In-Plane Fracture of Paper
Abstract: The in-plane failure of paper is studied in this work by means of a cohesive crack model from experimental as well as theoretical perspectives. Localized damage at in-plane tension of short paper strips is studied for low strain rates. It is observed that under uniaxial in-plane tensile tests, the evolution of the failure is stable and the damage of the paper strip is localized into a narrow zone. The damage in the paper strip develops only after the tensile strength has been reached. The uniaxial fracture properties of paper are defined and characterized by a descending stress-crack widening curve. From this curve the fracture energy can be obtained. A characteristic material parameter of a length dimension is introduced and depends on the fracture energy, the elastic modulus and the fracture strength. The material parameters are found to vary with the material orientation of the paper. A method to measure the fracture material parameters is proposed, where only the load and the elongation of the test specimen need to be recorded. Newsprint, kraft paper and paperboard are examined in this investigation. The cohesive crack model is used as a basis in the formulation of an orthotropic smeared crack constitutive relation to be used in finite element codes. The advantage of this approach is that it provides a theoretical tool in the study of the initiation and stable growth of a localized damage zone or crack in an arbitrary structure subjected to an arbitrary in-plane loading. The model proposed includes a failure criterion and a failure potential. The failure criterion changes its size and shape during the course of fracture softening. The failure potential determines the orientation of the fracture zone and the subsequent crack. The cohesive crack constitutive model is calibrated against one newsprint and one board paper. Simulation results from a single central notch specimen loaded in mode I are compared with experimental results. It was found that the fracture process region is of significant size and that the deviation from an autonomous fracture performance is considerable. The constitutive model developed is used in the investigation of the behavior of a fiber-based package material, with a punched opening, in the converting process at constant web tension. Finite element simulations of the converting process are made in order to understand how punched paperboard behaves in converting processes. The simulations are compared with experimental results and a reasonable agreement is obtained.
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