Fatigue Crack Thresholds Significantly Affected by
Thermo-Mechanical Loading Histories in An
Austenitic and A Ferritic Low alloy Steel
M. Okazaki1, a, M. Muzvidziwa1,b R. Iwasaki1,c
and N. KASAHARA2,d
1Nagaoka
University of Technology, Nagaoka, JAPAN
2*The University of Tokyo, Hongo, Tokyo, JAPAN
ACKNOWLEDGEMENT:
A part of this work was conducted as one of Nuclear Regulatory Agency programs
in Japan. The author (M.Okazaki) expresses his special gratitude to the finalfical
support by the Grant-in-Aid A by JSPS (#25249003).
High cycle thermal
fatigue loadings
resulting from Start-up and Shut-down
Thermal Stress
induced by fluid temperature change
Fluid
Temperature
Low-Cycle &
Thermo-Mechanical
Fatigue Loadings
Time
The rmal
Fatigue
Time
Hot Fluid
ã«èä ìI Ç»î¬ åÝì‡ â
ìx ï™ïz Ç…
ÇÊÇË
îMâû
óÕÇ™
î° êŽ
Cold Fluid
Mixing hot/cold fluids
Tradition criterion:
D ≅1
“High Cycle Thermal Fatigue Failure”
JSME Guideline, S017 (2003)
Hot Fluid
板厚内と面内の温
度分布により熱応
力が発
生
ni
UF = ∑ ( ) ≤ D
Ni
i
Hot Spot
Cold Fluid
Hot spot
Q1:Is the UF concept applicable
under complicated loading sequences,
which involve LCF and HCF loadings ?
“High Cycle Thermal
Fatigue Failure”
Time
Time
Strain
HCF
Time
Strain
Strain
Strain
LCF
Time
JSME Guideline,
S017 (2003)
Tradition criterion
Time
Strain
Strain
UF = ∑(
i
NL
Time
ni
)≤ D
Ni
D≅1
Q2: what is(are) the effects of
Post severe earthquake damage recovery process;
on the high cycle thermal fatigue failure ?
by, e.g., heat treatment for recovery & weld repair…..
Steady
Steady
Earthquake
High cycle
NH
NH
ΔεH, NH, RH=0L
●
Time
NH /NL
stress
stress
ΔεH, NH, RH=0L
Time
NH /NL
ΔεL, NL,
RL≠0
NL
Flow of talk
Validity of UF for fatigue rupture life
under combined loading history.
？
DH
ɢɖ N R ÅÇ0
L, L, L
ɢɖ
L,
ds /dt
L
R
É–L
T
max
T
min
Strain
Fatigue crack propagation
depending on
loading history.
N :N
H L
Time
ɢɦ
H,
dɦ /dt
H
DL
R
T
T
Phase angle=0
ɦH
max miÅD
ÅD
？
Fatigue crack propagation behavior
depending on
*thermo-mechanical history
da/dN
∆K
Discussions on assessment based on crack growth.
Materials
SUS316:
Sol.
C
0.07
Si
0.9
SCM 440
(JIS):
AQ+tem.
R.T.
300
500
Mn
1.85
E(GPa)
215
195
156
P
0.045
static
0.2 % proof (MPa)
850
703
553
SUS316(cyclic hardening)
S
0.03
Ni
12.1
Cr
17.7
(Wt.%)
Mo
2,31
cyclic
0.2 % proof (MPa)
709
685
495
SCM 440(cyclic softening)
Strain
ΔεH, NH, RH=0L
Strain
NH
HCF
LCF
ΔεL, NL, RL=0
Loading sequence 3 focused on.
2 stage, 2 blocks
Loading sequence 1 focused on.
Loading sequence 2 focused on.
HCF
NL
Strain
Strain
LCF
ΔεH, NH, RH=0L
NH
NH /NL
NH /NL
2 stage, Multi-blocks
ΔεL, NL, RL=0
2 stage, Multi-blocks
Experimental variables.
* N LCF:N HCF.
* Loading sequences.
R15
Φ8
24
115
(a) Smooth specimen
Lower than σw,o
ΔσL,NL,RL≠0
ΔσL, dsL/dt
RσL Tmax Tmin
Strain
NH:NL
Time
ΔεH, dεH/dt RεH Tmax Tm． Phase ．
i angle=0
Notices in high cycle fatigue loading conditions
superimposed on low cycle TMF loading.
LCF:in-phase type of TMF loading (50−300℃, 1/10 cpm)
+
HCF・High cycle fatigue loading (300℃, σa=100 MPa)
・NH/NL: experimental variable
・Stress amplitude of HCF lower than fatigue limit
Loading sequence 1 focused on.
LCF 300℃
Loading sequence 2 focused on.
HCF
Strain
Strain
NL
ΔεH, NH, RH=0L
NH
NH /NL
NH /NL
R.T.〜300℃
ΔεL, NL, RL=0
ΔεH, NH, RH=0L
Strain
NH
ΔεL, NL,
R =0
Loading sequenceL 3 focused on.
DH+DL =1
Loading sequence 2 focused on.
Sequence 2&3
▲
▲
◆
Strain
Damage fraction by high cycle loading,DL
Fatigue lives under multi-stages block loadings.
NL
ΔεH, NH, RH=0L
N
H
DH+DL=1
NH /NL
◆▲
▲
◆
Sequence 1
Damage fraction by TMF cycles, DH
Alternative assessment criterion
Should be introduced !
ΔεL, NL, RL=0
Loading sequence 1
Investigation of crack behavior:
-in order to explore an alternative criterion.
R15
Φ8
Φ14
24
115
(a) Smooth specimen
Initial notch:
Depth: 50 µm
Diameter:100 µm
(b) Notch at the gage center
ΔσL,NL,RL≠0
ΔσL,
dsL/dt
RσL
Tmax Tmin
Strain
Experimental variable:
NH: NL
N :N
H L
Time
ΔεH, dεH/dt
RεH
Tmax Tmi． Phase angle=0
．
Approach based on crack behavior:
Notch
NL : NH = 1：200
（2400 block）
Crack length (µm)
ひずみ
NL : NH
µm
100 _m
Pure LCF
*Accelerated crack growth
rates, after a> acr
Strain
acr
NL NH
Time
Number of loading blocks
→ Resulting in Failure of applicability of Miner rule
Even when ∆σL < ∆σwo ,
The TMF/HCF interaction was significant in the crack growth process
after a > acr
specimen
with an initial notch
Strain
Time
Smooth specimen
NL：NH = 1：200
Fractograph
b=100
µm
b = 100 _m
b=200
µm
b = 200 _m
b=300
µm
b = 300 _m
O
b (μm)
Rupture
surface
bb=400
= 400 _mµm
bb=500
= 500 _mµm
b=600
µm
b = 600 _m
b：depth
Beach marks on the
rupture surface
b=700
µm
b = 700 _m
b=800
µm
b = 800 _m
b=900
µm
b = 900 _m
14
Key point: how to estimate acr ?
How to make use of these findings for life prediction ?
Key Point: Prediction of a critical crack length, acr,
above
which an interaction between high-cycle and low cycle loadings get
significant.
a [μm]
nL: nH=1:10
Thermo-mechanical fatigue cycle period.
∆εL=1.0%
1500
Stress
Crack length
1:0
1000
High cycle
fatigue
cycle
period
acr
500
∆σH=200
MPa
0
0
2000
4000
6000
N [block]
Assumption:
F
Strain
L(š acr)1/2
HCF loading level
ÅÜ Kth
Crack length nucleated by LCF cycles
A more reasonable and realistic method for remaining life
: based on crack propagation.
ΔεH=1.0 %, ΔσL=200 MPa
a [μm]
1500
1000
500
acr
0
0
2000 4000 6000
Q2: what is(are) the effects of
Post severe earthquake damage recovery process;
on the high cycle thermal fatigue failure ?
by, e.g., heat treatment for recovery & weld repair…..
NH
NH
ΔεH, NH, RH=0L
●
Time
stress
stress
ΔεH, NH, RH=0L
Time
NH /NL
NH /NL
High cycle
High cycle
Earthquake
Low cycle
ΔεL, NL,
RL≠0
NL
Low cycle
Q: How should we manage ?
Preparation for Thermo-mechanical history material
Introduction of
fatigue crack
Reheat treatment
at below Ac1
Fatigue crack
Growth test
?
Length=45
Initial EDM notch
t=2
(b)
Width=14
Virgin material
Thermal history
material
Thermomechanical history
material
Specimen
preparation
Thermal history*
Fatigue crack
propagation test
by virgin material
Fatigue crack
propagation
test
Fatigue crack
propagation test
Thermal history*
Fatigue crack
propagation test
*below Ac1 temp:740℃x10 min.FC in vac.
Φ14 +0.10
0.00
// 2.5 B
2
Φ1
A scale 2 : 1
(52)
20
B
A
135
Experimental variable
No.
1
2
3
4
5
1
3
4
Specimen type
Temperture
[℃ ]
Load ratio
Frequency
[Hz]
300
-1
0.2
0.5
0.8
-1
-1
0.5
0.8
10
Virgin
material
無履歴材
Thermal
history
熱履歴材
Thermo-mechanical
熱機械的負荷履歴材
history
Crack growth rate, da/dN (m/cycle)
-7
1.E
10-07
Virgin
無履歴材
Thermal history
熱履歴材
Thermo-mechanical
熱機械的負荷履歴材
history
-8
1.E
10-08
R=-1
-9
1.E
10-09
-10
1.E
10-10
1.E-11
-11
10
10
30
20
Stress intensity factor range, _ K[MPaﾃm]
?
Crack growth rate, da/dN (m/cycle)
Higher
ratio = 0.5, 0.8
R=0.5,R0.8
-7
10-07
1.E
Black: Virgin
Black : Bare
Red:
Thermo-mechanical
Red:
Trans History history
-8
1.E10-08
R=0.8
R=0.5
-9
10-09
1.E
-10
10-10
1.E
10-11
1.E -11
11
_Kth
10
10
1 Stress intensity factor range _ K[MPaΓm]
Stress
intensity factor range, ∆K (MPa1/2)
18
1/2
∆Kth
(MPam
)
Threshold
stress
intensity factor,
ΔK th, ΔK th,eff [MPa√m]
１Cr-Mo-V 490℃
16
A470 Class8 149℃
14
熱機械的負荷履歴材
A470 Class8 RT.
12
2.25Cr-Mo RT
10
SA387 RT
Present work
500℃
300℃
● Virgin
無履歴材 無履歴材
■ Thermal
熱履歴材
▲ Thermo-mechanical
本研究データ
8
6
Data band of
4
∆K eff,th
2
Data band of ΔKth,eff in steel
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
0
-1
R ratio
Stress ratio
Nishikawa,1987
Okazaki, 2005
1
1
Change in ferritic phase volume fraction in
the thermal and themo-mechanical history materials..
Thermal history
Thermo-mechanical
Thermal history
Thermo-mechanical
Near crack wake
Apart from crack wake
Virgin
24
Change in ferritic phase volume fraction in
the thermal and themo-mechanical history materials..
~4%
66
初期組織
64
熱履歴(左)
負荷⇒熱履歴(左)
き裂から十分離れた位置10点平均
62
□
組織観察領域：25×25[μm]
observed
area
60
ΔKth(無履歴材)
25
~8%
58
□
56
54
52
50
ΔKth(熱機械的負荷履歴材)
□
切欠き
負荷⇒熱
履歴領域
Original
Ferritic volume fraction, Vf[%]
熱機械的負荷履歴材組織
熱履歴材組織
熱履歴
熱履歴(右)
負荷⇒熱履歴(右)
1
き裂から十分
Apart
from
離れた位置
crack
face
熱履歴
Thermally
領域
affected
zone
負荷⇒熱履歴
Thermo領域
mechanically
affected
熱履歴
領域
Thermally
Thermo- 熱履歴時affected
mechani-き裂先端zone
cally
affected
zone
thermomechanical
treatment.
66
初期組織
Ferritic volume fraction, Vf[%]
熱機械的負荷履歴材組織
64
熱履歴(左)
負荷⇒熱履歴(左)
熱履歴材組織
熱履歴
熱履歴(右)
負荷⇒熱履歴(右)
~4%
62
60
58
~8%
56
54
52
50
1
き裂から十分
Apart
離れた位置
from
crack
face
熱履歴
Thermall
領域
y
affected
zone
負荷⇒熱履歴
Thermo領域
mechanic
-ally
affected
Change in mechanical property by thermo-mechanical histrory.
740℃ for 10min
(a)Virgin
Vickers Hardness[Hv(5)]
400
As-recieved
350
300
250
740℃ for 10min
100Hv
800℃ for 10min
Thermal history:
By 740℃, 10 min.
200
初期組織：一様なベイナイト
150
100
50
316
210
142
0
27
Heat treatment
Virgin
(a)無履歴材試験後
Residual
stress in crack
圧縮残留応力場
wake
(塑性ウェイク)
Release of residual stress
残留応力場の消失
in crack wake
Thermal history
(b)無履歴材試験⇒熱履歴
Ideal crack
Disappeared crack closure
Thermo-mechanical
(c)無履歴材試験⇒熱履歴⇒
history
ΔKth(無履歴材)
Prior
crack tip before
(熱履歴時のき裂先端)
thermo-mechanical
treatment.
熱機械的負荷
履歴材試験
ΔKth(熱機械的負荷履歴材)
Residual stress
reproduced
Illustration showing how the crack wake is changed
by the present thermo-mechanical history.
Brief Summary
(1)Non-conservative assessment by Miner rule, depending on
thermo-mechanical loading histories.
(2) Experimental background was found to the item (1) in
crack growth process:
(2-1) An critical length, acr above which the LCF/HCF
are interacted singificantly.
(2-2) Fracture surface
(3) Fatigue crack threshold; depending on
thermal and thermo-mechanical loading history．
(4) Importance to get quantitative knowledge on ∆Keff,th.
R15
Φ8
Φ14
24
115
Initial notch:
Depth: 50 µm
Diameter:100 µm
(a)
Length=45
Initial EDM notch
Width=14
t=2
(b)
Fig.2 Geometry of specimens used. (a) SUS316 specimen with a surface notch,
(b) SCM 440 specimen with a through-thickness center notch.
Why？
n : n =1:10
Stress
ratio during HCF loading period,
LCF period
.
built-up
depending
on the prior LCF loadings.
∆ε =1.0%
L
H
L
Stress
HCF period.
Sequence 1
∆σH=200 MPa
LCF period.
Strain
Expectation: UF
can be available when the mean stress effect is considerd.
Traditional
criteria to
consider
the stress ratio
effect.
σm 2
Gerber： σ a = σ wo{1− ( σ ) }
B
σ
Goodman： σ a = σ wo{1− ( m )}
σB
σ
Sonderberg： σ a = σ wo{1− ( m )}
σY
Ex：
Life assessment based on a modified S-N curve
(mean stress modification)
Sonderberg modification
σm
σ a = σ wo{1− ( )}
σY
Sequence 1
HCF
LCF
Strain
DH
DH+DL =1
DL
NH /NL
Q3: what is(are) the effects of
* Thermal history during in-service period,
** Weld repair,
on the post high cycle thermal fatigue failure (∆Kth ) ?
SCM 440
(JIS):
Reheat treatment
as a repair process
by 740℃ x 10 min.
Fatigue crack
(~ Ac1)
propagation test
up to ∆Kth at 300℃
∆Kth at
300℃
???
ΔKth vs. R (SCM)
[4]
[3]
[6]
∆Keff,th
[3] P. K. Liaw, Acta metallurgica, Vol.33, No.8, pp1489-1502, 1985
[6] SURESH et al on fatigue crack propagation behavior pp57
[4]J.H.Bulloch，Theoretical and Applied Fracture Mechanics 23 (1995) pp89-101
Fatigue threshold depending on stress ratio
(low alloy steel)
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