Measured and calculated bending stiffness of individual fibers

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1 Measured and calculated bending stiffness of individual fibers W. J. FISCHER 1,2, C. LORBACH 1, M. JAJCINOVIC 1,2, U. HIRN 1 and W. BAUER 1,2 1 Graz University of Technology, Institute of Paper, Pulp and Fiber Technology, NAWI Graz, Inffeldgasse 23, 8010 Graz, Austria 2 Doktoratsinitiative DokIn Holz Holz- Mehrwertstoff mit Zukunft wolfgang.fischer@tugraz.at 1 INTRODUCTION The bending stiffness of individual pulp fibers is of great importance for the formation of fiber to fiber joints [1, 2, 3] and this in turn has a direct impact on the strength of the paper network [4,5]. It is defined to be the product of the modulus of elasticity (E) and the area moment of inertia (I). The E-modulus is influenced by the fibril angle [6] of the secondary wall, natural or induced defects (due to handling) as well as the type of the fiber (early- / latewood) [7]. Factors influencing I are the size and shape of the fiber cross section, fiber collapse and the fiber wall thickness [8]. Furthermore it is influenced by the bending direction (see Figure 1) [9]. Figure 1. Influence of bending direction. If a bending load is applied horizontally to the fibers shown in Figure 1, the left fiber is bent around the y-axis and the right one around the z-axis. The bending stiffness is higher for the fiber on the right hand side. If the load is applied vertically, it is the other way around [9]. In the scope of this study we define I z as the maximum possible area moment of inertia, it occurs when the fiber is bent around the z- axis. I y is defined to the minimum possible area moment of inertia, it occurs when the fiber is bent around the y-axis. Single fiber bending stiffness can either be determined in the wet or the dry state. Until recently, studies carried out in this field of research mainly focused on the determination of the wet fiber flexibility as it plays an important role during the sheet forming process. The flexibility (1 / E I) of fibers in the wet state which is the reciprocal of the bending stiffness is measured using flow cell based devices [2, 8, 10, 11]. However, there is less literature about the determination of the dry bending stiffness. In the work of Schniewind et al. [12] and Seborg and Simmonds [13] single dry fibers were deflected using a spring. For their tests they assumed the fiber as a cantilever beam (principle is shown in Figure 2). The present work compares dry bending stiffness values calculated from measurements of E and I (E I calculated dry), to values determined with a single fiber testing apparatus (E I measured) where the bending deformation is photographed and the bending force is measured. Furthermore, estimated wet fiber bending stiffness values (E I calculated wet) are compared to measurements of wet fiber bending stiffness using flow cell based techniques. 2 MATERIALS AND METHODS All investigations were performed using an unbleached softwood kraft pulp (mixture of spruce and pine). With this pulp individual fibers and fiber to fiber joints were prepared according to the method of Kappel et al. [14]. After preparation the fibers and joints were glued on custom designed sample holders and tested using a micro bond tester developed and designed at Graz University of Technology [15] as well as Dynamic Mechanical Analysis (DMA Q 800-RH from TA Instruments USA). Cross sectional fiber properties were determined using a three dimensional serial sectioning technique [16, 17]. 2.1 Determination of mechanical fiber properties in the dry state The mechanical properties of single fibers are determined by using the device of Fischer et al. [15]. This device offers the possibility to determine the flexural rigidity of single fibers in two different ways. Determination of bending stiffness Method I In this case we assume the deflected fiber to be a cantilever beam (see Figure 2) [15]. Figure 2. Cantilever beam. Figure 3. Joint configuration used for bending stiffness measurement (Method I). Unloaded state (left) and deflection of horizontal fiber by vertical load applied through vertical fiber (right).

2 For measuring the bending stiffness of a single fiber a fiber - fiber joint configuration as shown in Figure 3 is used. From the figure it is apparent that only one end of each fiber is glued on the sample holder. For determination of the bending stiffness of the horizontal fiber the vertical fiber is pulled upwards and the horizontal fiber is deflected. Determination of bending stiffness Method II Method II uses the principle of a beam fixed at both ends (see Figure 4). area A cross obtained from serial sectioning. The modulus of elasticity is calculated using equation 3 and 4. (3) (4) 2.2 Determination of fiber cross sectional properties In order to determine the cross sectional properties of fibers, pulp samples (dry and wet state) as well as fibers broken during tensile testing a three dimensional serial section technique is used [16, 17]. For this the samples are embedded in resin and after curing of they are mounted and cut by an automated microtome (see Figure 7). Figure 4. Beam fixed at both ends. Here the longitudinal fiber is replaced by a hook which is used to deflect the cross fiber (see Figure 5). Figure 5. Bending stiffness measurement with hook (Method II). The testing procedure is filmed and from the images the free fiber length l as well as the deflection w is measured. The bending force (F bend) is measured using a load cell. Knowing these parameters the bending stiffness of the deflected fiber is calculated by equation 1 (Method I) and equation 2 (Method II). Figure 7. Microtome used for determination of cross sectional properties. From the images (see Figure 8) the cross sectional area A cross and the area moments of inertia I y and I z are calculated using MATLAB. (1) (2) Determination of E-modulus The elastic modulus E in two different ways, first by single fiber tensile testing (using the device described in [15]) and second by dynamic mechanical analysis (DMA) [9] of single fibers. For these tests a single fiber is mounted on a sample holder and loaded until it is breaks (see Figure 6). Figure 6. Sample holder used for single fiber tensile testing. In case of DMA the modulus of elasticity is directly obtained whereas for single fiber tensile testing it is calculated from the measured breaking force F break, the strain to failure ε as well as the cross sectional Figure 8. Imaging of fiber cross section using the microtome method. Using the results of the microtome investigations in combination with the modulus of elasticity, the bending stiffness in the dry state based on the fiber cross section (based on A cross) can be determined. In the present study three specific fibers are analyzed. 2.3 Estimation of fiber properties in the wet state Cross sectional area (A cross) For calculating the properties of single fibers in the wet state, changes in cross sectional size due to swelling have to be taken into account. In order to

3 clarify this, a comparison of microtome cross sections (see section 2.2) in the dry state (50% R.H.) and those of swollen and freeze dried fibers are used to determine the increase of A cross due to swelling. Knowing the cross sectional area in the dry (A cross dry) and wet state (A cross wet), a swelling factor S [9] can be calculated. 100 (5) Area moment of inertia in the wet state (I wet) The wet area moment of inertia is calculated from measurements with the microtome method on dry fibers (see section 2.2). A cross wet is determined using equation 5. Assuming that the fiber cross section grows without any change in shape, the wet fiber thickness and width can be calculated which turn are used to determine I y wet and I z wet. Modulus of elasticity (E) The influence of water on the modulus of elasticity is estimated by using the results obtained by Kersavage [18]. The modulus of elasticity in the wet state (15.49 GPa) in conjunction with E at 50% R.H. (28.98 GPa) of Kersavage is used to give an estimate of the reduction of E (ERF = E-modulus reduction factor) [9]. $% 100 & & (6) Using the results of Kersavage the wet modulus of elasticity is calculated to be 47% smaller than the one at 50% relative humidity (dry state). Wet fiber bending stiffness (WFBS) In the present study a combination of tensile testing (measurement of E), the microtome method (measurement of A cross, I) and the results of Kersavage [18] is used to give an estimate of the bending stiffness in the wet state. The wet fiber bending stiffness is calculated according to equation 7 (referred to as E I calculated based on A cross, see Figure 11 and Figure 12) [9]. 3 RESULTS 3.1 Cross sectional properties Table 1 shows the mean cross sectional areas of dry and wet fibers measured with the microtome method. Table 1. Measured mean cross sectional areas in the dry (280 cross sections) and wet (129 cross sections) state [9]. A cross dry A cross wet 154 µm² 184 µm² Using these results the increase in fiber cross sectional area (swelling factor S) is calculated to be S = 19.5%. Furthermore the cross sectional properties of three individual fibers were analyzed. The measured moments of inertia I y dry ranged from m 4 to m 4, and from m 4 to m 4 for I z dry. The cross sections ranged from 206 to 318 µm². For estimating the area moment of inertia in the wet state swelling under preservation of the cross sectional shape was assumed i.e., no change in cross sectional shape. From that enlarged fiber cross section, the area moments of inertia are calculated. I y wet ranged from m 4 to m 4, and I z wet from m 4 to m Modulus of elasticity Figure 9 shows a comparison between E-modulus values obtained from single fiber tensile testing (SFTT), dynamic mechanical analysis (DMA) and those of previous studies at 50% relative humidity (dry state). Figure 9 demonstrates that the results of previous studies and the DMA measurements indeed verify the determination of the modulus of elasticity using a micro bond tester [15]. '%( ( *&+,-. ) 01 (7) Furthermore the results obtained by Schniewind et al. [12] are also used to estimate the bending stiffness of wet fibers. In the work of Schniewind, E I in the dry and wet state were measured. They found that E I wet is about 81.65% smaller than E I dry. Here the wet flexural rigidity is calculated using equation 8 (referred to as E I calculated based on Schniewind et al. 1965, see Figure 11 and Figure 12). '%( ( )( 3:3.,-. ) (8) Figure 9. E-modulus values obtained in different studies. From the figure it is apparent that all values are within the same range. Explanation for the variations are natural of induced fiber defects, differences in

4 the fibril angle as well as the method used for fixing and testing the fibers. Using the ERF (see section 2.3) the wet modulus of elasticity was estimated to be GPa for single fiber tensile testing (SFTT) and 9.00 GPa for DMA. An explanation for the reduction of E in the wet state is that the cohesiveness of the cell wall or bonding between cellulosic materials is reduced. Furthermore, water on intramolecular surfaces leads to slippage of microfibrils and this in turn also reduces the modulus of elasticity [18, 23]. 3.3 Single fiber bending stiffness in the dry state Figure 10 shows the results of the measured and calculated bending stiffness values in the dry state. Variations within the measured values can be explained by changes of the cross sectional dimensions, the fiber wall thickness (earlywood or latewood fibers), the degree of fiber collapse and weak spots along the fiber [8]. These factors influence the area moment of inertia I and this in turn the bending stiffness (E I). Furthermore, differences in the fibril angle between fibers [6] lead to different values of the modulus of elasticity. On this account it has been decided to use the results of [12] only for calculating E I y calculated wet (see Figure 11 and Figure 12). Summing up it can be said, that the results of Schniewind confirm our results for E I y calculated and our measurements of E I measured agree well with the calculated bending stiffness values E I z calculated. 3.4 Wet fiber bending stiffness Figure 11 shows a comparison between the calculated dry and wet bending stiffness of individual fibers. Figure 11. Comparison of calculated dry and wet bending stiffness values (3 fibers analyzed). Figure 10. Comparison of measured and calculated bending stiffness values of softwood kraft fibers in the dry state. The results also show that the E I y calculated is lower than the measured bending stiffness. An explanation for this is that in our bending stiffness measurements (see section 2.1) the fibers are bent around the z-axis which has a higher area moment of inertia. On this account E I z calculated has to be compared with the measured bending stiffness values. In case of Schniewind et al. [12] it is not known if the fibers are bend about the y- or z-axis. Due to the fact that his values are smaller than those measured in the present study it is assumed that Schniewind is measuring E I y. This assumption is confirmed by a t-test which showed that the results of Schniewind are statistical significant different from those of method I, II and E I z calculated. The t-test also showed that there is no statistical significant difference between E I y calculated and the results of Schniewind. From the results it is apparent that there is a great difference between the bending stiffness values E I y and E I z for dry state and wet state estimations. This is due to the highly different values for the moments I y and I z. The lower bending stiffness in the wet state can be explained by the reduction of the modulus of elasticity due to swelling i.e., the reduction of E is greater than the increase in I. Figure 12 shows a comparison of the wet bending stiffness values estimated in the present work and those obtained in other studies. The results of our study show good agreement for E I y. The estimated bending stiffness values around the z-axis (E I z = Nm²) are higher than the measured values. Figure 12. Wet bending stiffness values obtained in different studies.

5 When using flow cell methods [2, 10, 11] the bending force is exerted towards the flat side of the fiber inducing a moment that corresponds to the moment of inertia I y calculated in this study. The suspended fiber is bent by the load of a water stream, which deforms the fiber. The tested fiber is free to twist in the water current, and it always bends in the direction giving the least resistance to the current, which is the direction with the minimum bending resistance, i.e., I y. The wet bending stiffness values which are estimated based on the assumption made from the results of [12] indicates that the reduction of the modulus of elasticity seems to be higher than the one calculated using the results of [18]. 4 CONCLUSIONS In this study, we have proposed an alternative method to determine wet and dry bending stiffness of individual fibers. The bending stiffness values calculated from the E-modulus and area moment of inertia (E I calculated based on A cross) are compared to measured values (E I measured). Bending stiffness values obtained from experiments (see section 2.1 and Schniewind et al. [12]) agree well with the results of our method for calculating the flexural rigidity in the dry state (E I calculated dry). The calculated bending stiffness in the wet state (E I calculated wet based on A cross) is higher than measured values (see Figure 12). The reason for this is that the reduction of the modulus of elasticity due to swelling seems to be higher than ERF = 47% (see section 2.3). This is also confirmed when calculating the wet bending stiffness using the results of Schniewind et al. (E I calculated wet based on Schniewind). We have also successfully verified our method for measuring the modulus of elasticity using the micro bond tester. Acknowledgements Financial support for this work in the framework of the PhDSchool DokIn Holz funded by the Austrian Federal ministry of Science, Research and Economy, Sappi and Mondi is gratefully acknowledged. REFERENCES [1] B. Leopold and D.C. McIntosh. Chemical composition and physical properties of wood fibers III. Tensile strength of individual fibers from alkali extracted loblolly pine Holocellulose. Tappi J. 44(3): (1961). [2] L. Paavilainen. Conformability flexibility and collapsibility of sulphate pulp fibres. Pap. Puu-Pap. Tim. 75(9): (1993). [3] J. Forström, A. Torgnysdotter and L. Wågberg. Influence of fibre/fibre joint strength and fibre flexibility on the strength of papers from unbleached kraft fibres. Nord. Pulp Paper Res. 20(2): (2005). [4] J. d A. Clark. Pulp Technology and Treatment for Paper. Miller Freeman Publications, edition 2, (1985). [5] A. Torgnysdotter and L. Wågberg. Influence of electrostatic interactions on fibre/fibre joint and paper strength. Nord. Pulp Paper Res. 19(4): (2004). [6] D.H. Page, F. El-Hosseiny, K. Winkler and A. Lancaster. Elastic modulus of single wood pulp fibers. Tappi J. 60(4): (1977). [7] B.A. Jayne. Mechanical properties of wood fibers. Tappi J. 42(6): (1959). [8] A.A. Robertson, Meindersma, E. and S.G. Mason. The measurement of fibre flexibility. Pulp Paper Mag. Can. 62(1):T3-T10 (1961). [9] C. Lorbach, W.J. Fischer, A. Gregorova, U. Hirn and W. Bauer. Pulp fiber bending stiffness in wet and dry state measured from area moment of inertia and modulus of elasticity. BioResources 9(3): (2014). [10] D.C.S. Kuhn, X. Lu, J.A. Olson and A.G. Robertson. A dynamic wet fibre flexibility measurement device. J. Pulp Pap. Sci. 21(10):J337-J342 (1995). [11] P.A. Tam Doo and R.J. Kerekes. A method to measure wet fiber flexibility. Tappi J. 64(3): (1981). [12] A.P. Schniewind, G. Ifju and D.L. Brink. Effect of drying on the flexural rigidity of single fibers. Transaction of the 3 rd Fundamental Research Symposium, Cambridge, Technical Section of the British paper and Board Makers Association, , (1965). [13] C.O. Seborg and F.A. Simmonds. Measurement of the stiffness in bending of single fibers. Paper Trade J. 113(17):49-50 (1941). [14] L. Kappel, U. Hirn, W. Bauer and R. Schennach. A novel method for the determination of bonded area of individual fiber-fiber bonds. Nord. Pulp Paper Res. 24(2): (2009). [15] W.J. Fischer, U. Hirn, W. Bauer and R. Schennach. Testing of individual fiber-fiber joints under biaxial load and simultaneous analysis of deformation. Nord. Pulp Paper Res. 27(2): (2012). [16] M. Wiltsche, M. Donoser, J. Kritzinger and W. Bauer. Automated serial sectioning applied to 3D paper structure analysis. J. Microscopy 242(2): (2011). [17] C. Lorbach, U. Hirn, J. Kritzinger and W. Bauer. Automated 3D measurement of fiber cross section morphology in handsheets. Nord. Pulp Paper Res. 27(2): (2012). [18] P.C. Kersavage. Moisture content effect on tensile properties of individual douglas-fir latewood tracheids. Wood Fiber 5(2): (1973). [19] L. Groom, L. Mott and S. Shaler. Mechanical properties of individual southern pine fibers. Part I. Determination and variability of stress-

6 strain curves with respect to tree height and juvenility. Wood Fiber Sci. 34(1):14-27 (2002). [20] L. Mott, L. Groom and S. Shaler. Mechanical properties of individual southern pine fibers. Part II. Comparison of earlywood and latewood fibers with respect to tree height and juvenility. Wood Fiber Sci. 34(2): (2002). [21] E.M.L. Ehrnrooth and P. Kolseth. The tensile testing of single wood pulp fibers in air and in water. Wood Fiber Sci. 16(4): (1984). [22] O.J. Kallmes and M. Perez. Load/elongation properties of fibres. Transaction of the 3 rd Fundamental Research Symposium, Cambridge, Technical Section of the British paper and Board Makers Association, , (1965). [23] K.M. Sedlachek. The effect of hemicelluloses and cyclic humidity on the creep of single fibers. PhD thesis, Institute of Paper Science and Technology, Atlanta, GA, USA (1995). [24] N. Navaranjan, J.D. Richardson, A.R. Dickson, R.J. Blaikie and A.N. Prabhu. A new method for the measurement of longitudinal fibre flexibility. 61 st Appita Annual Conference and Exhibition, Gold Coast, Australia, Appita Inc., (2007).