Predicting tearing paths in thin sheets

Abstract

This study investigates the tearing of a thin notched sheet when two points on the sheet are pulled apart. The concepts that determine the crack trajectory are reviewed in the general anisotropic case, in which the energy of the fracture depends on the fracture direction. When observed as a flat sheet a purely geometric "tearing vector" is defined through the location of the crack tip and the pulling points. Both the Griffiths's criterion and the "maximum energy release rate criterion" (MERR) predict a fracture path that is parallel to the tearing vector in the isotropic case. However, for the anisotropic case, the application of the MERR leads to a crack path that deviates from the tearing vector, following a propagation direction that tends to minimize the fracture energy. In the case of strong anisotropy, it is more difficult to obtain an analytical prediction of the tearing trajectory. Thus, simple geometrical arguments are provided to give a derivation of a differential equation accounting for crack trajectory, according to the natural coordinates of the pulling, and in the case that the anisotropy is sufficiently weak. The solution derived from this analysis is in good agreement with previous experimental observations.

Combining experimental and cosmological constraints on heavy neutrinos

“…For n = 2 these have e.g. been studied in detail in [22,96,104,278]. For n = 3 they are more complicated, but general tendencies can still be identified easily.…”

“…Such signals are suppressed by the small parameters in (34) in the B − L-conserving limit. The relatively large U 2 α imply that the experimental perspectives for a discovery are particularly promising [16,18,46,60,62,63,68,76,[96][97][98][99].…”

“…We do not include bounds from the process µ → eee [178], which at present appear to be subdominant [1]. The non-observation of µ → eγ decays imposes rather strong constraints on U 2 αI in models with M I ∼ TeV [96], see also [179]. For GeV masses, however, the bounds are known to be much less important already for n = 2 [180], as there exist stronger bounds from other sources.…”

Recent progress on crack pattern formation in thin films

“…Because of the simplicity of this configuration, it is often used to study the effect of material anisotropy on crack propagation. [49][50][51][52] Takei et al performed tearing experiments in both weakly and strongly anisotropic thin sheets (see Fig. 5(b)-(i-ii)).…”

Guided tearing: The ruler test

“…In brittle thin sheets, controlled model experiments show that tearing crack paths can be surprisingly regular. Logarithmic spirals [8,9], oscillating [10][11][12][13], converging [14] or hyperbolic [15,16] paths have for instance been observed and described [17].…”