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

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29 Νοε 2013 (πριν από 4 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

-
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

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

a/W = 0.2 a/W = 0.4

J
-
Integral)

-
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)
106KV
107KV
108KV
109KV
110KV
111KV
112KV
113KV
114KV
115KV

Out of Plane Compression

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)
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

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
-
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:

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
a/W = 0.42 Residual
Stress
a/W = 0.22 Residual
Stress
Experimental Results

Specimens with residual

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

-
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