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Effects of complex loadings on plastic deformation of stainless steel (SUS 304) at high temperature
Nuclear Engineering and Design 114 (1989) 355-364 North-Holland, Amsterdam
355
EFFECTS OF COMPLEX LOADINGS ON PLASTIC DEFORMATION ( S U S 304) A T H I G H T E M P E R A T U R E
OF STAINLESS STEEL
K o z o I K E G A M I a n d Yasushi N I I T S U
Research Laboratory of Precision Machinery and Electronics, Tokyo Institute of Technology, Nagatsuta, Midoriku, Yokohama, Japan Received October 1987
The plastic deformation for complex ioadings are experimentally investigated under various high temperature conditions. The experiments are conducted by subjecting thin wall tubular specimens to combined axial load and torsion. The stress-strain curves after plastic prestraining are obtained by subsequent loading along the stress path with corners. The subsequent loadings are given at a different temperature from that of the prestrained temperature. The effects of plastic prestraining as well as temperature history on the stress-strain curves are examined under variable temperature conditions. The stress-strain curves after creep straining are determined by subsequent loading at constant temperature. The effects of creep strain on plastic hardening are observed by comparison with the stress-strain curves without creep straining. The stress-strain curves for cyclic loading are obtained under various temperature conditions. The cyclic loadings are performed between fixed strain limits. The effects of cyclic loadings on the saturation properties of cyclic hardening are examined at constant and variable temperatures.
1. Introduction The structural components used at high temperature are subjected to the severe condition of combining complex loading and temperature history. For the strength design of such components, it is neccessary to investigate the deformation behavior of materials used at high temperature. The high temperature deformation is correlated with loading conditions and temperature state in a complicated manner. Experimental investigations on high temperature deformation have been reported by several researchers. The results are summarized by the authors [1]. Extensive and systematic experiments are neccessary to understand high temperature deformation of metals. The authors [1-9] continue experimental work on plastic deformation at high temperature and report the results in the papers listed in the reference. This paper presents more characteristic properties of the deformation of stainless steel at high temperature on the basis of the authors' experimental results.
2. Experimental methods The experiments were conducted by subjecting thinwalled tubular specimens to combined axial load
and torsion by a combined stress testing machine. The specimen was heated by a high-frequency induction heating apparatus. The testing temperature ranged from room temperature to 600°C. The temperature of the specimen was measured by three P - P R thermocouples. Two lever-type measuring devices were used to obtain the axial and torsional strains of the specimen. The loading conditions were controlled with equivalent values of true stress at 0.653 M P a / s on the loading path. The detailed experimental method is described in a previous paper [1].
3. Experimental results and discussions
3.1. Effect of complex loading Fig. 1 shows complex loading paths with comers. A specimen was loaded to a certain magnitude of prestraining (about 3%) by tension or torsion. Then the loading direction was changed with 0o = 135°C from the initial loading points. The experimental stress-strain curves were uniquely represented by the equivalent form as shown in fig. 2. The notations I ol and p are the equivalent stress and strain components. The testing temperature is 200 o C. The flow stresses after the change
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356
K. lkegami, Y. Niitsu / Effect of complex loadings R.T. p~
~I
400
MPa
: 3.0% ,
~ A / O
0.3%
o --
0.1%
\x
/ ,i i [iI -300
o.
1.0%
~ - -
\
iIi ~
Fig. 1. Stress paths with a comer.
300
z
H
-200
-100
0
100
200
O
300 MPa
200"C o& ° ~ o ~ 400°C
~.~ 100
T e n s i o n --. T o r s i o n
Lx
Torsion ~Tenslon Tensile I 1
0
MPa
~
o
-.-
2 5 0 T- " ~ " £
stress I 2
strain
curve
i 3
t 4
p
I 5
%
Fig. 2. Stress-strain curves for the stress path with a comer. -200
-100
0
100
200 O
of loading direction become higher than the stress-strain curve for monotonic loading. It seems that latent hardening is produced by the loading process with changing direction. Fig. 3 shows subsequent loading paths after tensile prestraining. The specimens were loaded to 3% of tensile plastic strain and then reloaded in different directions. The testing temperatures are 27 (room temperature), 200, 400 and 600°C. The subsequent plastic behavior at room temperature and 400°C are represented in the tensile and shear stress planes shown in fig. 4. The points in the figure are the stress points corresponding to the defined values of equivalent plastic strain in
#"3T 1135°
115°
0or
Fig. 4. Equi-plastic strain surfaces subsequent to tensile prestraining.
subsequent loading from the prestressed point. Curves connecting stress points with the same subsequent plastic strain values are defined as equi-plastic strain surfaces by the authors [5]. The surfaces are formulated by the following equations.
(o- o,)~ t+~ sgn(°-o.)
18 OI
oP--~ ^ . , r l = .~.u /o
O
Fig. 3. Stress paths subsequent to tensile prestraining.
+
3"r2
1 =0'
(°~-o~)
= {(o~- .,)~ + (o, + o~- o~)~}/2 = { ( ° ~ - ° , ) ~ - (°. + o~- o~)~}/2 sgn(x)=
158 °
MPa
1 0 -1
(1)
x>O x=0 x<0.
The one surface clztermined by eq. (1) is schematically illustrated in fig. 5. The curves of broken line are part of a circle with radius oF, where the notation ar is the flow stress in uniaxial tension. This circle is the
357
K. lkegami, Y. Niitsu / Effect of complex loadings
aC.
O
/:
Fig. 5. Schematic figure of the equi-plastic strain surface.
reference used to define the notations o B, oc and o, in eq. (1). The notation o B is a decrease of the flow stress in the opposite direction to the preloading, oc a decrease of the flow in the perpendicular direction to the preloading and o, a shift of the center of the curve. These values are correlated with the plastic strains oP, p~' and the temperature T by the following equations. O F = Oy +
OB
no a
= OBO + A O B
I
oB0 = o 1 ( - 1.12 × 1 0 - 4 T + 0.113) × ( 1 - exp( - 0.39Plp) }
g = 5.31 + (1 - 9.85 × 1 0 - a T )
,,
× { - 2.26 + 2.37 exp( - 0 . 6 1 0 ( ) } o
p 1/2
oB(600 C ) = O l { 1 . 6 1 e x p [ - 6 . 1 8 ( P 2 )
(2)
/
]
× + 0.0711} O c = 0 . 4 9 9 o B exp[-2.1(PEP) 1/2] - o h p
o. = 0.499o n e x p [ - 0 . 8 0 2 ( p 2 )
1/2
/
],
where o I = o F ( p = p[')
27 < T_< 4 0 0 ( ° C )
(3)
and o h (RT, 3%)' = 26 MPa
state which are determined by proportional loadings. By comparing the equi-plastic strain surfaces of the subsequent state with those of the initial state, the expansion and translation of the surfaces by preloading was observed. The hardening in the transverse direction to preloading is remarkable. It seems that latent hardening is produced in this direction. The arrows in the curves are the directions of the plastic strain vectors at the stress points. The directions are normal to the curves. The plastic strain can be calculated by applying the flow rule to the equi-plastic strain surfaces. Fig. 6 shows the equivalent stress and plastic strain relations for the subsequent loading in fig. 3. The curves in the figure are calculated by using the equi-plastic strain surfaces. The flow stresses in the directions of 135 ° and 115 ° are larger than the flow stress in monotonic tensile loading. The ratio of hardening rate to flow stress becomes a maximum at 400 o C. 3.2. Effect o f temperature history
The tensile loading test was conducted under the condition of changing temperature in the range of room temperature to 600°C. The loading and temperature conditions are shown in fig. 7. The testing temperature was changed at the rate of about 2 . 0 ° C / s in a partial unloaded state and held before loading for 5 min. Fig. 8 shows the tensile stress-strain relation obtained. The marks are the experimental results and the chain curves are the tensile stress-strain curves under constant temperatures. The strain is indicated by the plastic strain minus thermal strain. The stress-strain under variable temperatures coincides with that under constant temperature. The flow stress does not depend on the temperature history but depends on the accumulated plastic strain for monotonic loading. The compressive loading tests subsequent to tensile loading were conducted at variable temperatures. Fig. 9 shows Bauschinger curves at 600 ° C and room temperature after tensile prestraining at various temperatures. The full curves are Bauschinger curves under constant temperature. Bauschinger curves at 6 0 0 ° C seem to be
]
o h (200°C, 3%) = 18 MPa
oh(400°C, 3%) = 20 MPa /
(4)
oh(600°C, 3%) = 12 M P a . ] The parameters in o F are given in table 1. The full curves in fig. 4 are the subsequent equiplastic strain surfaces calculated by eq. (1). The broken line curves are the equi-plastic strain surfaces for the initial
Table 1 Material constants for the stress-strain curves Temp. (°C)
oy (MPa)
H (MPa)
a
27 o 200 ° 400 o 600 °
189.8 112.8 93.3 72.1
48.7 34.9 36.5 37.1
0.69 0.80 0.78 0.76
K. lkegami, Y. Niitsu / Effect of complex loadings
358
200"C 27"C
~
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Ol
20
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600°C
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o ~o
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°
o
0
I
0.5
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(c)
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0.5
1.O
1.0
(d)
%
of
Fig. 6. Equivalent stress-strain curves subsequent to tensile prestraining.
J=°°I °.o~ /A ~ ~ 100 1 0 I I
~
,#
~ I,~' i i
400
300
time
0ooi~ I~!-~ ~ 7,1/
g . ~ - - _ _ ~ y og" -
R.T.
200
e
Fig. 7. Loading program under variable temperatures.
100 ~
~ -~o R.T. o o 600 "C I
1
independent of the prestraining temperature as seen in fig. 9(a). But the curves at room temperature in fig. 9(b) are affected by the prestraining temperature. The plastic behavior subsequent to tensile prestrain was investigated for variable temperatures. The loading conditions are shown in fig. 10. The tensile loading was given at room temperature or 6 0 0 ° C and then the
t
2
200=C
I
3
£ 4005C
,~
400"C 600"C
I
5
i
6
I
7
t
I
8
EP
9 %
Fig. 8. Stress-strain curves under variable temperatures. temperature of the specimen was changed to 6 0 0 ° C or room temperature. Various directions were used for the subsequent combined loading; that is 0 o = 0 °, 90 °, 135 °, 158 ° and 180 °. The equi-plastic strain surfaces
K. lkegami, Y. Niitsu / Effect of complex loadings
600°C ' 600°C 400°C • --> & 600°C
R.T. --
300
@
600°C o - - ~ e R.T.
•
@ @@0
•
g_
400°C a "--'> • R.T. t, '~ ~ o o o o
200
•
ee
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R.T,
200oC ~ - - - ) A R.T.
R.T. l ~> o 600°C
300
359
o
:~
k~
o D ~
i
CO
100
i
0
b
100
I
0
I
1
2
~p%
-20C
-200 -300
(a)
[ 2
¢P%
-10(3
-100 o
I-1
S
(b) Fig. 9. Bauschinger curves under variable temperatures.
Stress path at R.T. ......
E x p . Cal.
3.0% Pre-strain at R.T.
Stress path at 6 0 0 ° C
~3- T f~--]-300~
Vt~"
R.T. -,' 600°C
/ "-weo J
"_, ~
O~
o1
~X~°C
6l
. . . . .
,_~ cro
~. R.T.
o(
GO# 283 MPa
0 O- 155 MPa
O"1= 120 MPa
O l = 260 MPa
(a)
~
'
o~
Cb)
~--
//
-300
-200
-100
o
--
0.05
•
--
0.2
\
x
%',~
, 100
%
x \\\
0
P~P
200
300
0
Fig. 10. Stress paths with temperature variations. for the subsequent plastic strain of 0.05%, 0.2% and 1.0% are represented with the full-time curves in fig. 11. The curves are the results calculated using eq. (1). The experimental stress points in the equi-plastic strain surfaces at 600 °C agree with the calculated curves. But the discrepancy between calculated and experimental results at room temperature becomes large in the opposite direction to prestraining. The broken-line curves are the equi-plastic strain surfaces at 600°C in fig. 11(a) and at room temperature in fig. 11(b), respectively. The equi-plastic strain surfaces determined at 600°C subsequent to prestraining at room temperature contracts with the retreat of the surfaces at room temperature. But the surfaces determined at room temperature subse-
(a)
Equi-plastic
strain surfaces
3,0% Pre-strain at 600°C T ~-~-300
/ / -300
-200
/
-100
MPa at 600°C
Exp. o • ~
Cal. P~ % - - 0.05 --0.2 -1
/ 0
100
200 O
300 MPa
(b) Equi-plastic Strain Surfaces at R.T,
F i g . 11. Equi-plastic strain surfaces subsequent to tensile pre-
straining at different temperature.
K. Ikegami, Y. Niitsu / Effect of complex loadings
360
Exp.
3.0% P r e - s t r a i n
Cal.
o ~, c~
°
o° 90° 135° 158° 180°
.. ..... ......
,L
3
0
R,T.
Oc~
0
~
t~
300
12 h ours ~ : ~ 3 ¢ - ~ 1 2 h o u ~ J . . ~
Q-
...... 7 h
200
l~
400"C
~, ~.o_ -o- -~.--~ --~':
-
..o..+o. +o-~+ - ~ - . ~ "
100 ~
14 h
600°C
olOI =0 • IOI = ' ~ T
_ ,50
+," . . .
200 '- , , ' y
0
---1"
2
3
4
5
P %
Fig. 13. Equivalent stress-strain curves including creep strain.
,5OI R.T. -* 6OO°C
o
0.5
(a)
1 et]
o
(b)
0.5 P2P %
Fig. 12. Equivalent stress-strain curves subsequent to tensile prestraining.
quent to prestraining at 600°C expands with the translation of the surfaces at 600 o C. Fig. 12 shows the equivalent stress-strain relations for the subsequent loading of fig. 10. The curves are calculated by applying the flow rule to the equi-plastic strain surfaces of eq. (1) on the assumption of neglecting temperature history. The calculated results at 600 ° C coincide with the experimental results. In the results at room temperature, the calculated curve does not fit the experimental result in the opposite side to the prestraining direction. This means that the effect of temperature history is remarkable for the Bauschinger curves for falling temperature.
3.3. Effect ofcreep strain The monotonic loading tests including creep straining were conducted by tensile or torsional test at room temperature, 400°C and 600°C. The equivalent stress and inelastic strain curves are shown in fig. 13. The full, broken and chain curves are the stress and plastic strain relations under constant temperature. The holding time for creep straining and its magnitude are indicated by the broken lines in the figure. At room temperature, the plastic strain subsequent to creep prestraining was not produced until the increasing stress approached the full curve. After the stress reached the full curve, the plastic strain was produced again and the flow stress coincided with the full curves. This tendency is observed both in
tensile and torsional loading tests. This means that creep strain has the same hardening effect as plastic strain at room temperature. In the results at 600°C, a similar tendency of hardening by creep strain is observed, but the magnitude is small compared with that produced by plastic strain. The creep strain produced at 400°C was small in magnitude and the hardening effect was not confilTned. The compressive tests were conducted at room temperature and 600°C after tensile plastic strain and creep strain. The stress-strain curves are shown in fig. 14. Two Bauschinger curves are illustrated in fig. 14(a) for tensile strains of 0.12% and 1.4% at room temperature and in fig. 14(b) for the tensile strains of 2.6% and 3.8% at 600°C. The Bauschinger curve at room temperature subsequent to both plastic strain of 0.1% and creep strain of 1.0% is indicated by circles in fig. 14(a). Those results fit the Bauschinger curve after tensile plastic strain of 1.4%. A similar comparison between the Bauschinger curves at 600°C with and without creep strain is illustrated in fig. 14(b). The flow stress of the Bauschinger curve subsequent to both plastic strain of 2.6% and creep strain of 1.2% is slightly higher than the curve for plastic strain of 3.8%. This means that the effect of creep strain on the Bauschinger's curve is
m
R,T.
o~---~ 100~
eP %
-100~
/%
-200L Fig. 14. Bauschinger curves including creep strain.
K. Ikegami, Y. Niitsu / Effect of complex loadings
Fig. 15. Stress paths with creep straining.
almost the same as plastic strain at room temperature, but the effect becomes weak at high temperature. The subsequent combined loading tests were conducted after creep straining under constant temperature. The stress paths used in the experiments are shown in fig. 15. The specimens wcrc loaded into the plastic range by tension and the stress on the specimens was held at 250 MPa for about 6 h at room temperature or at 154 MPa for about 24 h. With those preloading processes, the plastic and creep prestrains (p~' and p~) were given to the specimens. The values of plastic and creep strains were 1.4% and 1.6% at room temperature, and 2.6% and 1.2% at high temperature, respectively.
The specimens were subsequently loaded at in various angles 8o different from the prestress points. The loading directions 0o were chosen to be 0 °, 90 °, 135 °, 158 ° and 180 ° . The plastic behavior subsequent to plastic and creep prestraining is compared with the equiplastic strain surfaces in fig. 16. The full time curves are the surfaces calculated by using eq. (1) on the assumption of neglecting the hardening effect of creep strain. The broken line curves are the results of including the hardening by creep strain on the assumption of equivalent hardening effect between plastic and creep deformation. At room temperature, the subsequent stress points coincide with the broken line curves. The hardening effect of creep strain is nearly equal to that of plastic strain in combined stress state. The experimental stress points at 600°C are close to the broken curves or between the broken and full curves. The hardening
R.T Cal. --
Pl : t . 4 %
....
R.T
Exp.
Cal. p, :t.4%
--
~ *~ ,,
GH : 2 5 0 M P a 1.4%
I-
.....
-.
pC : 1 . 6 %
.
\
....
~
~. pP
x
t
,I
\
/,,
oo4;
I
-200
-100
0
100
200
p~ :3.8%
~-~"
/ /
"
G'xP" o
~
MPa ~.
,
:~" :t3~"
o
. o.s
•• - 1
#i -
,<-~" dE ~
='
-0.5
0
0.5
1
S u b s e q u e n t a x i a l plastic strain
%
(a)
MPa
600°C --
P l :2.6%
....
p , :&8%
Exp. Torsional
flastic strain/%/'~
1
%
o
OH : 154MPa RP : 2.6% pC : 1.2%
- 200
eo:O-
" 0 4%
Exp. ~__
',
%
Ca I.
C3"[
p, : 2 . 6 %
,
I T 1 //
300
0
600°C
_ _
\
\g':, iX,,
(a)
Cal,
Torsional plastic strain /*.v/~
:3.0%
" x
/:
,,:=04%
p!
\
"[ MPa [300
~
361
~ \ ' - " ,
~
Pt
Oo:o°
~.
-90°
13
:135"
•
:158"
•
:180~
0.5
o.s%
too\
[ -200
;1 -100
1 o
(b)
lOO
200 (3
MPa
Fig. 16. Equi-plastic strain surfaces subsequent to plastic and creep straining.
-0.5
0 Subsequent
0.5
1
axial plastic strain %
(b)
Fig. 17. Plastic strain trajectories subsequent to plastic and creep straining.
K. lkegamL Y. Niitsu / Effect of complex loadings
362
+
I:LT. ~
.
1.0%~
~
_;
Fig. 18. Cyclic stress-strain curves under constant temperature.
effect due to creep strain at high temperature is slightly weaker than hardening by plastic strain. By comparing two curves illustrated by the full and broken lines in fig. 16, it is found that the hardening mode by creep strain at room temperature is similar to kinematic hardening and, at high temperature, the mode resembles isotropic hardening. Fig. 17 is the comparison of the strain trajectories corresponding to the results of fig. 15. The full and broken lines are the trajectories calculated by applying the flow rule to the equi-plastic strain surfaces. The results indicated with the full and broken lines are respectively obtained on the assumption of neglecting and including the hardening effect by creep strain in the above-mentioned way. The experimental trajectories both at room temperature and 600°C are close to the results of the broken line. The plastic hardening is produced by creep strain.
3.4. Effect of cycfic loading The stress-strain curves in cyclic loading by tension and compression were obtained under various temperature conditions. The cyclic loading was performed between fixed strain amplitude. Fig. 18 shows the cyclic stress-strain curves under a strain amplitude of 1.0% for 20 cycles at room temperature and for 30 cycles at 600°C. The maximum tensile stress in cyclic stress-
strain curves at room temperature varies from 230 MPa in the initial cycle to 295 MPa in 20 cycles. The flow stress at room temperature exhibits an increase of 30% with cyclic loading. In the cyclic stress-strain curves at 600°C, the flow stress increases by 150% during 20 cycles. The hardening properties in cyclic loading depend strongly on the temperature state. Fig. 19 shows the cyclic hardening behavior during 20 cycles with a strain amplitude of 1.0% under the condition of changing temperature between room temperature and 200°C or between room temperature and 600 o C. The sequence of testing temperature is the cyclic change of room temperature and high temperature. In the cyclic test between room temperature and 200°C, the maximum flow stress is about 300 MPa in the second and third cyclic loading at room temperature. The value is equal to the maximum flow stress in the initial cyclic loading. But the maximum flow stress of cyclic loading between room temperature and 600°C becomes 400 MPa in the second and third cyclic loading at room temperature. The effect of temperature history is observed on the saturation properties of cyclic hardening. Fig. 20 shows the variation of the maximum stress in cyclic loading at different temperature conditions. The notations o(~) and o(~) are the maximum stresses in tension and compression, respectively. In the tests between room temperature and 200°C of fig. 20(a), the maximum stress after the second cyclic loading is nearly constant. In fig. 20(b), the maximum stresses at room temperature and 600°C are varied by cyclic loading. The increase of the maximum stress in the first cyclic loading is remarkable at 600°C. The maximum stress increases also in the second and third cyclic loadings. But, in the cyclic loading at room temperature, the maximum stress decreases during cyclic loading, though the initial maximum stress in each cyclic loading process increases compared with the final maximum stress in the previous cyclic loading at room temperature. The results of fig. 20(c) shows a similar tendency to fig. 18(b). The variation of the maximum stress of fig. 20(d) is different from the results of figs. 18(a) to (c). The softening by decrease of the maximum stress is not observed and the cyclic hardening is produced in each cyclic loading process at both 400°C and 600°C.
4. Conclusions
The plastic deformation of 304 stainless steel was experimentally investigated at high temperature by subjecting thin-walled tubular specimens to combined axial
363
K. Ikegami, Y. Niitsu / Effect of complex loadings
.....
~ - 7 - - - T - - 7 - - - r ,
'
R.T.;
i
......
:
y--.
200C
2_.
'
o
T - T . . ,
,
. . . . . . . .
J_2
;
.
.
PLT.
.
.
.
. . . . . . . R~T. p
:
2
0
o
0C
LL
// T
~
~ - - 7
--]
. . . . .
-]
F
-
. . . .
i---TI Tf?Fig. 19. Cyclic stress-strain curves under variable temperatures.
load and torsion. The effect of plastic prestraining, temperature history, creep prestraining and cyclic loading was examined on the equivalent stress-strain curves and the equi-plastic strain surfaces under various loadhag conditions. The equi-plastic strain surfaces were defined by the loci of stress points with the equivalent plastic strain hardening magnitude under combined stress state. The obtained results are summarized as follows. (1) The plastic hardening is remarkable in the transverse direction to prestraining. The hardening behavior
is represented by the egg-shaped equi-plastic strain surfaces. (2) The effect of temperature history on flow stress was small for monotonic loading, but the effect was observed in the stress-strain relations in reverse loading. (3) The creep strain had the same hardening effect as the plastic strain at room temperature. But the effect of creep strain on plastic hardening was weak at high temperature compared with that of hardening by plastic strain.
K. lkegami, Y. Niitsu / Effect of complex loadings
364 400
40O
==
R.T.
R,T,
R.T
g
RT.
a,~ 300
1
,~
200"C
200"C
C
30C
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200"C
200"C
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I0C
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210
40
---
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810
100
cycle
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loc
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120
80
. . . . .
240
400
,
r
l
iI~600o C
600"C
1001
,~ 300
~
I
1
40
I
60
600"C
600"C 100
•
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*'"
~1~ 2 0 0
600 C
AE=I.0%
20
d
400"C
400"C
,oo'o
L
200 N
b
#. =E
+ ;¢ 300
0
160 cycle
,~ 4eel
2001
120
N
600 °C &E: 1.0%
z
80 cycle
I
I
100
120
N
210
410
8~0
60 cycle
i 1oo N
12o
Fig. 20. Maximum cyclic stress under variable temperatures.
(4) T h e cyclic h a r d e n i n g was m o r e r e m a r k a b l e at high t e m p e r a t u r e t h a n at r o o m t e m p e r a t u r e . T h e coup l e d effect b e t w e e n l o a d i n g a n d t e m p e r a t u r e c o n d i t i o n s was f o u n d in cyclic h a r d e n i n g at variable t e m p e r a t u r e s .
References [1] K. Ikegami and Y. Niitsu, Effect of creep prestrain on subsequent plastic deformation, Int. J. Plasticity 1 (1985) 331-345. [2] Y. Niitsu, K. Ikegami and E. Shiratori, Effect of prior creep deformation and temperature variations on the plastic deformation of SUS 304, Bull. Japan Soc. Mech. Engrs. 27 (1984) 1585-1591. [3] Y. Nittsu and K. Ikegami, Plastic and creep deformation of stainless steel SUS 304 under combined stress states at room temperature, Bull. J a p a n SOC. Mech. Engrs. 27 (1984) 2332-2338.
[4] Y. Niitsu and K. Ikegami, Plastic and creep deformation of stainless steel SUS 304 under combined stress states at 600 C, Trans. Japan Soc. Mech. Engrs. Ser. A, 50 (1984) 996-1002. [5] K. Ikegami and Y. Niitsu, Experimental evaluation of the interaction effect between plastic and creep deformation, Engrg. Fracture Mech. 21 (1985) 897-907. [6] Y. Niitsu and K. Ikegami, Plastic behavior of SUS 304 subsequent to creep prestrain at various temperatures, Bull. Japan Soc. Mech. Engrs. 28 (1985) 1853-1858. [7] Y. Niitsu and K. Ikegami, Effect of temperature variation on plastic behavior of SUS 304 stainless steel, Bull. Japan Soc. Mech. Engrs. 28 (1985) 2853-2858. [8] Y. Niitsu, D. Tsuji and K. Ikegami, Cross effect of SUS 304 under combined axial and torsional stress state, Trans. Japan Soc. Mech. Engrs. Set. A52 (1986) 486-492. [9] Y. Niitsu and K. Ikegarni, Effect of temperature variation on cyclic elastic-plastic behavior of SUS 304 stainless steel, Trans. Japan Soc. Mech. Engrs. Ser. A52 (1986) 1621-1627.
355
EFFECTS OF COMPLEX LOADINGS ON PLASTIC DEFORMATION ( S U S 304) A T H I G H T E M P E R A T U R E
OF STAINLESS STEEL
K o z o I K E G A M I a n d Yasushi N I I T S U
Research Laboratory of Precision Machinery and Electronics, Tokyo Institute of Technology, Nagatsuta, Midoriku, Yokohama, Japan Received October 1987
The plastic deformation for complex ioadings are experimentally investigated under various high temperature conditions. The experiments are conducted by subjecting thin wall tubular specimens to combined axial load and torsion. The stress-strain curves after plastic prestraining are obtained by subsequent loading along the stress path with corners. The subsequent loadings are given at a different temperature from that of the prestrained temperature. The effects of plastic prestraining as well as temperature history on the stress-strain curves are examined under variable temperature conditions. The stress-strain curves after creep straining are determined by subsequent loading at constant temperature. The effects of creep strain on plastic hardening are observed by comparison with the stress-strain curves without creep straining. The stress-strain curves for cyclic loading are obtained under various temperature conditions. The cyclic loadings are performed between fixed strain limits. The effects of cyclic loadings on the saturation properties of cyclic hardening are examined at constant and variable temperatures.
1. Introduction The structural components used at high temperature are subjected to the severe condition of combining complex loading and temperature history. For the strength design of such components, it is neccessary to investigate the deformation behavior of materials used at high temperature. The high temperature deformation is correlated with loading conditions and temperature state in a complicated manner. Experimental investigations on high temperature deformation have been reported by several researchers. The results are summarized by the authors [1]. Extensive and systematic experiments are neccessary to understand high temperature deformation of metals. The authors [1-9] continue experimental work on plastic deformation at high temperature and report the results in the papers listed in the reference. This paper presents more characteristic properties of the deformation of stainless steel at high temperature on the basis of the authors' experimental results.
2. Experimental methods The experiments were conducted by subjecting thinwalled tubular specimens to combined axial load
and torsion by a combined stress testing machine. The specimen was heated by a high-frequency induction heating apparatus. The testing temperature ranged from room temperature to 600°C. The temperature of the specimen was measured by three P - P R thermocouples. Two lever-type measuring devices were used to obtain the axial and torsional strains of the specimen. The loading conditions were controlled with equivalent values of true stress at 0.653 M P a / s on the loading path. The detailed experimental method is described in a previous paper [1].
3. Experimental results and discussions
3.1. Effect of complex loading Fig. 1 shows complex loading paths with comers. A specimen was loaded to a certain magnitude of prestraining (about 3%) by tension or torsion. Then the loading direction was changed with 0o = 135°C from the initial loading points. The experimental stress-strain curves were uniquely represented by the equivalent form as shown in fig. 2. The notations I ol and p are the equivalent stress and strain components. The testing temperature is 200 o C. The flow stresses after the change
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356
K. lkegami, Y. Niitsu / Effect of complex loadings R.T. p~
~I
400
MPa
: 3.0% ,
~ A / O
0.3%
o --
0.1%
\x
/ ,i i [iI -300
o.
1.0%
~ - -
\
iIi ~
Fig. 1. Stress paths with a comer.
300
z
H
-200
-100
0
100
200
O
300 MPa
200"C o& ° ~ o ~ 400°C
~.~ 100
T e n s i o n --. T o r s i o n
Lx
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0
MPa
~
o
-.-
2 5 0 T- " ~ " £
stress I 2
strain
curve
i 3
t 4
p
I 5
%
Fig. 2. Stress-strain curves for the stress path with a comer. -200
-100
0
100
200 O
of loading direction become higher than the stress-strain curve for monotonic loading. It seems that latent hardening is produced by the loading process with changing direction. Fig. 3 shows subsequent loading paths after tensile prestraining. The specimens were loaded to 3% of tensile plastic strain and then reloaded in different directions. The testing temperatures are 27 (room temperature), 200, 400 and 600°C. The subsequent plastic behavior at room temperature and 400°C are represented in the tensile and shear stress planes shown in fig. 4. The points in the figure are the stress points corresponding to the defined values of equivalent plastic strain in
#"3T 1135°
115°
0or
Fig. 4. Equi-plastic strain surfaces subsequent to tensile prestraining.
subsequent loading from the prestressed point. Curves connecting stress points with the same subsequent plastic strain values are defined as equi-plastic strain surfaces by the authors [5]. The surfaces are formulated by the following equations.
(o- o,)~ t+~ sgn(°-o.)
18 OI
oP--~ ^ . , r l = .~.u /o
O
Fig. 3. Stress paths subsequent to tensile prestraining.
+
3"r2
1 =0'
(°~-o~)
= {(o~- .,)~ + (o, + o~- o~)~}/2 = { ( ° ~ - ° , ) ~ - (°. + o~- o~)~}/2 sgn(x)=
158 °
MPa
1 0 -1
(1)
x>O x=0 x<0.
The one surface clztermined by eq. (1) is schematically illustrated in fig. 5. The curves of broken line are part of a circle with radius oF, where the notation ar is the flow stress in uniaxial tension. This circle is the
357
K. lkegami, Y. Niitsu / Effect of complex loadings
aC.
O
/:
Fig. 5. Schematic figure of the equi-plastic strain surface.
reference used to define the notations o B, oc and o, in eq. (1). The notation o B is a decrease of the flow stress in the opposite direction to the preloading, oc a decrease of the flow in the perpendicular direction to the preloading and o, a shift of the center of the curve. These values are correlated with the plastic strains oP, p~' and the temperature T by the following equations. O F = Oy +
OB
no a
= OBO + A O B
I
oB0 = o 1 ( - 1.12 × 1 0 - 4 T + 0.113) × ( 1 - exp( - 0.39Plp) }
g = 5.31 + (1 - 9.85 × 1 0 - a T )
,,
× { - 2.26 + 2.37 exp( - 0 . 6 1 0 ( ) } o
p 1/2
oB(600 C ) = O l { 1 . 6 1 e x p [ - 6 . 1 8 ( P 2 )
(2)
/
]
× + 0.0711} O c = 0 . 4 9 9 o B exp[-2.1(PEP) 1/2] - o h p
o. = 0.499o n e x p [ - 0 . 8 0 2 ( p 2 )
1/2
/
],
where o I = o F ( p = p[')
27 < T_< 4 0 0 ( ° C )
(3)
and o h (RT, 3%)' = 26 MPa
state which are determined by proportional loadings. By comparing the equi-plastic strain surfaces of the subsequent state with those of the initial state, the expansion and translation of the surfaces by preloading was observed. The hardening in the transverse direction to preloading is remarkable. It seems that latent hardening is produced in this direction. The arrows in the curves are the directions of the plastic strain vectors at the stress points. The directions are normal to the curves. The plastic strain can be calculated by applying the flow rule to the equi-plastic strain surfaces. Fig. 6 shows the equivalent stress and plastic strain relations for the subsequent loading in fig. 3. The curves in the figure are calculated by using the equi-plastic strain surfaces. The flow stresses in the directions of 135 ° and 115 ° are larger than the flow stress in monotonic tensile loading. The ratio of hardening rate to flow stress becomes a maximum at 400 o C. 3.2. Effect o f temperature history
The tensile loading test was conducted under the condition of changing temperature in the range of room temperature to 600°C. The loading and temperature conditions are shown in fig. 7. The testing temperature was changed at the rate of about 2 . 0 ° C / s in a partial unloaded state and held before loading for 5 min. Fig. 8 shows the tensile stress-strain relation obtained. The marks are the experimental results and the chain curves are the tensile stress-strain curves under constant temperatures. The strain is indicated by the plastic strain minus thermal strain. The stress-strain under variable temperatures coincides with that under constant temperature. The flow stress does not depend on the temperature history but depends on the accumulated plastic strain for monotonic loading. The compressive loading tests subsequent to tensile loading were conducted at variable temperatures. Fig. 9 shows Bauschinger curves at 600 ° C and room temperature after tensile prestraining at various temperatures. The full curves are Bauschinger curves under constant temperature. Bauschinger curves at 6 0 0 ° C seem to be
]
o h (200°C, 3%) = 18 MPa
oh(400°C, 3%) = 20 MPa /
(4)
oh(600°C, 3%) = 12 M P a . ] The parameters in o F are given in table 1. The full curves in fig. 4 are the subsequent equiplastic strain surfaces calculated by eq. (1). The broken line curves are the equi-plastic strain surfaces for the initial
Table 1 Material constants for the stress-strain curves Temp. (°C)
oy (MPa)
H (MPa)
a
27 o 200 ° 400 o 600 °
189.8 112.8 93.3 72.1
48.7 34.9 36.5 37.1
0.69 0.80 0.78 0.76
K. lkegami, Y. Niitsu / Effect of complex loadings
358
200"C 27"C
~
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%
of
Fig. 6. Equivalent stress-strain curves subsequent to tensile prestraining.
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~
,#
~ I,~' i i
400
300
time
0ooi~ I~!-~ ~ 7,1/
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e
Fig. 7. Loading program under variable temperatures.
100 ~
~ -~o R.T. o o 600 "C I
1
independent of the prestraining temperature as seen in fig. 9(a). But the curves at room temperature in fig. 9(b) are affected by the prestraining temperature. The plastic behavior subsequent to tensile prestrain was investigated for variable temperatures. The loading conditions are shown in fig. 10. The tensile loading was given at room temperature or 6 0 0 ° C and then the
t
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3
£ 4005C
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7
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Fig. 8. Stress-strain curves under variable temperatures. temperature of the specimen was changed to 6 0 0 ° C or room temperature. Various directions were used for the subsequent combined loading; that is 0 o = 0 °, 90 °, 135 °, 158 ° and 180 °. The equi-plastic strain surfaces
K. lkegami, Y. Niitsu / Effect of complex loadings
600°C ' 600°C 400°C • --> & 600°C
R.T. --
300
@
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•
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~3- T f~--]-300~
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(a)
~
'
o~
Cb)
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//
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-200
-100
o
--
0.05
•
--
0.2
\
x
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, 100
%
x \\\
0
P~P
200
300
0
Fig. 10. Stress paths with temperature variations. for the subsequent plastic strain of 0.05%, 0.2% and 1.0% are represented with the full-time curves in fig. 11. The curves are the results calculated using eq. (1). The experimental stress points in the equi-plastic strain surfaces at 600 °C agree with the calculated curves. But the discrepancy between calculated and experimental results at room temperature becomes large in the opposite direction to prestraining. The broken-line curves are the equi-plastic strain surfaces at 600°C in fig. 11(a) and at room temperature in fig. 11(b), respectively. The equi-plastic strain surfaces determined at 600°C subsequent to prestraining at room temperature contracts with the retreat of the surfaces at room temperature. But the surfaces determined at room temperature subse-
(a)
Equi-plastic
strain surfaces
3,0% Pre-strain at 600°C T ~-~-300
/ / -300
-200
/
-100
MPa at 600°C
Exp. o • ~
Cal. P~ % - - 0.05 --0.2 -1
/ 0
100
200 O
300 MPa
(b) Equi-plastic Strain Surfaces at R.T,
F i g . 11. Equi-plastic strain surfaces subsequent to tensile pre-
straining at different temperature.
K. Ikegami, Y. Niitsu / Effect of complex loadings
360
Exp.
3.0% P r e - s t r a i n
Cal.
o ~, c~
°
o° 90° 135° 158° 180°
.. ..... ......
,L
3
0
R,T.
Oc~
0
~
t~
300
12 h ours ~ : ~ 3 ¢ - ~ 1 2 h o u ~ J . . ~
Q-
...... 7 h
200
l~
400"C
~, ~.o_ -o- -~.--~ --~':
-
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100 ~
14 h
600°C
olOI =0 • IOI = ' ~ T
_ ,50
+," . . .
200 '- , , ' y
0
---1"
2
3
4
5
P %
Fig. 13. Equivalent stress-strain curves including creep strain.
,5OI R.T. -* 6OO°C
o
0.5
(a)
1 et]
o
(b)
0.5 P2P %
Fig. 12. Equivalent stress-strain curves subsequent to tensile prestraining.
quent to prestraining at 600°C expands with the translation of the surfaces at 600 o C. Fig. 12 shows the equivalent stress-strain relations for the subsequent loading of fig. 10. The curves are calculated by applying the flow rule to the equi-plastic strain surfaces of eq. (1) on the assumption of neglecting temperature history. The calculated results at 600 ° C coincide with the experimental results. In the results at room temperature, the calculated curve does not fit the experimental result in the opposite side to the prestraining direction. This means that the effect of temperature history is remarkable for the Bauschinger curves for falling temperature.
3.3. Effect ofcreep strain The monotonic loading tests including creep straining were conducted by tensile or torsional test at room temperature, 400°C and 600°C. The equivalent stress and inelastic strain curves are shown in fig. 13. The full, broken and chain curves are the stress and plastic strain relations under constant temperature. The holding time for creep straining and its magnitude are indicated by the broken lines in the figure. At room temperature, the plastic strain subsequent to creep prestraining was not produced until the increasing stress approached the full curve. After the stress reached the full curve, the plastic strain was produced again and the flow stress coincided with the full curves. This tendency is observed both in
tensile and torsional loading tests. This means that creep strain has the same hardening effect as plastic strain at room temperature. In the results at 600°C, a similar tendency of hardening by creep strain is observed, but the magnitude is small compared with that produced by plastic strain. The creep strain produced at 400°C was small in magnitude and the hardening effect was not confilTned. The compressive tests were conducted at room temperature and 600°C after tensile plastic strain and creep strain. The stress-strain curves are shown in fig. 14. Two Bauschinger curves are illustrated in fig. 14(a) for tensile strains of 0.12% and 1.4% at room temperature and in fig. 14(b) for the tensile strains of 2.6% and 3.8% at 600°C. The Bauschinger curve at room temperature subsequent to both plastic strain of 0.1% and creep strain of 1.0% is indicated by circles in fig. 14(a). Those results fit the Bauschinger curve after tensile plastic strain of 1.4%. A similar comparison between the Bauschinger curves at 600°C with and without creep strain is illustrated in fig. 14(b). The flow stress of the Bauschinger curve subsequent to both plastic strain of 2.6% and creep strain of 1.2% is slightly higher than the curve for plastic strain of 3.8%. This means that the effect of creep strain on the Bauschinger's curve is
m
R,T.
o~---~ 100~
eP %
-100~
/%
-200L Fig. 14. Bauschinger curves including creep strain.
K. Ikegami, Y. Niitsu / Effect of complex loadings
Fig. 15. Stress paths with creep straining.
almost the same as plastic strain at room temperature, but the effect becomes weak at high temperature. The subsequent combined loading tests were conducted after creep straining under constant temperature. The stress paths used in the experiments are shown in fig. 15. The specimens wcrc loaded into the plastic range by tension and the stress on the specimens was held at 250 MPa for about 6 h at room temperature or at 154 MPa for about 24 h. With those preloading processes, the plastic and creep prestrains (p~' and p~) were given to the specimens. The values of plastic and creep strains were 1.4% and 1.6% at room temperature, and 2.6% and 1.2% at high temperature, respectively.
The specimens were subsequently loaded at in various angles 8o different from the prestress points. The loading directions 0o were chosen to be 0 °, 90 °, 135 °, 158 ° and 180 ° . The plastic behavior subsequent to plastic and creep prestraining is compared with the equiplastic strain surfaces in fig. 16. The full time curves are the surfaces calculated by using eq. (1) on the assumption of neglecting the hardening effect of creep strain. The broken line curves are the results of including the hardening by creep strain on the assumption of equivalent hardening effect between plastic and creep deformation. At room temperature, the subsequent stress points coincide with the broken line curves. The hardening effect of creep strain is nearly equal to that of plastic strain in combined stress state. The experimental stress points at 600°C are close to the broken curves or between the broken and full curves. The hardening
R.T Cal. --
Pl : t . 4 %
....
R.T
Exp.
Cal. p, :t.4%
--
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.....
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pC : 1 . 6 %
.
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0
0.5
1
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%
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MPa
600°C --
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....
p , :&8%
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flastic strain/%/'~
1
%
o
OH : 154MPa RP : 2.6% pC : 1.2%
- 200
eo:O-
" 0 4%
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',
%
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,
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,,:=04%
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~
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13
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•
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•
:180~
0.5
o.s%
too\
[ -200
;1 -100
1 o
(b)
lOO
200 (3
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Fig. 16. Equi-plastic strain surfaces subsequent to plastic and creep straining.
-0.5
0 Subsequent
0.5
1
axial plastic strain %
(b)
Fig. 17. Plastic strain trajectories subsequent to plastic and creep straining.
K. lkegamL Y. Niitsu / Effect of complex loadings
362
+
I:LT. ~
.
1.0%~
~
_;
Fig. 18. Cyclic stress-strain curves under constant temperature.
effect due to creep strain at high temperature is slightly weaker than hardening by plastic strain. By comparing two curves illustrated by the full and broken lines in fig. 16, it is found that the hardening mode by creep strain at room temperature is similar to kinematic hardening and, at high temperature, the mode resembles isotropic hardening. Fig. 17 is the comparison of the strain trajectories corresponding to the results of fig. 15. The full and broken lines are the trajectories calculated by applying the flow rule to the equi-plastic strain surfaces. The results indicated with the full and broken lines are respectively obtained on the assumption of neglecting and including the hardening effect by creep strain in the above-mentioned way. The experimental trajectories both at room temperature and 600°C are close to the results of the broken line. The plastic hardening is produced by creep strain.
3.4. Effect of cycfic loading The stress-strain curves in cyclic loading by tension and compression were obtained under various temperature conditions. The cyclic loading was performed between fixed strain amplitude. Fig. 18 shows the cyclic stress-strain curves under a strain amplitude of 1.0% for 20 cycles at room temperature and for 30 cycles at 600°C. The maximum tensile stress in cyclic stress-
strain curves at room temperature varies from 230 MPa in the initial cycle to 295 MPa in 20 cycles. The flow stress at room temperature exhibits an increase of 30% with cyclic loading. In the cyclic stress-strain curves at 600°C, the flow stress increases by 150% during 20 cycles. The hardening properties in cyclic loading depend strongly on the temperature state. Fig. 19 shows the cyclic hardening behavior during 20 cycles with a strain amplitude of 1.0% under the condition of changing temperature between room temperature and 200°C or between room temperature and 600 o C. The sequence of testing temperature is the cyclic change of room temperature and high temperature. In the cyclic test between room temperature and 200°C, the maximum flow stress is about 300 MPa in the second and third cyclic loading at room temperature. The value is equal to the maximum flow stress in the initial cyclic loading. But the maximum flow stress of cyclic loading between room temperature and 600°C becomes 400 MPa in the second and third cyclic loading at room temperature. The effect of temperature history is observed on the saturation properties of cyclic hardening. Fig. 20 shows the variation of the maximum stress in cyclic loading at different temperature conditions. The notations o(~) and o(~) are the maximum stresses in tension and compression, respectively. In the tests between room temperature and 200°C of fig. 20(a), the maximum stress after the second cyclic loading is nearly constant. In fig. 20(b), the maximum stresses at room temperature and 600°C are varied by cyclic loading. The increase of the maximum stress in the first cyclic loading is remarkable at 600°C. The maximum stress increases also in the second and third cyclic loadings. But, in the cyclic loading at room temperature, the maximum stress decreases during cyclic loading, though the initial maximum stress in each cyclic loading process increases compared with the final maximum stress in the previous cyclic loading at room temperature. The results of fig. 20(c) shows a similar tendency to fig. 18(b). The variation of the maximum stress of fig. 20(d) is different from the results of figs. 18(a) to (c). The softening by decrease of the maximum stress is not observed and the cyclic hardening is produced in each cyclic loading process at both 400°C and 600°C.
4. Conclusions
The plastic deformation of 304 stainless steel was experimentally investigated at high temperature by subjecting thin-walled tubular specimens to combined axial
363
K. Ikegami, Y. Niitsu / Effect of complex loadings
.....
~ - 7 - - - T - - 7 - - - r ,
'
R.T.;
i
......
:
y--.
200C
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o
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,
. . . . . . . .
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;
.
.
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.
.
.
. . . . . . . R~T. p
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2
0
o
0C
LL
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~
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--]
. . . . .
-]
F
-
. . . .
i---TI Tf?Fig. 19. Cyclic stress-strain curves under variable temperatures.
load and torsion. The effect of plastic prestraining, temperature history, creep prestraining and cyclic loading was examined on the equivalent stress-strain curves and the equi-plastic strain surfaces under various loadhag conditions. The equi-plastic strain surfaces were defined by the loci of stress points with the equivalent plastic strain hardening magnitude under combined stress state. The obtained results are summarized as follows. (1) The plastic hardening is remarkable in the transverse direction to prestraining. The hardening behavior
is represented by the egg-shaped equi-plastic strain surfaces. (2) The effect of temperature history on flow stress was small for monotonic loading, but the effect was observed in the stress-strain relations in reverse loading. (3) The creep strain had the same hardening effect as the plastic strain at room temperature. But the effect of creep strain on plastic hardening was weak at high temperature compared with that of hardening by plastic strain.
K. lkegami, Y. Niitsu / Effect of complex loadings
364 400
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,~
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bE = 1.0%
120
80
. . . . .
240
400
,
r
l
iI~600o C
600"C
1001
,~ 300
~
I
1
40
I
60
600"C
600"C 100
•
r
*'"
~1~ 2 0 0
600 C
AE=I.0%
20
d
400"C
400"C
,oo'o
L
200 N
b
#. =E
+ ;¢ 300
0
160 cycle
,~ 4eel
2001
120
N
600 °C &E: 1.0%
z
80 cycle
I
I
100
120
N
210
410
8~0
60 cycle
i 1oo N
12o
Fig. 20. Maximum cyclic stress under variable temperatures.
(4) T h e cyclic h a r d e n i n g was m o r e r e m a r k a b l e at high t e m p e r a t u r e t h a n at r o o m t e m p e r a t u r e . T h e coup l e d effect b e t w e e n l o a d i n g a n d t e m p e r a t u r e c o n d i t i o n s was f o u n d in cyclic h a r d e n i n g at variable t e m p e r a t u r e s .
References [1] K. Ikegami and Y. Niitsu, Effect of creep prestrain on subsequent plastic deformation, Int. J. Plasticity 1 (1985) 331-345. [2] Y. Niitsu, K. Ikegami and E. Shiratori, Effect of prior creep deformation and temperature variations on the plastic deformation of SUS 304, Bull. Japan Soc. Mech. Engrs. 27 (1984) 1585-1591. [3] Y. Nittsu and K. Ikegami, Plastic and creep deformation of stainless steel SUS 304 under combined stress states at room temperature, Bull. J a p a n SOC. Mech. Engrs. 27 (1984) 2332-2338.
[4] Y. Niitsu and K. Ikegami, Plastic and creep deformation of stainless steel SUS 304 under combined stress states at 600 C, Trans. Japan Soc. Mech. Engrs. Ser. A, 50 (1984) 996-1002. [5] K. Ikegami and Y. Niitsu, Experimental evaluation of the interaction effect between plastic and creep deformation, Engrg. Fracture Mech. 21 (1985) 897-907. [6] Y. Niitsu and K. Ikegami, Plastic behavior of SUS 304 subsequent to creep prestrain at various temperatures, Bull. Japan Soc. Mech. Engrs. 28 (1985) 1853-1858. [7] Y. Niitsu and K. Ikegami, Effect of temperature variation on plastic behavior of SUS 304 stainless steel, Bull. Japan Soc. Mech. Engrs. 28 (1985) 2853-2858. [8] Y. Niitsu, D. Tsuji and K. Ikegami, Cross effect of SUS 304 under combined axial and torsional stress state, Trans. Japan Soc. Mech. Engrs. Set. A52 (1986) 486-492. [9] Y. Niitsu and K. Ikegarni, Effect of temperature variation on cyclic elastic-plastic behavior of SUS 304 stainless steel, Trans. Japan Soc. Mech. Engrs. Ser. A52 (1986) 1621-1627.