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Study of internal pressure creep strength of Hastelloy X cylindrical specimen containing an axial surface notch
Int. J. Pres. Ves. & Piping 30 (1987) 37-56
Study of Internal Pressure Creep Strength of Hastelioy X Cylindrical Specimen Containing an Axial Surface Notch Ryoichi K u r i h a r a a n d Syuzo U e d a Department of Reactor Safety Research, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, Japan (Received 10 March 1987; accepted 17 March 1987)
A BS TRA C T Creep tests of Hastelloy X were performed at 900°C under in ternalpressure, using cylindrical test specimens with artificial defects. The purpose of these tests is to investigate the influences of depth and length of the defect on the creep strength. Two kinds o f cylindrical specimens were used. One was 3"0 mm in thickness and another was 6.0mm in thickness. Axial notches were machined on the outer surface of these specimens by a milling cutter. Diametral deformation of the specimen was measured during the test by dial gauges mounted on quartz rods. The growing depth of the creep crack was measured using the electrical potential method.
INTRODUCTION A material like Hastelloy X, a nickel base superalloy, will be used for structural components in High Temperature Gas Reactor (HTGR) plants which are being developed at the Japan Atomic Energy Research Institute (JAERI). It depends on the quality of the products whether or not high temperature structural components can complete their intended purpose under creep temperature for a long time during running of the plants. For example, if the material contains defects, its creep strength might be decreased considerably. Therefore, it is very important to know the creep behaviour of the structural component having defects when designing for the HTGR. Udoguchi and Nakanishi 1 reported an experimental study 37 Int. J. Pres. Ves. & Piping 0308-0161/87/$03-50© ElsevierApplied Science Publishers Ltd, England, 1987. Printed in Great Britain
Ryoichi Kurihara, Syuzo Ueda
38
about structural behaviour of a welded Hastelloy X cylinder with internal pressure in a high temperature environment. The present study is concerned with the investigation of internal pressure creep strength of a cylindrical specimen containing an axial surface notch, in order to give data for designing HTGR. A previous paper 2 reported experimental results using a cylindrical specimen made of type 304 stainless steel, and showed conclusions that fracture mechanical approaches using a net section stress a,e ' and a stress intensity factor K~ are also effective under the temperature of 650°C. The present paper reports the experimental results of the creep tests using a Hastelloy X cylindrical specimen with internal pressure at a temperature of 900°C, and the numerical results of a cylindrical model containing a surface notch at initial creep when the crack does not seem to propagate, using a finite element program A D I N A (Automatic Dynamic Incremental Nonlinear Analysis). 3
EXPERIMENTAL METHOD
Equipment A schematic drawing of the test equipment is shown in Fig. 1. This equipment was developed for the creep testing of piping components loaded by internal pressure at high temperature. The pressurizing medium was argon gas supplied from a commercial gas tank, and heating was by an electric furnace. Internal pressure was controlled by a semi-automatic regulator valve. The temperature along the axis of the test tube was found to be 900 +_ 5°C throughout a length _+8 0 m m from the center of the test specimen. Diameters were measured at three locations along the length of the
EXIT
,~ I--
REGULATION VALVE
~o J
o
Z
t~
Fig. I.
Flow diagram of the test apparatus.
Pressure creep strength o f Hastelloy X specimen
39
test specimen as shown in Fig. 1. Six quartz glass rods were inserted from the outer surface of the furnace. Three sets of displacement transducers were installed at the tips of the quartz rods in order to measure the creep deformation which was recorded continuously on multi-pen recorders. Rupture time of the test specimen was measured from the pen recorder by reading the time of a sudden depressurizing of internal pressure.
Test specimens and test conditions The Hastelloy X cylindrical specimens were fabricated by hot extrusion and soaking at 1190°C for one hour. Table 1 shows the chemical composition of TABLE 1 Chemical Composition of Hastelloy X Material in wt % C
Mn
0'08
0'61
Si
P
S
0 " 4 2 0"014
Cr
<0"005
Co
Mo
21-01 1"39 8'69
W
Fe
B
0 " 6 6 18"00 <0"001
Ni Bal.
Grain size > ASTM No. 4.
the Hastelloy X material. Grain size of the material was almost ASTM 4 The shape of the test specimens is shown in Fig. 2. Two kinds of the cylindrical specimens were used. One was 62 mm in outer diameter, 3.0 mm in thickness and 240 mm in length. Another was 66 m m in outer diameter, 6-0 m m in thickness and 240 mm in length. In the present paper the former is called type A test specimen, and the latter is called type B test specimen. A steel core was placed in the test specimen to reduce the gas volume. Artificial surface notches were machined by the cutter on the outer surface of the test specimens in the axial direction. Figure 3 shows a schematic shape of the axial surface notch which is 2 c m m in length, d m m deep and 0"5 mm wide. 420 ~
L
m
240
1
+1
- - -
J
31 (60 Fig. 2.
Geometry of the cylindrical specimen for internal pressure testing.
Ryoichi Kurihara, Syuzo Ueda
40
.
Fig. 3.
.
.
.
.
Schematic shape of a notch manufactured on the surface of the cylindrical specimen.
Electric potential method for creep crack growth measurement The electric potential method was used to measure the creep crack growth from the notch root. The arrangement of electric potential probes around the notch is illustrated in Fig. 4. Probes were made of Hastelloy X welding rods of 1.0 mm in diameter. They were welded at the center of the notches with 3 or 6mm intervals. Constant electric current of five amperes was applied between the outer two probes in these tests. The variation of electric potential between the inner two probes was monitored during the tests.
F
CYLINDRICAL
TUBE
NOTCH• ----2
ARGON GAS
'
I
OUTPUT J
"
1
INPUT
V O L T A G E CURRENT
l
5A
1 HAS'TELLOYTIG X TERMINALwELDED} RODS
Fig. 4.
RODS FOR MEASURING CREEP DEFORMATION Arrangement of elastic potential probe for measuring crack propagation from the notch bottom.
Pressure creep strength of Hasteltoy X specimen 51 0
~
l' ~
. . . .
0 : 2C : 1 3 r n r n ,
h:
30rr, m
"
h:
3.0rnm
: 2C:25mrn,
41
(3 : 2C : 50rrrn, h : 3.Omm
40
x : 2C = IOOmm, h : 3~Omrn {: : 2C = 5 0 r a m , h : 6.0ram INPUT
> E
CURRENT : 5A
3.0
> ILl (..9 <: >
S
2.0
O
l.O
0.0: 0
,L
L
I O0
200
300
NOTCH AREA S (mrn~)
Fig. 5.
Calibration curves at I0°C for the cylindrical specimen in Fig, 4.
A calibration curve is needed to convert the output voltage into a measurement of the crack growth. Such a calibration curve was made by using Hastelloy X plate with artificial notches of known dimensions, and by measuring electric potential of those notches against five amperes input. The calibration curves to transform the output voltage to crack growth are shown in Fig. 5. The output voltage for each notch length increases linearly with the notch area just before penetration of the notch.
3-0 3"0 3"0 3"0 3"0 3"0 3"0 6"O 6"0 6"0 6"0 6"0 6"0
A1 A2 A3 A4 A5 A6 A7
Temperature: 900°C.
B2 B3 B4 B5 B6
B1
Shell thickness h (mm)
Specimen no.
TABLE 2
Notch depth d (mm)
0-0 0"0 1"0 1"0 1"0 1"0 1"0 0"0 I'0 2"0 3"0 0"0 0"0
Notch length 2c (ram)
0 0 100 100 50 25 50 0 50 50 50 0 0
3-43 2'45 2"45 2'45 2"45 2"45 3"43 6"37 6"37 6'37 6-37 6"37 7"35
Internal pressure P (MPa)
33"7 24"0 24"0 24"0 24"0 24'0 33'7 31'9 31"9 31"9 31"9 31"9 36"8
404 1 515 300 443 597 977 344 1 212 1 663 977 493 603 362
Circum3"erenthTl Rupture stress time fr (MPa) t~ (h)
63"5 36'6 5"0 5'5 4"8 6' l 8"4 70'6 2t"4 12'4 9'4 50"2 40"8
.... ( % )
Maximum creep strain
Test C o n d i t i o n s a n d Results of Internal Pressure Creep Tests
1"66 3"33 5'70 5'70 2"60 9'09 1'66 4'17 2"35 1'76 1'76 1"75 1'16
10 -'~ 10 -5 10 -5 10- 5 10- ~ 10 -4 10 ' 5 10- 5 10 -5 10- 5 10 -4 × t0 -4
x x x × × x
x 10 -~6
x × × × x
Minimum creep strain rate gmi. (h- 1)
1"0 1'0 0"66 0"73 0-79 0"89 0"95 1'0 1"05 0"95 0'87 0"90 1"0
fr0,smooth
tr,smooth
1"0 1"0 0"20 0"29 0"39 0"65 0"85 1'0 1"37 0"81 0'41 -1"0
fr0,notch
/rmotch
b~
Pressure creep strength of Hastelloy X specimen
43
Supposing that the crack from the notch as shown in Fig. 3 propagates as a semi-elliptical crack with 2c in the long diameter and 2a in the short diameter, the total area of the crack including the notch becomes S = 2 c d + fecal2
(1)
Therefore, the crack depth a is obtained from Eqn (1) using the calibration curves of Fig. 5.
Test conditions Seven cylindrical specimens of type A having 3-0 mm shell thickness were tested to study an influence of the notch length on a creep strength. Five of these had axial notches which were 1"0 mm in depth and 25, 50 and 100 mm long, respectively. Others had no axial notches. Six cylindrical specimens of type B having 6.0 mm shell thickness were tested to study the influence of the notch depth on the creep strength. Three of these had axial notches which were 50 mm in length and 1-0, 2.0 and 3-0 mm deep, respectively. Others had no axial notches. The test conditions and results using the cylindrical specimens of types A and B are summarized in Table 2.
TEST RESULTS
Influence of notch length using a cylindrical specimen of type A The representative time histories of the diametral creep strain at the center of the cylindrical specimens of type A with and without axial notches are shown in Fig. 6. The diametral creep strain for the cylindrical specimen A2 without a notch shows a steep tangential line of the curve, like the third stage of creep deformation near breaking point. The longer the initial notch of the specimen, the steeper the tangential line of the curve and the shorter the rupture time of the specimen. The creep strain of the diameter of the notched cylindrical specimen was measured at a right-angled direction to the notched axial section and was about 4% which was smaller than that of the unnotched cylindrical specimen. The minimum creep strain rates gmi, as shown in Table 2, were measured from the smallest tangential line of the diametral creep strain curves. The creep crack growth curves obtained from specimens A4, A5 and A6 are shown in Fig. 7. These curves were obtained by calculating the creep crack growth from the output voltage of the electric potential probes using the calibration curves. Typical appearances of the cylindrical specimens of type A after creep
30
I
I
I
A2
TEMP, : 900*C
J /
/
o
20
q~ Z t~ I--t,o
Io
%
500
IO00
1500
2000
TIME t (h) Fig. 6.
Creep strain curves obtained from cylindrical specimens of type A. 50
E
E
ZO
I I,-(3_
t.b ,,~
1.0 o : A4(C:
50)
/", : A 5 ( C : 2 5 } o : A 6 (C = 12.5)
0
500 TIME:
Fig. 7.
t
I000 (h)
Creep crack propagation curves obtained from cylindrical specimens of type A.
Pressure creep strength of Hastelloy X specimen
45
(a)
(b) Fig. 8. Appearance of cylindrical specimens of type A after creep testing: (a) A2 specimen, P = 2-45 MPa, 2¢ = 0'0mm, d = 0"0ram; (b) A6 specimen, P = 2-45 MPa, 2c = 25.0ram, d = 1"0 mm.
testing are shown in Fig. 8. The unnotched specimen A2 bulged and ruptured at the center of the specimen, and deformed more than the notched specimens. The diametral residual strain distribution along the axis of the cylindrical specimen A6 is shown in Fig. 9. The solid line shows the residual strain distribution along the axis at the right-angled direction to the notched axial section. The broken line shows the strain distribution at the notched axial section. Average diametral residual strain of the notched specimen A6 was about 6 per cent. The diametral residual strain at the center of the notched axial section is larger than that of the other part, because a local bulging is caused around the notch. The maximum creep strain emax as shown in Table 2 was measured from the maximum diametral strain distribution after the tests. It was observed after the tests that cracks only grew from the notch root in the thickness direction and did not propagate to the axial direction in all tests. Moreover, the unnotched specimens ruptured stably and showed the fracture mode like pinholing after the tests.
Influence of notch depth using a cylindrical specimen of type B The representative time histories of the creep strain of the diameter at the center of the cylindrical specimens of type B with and without axial notches are shown in Fig. 10. The creep strain of the unnotched specimen B1 is plotted using the data at the maximum swollen point 8 0 m m from the center, and that of the notched specimens B2, B3 and B4 was measured at the center of the right-angled direction to the notched axial section. The deeper
•
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80
40 Z I/J N Q_
n..kl_
0
- 40
I Z I-..-
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a
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,
/ /
-120
0
Fig. 9. 64
6t
2O
I
I
h'
I
2
4
6
8
tO
D IAMETRAL STRAIN (%) Residual strain distribution along the axis of cylindrical specimen A6. i
i
i
TEMP. : 900 °C
~.~81
PRESS. : 6.57 MPa THICK, : 6 0 mm
/
16 z
12 I.-o'3
0 0
500
1000
1500
TIME ! (h)
Fig. 10. Creep strain curves obtained from cylindrical specimens of type B.
000
Pressure creep strength of Hastelloy X specimen
47
(a)
(b) Fig. 11. Appearanceof cylindrical specimens of type B after creep testing: (a) B1 specimen, P=6.37MPa, 2c=0.0mm, d=0.0mm; (b) B2 specimen, P=6.37MPa, 2c=50.0mm, d = 1.0 ram.
the initial notch of the specimen, the smaller the creep strain at the rupture. It is obvious from Fig. 10 that the notch depth does not influence the creep strain rate at the right-angled direction to the notched axial section, since three creep strain curves of specimens B2, B3 and B4 are almost on the same curve. The rupture time of the unnotched specimen B1 is less than that of the notched specimen B2 with the notch depth 1.0 ram. It is considered that this phenomenon is caused by an inner defect or a stress concentration of the unnotched specimen B1 at the point 80 mm from the center as shown in Fig. 11. The creep crack growth curves obtained from the specimens B2, B3 and B4 are shown in Fig. 12. The shallower the crack depth, the faster the crack growth rate just before the rupture. It is considered that this phenomenon is caused by thinning of the shell thickness just before the rupture, i.e. the thinning shell thickness causes an increasing output voltage for the electric potential method to measure the crack growth. However a calculation of the crack growth rate da/dt as mentioned in the following section neglected the influence of the thinning of the shell thickness which is difficult to evaluate. The typical appearance of the cylindrical specimen of type B after creep testing is shown in Fig. 11. The unnotched specimen B1 bulged locally and ruptured at the point 80 mm from the center, while the notched specimen B2 ruptured at the notch root and did not bulge locally. The diametral residual strain distribution along the axis of the cylindrical specimen B2 is shown in Fig. 13. The average diametral residual strain of the notched specimen B2 was about 20%, and greater than that of the notched specimen A6 as shown in Fig. 9.
Ryoichi Kurihara, Syuzo Ueda
48 6
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i
v ,,< n,,',D
2, 0
00
ram)
tX
B~
(d:
2ram)
U
B2
(d =
I rnm)
J
I
I
500
1000
1500
TIME
Fig. 12.
:
2000
t (hi
Creep crack propagation curves obtained from cylindrical specimens of type B.
Interpretation of test results The nominal circumferential stress against the rupture time of each specimen plotted on a log-log graph is shown in Fig. 14. Solid and broken lines refer to the rupturing strength line of A and B type unnotched specimens, respectively. The former has a lesser rupturing strength than the latter, because the circumferential stress distribution from the inner surface to the outer surface of the unnotched specimens of type B is greater than that of the unnotched specimens of type A even if the nominal circumferential stress is the same. The longer the notch length, the shorter the rupture time of the specimen of type A. On the other hand, in the specimen of type B, the rupture time of the notched specimen B2 with 1.0 m m depth was longer than those of the unnotched specimens B1 and B5. Moreover, the rupture times of the unnotched specimens B 1 and B5 were very different in spite of the same test conditions. It is interpreted that these phenomena result from the thick shell of the specimen of type B, i.e. if there is a weak point like an inner defect in the shell of the unnotched specimen of type B, the stress locally concentrates
Pressure creep strength of Hastelloy .Y specimen t
I
I
\
120
49
i
•
Df
o
D2
80 I-Z I.~
40 Z
13_ cp~
0 n~ b-
0
-40
Z I-(Jr}
- 80
/
-I 20
0
I
I
I
I
I0
20
30
40
DIAMETRAL STRAIN Fig. 13.
50
(%)
Residtial strain distribution along the axis of cylindrical specimen B2.
20~
I
FIGURE
g~ N
I
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4
i
i i i
INDICATES
1oo
i
i
SPECIMEN
i
No.
0
A TYPE
D
B TYPE
0") ...1
--
I-Z
50
LI-
~
2o
I
10
IO2
Fig. 14.
I
I
I
I
I III
I
10s
I
I
I
I
I I
104
RUPTURE TIME tr (h) Relationship between nominal stress and rupture time.
Ryoichi Kurihara, Syuzo Ueda
50 1.4
B4 1.2
B3 B2
~f
U 1.0
O I'-rr"
0.8
Z O
06
L~ rr I
04
Z L~ rr (/3
. . .=. . . . .
M = ( l + l . B l - -_~_-c'h ,,))~
02
0L~ r~
J
00
0'2
i
04
0'6
08
10
NOTCH DEPTH VS. SHELL T H I C K N E S S Fig. 15.
d/h
Creep strength reduction ratio obtained from cylindrical specimens of type B. 10 -I
I
O:
.-..
I
I
A4
/X:A5 [3 : A6
EE
•
I,'B4 A:B3
0
re:B2
•
•
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o II E3A
10-2 -m'-
[] 0 (3:: (.9
© zx
o
•
(._)
c ~~
c._.l
o 10"05
,
o
AA
rnl
I
f
2
•
L 5
I0
STRESS INTENSITY FACTOR KI (MN.mm-~-) Fig. 16.
Relationship between creep crack growth rate and stress intensity factor.
Pressure creep strength of Hastelloy X specimen
51
and non-uniformly distributes. In Table 2, the ratio of tr,notch//r,smooth m e a n s the ratio of the rupture times between the notched and unnotched specimens; the ratio of the ratio of the circumferential stresses at the same rupture time. King et aL 4 and Guest and Hutching 5 applied the ductile fracture theory to the evaluation of the creep strength reduction in the tubes with axial notches. In their estimates the creep strength reduction at the same rupture time is evaluated from the equation
ri0,notch/ri0,smooth means
ri0,notch
(h/d)- 1 (h/d)-(1/i)
M---(1
l'61c2-'] 1/2 Rh ,I
ri0,smooth
(2) (3)
where R is a mean radius of the test tube and M the Folias stress magnification factor. The comparison between the calculated results obtained from eqn (2) and the test results of the cylindrical specimens of type B is shown in Fig. 15. The test result is a little different from the calculated result, since the specimens of type B have the thick shell and ri0,smoothis not precisely obtained as mentioned before. The crack growth rates obtained from the creep crack growth curves as shown in Fig. 7 and Fig. 12 are related with the stress intensity factor/(i which is defined as 6
g I . I1 . 0"12(1 12h rca]l/2 . . a)l ri(7~a)l/2 (I) ~a tan ~-~j
(4)
o= ff/2[1-C~)sin2ck]l/2d~k
(5)
where ri is the circumferential stress, and the effect of the shell curvature is neglected in these equations. The relationship between the creep crack growth rate da/dt and the stress intensity factor KI is shown in Fig. 16. There is a good relationship between both on the logarithmic graph. A little scattering seems to be because the bending effect due to the local bulging around the surface notch is neglected when calculating the stress intensity factor. N U M E R I C A L ANALYSIS USING THE FINITE E L E M E N T METHOD The elastic-plastic creep analysis was performed in order to investigate the stress distribution around the axial notch of the cylindrical specimen of type
Ryoichi Kurihara, Syuzo Ueda
52
/
NOTCH
I tp O.03mm
~ \ ~-~\~
\\~\\
. . . . : ORIGINAL 0
Fig. 17.
~"
:DEFORMED
SHAPE SHAPE
AFTER
30
Finite element mesh for analysis and creep deformation after 3.0hours.
A. The computer code is the general purpose finite element code A D I N A developed by Bathe. 3 The mechanical properties of Hastelloy X are summarized in Table 3. On the basis of the time histories of creep strain in the unnotched specimens AI and A2 as shown in Fig. 6, the creep construction equation becomes ~'c = 1"239 x 10 60-4'831./
(6)
where ec is the creep strain, o- is the stress and t is the time. Figure 17 shows the finite element mesh for this analysis and the deformed
TABLE 3 Mechanical Properties of Hastelloy X Material
(oc)
Young's modulus (MPa)
20 900 1000
1'961 x 105 1'344 x 105 1'265 x 105
Temperature
Poisson's ratio
Yield stress (MPa)
0"3 0'3 0"3
Strain hardening modulus (MPa)
3"60 x 102 1-31 x 102 6"67 x l0 t
1"96 X 104 6"90 x 102 1"34 x 102
Thermal expansion rate
1"38 x 10 -5 1"63 x 10 5 1"66 x 10 5
0.40
E E
0.32
?
O
0.24 I--Z
I.O
0.16
<£ ...J
0.08
I
OJ.4
I
0'8
I
I
1'2
I
1.6 TIME
I
2J.O
I
21.4
'
2'.8
3.2
(h)
(a) 0.40
0.32
E T
0 x
I.-Z la_l la_l
0.24
0.16
._J t'~ 008
0
i
014
i
0'8
k
~12
I
,i~
I
210
t
214 '2'8
i
32
TIME (h)
(b) Fig. 18.
Time histories of circumferential and diametral displacements at the tip of the notch: (a) circumferential displacement; (b) diametral displacement.
54
Ryoichi Kurihara. Syuzo Ueda
120;
,
1O 0 / \ \
\
AFTER Q 0 I h \
\
....
\
AFTER 3.0 h
8O Q_
(/) LIJ
60
\~\k\
(.r)
-J F.-., Z .,",v"
"'U -
40
20
(...9
0 \ \ \
-20
-40
04
0.8
1.2
1.6
2.0
DISTANCE FROM NOTCH BOTTOM(mm) Fig. 19.
Circumferential stress along the section from notch bottom to inside wall of the cylindrical specimen.
shape at 3"0 hours after starting load. The analytical model represents onehalf of the cylindrical specimen which is 56-0mm in inner diameter and 3.0 mm in thickness, and has the axial notch of 1-0 mm in depth with infinite length. This model was analysed using the 95 two-dimensional plane strain elements with the 173 variable nodes. Elastic-plastic and creep analysis of this model was carried out by the incremental method for a time step of 0.01 hours under the conditions of 2"45MPa inner pressure and 900°C temperature. In Fig. 17, the solid lines show the deformed shape at 3"0 hours after starting load and the broken lines show the original shape. The creep crack propagation is not considered in this analysis. The lowest node was fixed, and the maximum diametral deformation was about 0"03 mm at some nodes around the notch. The histories of circumferential and diametral displacement at the tip of notch are shown in Fig. 18(a) and (b), respectively. At 3"0 hours after starting load, the circumferential displacement becomes 3.4 x 10 3mm and the diametral one becomes about 0.03 mm.
Pressure creep strength of Hastelloy ,Y specimen
55
Figure 19 shows the circumferential stress distribution along a section from the notch bottom to the inside wall of a cylindrical specimen at 0.01 hours and 3.0 hours after starting load. The circumferential stress tends to increase with closing to the notch bottom. The stress at 3.0 hours after starting load is almost higher than that at 0.01 hours.
CONCLUSIONS The creep strength reduction of a Hastelloy X cylindrical specimen containing an axial surface notch was investigated at 900°C under internal pressure. The following conclusions were obtained. (1) Axial notches were machined on the outer surface of the cylindrical specimens of type A with 3"0 mm wall thickness, to examine the influence of the notch length on the creep strength reduction. The creep rupture time decreases with increasing notch length. Diametral strain after the rupture is about 4% in the case of the cylindrical specimens of type A with a notch of 1"0 mm depth. (2) Axial notches were machined on the outer surface of the cylindrical specimens of type B with 6-0mm wall thickness, to examine the influence of the notch depth on the creep strength reduction. The creep strength reduction ratio can be conservatively predicted by the ductile fracture theory proposed by King e t al. 4 (3) Cracks only grow from the notch root in the thickness direction in all experiments. (4) The electric potential method is very useful for measuring the creep crack growth depth. (5) There is a correlation between the creep crack growth rate and the stress intensity factor on the logarithmic graph. (6) The initial creep deformation around the notch is obtained from the finite element analysis.
ACKNOWLEDGEMENTS The authors would like to thank Dr S. Miyazono, Head of the Mechanical Strength and Structure Laboratory at JAERI, for his fruitful comments on this study. They also appreciate the great support given by Dr K. Sato, Director of the Department of Reactor Safety Research at JAERI.
56
Ryoichi Kurihara, Syuzo Ueda REFERENCES
1. Udoguchi, T. and Nakanishi, T., Structural behaviour of a welded superalloy cylinder with internal pressure in a high temperature environment, Int. J. Pres. Ves. & Piping 9 (1981) p. 107. 2. Ueda, S., Kurihara, R. and Ohba, T., Creep test of type 304 stainless steel tube containing a notch subjected to internal pressure, Int. J. Pres. Ves. & Piping 10 (1982) p. 465. 3. Bathe, K. J., A solution procedure for thermo-elastic and creep problems, Nucl. Eng. Des., 40 (1981) p. 49. 4. King, R. T., Cook, K. V. and Reimann, G. A., Biaxial Creep Rupture Properties of Defective Stainless Steel Tubing, ORNL-TM-3711. 5. Guest, J. C. and Hutching, J. A., Pressure tests to assess the significance of defects in boiler superheater tubing, C221/73, Proc. of Int. Conference on Creep and Fatigue in Elevated Temperature Applications. 6. Paris, P. C. and Shih, C. F., Stress analysis of cracks, A S T M STP, No. 381 (1965) p. 30.
Study of Internal Pressure Creep Strength of Hastelioy X Cylindrical Specimen Containing an Axial Surface Notch Ryoichi K u r i h a r a a n d Syuzo U e d a Department of Reactor Safety Research, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, Japan (Received 10 March 1987; accepted 17 March 1987)
A BS TRA C T Creep tests of Hastelloy X were performed at 900°C under in ternalpressure, using cylindrical test specimens with artificial defects. The purpose of these tests is to investigate the influences of depth and length of the defect on the creep strength. Two kinds o f cylindrical specimens were used. One was 3"0 mm in thickness and another was 6.0mm in thickness. Axial notches were machined on the outer surface of these specimens by a milling cutter. Diametral deformation of the specimen was measured during the test by dial gauges mounted on quartz rods. The growing depth of the creep crack was measured using the electrical potential method.
INTRODUCTION A material like Hastelloy X, a nickel base superalloy, will be used for structural components in High Temperature Gas Reactor (HTGR) plants which are being developed at the Japan Atomic Energy Research Institute (JAERI). It depends on the quality of the products whether or not high temperature structural components can complete their intended purpose under creep temperature for a long time during running of the plants. For example, if the material contains defects, its creep strength might be decreased considerably. Therefore, it is very important to know the creep behaviour of the structural component having defects when designing for the HTGR. Udoguchi and Nakanishi 1 reported an experimental study 37 Int. J. Pres. Ves. & Piping 0308-0161/87/$03-50© ElsevierApplied Science Publishers Ltd, England, 1987. Printed in Great Britain
Ryoichi Kurihara, Syuzo Ueda
38
about structural behaviour of a welded Hastelloy X cylinder with internal pressure in a high temperature environment. The present study is concerned with the investigation of internal pressure creep strength of a cylindrical specimen containing an axial surface notch, in order to give data for designing HTGR. A previous paper 2 reported experimental results using a cylindrical specimen made of type 304 stainless steel, and showed conclusions that fracture mechanical approaches using a net section stress a,e ' and a stress intensity factor K~ are also effective under the temperature of 650°C. The present paper reports the experimental results of the creep tests using a Hastelloy X cylindrical specimen with internal pressure at a temperature of 900°C, and the numerical results of a cylindrical model containing a surface notch at initial creep when the crack does not seem to propagate, using a finite element program A D I N A (Automatic Dynamic Incremental Nonlinear Analysis). 3
EXPERIMENTAL METHOD
Equipment A schematic drawing of the test equipment is shown in Fig. 1. This equipment was developed for the creep testing of piping components loaded by internal pressure at high temperature. The pressurizing medium was argon gas supplied from a commercial gas tank, and heating was by an electric furnace. Internal pressure was controlled by a semi-automatic regulator valve. The temperature along the axis of the test tube was found to be 900 +_ 5°C throughout a length _+8 0 m m from the center of the test specimen. Diameters were measured at three locations along the length of the
EXIT
,~ I--
REGULATION VALVE
~o J
o
Z
t~
Fig. I.
Flow diagram of the test apparatus.
Pressure creep strength o f Hastelloy X specimen
39
test specimen as shown in Fig. 1. Six quartz glass rods were inserted from the outer surface of the furnace. Three sets of displacement transducers were installed at the tips of the quartz rods in order to measure the creep deformation which was recorded continuously on multi-pen recorders. Rupture time of the test specimen was measured from the pen recorder by reading the time of a sudden depressurizing of internal pressure.
Test specimens and test conditions The Hastelloy X cylindrical specimens were fabricated by hot extrusion and soaking at 1190°C for one hour. Table 1 shows the chemical composition of TABLE 1 Chemical Composition of Hastelloy X Material in wt % C
Mn
0'08
0'61
Si
P
S
0 " 4 2 0"014
Cr
<0"005
Co
Mo
21-01 1"39 8'69
W
Fe
B
0 " 6 6 18"00 <0"001
Ni Bal.
Grain size > ASTM No. 4.
the Hastelloy X material. Grain size of the material was almost ASTM 4 The shape of the test specimens is shown in Fig. 2. Two kinds of the cylindrical specimens were used. One was 62 mm in outer diameter, 3.0 mm in thickness and 240 mm in length. Another was 66 m m in outer diameter, 6-0 m m in thickness and 240 mm in length. In the present paper the former is called type A test specimen, and the latter is called type B test specimen. A steel core was placed in the test specimen to reduce the gas volume. Artificial surface notches were machined by the cutter on the outer surface of the test specimens in the axial direction. Figure 3 shows a schematic shape of the axial surface notch which is 2 c m m in length, d m m deep and 0"5 mm wide. 420 ~
L
m
240
1
+1
- - -
J
31 (60 Fig. 2.
Geometry of the cylindrical specimen for internal pressure testing.
Ryoichi Kurihara, Syuzo Ueda
40
.
Fig. 3.
.
.
.
.
Schematic shape of a notch manufactured on the surface of the cylindrical specimen.
Electric potential method for creep crack growth measurement The electric potential method was used to measure the creep crack growth from the notch root. The arrangement of electric potential probes around the notch is illustrated in Fig. 4. Probes were made of Hastelloy X welding rods of 1.0 mm in diameter. They were welded at the center of the notches with 3 or 6mm intervals. Constant electric current of five amperes was applied between the outer two probes in these tests. The variation of electric potential between the inner two probes was monitored during the tests.
F
CYLINDRICAL
TUBE
NOTCH• ----2
ARGON GAS
'
I
OUTPUT J
"
1
INPUT
V O L T A G E CURRENT
l
5A
1 HAS'TELLOYTIG X TERMINALwELDED} RODS
Fig. 4.
RODS FOR MEASURING CREEP DEFORMATION Arrangement of elastic potential probe for measuring crack propagation from the notch bottom.
Pressure creep strength of Hasteltoy X specimen 51 0
~
l' ~
. . . .
0 : 2C : 1 3 r n r n ,
h:
30rr, m
"
h:
3.0rnm
: 2C:25mrn,
41
(3 : 2C : 50rrrn, h : 3.Omm
40
x : 2C = IOOmm, h : 3~Omrn {: : 2C = 5 0 r a m , h : 6.0ram INPUT
> E
CURRENT : 5A
3.0
> ILl (..9 <: >
S
2.0
O
l.O
0.0: 0
,L
L
I O0
200
300
NOTCH AREA S (mrn~)
Fig. 5.
Calibration curves at I0°C for the cylindrical specimen in Fig, 4.
A calibration curve is needed to convert the output voltage into a measurement of the crack growth. Such a calibration curve was made by using Hastelloy X plate with artificial notches of known dimensions, and by measuring electric potential of those notches against five amperes input. The calibration curves to transform the output voltage to crack growth are shown in Fig. 5. The output voltage for each notch length increases linearly with the notch area just before penetration of the notch.
3-0 3"0 3"0 3"0 3"0 3"0 3"0 6"O 6"0 6"0 6"0 6"0 6"0
A1 A2 A3 A4 A5 A6 A7
Temperature: 900°C.
B2 B3 B4 B5 B6
B1
Shell thickness h (mm)
Specimen no.
TABLE 2
Notch depth d (mm)
0-0 0"0 1"0 1"0 1"0 1"0 1"0 0"0 I'0 2"0 3"0 0"0 0"0
Notch length 2c (ram)
0 0 100 100 50 25 50 0 50 50 50 0 0
3-43 2'45 2"45 2'45 2"45 2"45 3"43 6"37 6"37 6'37 6-37 6"37 7"35
Internal pressure P (MPa)
33"7 24"0 24"0 24"0 24"0 24'0 33'7 31'9 31"9 31"9 31"9 31"9 36"8
404 1 515 300 443 597 977 344 1 212 1 663 977 493 603 362
Circum3"erenthTl Rupture stress time fr (MPa) t~ (h)
63"5 36'6 5"0 5'5 4"8 6' l 8"4 70'6 2t"4 12'4 9'4 50"2 40"8
.... ( % )
Maximum creep strain
Test C o n d i t i o n s a n d Results of Internal Pressure Creep Tests
1"66 3"33 5'70 5'70 2"60 9'09 1'66 4'17 2"35 1'76 1'76 1"75 1'16
10 -'~ 10 -5 10 -5 10- 5 10- ~ 10 -4 10 ' 5 10- 5 10 -5 10- 5 10 -4 × t0 -4
x x x × × x
x 10 -~6
x × × × x
Minimum creep strain rate gmi. (h- 1)
1"0 1'0 0"66 0"73 0-79 0"89 0"95 1'0 1"05 0"95 0'87 0"90 1"0
fr0,smooth
tr,smooth
1"0 1"0 0"20 0"29 0"39 0"65 0"85 1'0 1"37 0"81 0'41 -1"0
fr0,notch
/rmotch
b~
Pressure creep strength of Hastelloy X specimen
43
Supposing that the crack from the notch as shown in Fig. 3 propagates as a semi-elliptical crack with 2c in the long diameter and 2a in the short diameter, the total area of the crack including the notch becomes S = 2 c d + fecal2
(1)
Therefore, the crack depth a is obtained from Eqn (1) using the calibration curves of Fig. 5.
Test conditions Seven cylindrical specimens of type A having 3-0 mm shell thickness were tested to study an influence of the notch length on a creep strength. Five of these had axial notches which were 1"0 mm in depth and 25, 50 and 100 mm long, respectively. Others had no axial notches. Six cylindrical specimens of type B having 6.0 mm shell thickness were tested to study the influence of the notch depth on the creep strength. Three of these had axial notches which were 50 mm in length and 1-0, 2.0 and 3-0 mm deep, respectively. Others had no axial notches. The test conditions and results using the cylindrical specimens of types A and B are summarized in Table 2.
TEST RESULTS
Influence of notch length using a cylindrical specimen of type A The representative time histories of the diametral creep strain at the center of the cylindrical specimens of type A with and without axial notches are shown in Fig. 6. The diametral creep strain for the cylindrical specimen A2 without a notch shows a steep tangential line of the curve, like the third stage of creep deformation near breaking point. The longer the initial notch of the specimen, the steeper the tangential line of the curve and the shorter the rupture time of the specimen. The creep strain of the diameter of the notched cylindrical specimen was measured at a right-angled direction to the notched axial section and was about 4% which was smaller than that of the unnotched cylindrical specimen. The minimum creep strain rates gmi, as shown in Table 2, were measured from the smallest tangential line of the diametral creep strain curves. The creep crack growth curves obtained from specimens A4, A5 and A6 are shown in Fig. 7. These curves were obtained by calculating the creep crack growth from the output voltage of the electric potential probes using the calibration curves. Typical appearances of the cylindrical specimens of type A after creep
30
I
I
I
A2
TEMP, : 900*C
J /
/
o
20
q~ Z t~ I--t,o
Io
%
500
IO00
1500
2000
TIME t (h) Fig. 6.
Creep strain curves obtained from cylindrical specimens of type A. 50
E
E
ZO
I I,-(3_
t.b ,,~
1.0 o : A4(C:
50)
/", : A 5 ( C : 2 5 } o : A 6 (C = 12.5)
0
500 TIME:
Fig. 7.
t
I000 (h)
Creep crack propagation curves obtained from cylindrical specimens of type A.
Pressure creep strength of Hastelloy X specimen
45
(a)
(b) Fig. 8. Appearance of cylindrical specimens of type A after creep testing: (a) A2 specimen, P = 2-45 MPa, 2¢ = 0'0mm, d = 0"0ram; (b) A6 specimen, P = 2-45 MPa, 2c = 25.0ram, d = 1"0 mm.
testing are shown in Fig. 8. The unnotched specimen A2 bulged and ruptured at the center of the specimen, and deformed more than the notched specimens. The diametral residual strain distribution along the axis of the cylindrical specimen A6 is shown in Fig. 9. The solid line shows the residual strain distribution along the axis at the right-angled direction to the notched axial section. The broken line shows the strain distribution at the notched axial section. Average diametral residual strain of the notched specimen A6 was about 6 per cent. The diametral residual strain at the center of the notched axial section is larger than that of the other part, because a local bulging is caused around the notch. The maximum creep strain emax as shown in Table 2 was measured from the maximum diametral strain distribution after the tests. It was observed after the tests that cracks only grew from the notch root in the thickness direction and did not propagate to the axial direction in all tests. Moreover, the unnotched specimens ruptured stably and showed the fracture mode like pinholing after the tests.
Influence of notch depth using a cylindrical specimen of type B The representative time histories of the creep strain of the diameter at the center of the cylindrical specimens of type B with and without axial notches are shown in Fig. 10. The creep strain of the unnotched specimen B1 is plotted using the data at the maximum swollen point 8 0 m m from the center, and that of the notched specimens B2, B3 and B4 was measured at the center of the right-angled direction to the notched axial section. The deeper
•
D+
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80
40 Z I/J N Q_
n..kl_
0
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I Z I-..-
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,
/ /
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Fig. 9. 64
6t
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h'
I
2
4
6
8
tO
D IAMETRAL STRAIN (%) Residual strain distribution along the axis of cylindrical specimen A6. i
i
i
TEMP. : 900 °C
~.~81
PRESS. : 6.57 MPa THICK, : 6 0 mm
/
16 z
12 I.-o'3
0 0
500
1000
1500
TIME ! (h)
Fig. 10. Creep strain curves obtained from cylindrical specimens of type B.
000
Pressure creep strength of Hastelloy X specimen
47
(a)
(b) Fig. 11. Appearanceof cylindrical specimens of type B after creep testing: (a) B1 specimen, P=6.37MPa, 2c=0.0mm, d=0.0mm; (b) B2 specimen, P=6.37MPa, 2c=50.0mm, d = 1.0 ram.
the initial notch of the specimen, the smaller the creep strain at the rupture. It is obvious from Fig. 10 that the notch depth does not influence the creep strain rate at the right-angled direction to the notched axial section, since three creep strain curves of specimens B2, B3 and B4 are almost on the same curve. The rupture time of the unnotched specimen B1 is less than that of the notched specimen B2 with the notch depth 1.0 ram. It is considered that this phenomenon is caused by an inner defect or a stress concentration of the unnotched specimen B1 at the point 80 mm from the center as shown in Fig. 11. The creep crack growth curves obtained from the specimens B2, B3 and B4 are shown in Fig. 12. The shallower the crack depth, the faster the crack growth rate just before the rupture. It is considered that this phenomenon is caused by thinning of the shell thickness just before the rupture, i.e. the thinning shell thickness causes an increasing output voltage for the electric potential method to measure the crack growth. However a calculation of the crack growth rate da/dt as mentioned in the following section neglected the influence of the thinning of the shell thickness which is difficult to evaluate. The typical appearance of the cylindrical specimen of type B after creep testing is shown in Fig. 11. The unnotched specimen B1 bulged locally and ruptured at the point 80 mm from the center, while the notched specimen B2 ruptured at the notch root and did not bulge locally. The diametral residual strain distribution along the axis of the cylindrical specimen B2 is shown in Fig. 13. The average diametral residual strain of the notched specimen B2 was about 20%, and greater than that of the notched specimen A6 as shown in Fig. 9.
Ryoichi Kurihara, Syuzo Ueda
48 6
E
"1I.-i1. Ld
i
v ,,< n,,',D
2, 0
00
ram)
tX
B~
(d:
2ram)
U
B2
(d =
I rnm)
J
I
I
500
1000
1500
TIME
Fig. 12.
:
2000
t (hi
Creep crack propagation curves obtained from cylindrical specimens of type B.
Interpretation of test results The nominal circumferential stress against the rupture time of each specimen plotted on a log-log graph is shown in Fig. 14. Solid and broken lines refer to the rupturing strength line of A and B type unnotched specimens, respectively. The former has a lesser rupturing strength than the latter, because the circumferential stress distribution from the inner surface to the outer surface of the unnotched specimens of type B is greater than that of the unnotched specimens of type A even if the nominal circumferential stress is the same. The longer the notch length, the shorter the rupture time of the specimen of type A. On the other hand, in the specimen of type B, the rupture time of the notched specimen B2 with 1.0 m m depth was longer than those of the unnotched specimens B1 and B5. Moreover, the rupture times of the unnotched specimens B 1 and B5 were very different in spite of the same test conditions. It is interpreted that these phenomena result from the thick shell of the specimen of type B, i.e. if there is a weak point like an inner defect in the shell of the unnotched specimen of type B, the stress locally concentrates
Pressure creep strength of Hastelloy .Y specimen t
I
I
\
120
49
i
•
Df
o
D2
80 I-Z I.~
40 Z
13_ cp~
0 n~ b-
0
-40
Z I-(Jr}
- 80
/
-I 20
0
I
I
I
I
I0
20
30
40
DIAMETRAL STRAIN Fig. 13.
50
(%)
Residtial strain distribution along the axis of cylindrical specimen B2.
20~
I
FIGURE
g~ N
I
I
I
4
i
i i i
INDICATES
1oo
i
i
SPECIMEN
i
No.
0
A TYPE
D
B TYPE
0") ...1
--
I-Z
50
LI-
~
2o
I
10
IO2
Fig. 14.
I
I
I
I
I III
I
10s
I
I
I
I
I I
104
RUPTURE TIME tr (h) Relationship between nominal stress and rupture time.
Ryoichi Kurihara, Syuzo Ueda
50 1.4
B4 1.2
B3 B2
~f
U 1.0
O I'-rr"
0.8
Z O
06
L~ rr I
04
Z L~ rr (/3
. . .=. . . . .
M = ( l + l . B l - -_~_-c'h ,,))~
02
0L~ r~
J
00
0'2
i
04
0'6
08
10
NOTCH DEPTH VS. SHELL T H I C K N E S S Fig. 15.
d/h
Creep strength reduction ratio obtained from cylindrical specimens of type B. 10 -I
I
O:
.-..
I
I
A4
/X:A5 [3 : A6
EE
•
I,'B4 A:B3
0
re:B2
•
•
L~J F--
o II E3A
10-2 -m'-
[] 0 (3:: (.9
© zx
o
•
(._)
c ~~
c._.l
o 10"05
,
o
AA
rnl
I
f
2
•
L 5
I0
STRESS INTENSITY FACTOR KI (MN.mm-~-) Fig. 16.
Relationship between creep crack growth rate and stress intensity factor.
Pressure creep strength of Hastelloy X specimen
51
and non-uniformly distributes. In Table 2, the ratio of tr,notch//r,smooth m e a n s the ratio of the rupture times between the notched and unnotched specimens; the ratio of the ratio of the circumferential stresses at the same rupture time. King et aL 4 and Guest and Hutching 5 applied the ductile fracture theory to the evaluation of the creep strength reduction in the tubes with axial notches. In their estimates the creep strength reduction at the same rupture time is evaluated from the equation
ri0,notch/ri0,smooth means
ri0,notch
(h/d)- 1 (h/d)-(1/i)
M---(1
l'61c2-'] 1/2 Rh ,I
ri0,smooth
(2) (3)
where R is a mean radius of the test tube and M the Folias stress magnification factor. The comparison between the calculated results obtained from eqn (2) and the test results of the cylindrical specimens of type B is shown in Fig. 15. The test result is a little different from the calculated result, since the specimens of type B have the thick shell and ri0,smoothis not precisely obtained as mentioned before. The crack growth rates obtained from the creep crack growth curves as shown in Fig. 7 and Fig. 12 are related with the stress intensity factor/(i which is defined as 6
g I . I1 . 0"12(1 12h rca]l/2 . . a)l ri(7~a)l/2 (I) ~a tan ~-~j
(4)
o= ff/2[1-C~)sin2ck]l/2d~k
(5)
where ri is the circumferential stress, and the effect of the shell curvature is neglected in these equations. The relationship between the creep crack growth rate da/dt and the stress intensity factor KI is shown in Fig. 16. There is a good relationship between both on the logarithmic graph. A little scattering seems to be because the bending effect due to the local bulging around the surface notch is neglected when calculating the stress intensity factor. N U M E R I C A L ANALYSIS USING THE FINITE E L E M E N T METHOD The elastic-plastic creep analysis was performed in order to investigate the stress distribution around the axial notch of the cylindrical specimen of type
Ryoichi Kurihara, Syuzo Ueda
52
/
NOTCH
I tp O.03mm
~ \ ~-~\~
\\~\\
. . . . : ORIGINAL 0
Fig. 17.
~"
:DEFORMED
SHAPE SHAPE
AFTER
30
Finite element mesh for analysis and creep deformation after 3.0hours.
A. The computer code is the general purpose finite element code A D I N A developed by Bathe. 3 The mechanical properties of Hastelloy X are summarized in Table 3. On the basis of the time histories of creep strain in the unnotched specimens AI and A2 as shown in Fig. 6, the creep construction equation becomes ~'c = 1"239 x 10 60-4'831./
(6)
where ec is the creep strain, o- is the stress and t is the time. Figure 17 shows the finite element mesh for this analysis and the deformed
TABLE 3 Mechanical Properties of Hastelloy X Material
(oc)
Young's modulus (MPa)
20 900 1000
1'961 x 105 1'344 x 105 1'265 x 105
Temperature
Poisson's ratio
Yield stress (MPa)
0"3 0'3 0"3
Strain hardening modulus (MPa)
3"60 x 102 1-31 x 102 6"67 x l0 t
1"96 X 104 6"90 x 102 1"34 x 102
Thermal expansion rate
1"38 x 10 -5 1"63 x 10 5 1"66 x 10 5
0.40
E E
0.32
?
O
0.24 I--Z
I.O
0.16
<£ ...J
0.08
I
OJ.4
I
0'8
I
I
1'2
I
1.6 TIME
I
2J.O
I
21.4
'
2'.8
3.2
(h)
(a) 0.40
0.32
E T
0 x
I.-Z la_l la_l
0.24
0.16
._J t'~ 008
0
i
014
i
0'8
k
~12
I
,i~
I
210
t
214 '2'8
i
32
TIME (h)
(b) Fig. 18.
Time histories of circumferential and diametral displacements at the tip of the notch: (a) circumferential displacement; (b) diametral displacement.
54
Ryoichi Kurihara. Syuzo Ueda
120;
,
1O 0 / \ \
\
AFTER Q 0 I h \
\
....
\
AFTER 3.0 h
8O Q_
(/) LIJ
60
\~\k\
(.r)
-J F.-., Z .,",v"
"'U -
40
20
(...9
0 \ \ \
-20
-40
04
0.8
1.2
1.6
2.0
DISTANCE FROM NOTCH BOTTOM(mm) Fig. 19.
Circumferential stress along the section from notch bottom to inside wall of the cylindrical specimen.
shape at 3"0 hours after starting load. The analytical model represents onehalf of the cylindrical specimen which is 56-0mm in inner diameter and 3.0 mm in thickness, and has the axial notch of 1-0 mm in depth with infinite length. This model was analysed using the 95 two-dimensional plane strain elements with the 173 variable nodes. Elastic-plastic and creep analysis of this model was carried out by the incremental method for a time step of 0.01 hours under the conditions of 2"45MPa inner pressure and 900°C temperature. In Fig. 17, the solid lines show the deformed shape at 3"0 hours after starting load and the broken lines show the original shape. The creep crack propagation is not considered in this analysis. The lowest node was fixed, and the maximum diametral deformation was about 0"03 mm at some nodes around the notch. The histories of circumferential and diametral displacement at the tip of notch are shown in Fig. 18(a) and (b), respectively. At 3"0 hours after starting load, the circumferential displacement becomes 3.4 x 10 3mm and the diametral one becomes about 0.03 mm.
Pressure creep strength of Hastelloy ,Y specimen
55
Figure 19 shows the circumferential stress distribution along a section from the notch bottom to the inside wall of a cylindrical specimen at 0.01 hours and 3.0 hours after starting load. The circumferential stress tends to increase with closing to the notch bottom. The stress at 3.0 hours after starting load is almost higher than that at 0.01 hours.
CONCLUSIONS The creep strength reduction of a Hastelloy X cylindrical specimen containing an axial surface notch was investigated at 900°C under internal pressure. The following conclusions were obtained. (1) Axial notches were machined on the outer surface of the cylindrical specimens of type A with 3"0 mm wall thickness, to examine the influence of the notch length on the creep strength reduction. The creep rupture time decreases with increasing notch length. Diametral strain after the rupture is about 4% in the case of the cylindrical specimens of type A with a notch of 1"0 mm depth. (2) Axial notches were machined on the outer surface of the cylindrical specimens of type B with 6-0mm wall thickness, to examine the influence of the notch depth on the creep strength reduction. The creep strength reduction ratio can be conservatively predicted by the ductile fracture theory proposed by King e t al. 4 (3) Cracks only grow from the notch root in the thickness direction in all experiments. (4) The electric potential method is very useful for measuring the creep crack growth depth. (5) There is a correlation between the creep crack growth rate and the stress intensity factor on the logarithmic graph. (6) The initial creep deformation around the notch is obtained from the finite element analysis.
ACKNOWLEDGEMENTS The authors would like to thank Dr S. Miyazono, Head of the Mechanical Strength and Structure Laboratory at JAERI, for his fruitful comments on this study. They also appreciate the great support given by Dr K. Sato, Director of the Department of Reactor Safety Research at JAERI.
56
Ryoichi Kurihara, Syuzo Ueda REFERENCES
1. Udoguchi, T. and Nakanishi, T., Structural behaviour of a welded superalloy cylinder with internal pressure in a high temperature environment, Int. J. Pres. Ves. & Piping 9 (1981) p. 107. 2. Ueda, S., Kurihara, R. and Ohba, T., Creep test of type 304 stainless steel tube containing a notch subjected to internal pressure, Int. J. Pres. Ves. & Piping 10 (1982) p. 465. 3. Bathe, K. J., A solution procedure for thermo-elastic and creep problems, Nucl. Eng. Des., 40 (1981) p. 49. 4. King, R. T., Cook, K. V. and Reimann, G. A., Biaxial Creep Rupture Properties of Defective Stainless Steel Tubing, ORNL-TM-3711. 5. Guest, J. C. and Hutching, J. A., Pressure tests to assess the significance of defects in boiler superheater tubing, C221/73, Proc. of Int. Conference on Creep and Fatigue in Elevated Temperature Applications. 6. Paris, P. C. and Shih, C. F., Stress analysis of cracks, A S T M STP, No. 381 (1965) p. 30.