Eng 2023 , 4
86
without perforation but with the orientation of the corresponding angle to annulate the fiber orientation contribution (see Figure 4)
Figure4. Experimental set-up to test non-perforated and perforated toilet papers. (F shows the force direction applied in the tensile test). The cut and blank distances measurements were made with a paquimeter and repeated in 10 different perforations for each toilet paper sample. 4. Results and Discussion Structural characterizations were carried out on the four commercial two-ply toilet papers samples, according to the above-referred standards. Table 1 shows the results in terms of grammage, thickness, bulk, cut and blank distances for all toilet paper samples. Table1. Physical characterization of the toilet papers: number of plies, grammage, thickness, bulk, cut and blank distance.
Ш
Ш
Ш
Ш
Ш
Grammage (g/m 2 )
Thickness ( μ m)
Bulk (cm 3 /g)
Cut Distance (mm)
Blank Distance (mm)
Toilet Paper ID
N ◦ Plies
x
x
x
x
x
σ
σ
σ
σ
σ
2 2 2 2
36.6 35.4 32.4 44.9
± 0.64 374 ± 0.26 305 ± 0.42 611 ± 0.71 345
± 10.4 10.2 ± 12.4 8.6 ± 4.4 19.1 ± 8.7 7.7
± 0.36 1.5 ± 0.37 1.9 ± 0.41 4.0 ± 0.27 2.3
± 0.05 1.0 ± 0.05 1.2 ± 0.05 1.0 ± 0.05 1.0
± 0.05 ± 0.10 ± 0.05
A B C D
± 0.05 Looking at Table 1, the grammage shows values in the range of 32.4–44.9 g/m 2 . Evaluating the outcomes for the thickness and bulk, values vary between 51% and 60%, respectively, due to the embossing process type. Figure 5 shows the perforation efficiency behavior as function of the perforation line angle obtained for all toilet paper samples. Analyzing Figure 5, a decreasing trend in perforation efficiency can be observed with an increasing perforation line angle. Although the selected toilet papers present different characteristics, it was demonstrated that they present the same tendency in this regard. This fact is in line with what it was found by Vieira et al. [9], who stated that the perforation efficiency depends on the cut dimensions and not on the fibrous composition and/or the number of plies. To validate the FE model, the perforation efficiency for papers B and C (Table 1), with a cut distance, c , of 1.9 mm and 4.0 mm, respectively, was simulated. The experimental and simulated results are compared in Figure 6. For these simulations, the FE model considered the same conditions (boundary conditions and fiber orientation) as the experiments with and without perforation. There are some differences between the numerical and experimental results regarding the perforation efficiency (see Figure 6) that could be related to how the failure evolves in the FE model, resulting in higher failure loads (see Equation (1)). Despite these two cases, the FE model showed the same trend, and therefore optimization can be performed using this model (Figure 6). For the 4 mm perforation, the average error between the simulations and experiments was 5.2%, with the error being 8.8% for the 2 mm perforation.
Made with FlippingBook flipbook maker