Dual Scale Simulation of Grain Growth Using a Multi Phase Field Model
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Dual Scale Simulation of Grain Growth Using a Multi Phase Field Model
Ingo Steinbach, Markus Apel ACCESS e.V. RWTH-Aachen ABSTRACT The kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and interfacial stress balance at the vertices of the grain boundaries. A comprehensive way to treat both effects in one model is given by the time dependent Ginzburg Landau model or phase field model. The paper presents the application of a multi phase field model, recently developed for solidification processes to grain growth of a multicrystalline structure. The specific feature of this multi phase field model is its ability to treat each grain boundary with its individual characteristics dependent on the type of the grain boundary, its orientation or the local pinning at precipitates. The pinning effect is simulated on the nanometer scale resolving the interaction of an individual precipitate with a curved grain boundary. From these simulations an effective pinning force is deduced and a model of driving force dependent grain boundary mobility is formulated accounting for the pinning effect on the mesoscopic scale of the grain growth simulation. 2-D grain growth simulations are presented.
INTRODUCTION Reduction of total free energy is the basic driving force of any phase transformation process. Based on this principle, the phase-field method has emerged as a method of choice to simulate microstructural evolution during materials processing [1–5]. The applications reach from the investigation of morphological instabilities e.g. dendritic growth [7-10] to structural phase transitions in solid-solid systems [11-13].The multi phase field method [14, 15] being a natural extension of the basic phase field concept to the interaction of more than two individual phases, is especially suited to simulate ripening effects and grain growth in solids. A serious demand to technical applications, however, is the incorporation of realistic models for grain boundary mobilities into the general framework of the multi-phase field method. These models may relay on various material constants and process conditions on one hand as well as on the specific solution of the grain growth problem like local curvature and velocity of grain boundaries and triple junctions. The paper summarizes shortly the underlying multi-phase field model and the selected model for grain boundary mobility. On the scale of secondary phase precipitates the interaction between particles and grain boundaries is calculated explicitly. In the case of a regular particle distribution the variation of drag force with particle density is predicted. In the case of random distribution the influence of this distribution on the effective drag force is discussed. From these examples an effective drag force dependent mobility is deduced for mesoscopic grain growth simulations.
AA7.14.1
THE MULTI-PHASE FIELD MODEL r
We consider a system of N field variables φα ( x ,t), α=1…N, 0RφαR1. These variables may be ident
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