Characterisation of the Effect of Residual Stress on Brittle Fracture in Pressure Vessel Steel

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29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Presented by

Robert Hurlston

UNTF Conference 2011


Characterisation of the Effect of Residual Stress
on Brittle Fracture in Pressure Vessel Steel

Content


Introduction


Residual Stress


Constraint


Work Undertaken


Finite Element Modelling


Experimental


Results


Finite Element Modelling


Experimental


Two
-
Parameter Analysis (J
-
Q)


Summary

Introduction


It is extremely important that the integrity of nuclear plant can be
ensured



Failure assessment


Fracture toughness of materials within the structure are commonly used in
failure assessments


This can be difficult to evaluate where weld residual stresses are present



Therefore,


We need to understand the effects of residual stress on fracture toughness

Residual Stress



is
defined as:



stress existing in a material when
it is under no primary load



This can contribute to crack
driving force



How else does it affect crack
-
tip
conditions?

-600
-400
-200
0
200
400
600
800
0
5
10
15
20
25
30
35
40
45
50
Residual Stress (MPa)
Dinstance from Plate Surface (mm)
Transverse A508
Longitudinal A508
Constraint


It is well known that geometry and loading affect crack
-
tip constraint

Effect of Residual Stress on Constraint?


Can residual stress affect constraint of crack
-
tip material?



Yes!


It has been demonstrated by many authors



However, these effects are not well understood


Problematic associated plastic strains



Can we characterise these effects?

Work Undertaken

Out
-
of
-
Plane Compression


Based on work by Mahmoudi et
al.



Double punch pair situated
ahead of crack



Developed to generate residual
stresses with no associated
plastic strain

R

x

y

I = Indentation

W (= 50mm)

a

Punches

Notch

Finite Element Modelling (Models)


Single edge notched bend specimens modelled with cracks of a/W =
0.2 and a/W = 0.4 (where W = 50mm)



Circular features simulated punch contact with surface



Finite Element Modelling (Residual Stresses

Generated)


Out
-
of
-
plane compression used double, 5mm radius ‘punches’



Stress was generated ahead of crack
-
like notch before crack was
grown to final length (5mm growth)

-400
-200
0
200
400
600
800
0
5
10
15
20
25
30
35
40
x ahead of notch (mm)
Opening mode stress (MPa)
-400
-200
0
200
400
600
800
0
5
10
15
20
25
30
35
40
x ahead of notch (mm)
Opening mode stress (MPa)

a/W = 0.2 a/W = 0.4

Finite Element Modelling (Loading and

J
-
Integral)


Loading was simulated in 3
-
point bending (span = 200mm)


-
140
o
C to ensure cleavage fracture conditions



A boundary layer model was also loaded in tension to simulate small
-
scale yielding conditions (for calculation of Q)


Experimental (Out
-
of
-
Plane Compression)


Carried out to validate the Finite Element findings


-300
-250
-200
-150
-100
-50
0
0.0
0.2
0.4
0.6
0.8
LVDT Displacement (mm)
Load (kN)
106KV
107KV
108KV
109KV
110KV
111KV
112KV
113KV
114KV
115KV


Out of Plane Compression

Experimental (Loading)


3
-
point bend testing carried out at
-
140
o
C



Good agreement between experiment and Finite Element data

0
20
40
60
80
100
120
140
0.00
0.10
0.20
0.30
0.40
Crack Opening Displacement (mm)
Load (kN)
Experiment (No RS)
FE (No RS)
Experiment (RS)
FE (RS)
Results

Constraint Based Fracture Mechanics


Elastic
-
plastic crack
-
tip fields can be characterised via a two
parameter approach where:


J describes the crack
-
tip driving force and


Q describes crack
-
tip constraint condition





The approach allows ‘apparent’ fracture toughness to be
determined







ij
ij
ij
Q
J
r
J
r








0
0
*
0
,
/
,
/


J
-
Q Space


J
-
Q space



Loading line (evolution of
constraint with increasing J)



Failure Line (J for failure
increases as constraint is lost)



Failure deemed to occur where
lines intersect

Constraint corrected J
(J
c
)

0

J

Q

J*
c

2
2.5
3
3.5
4
1
2
3
4
5

0
/J
σ
θθ

0
J = 10.3kN/m
J = 26.06kN/m
J = 49.0kN/m
J = 79.2kN/m
J = 116.5kN/m
2
2.5
3
3.5
4
1
2
3
4
5

0
/J
σ
θθ

0
SSY
J = 26.7kN/m
J = 51.9kN/m
J = 73.9kN/m
J = 103.6kN/m





No
Residual
Stress




Crack
-
tip stress fields, generated during loading of the boundary layer
model, are plotted at increasing J
-
integrals

Finite Element Results


a/W = 0.2 a/W = 0.4


Residual
Stress



2
2.5
3
3.5
4
1
2
3
4
5

0
/J
σ
θθ

0
SSY
J = 9.7kN/m
J = 25.1kN/m
J = 52.6kN/m
J = 76.8kN/m
J = 100.6kN/m
2
2.5
3
3.5
4
1
2
3
4
5

0
/J
σ
θθ

0
SSY
J = 11.2kN/m
J = 25.3kN/m
J = 52.4kN/m
J = 76.3kN/m
J = 103.6kN/m
2
2.5
3
3.5
4
1
2
3
4
5

0
/J
σ
θθ

0
SSY
J = 26.1kN/m
J = 51.9kN/m
J = 74.0kN/m
J = 99.5kN/m
0
10
20
30
40
50
60
70
80
90
100
-0.20
-0.15
-0.10
-0.05
0.00
0.05
Q
J (kNm
-1
)
a/W = 0.22 No RS
a/W = 0.42 No RS
a/W = 0.22 RS
a/W = 0.42 RS
a/W = 0.22 No RS Jc
a/W = 0.42 No RS Jc
a/W = 0.22 RS Jc
a/W = 0.42 RS Jc
0
10
20
30
40
50
60
70
80
90
100
-0.20
-0.15
-0.10
-0.05
0.00
0.05
Q
J (kNm
-1
)
a/W = 0.22 No RS
a/W = 0.42 No RS
a/W = 0.22 RS
a/W = 0.42 RS
0
10
20
30
40
50
60
70
80
90
100
-0.20
-0.15
-0.10
-0.05
0.00
0.05
Q
J (kNm
-1
)
a/W = 0.22 No RS
a/W = 0.42 No RS
a/W = 0.22 RS
a/W = 0.42 RS
Jc SSY
a/W = 0.22 No RS Jc
a/W = 0.42 No RS Jc
a/W = 0.22 RS Jc
a/W = 0.42 RS Jc
Closed Form Jc
J
-
Q Analysis


Using constraint based
fracture mechanics:


Loading lines can be plotted


Their associated fracture
toughness curves can be
plotted using RKR



Closed form equation is in
good agreement



1
0
*
/
1



n
f
c
c
Q
J
J


0
20
40
60
80
100
120
140
Specimen Type
Failure Load (kN)
a/W = 0.42 Residual
Stress
a/W = 0.42 As-received
a/W = 0.22 Residual
Stress
a/W = 0.22 As-received
Experimental Results


Specimens with residual
stress fail at lower loads



Large degree of scatter


A533B laminate
microstructure




Experimental Validation


Mean experimental results validate the use of unique toughness curve


All within 7% of the closed form failure curve

0
10
20
30
40
50
60
70
80
90
100
-0.20
-0.15
-0.10
-0.05
0.00
0.05
Q
J (Nmm
-1
)
a/W = 0.22 No RS
a/W = 0.42 No RS
a/W = 0.22 RS
a/W = 0.42 RS
Closed Form Jc
a/W = 0.22 No RS (Exp failure)
a/W = 0.42 No RS (Exp failure)
a/W = 0.22 RS (Exp failure)
a/W = 0.42 RS (Exp failure)
95% Pf
5% Pf
Summary

Summary


It is known that residual stresses can affect crack
-
tip constraint


How it does was not well understood



This work has validated the use of a unique failure curve in J
-
Q space
when residual stresses affect crack
-
tip conditions


Where no associated plastic strain is present


Using novel adaptation of out
-
of
-
plane compression



Future work might consider the effect of plastic strain on constraint and
the use of unique a material toughness curve


Allowing inclusion into failure assessment guidance


Questions???


References:


Hill M R and Panontin T L. Effect of residual stress on brittle fracture testing. Fatigue and Fracture Mechanics29, ASTM STP
1332. 1998


Sumpter J. The effect of notch depth and orientation on the fracture toughness of multi
-
pass weldments. Int. J. Pres. Ves. and
piping 10. 1982


Mahmoudi A H, Truman C E and Smith D J. Using local out
-
of
-
plane compression (LOPC) to study the effects of residual stress
on apparent fracture toughness. Engineering Fracture Mechanics 75 1516

1534. June 2007