Discontinuous Galerkin solution of a phase-field model in isothermal chemical vapor infiltration of SiC

2011 ◽  
Vol 78 (1) ◽  
pp. 261-274 ◽  
Author(s):  
Fengwen Wang ◽  
Eckart Schnack ◽  
Yaochan Zhu
2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yaochan Zhu ◽  
Eckart Schnack

The multiphase field model for chemical vapor infiltration (CVI) of SiC/SiC composites is developed in this study, thereby to reproduce the microstructure evolution during CVI process and to achieve better understanding of the effect of process parameters (e.g., temperature, pressure, etc.) on the final product. In order to incorporate the thermodynamics of methyltrichlorosilane (MTS) pyrolysis into phase field model framework, the reduced chemical reaction mechanism is adopted. The model consists of a set of nonlinear partial differential equations by coupling Ginzburg-Landau type phase field equations with mass balance equations (e.g., convection-diffusion equation) and the modified Navier-Stokes equations which accounts for the fluid motion. The microstructure of preferential codeposition of Si, SiC under high ratio of H2to MTS is simulated and the potential risk of blockage of the premature pores during isothermal CVI process is predicted. The competitive growth mechanism of SiC grains is discussed and the formation process of potential premature pore blockage is reproduced.


2020 ◽  
Vol 54 (3) ◽  
pp. 1003-1023
Author(s):  
Annika Bach ◽  
Liesel Sommer

In this paper we provide a rigorous asymptotic analysis of a phase-field model used to simulate pressure-driven fracture propagation in poro-elastic media. More precisely, assuming a given pressure p ∈ W 1,∞ (Ω) we show that functionals of the form $$ E(\vec{u})={\int }_{\mathrm{\Omega }} e(\vec{u}):\mathbb{C}e(\vec{u})+p\nabla \cdot \vec{u}+\left\langle \nabla p,\vec{u}\right\rangle\enspace \mathrm{d}x+{\mathcal{H}}^{n-1}({J}_{\vec{u}}),\enspace \vec{u}\in \mathrm{G}{SBD}(\mathrm{\Omega })\cap {L}^1(\mathrm{\Omega };{\mathbb{R}}^n) $$ can be approximated in terms of Γ-convergence by a sequence of phase-field functionals, which are suitable for numerical simulations. The Γ-convergence result is complemented by a numerical example where the phase-field model is implemented using a Discontinuous Galerkin Discretization.


2016 ◽  
Vol 31 (3) ◽  
pp. 298
Author(s):  
TANG Zhe-Peng ◽  
ZHANG Zhong-Wei ◽  
FANG Jin-Ming ◽  
PENG Yu-Qing ◽  
LI Ai-Jun ◽  
...  

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