Available online at www.sciencedirect.com

·* ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2013, 20(7): 50-56

Effects of Strain Rate on Low Cycle Fatigue Behaviors of High-Strength Structural Steel

LUO Yun-rong1·2, HUANG Chong-xiang1, TIAN Ren-hui1, WANG Qing-yuan1

( 1 . College of Architecture and Environment, Sichuan University, Chengdu 610065, Sichuan, China; 2. College of Mechanical Engineering, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China)

Abstract: The low cycle fatigue (LCF) behavior of a high-strength structural steel was investigated in the strain rate range of 4 X 1 0 - 5 — 0. 12 s _ 1 (0. 001 — 3 Hz) under constant total strain ( ± 1 % ) control. The cyclic stress response at all strain rates exhibited behavior of rapid softening in the early stage of fatigue life and subsequent saturation up to failure. It was found that the stress amplitude, the plastic strain amplitude, the plastic strain energy density and the fatigue life depend mainly on the strain rate. The strain rate of 0. 012 s _ 1 was found as a transition point where the LCF of the steel showed different behavior from low strain rate to high strain rate. The relationship between the time to failure and strain rate was expressed well by a power law relation. The fracture surfaces of the fatigue sam­ples were characterized by using a scanning electron microscope (SEM) and the fracture mechanisms were discussed in terms of time-dependent deformation of the steel. Key words : low cycle fatigue; high strength steel; strain rate; fatigue life

The high-strength structural steel is commonly used in buildings and ship crafts owing to its excel­lent mechanical properties. These engineering struc­tures experience continuous cyclic loads due to wave pressures and ship motions[1]. Buildings experience dynamic loading in service life during earthquakes and experience a process of low cycle fatigue (LCF). The seismic frequency is generally in the range of 1. 0 — 3. 0 Hz1-2-1. Hence it is important to assess the effect of strain rate (frequency) on the LCF behavior of structural steels.

The LCF behavior of metallic materials depends on the strain range, strain ratio, frequency (strain rate) and temperature. D Grenier et al1-1-1 recently in­vestigated the effect of fatigue strain range on the mechanical properties of a high-strength structural steel. They found that the fatigue life at different cycles in strain range of 2 000 — 3 000 micro-strains exhibi­ted minor effect on the ultimate tensile strength and ductility of the material. The effect of strain ratio on the LCF life of a structural steel showed that the

higher the strain ratio was, the more the fatigue life could be extended1-3-*-1. There is some literatures which discusses the effect of the strain rate on the fatigue life[5~12] and it has been reported that the LCF behavior of the metallic materials strongly de­pended on the strain rate. S Begum et al1-9-1 investiga­ted the influence of strain rate (1X 10~3 —8X10"2 s"1 ) on the fatigue behavior of AZ31 extruded alloy. They observed that the fatigue life increased with in­crease in strain rate. The effects of strain rate on the LCF behavior of stainless steels in different studies, such as 316LC10], 17-4 PHC11], and AISI 304L[12;|, have been explored extensively in recent years. It was found that fatigue resistance decreased with de­crease in strain rate. The reduction in fatigue strength was attributed to the enhanced crack initia­tion and propagation due to the effect of dynamic strain aging (DSA). It was also found that the fa­tigue life of AISI 304L stainless steel was saturated

creep [12]

Foundation Itemiltem Sponsored by National Natural Science Foundation of China (50978174, 10925211) Biography : LUO Yun-rong(1974—), Female, Doctor, Lectureship; E-mail: luoyunrong2004@yahoo.com.cn; Received Date: September 25, 2012 Corresponding Author : WANG Qing-yuan(1965 —) , Male, Doctor, Professor; E-mail: wangqy@scu.edu.cn

Issue 7 Effects of Strain Rate on Low Cycle Fatigue Behaviors of High-Strength Structural Steel · 51 ·

The LCF behavior of materials depends on the strain rate significantly. Hence it is important to study the effect of strain rate for the reliable assess­ment of buildings. Although some investigations have studied the influence of strain rate on the LCF behaviors of high-strength structural steels in the seismic range of frequencies, thorough understand­ing of the LCF mechanism is yet to be established. This study explains the LCF behavior of a high-strength structural steel with particular emphasis on the-effects of strain rate from 4 X 10~5 to 0. 12 s_ 1

CO. 001 — 3 Hz) . Based on the fatigue mechanism, the relationship between time to failure and strain rate was used for lifetime prediction. The results ex­plain the effect of strain rate on the LCF behavior of high-strength structural steels effectively.

1 Material and Testing Arrangements The specimens were machined from a low al­

loyed high-strength structural steel (using 20. 0 mm cold-rolled bars) with diameter of 20 mm. The chemical compositions and mechanical properties of the high-strength structural steel made according to standard1-13-1 are given in Table 1 and Table 2, re­spectively ( the microstructure of the steel can be seen in Ref. [ 1 4 ] ) . The cylindrical fatigue speci­mens with gauge length of 20 mm and diameter of 10 mm were used (Fig. 1). The staircases designed on both sides of the specimen were according to the range of the jaws of the testing machine (from 8 to 18 mm). The dimension of the specimen was set to avoid the buckling under the highest compressive force

Table 1

C Si Mn

0. 153 0. 166 0. 420

Chemical composition of test material (mass percent, % )

P S Cu Cr Ni Mo V Fe

0.036 0.031 0.037 0.014 0.008 0.003 0.002 Balance

Table 2 Mechanical properties of test material

0. 2% proof strength/MPa

536

Tensile strength/MPa Elongation Reduction of area ARV(20 "C)/J

563 0.136 0.577 68

1.6, «25

^ '

0

fÖ£„ 1

'

§> 40 10

-«

g 1 OO

O ■ * .

«2 0 . 150

-IÔI <*o.oi Ι Α Ι Β Γ 1

10

8'

40

►-

, 1

Φ

Unifcmm

Fig. 1 Geometry of test specimen

anticipated in the test . Before fatigue t es t ing , the specimen surfaces were carefully ground and pol­ished by using SiC papers to remove scratches.

T h e fatigue tes t s were conducted on a servo-valve controlled electro-hydraulic tes t ing machine (Shimadzu model : EHF-EM200k2-040) in ambient air at room tempera ture . T h e machine was capable to produce wide range of frequencies from 10~5 to 2000 Hz. T h e tes ts were carried out under uniaxial tension-compression loading wi th total s t rain control at a given strain ampli tude of ± 1 % and a strain ratio of — 1 . T h e total strain was measured by a dynamic

extensometer at tached to the specimen having span length of 12. 5 mm. Tr iangular waveform was used for all the fatigue tests. The cyclic loading started from the tensile side. The displacement, load and strain signals were measured for each cycle. One cy­cle comprises 200 data points. The tests were carried out at eight different frequencies from 0. 001 to 3 Hz to investigate the effect of strain rate. The strain rate e was calculated by Eqn. (1)

e = e / i = 2 · / · Δε, (1) where, e is the strain; t is the time; / is the frequency; and ΔΕΙ is the total strain range. In the current study, the strain rate range was 4 X 1 0 - 5 — 0.12 s_1 corre­sponding to the frequencies of 0. 001 —3 Hz.

The fatigue tests were stopped at fracture (or failure). The data were considered ineffective unless the fracture occurred within the gauge length of the dynamic extensometer. The number of cycles to fail­ure was recorded as the fatigue life. The response at half of the fatigue life was used to obtain cyclic stress-strain curves in this study. At least three specimens were tested at each strain rate in order to obtain the effective data, such as average stress am­plitude (eB

= Ae t/2) and average fatigue life. A JSM-

• 52 · Journal of Iron and Steel Research, International Vol. 20

5900LV scanning electron microscope ( S E M ) was used to investigate the fracture surface.

2 Results and Discussion

2 . 1 Cyclic softening behaviors Fig. 2 shows the cyclic s t ress response at differ­

ent strain rates of the test material . T h e material showed significant cyclic softening at the initial stage of fatigue life ( u p to 2 0 % ) for all s train ra tes . T h e cyclic softening of this material may be due to the annihilation of dislocations wi th a net decrease in dislocation density and rearrangement of dislocations into the configuration of cells and subgrains1-11'15-1. After the initial softening, the cyclic s t ress sa turated gradually until the initiation of macro-crack where a rapid decrease in the cyclic s t ress occurred, as shown in Fig. 2. It can be seen tha t the macro-crack in the sample fatigued at a lower strain rate initiated earlier as compared to the higher strain rate sample. T h e crack propagated for a longer t ime prior to the final failure in the low s t ra in rate fatigue as compared to the higher strain rate. Th i s showed tha t at low strain rates the macro-crack initiates earlier but propagates for a longer durat ion before failure.

0.4 0.6 N/N,

N—Number of cycles; Ni—Number of cycles to failure.

Fig. 2 Cyclic stress response of test material under different strain rates at e. = ± 1. 0 %

T o quantify the degree of cyclic softening during L C F , the softening ratio J?sr is defined as1-10-1

■Rs. "ffa I N,/2

(2)

where a™* and aa | N /2 represent the maximum peak s t ress in fatigue life and the peak s t ress at the half of fatigue life, respectively. T h e variation of the sof­tening ratio wi th s train rate is shown in Fig. 3. It can be found tha t the softening ratio decreases gradually with increase in s train rate up to 0. 02 s _ 1 (0. 5 Hz) .

0.37

0.35

| 0 . 3 3

. | 0.31

5 0.29

0.27

0.25

-

-

■ - · * ^ _ ^ _ ^ ,

\ J

0.000 01 0.0001 0.001 0.01 Strain rate/s"1

0.1 1

Fig. 3 Variation of softening ratio with strain rate at ε, = ± 1. 0%

T h e softening ratio s tar ted to increase wi th a sharper gradient for the strain rate higher than 0. 02 s" 1 .

2. 2 Strain rate-dependent LCF behaviors T h e variation of fatigue life wi th strain rate is

shown in Fig. 4. It can be seen tha t the LCF life in­creases gradually with increasing strain rate in the s train rate range of 4 X 1 0 ~ 5 — 0. 012 s _ 1 . However , once the strain rate exceeds 0. 012 s _ 1 , the LCF life decreases wi th increasing strain rate. It is found that the strain rate of approximately 0. 012 s _ 1 is the t ransi t ion point for the L C F life of the studied steel. In order to bet ter unders tand the effect of strain rate on the LCF life, the s train rate-dependent LCF be­haviors are investigated and discussed in detail in the following text .

Fig. 5 shows the hysteresis loops at half of the fatigue life. T h e plastic strain range ΔεΡ was deter­mined from the width of hysteresis loop by subtrac­ting the elastic strain range Δεβ from the total strain range Ae t. T h e hysteresis energy per cycle of the material was represented by the area of the s tress-strain hysteresis loop. It is found that at total strain

900

cles

to f

ailu

re

1 1

Z 300

1 Z 100

0

■ T t _L

' ■ Average ■

1

Ϊ

value ■

1 ""! 1 I

0.000 01 0.000 1 0.001 0.01 Strain rate/s"1

0.1

Fig. 4 Total fatigue life versus strain rate at strain amplitude of 1 %

Issue 7 Effects of Strain Rate on Low Cycle Fatigue Behaviors of High-Strength Structural Steel · 53 ·

0 StrainÄ

Fig. 5 Hysteresis loops at strain range of 2 % with strain rates of 4X 1<T2 and 4X 1<T4 s~' (at half life)

range of 2%, the s t ress ampli tude at 4 X 1 0 - 2 s _ 1 is lower than tha t at 4 X 10~4 s _ 1 , but the plastic strain ranges are close to each o the r , as shown in Fig. 5. This implies tha t at the higher strain rate lower hys­teresis energy is obtained.

Fig. 6 shows the relat ions for the s t ress ampli­tude and plastic strain ampli tude (half of the width of the hysteresis loop) wi th strain rate. It is clear that for s t ress and plastic strain ampli tude variation with strain rate a t ransi t ion in t rend is obtained at strain rate of 0. 012 s _ 1 (0 . 3 H z ) . T h e s tress am­plitude increases gradually wi th increase in the strain rate for the strain rate lower than 0. 012 s _ 1 . H o w ­ever, for the s train rates higher than 0. 012 s _ 1 the stress ampli tude decreased significantly with a sharper gradient. An opposite t rend is obtained for plastic strain ampli tude dependence on the strain rate. T h e plastic strain ampli tude decreases wi th the increase in the s train rate up to the t ransi t ion point. However , for strain rates higher than 0. 012 s _ 1 the plastic strain ampli tude increases wi th a sharper gra­

dient. T h e opposite t rend is due to the reason that the plastic strain ampli tude is calculated from the difference between total strain ampli tude and elastic s t rain ampli tude as represented in Eqn. (3 )

Δε£ = Δε 1 _Δε» = Δ ε 1 _ Δ σ . „ . 2 2 2 2 2E u ;

where Δσ/2 and E are the s t ress amplitude and elas­tic modu lus , respectively.

According to the model proposed by E W Har t [ 1 6 ] , the t ime-dependent deformation ( Fig. 6 ) and the cyclic softening ratio (Fig. 3) are due to the linear shear sliding of the grain boundaries. In the s train rate region below 0. 012 s _ 1 , the grain bound­aries showed higher shear resistance to prevent any sliding. Howeve r , in the high stain rate region the grain boundaries showed relatively lower shear re­sistance which was unable to prevent sliding. The re ­fore , for the low strain rates the plastic strain ampli­tude and softening ratio decreased up to the transi­tion point of 0. 012 s _ 1 but increased wi th a sharper gradient for strain rates higher than 0 .012 s - 1 . A similar behavior of the plastic strain amplitude at lower strain rates was observed by D J Kim et al [12 ] . They a t t r ibuted the saturat ion of plastic strain am­pli tude at lower strain rates to the creep damage in the material .

Fig. 7 shows the relation between plastic strain en­ergy density and strain rate at the half of fatigue life. The average plastic strain energy density was calculated from the hysteresis loop at half life ( N f / 2 ) [ 1 7 ] . T h e plastic strain energy density increases with increase in the strain rate up to the transit ion point for the s train rates lower than 0. 012 s _ 1 but decreases rap­idly higher than this value. A similar transit ion was also found in other s tudy™. J D Morrow et al showed tha t the plastic strain energy per cycle could be regarded as a composite measure of the amount of

355 350

* Stress amplitude ♦ Plastic strain amplitude

0.000 010.0001 0.001 0.01 Strain rate/s-1

0.1

0.798

0.794

0.790

0.786

0.782 0.780

!

I 1

Fig. 6 Relationships of stress amplitude and plastic strain amplitude to strain rate

's

I eu

0.2

0.0

9.8

9.6

9.4 9 3

· /

_

S·

,

\ · • \

1 \

0.000 01 0.0001 0.001 0.01 Strain rate/s"1

0.1

Fig. 7 Relationship between plastic strain energy density and strain rate at half life

• 54 · Journal of Iron and Steel Research, International Vol. 20

fatigue damage per cycle, since the cyclic plastic strain was related to the slip length of dislocations and the cyclic s t ress was related to the resistance to dislocation movement1-10-1. T h e fatigue resistance of a material can be evaluated in te rms of its capacity to absorb and dissipate the plastic strain energy. It is found tha t the fatigue damage per cycle decreases with decrease in strain rate for strain rates lower than 0. 012 s _ 1 , as shown in Fig. 7. Howeve r , it ex­hibits an inverse tendency with decreasing strain rate higher than 0 .012 s" 1 .

Fig. 8 shows the relation between the fatigue life and strain rate. If the total energy of each speci­men is assumed as cons tan t , the theoretical relation­ship between the fatigue life and strain rate could be established from the relation between plastic strain energy density and strain rate (Fig. 7) , as shown by the dashed line in Fig. 8. T h e relationship between the experimental fatigue life and theoretical fatigue life could be classified into three regions. In region I (0 . 08 — 0. 12 s~ l ) , the theoretical fatigue life increa­ses wi th increase in the strain rate which is contrary to the experimental fatigue life resul ts . T h e speci­mens become extremely hot at s train rates above 0. 04 s _ 1 ( 1 H z ) which leads to the decrease in fa­tigue life in region I. In region II (0. 012 —0. 08 s"1 ) , the t rend of the experimental fatigue life agrees well with the theoretical fatigue life. Howeve r , in region III ( 4 X 10"5 - 0 . 012 s " 1 ) , the t rend of the experi­mental fatigue life is opposite to the theoretical fa­t igue life. I t is known tha t creep deformation can take place gradually with a decrease in strain ra te [ 1 2 ] . T h e creep-fatigue interaction can be elevated at lower strain rates as the deformation of grain boundary sliding is more prevalent at lower strain r a t e s M . Therefore , the lower fatigue life at lower strain rates can be a t t r ibuted to the accumulated creep

800

I 700 h

% 600

500 -

400

♦ Experimental data A Tendency of theoreotical

fatigue life

0.000 01 0.000 1 0.001 0.01 Strain rate/s "'

0.1

damage during fatigue. Longer tensile loading time per cycle is needed for the lower strain rate experi­ment and damage is accumulated which resul ts in in­crease in creep damage1-10-1. Wi th the decrease in strain rate from 0. 012 to 4 X 10~4 s _ 1 , the absolute t ime to failure increases significantly. This allows more time to develop creep damage and leads to low­er fatigue life1-5-1. This explains the differences be­tween the est imated and experimental data.

In this s tudy , the t ime-dependent mechanism'-6-' was found as the dominant fatigue mechanism for the studied steel. Fig. 9 shows the relation between time to failure U and strain rate e. It can be seen that time to failure decreases wi th increase in strain rate. The experimental data can be expressed as a power law relation given by

£f = 35. 68 · έ~0-93 (4) It can be seen that the fitted curve is very close to

the experimental da ta , suggesting that the predicted fatigue life coincides well with the experimental data.

1000 000

100 000

Ì & 10 000 s

1000

100

— Fitted curve • Experimental data

\

Fig. 8 Relationship between number of cycles to failure and strain rate

0.000 01 0.0001 0.001 0.01 0.1 1 Strain rate/s"1

Fig. 9 Relationship between time to failure and strain rate

2. 3 Fracture behaviors Fig. 10 shows the fracture surfaces of the sam­

ples fatigued at different strain rates of 4 X 1 0 ~ 5 , 4Χ 10~4 and 4 X 1 0 - 2 s _ 1 , represent ing fracture mecha­nisms at very low, medium and high strain r a t e s , re­spectively. In the crack initiation zone, the fracture surfaces of all samples show secondary cracks-and cavities, as shown in Fig. 10 ( a ) , ( d ) and ( g ) . H o w e v e r , secondary cracks dominate the fracture of the sample fatigued at low strain r a t e s , while cavi­ties are prevalent for high strain rates. T h e cavitati-ons may originate from the nucleation of voids at grain boundary ledges or second phase particles [ 1 8 ] . The propagation of fatigue crack is mainly characterized by the fatigue striations, as shown in Fig. 10 ( b ) , (e) and ( h ) . Very thin slips wi th dense str iat ions are observed on the fracture surface fatigued at very low

Issue 7 Effects of Strain Rate on Low Cycle Fatigue Behaviors of High-Strength Structural Steel · 55 ·

(a) Crack initiation, 4X10"5 s~ (d) Crack initiation, 4X10~4 s" (g) Crack initiation, 4X10~2 s~

(b) Fatigue striations, 4 X 1 0 - 5 s~ (e) Fatigue striations, 4X10~4 s~ (h) Fatigue striations, 4X10~2 s"

(c) Dimple, 4X1(T5 s - 1 i (f) Dimple, 4X10"4 s"1 ; (i) Dimple, 4X10"2 s"1.

Fig. 10 SEM micrographs of fracture surfaces fatigued at different strain rates

strain rate [Fig. 10 ( b ) ] . However, it is revealed from Fig. 10 (h) that failure at high strain rates oc­curred with sharp hill and valley type appearance, which was also observed in IBQ30 steel under condi­tions of fatigue crack propagation at strain rate of 10~2 s~1[19]. These hills and valleys may be attribu­ted to the short stage of fatigue crack propagation at the high strain rate, as shown in Fig. 3.

3 Conclusions

The LCF behavior of a high-strength structural steel was found as strain rate-dependent over a wide range of 4 X 10"5 — 0.12 s"1 (0.001 —3 Hz). The cyclic stress response exhibited apparent cyclic sof­tening. At the low strain rate, the macro-crack initi­ated earlier and propagated for longer duration. The variation of stress amplitude, plastic strain amplitude, and plastic strain energy density with strain rate showed a transition point at strain rate of 0. 012 s"1. Time to

failure decreased linearly with increase in strain rate. Fatigue crack was mainly characterized by duc­tile fracture features. Secondary cracks were found at lower strain rates while cavities were prevalent at higher strain rates.

It was concluded that the fatigue life of the steel was mainly dependent on strain rate. Owing to the strong dependence of LCF life on strain rate, safe coefficient must be considered in designing and eval­uating the fatigue life to avoid the catastrophic loss change in strain rate.

The authors would like to thank the laboratory technicians, especially Dr. Muhammad Kashif Khan in Sichuan University for their careful comments, ■warm encouragement and review of the paper.

References:

[1] Grenier D, Das S, Hamdoon M. Effect of Fatigue Strain Range

• 56 · J o u r n a l of I r o n and S tee l R e s e a r c h , I n t e r n a t i o n a l Vol. 20

on Properties of High-Strength Structural Steel [ J ] . Journal of Marine Structure, 2010, 23(1) · . 88.

[ 2 ] Sheng G M , Gong S H. Investigation of Low Cycle Fatigue Be­haviour of Building Structural Steels Under Earthquake Loading [ J ] . Journal of Acta Metallur Sin (English Le t t e r s ) , 1997, 10 ( 1 ) : 51.

[ 3 ] Luo Y R, Wang Q Y , Yang B. Low Cycle Fatigue Tes ts on Low Carbon Steel [ C J / / B M E I 2011—Proceedings 2011 Inter­national Conference on Business Management and Electronic Information. Guangzhou, 2011 , 4 : 741.

[ 4 ] Luo Y R, Guo Y , Wang Q Y , et al. Low Cycle Fatigue Behav­ior of High-Strength Structural Steel Under Biased Strain Con­trol [ J ] . Journal of Applied Mechanics and Materials, 2011 , 71-78 j 4020.

[ 5 ] Shi X Q , Pang H L J , Zhou W , et al. Low Cycle Fatigue Anal­ysis of Temperature and Frequency Effects in Eutectic Solder Alloy [ J ] . International Journal of Fatigue, 2000, 2 2 ( 3 ) : 217.

[ 6 ] Kanchanomai C, Miyashita Y , Mutoh Y. Strain-Rate Effects on Low Cycle Fatigue Mechanism of Eutectic Sn-Pb Solder [ J ] . International Journal of Fatigue, 2002, 24(9) : 987.

[ 7 ] Hassouni A , Plumier A , Cherrabi A. Experimental and Nu­merical Analysis of the Strain-Rate Effect on Fully Welded Connections [ J ] . Journal of Constructional Steel Research, 2011 , 6 7 ( 3 ) : 533.

[ 8 ] Holper B , Mayer H , Vasudevan A K, et al. Near Threshold Fatigue Crack Growth at Positive Load Ratio in Aluminium Al­loys at Low and Ultrasonic Frequency: Influences of Strain Ra te , Slip Behaviour and Air Humidity [ J ] . International Jour­nal of Fatigue, 2004, 2 6 ( 1 ) : 27.

[ 9 ] Begum S, Chen D L , Xu S, et al. Effect of Strain Ratio and Strain Rate on Low Cycle Fatigue Behavior of AZ31 Wrought Magnesium Alloy [ J ] , Journal of Materials Science and Engi­neering, 2009, 5 1 7 A O / 2 ) : 334.

[10] Hong S G, Lee S B. The Tensile and Low-Cycle Fatigue Be­

havior of Cold Worked 316L Stainless Steel: Influence of Dy­namic Strain Aging [ J ] , International Journal of Fatigue, 2004, 2 6 ( 8 ) : 899.

[ 1 1 ] Wu J H , Lin C K. Effect of Strain Rate on High-Temperature Low-Cycle Fatigue of 17-4 P H Stainless Steels [ J ] . Journal of Materials Science and Engineering, 2005, 3 9 0 A ( l / 2 ) : 291.

[ 1 2 ] Kim D J , Nam S W. Strain-Rate Effect on High Temperature Low-Cycle Fatigue Deformation of AISI 304L Stainless Steel [ J ] , Journal of Materials Science, 1988, 2 3 ( 3 ) : 1024.

[ 1 3 ] General Administration of Quality Supervision, Inspection and Quarantine of the People' s Republic of China. GB/T228— 2002. Metallic Materials—Tensile Testing at Ambient Tem­perature [ S ] . Beijing: China Standards Institution: 2002.

[ 1 4 ] LUO Yun-rong, H U A N G Chong-xiang, G U O Yi, et al. En­ergy-Based Prediction of Low Cycle Fatigue Life of High-Strength Structural Steel [ J ] . Journal of Iron and Steel Re­search, International, 2012, 1 9 ( 1 0 ) : 47.

[ 1 5 ] Nagesha A , Valsan M , Kannan R, et al. Influence of Tem­perature on the Low Cycle Fatigue Behaviour of a Modified 9Cr- lMo Ferritic Steel [ J ] . International Journal of Fatigue, 2002, 2 4 ( 1 2 ) : 1285.

[16] Har t E W, A Theory for Flow of Polycrystals [ J ] . Journal of Acta Metallurgica, 1967, 1 5 ( 9 ) : 1545.

[ 1 7 ] Callaghan M D, Humphries S R , Law M , et al. Energy-Based Approach for the Evaluation of Low Cycle Fatigue Behaviour of 2. 25Cr-lMo Steel at Elevated Temperature [ J ] . Journal of Materials Science and Engineering, 2010, 527A ( 2 1 / 2 2 ) : 5619.

[ 1 8 ] Goods S H , Brown L M. The Nucleation of Cavities by Plastic Deformation [ J ] . Journal of Acta Metallurgica, 1979, 27 (1 ) : 1.

[19 ] Chakraborti P C , Mitra M K. Room Temperature Low Cycle Fatigue Behaviour of Two High Strength Lamellar Duplex Ferrite-Martensite (DFM) Steels [ J ] . International Journal of Fatigue, 2005, 2 7 ( 5 ) : 511.