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Energy dissipation in paper tearing as time-dependent phenomenon Sun, Bernard Ching-Huey

Abstract

The nature of ballistic-type internal paper tear test methods has been reviewed. The kinetic energy of the tester sector is considered to be the prime contributor to paper rupture. In agreement with energy dissipation concepts and the principle of energy conservation, a mathematical model expressing tearing energy was derived based on kinetic energy variations in paper during tearing. It is shown that this mathematical model can be used to calculate the net energy of the tester sector, which is available for tearing paper, and the residual energy. Consequently, the difference between net and residual energy, or tearing energy, is that portion expended in the rupture process. Furthermore, the mathematical model relates tearing energy to velocity, hence can be used to examine the effect of tear rate and time-dependent properties of paper subjected to tearing stress. A method was devised for measuring the time required to tear standard samples. From an oscilloscope trace, the tear distance and time relationship was measured and represented by a quadratic equation. From this equation, sector swing and tearing velocities were calculated for computing various energy factors and their variation at any instant of the tearing process. Results have shown that ballistic-type tear test methods are time-dependent, in that time required to tear paper varies with the sample condition. The higher the number of plies torn simultaneously, the longer was the time required to tear a paper sheet. The energy required to tear paper was also time-dependent, increasing with decreasing tear rate. It was found that the direct relationship between tearing strength and number of plies torn simultaneously does not always hold, but that a constant direct relationship exists between tearing strength and tearing energy. Although the ballistic-type tear test is time-dependent, inherent specimen properties may have a profound effect on results. Test results with an Elmendorf tear tester on five paper grades varying in tearing strength from 14 to 156 g/sheet have confirmed that the energy dissipation concept is adequate.

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