On the role of moisture in triggering out-of-plane displacement in paper: From the network level to the macroscopic scale

Abstract

The response of paper to humidity variations is a complex, inherently multi-scale problem. The hygroscopic swelling of individual fibres and their interactions within the fibrous network govern the macroscopic, sheet-level response. At this scale, moisture induced instabilities and out-of-plane deformations may occur, which are critical for a number of industrial applications. This work specifically focuses on several aspects of this important issue. A macroscopic phenomenological hygro-mechanical model is first proposed, which aims at predicting moisture induced out-of-plane deformations in paper sheets. The constitutive model is based on the relation between these deformations and typical irreversible phenomena associated to the history of paper manufacturing, i.e. the release of dried-in strains. The model is used to describe bending induced by moisture gradients through the thickness of the sheet as well as buckling due to moisture variation in the presence of mechanical constraints. The results of the model show that the anisotropic sheet-level hygro-expansion has a strong influence on the instability phenomena. Moreover, a comparison with experiments provides adequate semiquantitative estimates. An additional step is made towards the multi-scale understanding of paper hygro-mechanics. The fundamental physical mechanisms governing the macroscopic moisture induced response are investigated on the basis of the underlying fibrous network. To this aim, a meso-structural model is developed which consists of a network of fibres randomly positioned in a planar region according to an orientation probability density function. A series of network simulations reveals that upon moisture content variations the expansion of the inter-fibre bonding regions essentially drives the overall deformation. Particularly in the case of anisotropic fibre orientation, this explains the origin of the macro-scale anisotropic hygro-expansion, which is essential for the observed sheet-level instability phenomena.

Effects of press-forming parameters on the dimensional stability of paperboard trays

“…The larger dimensional changes in the tray width were linked to the fiber direction of the material. Moisture absorption in paperboard occurs with different gradients for the cross and machine directions of the paperboard fibers (Bosco et al 2018). Swelling and shrinking of paper substrates in the paperboard occur likewise with different gradients (Bosco et al 2018).…”

Chemo-mechanical ageing of paper: effect of acidity, moisture and micro-structural features

“…The network unit cell Q is modeled as a square domain with edges of length L. The individual fibers in the network have a rectangular shape with length l and width w, and a rectangular cross-section wh where h is the fiber thickness. The network is generated by depositing each individual fiber in the region Q, with the location of the geometrical center of the fiber determined by a uniform random point field [50]. The orientation of the fibers in the fibrous network follows a wrapped Cauchy orientation distribution [51]:…”

Effect of Polydispersity on the Transport and Sound Absorbing Properties of Three-Dimensional Random Fibrous Structures

“…The main constituents of nonwoven are fibers that are linked together by cohesive bounds induced by the manufacturing process in the form of fibrous networks with transverse isotropy. Nonwoven fibrous media with a wide diversity of physical and mechanical properties (Dirrenberger et al [1], Altendorf et al [2], Bosco et al [3]) can be manufactured by tailoring the nature of the raw materials and the manufacturing process conditions (e. g., type of geometry, bale opening and weighting of the fibers, fibers web creation, thermal bounding thickness adjustment and cutting). However, the links between the composite nonwoven manufacturing parameters, the resulting fibrous microstructures, and the product performances are still not fully evidenced.…”