FRACTURE MODELS FOR RPV AND FOR THE IASCC OF INTERNALS

Task leader: Peter James (Wood) Contributing partners: Wood, CEA, EDF, AR-G, JRC

07/05/2018 SOTERIA Mid-Term Workshop – 9-10 & 12 April. 2018 1

Fracture Models for RPV • To consider final stage of multi-scale modelling – fracture; Review effect of crack-tip plasticity on cleavage fracture models, Improve understanding of variation / outlying results, Further experimental validation / comparison of models.

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Specific objectives [I]

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2,5E-9 5,3E-8 1,0E-7 1,5E-7 2,0E-7 2,5E-7 3,0E-7 3,5E-7

Frac

tion

of c

arbi

de s

ize

in ra

nge

(%)

r (m)

MxC

Carbide Distributions

Tensile Curves

Fracture Models for Internals • To further develop physically based models to encapsulate physical

understanding of current IASCC processes; Update models (e.g. INITEAC) to include understanding from elsewhere

within SOTERIA, Further develop local/grain sized modelling approaches to allow improved

modelling of IASCC processes.

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Specific objectives [II]

Di5.1 – Treatment of plasticity in existing fracture models (CEA) [M12]

• Provide an overview of the way that plasticity is included in existing fracture models.

• This will be used to provide advice on potential modifications.

Di5.4 – Prediction of crack-tip stress fields and adaptation of fracture models (EDF, CEA) [M24]

• Consider detailed, state-of-the-art, assessment of the crack-tip stress fields and the effects of plasticity.

• This will be used to update the Beremin model developed in Perform 60 which may allow a modified Weibull type expression.

D5.4 - Effect of localised heterogeneities on cleavage fracture (Wood, CEA, AR-G) [M42]

• Consider comparisons against available validation data. • Effect of spatial heterogeneity of carbides. • Look at outlying results and see if models are able to capture this within

expected variations of material properties.

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Outputs - RPV

Di5.2 – Prediction of stress fields and their influence on IASCC (CEA,

JRC) [M24] • Review work to understand stress fields at/between grain boundaries and

potential influence on grain boundary cracking.

Di5.6 – Effect of grain boundary on fracture (CEA, EDF) [M36] • Further develop approaches to model grain boundary fracture methods when

incorporating IASCC phenomena.

D5.3 – Integration of INITEAC updated code in the platform (Wood) [M36]

• Update INITEAC code for IASCC initiation and crack growth to enable the model to incorporate developed understanding from SOTERIA modelling and testing.

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Outputs - Internals

Good progress on tasks and links to Platform

Further work on the information about the comparative material for LA models

Some specific aspects detailed over following slides..

Technical Work Achieved

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Di5.1 – Treatment of plasticity in existing fracture models

This deliverable conducted a review of different brittle fracture models while focussing on different items:

• How do they model the nucleation of the micro-defects that will lead to cleavage?

• How do they model the propagation of these micro-defects towards a macroscopic crack?

• How are the initiation sites for these micro-defects modelled?

• What role does plastic strain play in the various assumptions of the model?

Treatment of Plasticity in Cleavage LA Models (Di5.1)

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Carbide size distribution Nucleation Propagation

Non explicit power law β/rα

Beremin

Mod Beremin

Bernauer CN

Bernauer DBT

Bordet

Plasticity induced

All Griffith All except Promethey

Carbide strength

distribution

Promethey Deterministic propagation

Promethey

Continuous nucleation

Bordet Truncating Bordet

Explicit asymptotic power law

MIBF Continuous nucleation

Bernauer CN Blunting JFJ

Energy density WST

Lee MIBF Energy density JFJ

Jayatilaka WST

MIBF

Debonding of carbides

Bernauer DBT

Ortner JFJ

MIBF

(Mathieu)

Ductile propagation

GTN Bernauer DBT

Crystal plasticity

Normalized power law

MIBF Bainitic microstructure MIBF

Explicit carbide population

Mathieu Explicit bainitic microstructure Mathieu

It has been shown than all models developed in PERFORM60 are compatible with the MIBF model (which also allows crystal plasticity to be considered).

Simulation of Charpy Tests

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Modelled Charpy test with elastic-viscoplastic behaviour for brittle fracture and post-processing for cleavage with Beremin model

Probability of failure 𝐏𝐏𝐟𝐟 vs. 𝐭𝐭 for different 𝐓𝐓

DBTT curve Range of assumptions for material properties

Promising results, and good prediction of ∆T Have included to platform Looking to introduce the model of the

ductile tearing with the use of Gurson model to be able to construct the full DBTT curve (in process)

To consider variation in the material initiating particles and their impact on fracture toughness. Probabilistic assessments considering localised variation in the calibration parameters of the brittle fracture model(s).

Successful use of Beremin and JFJ LA models in a deterministic and probabilistic methods.

For materials selected within the programme (parent and weld).

Monte Carlo Implementation of LA Models (towards D5.4 – M42)

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Deterministic

Probabilistic

UH

IL

FE runs using a range of tensile properties were performed.

JFJ model applied to these to investigate the effect of varying the tensile properties.

Applied to parent reference material so far, intend to apply to weld.

Effect of variation in Tensile Properties on Predictioned Toughness (towards D5.4 – M42)

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To provide experimental data on void growth and coalescence in irradiated materials. These data would also be useful to calibrate constitutive equations for irradiated austenitic stainless steels.

Ion-irradiated thin tensile samples - Focused Ion Beam (FIB) drilling of cylindrical holes. SEM observations of the evolution of void dimensions under tensile loading.

Strong dependence of void deformation to crystallographic orientations. Strong influence of activated slip systems on void coalescence. Now in position to progress to stainless steel experiments.

Void Growth and Coalescence

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CP constitutive law of neutron-irradiated SS applied to large polycrystalline aggregates. This will provide grain and GB stresses at different dpa levels and link to IASCC.

Data sets, curtsey of UoM: Wire_1: 378 grains, 2276 grain boundaries. Wire_2: 1429 grains, 8882 grain boundaries.

Stress fields in large aggregates obtained. Inconsistency: Wire_1 stiffer response versus Wire_2 – further investigations in-hand. Distributions to feed into INITEAC for improved estimate of IASCC.

Stress Fields in Large Poly-Crystalline Aggregates

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INITEAC (I) (INITiation modelling for Environmentally-Assisted Cracking)

Predicts nucleation, propagation and coalescence of IGSCC & IASCC

Continuum scale modelling (2.5 D) The model continually assesses:

• Likelihood of crack nucleation • Where cracks occur • Rates of small and long crack growth • Crack coalescence

Capable of modelling SCC by internal oxidation or slip dissolution

Parameters • User configurable GB properties (grain info, Si, Cr) • User configurable rules by which GB properties affect damage

propagation on GB’s • Stochastic crack development • Input: time profile of stress • Outputs: Crack maps & histogram of crack lengths

INITEAC (II) – Typical Results Test results plotted in space defined by test stress / yield for different fluence’s. Open symbols no cracking observed. Cracking seen in closed symbols.

INITEAC:

•Low dose threshold slope reproduced •Reduced threshold slope at higher dose

Original plotted data from SCK-CEN/CEA P60 D2-1.7

Complete agreed actions and progress work on remaining deliverables:

• Di5.6 – Effect of grain boundary on fracture (CEA, EDF) [M36] • D5.3 – Integration of INITEAC updated code in the platform (Wood) [M36] • D5.4 - Effect of localised heterogeneities on cleavage fracture (Wood, CEA,

AR-G) [M42]

Further develop INITEAC code (feeds into D5.3, plus updates).

• The approach for this has been discussed. • INITEAC will also be included within the platform.

Comparisons of LA models applied to Reference Case materials (feeds into D5.4).

Continue support PhD work to void growth (D2.3). Continue to support platform/workshops/teaching etc.

Future Plans

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