FORMULAS Emax = VjEj + (1 - V₁) Em 1 [r+rs(f − 2)]¹/2 Olgel/nQ2 You are a composites engineer in a company that is currently producing carbon fibre reinforced composites using

a blend of a tetrafunctional epoxy and an aromatic diamine with the following characteristics: functionality of the crosslinking groups, f = 4, molar ratio of the epoxy groups to amine hydrogen atoms, r= 1, and the fraction of the amine hydrogen atoms in the reactants, s = 1. The matrix is predicted to undergo gelation at agel of 0.577 (around 58%). (a) Unfortunately, there has been an error in procurement and your materials supplier has provided a trifunctional epoxy for use with the same diamine. You can assume that the fraction of amine hydrogen atoms in the reactant formulation remains the same. Show, using Flory-Stockmayer theory, the polymer conversion at which your new matrix for- mulation reaches gelation. The polymer undergoes a change from a rubbery material to a cross-linked polymer, what do we call this? If you keep the other processing conditions the same, what effect will this have on the manufacturing time for the composite? (5 marks) (b) Fortunately, you realise the mistake before processing the composite, but you have to proceed using the same trifunctional epoxy and diamine. What two steps could you take to shorten the time to reach gelation? Justify your answer by showing the effect on Orgel- (5 marks) (c) A Time-Temperature-Transformation (TTT) diagram for your trifunctional epoxy and diamine blend is shown in Figure Q2. Sketch the TTT diagram and annotate on the dia- gram the isothermal processing temperature that you would propose to get the best ma- terial properties from your resin. Justify your reasoning by describing how your choice influences the manufacturing process. (5 marks) (d) Your cured epoxy resin develops a Young's modulus of 3.4 GPa and is combined with intermediate modulus carbon fibres (250 GPa). If the target fibre volume fraction for your composite is 55%, what is the maximum stiffness (Emaz) that you would expect along the fibre direction in each ply? Sketch a diagram to represent relative stiffness of the laminate against ply angle to show what Emax becomes in: (i) a unidirectional laminate, (ii) a cross-ply laminate, (iii) a quasi-isotropic laminate./nCure temperature (°C) Tg gel To Tso Gelled rubber gelation Liquid Oxidation Log time (min) Figure Q2 Tg Gelled glass Ungelled glass