Creep-fatigue life assessment of high-temperature weldments using the linear matching methodYevgen Gorash & Haofeng Chen
Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, [email protected] [email protected], http://www.thelmm.co.uk&
1. Theoretical Background and the Linear Matching Method
max�
min�
�
�
max�
min�
�
�
max�
min�
�
�
max�
min�
�
�
max�
min�
�
�
purelyelasticbehavior
elasticshakedown
max�
min�
�
�r& low-cycle fatigueeverse plasticity
ratchettingfollowed byincrementalcollapse
instantaneouscollapse
100
1
2
lim/P P
tm y/� � �
�
�
�
variable von Mises thermo - mechanical stress
yield stress taken as 0.2% plastic strain offset
constant component of applied mechanical load
limit load, the maximum load that a structure
can s
tm
y
lim
P
P
�
�
afely carry without instantaneous collapse
1.1 Bree diagram with responses to cyclic loading1
y�
�
�
1iE �
iE
2iE �
3iE �
3i� �
2i� �
1i� �
i�
1.2 Fundamentals of the Linear Matching Method2
• belongs to the group of modified elastic modulus methods;• has the character of a non-linear programming method;• with each step involves the solution of a linear problem;• each solution satisfies the condition of force equilibrium;• non-linear constitutive assumptions are imposed sequentially;• strain rate histories give rise to equilibrium residual stress fields;• solution is the minimum of a functional of the strain rate history;• generates inelastic solutions for the stabilized cyclic state;• compatible with standard finite element codes, e.g. ABAQUS.
• Life Assessment Methods and Design Codes – R5 Procedure, ASME N47 and RCC-MR(1980's – today) based on Neuber's Rule
• Conventional incremental (transient) FEA• Direct Cyclic Analysis (DCA) incorporated into ABAQUS• Direct Methods using Static or Kinematic Bounding Theorem (Koiter, 1960)
Alternatives to the LMM:
• Modified Modulus Method (MMM) for limit load analysis (Ponter, early 1990’s)• MMM modified for elastic shakedown analysis (Ponter & Carter, 1997)• MEM implemented as ABAQUS UMATs (Ponter & Engelhardt, 2000)• Linear Matching Method (LMM) implemented in ABAQUS for reverse plasticity
(global shakedown) & ratchet boundary evaluation (Ponter & Chen, 2001)• LMM further developed to evaluate R5 related parameters (Ponter & Chen, 2005)
Development of the LMM framework:
2. Testing & modelling of cruciform weldment
2.1 Experimental facility and specimen with typical failures3
620800
1500
Load points FurnanceWeld
Servo motor
Moving crosshead
Furnance
Deflectionmonitor
Load cell
Specimen
RollerBox
550 C°
1) fatigue failure at weld toe corresponding to1.0% of total strain range
2) fatigue failure remote from weldcorresponding to 0.4% of total strain range
Typical failure locations:
1
2
2.2 Dimensions (mm) of the cruciform weldment specimen3
2.3 Parameters of the FE-model
10
0
26
60°
72
200
3
3
3
26
3
592
R25
50
M
M
Temperature: 550 C°
P
parent material
heat-affected zone
weld metal
material without creep
totally elastic material
1) 977 CPE8R finite elements: 8-node biquadratic
plane strain quadrilaterals with reduced integration
2) 3 variants of dwell period - pure fatigue, 1 hour, 5 hours
3) 5 variants of reverse bending moment corresponding to
equal to 1.0%, 0.6%, 0.4%, 0.3% and 0.25% of total strain
M
εΔ
� � � �3200 26
Area Moment of Inertia: , 13...1312
X
X
M yI P y y
I
� � � �
X
Y
4. Creep-Fatigue Evaluation Procedure
4.1 Creep-fatigue evaluation procedure with time fraction rule4
�1
2
3
tot �
cr �
�
�
cr�
�
tota
l str
ain
range
number of cycles to failure
tot �
N �
Saturated hysteresis loop
S-N diagram forlow-cycle fatigue
f
1c
1
N ��
Fatigue damageaccumulated per
1 cycle:
stre
ss
time
� �1
0
1, ,
t
t Z dtt
�� � �
Stress relaxationbehaviour
t
1� Z
1�
2�
2�
stre
ss
time to rupture
t�Creep rupture
curve
cr
1c
t
t�
�
Creep damageaccumulated
1 cycle:per
fatig
ue d
am
age
creep damage
Creep-fatigueinteraction diagram
1
f�
cr�
1
f cr
f
f 1c
cr
cr 1c
1
N N
N
� � ��
�� �
� �
�
� �
� �
� �
1
2
3
5
4
4.2 FEA/LMM results corresponding to Δ = 1% and Δ = 5hε ttot
01.287e-032.617e-033.947e-035.277e-036.607e-037.937e-039.268e-031.060e-021.193e-021.326e-021.459e-021.592e-02
01.782e-043.576e-045.370e-047.164e-048.958e-041.075e-031.255e-031.434e-031.613e-031.793e-031.972e-032.152e-03
028.80459.07989.354119.629149.904180.178210.453240.728271.003301.278331.553361.828
024.06949.60175.132100.664126.195151.727177.258202.790228.321253.853279.384304.916
totalstrainrange
Δεtot
equiv.creepstrain
εcr
equiv.vM
stress(MPa)
5 ht equiv.
vMstress(MPa)
eq
vM�eq
vM�
4.3 Creep-fatigue evaluation results of the cruciform weldment
0.2
1
tota
l str
ain
range (
%)
200 1000 10000 100000
number of cycles to failure
0.5
Resultsof FEA
with LMM:
X-weld fatigue
X-weld = 1h
X-weld = 5h
Δt
tΔ
AvailableLCF tests
fittings :5
parent R66 curve
weld R66 curve
X-weld LCF tests
Resultsof X-weldtesting :3
X-weld fatigue
X-weld = 1h
X-weld = 5h
Δt
tΔ
Δεtot,%
Δt = 0 h Δ = 1 ht Δ = 5 ht
FEA/LMM experiments3 FEA/LMM experiments3 FEA/LMM experiments3
N* failure N* failure N* failure N* failure N* failure N* failure
1.0 857 T 918 T 430 T 562 U 278 T 275 P
0.6 4062 T 2499 U 1673 T 1048 U 967 T 943 W
0.4 17025 T 15747 P 6270 T 6512 U 3168 T — —
0.3 45374 W 38127 P 19776 T 21488 W 9679 T — —
0.25 90056 W 66847 P 52221 T — — 26901 T — —
(U) Specimen failed at the undercut close to the weld toe in the parent plate(T) Specimen failed at the weld toe propagating through the HAZ(P) Specimen failed in parent plate remote from weld(W) Specimen failed in weld metal
5. Analysis of the Obtained Results
5.1 Analytical functions for cycles to failure and residual life
Δt, dwell time (hours)
0 0.5 1 2 5 10 100 1000 10000
1.470528 857 500 430 362 278 223 95 33 8
1.153799 4062 2037 1673 1339 967 746 307 122 42
0.925507 17025 7963 6270 4756 3168 2294 799 308 121
0.777426 45374 24952 19776 14931 9679 6755 1963 635 230
0.691045 90056 63964 52221 40511 26901 18869 5116 1415 434
var
sh
MM
M
�
norm
aliz
ed m
om
ent
a1 a2 b1 b2
−0.4921 3.708929 0.0255 0.754959
� � � �
� � � �� � � �
3
1 2
tot
tot 1 2 2
2
1 3
1
2 ( )log( ) ,
365·24 (365·24·60·60)
0.2817, 0.17649
log 1
l
, 3.110
og 1
( ) 51
b t
p
t
a t a t a
b t b
MtN a t M L N
M p M p M p p
t b
p
�
�
�
� � � �� �
� �
�
� �
� �
�
�
�
� � �
� � �
where - dependent parameter
with
s :
5.2 Design contour plot for creep-fatigue durability
0.01 0.1 1 10 100 1000 10000
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
dwell time (hours)
no
rma
lise
d m
om
en
t
10205010020050010002000500010000200005000010000020000050000010000002000000
No. of cycles
life (years)tests
1000
300
100
30
10310.30.10.030.010.003
fatigue dominant creep dominant
5.3 Comparison of the observed and predicted *N
100
1000
10000
100000
100 1000 10000 100000
optimal match
factor of 2
factor of 1.6
LMM (fatigue)
LMM (Δt = 1h)
LMM (Δt = 5h)
analitic (fatigue)
analitic (Δt = 1h)
analitic (Δt = 5h)
Non-conservative
Conservative
experimental cycles to failure
pre
dic
ted c
ycle
s to
failu
re
5.4 Dependence of FSRF on duration of dwell period7 Δt
1
2
3
4
5
6
7
8
0.01 0.1 1 10 100 1000 10000
maximum
average
minimum
FSRF
dwell time (hours)
FS
RF
2 3
0 1 2 3
0 1 2 3
,FSRF( ) log( 1) log( 1) log( 1)
1.7685, 0.53422, 0.00574, 0.02509
t f f t f t f t
f f f f
� � � � � �
where
� � � � � �
� �� �
� � � �� �
� �3
2
tot 0 1 2
1
tot 1
p
2
0 1
arent
x-weld
2
log log log ,
,log log
2.2274, 0.94691 and 0.085943
p
b t b t
m m N m N
a t a tp p
N N
m m m
� �
� � � � � � � � �� � � �� �
�
� �
� �
�
�
� � � �� �
parent
tot
x-weld
tot
FSRF ,,
NN t
N t
�
�
�
�
�
3. Properties of the steel AISI type 316N(L) at 550°
-0.01 -0.005 0 0.005 0.01-400
-300
-200
-100
0
100
200
300
400
-0.01 -0.005 0 0.005 0.01-400
-300
-200
-100
0
100
200
300
400
total straintotal strain
stre
ss
stre
ss
saturated (R-O)1st cycle (R-O)saturated (EPP)saturated (tests)1st cycle (tests)
parent material MMA weld metal
3.1 Rate-independent cyclic plasticity3
1
tot 3
2(,
2 2 2 1 )E B
EE
� � � � ��
�
�� �
�
�
Zone E (MPa) B (MPa) β σy (MPa)
Parent 160000 1741.96 0.29960 270.662
Weld 122000 578.99 0.10162 307.894
HAZ 154000 1632.31 0.25304 338.731
Deformation plasticity (Ramberg-Osgood model):
3.2 Creep strain and rupture3,6
0
0.01
0.02
0.03
0.04
0.05
0 500 1000 1500 2000 2500
time
creep s
train
100
1000
100 1000 10000 100000
parent tests
weld tests
parent model
weld model
stre
ss
time to rupture
parent material: 390, 349, 310 and 285 MPaMMA weld metal: 270, 250 and 215 MPa
3
6
parent test (285 MPa)
weld test (270 MPa)
parent model (285 MPa)
weld model (270 MPa)
3
3
cr
cr 1
1
n m
n m
A t
At
m
�
�
�� �
� �
� �
Time to creep rupture:
k
Bt� �
�
Time-hardening power-law: ZonePrimary creep strain Time to creep rupture
A (MPa /h )-n m+1 n m B (MPa h)k k
Parent 6.604E-19 5.769 -0.55 2.172E+26 8.927
Weld 6.597E-23 7.596 -0.5 5.993E+29 10.61
HAZ 6.600E-21 6.683 -0.525 1.291E+28 9.768
0.1
1
1000 10000 100000
parent material
MMA weld metal
R66 fatigue endurance curves5
number of cycles
tota
lstr
ain
ran
ge
(%
)
3.3 Low-cycle fatigue endurance5
tot 2
0 1 2
tot 2 3
0 1 2 3
log( ) log( ) log( )
log( ) log( ) log( ) log( )
m m N m N
m m N m N m N
� �
� � �
� �
� � �
and�
�
ZoneQuadratic Cubic
parent MMA weld parent MMA weld
m0 1.73339 1.85169 2.40906 1.93432
m1 -0.72959 -0.76094 -1.25128 -0.82500
m2 0.06170 0.05951 0.19399 0.07585
m3 -0.01102 -0.00137
References
[1] Bree J. Elastic-plastic behaviour of thin tubes subjected to internal pressure andintermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements.
, 1967; : 226-238// In:
[2] Chen H.F., Chen W. and Ure J. Linear matching method on the evaluation of cyclic behaviourwith creep effect. // In: . Toronto,Canada: ASME; 2012, July 15-19
[3] Bretherton I. Reports by AEA Technology plc. and Serco Assurance (Warrington, UK)for British Energy Generation Ltd.: no. (1998), no. (1999), no.
(2000), no. (2004)
[4] Wada Y., Aoto K. and Ueno F. Creep-fatigue evaluation method for type 304 and 316FR SS.// In: . Vienna, Austria: IAEA;1997, p. 75–86
[5] Bate S.K. Further analyses to validate the R5 volume 2/3 procedure for the assessmentof austenitic weldments. // Report for British Energy Generation Ltd. no.
; SercoAssurance (Warrington, UK); 2005
[6] Data sheets on the elevated-temperature properties for base metals, weld metals andwelded joints of 18Cr-12Ni-Mo-middle N-low C hot rolled stainless steel plates (SUS 316-HP). ; National Institute for Materials Science; Tsukuba,Japan; 2005
[7] Ainsworth R.A., editor. R5:British Energy Generation Ltd (Gloucester, UK); 2003
Journal of Strain Analysis 2(3)
Proc. ASME Pressure Vessels & Piping Conf.
et al.R/NE/432 AEAT-3406 AEAT-
3406 RJCB/RD01186/R01
Creep-fatigue damage rules for advanced fast reactor design
et al.
SA/EIG/11890/R002
NIMS Creep Data Sheet No. 45A
An Assessment Procedure for the High Temperature Responseof Structures. Procedure R5: Issue 3.
(PVP2012)
Acknowledgements
The authors deeply appreciate the EPSRC of the United Kingdomfor the financial support in the frames of research grant no.EP/G038880/1, the University of Strathclyde for hosting during thecourse of this work, and EDF Energy for the experimental data.
Engineering and Physical
Sciences Research Council
6. Conclusions
1)
2)
3)≤
4)cases
cases
5)
6)
The series of have been implemented with LMM using:and corresponding constants to describe plastic strains under
saturated cyclic conditions;and corresponding constants to describe creep strains
during primary creep stage.The amount of damage per cycle caused by is estimated using:
experimentally defined dependent on numericallydefined total strain range for the fatigue damage ( );experimentally defined dependent on the average stress duringdwell period for the creep damage ;the during dwell period is defined as a mean value of analytical function for stressduring relaxation dependent on elastic follow-up factor ( ), initial stress and time.
A non-linear is used to define the caused by both creep andfatigue, which can’t exceed one ( + 1). Basing upon this interaction, the number of cycles tocreep-fatigue failure ( � ) is defined.Comparison of the observed and predicted cycles to failure with creep-fatigue FEA/LMM for 3 typesof experiments shows, that simulation of 9 of total available 11 is very close to .Simulation of other 2 produces results with factor of difference equal to ,which is even better than the factor acceptable for engineering analysis equal to .Sets of creep-fatigue FEA/LMM results analysis corresponding to 0, 0.5, 1, 2, 5 and 10 hours arefitted by and used for of cycles to failure ( *) depending on dwellperiod and normalized moment intended for design application.Further research will be devoted to parametric studies of the influence of variation of weldmentgeometrical parameters on the number of cycles to failure ( *) and formulation of a
to describe the corresponding dependence.
creep-fatigue analyses
creep-fatigue interaction
creep-fatigue diagram
1.62
• Ramberg-Osgood material model
power-law model in “time hardening” form
relation for number of cycles to fatigue failure ( *)
relation for time to creep rupture ( *)
average stress
total damage
optimal matchnon-conservative
analytical function contour plot
mathematicalrelation
•
•
•
•
N
tω
Z
ω ωN
N
N
f
f cr
( )ωcr
