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Bastiaan van der Boor

Title slide. Bastiaan van der Boor. Curvature driven grain growth. INSERT AN IMAGE. 1. 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 ’

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Bastiaan van der Boor

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  1. Title slide Bastiaan van der Boor Curvature driven grain growth INSERT AN IMAGE 1 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’ 2 3 4 Curvature-driven grain growth TATA STEEL COLORS

  2. Curvature-driven grain growth

  3. Curvature-driven grain growth

  4. Curvature-driven grain growth

  5. Index slide Content 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 SLIDE EXAMPLE

  6. Colored bar - 100% text Microstructure Microstructure determines the mechanical properties of steel Example of grain growth in a micro-structure of austenite at 1200°C TEXT LEVELS Curvature-driven grain growth PPT2003 PPT2000 SLIDE EXAMPLE

  7. Colored bar - 100% text Three processes that determines the micro-structure Phase transformations Austenite to ferrite transformation Recrystallization & Recovery Austenite to austenite Grain growth by curvature Austenite to austenite Goal of this master thesis is to extend the existing model of Tata Steel with grain growth by curvature TEXT LEVELS Curvature-driven grain growth 7 PPT2003 PPT2000 SLIDE EXAMPLE T.B.D.

  8. Colored bar - 100% text Soap froth The growth of metal grains is similar to soap bubbles TEXT LEVELS Curvature-driven grain growth 8 PPT2003 PPT2000 SLIDE EXAMPLE

  9. Colored bar - 100% text 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 TEXT LEVELS Curvature-driven grain growth 9 PPT2003 PPT2000 SLIDE EXAMPLE

  10. Colored bar - 100% text Triple points, where three grains meet Every triple point seeks it equilibrium state, which depends on the grain boundary energy γ TEXT LEVELS Curvature-driven grain growth 10 PPT2003 PPT2000 SLIDE EXAMPLE Equilibrium if

  11. Colored bar - 100% text Examples A grain with 6 corners is in equilibrium state if the angle is 120 degrees Two vertices determine the curvature of a grainboundary TEXT LEVELS Curvature-driven grain growth 11 PPT2003 PPT2000 SLIDE EXAMPLE

  12. Graphic slide Structure of presentation COPY THE SLIDE 1 To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’(shortcut: Ctrl+C). Cellular Automata Vertex Methods Nippon Kawasaki Lazar 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 Choosing the method Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion

  13. Colored bar - 100% text Cellular Automata CA model first developed by John von Neumann TEXT LEVELS Curvature-driven grain growth 13 PPT2003 PPT2000 SLIDE EXAMPLE Each cell has assigned a • State • Neighborhood definition • Transformation rule

  14. Colored bar - 100% text Counting cell method TEXT LEVELS Curvature-driven grain growth 14 PPT2003 PPT2000 Due to the sharp interface, interpolation is needed. Hence, a lot of calculations have to be made SLIDE EXAMPLE Computational costly

  15. Colored bar - 100% text Vertex method TEXT LEVELS Curvature-driven grain growth 15 PPT2003 PPT2000 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

  16. Colored bar - 100% text Tests TEXT LEVELS Curvature-driven grain growth 16 PPT2003 PPT2000 Three polygon have been constructed to test the different methods on their performance SLIDE EXAMPLE

  17. Colored bar - 100% text Comparing vertex methods TEXT LEVELS Curvature-driven grain growth 17 PPT2003 PPT2000 The method by Lazar shows the best results SLIDE EXAMPLE

  18. Colored bar - 100% text Comparing vertex methods TEXT LEVELS Curvature-driven grain growth 18 PPT2003 PPT2000 Problem in Kawasaki: the connection of a triple point with a virtual vertex SLIDE EXAMPLE

  19. Graphic slide Structure of presentation COPY THE SLIDE 1 To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’(shortcut: Ctrl+C). 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 Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion

  20. Colored bar - 100% text Exact relation of grain growth 2D Neumann-Mullins (1956) revived by expansion to 3D in 2007 by MacPherson and Srolovitz TEXT LEVELS Curvature-driven grain growth 20 PPT2003 PPT2000 2D: Neumann-Mullins SLIDE EXAMPLE • Closed curve, enclosing area grows with the same rate • Growth of a grain enclosed by others:

  21. Colored bar - 100% text 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 TEXT LEVELS Curvature-driven grain growth 21 PPT2003 PPT2000 SLIDE EXAMPLE

  22. Colored bar - 100% text Hybrid Cellular Automata – Lazar model TEXT LEVELS Curvature-driven grain growth 22 PPT2003 PPT2000 Overview Triples SLIDE EXAMPLE Virtual vertex CA model Lazar T-changes Grains Edges Extract Move by Lazar Place back information

  23. Graphic slide Structure of presentation COPY THE SLIDE 1 To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’(shortcut: Ctrl+C). 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 Choosing the method Cellular Automata Vertex Methods Nippon Kawasaki Lazar Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion

  24. Curvature-driven grain growth Results Moving an isolated grain with three edges

  25. Curvature-driven grain growth Results Average grain growth of grains with different total number of triples

  26. Curvature-driven grain growth Results Grainsize distribution for time t=0 and t=20

  27. Curvature-driven grain growth Results Distribution of the number of triples belonging to a grain. For t=0 and t=20

  28. Colored bar - 100% text Conclusion Successful implementation of 2D grain growth by curvature TEXT LEVELS Curvature-driven grain growth 32 PPT2003 PPT2000 • 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

  29. Title slide Bastiaan van der Boor Grain growth by curvature INSERT AN IMAGE 1 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’ 2 3 4 Curvature-driven grain growth TATA STEEL COLORS

  30. Colored bar - 100% text Neumann-Mullins (3/3) Governing equations of a triple point, who satisfy the Neumann- Mullins relation TEXT LEVELS Curvature-driven grain growth 34 PPT2003 PPT2000 SLIDE EXAMPLE

  31. Graphic slide Structure of presentation COPY THE SLIDE 1 To copy the graphic correctly, you need to copy the enitre slide. Select the slide in the overview and choose ‘Copy’(shortcut: Ctrl+C). Cellular Automata Vertex Methods Nippon Kawasaki Lazar 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 Choosing the method Implementation Lazar Hybrid CA Lazar model Results Topological change Example of a microstructure Conclusion

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