1997 Volume 2

In-plane (Mode I) fracture of paper is tested at both cryogenic and standard temperatures . It is shown that newsprint tested at cryogenic temperatures is very nearly linear elastic but does not obey classical linear elastic fracture mechanics (LEFM). The discrepancy is traced to changes in the crack tip stress
field due to the sheet’s fibrous structure.

A new fracture model is proposed which integrates the Griffith energy method, Irwin’s correction for nonlinear material behavior, and a similar correction for the fibrous structure. The statistical distribution of mass and local fibre orientation (structural formation) are explicitly considered, and the model thereby links fracture and tensile strength of paper. This approach is consistent with Bazant’s
theoretical treatment of quasi-brittle fracture.

The separation of material nonlinearity and structural formation permits :

• computing the Essential Work, linking the model to an established approach
• estimating the fast fracture response that might occur in practice
• normalizing strength for the paper machine dependent structural formation

In this study, a mechanistic model was developed for the Elmendorf tear strength of paper based on the fundamental physics of the tear process . In the model, the tear strength was calculated as the sum of fibre fracture energy and fibre pull-out energy. The model also included statistical considerations, such as the distribution of fibre lengths. Through dimensional analysis, a “dimensionless tear index” was identified and was found to be a universal function of three dimensionless parameters. Using a bond strength obtained through non-linear regression analyses on a particular experimental data set, the model was validated with other sets of data. It was found that the model gave good quantitative predictions of tear strength of kraft papers without the need for adjustable fitting parameters. With a slight modification to account for the role of fines in the furnish, the model was also successfully applied to handsheets made from TMP pulps.

We present a novel approach to study the three-dimensional network structure of paper. In the KCL-PAKKA simulation model, the porous sheet structure is compiled from the different papermaking raw materials, fibres, fillers and fines. The model geometry is simplified in order to enable effective numerical experiments with arbitrary composition and layering. The KCL-PAKKA model gives realistic predictions for many paper properties. In this paper we describe the cross-over that occurs with increasing grammage from a thin strictly two-dimensional network to a thick layered networks. According to our simulations the cross-over occurs at low grammages, around 20 – 30 g/m2, for papers made of stifffibres (e.g. mechanical pulp) and at higher grammages, 40 – 80 g/m2, for flexible fibres (e.g. beaten kraft). We discuss the statistical properties of the three-dimensional but layered random fibre network, particularly the bonding degree and pore geometry. In thick networks the pore geometry is isomorphic and only the length scale of the pores depends on fibre properties.

So far little attention has been paid to the orientation of flocs in paper sheets . It can be measured by means of an image analyser and the two-dimensional Fourier transform. The principal direction in the power spectrum of a paper in transmitted light is a measure of the floc orientation.

It can be shown that the coefficient of correlation between fibre orientation (Lippke – Tester) and floc orientation amounts on average to 0.7, when profiles across the web are taken into account. Papers, particularly those which are made on hybrid formers, show a two-sidedness concerning floc orientation and anisotropy . The orientation has no significant effect on the uniformity of formation but determines the orientation of cockles. The power spectrum of the local orientation of a paper seems to be very useful in the detection of deterministic variations in orientation, which are invisible in light transmission images.

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Three test methods for the determination of the coefficient of friction of paper have been investigated : inclined-plane, horizontal-plane and strip-on-drum. Significantly different friction values were obtained for the same paper samples by each of the tests and the reasons for some of these differences were studied. Aspects such as contact deformation, contact pressure, testing procedures both environmental and mechanical and the presence of extractives were found to influence the frictional properties of paper and board.

Over the years, large research efforts have been spent on determining the pore volume distributions of graphic papers . The pore volume distributions determine the absorption properties and light scattering properties of these papers and can be modified by a variety of calendering conditions.

In the present work we apply a variety of tests and void space modelling techniques to a series of five paper samples. The tests range from the standard to the novel, and all depend in some way on the void space structure of the samples. Three void space modelling techniques are presented. The first, traditional, method is based on the Laplace equation. The second model, developed by Yamasaki, implicitly assumes unconnected pores of a range of sizes, some of which saturate. The third, ‘Pore-Cor’, assumes a simplified three-dimensional structure. The samples all used the same 51 gM-2 SC grade paper, the first being uncalendered, and the other four involving combinations of soft- and super-nip , with and without the prior application of steam.

Advanced imaging techniques such as optical microscopy and Environmental Scanning Electron Microscopy (ESEM) were used to obtain structural details of the paper cross-sections and paper surfaces, and with the ESEM it was also possible to investigate the effect of moisture on sheet structure.

Absorption properties of the sheets were determined by using the well-known Bristow equipment and newly-developed equipment for determining liquid absorption by fibrous sheets based on Liquid / Air Displacement Analysis (LADA). The LADA equipment applies liquid in a well-defined way which enables valid comparisons to be made with common absorption theories.

Results from the investigation with liquid porosimetry using water and hexadecane probe liquids show that there is considerable sheet expansion when the sheets are exposed to water. Undoubtedly this will lead to a change in the absorption process when the sheets are in contact with moisture . The shape of the absorption curves in both the LADA and the Bristow test equipment also indicate that this expansion will affect the absorption process. A simple mathematical model was also used to take this into account.

The mercury porosimetry data and the liquid porosimetry data were combined to yield a complete pore volume distribution curve for the sheet -structure. These data were then used in the Yamasaki absorption model to simulate absorption, and were compared with the measured absorption values. These results show that the absorption can be simulated with a knowledge of the pore volume distribution curve and basic properties of the absorbed liquid. Large pores dominate the liquid absorption at short contact times (<Is), whereas the smaller pores dominate the absorption at larger contact times, as simulated with Yamasaki model. The overall time limit for absorption is naturally dependent on the total pore volume in the paper.

The combined porosimetry curves were also simulated using a recently developed three-dimensional void space modelling package, named Pore-Cor. This package generated three-dimensional structures with the same percolation characteristics and porosity as the experimental samples. The absolute gas permeabilities, of these structures showed the same trend as the permeabilities measured by a Gurley Densometer. The simulated structures facilitate the mathematical investigation of other effects, such as the trapping of non-wetting fluids and the effect on permeability of the inclusion of colloids, Matthews (1).

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