Development of a mathematical model for the pultrusion process

A mathematical model has been developed to simulate the pultrusion process, namely the profiles of temperature and the degree of cure in both the axial and radial directions in a pultrusion die of cylindrical shape. For the study, the equations of continuity and energy transport, coupled with a kinetic expression for the curing reaction, were solved numerically, using a finite difference method. For the kinetic expression, we used an empirical expression of the form dα/dt = (k 1 + k 2 α m )(1 − α) n to describe the curing behavior of both unsaturated polyester and epoxy resins. Differential scanning calorimetry (DSC) was used to investigate the curing behavior of the following systems: unsaturated polyester resin/glass fiber, epoxy resin/glass fiber, and epoxy resin/carbon fiber. The results of DSC runs were used to determine the kinetic parameters, which enabled us to predict the effects on the pultrusion characteristics of the following variables: (1) the type of initiator; (2) the type of fiber reinforcement; (3) the type of resin; and (4) the pulling speed and hence the residence time.