Simulation of a resin transfer molding process using a phase field approach within the theory of porous media

Abstract

In an RTM process the mold contains three constituents including fibres, a resin and a gas. Due to its similarity to a porous medium, the process can be modeled within the Theory of Porous Media (TPM), where the simulation of the moving resin front generates an inherent difficulty: In widely used approaches for mold filling simulations, that are element/control volume methods (Bruschke and Advani, 1990) and Level set methods (Soukane and Trochu, 2006), the moving resin front is either approximated roughly, such that an interface thickness of multiple finite elements arises, or respectively by a sharp interface with zero-thickness which requires a special numerical treatment. The present study intends to close this gap. To this end, we outline regularizations of the sharp interface such that the above mentioned difficulties can be overcome with a regularized sharp interface theory as a branch of phase-field models which go back to the classical Ginzburg-Landau equation. In this way, the sharp discontinuities between different phases, i.e. resin and gas, are approximated by smooth transitions of suitable order parameters, of which one is the resin fraction. Thus, the sharp interface topology as well as the surface energy of the interface are smeared out over a region proportional to a chosen regularization length scale. As an additional advantage, the phase-field method facilitates a thermodynamic treatment of phase interfaces rendering it more physically consistent in combination with the TPM, which also works within a thermodynamically sound framework. To this end, a coupled finite-element strategy is presented accounting for both, a Ginzburg-Landau- and Cahn-Hilliard-type regularization scheme for the interface. Two boundary value problems are formulated in the context of the TPM. They consider a multiphase-system, represented by deformable fibres interacting with the resin saturating the pores, that is coupled to one of both regularization schemes. Accordingly, two numerical examples demonstrate the capabilities of both regularized formulations by simulations of an RTM process.