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

August Brandberg,Sofia Reyier Österling,Artem Kulachenko,Ulrich Hirn

doi:10.1016/j.ijsolstr.2022.111438

Abstract

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.

Highlights

Cellulose fibers are a major industrial input in the production of packaging and for use in printing
We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have
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

Summary

Introduction

Cellulose fibers are a major industrial input in the production of packaging and for use in printing. Operations like the folding of a sheet to make a box are studied using continuum models (Borgqvist et al, 2015; Li et al, 2016; Beex and Peerlings, 2009; Xia et al, 2002) These models rely on a large number of material parameters that are determined by laboratory trials or fitting. Improving the mechanical properties of the sheet requires an understanding of how the process inputs interact For this purpose, a number of models have been presented that model the microscopic structure of the sheet (Kulachenko and Uesaka, 2012; Karakoç et al., 2017; Silberstein et al, 2012; Ban et al, 2016). Such so-called ‘‘network models’’ connect the properties of the fibers, bonds, and structure of the network to the properties of the continuum

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