Dynamic strain aging in the high-temperature low-cycle fatigue of SA508 Cl. 3 forging steel

EISEVIER

Journal of Nuclear

Materials

226 (1995) 216-225

journal of nuclear materials

Dynamic strain aging in the high-temperature low-cycle fatigue of SA508 Cl. 3 forging steel Byung Ho Lee, In Sup Kim * lkpurtment of Nuclear Engineering, Korea Advanced Institute of Science and Technology, 373-l Kusong-dong, Yusutrg-KU, Taejon 305-701, South Korea Received

13 July 1994; accepted

12 May 1995

Abstract The effect of dynamic strain aging on cyclic stress response and fatigue resistance of ASME SA508 Cl.3 forging steel for nuclear reactor pressure vcsscls has been evaluated in the temperature range of room temperature to 500°C. Total strain ranges and strain rates were varied from 0.7 to 2.0% and from 4 X 10m4 to 1 X IO-’ s- ‘, respectively. The cyclic stress response depended on the testing temperature, strain rate, and strain range. Generally, the initial cyclic hardening was immediately followed by cyclic softening at all strain rates. However, at 3OO”C, the operating temperature of nuclear reactor pressure vessels, the variation of cyclic stress amplitude showed the primary and secondary hardening stages dependent on the strain rate and strain range. Dynamic strain aging was manifested by enhanced cyclic hardening, distinguished secondary hardening, and negative strain rate sensitivity. A modified cell shuttling model was described for the onset of the secondary hardening due to the dynamic strain aging and it was in good agreement with the experimental results. Fatigue life increased with increase in strain rate at all testing temperatures. Specifically the fatigue life was longer at the dynamic strain aging temperature. Further, the dynamic strain aging was easy to initiate the crack, while crack propagation was retarded by crack branching and suppression of plastic zone, hence the dynamic strain aging caused the improvement of fatigue resistance.

1. Introduction The nuclear reactor pressure vessel is the most critical pressure boundary component in the light water reactor in terms of plant safety [l]. Therefore, the vessel requires superior integrity during plant operation [2-41. The low cycle fatigue failure prevention is an important issue for the structural components in plant life extension and advanced reactor design [5]. Bccausc the reactor vcsscls arc operated at about 3OO”C, at which carbon atoms in the steel matrix can

* Corresponding 42-869-38

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author.

Tel.

+ 82-42-869-3815,

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0 1995 Elsevier

0022-3115(95)00092-5

Fax

+X2-

interact with dislocations and form Cottrell atmospheres [4], the dynamic strain aging effect on the low cycle fatigue behaviors must be considered [5]. The most common alloys showing dynamic strain aging are carbon steels and a number of investigations have been carried out and well established for monotonic tensile deformation. The characteristics of dynamic strain aging are increase of strength, reduction of ductility, and discontinuous yielding during serrated flow known as the Portevin-Le Chatcrlicr effect [h-8]. However, few systematic investigations of dynamic strain aging effect on the low cycle fatigue have been carried out [9-121. Abdel-Raouf et al. reported that in Ferrovac E iron containing 0.007% carbon the dynamic strain aging caused the decrease of fatigue life and a secondary hardening with scrralion in hysteresis curve

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217

B.H. Lee, LS. Kim /Journal of Nuclear Materials 226 (1995) 216-225

at the elevated temperature [9]. But in a 0.1% carbon steel with a ferrite and pearlite structure, Coffin reported that such secondary hardening was not observed during dynamic strain aging [10]. Recently, Tsuzaki et al. reported that the temperature range for dynamic strain aging was lower in fatigue deformation than in monotonic deformation in Type 304 austenitic stainless steel [11]. And they reported that in a plain carbon eutectoid steel the dynamic strain aging resulted in the decrease of fatigue resistance [12]. They proposed an arrest time of dislocations with cell shuttling motion in the saturated stage of cyclic stress. In the cell shuttling motions, dislocations quickly glide between cell walls and pile up against a cell wall and are arrested there, and then dislocations move to the opposite wall of the cell when the stress direction changes. The objective of the present work was to examine the dynamic strain aging effects on the low cycle fatigue properties of ASME SA508 forging steel. The strain rate, strain range, and test temperature were varied to clarify the effect of dynamic strain aging on the fatigue behaviors such as variation of cyclic stress amplitude and fatigue life.

2. Experimental procedure The ASME SA508 C1.3 forging steel for nuclear reactor pressure vessel was taken from a cylindrical shell manufactured by Korea Heavy Industries and Construction Co. Ltd. The chemical composition is given in Table 1. Fig. 1 shows the as-received microstructure which is characterized by dislocation cell networks. Fatigue specimens were in parallel to the tangential direction of the vessel shell and of uniform cylinder type with the gauge section of 7 mm in diameter and 8 mm in length as shown in Fig. 2. Prior to the test, the specimen surface was finished on grit-1200 emery paper in parallel to the stress axis and rinsed with acetone in an ultrasonic cleaning device in order to minimize the surface effect on fatigue properties. Total strain-controlled fatigue tests were carried out in air in a closed-loop servohydraulic fatigue test machine (INSTRON 8501). The axial strain was measured with an extensometer fitted on the extended jig which was calibrated at room temperature (RT). The cyclic strain of a triangular form of strain rates of 4 × 10 -4 to

Table 1 Chemical composition (wt%) of SA508 forging steel

Fig. 1. Transmission electron micrograph showing the dislocation cell structure of SA508 forging steel.

1 × 10 -2 s-1 were employed. The applied total strain range was altered from 0.7 to 2.0%. The test temperatures were between RT and 500°C. The specimens were heated in an infra-red furnace. And the temperature of the specimen was maintained within _+2°C at a desired test temperature. The data of tensile and compressive stresses, strains, and cycles were stored in the Hewlett Packard(HP) 900 series 300 workstation through HP data acquisition and control system (HP 3852A) which was operated by HP-BASIC and Xwindow [13]. At the same time stress-strain hysteresis loops were plotted by an X - Y recorder if necessary. Fatigue life was defined to be the number of cycles at which the peak tensile stress descended to 75% of the maximum peak tensile stress [14]. The fracture surface of fatigued samples was examined by a Philips 515 scanning electron microscope to characterize crack initiation and propagation (striation). Optical microscopy was also conducted on longitudinal sections of fatigued specimens to characterize the crack propagation mode.

1OR

104 ....

Fe

C

Si

Mn

Ni

Cr

Mo

Balance

0.18

0.03

1,48

(I.91

(/.21

0.54

(unit:ram)

Fig. 2, Dimensions of a fatigue specimen.

B.H. Lee, I.S. Kim /Journal of Nuclear MateriaL7 226 (1995)216-225

218 600

60O ~.,

%"

500 '

."a[,,~l----m._

400

m 150"C

'~._~'o-._'r

----tit- - ~ "

0-

:[

0,.

e~

"A

i = 4X10-4 s-]

3oo'c

N

~: = I X I 0 -3 s - l

o 400"C

O

•

[]

~ = 4XI0 -3 s - I ~'-- IXI0-2 s-1

•

300

400

500"C .......................... 10

30£ 100

........

1000

,

................

10

Number of cycles

100

1000

Number of cycles

Fig. 3. Variation of stress amplitude with the number of cycles for a total strain range of 2.0% and a strain rate of 4;<10 -3

Fig. 5. Cyclic stress amplitude as a function of strain rate at 300°C for a total strain range of 2.0%.

S -1.

3.

Results

3. l. Cyclic stress ampfitude variation T h e variation of stress amplitudes with n u m b e r of cycles in the t e m p e r a t u r e r a n g e of R T to 500°C is shown in Fig. 3 for a strain rate of 4 × 1 0 3 s ~ a n d i n Fig. 4 for 4 × 10 -4 s -~. T h e total strain r a n g e (Ae t) was fixed at 2.0%. As shown in Figs. 3 and 4, the stress a m p l i t u d e s increased during a few cycles of initial stage, followed by a c o n t i n u o u s d e c r e a s e until the final load d r o p d u e to crack initiation a n d p r o p a g a t i o n at RT, 150, 400, a n d 500°C for the two strain rates. T h e cyclic softening c o n t i n u e d over 95% of the fatigue life.

On the o t h e r hand, Fig. 3 reveals that the t e n d e n c y of cyclic stress a m p l i t u d e at 300°C is unique and different from that at the o t h e r t e m p e r a t u r e s . T h e stress amplitude shows that an initial or a primary h a r d e n i n g was followed by a softening and then with f u r t h e r cycles the stress a m p l i t u d e increased again, i.e. secondary h a r d e n i n g a p p e a r e d . T h e secondary h a r d e n i n g continued over 90% of the fatigue life. Fig. 4 shows t h a t the m a x i m u m s t r e n g t h was observed at 300°C for tests with a strain rate of 4 × 10 -4 s - ] a n d the cyclic h a r d e n i n g from N = 1 was m a i n t a i n e d up to failure. In this case the distinction b e t w e e n the primary a n d the secondary h a r d e n i n g such as in Fig. 3 was not observed. It was r e p o r t e d that the secondary h a r d e n i n g was caused by h a r d e n i n g controlled by dynamic strain aging [9].

600

58O III /~=4x 10-3s -I %" o_

~oo~

13..

560

"=

~

s-l

540

@ "o

t~

520

cn

300

•

150"C

•

300"C

o

400"C

•

500"C ........

5o0

:~ ' 10

................. 100

1000

Number of cycles

Fig. 4. Variation of stress amplitude with the number of cycles for a total strain range of 2.0% and a strain rate of 4 x 11)-4 S

I.

48o 460

i 100

i 200

i 300

,

i 400

,

i 500

, 600

Temperature('C)

Fig. 6. Effects of temperature and strain rate on the maximum stre~ amplitude for a total strain range of 2.0% showing the negative strain rate sensitivity.

B.H. Lee, I.S. Kim /Journal of Nuclear Materials 226 (1995) 216-225

60O

260

10-3 s-I 1:3 ~ = 4 x 10-4s -1

• ~=4x

250

~ = 4 × 1 0 - 3 s -1

KI

~" 0_

230 ,0

220

o

210

.s_

5O0

X~

¢

400

E .~

200

¢.D >

219

190 I

180

,

;

0

,

1 0

I

i

200

I

i

300

a

,

400

I

•

As,= 1.5%

0

&~, = L 0 %

I":1 As,= 0.7%

,

500

300

. . . . .

,,,I

10

........

I

........

100

I

........

1000

I

........

10000

100000

Temperature('C)

Fig. 7. Effects of testing t e m p e r a t u r e and strain rate on Vickers h a r d n e s s a f t e r fatigue d e f o r m a t i o n .

Fig. 5 shows the more detailed strain rate effect on the stress amplitude in order to investigate the uncommon cyclic response at the temperature of 300°C. The cyclic stress amplitude is the greatest at the strain rate of 1 x 10 -3 s-~. Until this strain rate, the decrease in strain rate produced the increase of stress amplitude, i.e. strain rate sensitivity (b log o-/i) log ~) is negative. Over the strain rate (1 x 10 .3 s-~), the stress amplitude decreased and the strain rate sensitivity changed from a negative to a positive dependence. The degree of work hardening was examined as a function of temperature. Fig. 6 shows the maximum stress amplitudes with the testing temperature for strain rates of 4 × 10 - 3 S - 1 and 4 x 10 - 4 S - l . The maximum stress amplitudes were located at the primary stage at RT, 150, 400, and 500°C, while at the secondary hard-

Number of cycles Fig. 9. C h a n g e of stress a m p l i t u d e with the n u m b e r of cycles up to fatigue life for a strain rate of 4 × 10 - 3 s - i at 300°C.

ening stage at 300°C. The total strain range was 2.0%. Fig. 6 exhibits a peak of stress amplitude at 300°C for a strain rate of 4 X 10 -4 s ~. Also the strain rate sensitivity was negative at that temperature region. On the other hand, at RT the stress amplitudes were nearly equal at both strain rates. Above 400°C, the strain rate sensitivity changed to positive and the maximum stress amplitudes decreased with increasing test temperature. Fig. 7 shows the Vickers hardness in as-received condition and the change of hardness of the fatigued specimens with two strain rates as a function of testing temperatures. The hardness variation revealed that the maximum stress amplitude during low cycle fatigue was resulted from the change of bulk strength. The variation is consistent with the cyclic softening and harden-

600

tO -2

~=4x

0_

500

10-3 s-1

~=4x

10-3S -1

(D

"10

.

E .=_

RT

l0 -3

._o A~, = 1.5% @ []

300

As, = 1.0% ~ , = 0.7%

........

'

10

1

K"

300"C

~1

........

i ........ , ........ 100 1000 10000

Number of cycles

Fig. 8. C h a n g e of stress a m p l i t u d e with tile n u m b e r of cycles up to fatigue life for a strain rate o f 4 X l l ) -~ s I at RT.

Tt~-4 iv

10 3

. . . . . . . .

t

. . . . . . . .

10 4

10 5

Number of reversals to failure, 2 N f

Fig. 10. C o f f i n - M a n s o n plots of plastic strain a m p l i t u d e vs. n u m b e r of reversals to failure (2 N r) at R T and 300°C.

B.H. Lee, 1.S. Kirn /Journal of Nuclear Materials 226 (1995) 216-225

220 10

In low cycle fatigue tests, the Coffin-Manson law [15] is expressed by

/ ; = 4 x 10-3s-I

AEP

2 t~

30o°C ~

1

t

c

=ef(2Nf) ,

(1)

wherc A e o / 2 is the plastic strain amplitude, e'f the fatigue ductility coefficient, N t. the n u m b e r of cycles to

RT o.

O2

10:

.

.

.

.

.

.

10..4

.

I

.

.

.

.

.

.

.

.

lO-S

10a ASp

Plastic strain amplitude,

Fig. 11. Cyclic stress-strain relationship at RT and 300°C.

ing behaviors, and with the negative strain rate sensitivity in Fig. 6.

3.2. Fatigue life In order to study the effect of dynamic strain aging on the low cycle fatigue life, fatigue tests with a strain rate of 4 × 1 0 -3 s ~ were carried out at R T and 300°C. Figs. 8 and 9 show the change of stress amplitude with the n u m b e r of cycles up to fatigue life. Applied total strain ranges were 0.7, 1.0, 1.5, and 2.0%. At R T the initial cyclic hardening was immediately followed by the cyclic softening in all strain ranges. In contrast to the above cyclic softening, the marked primary and steady or secondary hardening stages were distinguishable in all strain ranges at 300°C.

(c)i

800

70O 600 ~D

:=

500

RT 300"C

I.L

4OO

3OO

150"C 500"C

200 ........ 1XIO-4 4XIO-4

' ........ IXIO-3 4XlO-3

1XIO-2

Strain rate(s -1 )

Fig. 12, Fatigue life dependence on strain rate with a strain range or 2.0% at various temperatures.

Fig. 13. Scanning electron micrographs showing the shape of the crack initiation at (a) RT, (b) 3tX)°C, and (c) 500°C for a total strain range of 2.0%,.

B.H. Lee, LS. Kim /Journal of Nuclear Materials 226 (1995) 216-225 failure, and c the fatigue ductility exponent. Fig. 10 shows the plots of log(Aep/2) vs. Iog(2N0. The values of plastic strain amplitude were adopted at the mid-life of the specimens. At the same plastic strain amplitude, the fatigue life at 300°C is shorter than that at RT. This is considered due to dynamic strain aging effect. That is, dynamic strain aging resulted in the reduction of ductility as the case of monotonic deformation. The fatigue life is also closely associated with cyclic stress amplitude as well as plastic strain amplitude. The stress amplitude (Ao-/2) is generally expressed by a power law [16] as

221

amplitudes at 300°C are higher by 100 MPa than those at RT. This is considered as another dynamic strain aging effect which is similar at monotonic tensile deformation. Fatigue lives at a total strain range of 2.0% are plotted as a function of strain rates in a semi-log scale as shown in Fig. 12. Fatigue lives are strongly dependent on the cyclic strain rate and the testing temperature. As the strain rate increases, the life increases. However, fatigue life tested at 300°C was longer than that of 150°C although the oxidation damage should bc more severe at 300°C than at the lower temperature. 3.3. Fractography

where K' is the cyclic hardening coefficient and n' the cyclic hardening exponent. Fig. 11 shows the log(A~r/2) versus log(Aep/2) plots at RT and 300°C. The values of both the stress amplitude and the plastic strain amplitude were chosen at the mid-life of the specimens. At the same plastic strain amplitude, the stress

OQ

Fractographic examination of the fracture surface was carried out by using a scanning electron microscope and an optical microscope. Figs. 13a and 13c show that at a strain rate of 4 × 10 -3 s -1 at RT and 500°C, crack initiation was developed from a main initial crack site. On the other hand, at 300°C, the crack initiation sites were multiple as shown in Fig.

Stress axis

Fig. 14. Optical micrographs showing the fatigue crack propagation modes in fatigued at (a) RT and (b) 300°C for a total strain range of 2.0%.

222

B.H. Lee, LS. Kim /Journal of Nuclear Materials 226 (1995) 216-225 4. Discussion

Under relevant testing conditions during low cycle fatigue deformation, dynamic strain aging in SA508 steel used for nuclear reactor pressure vessels is manifested at the nuclear power plant operating temperature: the dynamic strain aging causes enhanced cyclic hardening and secondary hardening, and negative strain rate sensitivity [7,9].

4.1. Cyclic stress' amplitude response

Fig. 15. Scanning electron micrographs showing the fatigue striation of fractured surfaces; (a) RT, (b) 300°C, and (c) 500°C for a total strain range of 2.0%.

13b. When the crack propagation mode by optical microscope was observed as in Fig. 14, the more branching at 300°C was noticed than at RT, while the transgranular mode appeared at both temperatures. And the striations in the middle of cracks in samples in Fig. 13 to investigate the crack propagation were observed at all temperatures. Fig. 15 shows that the striation width at 300°C is nearly equal to that at RT and much narrower than that at 500°C. In the other words, the crack propagation rate at 300°C is equal to that at RT but much sh)wcr than that at 5(1(t°(?.

The observed cyclic stress variation at RT shows that the initial cyclic hardening is followed by the cyclic softening in the higher Aet while the steady stage followed by cyclic softening in the lower Aet (Fig. 8). Also, the cyclic response at 150, 400 and 500°C shows the similar variations independent of the strain rate (Figs. 3 and 4). The softening behavior resulted from the quenched and fully tempered microstructure of SA508 forging steel [17]. But at 300°C for a strain rate of 4 × 10 -3 s J, the marked primary and secondary hardening stages were distinguishable in all strain ranges (Fig. 9). The onset of secondary hardening is dependent on the strain rate and testing temperature indicating that a thermally activated process is responsible. Because this phenomenon is unique in metals having a high interaction energy between dislocations and impurity atoms, it is reasonable that the hardening resulted from the strong interaction between mobile dislocations and interstitial carbon and nitrogen atoms. Therefore this results revealed that the dynamic strain aging controlled the hardening process [9]. The interaction can be caused by dislocation shuttling motion between cell walls in Fig. 1 [11,18]. And Abdel-Raouf [9] reported that dynamic strain aging resulted in the secondary hardening with serrations in hysteresis loops. Therefore the primary hardening and the secondary hardening in the cyclic stress variation are caused by cyclic strain hardening and dynamic strain age hardening, respectively. In the dynamic strain aging temperature regime in Fig. 5, as strain rate was slower, the cyclic stress amplitude was varied as follows: 11 primary and steady, 2) primary and secondary, and 3) simultaneously primary and secondary hardening from the beginning. The maximum hardening of cyclic stress amplitude appears for a strain rate of 1 × 10 3 s-J. With the strain rates slower than 4 × 10 3 s n, the secondary hardening began early in the fatigue life and started at the initial cycles with accompanying the primary fatigue cyclic hardening, which resulted in a rapid hardening due to cumulative effects of the two hardening processes.

B.H. Lee, LS. Kim /Journal of Nuclear Materials 226 (1995) 216-225 4.2. Occurrence of secondary hardening during the fatigue deformation The secondary hardening reveals the onset of dynamic strain aging, and the cell wall during dislocation shuttling motion is assumed to be the obstacle for arresting dislocations [11]. Because initial cell structure in the SA508 steel did not show any appreciable change to the end of fatigue life in the TEM observations [18], the cell shuttling motion of dislocations can be applicable to the present cyclic deformations for the onset of dynamic strain aging. For such a cell shuttling motion [11], a total time t t in which dislocations shuttle between cell walls can be expressed as t t = t w + tf,

as Ae~

tt( --- tw) = - 7 - . E

(4)

If the waiting time is sufficiently long, the dislocations may be locked at cell wall. With increasing the number of cycles and plastic deformations in cyclic deformation, the aging time, t a required to lock the waiting dislocations at the cell wall may decrease so that at the critical cycles, Arc, t a becomes equal to t w [19]. In general, t a for short-aging time is expressed as [201 2

compared with the monotonic deformation in SA508 steel [4], the solute atoms such as carbon and nitrogen atoms at the temperature of 300°C are fast enough to move and age the dislocations at the cell wall. But the primary stage of stress amplitude variation in Fig. 9 showed that the dynamic strain aging did not occur fast enough in the initial cycles. For the onset of dynamic strain aging, it is considered that the controlling factor for an aging time may not be only solute concentration but also dislocation density at the cell wall. With increasing diflusion coefficient of interstitial atoms [20] and with multiplying dislocation density at the cell wall [21], the aging time for locking or pinning the mobile dislocation decreases so that the aging time is dependent on 1/D as well as 1/p" [19]. Then, the aging time required to lock dislocations may be assumed by

(3)

where t w is a waiting time at the cell wall and tf a flight time across the cell. Because the flight time in Eq. (3) is negligible on the assumption of t w >> tf [19], the waiting time is approximately equal to the total time. The total time in Eq. (3) is the half period of a fatigue cycle. Thus, the total time [11] can be expressed in terms of a strain rate g and a total strain range &e t

/a=(

223

1/2(C1]3/2kTb3

where C i is the solute concentration at the dislocation line, C o the mean solute concentration in the matrix, k the Boltzmann constant, b the Burgers vector, A a parameter representing the strength of interaction between a solute atom and a dislocation, and D the diffusion coefficient of solute atoms. But the aging time by Eq. (5) is difficult to apply directly to the cyclic deformation because Co, Cj and A are difficult to determine in the engineering alloys such as SA508 steel. In SA508 steel with the dislocation cell structure as shown in Fig. 1, dislocations at the cell wall act as the controlling factor [8] so that the dislocation motions are controlled not only by a solute-dislocation but also by dislocation-dislocation interactions [19]. And when

1

to ~ p'~'v

(6)

where p is the total dislocation density and D the diffusion coefficient of carbon atoms. When the dimensional analysis was introduced [22], the parameter n becomes equal to 1. Then the above Eq. (6) is expressed by 1 ta ~ /3p~ "

The dislocation density in monotonic deformation increases almost linearly with plastic strain [19,23] so that the dislocation density in cyclic deformation is assumed to increase linearly with plastic deformation. Therefore, the increase of total dislocations can be expressed by p ~ p0NAep,

(7)

where P0 is the initial dislocation density within the cell interior, N the number of cycles, and Ae o a plastic strain range. If the obstacles are assumed to be forest dislocations at cell walls, P0 is given in terms of the average distance L between arresting obstacles [24] P0 CC L -2"0,

(8)

where the distance, L, appeared to be the cell size, 0.5 ixm as shown in Fig. 1 and the size is good agreement with Nakagawa's result [18]. Then Eq. (6) is rewritten by L2 t;, = K N A % ~ ,

(9)

224

B.H. Lee, LS. Kim /Journal of Nuclear Materials 226 (1995) 216-225

where K is a proportional constant. By using the condition for locking (t W= t,), the critical cycles, Nc, are given by

10 4 • N~calculated)

o

A Nc(expedmental)

L2 Uc =KAspDt--~~

,

(10)

g

10 3

"6

10 2

and the diffusion coefficient in Eq. (10) is expressed as ZX A

where D o is the temperature4ndependent constant, Q the activation energy of the diffusion process and R the molar gas constant, 8.31 J K-~ mol-L The constants for the carbon in c~-iron [25] are D 0=0.02 cm2/s, and Q = 84.1 kJ/mol. At 300°C, the diffusion coefficient is 4.27 X 10 -~° cm2/s. Eqs. (4) and (10) are applied to predict the onset of dynamic strain aging based on the experimental results at Aet = 1.0% at which dynamic strain aging occurred with the distinguishable secondary hardening and K sccms to approximate to 1. The critical number of cycles at 300°C with a strain rate of 4 x 1 0 3 s n is about 97 for 0.012 plastic strain range (Aet = 2.0%). The critical number of cycles from experiments was 50 determined for the minimum cyclic stress amplitude at the beginning stage of secondary hardening as in Fig. 9. The calculated critical number of cycles with typical experimental results are given in Table 2 and Fig. 16. The results show that at a lower strain range N~ is slightly underestimated, while at a higher strain range N~ is overestimated. This difference may be caused by the assumption of negligible flight time, initial dislocation density and change of cell structures. 4.3. Negative strain rate sensitivity It has been well established in monotonic tensile deformations that the negative strain rate dependence of flow stress (/1 log o-/~ log g) occurs in the temperature range where dynamic strain aging takes place [7]. An increase in the stress with reduced strain rate due to dynamic strain aging during low cycle fatigue deformation has becn observed in some investigations [9,26]. The negative strain rate dependence in Figs. 5 and 6 can clearly point the occurrence of dynamic strain aging at the operating temperature of nuclear pressure vessels and that the dominant cyclic hardening mechaTable 2 Typical waiting time and critical number of cycles with a strain rate of 4× l0 -3 s -~ at 300°C /~F~

A%

t,v

N~ (calculated)

N~ (experimental)

0.7%

0.001

1.75

3345

4500

1.0% 1.5%

0.004 2.51) 0.007 3.75 0.012 5.00

555 223 97

611 125

2.0%

50

Z 10 1

,

0.0

=

i

2.0 Total strain range(%) 1.0

3.0

Fig. 16. Comparison of number of critical cycles between calculated and experimental results. nism is the dynamic strain aging. Vickers hardness after cyclic deformation also showed the negative strain rate sensitivity and revealed that the hardening by dynamic strain aging occurred not only in the surface and but also in the matrix of SA508 steel, causing an increase in stress needed to impose the constant total strain. 4.4. Fatigue resistance AbdeI-Raouf [9] observed that the fatigue life did not vary with the strain rate except for the dynamic strain aging region and the shorter life was resulted from dynamic strain aging. But in the present study, as the strain rate increases, the life increases markedly at all testing temperatures and the fatigue life at the dynamic strain aging temperature is longer than the expected life as shown in Fig. 12. The longer fatigue life at 300°C than at 150 and 500°C is considered due to fatigue resistance improvement by dynamic strain age hardening. For the crack initiation in SA508 steel, dynamic strain aging would increase the degree of inhomogeneity of deformation during low cycle fatigue by solute locking of moving dislocations so that dynamic strain aging enhanced the partitioning of cyclic strains into separate regions [26]. This localized deformation leads to multiple crack initiation sites in Fig. 13. Although dynamic strain aging promoted the crack initiation, the overall fatigue resistance was improved by crack branching due to the hardening or strengthening of the matrix by dynamic strain aging as shown in Fig. 14. This may be caused by the very small portion of crack initiation cycles compared to the failure cycles in SA508 steel [18]. On the other hand, from the view point of plastic zone size, it is generally accepted that the plastic zone size is proportional to the rate of crack propagation [27] and the slip motion is important to produce the plastic deh)rmation. Dynamic strain aging occurred with Cottrell atmosphere formation so that the slip motion by dislocations was inhibited. There-

B.H. Lee, LS. Kim /Journal of Nuclear Materia& 226 (1995) 216-225 fore, dynamic strain aging at 300°C may suppress the plastic zone and the crack propagation rate was slower than that at the other temperatures. Furthermore, Logsdon [28] also reported that in the fatigue crack growth rate test by compact tension specimen of SA508 steel, the crack growth rate ( d a / d N ) at 300°C was only slightly faster than that at RT or nearly the same, which is dependent on the frequency and R ratio which, in turn, could influence the dynamic strain aging. On the other hand, for SA533B steel, d a / d N at 300°C was slightly slower than that at RT. These results revealed that the decreased crack growth rate or the improved fatigue resistance may be caused by dynamic strain age hardening. Because the crack initiation life is much shorter than the crack propagation life in the low cycle fatigue, the dominant life is crack propagation and the increased fatigue life can be observed in SA508 steel. Therefore, with the above mentioned crack branching and the plastic zone size, the crack growth rate was slower, accordingly the fatigue resistance is improved by dynamic strain aging.

5. Conclusions The low cycle fatigue deformation behavior of a nuclear pressure vessel steel, ASME SA508 C1.3, at the elevated temperatures up to 500°C has been studied in order to clarify the effect of dynamic strain aging on the cyclic stress response and the fatigue resistance. The results obtained are as follows. 1) Except for the region of dynamic strain aging, 300°C, the initial cyclic hardening was immediately followed by cyclic softening at all strain rates. The cyclic softening continued over 95% of the fatigue life. 2) At the dynamic strain aging temperature, the operating temperature of nuclear pressure vessel, the cyclic stress amplitude showed the primary and secondary hardening dependent on the strain rate and the total strain range. Dynamic strain aging was manifested as secondary hardening and a negative strain rate sensitivity. 3) A modified cell shuttling model was described for the onset of the secondary hardening due to the dynamic strain aging which was based on the cell shuttling motion and it was in good agreement with the experimental results. 4) As the strain rate increased, the fatigue resistance increased at all temperatures. And the effect of dynamic strain aging on fatigue life was larger than the oxidation effect. 5) Dynamic strain aging increased the number of crack initiation sites by partitioning the local deformation but retarded the crack propagation rate by crack branching and by the suppressed plastic zone size.

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Acknowledgements The authors acknowledge financial support from Korea Science and Engineering Foundation through the Center for Advanced Reactor Research.

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