Self-Affine Crack Pattern in Filter Paper Sheets

Abstract

In this work the self-affine crack pattern in Filter Paper sheets is studied. This paper has a well-defined anisotropy of mechanical properties associated with visible preferable orientation of fibers in the machine direction. Fracture behavior is in essence brittle, the rupture lines have self-affine invariance, and the stresses ahead of the straight notch follow a power-law behavior. The roughness exponent value is of H = 0.50 0.01, different from the suggested universal value H = 0.8. The classical theory has demonstrated that, in materials such as metal, there is a relationship between the size and the starting crack stress, which does not happen in this material. The tests show that the starting crack stress from stress-strain behavior curves remains stable for the different specimen sizes w and crack length size. Moreover, different types of geometric groove, circular and linear, and without a crack, were tested and show almost the same behavior.

Failure Stress in Notched Paper Sheets

“…( 3)-( 4) by the self-affine crack mechanics the fracture behavior in paper is analyzed evaluating the resulting crack surface roughness as well as the crack initiation stress. By the first method, experimental results have shown a statistical invariance under a self-affine transformation characterized by the Hurst exponent in filter paper of H = 0.50 ± 0.01in MD, and H = 0.48 ± 0.01in CD, which corresponds with the characteristic value of a random crack growth path [20]. As observed in figures 3 and 4, during the crack propagation the random arrangement of fibers and due to own fracture mechanisms of paper, let to distribute in a similar way the loading in both directions of preferential orientation of fibers causing the similar fracture surface roughness (Figure 5).…”