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.