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

2

Temperature

KJC

Baselinetoughness

Q effect

Geometry relatedconstraint

Tstress

Yielding relatedconstraint

Q

Tstress

effect

• Beyond basics

• “R&D” department


3

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]


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.


5

-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


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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


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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


8

Master Curve analysis of the Point Pleasant bridge failure

213 m

116 m

Originally built in 1928, bridge floor renovated in 1941.


9

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.


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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


11

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.


12

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 %


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


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Battelle full scale eye-bar test

-20 0 20 40 60 800

50

100

5 %

95 %


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 %


Eye-bar, s = 13 mm

T0 = 77 oC

B0 = 25 mm

KIE

p [

MP

am

]

T [oC]

T-stress max.max. plcorrection


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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.)


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