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Void swelling of modified 316 stainless steels observed in-situ by HVEM
1047
Journal of Nuclear Materials 103 & 104 (1981) 1047-1052
North-Holland PublishingCompany
VOID
SWELLING
OF MODIFIED
OBSERVED
Naohiro
Igata,
IN-SITU
316 STAINLESS
STEELS
BY HVEM
Kohno, Masatoshi Saito and Hideo Tsunakawa
Yutaka
Department of Materials Science, Faculty of Engineering University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Void swelling of Ti modified, Si modified and standard 316 stainless steels were investigatedby means of electron irradiation in a High Voltage Electron Microscope, In the modified steels, void swelling was suppressed compared with the standard steel through the decrease of the void number density. Linear swelling model was applied to the results of this investigation,and swelling behavior of these steels was analysed through the two parameters, incubation of swelling and linear growth rate. Linear increase of swelling was also theoreticallyderived by using the void growth theory of Bullough et al. as a guide.
1. INTRODUCTION
2. EXPERIMENTALPROCEDURE
Void swelling is an important problem for fusion reactor materials. As fusion reactor first wall materials, 316 austenitic stainless steel is intended to be used in the design of future fusion reactors. Above all, modified 316 stainless steel is expected to be a feasible candidate material for a prototypic nuclear fusion reactor(l). It is well known that the swelling behavior of 316 steel or other austenitic Fe-NiCr alloys are very sensitive to various conditions, such as chemical composition, heat treatment and degree of cold work(2)-(6). Compositional variation is a large factor that affects void swelling. There are many papers on the effect of additional elements in 316 steels by means of various irradiationmethods and conditions,(2),(4),(6). Ti and Si, as the minor alloying elements, have been proven to be effective in suppressing void swelling of 316 steels, but the details of the mechanism have not been elucidated. Under a high voltage electron microscope, it is advantageous to carry out radiation damage experiments by continuously observing the whole process in-situ up to about 20 dpa. The objective of this study is to clarify the effects of minor alloying elements Ti and Si on the swelling process of 316 steel by means of electron irradiation in a HVEM.
Vacuum melted 316 standard steel (316STD),Si modified steel (315SiM) and Ti modified steel (316TiM)were used in this experiment. Chemical compositions of these steels are listed in Table 1. The content of Si in 316Si.Mwas 2 weight percent, and that of Ti in 316TiM was 0.45 weight percent. The materials were reduced to sheet, 1 mmthick, by alternate cold rolling and vacuum annealing and then cut to,10 mm x 10 mm square shaped samples. Samples were wrapped in very thin stainless foils for protection from oxidation, and solution heat treated in air at llOO°C for 60 min in electric furnace and subsequently water quenched and cold rolled 20 percent. Aging treatment was performed for as solution treated samples at 5OO*C for 100 hours or 1000 hours in a vacuum of 1-2 x low6 torr. The specimens were mechanically thinned to about 700 pm thick and then punched out to 3 mm diameter discs. Thin foil specimens for HVEM observation were finally prepared by a twin jet electropolishing technique with an electrolyte of 90 percent methanol/l0 percent perchloric acid at about 5°C. No He gas was preinjected. The electron irradiation and in-situ observationwere carried out in a JEM7250 HVEM with an accelerating voltage of 10GOkV and the center area beam intensity of -3.1 x lOi electronslcm2.sec. The
Table I. Type
C
Si
Chemical Ti
of Used Stainless
Compositions Mn
P
S
Ni
Cr
Steels
(wt%)
Al
MO
v
Nb
316ST0 0.052
0.42
0.003
1.69
0.027
0.005
13.85
17.76
2.30
0.048
0.04
0.005*
316SiM 0.084
2.00
0.10
1.74
0.028
0.009
14.00
16.32
2.49
0.013
0.023 0,048
316TiM 0.059
0.93
0.45
1.76
0.024
0.005
13.72
16.39
2.56
0.028
0.02
0.035*
* value of Nb plus To 0022-3115/81~0000-0000!$02.75 01981 North-Holland
1048
h:. Igata et al. / Void swelling of modified
316 SS observed
by HVEM
(b)
I>O$E
Fig.1
I,,l”l
,:
Dose dependence of void (a) 316TiM and 316STD,
swelling of 20% cold worked (b) 316SiM and 316STD
incident produces
beam direction was. This beam displacements in steel at a rate of -1.3 x 10-j dpa/sec, assuming a displacement energy of 24eV (7). The maximum dose was about 20 The irradiation temperature was in the dpa. range from 300°C to 7OOOC. Determination of void parameters was performed according to the ASTM methods (8). Measurements of dislocation density were carried out at the same area as that of void measurements mainly at high temperature (over 600°C) for solution treated samples. 3. 3.1.
EXPERIMENTALRESULTS The effects
of
Ti and Si
on void
swelling;
Figures l(a) and l(b) show the results of void swelling for cold worked 316TiM and 316SiM respectively . Swelling curves for 20 percent cold worked 316STD are also plotted in both figures. Void swelling of both 316TiM and 316SiM were very much suppressed compared with 316STD. In all
Fig.2
i
,,,,,>N
316 steels.
swelling curves seem to consist of two stages, an incubation stage and a stage where swelling increases linearly with irradiation dose (linear swelling stage). The swelling behavior of these two stages is consistent with the linear after incubation swelling model (9). Tn the cases of 316TiM at 500°C and 316SiM at 500°C and 7OO”C, it is clearly observed that the swelling rate is much smaller than that of 316STD and the incubation dose is slightly shorter than that of 316STD. The temperature dependence of the swelling rate of modified steel seems to be larger than that of 316STD at 500°C and 7OO’C. cases,
3.2. The effects of Ti and Si on void number density; Figures 2(a) and 2(b) show the dose dependence of void number density of cold worked 316TiM and 316SiM respectively, compared with that of 316dependence of void number STD. The temperature density is also indicated. Void number densi-
Dose dependence of void number density of 209, cold (a) 316TiM and 316STD, (b) 316SiM and 316STD
worked
316
steels.
1049
N. Igata et al. / Void swelling of modified 316 SS observed by HVEM
8.1. 20%
3.w.
1OOh lOOOh
1
STD TiM
NET
0
.
3000’
0
a
n
5000
A
A
7000
DISPLACEMENTS
Aged
SiM
0
5
1
A.,ed
10 (dpo)
Fig.3 Net displacement dependence of mean void diameter of 20% cold worked 316TiM, 316SiM and 316STD.
ties of modified steels are about two orders of magnitude smaller than that of 316STD at the same irradiation temperature. The void number density saturates at about 5-8 dpa in all cases and the time for saturation seems to become shorter as the irradiation temperature rises. The time when void number density saturates in each modified steel is shorter than that of 316STD at the same irradiation temperature. 3.3. The effects of Ti and Si on void growth; Figure 3 shows the dose dependence of the mean void diameter of cold worked modified and standard steels. In figure 3, mean void diameters are plotted as a function of net displacements which are defined as the differences between total displacementsand displacementsfor incubation of swelling. Incubation displacements are defined as the points where the extrapolation of swelling lines intersect the horizontal axis in figures l(a) and l(b). From figure 3, the mean void diameter increases with one third of net irradiation displacements.
5
10 DOSE
15
20
ldpcl
Fig.4 Effect of aging on swelling of 316TiM irradiated at 5OOOC. while over about 15 dpa, swelling of cold worked steel was smaller than that of solution treated steel because of the smaller swelling rate. 4. DISCUSSION 4.1. Incubation stage; As shown in figure 1, swelling of cold worked 316 steels can be expressed by the incubation and linear swelling model (9). This behavior is expressed by the following equation, S:S(@--rs)
(1)
where S is swelling, S is the swelling rate, @t is total dose expressed by dpa and us is incubation dose of swelling expressed by dpa. During the incubation stage, electron irradiation forms interstitialdislocation loops and increases dislocation density and also enhances the recovery of dislocation through the precipitation of interstitial atans and vacancies on
3.4. The effect of heat treatment on void swelling of modified steels;
Void swelling of solution treated 316TiM and solution treated and aged 316TiM are indicated in figure 4 together with the results of cold worked 316TiM. Irradiation temperaturewas 5oooc. Void swelling of aged 316TiM were larger than that of cold worked or solution treated 316TiM, but it does not seem to obey the linear after incubation swelling model. There seemed to be a transient region between the incubation and linear swelling stages. As for 316TiM aged for lOOOhours, swelling rate did not seem to become constant in these displacement range, Swelling of aged steel became larger as the aging time increased. Swelling of 20 percent cold worked 316TiM was slightly larger than that of solution treated steel up to about 15 dpa because the incubation dose of cold worked steel was shorter than that of solution treated steel,
Fig.5 Relation between dislocation density and irradiation dose in solution treated 316STD and 316TiM at 700°C.
N. Igata et al. / Void swelling of modified 316 SS observed by H VEM
1050
dislocation lines. Thus, the dislocation density reaches the steady state value. Figure 5 shows the change of dislocation density of solution treated 316STD and 316TiM during irradiation at 7oooc. The saturated dislocation density of 316_ TiM was smaller than that of 316STD and the time for saturation of 316TiM was shorter than that of 316STD. Figure 6 shows the relation between the incubation dose for swelling and the time when the dislocation density reached the steady state and also the time when the void number density saturated. Data for solution treated 304 steels irradiated at 600°C are also indicated (IO). The time when dislocation density saturated is almost equal to the incubation dose for swelling. Dislocations behave as the preferential bias sink for interstitial atoms rather than vacancies. Therefore dislocations enhance the void nucleation. The number of void nuclei increased with irradiation time and reached the saturated value when the dislocation density reached the steady state density. Figure 6 shows this relation, Figure 7 shows the relation between the saturated void number density and the steady state dislocation density. In the low dislocation density side, the increase of void number density with the increase of dislocation density is expected (11). However, if the dislocations are not extended as in the specimens used, dislocation clustering or cell formation is observed. Therefore this affects the effective dislocation density. In figure 7, in the high dislocation density region, the decrease of void number density can be understood by the decrease of effective dislocation density due to dislocation clustering or cell formation. Recently as for the effect of Ti, the result that the dispersion of TiC precipitates increased void number density was reported (12), but in this experiment this mechanism does not seem to be the case since void number density decreased by Ti modification. Therefore there seems to be another role of Ti as in this experiment. In solution treated 316TiM, steady state dislocation density was -3.5 X
Fig.7 Relation between saturated dislocation density and saturated void number density in solution treated 316STD and 304 steels.
log cm-2, however, void number density was uncountable. Then the relation between the saturated dislocation density and the saturated void number density was not clear. However, if dislocations were decorated by Ti and other impurities, the decrease of void number density can be understood because of the less effective disloIn cold worked 316TiM and 316cation density. SiM, void number densities were much smaller than that of cold worked 316STD. Although the relation between the steady state dislocation density and the saturated void number density was not clear in the case of cold worked steels, the decoration of dislocations due to Ti, Si and other impurities can be considered.
4.2. Void growth
stage;
From figure 3, the mean void diameter incubation was expected as the following tion, d, = Ad ( @t - 'rs ) I/3
after equa(2)
where d, is the mean void diameter and Ad is the Swelling S is decoefficient of void growth. noted in equation (3) through void number density Nv and the mean void diameter dv, s: +-NV
dv3
From equations (l),(2) and (3), theanext sion is obtained for swelling rate S, ST0
5
Nl
j 5
10 5
15
id”Oi
Fig.6 Relation between incubation dose of swelling and dose of dislocation density saturation, and of void number density saturation in solution treated 316STD and 304 steels.
S +Nv
Ad3
(3) AxPres(4)
Since Ad is the value of d, at (ot-.rs):l in figure 3, Ad of 316TiM or 316SiM is about five times larger than that of 316STD at the same irWhile! as previously radiation temperature. mentioned, the swelling rate S of modified steels are much smaller than that of 316STD which could be interpreted by two parameters NV and Ad in equation (4). NV of modified steels are about two orders of magnitude smaller than that of 316STD, while Ad of modified steels are about five In the result, times larger than that of 316STD.
N. Igata et al. 1 Void swelling of modified 316 SS observed by HVEM
1051
swelling rate became smaller in the case of modified steels, because the decrease of Nv overcame the increase Of Ad. Swelling of modified steels decreased compared with 316STD both because of the decrease of swelling rate and because of the fact that incubation dose of modified steels and 316STD are nearly equal as shown in figure 1.
2) The swelling behavior was linear after an incubation swelling period. 3) Incubation dose and swelling rate were considered to be dominated by the dislocation behavior, such as saturation time of dislocation density and the saturated dislocation density. 4) Aging treatment caused larger void swelling as the aging time became longer.
4.3.
REFERENCES:
Analysis
on the linear increase
of swelling;
As for growth of void, Bullough et al. have shown the next equations as the steady state(l3), d2Cv + K -aCvCi-DvZvpdCvIO Dv(m +~~) (5) Di($$+$s)+K
-oCvCi-DiZipdCizO
where Dv and Di are diffusion constant for vacancies and interstitials respectively, and C,, Ci are concentration of vacancies and interstitials, r is the distance from the center of void, K is defect production rate, o is recombination factor, Z, and Zi are numbers, the order of unity(Zi>Z,), which respectively characterize the vacancy and interstitial capture volume associated with unit length of dislocation and pd is dislocation density. As the boundary conditions, the following are assumed.
dci _. =o at r=R dr 'dr(6) C" q c f Ci =O at r=rv where rv is void radius and R is the half distance between each void. From equation (5) and (6), the following are derived, \ dC K C) -L(8) ~3(-_ dr DvZvPd rv (7) dCi K L(8) dr=-----DiZipd rv where 8(=8v,8i) is defined as (Zpd);. L(8) is written as next form. ,(8),(R-rv)Bcosh6(R~rv)+(rvR82-l)sinhB(R-rv) R8cosh8(R-r,)-sinh@(R-r,) (8) Swelling rate is expressed as the next equation,
3.x
-$:(D,,$
- Di$$)rzr
4~rv20NoNv V
(9)
where R is atomic volume and No is number of atoms per unit volume. Substituting equation (7) to equation (9) and assuming R8<1, the following form for swelling is obtained, 4nR I 1 _ ’
=pd[K
($- - -)-b&j v Zi
And Ad in equation
]RN,N,t
(10)
(2) is shown as follows,
Ad =;[K($-,-$+Dv@d]~
(11)
7
Equation '(lo) shows-the relation between swelling and irradiation time, and the linear proportionality of swelling with irradiation time coincides with the experimental results. 5. SUMMARY 1) Ti or Si modification of 316 stainless steel was effective in suppressing void swelling by electron irradiation by HVEM through the decrease of swelling rate due to the decrease of void number density.
r11 INTOR Zero Phase, Report of the International Tokamak Reactor Workshop, IAEA, Vienna, 1980. [21 Bates, J.F., ASTM STP 57o(lg70)369-386. [31 Appleby, W.K., Bloom, E.E., Flynn, J.E. and Garner, F.A., Radiation Effects in Breeder Reactor Structural Materials, Eds. Bleiberg, M.L. and Bennet, J.W., AIME(1977)509-527. c41 Bates, J.F. and Johnston, W.G., Ibid., 625644. r51 Terasawa, M., Shimada, M., Kakuma, T., Yukitoshi, T., Shiraishi, K. and Uematsu, K., Ibid., 687-707. C61 Watkin, J.S. Gittus, J.H. and Standring, J., Ibid., 467-477. 171 Oen, O.S., ORNL Report, ORNL-3813(1965). [81 Annual Book of ASTM Standards, Part 45, (1977)983-1001. r91 Laidler, J.J., Mastel, B. and Garner, F.A., Ibid.,Reference [21, 451-468. [IO] Igata, N., Kohno, Y., Ohno, K. and Tsunakawa, H., to be published. [ll] Levy, V., Azam, N., LeNaour, L., Didout, G. and Delaplace, J., Ibid.,Reference [3], 709-725. [12] Wood, S., Spitznagel, J.A. and Choyke, W.J., Damage Analysis and Fundamental Studies, DOE/ER-0046/3 (1980)143-158. [13] Bullough, R. and Perrin, R.C., Voids Formed by Irradiation of Reactor Materials, Eds. Pugh, S.F., Loretto, M.H. and Norris, D.I.R., (1971)79-107.
Journal of Nuclear Materials 103 & 104 (1981) 1047-1052
North-Holland PublishingCompany
VOID
SWELLING
OF MODIFIED
OBSERVED
Naohiro
Igata,
IN-SITU
316 STAINLESS
STEELS
BY HVEM
Kohno, Masatoshi Saito and Hideo Tsunakawa
Yutaka
Department of Materials Science, Faculty of Engineering University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Void swelling of Ti modified, Si modified and standard 316 stainless steels were investigatedby means of electron irradiation in a High Voltage Electron Microscope, In the modified steels, void swelling was suppressed compared with the standard steel through the decrease of the void number density. Linear swelling model was applied to the results of this investigation,and swelling behavior of these steels was analysed through the two parameters, incubation of swelling and linear growth rate. Linear increase of swelling was also theoreticallyderived by using the void growth theory of Bullough et al. as a guide.
1. INTRODUCTION
2. EXPERIMENTALPROCEDURE
Void swelling is an important problem for fusion reactor materials. As fusion reactor first wall materials, 316 austenitic stainless steel is intended to be used in the design of future fusion reactors. Above all, modified 316 stainless steel is expected to be a feasible candidate material for a prototypic nuclear fusion reactor(l). It is well known that the swelling behavior of 316 steel or other austenitic Fe-NiCr alloys are very sensitive to various conditions, such as chemical composition, heat treatment and degree of cold work(2)-(6). Compositional variation is a large factor that affects void swelling. There are many papers on the effect of additional elements in 316 steels by means of various irradiationmethods and conditions,(2),(4),(6). Ti and Si, as the minor alloying elements, have been proven to be effective in suppressing void swelling of 316 steels, but the details of the mechanism have not been elucidated. Under a high voltage electron microscope, it is advantageous to carry out radiation damage experiments by continuously observing the whole process in-situ up to about 20 dpa. The objective of this study is to clarify the effects of minor alloying elements Ti and Si on the swelling process of 316 steel by means of electron irradiation in a HVEM.
Vacuum melted 316 standard steel (316STD),Si modified steel (315SiM) and Ti modified steel (316TiM)were used in this experiment. Chemical compositions of these steels are listed in Table 1. The content of Si in 316Si.Mwas 2 weight percent, and that of Ti in 316TiM was 0.45 weight percent. The materials were reduced to sheet, 1 mmthick, by alternate cold rolling and vacuum annealing and then cut to,10 mm x 10 mm square shaped samples. Samples were wrapped in very thin stainless foils for protection from oxidation, and solution heat treated in air at llOO°C for 60 min in electric furnace and subsequently water quenched and cold rolled 20 percent. Aging treatment was performed for as solution treated samples at 5OO*C for 100 hours or 1000 hours in a vacuum of 1-2 x low6 torr. The specimens were mechanically thinned to about 700 pm thick and then punched out to 3 mm diameter discs. Thin foil specimens for HVEM observation were finally prepared by a twin jet electropolishing technique with an electrolyte of 90 percent methanol/l0 percent perchloric acid at about 5°C. No He gas was preinjected. The electron irradiation and in-situ observationwere carried out in a JEM7250 HVEM with an accelerating voltage of 10GOkV and the center area beam intensity of -3.1 x lOi electronslcm2.sec. The
Table I. Type
C
Si
Chemical Ti
of Used Stainless
Compositions Mn
P
S
Ni
Cr
Steels
(wt%)
Al
MO
v
Nb
316ST0 0.052
0.42
0.003
1.69
0.027
0.005
13.85
17.76
2.30
0.048
0.04
0.005*
316SiM 0.084
2.00
0.10
1.74
0.028
0.009
14.00
16.32
2.49
0.013
0.023 0,048
316TiM 0.059
0.93
0.45
1.76
0.024
0.005
13.72
16.39
2.56
0.028
0.02
0.035*
* value of Nb plus To 0022-3115/81~0000-0000!$02.75 01981 North-Holland
1048
h:. Igata et al. / Void swelling of modified
316 SS observed
by HVEM
(b)
I>O$E
Fig.1
I,,l”l
,:
Dose dependence of void (a) 316TiM and 316STD,
swelling of 20% cold worked (b) 316SiM and 316STD
incident produces
beam direction was
EXPERIMENTALRESULTS The effects
of
Ti and Si
on void
swelling;
Figures l(a) and l(b) show the results of void swelling for cold worked 316TiM and 316SiM respectively . Swelling curves for 20 percent cold worked 316STD are also plotted in both figures. Void swelling of both 316TiM and 316SiM were very much suppressed compared with 316STD. In all
Fig.2
i
,,,,,>N
316 steels.
swelling curves seem to consist of two stages, an incubation stage and a stage where swelling increases linearly with irradiation dose (linear swelling stage). The swelling behavior of these two stages is consistent with the linear after incubation swelling model (9). Tn the cases of 316TiM at 500°C and 316SiM at 500°C and 7OO”C, it is clearly observed that the swelling rate is much smaller than that of 316STD and the incubation dose is slightly shorter than that of 316STD. The temperature dependence of the swelling rate of modified steel seems to be larger than that of 316STD at 500°C and 7OO’C. cases,
3.2. The effects of Ti and Si on void number density; Figures 2(a) and 2(b) show the dose dependence of void number density of cold worked 316TiM and 316SiM respectively, compared with that of 316dependence of void number STD. The temperature density is also indicated. Void number densi-
Dose dependence of void number density of 209, cold (a) 316TiM and 316STD, (b) 316SiM and 316STD
worked
316
steels.
1049
N. Igata et al. / Void swelling of modified 316 SS observed by HVEM
8.1. 20%
3.w.
1OOh lOOOh
1
STD TiM
NET
0
.
3000’
0
a
n
5000
A
A
7000
DISPLACEMENTS
Aged
SiM
0
5
1
A.,ed
10 (dpo)
Fig.3 Net displacement dependence of mean void diameter of 20% cold worked 316TiM, 316SiM and 316STD.
ties of modified steels are about two orders of magnitude smaller than that of 316STD at the same irradiation temperature. The void number density saturates at about 5-8 dpa in all cases and the time for saturation seems to become shorter as the irradiation temperature rises. The time when void number density saturates in each modified steel is shorter than that of 316STD at the same irradiation temperature. 3.3. The effects of Ti and Si on void growth; Figure 3 shows the dose dependence of the mean void diameter of cold worked modified and standard steels. In figure 3, mean void diameters are plotted as a function of net displacements which are defined as the differences between total displacementsand displacementsfor incubation of swelling. Incubation displacements are defined as the points where the extrapolation of swelling lines intersect the horizontal axis in figures l(a) and l(b). From figure 3, the mean void diameter increases with one third of net irradiation displacements.
5
10 DOSE
15
20
ldpcl
Fig.4 Effect of aging on swelling of 316TiM irradiated at 5OOOC. while over about 15 dpa, swelling of cold worked steel was smaller than that of solution treated steel because of the smaller swelling rate. 4. DISCUSSION 4.1. Incubation stage; As shown in figure 1, swelling of cold worked 316 steels can be expressed by the incubation and linear swelling model (9). This behavior is expressed by the following equation, S:S(@--rs)
(1)
where S is swelling, S is the swelling rate, @t is total dose expressed by dpa and us is incubation dose of swelling expressed by dpa. During the incubation stage, electron irradiation forms interstitialdislocation loops and increases dislocation density and also enhances the recovery of dislocation through the precipitation of interstitial atans and vacancies on
3.4. The effect of heat treatment on void swelling of modified steels;
Void swelling of solution treated 316TiM and solution treated and aged 316TiM are indicated in figure 4 together with the results of cold worked 316TiM. Irradiation temperaturewas 5oooc. Void swelling of aged 316TiM were larger than that of cold worked or solution treated 316TiM, but it does not seem to obey the linear after incubation swelling model. There seemed to be a transient region between the incubation and linear swelling stages. As for 316TiM aged for lOOOhours, swelling rate did not seem to become constant in these displacement range, Swelling of aged steel became larger as the aging time increased. Swelling of 20 percent cold worked 316TiM was slightly larger than that of solution treated steel up to about 15 dpa because the incubation dose of cold worked steel was shorter than that of solution treated steel,
Fig.5 Relation between dislocation density and irradiation dose in solution treated 316STD and 316TiM at 700°C.
N. Igata et al. / Void swelling of modified 316 SS observed by H VEM
1050
dislocation lines. Thus, the dislocation density reaches the steady state value. Figure 5 shows the change of dislocation density of solution treated 316STD and 316TiM during irradiation at 7oooc. The saturated dislocation density of 316_ TiM was smaller than that of 316STD and the time for saturation of 316TiM was shorter than that of 316STD. Figure 6 shows the relation between the incubation dose for swelling and the time when the dislocation density reached the steady state and also the time when the void number density saturated. Data for solution treated 304 steels irradiated at 600°C are also indicated (IO). The time when dislocation density saturated is almost equal to the incubation dose for swelling. Dislocations behave as the preferential bias sink for interstitial atoms rather than vacancies. Therefore dislocations enhance the void nucleation. The number of void nuclei increased with irradiation time and reached the saturated value when the dislocation density reached the steady state density. Figure 6 shows this relation, Figure 7 shows the relation between the saturated void number density and the steady state dislocation density. In the low dislocation density side, the increase of void number density with the increase of dislocation density is expected (11). However, if the dislocations are not extended as in the specimens used, dislocation clustering or cell formation is observed. Therefore this affects the effective dislocation density. In figure 7, in the high dislocation density region, the decrease of void number density can be understood by the decrease of effective dislocation density due to dislocation clustering or cell formation. Recently as for the effect of Ti, the result that the dispersion of TiC precipitates increased void number density was reported (12), but in this experiment this mechanism does not seem to be the case since void number density decreased by Ti modification. Therefore there seems to be another role of Ti as in this experiment. In solution treated 316TiM, steady state dislocation density was -3.5 X
Fig.7 Relation between saturated dislocation density and saturated void number density in solution treated 316STD and 304 steels.
log cm-2, however, void number density was uncountable. Then the relation between the saturated dislocation density and the saturated void number density was not clear. However, if dislocations were decorated by Ti and other impurities, the decrease of void number density can be understood because of the less effective disloIn cold worked 316TiM and 316cation density. SiM, void number densities were much smaller than that of cold worked 316STD. Although the relation between the steady state dislocation density and the saturated void number density was not clear in the case of cold worked steels, the decoration of dislocations due to Ti, Si and other impurities can be considered.
4.2. Void growth
stage;
From figure 3, the mean void diameter incubation was expected as the following tion, d, = Ad ( @t - 'rs ) I/3
after equa(2)
where d, is the mean void diameter and Ad is the Swelling S is decoefficient of void growth. noted in equation (3) through void number density Nv and the mean void diameter dv, s: +-NV
dv3
From equations (l),(2) and (3), theanext sion is obtained for swelling rate S, ST0
5
Nl
j 5
10 5
15
id”Oi
Fig.6 Relation between incubation dose of swelling and dose of dislocation density saturation, and of void number density saturation in solution treated 316STD and 304 steels.
S +Nv
Ad3
(3) AxPres(4)
Since Ad is the value of d, at (ot-.rs):l in figure 3, Ad of 316TiM or 316SiM is about five times larger than that of 316STD at the same irWhile! as previously radiation temperature. mentioned, the swelling rate S of modified steels are much smaller than that of 316STD which could be interpreted by two parameters NV and Ad in equation (4). NV of modified steels are about two orders of magnitude smaller than that of 316STD, while Ad of modified steels are about five In the result, times larger than that of 316STD.
N. Igata et al. 1 Void swelling of modified 316 SS observed by HVEM
1051
swelling rate became smaller in the case of modified steels, because the decrease of Nv overcame the increase Of Ad. Swelling of modified steels decreased compared with 316STD both because of the decrease of swelling rate and because of the fact that incubation dose of modified steels and 316STD are nearly equal as shown in figure 1.
2) The swelling behavior was linear after an incubation swelling period. 3) Incubation dose and swelling rate were considered to be dominated by the dislocation behavior, such as saturation time of dislocation density and the saturated dislocation density. 4) Aging treatment caused larger void swelling as the aging time became longer.
4.3.
REFERENCES:
Analysis
on the linear increase
of swelling;
As for growth of void, Bullough et al. have shown the next equations as the steady state(l3), d2Cv + K -aCvCi-DvZvpdCvIO Dv(m +~~) (5) Di($$+$s)+K
-oCvCi-DiZipdCizO
where Dv and Di are diffusion constant for vacancies and interstitials respectively, and C,, Ci are concentration of vacancies and interstitials, r is the distance from the center of void, K is defect production rate, o is recombination factor, Z, and Zi are numbers, the order of unity(Zi>Z,), which respectively characterize the vacancy and interstitial capture volume associated with unit length of dislocation and pd is dislocation density. As the boundary conditions, the following are assumed.
dci _. =o at r=R dr 'dr(6) C" q c f Ci =O at r=rv where rv is void radius and R is the half distance between each void. From equation (5) and (6), the following are derived, \ dC K C) -L(8) ~3(-_ dr DvZvPd rv (7) dCi K L(8) dr=-----DiZipd rv where 8(=8v,8i) is defined as (Zpd);. L(8) is written as next form. ,(8),(R-rv)Bcosh6(R~rv)+(rvR82-l)sinhB(R-rv) R8cosh8(R-r,)-sinh@(R-r,) (8) Swelling rate is expressed as the next equation,
3.x
-$:(D,,$
- Di$$)rzr
4~rv20NoNv V
(9)
where R is atomic volume and No is number of atoms per unit volume. Substituting equation (7) to equation (9) and assuming R8<1, the following form for swelling is obtained, 4nR I 1 _ ’
=pd[K
($- - -)-b&j v Zi
And Ad in equation
]RN,N,t
(10)
(2) is shown as follows,
Ad =;[K($-,-$+Dv@d]~
(11)
7
Equation '(lo) shows-the relation between swelling and irradiation time, and the linear proportionality of swelling with irradiation time coincides with the experimental results. 5. SUMMARY 1) Ti or Si modification of 316 stainless steel was effective in suppressing void swelling by electron irradiation by HVEM through the decrease of swelling rate due to the decrease of void number density.
r11 INTOR Zero Phase, Report of the International Tokamak Reactor Workshop, IAEA, Vienna, 1980. [21 Bates, J.F., ASTM STP 57o(lg70)369-386. [31 Appleby, W.K., Bloom, E.E., Flynn, J.E. and Garner, F.A., Radiation Effects in Breeder Reactor Structural Materials, Eds. Bleiberg, M.L. and Bennet, J.W., AIME(1977)509-527. c41 Bates, J.F. and Johnston, W.G., Ibid., 625644. r51 Terasawa, M., Shimada, M., Kakuma, T., Yukitoshi, T., Shiraishi, K. and Uematsu, K., Ibid., 687-707. C61 Watkin, J.S. Gittus, J.H. and Standring, J., Ibid., 467-477. 171 Oen, O.S., ORNL Report, ORNL-3813(1965). [81 Annual Book of ASTM Standards, Part 45, (1977)983-1001. r91 Laidler, J.J., Mastel, B. and Garner, F.A., Ibid.,Reference [21, 451-468. [IO] Igata, N., Kohno, Y., Ohno, K. and Tsunakawa, H., to be published. [ll] Levy, V., Azam, N., LeNaour, L., Didout, G. and Delaplace, J., Ibid.,Reference [3], 709-725. [12] Wood, S., Spitznagel, J.A. and Choyke, W.J., Damage Analysis and Fundamental Studies, DOE/ER-0046/3 (1980)143-158. [13] Bullough, R. and Perrin, R.C., Voids Formed by Irradiation of Reactor Materials, Eds. Pugh, S.F., Loretto, M.H. and Norris, D.I.R., (1971)79-107.