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Curvature driven grain growth
Title slide INSERT AN IMAGE Right click on the image and choose ‘Format AutoShape’. Click on the arrow pointing down next to ‘Color’. Choose ‘Fill Efects’ and click on the tab ‘Picture’ Click on ‘Select picture’ and choose the picture you want. Click ‘Insert’ 1 2 3 4 Curvature-driven grain growth Bastiaan van der Boor Curvature driven grain growth TATA STEEL COLORS
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Curvature-driven grain growth
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Curvature-driven grain growth
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Curvature-driven grain growth
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1 2 3 4 5 Content Fundamentals Choosing the best method Implementation
Index slide USE THE INDEX Click on the index Edit the chapter numbers and titles Right-click on the rows to delete the rows you do not need and choose ‘Delete Rows’ 1 2 3 Insert rows Delete rows Curvature-driven grain growth Content 1 Fundamentals 2 Choosing the best method 3 Implementation 4 Results 5 Conclusion & Further Research SLIDE EXAMPLE
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Microstructure determines the mechanical properties of steel
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth PPT2003 PPT2000 Microstructure Microstructure determines the mechanical properties of steel Example of grain growth in a micro-structure of austenite at 1200°C SLIDE EXAMPLE
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Three processes that determines the micro-structure
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 7 PPT2003 PPT2000 Three processes that determines the micro-structure Goal of this master thesis is to extend the existing model of Tata Steel with grain growth by curvature Phase transformations Austenite to ferrite transformation Recrystallization & Recovery Austenite to austenite Grain growth by curvature SLIDE EXAMPLE T.B.D.
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The growth of metal grains is similar to soap bubbles
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 8 PPT2003 PPT2000 Soap froth The growth of metal grains is similar to soap bubbles SLIDE EXAMPLE
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circle which most closely approximates the curve near P
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 9 PPT2003 PPT2000 Curvature An arbitrarily simple, closed curve with a point P on it, there is a unique circle which most closely approximates the curve near P SLIDE EXAMPLE
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Triple points, where three grains meet
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 10 PPT2003 PPT2000 Triple points, where three grains meet Every triple point seeks it equilibrium state, which depends on the grain boundary energy γ SLIDE EXAMPLE Equilibrium if
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Two vertices determine the curvature of a grainboundary
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 11 PPT2003 PPT2000 Examples A grain with 6 corners is in equilibrium state if the angle is 120 degrees Two vertices determine the curvature of a grainboundary SLIDE EXAMPLE
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Structure of presentation
Graphic slide COPY THE SLIDE To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’ (shortcut: Ctrl+C). 1 2 Go back to your presentation and select ‘Paste’. (shortcut: Ctrl+V) 3 Select ‘Keep Sourcing Format’ when the Paste Options appear. Curvature-driven grain growth 12 Structure of presentation Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion
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CA model first developed by John von Neumann
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 13 PPT2003 PPT2000 Cellular Automata CA model first developed by John von Neumann SLIDE EXAMPLE Each cell has assigned a State Neighborhood definition Transformation rule
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Computational costly Counting cell method
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 14 PPT2003 PPT2000 Counting cell method Due to the sharp interface, interpolation is needed. Hence, a lot of calculations have to be made SLIDE EXAMPLE Computational costly
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Using vertices is the most efficient method to calculate the effect
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 15 PPT2003 PPT2000 Vertex method Using vertices is the most efficient method to calculate the effect of curvature Advantages SLIDE EXAMPLE Less points are needed to calculate Vertex points are most influential in the exact description of grain growth When more points are needed, virtual vertices can be added
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Three polygon have been constructed to test the different methods
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 16 PPT2003 PPT2000 Tests Three polygon have been constructed to test the different methods on their performance SLIDE EXAMPLE
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Comparing vertex methods
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 17 PPT2003 PPT2000 Comparing vertex methods The method by Lazar shows the best results SLIDE EXAMPLE Method Circle Neumann- Mullins n=6 NM, variable n, virtuals on a straight line NM variable n virtuals virtues on the circle Nippon + -- Kawasaki +/- ++ Lazar
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Comparing vertex methods
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 18 PPT2003 PPT2000 Comparing vertex methods Problem in Kawasaki: the connection of a triple point with a virtual vertex SLIDE EXAMPLE
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Structure of presentation
Graphic slide COPY THE SLIDE To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’ (shortcut: Ctrl+C). 1 2 Go back to your presentation and select ‘Paste’. (shortcut: Ctrl+V) 3 Select ‘Keep Sourcing Format’ when the Paste Options appear. Curvature-driven grain growth 19 Structure of presentation Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion
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Exact relation of grain growth
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 20 PPT2003 PPT2000 Exact relation of grain growth 2D Neumann-Mullins (1956) revived by expansion to 3D in 2007 by MacPherson and Srolovitz 2D: Neumann-Mullins SLIDE EXAMPLE Closed curve, enclosing area grows with the same rate Growth of a grain enclosed by others:
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Lazar method based on Neumann-Mullins
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 21 PPT2003 PPT2000 Lazar method based on Neumann-Mullins Governing equation of a virtual vertex (arbitrary point between only two grains) and triple points, satisfy Neumann-Mullins relation SLIDE EXAMPLE
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Hybrid Cellular Automata – Lazar model
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 22 PPT2003 PPT2000 Hybrid Cellular Automata – Lazar model Overview Triples SLIDE EXAMPLE Virtual vertex CA model Lazar T-changes Grains Edges Extract Move by Lazar Place back information
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Structure of presentation
Graphic slide COPY THE SLIDE To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’ (shortcut: Ctrl+C). 1 2 Go back to your presentation and select ‘Paste’. (shortcut: Ctrl+V) 3 Select ‘Keep Sourcing Format’ when the Paste Options appear. Curvature-driven grain growth 23 Structure of presentation Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion
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Moving an isolated grain with three edges
Curvature-driven grain growth Results Moving an isolated grain with three edges
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Average grain growth of grains with different total number of triples
Curvature-driven grain growth Results Average grain growth of grains with different total number of triples
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Grainsize distribution for time t=0 and t=20
Curvature-driven grain growth Results Grainsize distribution for time t=0 and t=20
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Curvature-driven grain growth
Results Distribution of the number of triples belonging to a grain. For t=0 and t=20
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Successful implementation of 2D grain growth by curvature
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 32 PPT2003 PPT2000 Conclusion Successful implementation of 2D grain growth by curvature Lazar method has been chosen Hybrid CA-Lazar method has been implemented Microstructure behaves as expected To be considered: Improve step 3 placing back information Extend to 3D using McPherson & Srolovitz relation SLIDE EXAMPLE
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Grain growth by curvature
Title slide INSERT AN IMAGE Right click on the image and choose ‘Format AutoShape’. Click on the arrow pointing down next to ‘Color’. Choose ‘Fill Efects’ and click on the tab ‘Picture’ Click on ‘Select picture’ and choose the picture you want. Click ‘Insert’ 1 2 3 4 Curvature-driven grain growth Bastiaan van der Boor Grain growth by curvature TATA STEEL COLORS
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Governing equations of a triple point, who satisfy the Neumann-
Colored bar - 100% text TEXT LEVELS Curvature-driven grain growth 34 PPT2003 PPT2000 Neumann-Mullins (3/3) Governing equations of a triple point, who satisfy the Neumann- Mullins relation SLIDE EXAMPLE
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Structure of presentation
Graphic slide COPY THE SLIDE To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’ (shortcut: Ctrl+C). 1 2 Go back to your presentation and select ‘Paste’. (shortcut: Ctrl+V) 3 Select ‘Keep Sourcing Format’ when the Paste Options appear. Curvature-driven grain growth 35 Structure of presentation Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion
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