A fast efficient multi-scale approach to modelling the development - PowerPoint PPT Presentation

A fast efficient multi-scale approach to modelling the development of hydride microstructures at the component level in zirconium alloys Hydrogen Diffusion and Hydride Precipitation in Zirconium Mitesh Patel † , Luca Reali † , Adrian P Sutton, Daniel S Balint and Mark R Wenman* † Theory and Simulation of Materials † Departments of Physics, Mechanical Engineering and Materials † Imperial College London ∗ Email : m.wenman@imperial.ac.uk

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE CONTEXT Component Scale Macroscopic Scale Mesoscopic Scale Figure : Cross-sectional schematic of a PHWR nuclear fuel pin clad. Microscopic Scale Mitesh Patel 2

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE RESEARCH AIMS Component Scale Macroscopic Scale Mesoscopic Scale Figure : A simplified stage-by-stage breakdown of DHC. Microscopic Scale Mitesh Patel 3

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE HYDRIDES IN ZIRCONIUM Component Scale Macroscopic Scale Source: [Bailey (1963)], [Perovic Source: [Carpenter (1973)] (1983)] Hydrostatic stress/GPa Opening stress/GPa 5 Mesoscopic Scale 0 -5 Source: [Patel (2017)] Figure : Micro-hydride needles and macro-hydride structures in zirconium . Microscopic Scale Mitesh Patel 4

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE HYDRIDES IN ZIRCONIUM Component Scale Macroscopic Scale Mesoscopic Scale Source: [Patel ( 2019 )] Source: [Carpenter (1973)] Figure : The hydride represented as a continuous distribution of dislocations, leading to the dislocation dipole approximation. Microscopic Scale Mitesh Patel 5

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE THE DI SLOCATION DIPOLE APPROXIMATION Component Scale Macroscopic Scale Mesoscopic Scale ρ 22 Microscopic Scale Figure : Co ntinuous distribution s of dislocations and relative dipole approximation. Mitesh Patel 6

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE A DISCRETE DISLOCATION SUBMODEL Source: [Patel (2017)] Component Scale Macroscopic Scale Figure : The stress of a hydride can induce plasticity in its neighbourhood. The discrete dislocation simulation investigates effects of multiple dissolution-reprecipitation cycles. Mesoscopic Scale ρ 22 Figure : Once it has dissolved, the hydride leaves behind a tensile region that is likely Microscopic Scale to aid subsequent hydride nucleation ("memory effect"). Mitesh Patel 7

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE MODELS OF DELAYED HYDRIDE CRACKING Component Scale Macroscopic Scale Source: [Cui (2009)] Source: [Cui (2009)] Figure : Micrographs of notch-tip hydride patterns. Mesoscopic Scale Feature Finite Element Phase-Field Present Work Diffusion ✓ ✓ ✓ Precipitation ✓ ✓ ✓ Macro-Hydrides ✗ ✓ ✓ Micro-Hydrides ✗ ✓ ✓ Texture ✗ ✗ ✓ Simulation Speed Hours–Days Hours–Days Seconds–Minutes Microscopic Scale Mitesh Patel 8

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE MODELS OF DELAYED HYDRIDE CRACKING Component Scale DFT : Density Functional Theory MD : Molecular Dynamics QPF : Quantitative Phase Field Macroscopic Scale FEM : Finite Element Method Adapted from : [ Kim ( 2007 )] Figure : Modelling techniques and typical lengthscales compared to the component size . Mesoscopic Scale Feature Finite Element Phase-Field Present Work Diffusion ✓ ✓ ✓ Precipitation ✓ ✓ ✓ Macro-Hydrides ✗ ✓ ✓ Micro-Hydrides ✗ ✓ ✓ Texture ✗ ✗ ✓ Simulation Speed Hours–Days Hours–Days Seconds–Minutes Microscopic Scale Mitesh Patel 8

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE MODELLING STRATEGY Component Scale Input Methods Notch geometry Planar elasticity Texture Voronoi tesselation Macroscopic Scale Thermomechanical Thermodynamics cycle Classical nucleation Mesoscopic Scale Diffusion Output Precipitation Hydrogen profile Hydride distribution Figure : Flowchart of simulation. Microscopic Scale Mitesh Patel 9

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE STRESS-DRIVEN DIFFUSION Component Scale Macroscopic Scale Mesoscopic Scale Source: [ El Chamaa ( 2018 )] Figure : A tethrahedral interstice in Figure : Stresses develop at notches. Zr, wherein the dipole tensor ρ ij is In the model, the theory of distributed defined. dislocations yields analytical expressions for a variety of geometries. Microscopic Scale Mitesh Patel 10

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE DIFFUSION-CONTROLLED PRECIPITATION Component Scale Macroscopic Scale Mesoscopic Scale ρ 22 Source: [Patel ( 2019 )] Figure : Implementation of nucleation sites within a mass balance approach. Microscopic Scale Mitesh Patel 11

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE DIFFUSION-CONTROLLED PRECIPITATION Component Scale Macroscopic Scale Mesoscopic Scale ρ 22 Source: [Patel ( 2019 )] Figure : Implementation of nucleation sites within a mass balance approach. Microscopic Scale Mitesh Patel 11

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE DIFFUSION-CONTROLLED PRECIPITATION Component Scale Macroscopic Scale Mesoscopic Scale Source: [Patel ( 2019 )] Figure : Model formulation for diffusion-controlled hydride precipitation. Microscopic Scale Mitesh Patel 1 2

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE THE AUTOCATAL Y TIC MECHANISM Component Scale Macroscopic Scale Mesoscopic Scale Source: [Patel ( 2019 )] Figure : The resulting macro- Figure : The autocatalytic nucleation: hydide and its deck-of-cards nucleation sites are added so that the global structure. Flexibility of ϕ leads to elastic energy is minimised with respect to ϕ . local stress reorientation . Microscopic Scale Mitesh Patel 1 3

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE COMPUTATIONAL GEOMETE T RY Component Scale Macroscopic Scale Mesoscopic Scale ρ 22 Figure : Hydride colonies reaching grain boundaries and allowed stacking configurations and are dealt with using computational geometry: the polygon-line segment intersection (PLSI) and the line segment intersection (LSI) algorithms. Microscopic Scale Mitesh Patel 14

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE SIMULATION METHODOLOGY Component Scale Macroscopic Scale Mesoscopic Scale Source: [Patel ( 2019 )] Figure : The architecture of the code . Microscopic Scale Mitesh Patel 1 5

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE THE REORIENTATION EFFECT 10 100 Component Scale 80 8 60 Macroscopic Scale 6 σ yy (x 1 , x 2 )/GPa c(x 1 , x 2 )/c 0 40 4 20 Mesoscopic Scale 2 0 0 -20 0 5 10 15 20 0 5 10 15 20 Microscopic Scale Figure : Elastochemical and mechanical equilibrium state. Mitesh Patel 1 6

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE HYDRIDE MORPHOLOGICAL EVOLUTION 100 10 Component Scale 80 8 60 Macroscopic Scale 6 σ yy (x 1 , x 2 )/GPa c(x 1 , x 2 )/c 0 40 4 20 Mesoscopic Scale 2 0 -20 0 0 5 10 15 20 0 5 10 15 20 Microscopic Scale Figure : Simulating micro-hydride needles and macro-hydride structures. Mitesh Patel 1 7

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE MICRO-HYDRIDE STACKING 10 Component Scale 8 6 Macroscopic Scale c(x 1 , x 2 )/c 0 Initial Concentration: 100.00 ppm 4 Mesoscopic Scale 2 0 0 500 1000 Microscopic Scale Figure : Formation of macoscopic hydride features. Mitesh Patel 10 November 2017

Multiscale Modelling of Delayed Hydride Cracking Rolls-Royce plc EXPERIMENTAL SCALE NOTCH-TIP MACRO-HYDRIDE FEATURES 10 10 Component Scale 8 8 6 6 Macroscopic Scale c(x 1 , x 2 )/c 0 c(x 1 , x 2 )/c 0 Initial Concentration: 100.00 ppm Initial Concentration: 100.00 ppm 4 4 Mesoscopic Scale 2 2 0 0 0 500 1000 0 500 1000 Figure : Formation of macoscopic hydride features for different notch geometries. Microscopic Scale Mitesh Patel 11 November 2017

Rolls-Royce plc November 2017 Figure : Formation of macoscopic hydride features with more realistic grain sizes. [Cui (2009)] Source: SIMULATED MICROGRAPHS 12 [Cui (2009)] Multiscale Modelling of Delayed Hydride Cracking Source: EXPERIMENTAL SCALE Macroscopic Scale Mitesh Patel Component Scale Mesoscopic Scale Microscopic Scale