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was applied on the reference point. A rigid link between the reference point and paper edge was used to connect the paper and the reference point.
Figure3. Finite element model and boundary conditions.
Modeling the tensile test using the reference point to apply the prescribed displacement was important for the post-processing once the number of procedures for the automatic results analysis had been reduced. This strategy does not affect the analysis results, as the resultant applied forces are the same for the case where a prescribed displacement is applied in each boundary node [8]. The paper was simulated using a four-node reduced integration membrane element (M3D4R). The model has a total of 11,086 elements and due to the cuts, a free mesh was used. It is important to mention that the mesh parameters did not change for all simulations. The material properties for the material model are: E 11 = 13.89 MPa, E 22 = E 33 =4.23MPa, μ = 0.33 and G 12 = 2.1 MPa. The parameters for the IPE model consider K 22 = K 33 since the mechanical behavior in the CD (direction 2) is similar to that in the thickness direction (direction 3). Thus, A =1, B =2.40, C =2.40 and D =1.38.
3. Experimental Tests–Materials and Methods 3.1. Materials
Four commercial two-ply toilet papers were selected. These toilet papers were identi- fied A to D. It was previously verified that two of the two-ply papers tear off the perforation when loaded manually (toilet papers A and B). The other two papers tear on the perforation when loaded manually. 3.2. Methods The grammage was determined accordingly with the standard ISO 12625-6:2005 [16] and defined as the mass per unit paper area (g/m 2 ). A Mettler Toledo PB303 Delta range analytical balance (Mettler Toledo, Columbus, OH, USA) was used to determine the paper sample weight. To determine the thickness, where a stack of sheets of paper or a sheet of paper were/was compressed at a given pressure between two parallel plates, a FRANK- PTI ® Micrometer (FRANK-PTI GMBH, Birkenau, Germany) was used, in accordance to the standard ISO 12625-3:2014 [17]. According to this standard [17], the bulk, which is the inverse of density, can be determined by using the grammage and thickness previously determined. According to the standard ISO 12625-12:2010 [5], the perforation line was evaluated. On a Thwing-Albert ® VantageNX Universal Testing Machine, tensile tests were performed in the MD for all samples. For each paper, samples were prepared with the perforation in the center (0 ◦ ) and with the line of perforation at different angles (20 ◦ , 30 ◦ , 37.5 ◦ , 41 ◦ and 45 ◦ ). Other samples were also prepared, of each paper, with the length of a single “sheet”
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