18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS NUMERICAL SIMULATION OF THE RTM LIGHT MANUFACTURING PROCESS J. Timms 1 , S. Bickerton 1 *, P.A. Kelly 2 1 Department of Mechanical Engineering, The University of Auckland, Auckland, New Zealand, 2 Department of Engineering Science, The University of Auckland, Auckland, New Zealand * Corresponding author (s.bickerton@auckland.ac.nz) Keywords: RTM Light, Infusion, VARTM, Simulation, Experimental 1 Introduction These simulations are predominantly based on the Finite Element/Control Volume (FE/CV) method, Liquid Composite Moulding (LCM) describes a because of its efficiency and the ease with which it range of composites manufacturing processes where can model complex part geometries [1, 4, 6]. This dry fibrous reinforcements are compacted in a mould allows for fast filling simulations of industrially before being impregnated with a liquid relevant parts. thermosetting matrix. Although all LCM processes use closed moulds, they can vary in stiffness from The RTM Light simulation presented in this paper fully rigid to fully flexible, with the heavy tooling of uses a coupled Finite Element scheme. A mesh of Resin Transfer Moulding (RTM) and Compression elements modelling Darcian flow through Resin Transfer Moulding (CRTM) processes at one deformable porous media (the ‘flow domain’) is end of the spectrum, and the thin flexible films used coupled with a second mesh of structural elements in Resin Infusion (a.k.a. VARTM) at the other. that represents the deformable mould (the ‘structural’ domain). The RTM Light manufacturing process differs from RTM by replacing one rigid mould half with a 3 Fluid flow problem lighter, less rigid component (Fig. 1). The flexible RTM Light involves the flow of resin through a mould is often manufactured from an isotropic glass (typically) thin fibrous preform in a deformable fibre composite, and clamping is usually provided mould. This type of flow may be modelled as by application of vacuum to a region at the periphery Darcian flow through thickness-varying porous of the mould cavity. Resin flow is driven by a cavity media, which is governed by the partial differential vacuum, an external injection system, or a equation combination of the two. RTM Light can allow for significant reductions in tooling costs as compared K h to RTM. This is at the expense of introducing some p (1) compliance into the mould, but still allows for h higher injection pressures and final part quality than flexible film processes. where K is the permeability tensor, µ is the fluid viscosity, p is the fluid pressure, h is the preform This paper focuses on the development of a 2D its first time derivative. numerical simulation of the RTM Light process, height and h capable of predicting resin flow front and laminate A conventional quasi-static FE/CV approach is thickness evolution during filling. adopted for the mould filling process, whereby p is 2 Simulation approach solved over the saturated domain using the Galerkin finite element method. The fluid flux is then Numerical simulations of rigid tool LCM processes calculated at the free boundary, and the flow front is have been in development for over 20 years, with advanced by choosing a time step that results in the several academic and commercial packages now complete saturation of at least one CV. available [1, 2]. In the last decade a number of flexible tool simulations have also been developed Non-conforming linear triangle elements are used so [3, 4], along with numerous advances in the areas of that the control volumes can be formed by the computational efficiency, process optimization, and elements themselves. It was shown in [2] for the part quality prediction [4, 5]. rigid mould case that non-conforming triangles
conserve fluid mass both within and between along with Green’s functions for deflection for elements. However, this does not hold in general for general loading states [8]. However, a useful RTM thickness varying elements, so a modification to the Light simulation requires deflection of non-regular fluid flux q a proposed by Kelly [7] has been adopted: mould geometries, as well as an ability to handle more advanced construction features, such as anisotropic materials, variable thickness, and the K h h q x p x x (2) application of stiffeners. For these reasons, it is a FE B 2 necessary to adopt a numerical solution procedure. While a number of alternative numerical procedures where x B is the barycentre of the element. Equation are available for thin plate problems, such as the 2 ensures intra-element mass conservation and, in boundary element method, the finite element method the case of constant or linearly varying forcing terms, is preferred in this simulation because of its flux continuity between elements. Height is treated numerical efficiency, established literature, and as constant across an element in this simulation, so versatility. It is easily extended into 2.5D by the condition holds. Flow into unsaturated elements adopting shell elements, and to thick plates by using adjacent to the front boundary can be then be found those based on Reissner-Mindlin thick plate theory by integrating the normal component of the linearly or 3D elasticity. Furthermore, many of the assembly varying flux across the element edge. This allows for and solver routines can be shared between the flow improved estimates of flow front progression and structural finite element modules. without resorting to more computationally expensive mixed-methods. The plate bending element is the 9 DOF discrete Kirchhoff triangle (DKT), implemented using the The current simulation is restricted to planar local coordinate formulation given by Batoz [9]. geometries, but this is sufficient to capture the While faster converging elements are available, the majority of key behaviour, and the extension to 2.5D DKT is suitable for this simulation because of its shell geometries is relatively straightforward. reliability and low numerical overhead. Clamped, 4 Structural problem simple support, and free edge boundary conditions can be specified. RTM Light mould compliance can potentially vary from near-rigid to very flexible due to differences in In the current simulation, the same mesh is used for mould construction (e.g. material, thickness, use of the structural and flow problems. Deflections and stiffeners, etc.), part size, target volume fractions, loads are lumped in a consistent manner and passed and injection pressures. This paper considers the between solvers during each iteration. canonical RTM Light process, which has a rigid A- 6 Coupling and solution procedure side mould, and a thin B-side mould constructed from a linearly elastic material. For planar The flow equation (Eq. 1) is coupled to the structural geometries, the structural behaviour of this type of problem by the dependence of height and mould can be modelled by the Kirchhoff thin plate permeability on mould displacement u : theory. This model requires that 1) the plate’s thickness is small relative to its characteristic length, K K h , x , t (4) and 2) the deflections are small relative to the thickness. Both these conditions can be met by h u x , t h x requiring the B-side mould to be constructed from a (5) 0 sufficiently stiff material. where h 0 is a reference height at zero deflection. In the case of isotropic, homogenous plates with a Similarly, the structural problem is coupled to the constant flexural rigidity D , deflection u is related to flow problem by the dependence of the lateral load q lateral distributed load b by on the resin pressure: b 4 u (3) b p p (6) D ext f Analytical solutions to Eq. 3 exist for simple geometries and loading and boundary conditions.
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