Prediction of Fibre Orientation and Stiffness Distributions in Paper – An Engineering Approach

Abstract

The orientation of the fibres in a paper directly influences many of its properties. The focus of this work was to predict the fibre orientation distribution and tensile stiffness distribution of a paper. The predictions were based on a proposed link between the two distributions and physical parameters measurable on the paper, no fitting parameters.

The fibre orientation distribution in paper was approximated by a probability density function. Both curve fitting type of distribution functions earlier used in paper physics and physical based functions derived from Fluid mechanics, Orthotropic analysis and a simple Stress/strain analysis were evaluated. The physical based functions used one measurable physical parameter, the fibre orientation anisotropy. The tensile stiffness distribution was predicted with a distribution function from the literature and functions derived from the Fluid mechanics and Orthotropic analysis approach. The predictions needed two measurable physical parameters, the MD and CD tensile stiffness.

Predictions of fibre orientation distribution and tensile stiffness distribution for restrained dried papers were compared with experimental data from restrained dried oriented handsheets with varying fibre orientation anisotropy. General approaches valid for all papers were compared with experimental data from pilot made papers with different drying restraint history. Both the predicted results for fibre orientation distribution and tensile stiffness distribution showed good agreement with experimental data.