1 CONSTRAINT CORRECTED FRACTURE MECHANICS IN STRUCTURAL INTEGRITY ASSESSMENT Application to a...
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Transcript of 1 CONSTRAINT CORRECTED FRACTURE MECHANICS IN STRUCTURAL INTEGRITY ASSESSMENT Application to a...
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CONSTRAINT CORRECTED FRACTURE MECHANICS IN STRUCTURAL INTEGRITY ASSESSMENTApplication to a failure of a steel bridge
Anssi Laukkanen, Kim Wallin
Safir Interim Seminar, January 2005
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Temperature
KJC
Baselinetoughness
Q effect
Geometry relatedconstraint
Tstress
Yielding relatedconstraint
Q
Tstress
effect
• Beyond basics
• “R&D” department
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T-Stress Effect on the Master Curve
-150 -120 -90 -60 -30 00
100
200
300
400
500
600
T0= -100oC
T-stress=0T-stress=-50 MPaT-stress=-100 MPaT-stress=-200 MPaT-stress=-400 MPaT-stress=-800 MPa
K 0 [M
Pa m
0.5 ]
T[oC]
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
4
250
25
250
0
4
25
25
2
25
.
minmaxmin
.
min
min
)(
cKKKK
dxKxK
KK
Immeff
I
mmeff
Uniform temperature
250
0
4
0
0 25
.
min
min
min
min )()(
)(
)(
dxKxK
KxK
KTK
KTKI
eff
Varying temperature
Treatment of Surface Cracks in the MC Method
Or divide crack in constant temperature sections.
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-800 -600 -400 -200 0 200-100
-80
-60
-40
-20
0
20
290-350 MPa Best fit 490-680 MPa Best fit 720-1380 MPa Best fit
T0 T
0DEEP + T
stress/10 MPa/oC
Tstress
< 0
T0-
T0D
EE
P [
oC
]
Tstress
[MPa]
Master Curve T0, nearly linearly dependent on T-stress
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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-600 -400 -200 0 200 400 600
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Based on modified boundary layer analysis of N = 10 material, yield strength = 700 MPa
Master Curve based prediction
KJC
T/K
JCT
=0
T-stress [MPa]
r0/J=1
r0/J=2
r0/J=4
-600 -400 -200 0 200
1.0
1.5
2.0
2.5
3.0
3.5
4.0
KJC
T/K
JC
T-stress [MPa]
m = 10 n = 20 n = 10 n = 7.5 n = 5
"Wallin"
Master Curve expression verified by analytical expressions
Direct stress comparison Local approach prediction
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Comparison of Local Approach and Constraint Corrected Master Curve
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
Pf = 0.95
Pf = 0.05
offsets: K
J c == 0
KJ c == 25 MPa m0.5
KJ c == 90 MPa m0.5
K Jc [M
Pa m
0.5 ]
KJ c [MPa m0.5], Master Curve, T-stress == 0
Master Curve, T-stress(KJ)
local approach, mean of m=22 and m=30
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Master Curve analysis of the Point Pleasant bridge failure
213 m
116 m
Originally built in 1928, bridge floor renovated in 1941.
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Bridge failed December 15, 1967 at 5:10 PM, 46 lives were lost.
•T = -1°C
•”Cracking” started 30 min before collapse.
•Cause of failure was identified to be brittle fracture of eye-bar 330 in joint C13N.
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Failure iniatiated from semielliptic stress corrosion crack in eyebar
Actual stress at the edge of the hole was estimated to be 585 MPa
3.2
mm
1.6
mm
≈ 10 mm
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0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80
90
100
SA
[%
]
KV [J]
SA [%] = 1.52 x KV [J]
KVUS
= 66 J
0 20 40 60 80 100 1200
10
20
30
40
50
T28J
= 112 oC
T41J
= 130 oC
T68J
= -- oC
Point Pleasant bridge eyebar C0, C3 & C9
C = 42.1 oC
T50
= 122 oC
US = 66 J
KV
[J]
T [0C]
TNDT
650C
•Heat-treated rolled carbon steel with forged heads, Y = 520 MPa
•The material has low upper-shelf energy and high transition temperature.
•Resembles, in properties, a highly embrittled pressure vessel steel.
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Master Curve analysis of fracture toughness results
SEN(T) specimens have T-stress ≈ -130 MPa.
-20 0 20 40 60 800
50
100
5 %
95 %
Point Pleasant bridge eyebar Y = 520 MPa B = 50 mm
SEN(B)
T0 = 77 oC
B0 = 25 mm
KIC
[M
Pa
m]
T [oC]-20 0 20 40 60 80
0
20
40
60
80
100
120
140
5 %
95 %
Point Pleasant bridge eyebar Y = 520 MPa B = 50 mm
SEN(T)
T0 = 57 oC
B0 = 25 mm
KIC
[M
Pa
m]
T [oC]
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Application of Master Curve and constraint correction for real cracks
Normally, the Master Curve parameters are determined using test specimens with "straight" crack fronts and comparatively uniform stress state along the crack front. This enables the use of a single KI value and single constraint value to describe the whole specimen.
For a real crack in a structure, this is usually not the case. Normally, both KI and constraint varies along the crack front and in the case of a thermal shock, even the temperature will vary along the crack front.
4
min0
min
0
exp1KK
KK
B
BP I
f
s
If B
ds
KK
KKP
0 0
4
min0
minexp1
Standard MC
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Application of Master Curve and constraint correction for real cracks
A visualisation, that is in line with ASME practice, can be achieved by defining an effective stress intensity factor KIeff corresponding to a specific reference temperature. The reference temperature can e.g. be chosen as the minimum temperature along the crack front.
The procedure is to determine an effective driving force, which would give the same failure probability as a standard Master Curve presentation.
minmin0
4/1
0 0
4
min0
min KKKB
ds
KK
KKK Tref
sI
IeffTref
KIis obtained from the stress analysis as a function of location (). K0Tref is the standard, high constraint, Master Curve K0, corresponding to a reference temperature along the crack front.
00 019.0exp7731 TTK refTref
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CMPa
stressTTTKK deepstressTT /10
019.0exp7731 0,00
Constraint correction
The expression is directly applicable with the ASME Code Case N-629 fracture toughness reference curve, since it is written in terms of the standard deep specimen T0 (RTTo).
-50 0 50 100 150 2000
50
100
150
200
250
KIe
ff,
KIC
[M
Pa
m]
Tmin
-T0deep
[oC]
KIC
5% MC
KIC
, N-629
KIeff
Constraint corrected
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Battelle full scale eye-bar test
a ≈ 9 mm, 2c ≈ 20 mm (s ≈ 30 mm)T = 0°Cf =393 MPa“KIC” = 51 MPam (original)
-10 -5 0 5 100
10
20
30
40
50
60
KI [
MP
am
], a
' [m
m]
c' [mm]
a'
KI (Newman-Raju)
51 MPam
Tstress ≈ -200 MPa
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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Battelle full scale eye-bar test
-20 0 20 40 60 800
50
100
5 %
95 %
Point Pleasant bridge eyebar Y = 520 MPa B = 50 mm
Eye-bar, s = 30 mm
T0 = 77 oC
B0 = 25 mm
KIE
ff [
MP
am
]
T [oC]
T-stress
Constraint corrected Full scale test decribed well with MC.
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ASSESSMENT OF THE FAILURE
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3.2
mm
≈ 10 mm
-4 -2 0 2 40
20
40
60
80
100
120
KIeff
(25 mm) = 55.2 MPam
KI (Newman-Raju) + SINTAP min.
KI (Newman-Raju)
KI (Newman-Raju) + SINTAP max.
KIe
p [
MP
am
]
c' [mm]
KIeff
(25 mm) = 83.3 MPam
Engineering assessment
T0 = +74°C
= 585 MPa
T = -1°C
Y =540 MPa
Flaw re-characterisation:
5.02
6
5.01
4.0exp7.03.0
Lr
LrLf r
SINTAP plasticity correction 2/125.01)(
LrLrf
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•SINTAP level 1 plasticity corrections:
•Conservative •Non-conservative
•Master Curve analysis•T-stress shallow flaw correction (T/≈-1)
Realistic but safe prediction of eye-bar failure.
ENGINEERING ASSESSMENT SAFE AND RELIABLE
-20 0 20 40 60 800
50
100
min. plcorrection
T-stress max. 5 %
95 %
Point Pleasant bridge eyebar Y = 520 MPa B = 50 mm
Eye-bar, s = 13 mm
T0 = 77 oC
B0 = 25 mm
KIE
p [
MP
am
]
T [oC]
T-stress max.max. plcorrection
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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FEM analysis of eye-bar 330
-local = 585 MPa
-global = 210 MPa
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0 30 60 90 120 150 1800
10
20
30
40
50
60
70
80
90
100
KI [
MP
am
]
[o]
62.2
Without plasticity correction
3.2
mm
6.5 mm
KIeff25mm= 54 MPam
s = 10 mm
Best estimate of eye-bar 330
-20 0 20 40 60 800
50
100
5 %
95 %
Point Pleasant bridge eyebar
Eye-bar, s = 10 mm
T0 = 77 oC
B0 = 25 mm
KIE
p [
MP
am
]
T [oC]
T-stress max.best est.correction
Best estimate prediction close to 50 % failure probability based on full MC analysis.
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CONCLUSIONS
•Master Curve based methods for pressure vessel integrity assessment are applicable also for other structures.
•Method validated for catastrophic failure of the Point Pleasant bridge, containing:
•real shallow surface crack (constraint effects, variable KI)
•brittle steel (resemble embrittled PV steel)•high primary stresses (nozzle corner etc.)
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
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