Failure stress in notched paper sheets

In this work the crack initiation stress of notched filter paper specimens is studied. The paper, which is used as a material model, in the microstructure has a random array in their fibers while macroscopically it behaves anisotropically. The self-affine crack mechanics is used to study the size effect in the tensile behavior of this kind of paper under the presence of several conditions of geometrical notches. While in the traditional fracture mechanics the crack initiation stress is a material parameter when is reached a critical level at the crack tip, in the self-affine crack mechanics, depends moreover of the resulting tortuosity of the crack. Four notch geometry arrangements in two width specimen sizes we considered: centered circular notch, centered lineal notch, sided circular notches and without notch at 10 and 300 mm width with a relation 2a/w = 0.25 under the same loading conditions. It was observed that the fracture surface is independent to and to preferential orientation of fibers and to geometry notch. Due to interfiber sliding and rupture bonds the notch tip behaves like radii giving the crack initiation stress constant under the studied scaling; that is, the crack growth is not affected by the geometry of notch. Because of filter paper has long fibers through full material; it distributes the load through all width of material causing a higher crack stress initiation. In spite of this difference, no one of the specimens reach the theoretical stress concentration of 3 as predicted the classical stress theory.