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Creep–fatigue damage assessment in high-temperature piping system under bending and torsional moments using wireless MEMS-type gyro sensor

  • Masayuki Arai EMAIL logo , Hiroyuki Hamada and Kazuma Okuno
Published/Copyright: September 20, 2024
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Journal of the Mechanical Behavior of Materials
From the journal Journal of the Mechanical Behavior of Materials Volume 33 Issue 1

Abstract

Piping systems in thermal power plants are generally subjected to creep–fatigue loading caused by internal pressure, bending moment, and torsional moment in a high-temperature environment. These loadings cause Type IV cracks to form in the heat-affected zone in the weldment of the piping. In this study, we attempt to predict the creep–fatigue Type IV crack initiation life using a wireless micro-electromechanical system-type gyro sensor to understand the damage progress in plant components for the establishment of digital twin technology, which has recently attracted attention. The strategy for developing the system is as follows: i) remotely and sequentially import signals from a sensor attached to the actual component to a personal computer and ii) identify mechanical conditions such as bending and torsional moments in the piping component even in a high-temperature environment. This study first shows how to identify both moments in a piping system based on the rotation angles (deflection and torsion angles) measured using a gyro sensor. Next, a creep–fatigue life diagram is constructed based on the equivalent bending moment, which can combine the two independent parameters of bending and torsional moments into a single parameter. Finally, creep–fatigue tests were performed on a P91 steel piping weldment specimen using the high-temperature bending–torsional creep–fatigue testing machine developed by our group, and it was shown that the equivalent bending moment identified from the gyro sensor attached to the piping specimen can predict the Type IV creep–fatigue crack initiation life at the weldment.

Keywords: piping system; weldment; Type IV cracking; creep–fatigue damage; bending moment; torsional moment; equivalent bending moment; MEMS-type gyro sensor; digital twin technology

1 Introduction

With the rise of renewable energies, such as solar power generation, thermal power generation is now limited to partial operation to compensate for daily fluctuations in power generation from renewable energies rather than the base load, as in the previous operation mode. Therefore, the accumulation of creep–fatigue damage in high-temperature components caused by the frequent startup–shutdown of thermal power generation equipment has become a major problem. In piping systems, which account for the majority of these high-temperature components, a combination of bending and torsional moments occurs owing to the thermal expansion of straight piping via the elbow section, in addition to the internal pressure caused by high-pressure steam. When these combined loads act on a weldment in a piping system, a Type IV crack occurs in the heat-affected zone (HAZ) [1,2,3]. The crack then propagates rapidly along the circumferential direction under constant shear stress owing to the torsional moment as the driving force, resulting in guillotine rupture of the pipe. Therefore, the leak before break concept known in linear fracture mechanics [4,5] is not acceptable for a piping problem subjected to such complex loading owing to bending and torsional moments, which requires the development of a more accurate prediction of crack initiation life owing to creep–fatigue loadings.

In recent years, digital twin technology has attracted significant attention for damage management in plant components [6]. A digital twin is a technology used to predict the future of components from a numerical model (digital twin) built on a computer based on information from multiple sensors attached to structural components in an actual plant (information in real space: physical twin). Currently, digital twin systems are being developed for the maintenance of gas turbine plants in power generation [7], thermal power plants [8], aircraft jet engines [9], chemical plants [10], wind power plants [11], factory facilities [12], and construction equipment [13]. In this context, wireless sensors required for physical twins and software systems for large-scale thermo-structural analysis of numerical models have been developed worldwide. Generally, the sensor information required for digital twinning is obtained using thermocouples [14], pressure gauges [15], and digital tachometers [16]. To obtain more detailed sensor information on the components, Moi et al. [17] installed multiple strain gauges on cranes and synchronized real-time data with finite element (FE) analysis to predict load fluctuations and fatigue damage accumulation during crane operations. For high-temperature components, as those targeted in this study, laser displacement transducers [18] and fiber bragg gradings [19] as heat-resistant sensors instead of strain gauges have been considered.

In this study, we focused on micro-electromechanical system (MEMS)-type gyro sensors, which are less expensive than the aforementioned sensors. The angular velocity measured by the gyro sensors is integrated over time to convert the rotation angle (deflection and torsion angles) at an evaluation point in the piping system. Although it is known that the gyro sensors have a low heat resistance temperature of about 313 K, this engineering problem can be avoided easily by moving the sensor away from the surface of the piping. In this study, the bending and torsional moments generated in the piping system are identified from the rotation angle measured in this way, and an equivalent bending moment is introduced to combine those two independent moments into a single parameter. Finally, creep–fatigue tests are performed on a piping specimen with weldment using the high-temperature bending–torsional creep–fatigue testing machine developed by our group, and it was proved that the Type IV creep–fatigue crack initiation life can be predicted from the gyro sensor attached to the specimen. In this study, P91 steel and its welding material were treated as candidate piping materials for ultra-supercritical thermal power plants [20].

The remainder of this article is organized as follows. Section 2 presents an overview of a high-temperature bending–torsional creep–fatigue testing machine that can simultaneously apply bending and torsional moments to piping specimens at high temperatures. This testing machine was developed by our group, and its details are described in the literature [21]. Section 3 describes the proposed technique for monitoring the rotation angle in piping systems using wireless MEMS-type gyro sensors. To demonstrate the effectiveness of this technique, tests were conducted at room temperature using the high-temperature bending–torsional creep–fatigue testing machine introduced in Section 2, in which bending and torsional moments were applied simultaneously. The results were compared to the rotation angles measured using the monitoring system. Bending and torsional creep–fatigue tests were conducted on a piping specimen with a weldment at high temperatures using the developed monitoring system, and the relationships between the rotation angle change with cyclic loading, equivalent bending moment, and rotation angle are presented in Sections 4–7. It is shown that the creep–fatigue life diagram constructed based on the equivalent bending moment can predict the Type IV crack initiation life of the pipe weldment from the gyro sensor information.

2 High-temperature bending–torsional fatigue testing machine [21]

Figure 1 shows a schematic of the loading mechanism devised in this study to simultaneously apply a bending moment M and torsional moment T to a piping specimen. Arms of length l are attached to both ends of the specimen in different directions. The other ends of the arms can rotate around an axis parallel to the axis of the piping specimen. A compressive load P is applied to two points on the top surface of the piping specimen, supported by the arms. Consequently, bending and torsional moments were generated simultaneously in the piping specimen.

(1) M = 1 2 P l 1 , T = 1 2 Pl ,

where l 1 is the distance between the fixed edge of the piping specimen and loading point. Therefore, the torsional moment can be freely changed by changing the arm length l while the bending moment remains constant.

Figure 1 Schematic of loading mechanism for applying bending and torsional moments simultaneously.
Figure 1

Schematic of loading mechanism for applying bending and torsional moments simultaneously.

Figure 2 shows the high-temperature bending–torsional creep–fatigue testing machine developed based on the loading mechanism described earlier. The testing machine consisted of the main body of a fatigue testing machine (EHF-UV050K2A-A10-2, Shimadzu Corporation, Japan), a loading section for transmitting the compression load applied by the main body of the testing machine to the piping specimen, a rotating fixture for supporting the arms attached to both ends of the piping specimen, and an electric furnace for heating the piping specimen. The details of this testing machine are provided in Okuno et al. [21].

Figure 2 High-temperature bending–torsion creep–fatigue tester developed in this study [21]: (a) 3-D CAD diagram and (b) appearance of creep–fatigue tester.
Figure 2

High-temperature bending–torsion creep–fatigue tester developed in this study [21]: (a) 3-D CAD diagram and (b) appearance of creep–fatigue tester.

3 Wireless gyro sensor for monitoring piping system

In this study, a MEMS-type gyro sensor was utilized to identify the rotation angles (deflection and torsion angles) of a piping system. When a mass m connected to the base oscillates at velocity v , the Coriolis force F on the mass, measured from the position vector r relative to the center of rotation of the base, is expressed as

(2) F = 2 m v × Ω ,

where × is the outer product, Ω is the angular velocity of the base, and the angle of rotation θ can be obtained by integrating the angular velocity over time, as follows:

(3) θ = ∫ 0 t Ω d t .

Figure 3 shows the application of the wireless MEMS-type gyro sensor monitoring system in a piping system. The gyro sensor used in this study is the WT901BLE (WT901BLECL, WitMotion, China), which can measure the angular velocity Ω = ( Ω x , Ω y , Ω z ) around the x , y , and z axes set inside the sensor. In this study, the angular velocity around the x - and y -axes, Ω = ( Ω x , Ω y ) , is used. The measurement results were sequentially transmitted to a PC via wireless communication (Bluetooth 5.0). The measurement range of angular velocity around each axis is from −2,000 to +2,000 deg/s. The data transmitted to the PC were subjected to noise processing by fast Fourier transform and then numerically integrated to obtain the rotation angle θ = ( θ x , θ y ) . Data conversion was conducted using an analysis program created by Physon. To confirm the measurement accuracy of the gyro sensor, the gyro sensor and tachometer were mounted on a circular table rotating at a constant rotational speed, and their angular velocities were compared. It was confirmed that the relative error of the angular velocity around each axis of the gyro sensor was within 1.0% for a wide range of angular velocity data compared to the measurement results from the tachometer.

Figure 3 Application of monitoring system using wireless MEMS-type gyro sensor to piping system.
Figure 3

Application of monitoring system using wireless MEMS-type gyro sensor to piping system.

4 Test procedure

4.1 Material and sample preparation

In this study, ASME SA335/ASTM A335 Grade 91 (9Cr-1Mo-Nb-V steel), a high-chromium ferritic steel, was used as the test material. Their chemical compositions are presented in Table 1. The geometries of the piping specimens used in the test are shown in Figure 4. The outer diameter, wall thickness, and length were 48, 5, and 900 mm, respectively. The center of the specimen was cut, and the cut surfaces were welded circumferentially by tungsten inert gass using TG-S9Cb welding rods. After welding, the weldment was heat-treated (1,023 K for at least 0.5 h), and MT inspection was performed again to confirm the absence of cracks.

Table 1

Chemical composition of piping test specimen (wt%)

C Mn P S Cu Si Ni Cr
0.09 0.38 0.011 0.003 0.19 0.27 0.18 8.36
Mo V Ti B Al Zr Nb N
0.91 0.216 0.02 0.0001 0.007 0.001 0.081 0.0414
Figure 4 Geometry of the piping test specimen: dimensions in mm.
Figure 4

Geometry of the piping test specimen: dimensions in mm.

4.2 Test conditions and procedure

The following two types of tests were conducted in this study.

4.2.1 Reliability test of gyro sensor using welded piping specimens

A reliability test was conducted to check the validity of the gyro sensor-monitoring system developed in this study by simultaneously applying bending and torsional moments to a welded piping specimen at room temperature and comparing the rotation angles measured by the gyro sensors at various load levels with the results of the FE analysis, as described in the following. To check the validity of the FE analysis results, rosette-type strain gauges (KFG-2-120-D17-11L3M2S, Kyowa Dengyo, Japan) were bonded to the underside of the piping specimen at the center of the weldment. Figure 5 shows an image of the underside of the piping specimen to which the strain gauges were bonded.

Figure 5 Bottom view of the piping test specimen with strain gauges.
Figure 5

Bottom view of the piping test specimen with strain gauges.

For the bending–torsional test condition, the distance between the loading points was set to 235 mm, the arm length l was 300 mm, and a gyro sensor was installed on the top surface of the piping specimen at l s = 70 mm from the fixed edge of the piping specimen arm. The compressive load P was then increased in 2 kN increments until it reached a maximum of 10 kN, and the strain values and data from the gyro sensor were acquired at that time. The loading speed was set to 0.2 kN/s.

4.2.2 High-temperature bending–torsional creep–fatigue tests

The high-temperature bending–torsional creep–fatigue testing machine, as described earlier, was also used for the creep–fatigue tests. Prior to conducting the creep–fatigue test, the temperature of the gyro sensor was checked using a thermocouple (K-type thermocouple, sheath length 50 mm, sheath outer diameter 1.0 mm, Toyo Thermochemical, Japan). At a set temperature of 923 K in an electric furnace, the sensor was left in an uncooled state for approximately 1 day. The results showed that the temperature did not exceed 303 K. Therefore, it was determined that the gyro sensor could be applied to monitor the rotation angle during high-temperature bending–torsional fatigue tests.

The creep–fatigue test procedure was as follows. The test temperature was set to 923 K, the minimum load was P min = 0 kN, the maximum load P max = 4.0 and 4.5 kN, and the holding time at the maximum load was 600 s under a load control. The loading speed was set to 0.2 kN/s. As in the previous verification test, the distance between the loading points was 235 mm, and arm length l was 300 mm. The gyro sensor was set at l s = 90 mm from the fixed edge of the arm of the piping specimen. The creep–fatigue life was defined as the number of cycles at which the maximum stroke change per cycle exceeded 0.1 mm/cycle. This definition of life corresponds to the initiation and propagation of cracks in the piping weldment, where a decrease in cross-sectional area causes a rapid increase in stroke.

5 FE analysis

Two types of FE analysis were conducted in this study: (i) reliability analysis of a gyro sensor using a welded piping specimen and (ii) bending–torsional creep–fatigue analysis under high-temperature conditions.

5.1 Reliability analysis of gyro sensor using welded piping specimens

Figure 6 shows the FE model used in this study. The geometry of the FE model was designed to match that of an actual piping specimen. Both ends of this model were fixed to rigid arms, as shown in the figure. The weld metal (4 mm wide) and HAZ section (2 mm wide) were introduced at the center of the FE model. The model was divided into three-dimensional rectangular elements (element seven). The weld metal and the area around the HAZ were divided more finely than the other areas. In this FE model, the minimum element size was 0.5 mm, the number of elements was 257,166, and the number of nodes was 298,486. For the boundary conditions, the displacement of a node on the rigid arm at a distance of arm length l from the center of the pipe axis was fixed in the direction shown in the figure. This condition allowed the piping model to be subjected to bending and torsional moments simultaneously, as in the actual test. A concentrated load P / 2 was applied vertically downward to the top surface of the piping model at a distance of l 1 = 235 mm from the rigid arm. In this model, the gyro sensor was set at l s = 70 mm from the fixed end of the arm. The concentrated load was applied in steps of 2 kN, up to a maximum of 10 kN, corresponding to the actual test method.

Figure 6 FE model for welded piping specimen subjected to bending moment and torsional moment at room temperature.
Figure 6

FE model for welded piping specimen subjected to bending moment and torsional moment at room temperature.

The deflection angle θ and torsion angle φ in the FE model were evaluated from the results of the FE analysis according to the method as follows. Figure 7 shows the deformation of the FE model before and after loading. Assume that point A on the top surface of the FE model is displaced to point A′ owing to loading. However, if an arbitrary point O along the axis center of the FE model is displaced to point O′ after loading, the following position vector is defined:

(4) R = OA → R ′ = O ′ A ′ ⃗ .

Figure 7 Evaluation method of deflection angle and torsional angle from FE model displaced before and after loading.
Figure 7

Evaluation method of deflection angle and torsional angle from FE model displaced before and after loading.

Next, let R d and R d ′ be the vectors projected onto the y - z plane from the position vectors R and R ′ and R t and R t ′ be the vectors projected onto the x - y plane. Then, taking the inner product of these vectors, the deflection angle θ and torsion angle φ can be obtained as follows:

(5) θ = cos − 1 R d · R d ′ | R d | | R d ′ | , φ = cos − 1 R t · R t ′ | R t | | R t ′ | ,

where (∙) is the inner product symbol and |-| is the norm, respectively. The nodal information in the FE model was entered into Eq. (5) for obtaining the deflection angle θ and torsion angle φ .

In this FE analysis, the Young’s modulus and Poisson’s ratio of the base metal and weldment of the FE model were set to 213 GP and 0.3, respectively [21], and the FE analysis was performed according to the loading procedure in the test. From the FE analysis results, the bending and shear stresses at the locations where the strain gauges were bonded and the rotation angles (deflection and torsion angles) at the locations where the gyro sensors were installed were evaluated. The commercial FE analysis program MARC (MSC Software, MARC Mentat 2021.2) was used for the FE analysis.

5.2 High-temperature bending–torsional creep–fatigue analysis

Figure 8 shows the FE model used in this study. The geometry of the FE model, element types, and element division methods are the same as those described in the previous section. The boundary conditions of the FE model were identical. In this case, the gyro sensor was set at l s = 90 mm from the fixed end of the arm. The concentrated load was applied at a loading rate of 0.2 kN/s up to the maximum load, which was set as the test condition to correspond to the actual high-temperature bending–torsional creep–fatigue test method, and the load was removed at a removal rate of 0.2 kN/s to a minimum load of 0 kN after 600 s of holding at the maximum load. Bending–torsional creep–fatigue analysis was conducted with this pattern as one cycle.

Figure 8 FE model for welded piping specimen subjected to bending moment and torsional moment at high temperature.
Figure 8

FE model for welded piping specimen subjected to bending moment and torsional moment at high temperature.

The material constants assumed in the FE model were determined from the results of high-temperature tensile, fatigue, and creep tests on the base metal, weld metal, and HAZ simulant at 923 K. The elastoplastic constitutive equations for all layers were assumed to be a multilinear hardening material and the isotropic hardening law. The material constants are summarized in Tables 2 and 3. Table 4 lists the creep constitutive equations and material constants used in this study [21,22,23]. Material constants at 923 K were applied to the region of the FE model corresponding to the region heated by the electric furnace, as shown in Figure 8. The material constants at room temperature were applied to the other regions. The validity of applying these material constants to FE models was confirmed in Okuno et al. [21].

Table 2

Young’s modulus and Poisson’s ratio of P91 steel [21]

Temperature (K) Base metal Weldment HAZ
Young’s modulus E (GPa)
RT 213
923 155 155 155
Poisson’s ratio V (−)
0.3
Table 3

Plastic property of P91 steel [21]

Plastic strain ε p (−) Stress σ (MPa)
Base metal Weldment HAZ
0.000 105 163 105
1.090 × 10−3 161 234.5 161
3.090 × 10−3 168 245 168
9.265 × 10−3 189.5 276.5 189.5
Table 4

Creep property of P 91 steel [21,22,23]

Creep strain ε c = C 1 { 1 ‒ exp ( ‒ r 1 t ) } + C 2 { 1 ‒ exp ( ‒ r 2 t ) } + ε ̇ m t
Rapture time log 10 ( α c t r ) = ‒ 33.1803 + 26794.7 T + 273.15 + 14058.0 T + 273.15 log 10 ( σ ) ‒ 5461.72 T + 273.15 { log 10 ( σ ) } 2
Minimum creep strain rate ε ̇ m = 2.04156 exp { ‒ 20196.8 / 8.31441 ( T + 273.15 ) } t r ‒ 1.15483
C 1 = ( 2.13822 ε ̇ m 0.59235 ) / r 1 r 1 = α r 1 317.0.902 t r ‒ 0.56858
Constants C 2 = ( 0.927675 ε ̇ m 0.81657 ) / r 2 r 2 = α r 2 14.3245 t r ‒ 0.82278
α c α r1 α r2
Temperature (K) BM WM HAZ BM WM HAZ BM WM HAZ
973 0.7 0.2 50 1 2 1 2 1 1

6 Results and discussion

6.1 Verification of the monitoring system

The validity of the proposed monitoring system was verified using gyro sensors. Before doing so, the bending and torsional moments evaluated from the outputs of the rosette-type strain gauges bonded to the underside of the welded pipe specimen and their results obtained by FE analysis were compared. Figure 9(a) and 9(b) shows the relationship between the bending moment and compressive load P , and between the torsional moment and compressive load P . The solid line indicates the results obtained from FE analysis. The circle symbol indicates the bending and shear stress components in the direction of the pipe axis obtained from the strain gauge. The bending moment and torsional moment were evaluated based on the formulas of material mechanics. The results of FE analysis agreed well with those evaluated from the strain gauge when the compressive load level was lower. However, the strain gauge results appear to be slightly lower than the FE results at higher compressive load levels. During the test, the piping specimen and the flange securing the arm were bolted. Therefore, as the compressive load increased, elastic deformation of the bolts and slipping occurred at the interface between the flange of the piping specimen and arm, which resulted in a slightly smaller deformation of the piping specimen under the same compressive load conditions as in the FE analysis. Consequently, it was considered that those effects bring about that the results by the strain gauge were estimated to be lower than that of the FE analysis.

Figure 9 Comparison in relationship between moments and load between FE and experimental results: (a) bending moment and (b) torsion moment.
Figure 9

Comparison in relationship between moments and load between FE and experimental results: (a) bending moment and (b) torsion moment.

Figure 10(a) and (b) shows the relationships between the deflection angle and compressive load P , and between the torsion angle and compressive load P . The solid line represents the results of the FE analysis, and the dashed line represents the results of the gyro sensor measurements. Similar to the previous results for the bending and torsional moments, the deflection and torsion angles measured by the gyro sensor were slightly lower than those obtained by the FE analysis. Compressive load values of 4 and 4.5 kN were set in the high-temperature bending–torsional creep–fatigue tests described below, and it was thus judged that the rotation angles estimated from the FE analysis results were acceptable.

Figure 10 Comparison in relationship between rotation angles and load between FE and experimental results: (a) deflection angle and (b) torsional angle.
Figure 10

Comparison in relationship between rotation angles and load between FE and experimental results: (a) deflection angle and (b) torsional angle.

6.2 Creep–fatigue test results

In this study, the following equivalent bending moment [21] for combining bending moment M and torsional moment T ,

(6) M e = M 2 + 3 4 T 2 ,

is introduced and related with various parameters.

Figure 11(a) and (b) shows the relationship between the equivalent bending moment and the deflection and torsion angles measured using the gyro sensor. The equivalent bending moments for the deflection and torsion angles exhibited linear responses during the loading and unloading processes. The rotation angle increased with the number of cycles. This was owing to the creep deformation of the piping specimen during maximum load holding, which accumulated with cyclic loading, resulting in an increase in the rotation angle.

Figure 11 Relationship between rotation angles and equivalent bending moment: (a) deflection angle and (b) torsional angle.
Figure 11

Relationship between rotation angles and equivalent bending moment: (a) deflection angle and (b) torsional angle.

Based on the results shown in Figure 11, the difference between the rotation angles at the maximum and minimum loads was defined as the rotation angle range (deflection and torsion angle ranges). Figure 12(a) and (b) shows the relationship between the equivalent bending moment and the deflection and torsion angle ranges. The solid line shows the results of the FE analysis, and the dashed line shows the results of the gyro sensor measurement at 2,000 cycles. The results show that the rotational angle range obtained by the gyro sensor is slightly lower than that obtained by the FE analysis; however, these results are in good agreement with sufficient accuracy.

Figure 12 Relationship between rotation angles and equivalent bending moment in comparison between experiment and FE results: (a) deflection angle range and (b) torsional angle range.
Figure 12

Relationship between rotation angles and equivalent bending moment in comparison between experiment and FE results: (a) deflection angle range and (b) torsional angle range.

Under the high-temperature bending–torsional creep–fatigue test conditions used in this study, the deformation behavior of the piping specimen under cyclic loading was found to respond elastically during the unloading process. In other words, a linear relationship was established between the rotation angle and the equivalent bending moment. Therefore, we assumed that the piping specimen was an elastic body and derived a formula for the equivalent bending moment from the rotation angle range based on material mechanics. Based on the problem setup shown in Figure 13, the following formula was derived. First, the relationship between bending moment and deflection angle is expressed as

(7) M ( θ ) = 2 E R I l 1 l 1 l M − l s 2 θ ,

where

(8) l M = l − 2 l H − l 1 + 2 l H E R E H ,

and the moment of inertia is

(9) I = π 64 ( D 4 − d 4 ) ,

where D and d are the outer and inner diameters of the pipe specimens, respectively.

Figure 13 Beam model to derive equivalent moment formula from deflection and torsional angles.
Figure 13

Beam model to derive equivalent moment formula from deflection and torsional angles.

The formula relating the torsional moment to the torsional angle is

(10) T ( ϕ ) = 2 G R I P l − 2 l w − 2 l 2 + 2 G R G H l H ϕ ,

where the polar moment of area is

(11) I P = π 32 ( D 4 − d 4 ) .

Substituting Eqs. (7) and (10) into Eq. (6), the following formula for the equivalent bending moment is obtained:

(12) Δ M e 2 = C M 2 Δ θ 2 + 3 4 C T 2 Δ ϕ 2 ,

where Δ M e is the equivalent bending moment range defined as the difference between the maximum and minimum loads, Δ θ is the deflection angle range, and Δ ϕ is the torsion angle range. Coefficients C M and C T are defined as

(13) C M = 2 E R I l 1 l 1 l M − l s 2

and

(14) C T = 2 G R I P l − 2 l w − 2 l 2 + 2 G R G H l H .

To verify the validity of the formula for the equivalent bending moment derived here, a comparison was made with the FE analysis, as shown in Figure 14. The figure includes a comparison of equivalent bending moments when the maximum load is varied from 1.0 to 5.0 kN. It can be confirmed that the equations derived herein agree well with the FE analysis results. Thus, the validity of Eq. (12) was verified.

Figure 14 Comparison in equivalent moment between FE results and the equivalent moment formula introduced in this study.
Figure 14

Comparison in equivalent moment between FE results and the equivalent moment formula introduced in this study.

6.3 Creep-fatigue damage assessment under bending and torsional moments

Among the results of high-temperature bending–torsional creep–fatigue tests conducted by our group, the relationships between creep–fatigue life N f and equivalent bending moment range ∆ M e for piping specimens obtained under test conditions with arm lengths of l = 240 and 300 mm are shown in Figure 15. The holding time at maximum load was set to 600 s. The circles in the figure indicate the test results for arm length l = 240 mm, and the solid symbol indicates the test results for l = 300 mm. The horizontal axis represents the logarithmic scale. The solid line is written according to the following Manson–Coffin equation:

(15) ∆ M e · N f m = C ,

where m = 0.369 and C = 11,803. The test results are in good agreement with the solid line, which indicates that the high-temperature bending–torsional creep–fatigue life can be well explained by using the equivalent bending moment and that the creep–fatigue life follows the Manson–Coffin equation. Here, it should be noted that the coefficients m and C are different for different holding times at maximum load.

Figure 15 Relationship between equivalent bending moment range and number of cycles to failure.
Figure 15

Relationship between equivalent bending moment range and number of cycles to failure.

From the high-temperature bending–torsional creep–fatigue life diagram in Figure 15, the creep–fatigue life can be estimated from the gyro sensor measurement results according to the following procedure. The change in the rotation angle (deflection and torsion angles) of the piping over time is measured using a gyro sensor attached to the piping specimen. Based on these results, equivalent bending moment range is evaluated. The creep–fatigue life is predicted from the creep–fatigue life diagram based on the equivalent bending moment range defined from the maximum and minimum equivalent bending moments. In order to check the validity of this procedure, we conducted high-temperature bending–torsional creep–fatigue tests using four different loading patterns: one cycle with a minimum load of 0 kN and maximum loads of 4.0, 4.5, and 5.0 kN, and finally one cycle with a maximum load of 4.5 kN for 10 cycles, and then a maximum load of 5.0 kN for 10 cycles under a minimum load of 0 kN. The creep–fatigue life prediction was attempted according to the aforementioned procedure. Figure 16 shows the comparison between the experimental and predicted results. The thick line corresponds to one when both match perfectly, and the thin line corresponds to one when the creep–fatigue life can be predicted within a factor of two. It was confirmed that the predicted creep–fatigue life agreed well with the test results under all test conditions.

Figure 16 Comparison in creep–fatigue life between experimental and predicted results.
Figure 16

Comparison in creep–fatigue life between experimental and predicted results.

7 Conclusions

In this study, high-temperature bending–torsional creep–fatigue tests were conducted on welded pipes at a test temperature of 923 K. To monitor the deformation of the pipes, gyro sensors were attached to their surfaces to measure their deflection and torsion angles occurring in the pipes. Based on these measurements, we attempted to predict the stress state and creep–fatigue life of the welded pipes. The results of this study are summarized as follows.

  1. A method was established to measure the deflection and torsion angles generated in welded pipes subjected to bending and torsion moments at room temperature using a gyro sensor. An FE analysis was performed to validate the measurement results. These results confirmed the validity of the gyro sensor measurements. It was verified that the established measurement method can be applied to high-temperature environments such as thermal power plant components.

  2. A creep–fatigue life evaluation method for welded pipes subjected to high-temperature bending–torsional creep–fatigue loading was investigated. For this purpose, attention was paid to the deflection and torsion angle ranges that occurred from loading to the start of holding in one cycle. Subsequently, a conversion equation was derived to determine the equivalent bending moment range Δ M e from the deflection angle range and torsion angle range based on material mechanics as

Δ M e 2 = C M 2 Δ θ 2 + 3 4 C T 2 Δ ϕ 2 ,

where Δ θ is the deflection angle range, Δ ϕ is the torsion angle range, and coefficients C M and C T are defined from material constants and geometry of the piping, respectively. Furthermore, the creep–fatigue life was evaluated based on the Manson–Coffin rule:

∆ M e · N f m = C ,

where m = 0.369 and C = 11,803, which relates the equivalent bending moment range to fatigue life. The creep–fatigue test for four different loading patterns (one cycle with a minimum load of 0 kN and maximum loads of 4.0, 4.5, and 5.0 kN, and finally, one cycle with a maximum load of 4.5 kN for 10 cycles, and then a maximum load of 5.0 kN for 10 cycles under a minimum load of 0 kN) could be estimated in the range of a factor of two.

Acknowledgements

This article is based on the results obtained from the Project JPNP16002 (Development of Carbon Recycling and Next Generation Thermal Power Generation Technology/Development of Next Generation Thermal Power Generation Technology/Development of Technology to Deal with Load Changes in Coal-Fired Power Plants/Development of Technology for Accurate Remaining Life Assessment of Boiler Creep-Fatigue Damage) commissioned by the New Energy and Industrial Technology Development Organization (NEDO). The authors express their gratitude to all the parties involved in this research.

  1. Funding information: This article is based on the results obtained from the Project JPNP16002 (Development of Carbon Recycling and Next Generation Thermal Power Generation Technology/Development of Next Generation Thermal Power Generation Technology/Development of Technology to Deal with Load Changes in Coal-Fired Power Plants/Development of Technology for Accurate Remaining Life Assessment of Boiler Creep-Fatigue Damage) commissioned by the New Energy and Industrial Technology Development Organization (NEDO). The authors express their gratitude to all the parties involved in this research.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2024-01-22
Revised: 2024-05-13
Accepted: 2024-07-15
Published Online: 2024-09-20

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jmbm-2024-0011
Keywords for this article
piping system; weldment; Type IV cracking; creep–fatigue damage; bending moment; torsional moment; equivalent bending moment; MEMS-type gyro sensor; digital twin technology
Creative Commons
BY 4.0

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