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Creep-ratcheting-fatigue life prediction of bainitic 2.25Cr1MoV steel
Available online at www.sciencedirect.com
ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000
ICSI 2019 The 3rd International Conference on Structuralwww.elsevier.com/locate/procedia Integrity
ScienceDirect Creep-ratcheting-fatigue life prediction of Procedia Structural Integrity 17 (2019) 555–561
bainitic 2.25Cr1MoV steel
ICSI 2019 The 3rd International Conference on Structural Integrity
Zizhen Zhaoa,b, Dunji Yua, Xu Chena*
Creep-ratcheting-fatigue life prediction of
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300354, China b School of Mechanical and Automotive Engineering, Qilu University of Technology (Shandong academy of sciences), Jinan 250353, China a
bainitic 2.25Cr1MoV steel
Abstract
Zizhen Zhaoa,b, Dunji Yua, Xu Chena*
a oC with School Chemical Engineering forged and Technology, University, Tianjin 300354, Chinahold periods at peak and Ratcheting fatigue behavior of of bainitic 2.25Cr1MoV steel wasTianjin investigated at 455 various b School of Mechanical and Automotive Engineering, Qilu University of Technology academy sciences), Jinan 250353,was China valley stress. The incorporation of peak stress holding widened stress-strain(Shandong hysteresis loop, ofand this enlargement more significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the Abstract holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and creep damage became dominant at long hold period, which was closely related to shortened fatigue lives with stress holding. The Ratcheting fatigue behaviorrule of bainitic 2.25Cr1MoV forged steel was investigated at 455 oCpredictions with variousforhold periods at peak linear damage summation was used for fatigue life prediction, and it gave satisfactory peak holding mode.and A valley stress. The incorporation of peak stress holding widened stress-strain hysteresis loop, and this enlargement was more new model was proposed by introducing stress ratio to consider the influence of asymmetric cycling, and estimates for peak/valley significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean holding were greatly improved. stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and © 2019 The Authors. Published by Elsevier B.V. creep damageunder became dominant at hold 2019 period, which was closely related to shortened fatigue lives with stress holding. The Peer-review responsibility oflong the ICSI organizers. linear damage summation rule was used for fatigue life prediction, and it gave satisfactory predictions for peak holding mode. A new modelCreepwas proposed by introducing stress ratio consider the influence of asymmetric cycling, and estimates for peak/valley Keywords: ratcheting-fatigue, Stress holding, Creeptodamage, Life prediction holding were greatly improved.
© 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. Keywords: Creep- ratcheting-fatigue, Stress holding, Creep damage, Life prediction * Corresponding author. Tel.: +86-13920573451; fax: +86-22-27403389. E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers.
* Corresponding author. Tel.: +86-13920573451; fax: +86-22-27403389. E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.074
Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
556 2
1. Introduction Various creep-fatigue life prediction models have been proposed. The linear damage summation (LDS) rule proposed by Miner (1945) and Robinson (1952) represents the earliest approach. Coffin (1974) introduced a frequency term into fatigue to account for holding period effect at elevated temperature and developed the frequency modified life prediction model. Coffin (1976) later proposed the frequency separation approach to account for unbalanced holding conditions. Manson (1972) and Halford et al. (1972) assumed that plastic flow and creep influenced the fracture behavior of material separately or interactively, and introduced the strain range partitioning (SRP) method. Goswami (2004) introduced a ductility model that considered dynamic viscosity as a damage parameter, which was suitable for plastic strain range dominant loadings. Fournier et al. (2008) put forward a model, which dealt with crack initiation and propagation separately and obtained favorable predictions for 9Cr1Mo martensitic steel. Among these life prediction models, the LDS rule has received considerable attention, and it has been adopted in design procedures such as ASME-NH and RCC-MR. 2.25Cr1MoV steel was developed as a modification of 2.25Cr1Mo steel to overcome the problem of temper brittleness in 1980’s. It has now been widely used in components and pipelines in petrochemical process and power generation industries because of its high strength, better resistance against creep and hydrogen attack at elevated temperatures. Fatigue properties and failure mechanisms of ferrite 2.25Cr1Mo steel with various holding periods have been comprehensively investigated by Brinkman et al. (1976), Challenger et al. (1983), Hecht et al. (1998). Corresponding researches of bainite 2.25Cr1Mo(V) steel were carried by Kschinka et al. (1989) and Tian et al. (2016) and Zhang et al. (2016). Yet, reports on ratcheting-fatigue or creep-ratcheting-fatigue behavior of the steel have not been found. The deformation behavior of bainitic 2.25Cr1MoV forged steel was investigated with various hold periods under asymmetric stress cycling at 455 oC in this work. Attention was paid to the influence of holding periods on stress-strain hysteresis loops, fatigue life and creep and fatigue damages. A fatigue life prediction approach for creepratcheting-fatigue was proposed in the study. Nomenclature ch Dc Df NCRF NRF Npf R Δt th tR σa σm σmax σmin
compressed hold period creep damage fatigue damage cycles to failure in CRF tests cycles to failure in RF tests predicted fatigue life stress ratio holding period in a cycle tensile hold period time to rupture under creep stress amplitude mean stress peak stress valley stress
2. Material and methods The tested 2.25Cr1MoV steel was provided as a tempered forged ring with its chemical composition given in Table 1. The microstructure was 100 percent bainite, where bainitic ferrite was supersaturated with uniformly distributed granular carbides, and the grain size was about 20μm.
Author name / Structural Integrity Procedia 00 (2019) 000–000
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Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561
557
Table 1 Chemical composition of 2.25Cr1MoV forged steel (wt. %) C
Si
Mn
P
S
Cr
Mo
Ni
V
Cu
Al
Fe
0.15
0.07
0.56
0.006
0.002
2.44
0.96
0.12
0.263
0.03
0.011
Bal.
Solid bars were firstly cut from the forged ring with its axial direction coinciding with the forging direction, and then machined into dumbbell specimens as shown in Fig. 1. The gauge section is 10mm in diameter and 27mm in length. The specimen’s surface was carefully polished to avoid the initiation of premature fatigue cracks in oxidative environment at elevated temperature.
Fig. 1 Geometry of the test specimen.
All tests were conducted in air on a closed-loop servo electro-hydraulic fatigue testing machine. Induction heating was employed to heat the specimen to the target temperature, which was chosen around the design temperature of most hydrogenation equipment, i.e. 455 oC. Three K type shielded thermocouples with a diameter of 0.5mm were secured in the gauge section to monitor the temperature, and a precision of ±2 oC was maintained during the test. An elevated-temperature applicable extensometer with a gauge length of 10mm was employed to measure the axial deformation. Stress controlled mode was used and three kinds of waveform were performed, i.e. ratcheting-fatigue (hereafter referred to as RF), creep-ratcheting-fatigue (CRF) tests with peak and peak/valley stress holding periods. The applied stress waveforms are shown in Fig. 2. A series of mean stresses and stress amplitudes were applied at a loading rate of 200 MPas-1, and various holding periods were incorporated, i.e. 2s, 5s, 10s, 30s and 60s.
Fig. 2 Applied stress wave forms in: (a) RF test; (b) CRF test with peak holding period; (c) CRF test with equal peak/valley holding periods.
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Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
3. Ratcheting-fatigue and creep-ratcheting-fatigue behaviors 3.1. Stress-strain hysteresis loops Typical stress-strain hysteresis loops in RF and CRF under σm=100 MPa and σm=300 MPa are compared in Fig. 3. The non-closure of hysteresis loop in the first cycle is remarkable, but its openness is significantly reduced with continuous cycling. Strain after loading in the first cycle increases when stress holdings are incorporated. The inelastic strain accumulates in the direction of mean stress, but the growth rate is much slower in RF test, as hysteresis loops of 500 and 1000 cycle almost overlap. Peak stress holding stimulates the growth of inelastic strain, while peak/valley holding makes it even larger. When 10 s holding period is applied at either peak stress or valley stress, remarkable creep strains are created, which widens the hysteresis loops. 3.2. Fatigue life The variation of fatigue life with stress holding periods is shown in Fig. 4. Trend lines are added for each stress condition for clarity, and the stress holding period for RF tests is taken as 0.1 s to fit the logarithmic coordinate. The increase of either mean stress or stress amplitude would reduce fatigue life in RF tests, and fatigue life drops exponentially when hold period is involved. The reduction in fatigue life becomes more significant when long holding period is applied at high stress level, as for the 30 s and 60 s holding cases under σm=125 MPa and σa =300 MPa. However, when the sum of holding periods is equal, the corresponding fatigue lives are quite close regardless of hold directions, as in cases when th= 10s and th= ch=5s.
Fig. 3 Comparison of stress-strain hysteresis loops in RF and CRF tests.
Fig. 4 The influence of stress holding periods on fatigue life.
3.3. Creep and fatigue damage The time fraction rule was used in the evaluation of fatigue and creep damage in CRF tests as follows, N (1) Df = CRF N RF N t (2) Dc = CRF tR where Df is the fatigue damage, Dc is the creep damage, NCRF is the number of cycles to failure in CRF tests, NRF is the number of cycles to failure in RF tests, Δt is the holding period in a cycle, tR corresponds to the creep rupture time under holding stress. tR was determined from short term creep tests of the steel, where a power-law relationship was found between creep stress and rupture time, with the coefficient and exponent being 453.5 MPa and -0.04
Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
559 5
respectively. The fraction of fatigue and creep damage in CRF tests is shown in Fig. 5, which also includes the damage envelope for 2.25Cr1Mo steel in ASME-NH, the diagonal line, and the envelope when the sum of Df and Dc is one. All data fall outside the envelope given by ASME-NH, and most data are within the envelope when the sum of Df and Dc is one. Df is a bit higher than Dc at short holding periods. When the hold period is longer than 5s, Dc becomes dominant, and Df is almost negligible when the hold period extends to 60s. This diagram indicates that creep damages created during stress holding periods lead to shortened fatigue lives in CRF tests. 4. Fatigue life prediction The LDS rule assumes the accumulation of time-dependent damage and time-independent damage govern the fatigue life of a specimen. It uses fraction rule to evaluate the fatigue damage and creep damage produced in each cycle, and failure occurs when total damage reaches a utility,
= N fp 1/ (
1 t + ) N f tR
(3)
where Nf is the fatigue life in continuous cycling, and Nfp is the predicted fatigue life. For prediction in CRF tests, fatigue life of the corresponding RF tests is taken as Nf. Predicted fatigue lives from the LDS rule for CRF tests are compared with observed ones in Fig. 6 (a), with scatter band of 1.5 and 2 being given. Obviously, the LDS rule provides better predictions for peak holding mode, as all the predictions fall within a scatter band of 1.5, but predictions for double hold is not as satisfactory. The inconsideration of unbalanced cycling in the LDS rule and the underestimate of creep damage in valley holding may be responsible. To compensate for this deficiency, stress ratio denoted by R was incorporated in the evaluation of creep damage per cycle as below.
= dc
1 (th + R ch ) tR
(4)
A new model has been developed by substituting Eq. (4) into Eq. (3), and the predicted results compared with the observed ones in Fig. 6(b). The new model keeps satisfactory predictions for peak holding mode, while the predicted fatigue lives for double holding mode are improved as they fall within a scatter band of 1.5.
Fig. 5 The influence of stress holding periods on (a) fatigue life, (b) creep and fatigue damage
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Author nameZhao / Structural Integrity Procedia (2019) 17 000–000 Zizhen et al. / Procedia Structural00 Integrity (2019) 555–561
Fig. 6 Fatigue life prediction for CRF tests by (a) LDS rule and (b) modified LDS rule
4. Conclusions Ratcheting-fatigue tests of 2.25Cr1MoV forge steel were conducted at 455 oC with various hold periods at peak and valley stress in this study. Effects of test parameters, i.e. mean stress, stress amplitude, holding period as well as holding direction on fatigue behavior were investigated. A creep-ratcheting fatigue life prediction model based on the linear damage summation rule was proposed. Main conclusions were drawn as below. (1) The existence of mean stress caused the accumulation of inelastic strain in the tensile direction. The incorporation of peak holding period widened the stress-strain hysteresis loop, while creep strains created in peak and valley holding periods made the hysteresis loop even wider. Stress holding stimulated the accumulation of inelastic strain. (2) The increase of mean stress or stress amplitude would shorten fatigue life, and fatigue life reduced exponentially when hold period was incorporated. Longer hold period resulted in shorter fatigue life. But the fatigue life was similar when the sum of hold period is equal, regardless of the holding direction. (3) Fatigue damage was a bit higher than creep damage at short hold period, but creep damage became dominant when hold period was longer than 5s. The creep damages created during stress holding led to shortened fatigue lives in CRF tests. (4) The linear damage summation rule provided satisfactory prediction results for peak holding mode. A new model was proposed by incorporating stress ratio to the linear damage summation rule, and the prediction for peak/valley hold was improved. Acknowledgements The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (No. 51435012) and Ph.D. Programs Foundation of Ministry of Education of China (No. 20130032110018). References Miner MA. Cumulative damage in fatigue. Journal of applied mechanics. 1945;12(3):159-164. Robinson EL. Effect of temperature variation on the long-time rupture strength of steels. Trans ASME. 1952;74(5):777-781. Coffin L. Fatigue at high temperature-prediction and interpretation. Proceedings of the Institution of Mechanical Engineers. 1974;188(1):109-127. Coffin L. Concept of frequency separation in life prediction for time-dependent fatigue. General Electric Co., Schenectady, NY (USA);1976. Manson S. The Challenge to Unify treatment of high-temperature fatigue: a partisan proposal based on strain range partitioning. National Aeronautics and Space Administration; 1972. Halford GR, Hirschberg MH, Manson S. Temperature effects on the strainrange partitioning approach for creep-fatigue analysis. 1972.
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Goswami T. Development of generic creep–fatigue life prediction models. Mater Design. 2004;25(4):277-288. Fournier B, Sauzay M, Caës C, et al. Creep–fatigue–oxidation interactions in a 9Cr–1Mo martensitic steel. Part III: Lifetime prediction. Int J Fatigue. 2008;30(10):1797-1812. Brinkman CR, Strizak JP, Booker MK, Jaske CE. Time-dependent strain-controlled fatigue behavior of annealed 2 14 Cr-1 Mo steel for use in nuclear steam generator design. J Nucl Mater. 1976;62(2–3):181-204. Challenger K, Vining P. The effects of hold period on the fatigue crack growth rate of 2 1/4 Cr-1Mo steel at elevated temperatures. J Eng Mater Technol. 1983;105(4):280-285. Hecht R, Weertman J. The effect of environment on high-temperature hold time fatigue behavior of annealed 2.25 pct Cr 1 pct Mo steel. Metall Mater Trans A. 1998;29(8):2137-2145. Kschinka BA, Stubbins AE. Creep-fatigue-environment interaction in a bainitic 2.25 wt.% Cr-1wt.% Mo steel forging. 1989;110:89-102. Tian Y, Yu D, Zhao Z, Chen G, Chen X. Low cycle fatigue and creep–fatigue interaction behaviour of 2.25 Cr1MoV steel at elevated temperature. Mater High Temp. 2016;33(1):75-84. Zhang J, Yu D, Zhao Z, Zhang Z, Chen G, Chen X. Low cycle fatigue of 2.25Cr1Mo steel with tensile and compressed hold loading at elevated temperature. Mater Sci Eng, A. 2016;667:251-260.
ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000
ICSI 2019 The 3rd International Conference on Structuralwww.elsevier.com/locate/procedia Integrity
ScienceDirect Creep-ratcheting-fatigue life prediction of Procedia Structural Integrity 17 (2019) 555–561
bainitic 2.25Cr1MoV steel
ICSI 2019 The 3rd International Conference on Structural Integrity
Zizhen Zhaoa,b, Dunji Yua, Xu Chena*
Creep-ratcheting-fatigue life prediction of
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300354, China b School of Mechanical and Automotive Engineering, Qilu University of Technology (Shandong academy of sciences), Jinan 250353, China a
bainitic 2.25Cr1MoV steel
Abstract
Zizhen Zhaoa,b, Dunji Yua, Xu Chena*
a oC with School Chemical Engineering forged and Technology, University, Tianjin 300354, Chinahold periods at peak and Ratcheting fatigue behavior of of bainitic 2.25Cr1MoV steel wasTianjin investigated at 455 various b School of Mechanical and Automotive Engineering, Qilu University of Technology academy sciences), Jinan 250353,was China valley stress. The incorporation of peak stress holding widened stress-strain(Shandong hysteresis loop, ofand this enlargement more significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the Abstract holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and creep damage became dominant at long hold period, which was closely related to shortened fatigue lives with stress holding. The Ratcheting fatigue behaviorrule of bainitic 2.25Cr1MoV forged steel was investigated at 455 oCpredictions with variousforhold periods at peak linear damage summation was used for fatigue life prediction, and it gave satisfactory peak holding mode.and A valley stress. The incorporation of peak stress holding widened stress-strain hysteresis loop, and this enlargement was more new model was proposed by introducing stress ratio to consider the influence of asymmetric cycling, and estimates for peak/valley significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean holding were greatly improved. stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and © 2019 The Authors. Published by Elsevier B.V. creep damageunder became dominant at hold 2019 period, which was closely related to shortened fatigue lives with stress holding. The Peer-review responsibility oflong the ICSI organizers. linear damage summation rule was used for fatigue life prediction, and it gave satisfactory predictions for peak holding mode. A new modelCreepwas proposed by introducing stress ratio consider the influence of asymmetric cycling, and estimates for peak/valley Keywords: ratcheting-fatigue, Stress holding, Creeptodamage, Life prediction holding were greatly improved.
© 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. Keywords: Creep- ratcheting-fatigue, Stress holding, Creep damage, Life prediction * Corresponding author. Tel.: +86-13920573451; fax: +86-22-27403389. E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers.
* Corresponding author. Tel.: +86-13920573451; fax: +86-22-27403389. E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.074
Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
556 2
1. Introduction Various creep-fatigue life prediction models have been proposed. The linear damage summation (LDS) rule proposed by Miner (1945) and Robinson (1952) represents the earliest approach. Coffin (1974) introduced a frequency term into fatigue to account for holding period effect at elevated temperature and developed the frequency modified life prediction model. Coffin (1976) later proposed the frequency separation approach to account for unbalanced holding conditions. Manson (1972) and Halford et al. (1972) assumed that plastic flow and creep influenced the fracture behavior of material separately or interactively, and introduced the strain range partitioning (SRP) method. Goswami (2004) introduced a ductility model that considered dynamic viscosity as a damage parameter, which was suitable for plastic strain range dominant loadings. Fournier et al. (2008) put forward a model, which dealt with crack initiation and propagation separately and obtained favorable predictions for 9Cr1Mo martensitic steel. Among these life prediction models, the LDS rule has received considerable attention, and it has been adopted in design procedures such as ASME-NH and RCC-MR. 2.25Cr1MoV steel was developed as a modification of 2.25Cr1Mo steel to overcome the problem of temper brittleness in 1980’s. It has now been widely used in components and pipelines in petrochemical process and power generation industries because of its high strength, better resistance against creep and hydrogen attack at elevated temperatures. Fatigue properties and failure mechanisms of ferrite 2.25Cr1Mo steel with various holding periods have been comprehensively investigated by Brinkman et al. (1976), Challenger et al. (1983), Hecht et al. (1998). Corresponding researches of bainite 2.25Cr1Mo(V) steel were carried by Kschinka et al. (1989) and Tian et al. (2016) and Zhang et al. (2016). Yet, reports on ratcheting-fatigue or creep-ratcheting-fatigue behavior of the steel have not been found. The deformation behavior of bainitic 2.25Cr1MoV forged steel was investigated with various hold periods under asymmetric stress cycling at 455 oC in this work. Attention was paid to the influence of holding periods on stress-strain hysteresis loops, fatigue life and creep and fatigue damages. A fatigue life prediction approach for creepratcheting-fatigue was proposed in the study. Nomenclature ch Dc Df NCRF NRF Npf R Δt th tR σa σm σmax σmin
compressed hold period creep damage fatigue damage cycles to failure in CRF tests cycles to failure in RF tests predicted fatigue life stress ratio holding period in a cycle tensile hold period time to rupture under creep stress amplitude mean stress peak stress valley stress
2. Material and methods The tested 2.25Cr1MoV steel was provided as a tempered forged ring with its chemical composition given in Table 1. The microstructure was 100 percent bainite, where bainitic ferrite was supersaturated with uniformly distributed granular carbides, and the grain size was about 20μm.
Author name / Structural Integrity Procedia 00 (2019) 000–000
3
Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561
557
Table 1 Chemical composition of 2.25Cr1MoV forged steel (wt. %) C
Si
Mn
P
S
Cr
Mo
Ni
V
Cu
Al
Fe
0.15
0.07
0.56
0.006
0.002
2.44
0.96
0.12
0.263
0.03
0.011
Bal.
Solid bars were firstly cut from the forged ring with its axial direction coinciding with the forging direction, and then machined into dumbbell specimens as shown in Fig. 1. The gauge section is 10mm in diameter and 27mm in length. The specimen’s surface was carefully polished to avoid the initiation of premature fatigue cracks in oxidative environment at elevated temperature.
Fig. 1 Geometry of the test specimen.
All tests were conducted in air on a closed-loop servo electro-hydraulic fatigue testing machine. Induction heating was employed to heat the specimen to the target temperature, which was chosen around the design temperature of most hydrogenation equipment, i.e. 455 oC. Three K type shielded thermocouples with a diameter of 0.5mm were secured in the gauge section to monitor the temperature, and a precision of ±2 oC was maintained during the test. An elevated-temperature applicable extensometer with a gauge length of 10mm was employed to measure the axial deformation. Stress controlled mode was used and three kinds of waveform were performed, i.e. ratcheting-fatigue (hereafter referred to as RF), creep-ratcheting-fatigue (CRF) tests with peak and peak/valley stress holding periods. The applied stress waveforms are shown in Fig. 2. A series of mean stresses and stress amplitudes were applied at a loading rate of 200 MPas-1, and various holding periods were incorporated, i.e. 2s, 5s, 10s, 30s and 60s.
Fig. 2 Applied stress wave forms in: (a) RF test; (b) CRF test with peak holding period; (c) CRF test with equal peak/valley holding periods.
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Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
3. Ratcheting-fatigue and creep-ratcheting-fatigue behaviors 3.1. Stress-strain hysteresis loops Typical stress-strain hysteresis loops in RF and CRF under σm=100 MPa and σm=300 MPa are compared in Fig. 3. The non-closure of hysteresis loop in the first cycle is remarkable, but its openness is significantly reduced with continuous cycling. Strain after loading in the first cycle increases when stress holdings are incorporated. The inelastic strain accumulates in the direction of mean stress, but the growth rate is much slower in RF test, as hysteresis loops of 500 and 1000 cycle almost overlap. Peak stress holding stimulates the growth of inelastic strain, while peak/valley holding makes it even larger. When 10 s holding period is applied at either peak stress or valley stress, remarkable creep strains are created, which widens the hysteresis loops. 3.2. Fatigue life The variation of fatigue life with stress holding periods is shown in Fig. 4. Trend lines are added for each stress condition for clarity, and the stress holding period for RF tests is taken as 0.1 s to fit the logarithmic coordinate. The increase of either mean stress or stress amplitude would reduce fatigue life in RF tests, and fatigue life drops exponentially when hold period is involved. The reduction in fatigue life becomes more significant when long holding period is applied at high stress level, as for the 30 s and 60 s holding cases under σm=125 MPa and σa =300 MPa. However, when the sum of holding periods is equal, the corresponding fatigue lives are quite close regardless of hold directions, as in cases when th= 10s and th= ch=5s.
Fig. 3 Comparison of stress-strain hysteresis loops in RF and CRF tests.
Fig. 4 The influence of stress holding periods on fatigue life.
3.3. Creep and fatigue damage The time fraction rule was used in the evaluation of fatigue and creep damage in CRF tests as follows, N (1) Df = CRF N RF N t (2) Dc = CRF tR where Df is the fatigue damage, Dc is the creep damage, NCRF is the number of cycles to failure in CRF tests, NRF is the number of cycles to failure in RF tests, Δt is the holding period in a cycle, tR corresponds to the creep rupture time under holding stress. tR was determined from short term creep tests of the steel, where a power-law relationship was found between creep stress and rupture time, with the coefficient and exponent being 453.5 MPa and -0.04
Zizhen Zhao et al. / Procedia Structural Integrity 17 (2019) 555–561 Author name / Structural Integrity Procedia 00 (2019) 000–000
559 5
respectively. The fraction of fatigue and creep damage in CRF tests is shown in Fig. 5, which also includes the damage envelope for 2.25Cr1Mo steel in ASME-NH, the diagonal line, and the envelope when the sum of Df and Dc is one. All data fall outside the envelope given by ASME-NH, and most data are within the envelope when the sum of Df and Dc is one. Df is a bit higher than Dc at short holding periods. When the hold period is longer than 5s, Dc becomes dominant, and Df is almost negligible when the hold period extends to 60s. This diagram indicates that creep damages created during stress holding periods lead to shortened fatigue lives in CRF tests. 4. Fatigue life prediction The LDS rule assumes the accumulation of time-dependent damage and time-independent damage govern the fatigue life of a specimen. It uses fraction rule to evaluate the fatigue damage and creep damage produced in each cycle, and failure occurs when total damage reaches a utility,
= N fp 1/ (
1 t + ) N f tR
(3)
where Nf is the fatigue life in continuous cycling, and Nfp is the predicted fatigue life. For prediction in CRF tests, fatigue life of the corresponding RF tests is taken as Nf. Predicted fatigue lives from the LDS rule for CRF tests are compared with observed ones in Fig. 6 (a), with scatter band of 1.5 and 2 being given. Obviously, the LDS rule provides better predictions for peak holding mode, as all the predictions fall within a scatter band of 1.5, but predictions for double hold is not as satisfactory. The inconsideration of unbalanced cycling in the LDS rule and the underestimate of creep damage in valley holding may be responsible. To compensate for this deficiency, stress ratio denoted by R was incorporated in the evaluation of creep damage per cycle as below.
= dc
1 (th + R ch ) tR
(4)
A new model has been developed by substituting Eq. (4) into Eq. (3), and the predicted results compared with the observed ones in Fig. 6(b). The new model keeps satisfactory predictions for peak holding mode, while the predicted fatigue lives for double holding mode are improved as they fall within a scatter band of 1.5.
Fig. 5 The influence of stress holding periods on (a) fatigue life, (b) creep and fatigue damage
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Author nameZhao / Structural Integrity Procedia (2019) 17 000–000 Zizhen et al. / Procedia Structural00 Integrity (2019) 555–561
Fig. 6 Fatigue life prediction for CRF tests by (a) LDS rule and (b) modified LDS rule
4. Conclusions Ratcheting-fatigue tests of 2.25Cr1MoV forge steel were conducted at 455 oC with various hold periods at peak and valley stress in this study. Effects of test parameters, i.e. mean stress, stress amplitude, holding period as well as holding direction on fatigue behavior were investigated. A creep-ratcheting fatigue life prediction model based on the linear damage summation rule was proposed. Main conclusions were drawn as below. (1) The existence of mean stress caused the accumulation of inelastic strain in the tensile direction. The incorporation of peak holding period widened the stress-strain hysteresis loop, while creep strains created in peak and valley holding periods made the hysteresis loop even wider. Stress holding stimulated the accumulation of inelastic strain. (2) The increase of mean stress or stress amplitude would shorten fatigue life, and fatigue life reduced exponentially when hold period was incorporated. Longer hold period resulted in shorter fatigue life. But the fatigue life was similar when the sum of hold period is equal, regardless of the holding direction. (3) Fatigue damage was a bit higher than creep damage at short hold period, but creep damage became dominant when hold period was longer than 5s. The creep damages created during stress holding led to shortened fatigue lives in CRF tests. (4) The linear damage summation rule provided satisfactory prediction results for peak holding mode. A new model was proposed by incorporating stress ratio to the linear damage summation rule, and the prediction for peak/valley hold was improved. Acknowledgements The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (No. 51435012) and Ph.D. Programs Foundation of Ministry of Education of China (No. 20130032110018). References Miner MA. Cumulative damage in fatigue. Journal of applied mechanics. 1945;12(3):159-164. Robinson EL. Effect of temperature variation on the long-time rupture strength of steels. Trans ASME. 1952;74(5):777-781. Coffin L. Fatigue at high temperature-prediction and interpretation. Proceedings of the Institution of Mechanical Engineers. 1974;188(1):109-127. Coffin L. Concept of frequency separation in life prediction for time-dependent fatigue. General Electric Co., Schenectady, NY (USA);1976. Manson S. The Challenge to Unify treatment of high-temperature fatigue: a partisan proposal based on strain range partitioning. National Aeronautics and Space Administration; 1972. Halford GR, Hirschberg MH, Manson S. Temperature effects on the strainrange partitioning approach for creep-fatigue analysis. 1972.
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