Characterization and impact of fiber size variability on the mechanical properties of fiber networks with an application to paper materials

Cellulose fibers come in a wide range of shapes and sizes. The heterogeneity of the fiber length, width, wall thickness, curl and external fibrillation is detrimental to the mechanical performance of products such as paper and paperboard. Although micro-mechanical models of these materials sometimes incorporate features of this heterogeneity, so far there is no standardized method of fully incorporating this. We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have. We find that the method must allow for both non-Gaussian distributions and dependence between the variables. We present a method of characterizing mechanical pulp under these conditions that views the individual fiber as outcome of a sampling process from a multivariate distribution function. The method is generally applicable to any dataset, even a non-Gaussian one with dependencies. Using a micro-mechanical model of a paper sheet the proposed method is compared with previously presented methods to study whether incorporating both a varying fiber size and dependencies is necessary to match the response of a sheet modeled with measured characterization data. The results demonstrate that micro-mechanical models of paper and paperboard should not neglect the influence of the dependence between the characteristic shape features of the fibers if the model is meant to match physical experiments.