, the smaller the life reduction factor.In addition, the longer the strain hold time, the smaller the fatigue life reduction factor, but the fatigue life reduction factor tended to saturate at the strain holding of about 30 min in all the strain ranges.Figure 6 compares the fatigue life reduction factors among Gr.91 steel at 600 • C, HR6W steel at 750 • C [8] and Alloy 617 at 700 • C [9].The fatigue life reduction factor of Alloy 617 was much smaller than that of Gr.91 steel or HR6W steel.In Alloy 617, the cause of the fatigue life reduction seems to be the creep effect during strain holding because the fracture mode clearly changed from transgranular cracking to intergranular cracking due to strain holding [10].However, the cause of the fatigue life reduction is not clear for Gr.91 steel because the change in the fracture mode is not as clear as that of Alloy 617.The cause of the fatigue life reduction for Gr.91 steel is discussed in Section 2.3.

Creep-Fatigue Life Estimation Results
The creep-fatigue lives were estimated based on the test results given in Section 2.1 [7].Fatigue damage is cyclic-dependent, while creep damage is time-dependent, but the linear damage summation rule estimates the creep-fatigue lives by linearly adding both damages [11,12].Figure 7 presents the calculation methods for the fatigue damage and creep damage.Fatigue damage was defined as the life reduction factor relative to the fatigue life without strain holding.Fatigue damage was calculated from the ratio of the creep-fatigue life with strain holding to the fatigue life without strain holding within the same strain range.The time exhaustion rule and the ductility exhaustion rule are generally used to calculate the creep damage.The time exhaustion rule is a stress-based estimation method where the creep damage is defined as the ratio of the time spent to rupture time.The creep damage was calculated by introducing the stress of the stress relaxation curve during strain holding into the creep rupture curve.On the other hand, the ductility exhaustion rule is a strain-based estimation method where the creep damage is defined as the ratio of consumed creep ductility to fracture ductility.Creep damage was calculated by introducing the creep rate of the stress relaxation curve during strain holding into the fracture ductility-creep rate diagram.Fracture ductility was defined as the true strain at the fracture, and it was calculated from the reduction area of the fractured test piece.Figure 8 shows the accumulated fatigue damage and creep damage until failure.All the creep damage values calculated using the time exhaustion rule were very small.While the sum of the fatigue damage and creep damage was much lower than 1 when the creep damage was calculated using the time exhaustion rule, it was closer to 1 when the creep damage was calculated using the ductility exhaustion rule.However, this result does not necessarily mean that the ductility exhaustion rule is better than the time exhaustion rule because fracture ductility values at low creep rates must be extrapolated from experimental values at high creep rates, and the accuracy of extrapolation significantly influences the creep damage values when using the ductility exhaustion rule.In other words, the results in Figure 8 could be a coincidence.It seems necessary to improve the accuracy of the fracture ductility values at low creep rates via long-term creep tests.The interpretations of the fact that the sum of the fatigue damage and creep damage was much lower than 1 when the creep damage was calculated by the time exhaustion rule are discussed in Section 2.3.

Creep-Fatigue Life Estimation Results
The creep-fatigue lives were estimated based on the test results given in Section 2.1 [7].Fatigue damage is cyclic-dependent, while creep damage is time-dependent, but the linear damage summation rule estimates the creep-fatigue lives by linearly adding both damages [11,12].Figure 7 presents the calculation methods for the fatigue damage and creep damage.Fatigue damage was defined as the life reduction factor relative to the fatigue life without strain holding.Fatigue damage was calculated from the ratio of the creep-fatigue life with strain holding to the fatigue life without strain holding within the same strain range.The time exhaustion rule and the ductility exhaustion rule are generally used to calculate the creep damage.The time exhaustion rule is a stress-based estimation method where the creep damage is defined as the ratio of the time spent to rupture time.The creep damage was calculated by introducing the stress of the stress relaxation curve during strain holding into the creep rupture curve.On the other hand, the ductility exhaustion rule is a strain-based estimation method where the creep damage is defined as the ratio of consumed creep ductility to fracture ductility.Creep damage was calculated by introducing the creep rate of the stress relaxation curve during strain holding into the fracture ductilitycreep rate diagram.Fracture ductility was defined as the true strain at the fracture, and it was calculated from the reduction area of the fractured test piece.Figure 8 shows the accumulated fatigue damage and creep damage until failure.All the creep damage values calculated using the time exhaustion rule were very small.While the sum of the fatigue damage and creep damage was much lower than 1 when the creep damage was calculated using the time exhaustion rule, it was closer to 1 when the creep damage was calculated using the ductility exhaustion rule.However, this result does not necessarily mean that the ductility exhaustion rule is better than the time exhaustion rule because fracture ductility values at low creep rates must be extrapolated from experimental values at high creep rates, and the accuracy of extrapolation significantly influences the creep damage values when using the ductility exhaustion rule.In other words, the results in Figure 8 could be a coincidence.It seems necessary to improve the accuracy of the fracture ductility values at low creep rates via long-term creep tests.The interpretations of the fact that the sum of the fatigue damage and creep damage was much lower than 1 when the creep damage was calculated by the time exhaustion rule are discussed in Section 2.3.

Discussions of the Creep-Fatigue Interaction
As shown in Figure 9, there are two possible interpretations of the fact that the sum of the fatigue damage and creep damage calculated using the time exhaustion rule was ε σ

Strain waveform
Fatigue curve

Stress waveform
Creep rupture curve

Discussions of the Creep-Fatigue Interaction
As shown in Figure 9, there are two possible interpretations of the fact that the s of the fatigue damage and creep damage calculated using the time exhaustion rule w ε σ

Strain waveform
Fatigue curve

Discussions of the Creep-Fatigue Interaction
As shown in Figure 9, there are two possible interpretations of the fact that the sum of the fatigue damage and creep damage calculated using the time exhaustion rule was much less than 1 (Figure 8).One is the interpretation that creep damage is underestimated.Many studies [13][14][15] have been conducted on this point, and several countermeasures have been developed.For example, the ductility exhaustion rule adopted by the British high-temperature structural design code R5 [16] is one of them.The second interpretation is that the effects of the creep-fatigue interaction are not considered in the linear damage summation rule.Figure 10  According to this concept, it is understood that the creep-fatigue interaction damage of Gr.91 steel at 600 • C is very large, and then D F + D C < 1 (Figure 8).Incidentally, as mentioned in Section 2.1, the fatigue life reduction due to strain holding was significant for Alloy 617 (Figure 6), and its cause seemed to be the creep effect during strain holding.In this case, the creep-fatigue interaction damage is very small (D IN = 0), and the sum of the fatigue damage and creep damage is expected to be 1 (D F + D C = 1).Little research has been carried out so far on the mechanism of the creep-fatigue interaction [17,18].Yokobori et al.'s [19] analysis is one of the few studies.They tried to treat creep-fatigue issues not as an individual combination of creep and fatigue, but as a simultaneous progress of a time-dependent fracture and a cycle-dependent one.Figure 11 shows the procedure for the creep-fatigue interaction analysis.An increased rate of creep-fatigue damage was expressed as a linear summation of the creep crack growth rate and the fatigue one.The term of the fatigue-crack growth was multiplied by a time-dependent coefficient, and similarly, that of the creep-crack growth was multiplied by a cycle-dependent coefficient.If coefficient α does not depend on time t, and coefficient β does not depend on cycle N, there is no creep-fatigue interaction (D F + D C = 1).Regarding the creep-fatigue life estimation, it seems that clarification of the creep-fatigue interaction mechanism and how to define the creep-fatigue interaction damage remain issues for the future.
Many studies [13][14][15] have been conducted on this point, and several c have been developed.For example, the ductility exhaustion rule adopte high-temperature structural design code R5 [16] is one of them.The secon is that the effects of the creep-fatigue interaction are not considered in th summation rule.Figure 10 illustrates this schematically.It follows the co is creep-fatigue interaction damage (DIN) in addition to fatigue damage damage (DC), and failure occurs when the sum of the three damages beco DIN = 1).Creep-fatigue interaction damage seems to depend on the mater ature range, stress level, and so on.If DIN = 0, then DF + DC = 1; if DIN > 0, and if DIN < 0, then DF + DC > 1.According to this concept, it is understoo fatigue interaction damage of Gr.91 steel at 600 °C is very large, and t (Figure 8).Incidentally, as mentioned in Section 2.1, the fatigue life reduct holding was significant for Alloy 617 (Figure 6), and its cause seemed to b during strain holding.In this case, the creep-fatigue interaction damage i = 0), and the sum of the fatigue damage and creep damage is expected to 1).Little research has been carried out so far on the mechanism of the cre action [17,18].Yokobori et al.'s [19] analysis is one of the few studies.Th creep-fatigue issues not as an individual combination of creep and fatig ultaneous progress of a time-dependent fracture and a cycle-dependen shows the procedure for the creep-fatigue interaction analysis.An increas fatigue damage was expressed as a linear summation of the creep crack the fatigue one.The term of the fatigue-crack growth was multiplied by a coefficient, and similarly, that of the creep-crack growth was multiplie pendent coefficient.If coefficient α does not depend on time t, and coeff depend on cycle N, there is no creep-fatigue interaction (DF + DC = 1).Rega fatigue life estimation, it seems that clarification of the creep-fatigue int nism and how to define the creep-fatigue interaction damage remain issu

Creep-Fatigue Test Results
To investigate the creep-fatigue properties of Gr.91 steel welded joints, a series of fundamental creep-fatigue tests were performed [20].Welded joints were prepared via the automated welding of ASME A387 Gr.91 Cl.2 steel plates followed by post-weld heat treatment at 740 °C for 8.4 h.The test was performed on a hydraulic servo-controlled fatigue test machine with a load capacity of 100 kN, and the test piece was heated with a high-frequency induction device.Figure 12 shows the test piece.It was a round bar with a diameter of 10 mm, which was cut off perpendicular to the weld line.The test section, with a gauge length of 25 mm, consisted of the base metal, weld metal and HAZ.The HAZ was located in the centre of the test section and its width was approximately 2 mm.The test temperature was 600 °C, and the axial strain in the test section was controlled.The loading waveform was a trapezoidal wave with tensile strain holding similar to Gr.91 steel

Creep-Fatigue Test Results
To investigate the creep-fatigue properties of Gr.91 steel welded joints, a series of fundamental creep-fatigue tests were performed [20].Welded joints were prepared via the automated welding of ASME A387 Gr.91 Cl.2 steel plates followed by post-weld heat treatment at 740 °C for 8.4 h.The test was performed on a hydraulic servo-controlled fatigue test machine with a load capacity of 100 kN, and the test piece was heated with a high-frequency induction device.Figure 12 shows the test piece.It was a round bar with a diameter of 10 mm, which was cut off perpendicular to the weld line.The test section, with a gauge length of 25 mm, consisted of the base metal, weld metal and HAZ.The HAZ was located in the centre of the test section and its width was approximately 2 mm.The test temperature was 600 °C, and the axial strain in the test section was controlled.The loading waveform was a trapezoidal wave with tensile strain holding similar to Gr.91 steel (Figure 3).The strain range was 0.5%, and the strain hold time was 1 to 300 min.

Creep-Fatigue Test Results
To investigate the creep-fatigue properties of Gr.91 steel welded joints, a series of fundamental creep-fatigue tests were performed [20].Welded joints were prepared via the automated welding of ASME A387 Gr.91 Cl.2 steel plates followed by post-weld heat treatment at 740 • C for 8.4 h.The test was performed on a hydraulic servo-controlled fatigue test machine with a load capacity of 100 kN, and the test piece was heated with a high-frequency induction device.Figure 12 shows the test piece.It was a round bar with a diameter of 10 mm, which was cut off perpendicular to the weld line.The test section, with a gauge length of 25 mm, consisted of the base metal, weld metal and HAZ.The HAZ was located in the centre of the test section and its width was approximately 2 mm.The test temperature was 600 • C, and the axial strain in the test section was controlled.The loading waveform was a trapezoidal wave with tensile strain holding similar to Gr.91 steel (Figure 3).The strain range was 0.5%, and the strain hold time was 1 to 300 min.Figure 13 Metals 2023, 13, 1880 9 of 14 compares the hardness distribution in the test pieces before testing, after the fatigue test and after the creep-fatigue test.Before testing, the Vickers hardness of the weld metal was about 250 and that of the base metal was about 220.The lowest hardness was about 200 near the HAZ.The Vickers hardness after the fatigue test decreased overall compared to that before testing.On the other hand, the hardness of the weld metal decreased significantly, resulting in a flat harness distribution overall after the creep-fatigue test.Based on the hardness distribution results, it is assumed that the strain concentrates and plastic restraint occurs in the HAZ. Figure 14 shows a cross-sectional view of the fractured test pieces for the strain hold time of 300 min.All the test pieces fractured in the fine-grained HAZ.This is so-called Type IV damage, and it is a creep-dominant failure caused by the stress triaxiality in the HAZ. Figure 15 shows the creep voids observed in the HAZ inside the fractured test piece and the microcracks observed in the HAZ on the fractured test piece's surface.It could be inferred that the microcracks generated on the surface due to fatigue damage were connected, with many voids generated by creep damage, and they propagated inside the test piece.Figure 16 shows the relationship between the fatigue life reduction factor and the strain hold time.The fatigue life reduction factor was defined as the ratio of the creep-fatigue life to pure fatigue life without strain holding.The longer the strain hold time, the smaller the fatigue life reduction factor, but the fatigue life reduction factor tended to saturate at a strain holding of about 300 min.The minimum fatigue life reduction factor was at approximately 0.2 for the 300 min strain holding.
Metals 2023, 13, x FOR PEER REVIEW 9 compares the hardness distribution in the test pieces before testing, after the fatigu and after the creep-fatigue test.Before testing, the Vickers hardness of the weld meta about 250 and that of the base metal was about 220.The lowest hardness was abou near the HAZ.The Vickers hardness after the fatigue test decreased overall compar that before testing.On the other hand, the hardness of the weld metal decreased sig cantly, resulting in a flat harness distribution overall after the creep-fatigue test.Base the hardness distribution results, it is assumed that the strain concentrates and plast straint occurs in the HAZ. Figure 14 shows a cross-sectional view of the fractured pieces for the strain hold time of 300 min.All the test pieces fractured in the fine-gra HAZ.This is so-called Type IV damage, and it is a creep-dominant failure caused b stress triaxiality in the HAZ. Figure 15 shows the creep voids observed in the HAZ in the fractured test piece and the microcracks observed in the HAZ on the fractured piece's surface.It could be inferred that the microcracks generated on the surface d fatigue damage were connected, with many voids generated by creep damage, and propagated inside the test piece.Figure 16 shows the relationship between the fatigu reduction factor and the strain hold time.The fatigue life reduction factor was defin the ratio of the creep-fatigue life to pure fatigue life without strain holding.The lo the strain hold time, the smaller the fatigue life reduction factor, but the fatigue life re tion factor tended to saturate at a strain holding of about 300 min.The minimum fa life reduction factor was at approximately 0.2 for the 300 min strain holding.compares the hardness distribution in the test pieces before testing, after the fatig and after the creep-fatigue test.Before testing, the Vickers hardness of the weld me about 250 and that of the base metal was about 220.The lowest hardness was abo near the HAZ.The Vickers hardness after the fatigue test decreased overall comp that before testing.On the other hand, the hardness of the weld metal decreased cantly, resulting in a flat harness distribution overall after the creep-fatigue test.Ba the hardness distribution results, it is assumed that the strain concentrates and pla straint occurs in the HAZ. Figure 14 shows a cross-sectional view of the fractur pieces for the strain hold time of 300 min.All the test pieces fractured in the fine-g HAZ.This is so-called Type IV damage, and it is a creep-dominant failure caused stress triaxiality in the HAZ. Figure 15 shows the creep voids observed in the HAZ the fractured test piece and the microcracks observed in the HAZ on the fractur piece's surface.It could be inferred that the microcracks generated on the surface fatigue damage were connected, with many voids generated by creep damage, an propagated inside the test piece.Figure 16 shows the relationship between the fatig reduction factor and the strain hold time.The fatigue life reduction factor was def the ratio of the creep-fatigue life to pure fatigue life without strain holding.The the strain hold time, the smaller the fatigue life reduction factor, but the fatigue life tion factor tended to saturate at a strain holding of about 300 min.The minimum life reduction factor was at approximately 0.2 for the 300 min strain holding.

Creep-Fatigue Life Estimation Results
Figure 17 shows the creep-fatigue life estimation method for welded j

Creep-Fatigue Life Estimation Results
Figure 17 shows the creep-fatigue life estimation method for welded joints [ is basically the same method as for Gr.91 steel (Figure 7), although there is no gu that it will apply to discontinuities such as welded joints.Fatigue damage was de the life reduction factors relative to the fatigue life of welded joints without strain

Creep-Fatigue Life Estimation Results
Figure 17 shows the creep-fatigue life estimation method for welded joints [20].This is basically the same method as for Gr.91 steel (Figure 7), although there is no guarantee that it will apply to discontinuities such as welded joints.Fatigue damage was defined as the life reduction factors relative to the fatigue life of welded joints without strain holding.Fatigue damage was calculated from the ratio of the creep-fatigue life with strain holding to the fatigue life without strain holding within the same strain range.Creep damage was defined as the ratio of the time spent to the rupture time of a welded joint based on the time exhaustion rule.Creep damage was calculated by introducing the stress of the stress relaxation curve during strain holding into the creep rupture curve of the welded joints.Figure 18 shows the creep rupture curve of the welded joints.It was a curve obtained by

Creep-Fatigue Life Estimation Results
Figure 17 shows the creep-fatigue life estimation method for welded joints [20].This is basically the same method as for Gr.91 steel (Figure 7), although there is no guarantee that it will apply to discontinuities such as welded joints.Fatigue damage was defined as the life reduction factors relative to the fatigue life of welded joints without strain holding.Fatigue damage was calculated from the ratio of the creep-fatigue life with strain holding to the fatigue life without strain holding within the same strain range.Creep damage was defined as the ratio of the time spent to the rupture time of a welded joint based on the time exhaustion rule.Creep damage was calculated by introducing the stress of the stress relaxation curve during strain holding into the creep rupture curve of the welded joints.Figure 18 shows the creep rupture curve of the welded joints.It was a curve obtained by lowering the creep rupture curve of Gr.91 steel by the creep strength reduction factor of welded joints, which was proposed by ORNL [21].Figure 19 plots the accumulated fatigue damage and creep damage until fracture.It was found that the test pieces fractured when the sum of the fatigue damage and the creep damage was considerably less than 1.One of the reasons may be that the effects of the creep-fatigue interaction were not considered in the linear damage summation rule, as is the case with Gr.91 steel (Section 2.3).However, the creep-fatigue interaction damage of welded joints does not seem to be as large as that of Gr.91 steel because the fracture mode of welded joints was creep-dominant due to the fact that many creep voids were observed inside the HAZ (Figure 15).Therefore, another possible reason may be the influence of the elastic follow-up phenomena peculiar to welded joints.The creep strain of the HAZ may increase due to the transfer of the elastic strain from the base metal and the weld metal according to the elastic follow-up phenomena during strain holding.If the elastic follow-up phenomena are not considered in the creep-fatigue life estimation, the creep strain of the HAZ may be underestimated.This is discussed in Section 3.3.lowering the creep rupture curve of Gr.91 steel by the creep strength reduction factor of welded joints, which was proposed by ORNL [21].Figure 19 plots the accumulated fatigue damage and creep damage until fracture.It was found that the test pieces fractured when the sum of the fatigue damage and the creep damage was considerably less than 1.One of the reasons may be that the effects of the creep-fatigue interaction were not considered in the linear damage summation rule, as is the case with Gr.91 steel (Section 2.3).However, the creep-fatigue interaction damage of welded joints does not seem to be as large as that of Gr.91 steel because the fracture mode of welded joints was creep-dominant due to the fact that many creep voids were observed inside the HAZ (Figure 15).Therefore, another possible reason may be the influence of the elastic follow-up phenomena peculiar to welded joints.The creep strain of the HAZ may increase due to the transfer of the elastic strain from the base metal and the weld metal according to the elastic follow-up phenomena during strain holding.If the elastic follow-up phenomena are not considered in the creep-fatigue life estimation, the creep strain of the HAZ may be underestimated.This is discussed in Section 3.3.lowering the creep rupture curve of Gr.91 steel by the creep strength reduction facto welded joints, which was proposed by ORNL [21].Figure 19 plots the accumulated fati damage and creep damage until fracture.It was found that the test pieces fractured w the sum of the fatigue damage and the creep damage was considerably less than 1. O of the reasons may be that the effects of the creep-fatigue interaction were not conside in the linear damage summation rule, as is the case with Gr.91 steel (Section 2.3).Howe the creep-fatigue interaction damage of welded joints does not seem to be as large as t of Gr.91 steel because the fracture mode of welded joints was creep-dominant due to fact that many creep voids were observed inside the HAZ (Figure 15).Therefore, anot possible reason may be the influence of the elastic follow-up phenomena peculia welded joints.The creep strain of the HAZ may increase due to the transfer of the ela strain from the base metal and the weld metal according to the elastic follow-up pheno ena during strain holding.If the elastic follow-up phenomena are not considered in creep-fatigue life estimation, the creep strain of the HAZ may be underestimated.Th discussed in Section 3.3.

Discussion of the Elastic Follow-Up Phenomena
One of the reasons why the life estimation results based on the linear damag mation rule were much less than 1 (Figure 19) is that the elastic follow-up phen peculiar to welded joints were not considered [2]. Figure 20 shows the concept of th tic follow-up phenomena [22].Rod 1, with low rigidity ξ1, and rod 2, with high rigid are connected in a series.When a forced displacement is applied to the connected high temperatures, assuming that only rod 1 creeps, the elastic deformation of r transferred to rod 1 with the stress relaxation of rod 1.As a result, the creep strain 1 at the initial state ε1a increases to the strain after the elastic follow-up ε1b.The str crease ratio ε1b/ε1a is determined by the rigidity ratio ξ1/ξ2 and the ratio of the length 1 to the total length α (=L1/(L1 + L2)).For example, the value of ε1b/ε1a exceeds 3.0 wh value of ξ1/ξ2 is 0.5 and the value of α is 0.1.
In Gr.91 steel welded joints, the base metal, the HAZ and the weld metal ar nected in a series (Figure 12), and the rigidity of the HAZ may be much lower than the base and weld metals.Furthermore, the value of α may be approximately mm/25 mm).Therefore, the creep strain of the HAZ may increase due to the tran the elastic strain from the base and weld metals according to the elastic follow-u nomena during the strain holding.Figure 21 illustrates this schematically.When th strain εt is kept constant, the average plastic strain εp av does not change, although th tic average strain εe av decreases and the average creep strain εc av increases with the relaxation.Here, the average creep strain εc av is the average among the creep strain base metal εc BM , that of the weld metal εc WM and that of the HAZ εc HAZ .While the strains of the base and weld metals hardly increase, the creep strain of the HAZ se increase significantly.In the future, it will be important to quantitatively evaluate fects of the elastic follow-up phenomena in the creep-fatigue life estimation of w joints.

Discussion of the Elastic Follow-Up Phenomena
One of the reasons why the life estimation results based on the linear damage summation rule were much less than 1 (Figure 19) is that the elastic follow-up phenomena peculiar to welded joints were not considered [2]. Figure 20 shows the concept of the elastic follow-up phenomena [22].Rod 1, with low rigidity ξ 1 , and rod 2, with high rigidity ξ 2 , are connected in a series.When a forced displacement is applied to the connected rod at high temperatures, assuming that only rod 1 creeps, the elastic deformation of rod 2 is transferred to rod 1 with the stress relaxation of rod 1.As a result, the creep strain of rod 1 at the initial state ε 1a increases to the strain after the elastic follow-up ε 1b .The strain increase ratio ε 1b /ε 1a is determined by the rigidity ratio ξ 1 /ξ 2 and the ratio of the length of rod 1 to the total length α (=L 1 /(L 1 + L 2 )).For example, the value of ε 1b /ε 1a exceeds 3.0 when the value of ξ 1 /ξ 2 is 0.5 and the value of α is 0.1.In Gr.91 steel welded joints, the base metal, the HAZ and the weld metal are connected in a series (Figure 12), and the rigidity of the HAZ may be much lower than that of the base and weld metals.Furthermore, the value of α may be approximately 0.1 (=2 mm/25 mm).Therefore, the creep strain of the HAZ may increase due to the transfer of the elastic strain from the base and weld metals according to the elastic follow-up phenomena during the strain holding.Figure 21 illustrates this schematically.When the total strain ε t is kept constant, the average plastic strain ε p av does not change, although the elastic average strain ε e av decreases and the average creep strain ε c av increases with the stress relaxation.Here, the average creep strain ε c av is the average among the creep strain of the base metal ε c BM , that of the weld metal ε c WM and that of the HAZ ε c HAZ .While the creep strains of the base and weld metals hardly increase, the creep strain of the HAZ seems to increase significantly.In the future, it will be important to quantitatively evaluate the effects of the elastic follow-up phenomena in the creep-fatigue life estimation of welded joints.

Conclusions
The creep-fatigue properties and their life estimation methods for Gr.91 steel and its welded joints were investigated.The results obtained are summarized below.
(1) In a series of creep-fatigue tests of Gr.91 steel at 600 °C, the fatigue life decreased with tensile strain holding, and the smaller the strain range, the smaller the fatigue life reduction factor.The minimum life reduction factor was approximately 0.3.Furthermore, the longer the strain hold time, the smaller the fatigue life reduction factor, but it tended to saturate at a strain holding of about 30 min.(2) The test pieces fractured when the linear summation of the accumulated fatigue damage and the creep damage calculated using the time exhaustion rule was much less than 1.One of the reasons is that the creep damage was underestimated, but another important reason is that the effect of the creep-fatigue interaction was not considered.In this material at 600 °C, the damage due to the creep-fatigue interaction is considered to be quite large.

Conclusions
The creep-fatigue properties and their life estimation methods for Gr.91 steel and its welded joints were investigated.The results obtained are summarized below.
(1) In a series of creep-fatigue tests of Gr.91 steel at 600 • C, the fatigue life decreased with the tensile strain holding, and the smaller the strain range, the smaller the fatigue life reduction factor.The minimum life reduction factor was approximately 0.3.Furthermore, the longer the strain hold time, the smaller the fatigue life reduction factor, but it tended to saturate at a strain holding of about 30 min.(2) The test pieces fractured when the linear summation of the accumulated fatigue damage and the creep damage calculated using the time exhaustion rule was much less than 1.One of the reasons is that the creep damage was underestimated, but another important reason is that the effect of the creep-fatigue interaction was not considered.In this material at 600 • C, the damage due to the creep-fatigue interaction is considered to be quite large.(3) The creep-fatigue life should be estimated using the linear summation rule of the fatigue damage, the creep damage, and the creep-fatigue interaction damage.In the future, it will be necessary to clarify the creep-fatigue interaction mechanism and define the damage value.(4) In a series of creep-fatigue tests of Gr.91 steel welded joints in the strain range of 0.5% at 600 • C, the fatigue life decreased with the tensile strain holding.The longer the strain hold time, the lower the fatigue life, and the minimum fatigue life reduction factor was approximately 0.2 in the case of the 300 min strain holding.All the test pieces fractured in the fine-grained HAZ.(5) The creep-fatigue life of the welded joint was estimated using the linear damage summation rule of the fatigue damage and the creep damage of the HAZ, which was the fracture location.All the test pieces fractured when the linear summation of the fatigue damage and the creep damage was considerably less than 1.One possible reason is the influence of the elastic follow-up phenomena peculiar to welded joints.(6) The creep strain in the HAZ may increase due to the transfer of the elastic strain from the base metal and the weld metal according to the elastic follow-up phenomena during the strain holding.In the future, it will be important to quantitatively evaluate the increase in the creep strain in the HAZ in order to estimate the creep-fatigue life of welded joints.

Figure 1 .
Figure 1.Thermal stress expected during operation in FBR plants [1] permissioned from Japan Society of Materials Science in 2023.(a) Steady thermal stress due to thermal expansion in the piping system.(b) Transient thermal stress due to the temperature gradient in the reactor vessel.

Figure 1 .
Figure 1.Thermal stress expected during operation in FBR plants [1] permissioned from Japan Society of Materials Science in 2023.(a) Steady thermal stress due to thermal expansion in the piping system.(b) Transient thermal stress due to the temperature gradient in the reactor vessel.

Figure 2 .
Figure 2. Routing and elements in the high-energy piping system of a thermal power pl

Figure 2 .
Figure 2. Routing and elements in the high-energy piping system of a thermal power plant.

Figure 4 .
Figure 4. Creep-fatigue test results for Gr.91 steel at 600 °C [7].permissioned from Japan Society of Materials Science in 2023.

Figure 4 .
Figure 4. Creep-fatigue test results for Gr.91 steel at 600 °C [7].permissioned from Japan Society of Materials Science in 2023.

Figure 6 .
Figure 6.Comparison of the fatigue life reduction factors among three materials.

Figure 7 .
Figure 7.The calculation methods for the fatigue damage and creep damage [7].

Figure 7 .Figure 7 .
Figure 7.The calculation methods for the fatigue damage and creep damage [7].
illustrates this schematically.It follows the concept that there is creep-fatigue interaction damage (D IN ) in addition to fatigue damage (D F ) and creep damage (D C ), and failure occurs when the sum of the three damages becomes 1 (D F + D C + D IN = 1).Creep-fatigue interaction damage seems to depend on the material type, temperature range, stress level, and so on.If D IN = 0, then D F + D C = 1; if D IN > 0, then D F + D C < 1; and if D IN < 0, then F + D C > 1.

Figure 17 .
Figure 17.Calculation method for the fatigue damage and creep damage of welded joints [20].

Figure 17 .
Figure 17.Calculation method for the fatigue damage and creep damage of welded joints [20].

Figure 21 .
Figure 21.Schematic diagram of the creep strain increase in the HAZ due to elastic follow-up.

Figure 21 .
Figure 21.Schematic diagram of the creep strain increase in the HAZ due to elastic follow-up.
Calculation method for the fatigue damage and creep damage of welded joints [20].