Per Gradin

The Link Between the Fiber Contact Zone and the Physical Properties of Paper : A Way to Control Paper Properties

Paper is a composite of fibers, air and additives where the fiber/fiber joints keep the network structure together. A study was undertaken to establish the link between the properties of the contact zone between fibers and paper performance under mechanical loading. The contact zone between fibers was investigated using light microscopy. A staining technique was developed for evaluating the influence of surface charge on fiber/fiber joint strength. The joint strength was linearly correlated with paper tensile strength and with the average amplitude of the acoustic events measured by acoustic emission testing. The fiber surface conformability was improved by changing the surface charge. This resulted in increased fiber/fiber joint strength as the relative contact area became larger. Increasing the molecular adhesion in the contact zone with the aid of strength additives also improved the fiber/fiber joint strength.

Fiber/Fiber Crosses: Finite Element Modeling and Comparison with Experiment

Fiber/fiber joints were analyzed using finite element analysis in order to characterize the influence of fiber and contact region properties on the stress— strain behavior of a single fiber/fiber cross. The output of the models was validated by comparison with experimental load—deformation curves. The contact zone of the fiber/fiber joint was studied with respect to the appearance of the contact zone, the contact area, and the contact pattern; the work of adhesion of the contact areas was also considered. It was shown that the two-dimensional appearance of the contact zone had little influence on the stress—strain behavior of the fiber/fiber cross under tensile loading. The maximum stress and hence the fiber/fiber joint strength was, however, affected by the degree of contact. It was concluded that knowledge of the material behavior of the contact zone (such as local plastic behavior), and of chemical effects (such as work of adhesion) are needed to predict the fiber/fiber joint strength.

Some Aspects on the Zero-span Tensile Test

In this paper, we present some analytical and numerical results concerning the zero-span testing method, frequently used for quality control of cellulose fiber for papermaking. Of particular interest is the relationship between an apparent modulus obtained from the zero-span testing method and the elastic properties of the fibers. The apparent elasticity modulus is estimated using two energy theorems in elasto-statics in which the role of span length is explored. Analytical results, derived under the assumption that slippage between specimen and clamps does not occur, clearly show that the apparent modulus strongly depends on the span length. This is verified by the numerical results obtained using the finite element method. In addition to the above analysis, the effect of slippage is investigated, also by utilizing the finite element method, and it is found that for a specific case, the contribution from slippage to the total displacement depends strongly on the length of the span. Tensile tests at nominal zero span were conducted in an effort to further validate the analysis with relevant experimental data and it was concluded that there is qualitative agreement between the experimental results and the result of the analysis.

A theoretical and experimental study of the circular sawing process

Abstract To gain further insight into the energy dissipation during the wood sawing process, a theoretical model has been developed. The model is based on the assumption that there are two basic causes for energy dissipation during sawing: the creation of a new surface and the compression of material below a saw tooth. It is assumed that both contributions can be dependent on the cutting angle (the angle between the fiber direction and the tangent to the path followed by a saw tooth) because a saw tooth changes its angle of attack during its way through a log. To determine this dependence of the dissipation on the cutting angle, a series of experiments with pine plank sawing were performed by means of different feeding rates and cutting angles while the electrical power supplied to the saw was measured. The parameters in the theoretical model were derived from the experimental findings. Finally, two tests were carried out under different conditions with respect to thickness and cutting angles and the validity of the model was confirmed concerning the prediction of the electrical power consumption.

A numerical and experimental study regarding the influence of some process parameters on the damage state in wood chips

Abstract The specific energy consumption during mechanical refining operation can be reduced by choosing the optimal process parameters in the wood chipping process such that a beneficial pretreatment is obtained. In the case of the utilization of a larger knife-edge angle, which is one such process parameter, the energy reduction is presumably due to the increased compressive loading parallel to the wood fibers. In the present article, a chip damage parameter D of spruce is in focus, which is relevant for cracking parallel to the fibers. D is defined and its dependence on the chip length and edge angle of the chipping knife is analyzed numerically by means of finite element analyses (FEA). The cutting force was measured in a pilot wood chipper for a number of knife-edge angles. There is a good correlation between the experimental results and those of FEA.

Properties of wood chips for thermomechanical pulp (TMP) production as a function of spout angle

Abstract Spruce wood chips were produced under well-controlled conditions in a laboratory wood chipper at spout angles of 30°, 40°, and 50° at a cutting rate of 20 m s-1 and with a nominal chip length of 25 mm. The chips were then refined under thermomechanical pulp (TMP) conditions in a pilot refiner plant. The pulp properties such as freeness, average fiber length, and shives content were determined and evaluated as a function of specific energy consumption. For a first stage refining and for a freeness value of 350 ml, a decrease in specific electrical energy consumption could be achieved by performing the wood chipping at a spout angle of 50° as compared to 30° which is the spout angle commonly used. A patent application regarding this method has been filed and is pending. It is realized that a freeness value is not directly indicative of any quality measure, such as, for example tensile index and light scattering coefficient but the obtained results can be interpreted to be promising. Further studies are needed regarding the impact of the modified chipping process.

On the energy consumption for crack development in fibre wall in disc refining - a micromechanical approach.

Abstract An analytical model has been applied to calculate the acquired strain energy density in order to achieve a certain damage state in a softwood fibre by uniaxial tension or shear load. The energy density was found to be dependent on the microfibril angle in the middle secondary wall, the loading case, the thicknesses of the fibre cell wall layers, and conditions, such as moisture content and temperature. At conditions, prevailing at the entrance of the gap between the plates in a refiner and at relative high damage states, more energy is needed to create cracks at higher microfibril angles. The energy density was lower for earlywood compared to latewood fibres. For low microfibril angles, the energy density was lower for loading in shear compared to tension for both earlywood and latewood fibres. Material parameters, such as initial damage state and specific fracture energy, were determined by fitting of input parameters to experimental data.

Stresses and strains in a race track strap with a radial clearance

In certain situations it is desirable to transfer only tensile loads between two points in a structure whilst minimising any stress concentrations. In such circumstances a so-called race track strap can be utilised. The strap consists of two semi-circular elements that transfer the load, from bolts at each end, to two parallel flexible elements joining the whole together. The strap is loaded in tension by means of these bolts. This paper considers the situation where there is clearance between the bolts and the semi-circular elements of the strap. To develop an analytical model, it is assumed that engineering beam theory is applicable, that the influence of the membrane strains can be ignored and that the clearance is small as compared with the bolt and strap radii. It was found that the simple analytical model compared well with both finite element calculations and experiments.

A Note on the Co-linearity of Forces and Displacements in an Elastic Structure

Theconditions under which force vectors and corresponding displacement vectors becomeco-linear are investigated under the assumption of a linear elasticstructure and for an arbitrary number of loading points. Itis shown that there exist an infinite number of directionsalong which the load and displacement vectors in each loadingpoint coincide. Moreover, the problem of co-linearity is analogous tothe problem of finding the extreme values of the workperformed on an elastic structure under the constraint that eachforce has a given magnitude. The result for a finitenumber of loading points is extended to a continuous loaddistribution on the boundary of an elastic structure, i.e., itis possible to find an infinite number of load distributionssuch that the displacement in a point on the boundaryis co-linear with the boundary stress vector in that samepoint.

Nonharmonic oscillations of nanosized cantilevers due to quantum-size effects

This thesis investigates the mechanics in two nanosized system. Paper I investigates a size effect in a cantilever nanowire affecting its resonance frequency. Paper II reveals a threshold field for the formation of a mound by the diffusion of surface atoms on a substrate under a STM-tip.Paper I: Using a one dimensional jellium model and standard beam theory we calculate the spring constant of a vibrating nanowire cantilever. By using the asymptotic energy eigenvalues of the standing electron waves over the nanometer sized cross section area, the change in the grand canonical potential is calculated and hence the force and the spring constant. As the wire bends, more electron states fits in its cross section. This has an impact on the spring ”constant” which oscillates slightly with the bending of the wire. In this way we obtain an amplitude dependent resonance frequency of the oscillations that should be detectable.Paper II: By applying a voltage pulse to a scanning tunneling microscope tip, the surface under the tip will be modified. In this paper we have taken a closer look at the model of electric field induced surface diffusion of adatoms including the van der Waals force as a contribution in formations of a mound on a surface. The dipole moment of an adatom is the sum of the surface induced dipole moment (which is constant) and the dipole moment due to electric field polarisation which depends on the strength and polarity of the electric field. The electric field is analytically modelled by a point charge over an infinite conducting flat surface. Based on this we calculate the force that cause adatoms to migrate. The calculated force is small considering the voltage used, typical 1 pN, but due to thermal vibration adatoms are hopping about the surface and even a small net force can be significant in the drift of adatoms. In this way we obtain a novel formula for a polarity dependent thresholdvoltage for mound formation on the surface for positive tip. Knowing the voltage of the pulse, we are then able to calculate the radius of the formed mound. A threshold electric field for mound formation of about 2 V/nm is calculated. In addition, we found that van der Waals force is of importance for shorter distances and its contribution to the radial force on the adatoms has to be considered for distances smaller than 1.5 nm for commonly used voltages.