Micro-mechanical modeling of the paper compaction process

Abstract

Double-roll compaction is a process to create extensible paper and paperboard suitable for replacing plastic in 3D forming applications. Understanding the macro- and micro-mechanisms governing the compaction process allows increasing the stretch potential while maintaining sufficient strength and bending stiffness. In this work, we approach the compaction process of paperboard with micro-mechanical methods featuring the unprecedented level of details otherwise inaccessible with currently available experimental tools. The loading scheme is based on experiments and continuum level simulations. The different levels of compaction and their continuous impact on the fibers’ geometry, void closures, and irreversible deformation of the fibers are thoroughly characterized. We find that the structural changes are concentrated in the fibers oriented within 30 degrees of the direction of compaction. The deformation accumulates primarily in the wall of the fibers in the form of irreversible strains. The spring-back effect beyond the compaction is negligible. For the first time, the role of normal and frictional fiber-to-fiber interactions in the compaction process is investigated and quantified. The frictional interaction between the fibers has a surprisingly low impact on the outcome of the compaction process, and the normal interaction between the fibers has a dominant response. The consequence of this finding is potentially limited impact of the surface modifications targeting the friction.

Iterative method for large-scale Timoshenko beam models assessed on commercial-grade paperboard

“…Out-of-plane micro-mechanical simulations of paperboard have been limited [41], with compaction simulations and out-of-plane responses [6,27] analyzed on smaller scales. In this work, the bending stiffness is evaluated on far larger and it is shown that linear models can predict the expected theoretical and experimental bending stiffness and tensile stiffness.…”

“…In this work, the bending stiffness is evaluated on far larger and it is shown that linear models can predict the expected theoretical and experimental bending stiffness and tensile stiffness. It would be interesting to evaluate the shear ratio, G/E, for network generation techniques other than randomization [6,23,42].…”

“…Using a stochastic approach to place fibers will lead to overlaps. A more realistic approach would be to simulate the laydown process [23,42] or to simulate compaction [6]. Here, randomization was used for simplicity, especially considering the scales of the problems considered.…”

“…These micro-mechanical models require properties of the individual cellulose fibers [10,11,21,45] and the fiber-fiber interactions in the material [19,22,34]. Early simulations with micro-mechanical models evaluated structural properties on sparse network structures [16,18,26,38] using linear beam models, with recent research analyzing the forming of paper products [6,23,42], and accurate failure mechanics [3,43,44].…”

“…Fig 6. Tensile stiffness for 200 g/m 2 three-ply paperboard models with different weight distributions for the surface/bulk layers in both machine-direction and cross-direction.…”