Numerical analysis of stresses and deformations in composite materials sheet forming: central indentation of a circular sheet

A finite element model is presented for the analysis of predominantly planar composite sheet-forming problems and the numerical results compared with experimental observations. The problem of diaphragm forming a small indentation in the centre of a large composite sheet is treated in detail, by considering uniform radial velocity or pressure boundary conditions at the inner radius. The analysis is carried out for a single ply, which 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 constructed by discretizing the weak forms of the constraint and governing equations for creeping flow, using independent interpolation of the velocity and tension stress fields. Deformation fields are depicted at each step in the forming process and are shown to be kinematically dominated by the inextensibility of the fibres. Two modes of instability are predicted in the composite laminates: shear-buckling due to the presence of tangential compressive stresses at 45° to the fibre directions; and columnar buckling due to compressive axial stresses in the fibre direction. These compressive stresses are shown to depend on the forming rate, material viscosities, composite sheet dimensions and diaphragm stiffness. Comparisons with relevant experimental observations are included throughout.