Numerical Simulations of Coarsening of Lamellar Structures: Applications to metallic alloys
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Numerical Simulations of Coarsening of Lamellar Structures: Applications to metallic alloys Rifa J. El-Khozondar 1, Hala J. El-Khozondar 2 1 Department of Physics, Al-Aqsa University, Gaza 2 Department of Electrical Engineering, Islamic University, Gaza ABSTRACT Understanding the microstructural evolution in metallic alloys helps to control their properties and improve their performance in industrial applications. The emphasis of our study is the coarsening mechanisms of lamellar structures. Coarsening of lamellar structure is modeled numerically using Monte Carlo Potts method. The initial microstructure consists of alternating lamellae of phase A and phase B with the spacing proportional to their volume fraction. Faults are introduced to the lamellae to induce instability in the system. We find that an isotropic lamellar structure degenerates via edge spheroidization and termination migration into nearly equiaxed grains with a diameter which is 2 to 3 times larger than the original lamellar spacing. The duration of this process is comparable with the time it would take Ostwald ripening to produce grains of the same size. Eventually grain growth reaches the asymptotic regime of coarsening described by a power-law function of time. Lamellae with anisotropic grain boundaries coarsen more slowly and via discontinuous coarsening mechanism. This produces larger grains upon degeneration of lamellae. Discontinuous coarsening was observed in lamellar alloys as well as termination migration.
INTRODUCTION Microstructural evolution due to aging determines the long-term reliability of materials in practical applications. The ability to control the properties of materials and enhance their performance depends upon the development of material models. Various numerical models have been developed to simulate the microstructural evolution of materials. The simulation methods can be classified into four specific groups [1]. The first one is made up of Voronoi [2] and modified Voronoi [3, 4] methods. The second contains curvature-driven grain growth [5, 6, 7, 8] simulations, followed by continuum thermodynamics methods such as finite different solutions of the Cahn-Hilliard equation, phase field models [9], and diffusion equation [10, 11, 12]. The last one consists of cellular automata models. Each of these simulations will be summarized briefly. Voronoi and modified Voronoi techniques simulate grain microstructures in two dimensions by defining nucleation rates and grain boundary velocity. The nucleated grain growth continues until the grains impinge on other growing grains. Although theses methods are applicable to the study of nucleation and growth conditions, they fail to give kinetic information. Curvature-driven grain growth simulations are based on the relationship between the grain boundary curvature and its velocity. In this method, discrete segments of the grain boundary are moved with velocities proportional to their curvature. Line tension and vertex driven techniques [13] suppose straight line boundaries which e
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