Curvature-driven grain growth Tata Steel Bastiaan van der Boor Curvature driven grain growth Slide Curvature-driven grain growth Tata Steel Slide 2 Curvature-driven grain growth Tata Steel Slide 3 Curvature-driven grain growth Tata Steel Slide 4 Curvature-driven grain growth Tata Steel Content 1 Fundamentals 2 Choosing the best method 3 Implementation 4 Results 5 Conclusion & Further Research Slide 5 Curvature-driven grain growth Tata Steel Microstructure Microstructure determines the mechanical properties of steel Example of grain growth in a micro-structure of austenite at 1200°C Slide 6 Curvature-driven grain growth Tata Steel Slide 7 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 1. Phase transformations • Austenite to ferrite transformation 2. Recrystallization & Recovery • Austenite to austenite 3. Grain growth by curvature • Austenite to austenite T.B.D. Curvature-driven grain growth Tata Steel Soap froth The growth of metal grains is similar to soap bubbles 2g v = aM R Slide 8 Curvature-driven grain growth Tata Steel Slide 9 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 1 R Curvature-driven grain growth Tata Steel Slide 10 Triple points, where three grains meet Every triple point seeks it equilibrium state, which depends on the grain boundary energy γ 12 13 23 Equilibrium if i 120 i 1,2,3 Curvature-driven grain growth Tata Steel Slide 11 Examples A grain with 6 corners is in equilibrium state if the angle is 120 degrees Two vertices determine the curvature of a grainboundary Tata Steel Curvature-driven grain growth Slide 12 Structure of presentation Choosing the method Implementation Results Conclusion Cellular Automata Lazar Topological change Vertex Methods Nippon Hybrid CA Lazar model Example of a microstructure Kawasaki Lazar Curvature-driven grain growth Tata Steel Cellular Automata CA model first developed by John von Neumann Each cell has assigned a State Neighborhood definition Transformation rule Slide 13 Tata Steel Curvature-driven grain growth Counting cell method Due to the sharp interface, interpolation is needed. Hence, a lot of calculations have to be made Computational costly Slide 14 Curvature-driven grain growth Tata Steel Slide 15 Vertex method Using vertices is the most efficient method to calculate the effect of curvature Advantages 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 Curvature-driven grain growth Tata Steel Tests Three polygon have been constructed to test the different methods on their performance Slide 16 Tata Steel Curvature-driven grain growth Slide 17 Comparing vertex methods The method by Lazar shows the best results Method Nippon Circle Neumann- NM, variable n, virtuals Mullins n=6 on a straight line NM variable n virtuals virtues on the circle + -- -- -- Kawasaki +/- ++ + -- Lazar ++ ++ ++ ++ Curvature-driven grain growth Tata Steel Slide 18 Comparing vertex methods Problem in Kawasaki: the connection of a triple point with a virtual vertex Tata Steel Curvature-driven grain growth Slide 19 Structure of presentation Choosing the method Implementation Results Conclusion Cellular Automata Lazar Topological change Vertex Methods Nippon Hybrid CA Lazar model Example of a microstructure Kawasaki Lazar Tata Steel Curvature-driven grain growth Exact relation of grain growth 2D Neumann-Mullins (1956) revived by expansion to 3D in 2007 by MacPherson and Srolovitz 2D: Neumann-Mullins Closed curve, enclosing area grows with the same rate Growth of a grain enclosed by others: dA M (6 n) dt 3 Slide 20 Curvature-driven grain growth Tata Steel 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 dA M (6 n) dt 3 Slide 21 Tata Steel Curvature-driven grain growth Slide 22 Hybrid Cellular Automata – Lazar model Overview Triples ① Virtual vertex CA model Lazar Grains Edges ③ ① Extract ② Move by Lazar ③ Place back information ② T-changes Tata Steel Curvature-driven grain growth Slide 23 Structure of presentation Choosing the method Implementation Results Conclusion Cellular Automata Lazar Topological change Vertex Methods Nippon Hybrid CA Lazar model Example of a microstructure Kawasaki Lazar Curvature-driven grain growth Tata Steel Results Moving an isolated grain with three edges Slide 24 Tata Steel Slide Tata Steel Slide Tata Steel Slide Tata Steel Slide Curvature-driven grain growth Tata Steel Results Average grain growth of grains with different total number of triples Slide 29 Curvature-driven grain growth Tata Steel Results Grainsize distribution for time t=0 and t=20 Slide 30 Curvature-driven grain growth Tata Steel Slide 31 Results Distribution of the number of triples belonging to a grain. For t=0 and t=20 Curvature-driven grain growth Tata Steel 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 32 Curvature-driven grain growth Tata Steel Bastiaan van der Boor Grain growth by curvature Slide Curvature-driven grain growth Tata Steel Slide 34 Neumann-Mullins (3/3) Governing equations of a triple point, who satisfy the NeumannMullins relation e1 e2 vi Mt e1 e2 n i 1 0 1 e1 e2 vi 2Mt e e 1 0 2 3 i 1 2 1 3 2 3 Tata Steel Curvature-driven grain growth Slide 35 Structure of presentation Choosing the method Implementation Results Conclusion Cellular Automata Lazar Topological change Vertex Methods Nippon Hybrid CA Lazar model Example of a microstructure Kawasaki Lazar
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