K.J. Niskanen

Planar random networks with flexible fibers.

The transition in random fiber networks from two-dimensional to three-dimensional planar structure driven by increasing coverage (total fiber length per unit area) is studied with a deposition model. At low coverage the network geometry depends on the scale-free product of fiber length and coverage while at high coverage it depends on a scale-free combination of flexibility, width and thickness of the fibers. With increasing coverage the roughness of the free surface decouples from the substrate, faster when fibers are stiffer. In the high coverage region roughness decreases exponentially with increasing fiber flexibility.

Microscopic mechanics of fiber networks

We report simulations of two‐dimensional fiber networks of random geometry. The stress distribution along a fiber agrees with the mean‐field Cox prediction, but the stress transfer factor is determined by the properties of the whole fiber and not by just the local segment stiffness as suggested by micromechanical models. This leads to a linear density dependence of the Young’s modulus of a network. The initial loss of stiffness at small strain can be explained with an exponential frequency distribution of microscopic stresses, and the asymptotic stiffness at large external strain agrees with mean‐field predictions. The simulated behavior is independent of the microscopic fracture mechanism in both regions.

Porous structure of thick fiber webs

The bulk properties and stochastic pore geometry of finite-thickness fiber webs are studied using a realistic model for the sedimentation of flexible fibers [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)]. The resulting web structure is controlled by a dimensionless number F=Tfwf/tf, where Tf is fiber flexibility, wf fiber width, and tf fiber thickness. The fiber length (≫wf,tf) is irrelevant. With increasing coverage c, a crossover occurs at c=c0≈1+2F from a vacancy-controlled two-dimensional (2D) structure to a pore-controlled 3D structure. The 3D structures are isomorphic in that the pore dimensions are exponentially distributed, with the decay rate dependent only on F.

Does the shear-lag model apply to random fiber networks?

The shear-lag type model due to Cox (Br. J. Appl. Phys. 3 , 72 (1952) is widely used to calculate the deformation properties of fibrous materials such as short fiber composites and random fiber networks. We compare the shear-lag stress transfer mechanism with numerical simulations at small, linearly elastic strains and conclude that the model does not apply to random fiber networks. Most of the axial stress is transferred directly from fiber to fiber rather than through intermediate shear-loaded segments as assumed in the Cox model. The implications for the elastic modulus and strength of random fiber networks are discussed.

Strength Distribution in Paper

Abstract Tensile strength distributions are studied in four paper samples that exhibit a variety of brittle-to-ductile properties. 1005 tensile specimens were measured in each case. The standard Gumbel and Weibull distributions, and a recently proposed double exponential modification of the former are compared with the observations visually and using chi-squared and Kolmogorov–Smirnov tests. The Gumbel distribution fails to fit the data while the Weibull distribution gives satisfactory agreement. However, the double exponential distribution fits the data best, regardless of the ductility of the material.

Kraft fibers in paper – Effect of beating

ABSTRACT Beating improves mechanical properties in papers made of kraft pulp. The effect is often assumed to arise from increased “bonding” in the dry paper, perhaps also from the removal of curl and other similar defects in the fibers. In contrast, it is argued here that bonding in dry paper does not explain the effect of beating when considering the elastic modulus of paper. Instead beating primarily influences the elastic modulus of fibers through the drying stresses and bonding in the wet web. The elastic modulus of paper made of a beaten kraft pulp is essentially equal to the average modulus of the fibers in the sheet. Because of the strong coupling with drying stresses, paper is dissimilar to ordinary fiber composite materials. The hypothesis put forward in this paper explains the results of a variety of experiments where beating, grammage, wet pressing, filler content or drying shrinkage were varied.

Crackling noise in paper peeling

Acoustic emission or crackling noise is measured from an experiment on splitting or peeling of paper. The energy of the events follows a power law, with an exponent β ~ 1.8 ± 0.2. The event intervals have a wide range, but superposed on scale-free statistics there is a time scale, related to the typical spatial scale of the microstructure (a bond between two fibers). Since the peeling takes place via steady-state crack propagation, correlations can be studied with ease and shown to exist in the series of acoustic events.

Fiber debonding along a crack front in paper

The authors follow the accumulation of microscopic damage ahead of the crack tip in paper. The fiber debonding process varies even within each specimen because of large variation in fiber and bond properties. In general, stiff and weakly bonded fibers tend to debond as a rigid body while ductile or well bonded fibers pull out gradually in a process that propagates from the crack line to the fiber ends. Particularly in the latter case the network ruptures coherently rather than through debonding of single fibers. Experimental analysis and simulations show that fracture energy correlates closely with the size of the fracture process zone (FPZ) irrespective of the nature of the debonding process. Only the cases of low bonding and stiff fibers seem to make an exception in that FPZ can grow in size without a corresponding increase in fracture energy.