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)

Din

sta

nc

e f

rom

Pla

te S

urf

ac

e (

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

Rx

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)

Ope

ning

mod

e st

ress

(MPa

)

-400

-200

0

200

400

600

800

0 5 10 15 20 25 30 35 40

x ahead of notch (mm)

Ope

ning

mod

e st

ress

(MP

a)

a/W = 0.2 a/W = 0.4

Finite Element Modelling (Loading and J-Integral)

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

– -140oC 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)

Lo

ad (

kN)

106KV107KV108KV109KV110KV111KV112KV113KV114KV115KV

Out of Plane Compression

Experimental (Loading)

3-point bend testing carried out at -140oC

Good agreement between experiment and Finite Element data

0

20

40

60

80

100

120

140

0.00 0.10 0.20 0.30 0.40Crack Opening Displacement (mm)

Lo

ad (

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

ijijij QJrJr 00*

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 (Jc)

0

J

Q

J*c

2

2.5

3

3.5

4

1 2 3 4 5

rσ0/J

σθθ

/σ0

J = 10.3kN/mJ = 26.06kN/mJ = 49.0kN/mJ = 79.2kN/mJ = 116.5kN/m

2

2.5

3

3.5

4

1 2 3 4 5

rσ0/J

σθθ

/σ0

SSYJ = 26.7kN/mJ = 51.9kN/mJ = 73.9kN/mJ = 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

rσ0/J

σθθ

/σ0

SSYJ = 9.7kN/mJ = 25.1kN/mJ = 52.6kN/mJ = 76.8kN/mJ = 100.6kN/m

2

2.5

3

3.5

4

1 2 3 4 5

rσ0/J

σθθ

/σ0

SSYJ = 11.2kN/mJ = 25.3kN/mJ = 52.4kN/mJ = 76.3kN/mJ = 103.6kN/m

2

2.5

3

3.5

4

1 2 3 4 5

rσ0/J

σθθ

/σ0

SSYJ = 26.1kN/mJ = 51.9kN/mJ = 74.0kN/mJ = 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 (k

Nm

-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 (k

Nm

-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 (k

Nm

-1)

a/W = 0.22 No RS

a/W = 0.42 No RSa/W = 0.22 RS

a/W = 0.42 RSJc SSY

a/W = 0.22 No RS Jca/W = 0.42 No RS Jc

a/W = 0.22 RS Jca/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

10

* /1 nfcc QJJ

0

20

40

60

80

100

120

140

Specimen Type

Fai

lure

Lo

ad (

kN) a/W = 0.42 Residual

Stress

a/W = 0.42 As-received

a/W = 0.22 ResidualStress

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 (

Nm

m-1

)

a/W = 0.22 No RSa/W = 0.42 No RSa/W = 0.22 RSa/W = 0.42 RSClosed Form Jca/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% Pf5% 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