Failure Stress in Notched Paper Sheets

Abstract

In this work the crack initiation stress of notched specimens of filter paper is studied. The paper 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 geometrical arrangements in two 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. In this, the without notch specimens present the higher stress, all other notched specimens presented a similar crack initiation stress about 1 % of difference among them, and the crack growth is not affected by the geometry of notch. In spite of this difference, no one of the specimens reach the theoretical stress concentration of 3 such as predicted the classical stress theory.

Characterization of the Crack Propagation in a Microstructurally Random Material

“…For the initial notch range considered the crack onset stress is approximately equal or less than the yielding stress ( y = 0.2%), this imply that in this kind of materials with crack like defect the yielding stress cannot be used as a design parameter, similar results have been found in other types of paper [4]. When a 0 /w = 0.1 the crack onset stress is approximately equal to the yielding stress and for a a 0 /w > 0.1 the crack initiation stress is less than it.…”

“…The microstructural disorder makes the study of the fracture in the paper complex, for example one of the main difficulties in the characterization of cracks is the specification of the instant in which the localized crack get started to grow [4]; also, it causes that the path of the propagation be random which difficult to follow. The fracture micromechanisms in this type of materials makes an intensification in the local strain in front of the crack [6]- [8] and it can be measured and followed each instant for all fracture process through the Digital Image Correlation Method (DIC).…”

“…During the fracture of the paper, the load causes an initial sliding between fibers and interfiber bonding (considered as two different phases due to the absence of a matrix) until the catastrophic failure of the material is finally reached with the breakdown of both phases [4]. These mechanisms are factor of energy consume during the crack propagation and related with the area of the microscopic damage and of the local deformation [5]- [8].…”