Modellierung und Simulation des Herstellungsprozesses thermisch und mechanisch hochbelasteter Bauteile aus faserverstärktem Siliziumkarbid
Zusammenfassung der Projektergebnisse
The phase-field model is presented in this research to predict the evolution of microstructures during the CVI process of SiC. The model consists of the Ginzburg-Landau equation, the modified mass conservation equation and the modified momentum conservation. A new form of the local free energy density is introduced to avoid the tendency of the phase-field parameter to overstep its limit [-1, 1] through the restriction of the minima of the local free energy density at the gaseous phase and solid phase. Meanwhile compared with the previous work, the Gibbs free energy take into account the influence of the concentration of the gaseous reactants. This initial attempt lies a foundation for the farther study of the description of the morphology distribution of the solid matrix Si, SiC and C from the pyrolysis of MTS. In the mass transport equation, the multicomponent diffusions are described with the Milke’s equation and both forward and reverse chemical reactions are considered to take into account the influence of by-product HCl. Both homogeneous process and heterogeneous process take place in the diffuse region, therefore the process intensities are introduced to describe the complex chemical processes in the diffuse region. The Navier-Stoke equation is used to describe the momentum transport during the CVI process with the interpolated physical parameters. A semi-discontinuous method is presented for the numerical approximation of this phase-field system. The implicit Euler backward formulations is implemented for the time discretization. The semi-discrete discontinuous Galerkin formulation of the phase-field system is deduced based on the weak formulation of it. The continuity and coercivity of the discontinuous Galerkin formulation are proven. Based on the uniqueness of the discontinuous Galerkin solution, the priori error analysis of the semi-discontinuous Galerkin approximation is derived as a function of mesh size, which is optimal in the size of meshment. The discontinuous Galerkin method has been performed for simulating the evolution of the 2D microstructure in the ICVI process of solid matrix SiC in the fiber axis. Two different preforms have been simulated to investigate the influence of the geometrical parameters on the evolution of microstructures.
Projektbezogene Publikationen (Auswahl)
- Phase-field model for deposition of pyrolytic carbon, Communications in Numerical Methods in Engineering 24(12): 2139-2154
A. V. Ekhlakov, S. Dimitrov, T.-A. Langhoff, E. Schnack
- Diffuse interface method for simulation of the chemical vapor deposition of pyrolytic carbon: Aspects of the mathematical formulation, Communications in Numerical Methods in Engineering, 24 (2008): 2155-2193
S. Dimitrov, A. Ekhlakov and T.-A. Langhoff
- Discontinuous Galerkin Solution in the Phase-Field Modeling in the ICVI Process of SiC, University Chemnitz, Germany, 28.11.2008
F. W. Wang, E. Schnack
- Discontinuous Galerkin Solution of Phase-Field Model with Convection in Isothermal Chemical Vapor Infiltration of SiC, Fraunhofer Institute for Chemical Technology, Karlsruhe, Germany, 15.07.2008
F. W. Wang, E. Schnack
- Modeling and simulation of composites in the design process, 7th International Symposium on Tools and Methods in Competitive Engineering , 2008
E. Schnack, F.W. Wang, T.-A. Langhoff, A. J. Li
- Modeling and Simulation of Composites in the Design Process, 7th International symposium on Tools and Methods in Competitive Engineering, Izmir, Turkey, 21-25, 04, 2008
E. Schnack, F. W. Wang, T. -A. Langhoff, A. J. Li
- Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem. Chemical Engineering Science 63(15), 3948-3959 (2008)
T.-A. Langhoff and E. Schnack
- Phase-Field Modeling of the Isothermal Chemical Vapor Infiltrition Process of MTS, Wessex Institute of Technology, Southampton, UK, 07.2008
F. W. Wang, T.-A. Langhoff, A. J. Li, E. Schnack
- Discontinuous Solution of Phase-Field Model in Chemical Vapor Infiltration of Silicon Carbide with Convection, MT Aerospace AG, Germany, 17.03.2009
F. W. Wang, E. Schnack
- Discontinuous Solution of Phase-Field Model in Chemical Vapor Infiltration of Silicon Carbide with Convection, Wessex Institute of Technology, Southampton, UK, 03.2009
F. W. Wang, E. Schnack
