Papers by Keyword: Finite Difference Modeling

Abstract: A three-dimensional numerical analysis was conducted to investigate the effects of a new shield tunnel excavation on the internal forces and deformation induced in an existing parallel tunnel and soil plastic zones around it. Special attention was paid to the influence of relative positions between two tunnels. The results of the analysis show that the relative positions affect the mechanical behavior of the existing parallel tunnel and the soil mass behavior around it. When a new tunnel is driven below or above an existing parallel tunnel, important increments are induced in deformation and bending moment in the lining of existing tunnel at its crown and springline, compared to that of induced by new tunnel excavation in horizontally parallel to the existing one. The plastic zones around tunnels also extend larger when tunnels are driven in vertically parallel than they are in horizontally parallel. For the safety concern, it is concluded that horizontally parallel configuration model between two tunnels should be adopted in practice.

Abstract: The presence of the residual element copper in recycled steels causes a surface cracking phenomenon during thermo-mechanical processing which is known as “hot shortness”. The cracks result from a copper-rich liquid that forms at the oxide/metal interface and subsequently embrittles austenite grain boundaries. Minimizing formation of the liquid phase would reduce or eliminate cracking. Thus, the evolution of the liquid layer is an important consideration when designing an optimal thermomechanical processing cycle in scrap-based steel plants. The time evolution of the liquid phase is dependent on the competing processes of enrichment rate due to iron oxidation and the rate of copper back-diffusion into the steel. This paper presents a fixed grid finite difference model that predicts the evolution of the enriched region as a result of a given oxidation kinetics and solution of Fick’s 2nd law. The model predictions are in agreement with measured data for the case of an iron alloy containing 0.3 wt% copper oxidized in air at 1150°C. Model predictions indicate that initial copper content, oxidation kinetics, and alloy microstructure (i.e. grain boundary diffusion) have the most significant influence on the copper-rich layer whereas the solubility increase due to nickel additions was not found to have an appreciable influence.

Abstract: A finite difference method based on control volume methodology and interface-tracking technique for simulation of rapid solidification accompanied by melt undercooling will be described and applied to analyze the solidification of alumina sample on copper substrate.