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Paper and Fibre Science and Technology Warren Batchelor, Australian Pulp and Paper Institute, Monash University |
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Jihong He. He developed a new method for analysing fibre shape and orientation in the sheet and then used the information to verify a model for paper structure and to propose a model for the tensile strength of paper. Individual chapters can be downloaded through the links given in the Chapter descriptions. The complete thesis can also be downloaded. The final accepted thesis is also subject to the following amendments and corrections. This chapter presents two pieces of theory. A simple model for paper strength is developed by assuming that the fracture of paper is triggered by the failure of fibres. The strength is determined by the fibre strength (as measured by the zero span test) and the stress distribution along fibres at the point of failure. A model for paper structure and fibre-fibre contacts was also presented. The model treats paper as being a matrix structure of rectangular blocks, which contain the fibres. The density of these blocks is less than the fibre wall density as the fibres don't completely fill the blocks. The void volume inside the blocks comes from the irregular shapes of the fibres and their lumens. The fraction of the block filled by fibre is called the fill factor. The model is used to derive the number of fibre-fibre contacts, and corresponding Relative Bonded Area (RBA), for a given sheet density and fill factor. Chapter 4: New experimental technique Jihong developed a new technique to measure fibre shape in the sheet as well as sheet structure. Sheets were fluorescently dyed, embedded in resin and then cut to expose the cross-section. The sample was then ground to expose the cross-section, followed by polishing. Fibre shape was measured for individual fibres at different depths below the cross-section surface. Simple geometry allowed the calculation of the fibre orientation, both in-plane and out-of-plane, with respect to the surface. The measurement technique was verified by comparing fibre wall area distributions measured in-situ in the sheet cross-section with those obtained from individual fibres dried onto glass slides. Chapter 5: Methods used to vary fibre and sheet properties A starting feedstock of a unbleached, never-dried radiata pine kraft pulp with a kappa number of 30 was used to prepare several furnishes. Hydrocyclone fractionation was used to change the fibre shape while preserving the fibre length. Cutting wet sheets and reslushing was used to keep the fibre shape constant while reducing the fibre length. This chapter describes these experiments. For each furnish, sets of sheets were made with different pressing pressure. Chapter 6: Microscopic study of sheet densification by wet pressing. The contributions of three mechanisms to the reduction in sheet thickness with wet pressing were quantified. These mechanisms were the deflection of the fibres to close the gaps between the fibres, the collapse of the fibres under increasing wet pressing pressure and the reduction of the effective height of the fibres in the thickness direction by rotating the fibre so that it's width was parallel to the plane of the sheet. The closure of gaps was found to be the predominant mechanism of densification at low pressing pressures, while fibre collapse and rotation became increasingly more important at high pressing pressures. Fibre-fibre contacts were measured in the paper cross-sections. Contacts were classified into either full or partial contacts, with full contacts occurring when the fibres were touching each across their whole width. Lightly pressed sheets had very high fractions of partial contacts. Heavily pressed sheets mostly contained full contacts. The fibre length was found to have no effect on the number of fibre-fibre contacts per unit length or on the split between partial and full contacts, provided that the fibre cross-sectional shape was constant. The distribution of lengths between fibre-fibre contacts (called the free fibre length) could be fitted with a two parameter Weibull function. The inverse exponential function previously proposed in the literature was found not be valid. The average distances between fibre-fibre contacts for the different samples was compared with the paper structure model presented in Chapter 3, with good agreement. Theoretical values of Relative Bonded Area (RBA) calculated from the model were also compared with the values measured either by nitrogen adsorption or light scattering with good agreement. The standard Ingmanson-Thode extrapolation method for determining RBA was shown to be invalid. Chapter 8: Verification of models for tensile strength of paper The chapter compares the measured data of tensile strength with three models for strength. The Page equation is shown to provide a good qualitative fit to the data, but only if the bond strength is used as a fitting parameter with the bond strength for the cut fibres 50% higher than the bond strength of the fractionated fibres. Next a simple model for paper strength based on the load distribution in the fibre at the point at which the fibre breaks was presented. Several formulations of the shear lag model were used to try and predict the load of failure. These models had limited success. There were substantial differences between the shear-lag stress transfer coefficient estimated from elastic modulus data compared to when estimated from strength data. A new method of calculating the stress distribution along a fibre in matrix was presented. The full derivation is given in the Appendix. This was based on stress transfer at individual contacts not a single uniform stress transfer. The model gave very high predicted strength if no bond breakage was allowed. When bond breakage was simulated using a bond strength of 3 MPa, the predicted strength was too low. Chapter 9: Conclusions and references.
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