Numerical Simulation of Fiber Orientation and Resulting Thermo-Elastic Behavior in Reinforced Thermo-Plastics

Abstract

In this work, we describe a numerical technique to predict fiber orientation during injection moulding of fiber reinforced polymers, and how the resulting part behaves regarding this process induced orientation. The orientation state of a set of fibers is described by a second order tensor. Its evolution is given by the Folgar and Tucker tensorial hyperbolic equation. Even if this equation contains a fourth order term, it may be expressed as a function of the second order tensor using a closure approximation. The resolution of Folgar and Tucker’s equation is carried out by a continuous approach based on the Standard Galerkin method, with stabilisation. The results are compared with experimental orientation measurements on an injected plate. Once the part solidifies it is considered as a biphasic material, composed by the fibers and the polymer matrix, where each phase has a linear elastic behaviour. The fhermo-elastic properties of the composite material are linked to the fiber orientation and the properties of each phase using a homogenisation technique. Finally, to validate the previous study on the prediction of the thermo-elastic properties at the solid state, a three-dimensional industrial case is deeply analysed.