Analysis of heat transfer and fluid flow in the resin transfer moulding process
Abstract: This thesis contains an analysis of fluid flow and heat transfer problems in the resin transfer moulding (RTM) process for manufacturing of polymer based fibre composites and it consists of five separate papers. The permeability of unidirectional fabrics, that are often used in advanced composites, is considered in Paper A and a theory for the permeability dependence on the micro geometry is developed. The theory is based on lubrication theory for narrow gaps which is motivated by the fact that most of the flow resistance comes from a small region where the fibres are closest to each other. Despite this limitation the results agree excellently with numerical results. 'Me best performance of the theory is expected at high fibre volume fractions (Vf) but the dependence on Vf is surprisingly good even at as low values as 0.3. Although the theory is formulated for an idealised geometry it can be used to predict the variation of the anisotropic permeability tensor with fibre volume fraction in real fabrics after fitting of three model parameters. Paper B is a study of the influence from different process parameters on the void content in the laminate. The void content is shown to be reduced strongly by an applied vacuum during mould filling. The main mechanism for void formation appears to be mechanical entrapment at the flow front. The voids are convected by the flow so that their concentration is highest close to the flow front. Microscopy investigation of the bubbles show that they are of two basic types, large spherical bubbles in the interstices between fibre bundles and smaller cylindrical bubbles inside the fibre bundles. The positive influence of vacuum compared to no vacuum can be explained as a combined effect of an increased mobility due to larger volume changes during mould filling and compression by the increased pressure during cure. In Paper C a comparison is made between the mould filling times for different injection strategies. The possible alternatives for a normal laminate are point injection, edge injection and peripheral injection. Theoretical results are derived that can be used to estimate the mould filling time with the different alternatives. In addition, fundamental theoretical results are derived from the governing equations showing the scaling of the mould filling time with the process parameters. This analysis also shows that the flow front motion during mould filling is only a function of the anisotropy of the reinforcement and the location of the gates. Paper D presents an analysis of the non-uniform flow at the flow front during impregnation of a stack of fabrics consisting of layers with different flow resistance. A detailed derivation of the theory and an analytical solution to the equations are presented in an addendum to Paper D. The theoretical model is compared with experimental results and is found to describe the experiment qualitatively well. The resulting permeability of a stack of different fabrics is derived from the basic equations and is found to be a weighted average of the permeability in the individual layers. This result is compared with experiments with different stacking sequences and it is found that the stacking sequence has no influence on the resulting permeability as expected from the theory. Experimental results in excellent agreement with Darcy's law are also presented for the case with radial flow and with unidirectional flow. Finally, Paper E is a theoretical study of the curing behaviour of thick laminates. A general solution independent of the cure kinetic model is derived. The solution is valid for low exothermal peak temperatures and it is characterised by two dimensionless numbers. The first parameter is the ratio between the time scales for the reaction and for heat conduction, the second parameter is the ratio between the processing temperature and the adiabatic temperature rise. The general solution is specialised to a second order autocatalytic cure model so that the results can be compared to numerical results. The agreement between the numerical and the analytical solution is excellent for small exothermal peak temperatures, as expected. The particular model used also serves as an example of the additional dimensionless parameters that are introduced by a specific kinetic model.
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