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EDF Energy R&D UK CentreAdvantages of Code_Aster for integrity assessments on large scale
structures featuring cracks within a residual stress field
Presented by Jefri Draup
On 16/13/2017 in EDF Saclay, Paris
Contents
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1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
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Background and Motivation
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Pre-stressed Concrete
Pressure VesselControl Rods
Graphite Brick Core Steam Generator
AGR Lifetime Extension Programme
• ~20% of UK electricity supply for 14 AGR reactors
• 30 year original design lifetime of AGRs (2014)
• Extension to 2024 in order to improve cost-benefit
• Meeting regulator (ONR) safety needs
• High temperature environment 600C
Background and Motivation
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AGR Lifetime Extension Programme
• ~20% of UK electricity supply for 14 AGR reactors
• 30 year original design lifetime of AGRs (2014)
• Extension to 2024 in order to improve cost-benefit
• Meeting regulator (ONR) safety needs
• High temperature environment 600C
Operational Issues
• Inspection of Heysham boiler spine revealed the presence
of a structural defect1
• Replacement of boilers not feasible due to design
• The need to understand the conditions within the steam
generator in-service is required
• The potential loss in revenue if boilers and reactors have to
be shut down is significant
~650oC / 40bar
CO2
Boiler Spine
Austenitic 316
stainless steel
Ferritic 9 Cr
Mild Steel1Specification of Heysham 1 reactor 2 boiler spine structural integrity safety case & justification for return
to full power following implementation of the spine cooling modification, NP-SC 7728, EC355061, Office
for Nuclear Regulation Report (ONR-HYA-PAR-15-012), 2015
1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
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Experimental Setup
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STYLE MU2 Specimen:
• 2 lengths of Esshete 1250 austenitic S.S.
• Joined by a girth weld (TIG) and cap dressing
• Introduce a manual repair weld (MMA) and cap dressing
• Residual Stress measurement (iDHD/contour)
Experimental Setup
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STYLE MU2 specimen:
• Electro Discharge Machining to introduce a
chevron notch
• Four point bending setup with extension arms
welded into place
• Fatigue pre-crack introduce through loading
Chevron notchFatigue Pre-crack
Experimental Setup
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A large-scale four point bending
test performed by CEA (France) as
part of the EU programme, STYLE
13m
1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
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Numerical Methods – Overall Strategy
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Generate FE-mesh
Run elastic model
Run elastic-plastic model
Run elastic-plastic model with RS
Quality check mesh and
Verify loads and BC applied
Run elastic model with RS
General aims
• Setup a validated model of the welded
structure in four point bending
• Assess the energy release rate, G,
under loading
• Assess the assumption of elastic and
elasto-plastic material properties
• Assess the influence of residual stress
fields on energy release rate
Numerical Methods – Model Details
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MU2 pipeExtension armExtension arm
11 m
1.0 m
13 m
Inner loading point Supporting point
( Outer loading point)
Supporting point
( Outer loading point)
Geometry
Half symmetry
Loading and Boundary Conditions
Mesh
• 8 node Hexahedron elements used to mesh structure (500,000el)
• Mesh refined towards weld region and crack region (0.15mm at
crack tip after mesh sensitivity study)
• Cracks modelled as sharp crack and notch
Numerical Methods – Model Details
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Crack Tip Crack Tip
Mesh 1 Mesh 2 Mesh 3
Sharp crack Notch crack
Sharp crack
Material Properties
• Studies run for cases assuming purely elastic properties and repeated for elasto-plastic properties
• Homogenised properties for the weld geometry included
Residual Stresses
• A residual stress field for both the girth weld and repair weld was measured experimentally
• The input residual stress field was adjusted iteratively until the post-equilibrium stress fields matched the
experimental data
Numerical Methods – Model Details
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-400
-300
-200
-100
0
100
200
300
400
500
50 55 60 65 70 75 80 85 90 95
Axi
al R
esid
ual
Str
ess
(MPa
)
Radius (mm)
-300
-200
-100
0
100
200
300
400
500
600
50 55 60 65 70 75 80 85 90 95
Ho
op
Res
idu
al S
tres
s (M
Pa)
Radius (mm)
Mechanical Analysis
• Mechanical analysis STAT_NON_LINE to compute global field variables
Post-Processing
• The energy release rate (G) around the crack was computed using CALC_G
• For elastic conditions the option ‘CALC_G’ was used and the solution compared to R6 guidelines
• For elasto-plastic conditions the option ‘CALC_GTP’ was used
• For each case the analysis was repeated for to include residual stresses
Benchmarking
• The prediction of energy release rate in Code_Aster was compared to J integral calculations in
ABAQUS
Numerical Methods – Model Details
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1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
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Results – Parametric Studies
• Mesh resolution study showed that element of 0.15mm at notched crack tip is optimal
• Parametric smoothing study indicates Legendre smoothing Degree 5 is optimal
• This mesh and smoothing function is used on subsequent analysis
0,00
0,05
0,10
0,15
0,20
0,25
50 55 60 65 70 75 80 85 90 95
G (
MJ/
m)
R(mm)
G at U2 = 75 mm (Bending Moment = 230 kN-m)Aster RI=0,001 RS =0,005
R6-Ref
CALC_K_G Smoothing default
CALC_G Smoothing default
CALC_K_G Smoothing LAGRANGE_REGU
CALC_G Smoothing LAGRANGE_REGU
CALC_K_G Smoothing LAGRANGE
CALC_G Smoothing LAGRANGE
CALC_K_G Smoothing LEGENDRE D3
CALC_G Smoothing LEGENDRE D3
Energy release
rate evaluated
here providing
a bending
moment of
~230kNm
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Results
0
50
100
150
200
250
0,0 0,5 1,0 1,5 2,0 2,5
Reactio
n F
orce (kN
)
CMOD (mm)
The Relationship between Reaction Force & CMOD
Experiment
1/4 model without residual stress (Do and Smith)
1/4 model with residual stress (Do and Smith)
Repeat 1/2 model Aster without residual stress
Repeat 1/2 model Aster with residual stress
1/2 model Aster without residual stress (Sutham)
1/2 model Aster with residual stress (Sutham)
1/2 model Abaqus without residual stress (Sutham)
1/2 model Aster with residual stress (Sutham)
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Results
• Notched crack used in both Code_Aster and ABAQUS
• Mesh M35 (35 segments at the crack front)
• This corresponds to element sizes of 0.15mm at crack tip
• Energy release rate around the crack calculated at fixed distance ahead of crack tip (G(θ) and J)
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Results
• For elastic conditions Code_Aster and ABAQUS are in good agreement (<2%)
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Results
• For elastic conditions Code_Aster and ABAQUS are in good agreement (<2%)
• Residual stress increases G and uncertainty but both software in good agreement (<5%)
• Code aster 2.5h,ABAQUS 3h
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Results
• For plastic conditions there is significant uncertainty between Code_Aster and ABAQUS (<10%)
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Results
• For plastic conditions there is significant uncertainty between Code_Aster and ABAQUS (<12%)
• Residual stress increases G and uncertainty but both software in good agreement (<15%)
• Significant impact on propagation behaviour
• Code aster 9h,ABAQUS 10h
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Results – Path Dependence Study
• Notched crack used in both Code_Aster and ABAQUS
• Mesh M35 (35 segments at the crack front)
• This corresponds to element sizes of 0.15mm
• Energy release rate around the crack calculated at fixed distance ahead of crack tip (G(θ) and J)
• Path dependence of G(θ) and J tested with increasing distance from crack tip
• For elastic conditions solutions using G(θ) method are stable and equivalent to J integral (<2%)
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Results – Path Dependence Study
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Results – Path Dependence Study
• For elastic conditions solutions using G(θ) method are stable and equivalent to J integral (<2%)
• Residual stresses do not affect the stability of the energy release rate in the relevant domain ahead
of the crack
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Results – Path Dependence Study
• For plastic conditions solutions using G(θ) method are unstable and differ to J integral (<40%)
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Results – Path Dependence Study
• For plastic conditions solutions using G(θ) method are unstable and differ to J integral (<40%)
• Residual stresses exacerbate instability of solution
• Large discrepancy in both software with respect to crack propagation
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
• The assumption actually does not describe irreversible plastic deformation but hyper-elastic or non-
linear elastic behaviour.
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
• The assumption actually does not describe irreversible plastic deformation but hyper-elastic or non-
linear elastic behaviour.
• It excludes any local unloading processes but also any local re-arrangement of local stress
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
• The assumption actually does not describe irreversible plastic deformation but hyper-elastic or non-
linear elastic behaviour.
• It excludes any local unloading processes but also any local re-arrangement of local stress
• All loading paths in the stress space are supposed to remain radial so that the ratios of principal
stresses do not change with time.
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
• The assumption actually does not describe irreversible plastic deformation but hyper-elastic or non-
linear elastic behaviour.
• It excludes any local unloading processes but also any local re-arrangement of local stress
• All loading paths in the stress space are supposed to remain radial so that the ratios of principal
stresses do not change with time.
• The condition of monotonous global loading of a structure is of course not sufficient to guarantee radial
stress paths in non-homogeneous stress fields.
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Results – Theoretical Explanation
THEORETICAL EXPLANATION
• Limitation of G results from the assumed existence of a strain energy density, as a potential from which
stresses can be uniquely derived.
• The assumption actually does not describe irreversible plastic deformation but hyper-elastic or non-
linear elastic behaviour.
• It excludes any local unloading processes but also any local re-arrangement of local stress
• All loading paths in the stress space are supposed to remain radial so that the ratios of principal
stresses do not change with time.
• The condition of monotonous global loading of a structure is of course not sufficient to guarantee radial
stress paths in non-homogeneous stress fields.
• Current solid mechanics methodologies require further research to better account for plasticity effects
under deformation
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Results – Potential Solutions
• A path independent Jmod is described in literature for initial strains
• This method is appropriate for non-proportional monotonic loading
• Method is not implemented in any FE software
𝐽𝑚𝑜𝑑 = Γ
𝜎𝑖𝑗𝜕𝑢𝑗𝜕𝑥𝑖
−𝑊𝛿1𝑖 𝑛𝑖𝑑𝑠 + 𝐴
𝜎𝑖𝑗𝜕휀𝑗𝜕𝑥1
−𝜕𝑊
𝜕𝑥1𝑑𝐴
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Results – Potential Solutions
• A path independent Jmod is described in literature for initial strains
• This method is appropriate for non-proportional monotonic loading
• Method is not implemented in any FE software
𝐽𝑚𝑜𝑑 = Γ
𝜎𝑖𝑗𝜕𝑢𝑗𝜕𝑥𝑖
−𝑊𝛿1𝑖 𝑛𝑖𝑑𝑠 + 𝐴
𝜎𝑖𝑗𝜕휀𝑗𝜕𝑥1
−𝜕𝑊
𝜕𝑥1𝑑𝐴
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Results – Potential Solutions
𝐽𝑚𝑜𝑑 = Γ
𝜎𝑖𝑗𝜕𝑢𝑗𝜕𝑥𝑖
−𝑊𝛿1𝑖 𝑛𝑖𝑑𝑠 + 𝐴
𝜎𝑖𝑗𝜕휀𝑗𝜕𝑥1
−𝜕𝑊
𝜕𝑥1𝑑𝐴
𝐺𝑚𝑜𝑑(𝜃) = Ω
𝜎𝑖𝑗𝜕𝑢𝑗𝜕𝑥𝑖
𝜕𝜃
𝜕𝑥𝑖− 𝜔𝑑𝑖𝑣𝜃 𝑑Ω +
Ω
𝜎𝑖𝑗𝜕휀𝑗𝜕𝑥1
𝜃 −𝜕𝜔
𝜕𝑥1𝜃 𝑑Ω
• A path independent Jmod is described in literature for initial strains
• This method is appropriate for non-proportional monotonic loading
• Method is not implemented in any FE software
• Existing G(θ) can be re-written in the same form as Jmod• OpenSource nature of Code_Aster is easy to develop and allows new methods to be implemented
• EDF R&D are developing an operator based on Jmod in Code_Aster during 2017
1. Background and motivation
2. Experimental setup
3. Numerical methods
4. Results
5. Conclusions
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
Systematic models of the experiment were built in Code_Aster to assess
energy release rate of cracks in a residual stress field
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
Systematic models of the experiment were built in Code_Aster to assess
energy release rate of cracks in a residual stress field
Code_Aster performs comparably to commercial FE software in the realm of
elasticity
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
Systematic models of the experiment were built in Code_Aster to assess
energy release rate of cracks in a residual stress field
Code_Aster performs comparably to commercial FE software in the realm of
elasticity
Some discrepancies found in G computation in the realm of plasticity
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
Systematic models of the experiment were built in Code_Aster to assess
energy release rate of cracks in a residual stress field
Code_Aster performs comparably to commercial FE software in the realm of
elasticity
Some discrepancies found in G computation in the realm of plasticity
G(θ) method can be extended to account for initial strains following the method of Lei in Jmod
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Conclusions
To better understand the Heysham (AGR) incident the STYLE project was
revisited
Systematic models of the experiment were built in Code_Aster to assess
energy release rate of cracks in a residual stress field
Code_Aster performs comparably to commercial FE software in the realm of
elasticity
Some discrepancies found in G computation in the realm of plasticity
G(θ) method can be extended to account for initial strains following the method of Lei in Jmod
This project has led to the development of Jmod based operator in Code_Aster
by EDF SA in 2017