Available Av ailable online online at www.sciencedire www.sciencedirect.com ct.com
ScienceDirect Procedia Materials Science 3 (2014 ( 2014)) 1773 – 1779
20th European Conference on Fracture (ECF20)
Effect of Loading Rate on Low-Cycle Fatigue Properties of Turbine Rotor Steel ∗
Jianjun He , Jian Chen, Qingmin Sun School of Energy and Power Engineering, ChangshaUniversity of Science and Technology, Changsha 410076, China
Abstract
Low-cycle fatigue properties of 30Cr1Mo1V steam turbine rotor steel were studied by RDL05 electronic creep fatigue test machine at 0.1%.s-1, 0.3%.s-1, 0.5%.s-1 loading rates applied the total strain controlled method. The results involve that with the loading rate increases at 538 538, cyclic stress of the rotor steel increases, and low-cycle fatigue life increases too; in the same strain range values, the increasing loading rate leads to the greater stress amplitude; with the increase of the strain range values, the stress increases and the low-cycle fatigue life decreases. The relationship of stress-strain and the loading rate is 0.06 0.0642 427 7 0.07 735 5 , the relationship of low-cycle fatigue life and the loading rate is ∆σ = 2051.56∆ε ε 0.0773 p
∆ε t = 0.8777 N f
−0.6147
ε 0.1627
+ 0.0106 N f
−0.11917
ε 0.03156
access under CC BY-NC-ND license. CC © by Elsevier Ltd. Open © 2014 2014Published The Authors. Published by Elsevier Ltd. Selection under responsibility of theofNorwegian University of Science and Technology (NTNU), Department Selectionand andpeer-review peer-review under responsibility the NorwegianUniversity of Science and Technology (NTNU), Department of of Structural Engineering Structural Engineering.
Keywords: turbine Keywords: turbine rotor; low-cycle fatigue; loading rate; 30Cr1Mo1V; life prediction
1. Introduction Introduction
Due to frequent start-stop or significant load change, turbine during operation, the steam turbine rotor is often in big load fluctuation working state and it is often under rapid heating or cooling caused by all kinds of transient thermal stress and mechanical stress, which causes local plastic deformation and low cycle fatigue and affects the
* Corresponding author. Tel.: +86-0731-85258408; fax: +86-0731-85258408. E-mail address:
[email protected]
2211-8128 © 2014 Published by Elsevier Ltd. Open access under CC under CC BY-NC-ND license. Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering doi:10.1016/j.mspro.2014.06.286 doi: 10.1016/j.mspro.2014.06.286
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
1774
safe operation of the steam turbine. Therefore, studying the effect of loading condition on characteristi cs of low cycle fatigue of steam turbine rotor is of great importance to the safety, economy, and stability of operation of the unit. Factors which influence the high temperature low cycle fatigue life of the rotor are load, frequency, loading rate and loading waveform (He J.R. 1998), etc.. Considering the influence of these factors, the researchers have studied the low cycle fatigue properties of other materials respectively(Melton1982, Shi X.Q. et al 2000, Nagesha et al 2002, Hong Seong-Gu et al 2007). 30Cr1Mo1V steel is a kind of typical material for our steam turbine high pressure rotor. At present, the researches of the rotor steel mainly focus on high temperature creep properties (Mao X.P.2006) and the influence of temperature on the low cycle fatigue(Li Y.W. et al 1998, Mao X.P. et al 2004,) , etc.. The effect of the loading rate on 30Cr1Mo1V rotor steel stress strain and low cycle fatigue properties in a simulated turbine operating condition has not been reported. In this paper, experimental results and theoretical correction formula based on the experimental results can provide important guidance for on the study of the strength and service life of steam turbine rotor steel, and even the safe operation of the steam turbine. 2. The experimental method
The heat-treated 30Cr1Mo1V steam turbine rotor steel was chosen as the raw material in this experiment, its components are as shown in Tab.1. Heat treatment process consists of the following steps: the preliminary heat treatment in which the temperature is at 1010, air cooling, then furnace cooling after 720 tempering; tempering heat treatment in which 955 air blast cooling then 680 furnace cooling; the stress relieving in which furnace cooling at least 620. The metallographic structures after heat treatment are made of are made of tempered bainite ferrite. Table 1. Components of 30Cr1Mo1V steel. C
Si
Mn
P
S
Ni
Cr
Mo
V
0.3
0.24
0.72
0.007
<0.01
0.39
1.17
1.15
0.29
The experiment is made on the RDL05 electronic creep fatigue test machine, the range of extensometer is 25mm and the deformation measurement range is 5 mm. Based on ASTM E606-92 and the national standard “the axial continuous low cycle fatigue test method”(GB/T 15248-94), the Φ6mm uniform cross section cylinders are chosen as samples, the axial total strain control is employed, and tension and compression is symmetrical triangle wave. With the strain range ± 0.4 % ± 1.0% and strain-ratio R=-1, 0.1%.s-10.3%.s-10.5%.s-1 are elected as the strain rate respectively. The experiment temperature is set at 538, the temperature fluctuation is ± 2. The threesection heating furnace is ready for heating. Heat preservation is about 30 min before the experiment. Stress drop to stable cycle of 70% of the peak tensile stress is chosen as the failure Frequency. 3. Results and Analysis
3.1 Effect of loading rate on the cyclic stress characteristics Fig.1 shows stable cycle hysteretic loop at different loading rates. And it can be seen from Fig.1 that different loading rates result in the different maximum compressive stress of two kinds of hysteresis loop. The Cyclic tensile stress increases accordingly with the increase of loading rate. Fig.2 is the Cycle stress life curves at 1.0% strain amplitude.
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
σ s s e r t s
loading rate
60 0
-0.6
500
40 0
0 0.0
loading rate:
600
20 0
-1.2
1775
loading rate
0.6
1.2
s400 s e r t s e l c300 y C
200
-200
strain ε 100
-400 0 0
-600
50
100
150
200
life
Fig.1. Stable cycle hysteretic loop at different loading rates.Fig.2. Cycle stress life curves at 1.0% strain amplitude.
It can be drawn from Fig.2 that under a certain life frequency circumstance the cyclic stress reaches the maximum when the loading rate is 0.5%.s -1. The cyclic tensile stress increases accordingly with the increase of loading rate. At 538, the cyclic stress of 30Cr1Mo1V rotor steel has softening feature along with the life of the rotor steel grades. the change of peak stress with circle life scores can be divided into three stages: softening stage in which the cyclic tensile stress scale begins dropping suddenly, and this stage corresponds to the micro crack initiation stage(Wang J.R.1987);stable stage in which the cyclic tensile stress scale changes slowly and this stage corresponds to the micro crack expansion stage; the stage in which the cyclic tensile stress decreases dramatically and this corresponds to the micro crack extending to fracture stage. 3.2 Effect of loading rate on the cyclic stress strain relations Through the further experimental study and theoretical analysis, the quantitative relationship of 30Cr1Mo1V steam turbine rotor steel cyclic stress strain and loading rate can be drawn. The relation between the average stress amplitude and plastic strain rate is the plastic flow rule(Solomon HD.1986 )shown as the following: α
β
1
p ∆σ = A∆ε p ε
In this formula, ∆σ is the stress range,
∆ ε p is
the plastic strain range,
ε p is the plastic strain rate.
Since the experiment is total strain-controlled low cycle fatigue experiment, the variation of loading rate can indicate the plastic strain rate change, so loading rate is used to replace plastic strain rate, which is: α
β
∆σ = A∆ε p ε
2
A α and β value in 30Cr1Mo1V steam turbine rotor steel relation formula can be obtained through the experiment.Fig.3 shows the Cycle stress-strain log-log curves at different loading rates, in which vertical and horizontal coordinates are taken double numerical value (in order to be understand easily, stress and strain values are marked).
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
1776
Loading rate:0.1%.s-1 Loading rate:0.3%.s-1 Loading rate:0.5%.s-1
e g n a r s s e r t S
4×10-
6×10- 8×10-2 10-2 1.2×10-2 1.6×10-2 Plastic strain range
Fig.3. Cycle stress-strain log-log curves at different loading rates.
It can be seen in Fig.3 that under the same strain, the greater the loading rate is, the greater the stress amplitude; when loading rate is stable, there is a linear relationship between the stress range and the plastic strain range in loglog coordinate. The stress range grows with the increase of the plastic strain. The slope of a straight line is α in formula (2), which can be calculated by data fitting and curve analysis, that is, α = 0.06427 . Fig.4 is about the cycle stress - loading rate log-log curves at different strains. It can be seen that under the same loading rate, the stress amplitude corresponding 1.0% strain reaches the maximum, while the stress amplitude corresponding 0.4% reaches the minimum. The greater the total strain, the more the corresponding stress amplitude. In log-log coordinate, when the plastic strain range is stable, the strain grows with the increase of loading rate, and there is a linear relationship between them. The slope of the straight line is β in formula (2), which can be calculated by data fitting and curve analysis, that is, β = 0.07735 .
1100
0.4%strain 0.6%strain 0.8%strain 1.0%strain
1050 1000 σ
950
e g n a r s s e r t S
e g n a r 900 s s e r t s
.
850
W 1
= ∆
α
ε p ε β
800
Loading rate
750 0 .3 8
Fig.4. Cycle stress-loading rate log-log curves at different strains.
0. 40
0. 42
0 .4 4
0 .46
0 .4 8
0 .5 0
0. 52
W 1 Fig.5. Relation curve of
α β to ∆ε p ε
∆δ .
Since α β are known, they can be put into the right side of formula (2), that is the plastic strain range and loading rate, then by data fitting the calculated value W1(marked in Fig.5) and the stress range value, the result is
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
1777
shown in Fig.5, it can be obtained that A=2051.56. therefore, considering the effect of loading rate, at 538 ,30Cr1Mo1V steam turbine rotor steel cyclic stress strain relation is as follows: 0.06427
∆σ = 2051.56∆ε p
ε 0.07735
3
3.3 Effect of total strain range on low-cycle fatigue life under a certain loading rate When total strain is under control, Coffiin-Manson formula is used as the calculation formula of low-cycle fatigue life. Due to not taking the operation condition of the loading rate into consideration, this formula can not accurately reflect the relation between low cycle fatigue life and the total strain range under a certain loading rate. Fig.6 is about the change of the low cycle fatigue life under different plastic strain range. The coordinate is the experimental data double logarithmic, points the experimental data and line data fitting.
e g n a r n i a r t s c i t s a l P
f
N e f i L
Loading rate: 0.1%.s
-1
Loading rate: 0.3%.s
-1
0.4% strain 0.6% strain 0.8% strain 1.0% strain
Loading rate: 0.5%.s-1
Life Nf Fig.6. Low cycle fatigue life-plastic strain range log-log curves.
Loading rate Fig.7. Low cycle fatigue life-loading rate log-log curves.
It can be seen from Fig.6 that the low-cycle fatigue life decreases with the growth of the strain amplitude and has the characteristic of linear decrease in log-log coordinate. The slopes of all curves are basically the same under different loading rate, which indicates that the slope has nothing to do with loading rate. Under the same strain amplitude, the higher the loading rate, the longer the low-cycle fatigue, which indicates loading rate obviously affects the low-cycle fatigue life. Fig.7 shows the relation between the low-cycle fatigue life and loading rate under different strain. It can be seen that the low cycle fatigue life increases with the increase of loading rate and has the linear characteristic in loglog coordinate. The slopes of all curves are basically the same under different strains, which indicates that the slope has nothing to do with strain amplitude. The change that the fatigue life of the material under high temperature reduces with the decrease of loading rate mainly results from the time-dependent damage mechanisms at work. Generally speaking, there are mainly two types of time-dependent damage in the high temperature cycle deformation, creep deformation and oxidation( Reuchet et al 1983) . Since 30Cr1Mo1V rotor steel has high temperature strength and creep strength and it can maintain good creep resistance, so in this experiment creep deformation doesn’t play decisive role in affecting the fatigue damage, while oxidation is the key factor in restraining the fatigue damage. Under the same strain amplitude in every circle, the longer the time that the material strands at high temperature, the greater the oxidative damage. Therefore, 30Cr1Mo1V steam turbine rotor steel has shorter life under lower loading rate. When calculating the fatigue life of 30Cr1Mo1V steam turbine rotor steel, the revised Coffiin-Manson formula is employed in which frequency item is taken into account:
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
1778
∆ ε t = ∆ ε p + ∆ ε e =
C 1 [ N f ν
k 1 −1 −α 1
+ C 2 [ N f ν
]
k 2 −1 −α 2
]
4
In this low-cycle fatigue experiment, no maintaining process, it is only fatigue experiment, the change of loading rate is corresponding to the change of frequency, therefore, when revising the formula (4), loading rate used to substitute for frequency item steel is as the following: ∆ε t = ∆ε p + ∆ε e = C1[ N f ε
ε is
ν , so the fatigue life prediction formula of 30Cr1Mo1V steam turbine rotor
k1 −1
]−α1
+ C2 [N f ε
k 2 −1
−α 2
]
5
In this formula, ∆ε t indicates the total strain range, ∆ε indicates plastic strain range, ∆ε e indicates elastic strain range, N indicates number of cycle life,
ε indicates loading rate C 1 C 2 k 1 k 2 α 1 and α 2 are
material constants.
α 1 and k 1 -1 can
be worked out respectively from the slope of the curves in Fig.6 and Fig.7,
calculated from Fig.8. by the same method,
C 1 can be
k 2 α 2 and C 2 can also be obtained. Therefore, considering the
effect of loading rate on the fatigue life, under the temperature 538 , the relation formula of 30Cr1Mo1V rotor steel fatigue life and the total strain range is as follows:
∆ε t = 0.8777 N f
−0.6147
ε0.1627 + 0.0106 N f −0.11917ε 0.03156
6
0.028 0.015
ε
0.010 0.005
0.024
ε
0.020 s e g n a r 0.016 n i a r t s l a0.012 t o t
. k 1 −1
S 1
=
[ N f ε
] − α 1
0.008
0.004
0.000 0.000
0.004
0.008
0.012
0
0.016
S 1
Fig.8. Relation curve of
∆ε t and
500
1000
1500
2000
2500
3000
life
k 1 −1
[ N f ε
−α 1
]
.
Fig.9. Life prediction curves at different total strain ranges.
Fig.9 is about the life prediction curves at different total strain ranges. It can be seen that the effect of loading rate on the fatigue life is less when the total strain is larger. The effect of loading rate increases with the narrowing of the total strain range. What’s more, with the increase of loading rate, the effect of loading rate on life has a decrease tendency. 4. Conclusion
1under the temperature 538, both the rotor steel cycle strain and low-cycle fatigue life increase with the
Jianjun He et al. / Procedia Materials Science 3 ( 2014) 1773 – 1779
1779
growth of loading rate; under the same strain, the greater the loading rate, the larger the corresponding stress amplitude; when the strain range value increases, the stress grows while the low-cycle fatigue life decreases; (2) Considering the effect of loading rate, under the temperature 538, the relation formula of 30Cr1Mo1V steam turbine rotor steel cyclic stress and strain is : ∆σ = 2051.56∆ε 0.06427 ε 0.07735 the relation formula of p
30Cr1Mo1V
rotor
∆ε t = 0.8777 N f
−0.6147
steel
ε0.1627
fatigue
+ 0.0106N f
life
−0.11917
and
the
total
strain
range
is:
ε 0.03156 .
References He, J.R. ,1988High Temperature Fatigue of Metal BeijingScience Press Nagesha, A., Valsan, M.,2002, Influence of Temperature on the Low Cycle Fatigue Behavior of a Modified 9Cr–1Mo Ferritic Steel. International Journal of Fatigue 24 :12851293. Shi,X.Q., Pang,H.L.J., 2000, Low Cycle Fatigue Analysis of Temperature and Frequency Effects in Eutectic Solder Alloy[J]. International Journal of Fatigue22: 217 228. Melton,K.N., 1982, Strain wave shape and frequency effects on the high temperature, low cycle fatigue behavior of a 1Cr-Mo-V ferritic steel. Materials Science and Engineering 55(1):21 28. Hong,Seong-Gu, Lee,Soon-Bok, 2007, Temperature Effect on the Low-Cycle Fatigue Behavior of Type 316L Stainless Steel: Cyclic nonStabilization and an Invariable Fatigue Parameter. Materials Science and Engineering A457 :139 147. Mao, X.P., Wang,G., Ma, Z.Y., Liu, Y.X.,2006,. Creep Characteristics of Rotor Steel 30Cr1Mo1V, Journal of Power Engineering26 (6): 904907. Mao,X.P., Wang,G., Ma,Z.Y.,2004 Study on Low-Cycle Fatigue Damage Behavior of 30CrlMolV Rotor Steel, China Power37105861. Li,Y.W., Li,C.B., Wang, M.Y.,1998,Study on Low-Cycle Fatigue Properties and Damage Evolution of 30CrlMolV rotor steel, Turbine Technology40(3): 184 187. Wang, J.R., Li, Y.M.,1987, Low-Cycle Fatigue Properties of Turbine Rotor Steel. Mechanical Engineering Materials (5): 22-27. Solomon, H.D., 1986, Creep Strain Rate Sensitivity and Low Cycle Fatigue of 60/40 Solder. Brazing and Soldering11 45. Reuchet, J., Remy,L.,1983,High Temperature Low Cycle Fatigue of MAR-M 509 super alloy. Materials Science and Engineering 58(1):33 42.
