Some Theoretical Considerations on the Mechanical Properties of Fibrous Structures

Abstract

Mathematical theories for some of the mechanical properties of a well-consolidated anisotropic fibrous web are developed in two major divisions : the elastic and the plastic regimes of stress/strain relationships . For each of the principal directions in the plane of the sheet, theories of the elastic regime are developed for external load, Poisson’s ratio, Young’s modulus and the modulus of rigidity. Applications of the theory to improve pulp evaluation and to studies of important sheet properties (in the elastic regime) such as stiffness and sheet rigidity are discussed. A complex of phenomena of the plastic regime is inferred from theory . Stresses tending to cause rupture of fibre-to-fibre bonds are found in two important groups: those associated with torque on bonds resulting from shearing force in fibre segments (and combined with stress caused by anisotropic shrinkage of the fibres) and those associated with tension in fibres (and combined with the anisotropic shrinkage stress) . The incidence of fibre-to-fibre bond rupture as the sheet strain is increased from the elastic range into the plastic regime is governed by equations developed for torque and tension bond failures. A brief discussion of the theory of the zero-span tensile test is included.