1. Engineering Doctorate – Nuclear Materials Development of Advanced Defect Assessment Methods Involving Weld Residual Stresses
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Presented by
Robert Hurlston

2. Content Introduction Problem Definition Basis for Project Project Plan
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

3. 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

4. Problem Definition

5. 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)

6. 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

7. 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

8. 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

9. Basis For Project

10. 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

11. 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

12. 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:

13. J annulus
Qσ0
Small-scale yielding
Finite geometry

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

15. 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

16. J annulus
margin B C
Qσ0
Small-scale yielding A
Finite geometry

17. 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 J
Constraint corrected J (Jc)
J*c Q

18. 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

19. 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

20. Work to Date

21. 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

22. 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

23. 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

24. 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

25. Questions???