Chapter 7 Implicit finite element modelling of composites sheet forming processes

Abstract

Abstract This chapter discussed implicit finite element methods of simulating composite sheet forming problems. Each ply is assumed to behave as a transversely isotropic, incompressible Newtonian fluid at forming temperature. The presence of high volume fractions of continuous elastic reinforcing fibres in the molten polymer leads to the kinematic constraint of inextensibility in the fibre direction, and associated arbitrary tension stresses. A mixed penalty numerical formulation is constructured by discretizing the weak forms of the constraint and governing equations for creeping flow, using independent interpolation of the velocity and tension stress fields. Numerical solutions are given for two types of planar problems, plane stress which is used to simulate the problem of diaphragm forming a small indentation in the centre of a large composite sheet, and plane deformation which is used to simulate single-curvature forming situations. The plane stress analysis calculates the stress and deformation patterns which are responsible for shear-buckling under rapid forming conditions, by considering uniform radial velocity or pressure boundary conditions applied at the inner radius of an annular sheet. Experimental results are presented which correspond with the numerical predictions. For multi-ply lay-ups, each ply is analysed individually, and average stress predictions for the laminate are obtained on this basis. A detailed comparison between numerical stress predictions and experimental buckling patterns is presented for central identation of circular uni-directional, cross-ply and quasi-isotropic preforms. Parameters influencing the magnitude and location of peak tangential stresses include tangential fibre lengths and diaphragm/composite viscosity ratios. The effect of sheet width and shape on the instability patterns is investigated for quasi-isotropic laminates using both numerical and experimental techniques. The plane strain finite element model presented can model isothermal shearing and plane transverse flows encountered in forming composite laminates into single-curvature shapes. These flows are the dominant mechanisms in the forming of important industrial shapes such as J- and U-beams for aerospace applications. The finite element formulation uses a mixed penalty approach with independent interpolation of the velocity, pressure and fibre tension stress fields. Results are shown which agree well with available analytical studies for both single-ply and multi-ply deformations. Experimental characterizations of the inter-ply slip behaviour are used to develop a general-purpose contact-friction algorithm for forming situations. The results shown are an important step towards the development of a simulation tool for single-curvature composite forming.