Evaluation of the tensile stress-strain properties in the thickness ...

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modulus of the sandwich and the elastic modulus of the mix according to Eq (9), by substituting Eqs (5) and (6) into (7), E paper Results F A t = = paper δ ⎛ paper t ⎜ ⎝ E The testing procedure presented in this paper was developed for the measurement of the stress-strain curve in the Z-direction of paper from which the extraction of the Zdirectional tensile strength, strain at break and elastic modulus for paper was possible. A selected number of handsheets were tested and the relations between the mechanical properties and the paper structure, in terms of structural density, were investigated. A summary of all the results is given in Appendix II. The analysis started by studying the change in thickness of the handsheets due to the pressing sequence (Table 3). The TMP handsheets showed a permanent deformation after the pressing, whereas no change was observed for the chemical handsheets. The penetration of the Photo Mounting Tissue adhesive into the handsheets was then determined by the “two-handsheets” technique. Fig 3 shows the data for the chemical pulp 1. The behavior was representative for all the investigated handsheets. The straight line is the linear fit to the data. The extrapolated value to zero-strength gave the penetration grammage into one handsheet. The results in terms of penetration grammage for all the investigated papers are summarized in Table 4. 52 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 t sandwich paper sandwich 2 t ⎞ mix [9] − E ⎟ ⎠ Table 3. Density after pressing and change in thickness of the handsheets due to pressing. Measurements were performed at 23°C and 50% RH. mix TMP 1 TMP 2 Chem 1 Chem 2 Grammage Density Change Density Change Density Change Density Change g/m 2 kg/m 3 % kg/m 3 % kg/m 3 kg/m 3 80 444 17 514 10 666 - 862 - 100 448 15 515 7 687 - 849 - 120 472 13 533 9 686 - 856 - 180 459 8 540 10 682 - 885 - 240 465 8 539 8 678 - 879 - 300 491 12 542 9 680 - 882 - Average 463 12 530 9 682 - 871 - Fig 3. Z-directional tensile strength versus grammage for one handsheet tested by the “two-handsheet” technique. Table 4. Penetration of the adhesive into the handsheets. The penetration thickness was evaluated by Eq (1). Pulp Penetration g/m 2 The penetration grammage was approximately 20 g/m 2 for all the investigated handsheets while the penetration thickness varied depending on the density of the handsheet, Fig 4. Based on the results in Table 4, the Z-strength tests for the evaluation of the elastic modulus of the mix were performed on 40 g/m 2 handsheets, using Eq (5). The elastic modulus for the adhesive was also evaluated using the custom built apparatus. The results are given in Table 5 and plotted as function of density in Fig 5. mm TMP1 19.7 0.054 TMP2 19.5 0.042 Chem1 19.5 0.029 Chem2 20.7 0.022 Fig 4. Penetration depth versus density for the handsheets tested by the “twohandsheets” technique. Table 5. Elastic modulus for the mix and the adhesive performed on 40 g/m 2 sheets. Material E, MPa TMP 1 33 TMP 2 61 Chem1 230 Chem2 302 Adhesive 1600 Fig 5. Relation between elastic modulus for the mix and handsheet density.

Testing speed Paper material and adhesives exhibit a visco-elastic behavior, i.e. their response in terms of strength will change depending on the testing speed. Rate dependency was not addressed in this paper. However the purpose was to test the material in a time window in which the strain rate had negligible influence on the material properties. The influence of the strain rate was studied for 120 g/m 2 paper sheets prepared with chemical pulp 2. Two different testing speeds were used, 0.025 mm/s and 0.0025 mm/s. The mean times to break were respectively 6.7 and 66 seconds. No influence on the Z-directional tensile strength was found. The tests in the following part of the article were therefore performed at 0.0025 mm/s speed. Stress strain curves Fig 6 presents four typical stress-strain curves for 300 g/m 2 , one for each type of pulp studied in the present investigation. The curves were calculated by Eq (8). The elastic moduli presented in this investigation were obtained by linear regression of the Z-directional stress-strain curves. The limit at which linearity was good approximation varied depending on the pulps. For TMP the elastic moduli were calculated up to 50% of the strength. For chemical pulp the calculation limit was set to 80% of the strength. Fig 6. True stress-strain curves for the investigated handsheets. Sheets prepared from chemical pulps were stiffer than the ones made of mechanical pulps. TMP was characterized by a strain at break around 8%, whereas strain at break for chemical pulp ranged from 1.4% to 1.8%. The postpeak behavior changed drastically for different pulps. For chemical pulp 2 the post-peak behavior was unstable at any grammage. For chemical pulp 1, post peak instability was also present for low grammage handsheets, but for higher grammage the failure was stable. For TMP handsheets the failure was always stable. Z-directional tensile strength In Figs 7 to 10 the Z-directional tensile strength is shown as a function of grammage. The strength values are obtained using two different techniques, i.e. measurements performed by the custom built apparatus using adhesive, and data measured using double adhesive tape. Fig 7. Grammage versus Z-directional tensile strength plot for TMP1 obtained using two different testing methods. Fig 8. Grammage versus Z-directional tensile strength plot for TMP2 obtained using two different testing methods. Fig 9. Grammage versus Z-directional tensile strength plot for chemical pulp 1 obtained using two different testing methods. Fig 10. Grammage versus Z-directional tensile strength plot for chemical pulp 2 obtained using two different testing methods. Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 53

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