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Modelling the effect of SiC particle size on crystallization of magnesium metal matrix composite; AZ91/SiC

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Grain size is one of the most important structural characteristic that determining mechanical properties. Knowing element properties, the proper application regions for it can be chosen to achieve best mechanical properties and performance. Nowadays simulation software can be use to predict the element microstructure. Those programs base on micro-macro model of crystallization. The model consists of partial differential equations (PDEs) that describe the nucleation rate, diffusion in the casting, casting cooling speed and every single grain growth rate. Often it is hard to find the theoretical value of the parameters that appear in those PDEs. It is possible to find them from experiment. The experimental data after applying statistical methods let us find approximated values of the so-called “fitting parameters" in the mentioned models [1÷4]. AZ91 alloy analyzed in this study is hypereutectic alloy. The magnesium primary α-Mg phase is dendritic. During crystallisation there appears eutectic reaction. In this study influence of eutectic is omitted because magnesium primary phase microstructure has most significant influence on mechanical properties of the casting. Model description In the mathematical model it is assumed that heat transfer is governed by Fourier-Kirchhoff (FK) equation: ∂ ∂T = - + c q p cp div gradT τ ρ ρ 1 ( λ ) , (1) where: T, K - is temperature, τ, s - time; cp, J·kg-1·K-1 - specific heat, ρ, kg·m-3 - density, λ, W·m-1·K-1 - thermal conductivity, q = L(dfs/dτ), W·kg-1 - heat of crystallization. During simulation the temperature change speed is calculated. Its value consists of two parts: one, that depends on the temperature gradient and second that is phase change effect. In this article there is an assumption that simulation runs in one element of the melt. With this assumption the gradient depend part of FK can [...]

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