Fiber orientation effect on polymer rheology

This option considers the fiber orientation effect on polymer rheology. This means that the flow resistance will vary in different directions depending on the local fiber orientation.

The constitutive equation of the polymer melt, which accounts for the anisotropic contribution from fibers, is expressed as [1]:

where:

• is the extra stress tensor,
• is the deformation rate tensor,
• is the isotropic viscosity,
• is the fourth-order fiber orientation tensor,
• is a scalar called the Particle Number.

The finite element forms of the momentum and energy equations are modified accordingly to incorporate the contribution of fibers.

As the viscosity data, supplied in the material database or specified via the Solver API, are the bulk viscosity of a composite with a certain fiber orientation, the isotropic viscosity is decomposed from the given viscosity value with an assumed fiber orientation.

The Particle Number is automatically calculated as a function of the fiber aspect ratio, the fiber volumetric fraction, and the strength of the fiber alignment.

Reference

1. Dinh, S.M. and Armstrong, R.C., A Rheological Equation of State for Semi-Concentrated Fiber Suspensions. J. Rheol., 28(3):207-227 (1984).