Presented by

Robert Hurlston

Engineering Doctorate – Nuclear Materials

Development of Advanced Defect Assessment Methods Involving Weld Residual Stresses

Content

Introduction

Problem Definition

– Evaluating Fracture Toughness in Weld Specimens

– Shortfalls in Methodology

Basis for Project

– Two Parameter Fracture Mechanics

– Effect of Residual Stress on Constraint

– Evaluation of Unique Material Toughness

– Work to Date

Project Plan

Summary

Introduction

It is essential that structural integrity of reactor pressure vessels in pressurised water reactors can be ensured

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

The aim of this project is to:

– assess the applicability of constraint based fracture mechanics to quantify 'unique material fracture toughness' in laboratory specimens containing residual stresses using the 'apparent fracture toughness' values derived from standard fracture toughness testing

Problem Definition

Evaluating Fracture Toughness

BS7448 is the British Standard containing methodology for experimental evaluation of critical fracture toughness in metallic materials

Pre-cracked bend or compact tension specimens are tested in displacement controlled monotonic loading at a constant rate of increase in stress intensity factor

Data obtained is used to determine plane strain fracture toughness (K, CTOD, J)

Residual Stress Modification

Part II of BS7448 is designated to describing methods for defining critical fracture toughness in areas of welding residual stress

Addresses two issues:

– To define suitability of weld notch placement

– To define protocol for modification of residual stress

This is generally done in order to reduce residual stress to a ‘negligible’ level via local compression of material at the crack tip

Local Compression

Residual stress shall be considered acceptably low provided that:

– The fatigue crack can be grown to an acceptable length

– The fatigue crack front is acceptably straight

However, it has become apparent, through research, that these methods can often have the opposite effect

– Modifying driving force and crack-tip constraint

Furthermore, triaxiality introduced via local compression can affect constraint, which can significantly influence measured fracture toughness

It is assumed that the compression reduces all residual stresses to low and uniform levels such that any remaining residual stress has no effect on fracture

Basis For Project

Constraint Based Approach to Fracture Mechanics

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

– J describes the crack tip driving force and T or Q (used in this project) describes crack tip constraint

– This forms the basis of two parameter fracture mechanics, where toughness is expressed as a function of constraint in the form of a J-Q locus

The approach allows enhanced ‘apparent’ fracture toughness associated with shallow cracks to be used via constraint matching

– Allows the high levels of conservatism associated with use of deeply cracked fracture toughness specimens to be relaxed

Constraint

Work into the effects of constraint has mostly focussed upon understanding and predicting the role of specimen/defect geometry

– When the plastic zone at the crack tip is infinitesimally small compared to all other characteristic lengths and is embedded in an elastic field small scale yielding conditions exist

– Q is essentially 0

– Loss of constraint occurs where the plastic zone at the crack tip is in contact with or near a traction free surface or plastic strain caused via gross deformation

Crack Tip Stress Fields

Constraint is calculated by comparing the crack tip stress distributions generated under small-scale yielding conditions and in real geometries

O’Dowd and Shih provide an approximate expression, where Q is the correction factor characterising this difference:

ijijij QJrJr 00*

0 ,/,/

Jr /0

J annulus

Small-scale yielding

Qσ0

Finite geometry

J-Q Locus

The Q stresses calculated can now be used to construct a load line in J-Q space

Q 0

J

RKR Model

When making fracture assessments, it is usually assumed that crack tip conditions in a standard fracture toughness specimen approximate high constraint

This is considered to be conservative as crack tip constraint is likely to be lower in the structure being assessed

Where fracture depends on the crack tip stress, effective (constraint corrected) fracture toughness, Jc, can be calculated by solving equations of the form:

– Ritchie, Knott and Rice provide a simple framework for its implementation *0*

00*

0 /// ccc JrQJrJr

f

c

c

J

r 0J

rc 0 Jr /0*0

c

c

J

r

B

C

A

margin

J annulus

Qσ0

Small-scale yielding

Finite geometry

Constraint corrected J (Jc)

RKR Model

The RKR model can be used to calculate Jc at all points along the J-Q loading line to produce a Jc-Q locus

The point at which the loading line intersects this locus is the corrected failure point for the specimen or component with given geometry

J*c is the materials fracture toughness

0

J

Q

J*c

Effect of Residual Stress and Biaxial Loading on Constraint

It has been shown in a number of studies that crack tip constraint is strongly influenced by both residual stress and biaxial loading

Xu, Burdekin and Lee (figure) report similar findings

0

20

40

60

80

100

120

140

160

180

200

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Qc (Case 3)

P-SENT

SENT

CT

P-CT

Fra

ctu

re t

ou

gh

ne

ss

, KJ

C (M

Pa√

m)

Correcting Weld Fracture Toughness

The main objective for this project is to demonstrate the applicability of a unique material (Jc-Q) fracture toughness curve where weld residual stresses are present within the material

Given knowledge of the effect of residual stresses present on constraint (from FE) it will be possible to correct measured weld fracture toughness data to find the unique (SSY) material toughness value

This:

– Removes the necessity of relaxing residual stresses in laboratory specimens

– Ensures that residual stress is only accounted for once in any subsequent failure assessment

Work to Date

Finite Element Modelling

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

Residual stresses generated using a novel adaptation of out-of-plane compression

-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)

Using constraint based fracture mechanics (described previously):

– Loading lines can be plotted for both geometries, with and without residual stress

– Their associated fracture toughness curves can be plotted using RKR

Fracture toughness curves collapse onto one another

0

50

100

150

200

250

300

350

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2Q

J (N

mm

-1)

0.2 no RS

0.4 no RS

0.2 RS

0.4 RS

Jc (SSY)

Jc (0.2)

Jc (0.4)

Jc (0.2 RS)

Jc (0.4 RS)

Jc Closed Form

Validation

Experimental work is planned to validate these results

Fracture toughness values to be obtained for each of the modelled cases

Agreement between simulation and experiment would allow a model to be developed for implementation of this methodology for use in acquisition of weld fracture toughness

Summary

Current BS7448 methodology for acquisition of fracture toughness in welds relies too heavily upon engineering judgement

Use of constraint based fracture mechanics model is proposed to correct for weld residual stresses using (FE) knowledge of their effect on constraint when evaluating fracture toughness

It is anticipated that preventing the need for stress relaxation before testing will provide significant benefits when evaluating weld fracture toughness

Questions???