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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




4. Results

5. Conclusions

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Background and Motivation


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


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




4. Results

5. Conclusions


Experimental Setup


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


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


A large-scale four point bending

test performed by CEA (France) as

part of the EU programme, STYLE

13m




4. Results

5. Conclusions


Numerical Methods – Overall Strategy


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


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



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



-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






4. Results

5. Conclusions



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


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)


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)


Results

• For elastic conditions Code_Aster and ABAQUS are in good agreement (<2%)


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


Results

• For plastic conditions there is significant uncertainty between Code_Aster and ABAQUS (<10%)


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


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%)





• 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



• For plastic conditions solutions using G(θ) method are unstable and differ to J integral (<40%)



• 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


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.











• 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


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










−𝜕𝑊

𝜕𝑥1𝑑𝐴







−𝜕𝑊

𝜕𝑥1𝑑𝐴

𝐺𝑚𝑜𝑑(𝜃) = Ω


𝜕𝜃

𝜕𝑥𝑖− 𝜔𝑑𝑖𝑣𝜃 𝑑Ω +

Ω


𝜃 −𝜕𝜔

𝜕𝑥1𝜃 𝑑Ω




• 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




4. Results

5. Conclusions



Conclusions

To better understand the Heysham (AGR) incident the STYLE project was

revisited


Conclusions


revisited

Systematic models of the experiment were built in Code_Aster to assess

energy release rate of cracks in a residual stress field


Conclusions


revisited



Code_Aster performs comparably to commercial FE software in the realm of

elasticity


Conclusions


revisited




elasticity

Some discrepancies found in G computation in the realm of plasticity


Conclusions


revisited




elasticity


G(θ) method can be extended to account for initial strains following the method of Lei in Jmod


Conclusions


revisited




elasticity


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


END!

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