Furnish and papermaking effects
Figure 1 shows some examples of the load-elongation curves of machine-made papers. In some cases, such as newsprint in MD, the curve is almost linear all the way to rupture. For many others, especially in CD, the curve consists of two almost linear parts. In microcreped sack papers, the high-strain part of the curve in MD bends upwards because of macroscopic waviness that was initially present in the sheet. Finally, in some grades, such as glassine in MD, the tangent modulus decreases almost continuously with increasing strain.
Figure 1. Characteristic load-elongation curves of machine-made paper grades in MD and CD. Load is expressed as elastic strain, εel = σ/E.
The load values in Figure 1 are expressed as the elastic strain, εel = σ/E. If one considers the ordinary load-elongation curve, the largest differences between paper grades arise from differences in the elastic modulus. As discussed above, the elastic modulus is sensitive to the density of paper, beating of chemical pulp, drying shrinkage and fibre orientation. Figure 2 in Microscopic yielding phenomena demonstrated that the shape of the load-elongation curve is essentially independent of density. It is also independent of the beating level of chemical pulp1 These factors only move the location of the breaking point on a single master curve.
The factors that influence the shape of the load-elongation curve are drying shrinkage, wood species, furnish type, and the curl, kinks and other defects in fibres 1. In machine-made papers, the elastic strain vs. total strain curves are usually different in MD and CD, as shown by Figure 1. This is presumably due to the anisotropic drying stresses on the paper machine. It is natural that mechanical and chemical pulps give different curves. Typically, chemical pulps give larger plastic elongation and correspondingly smaller elastic strain than mechanical pulps.
In cases where the elastic strain-total strain curve is unchanged, the location of the yield point should naturally also be constant. Experimental observations on this are limited. In a set of machine-made papers, the yield point in MD and CD was always at ε = εel = 0.45–0.50% when a 0.02-percentage point deviation from linearity was the criterion for the yield point 2. According to Htun 3, the yield strain is ε ≈ 0.16% in ordinary handsheets dried under full restraint independent of furnish type, wet pressing and beating. He may have used a deviation smaller than 0.02% as the criterion.
Breaking strain characterises the point where the load-elongation curve ends. Figures 2 and 3 present experimental data for the same samples as considered above and below (this refers to the pairs of 5 and 6 plus 40 and 41). Beating again has a strong positive effect on breaking strain, and wet pressing and grammage have only a weak effect, if any. Plotted against density, breaking strain behaves much like elastic breaking strain except that the range of variation of the ordinary breaking strain is larger.
Figure 2. Breaking strain vs. density when varying beating. Each line connects the data for one wood species, pulp type and fixed wet pressing level using in part the same samples as in 4,5 Figure 1 in Elastic constants and their measurement.
Figure 3. Breaking strain vs. density when wet pressing varies. Each line connects the data for one wood species, pulp type and fixed beating level using in part the same samples as in 5 Figure 2 in Elastic constants and their measurement.
Drying shrinkage influences the ordinary breaking strain in much the same way that it influences the elastic breaking strain. As shown in Figure 4, breaking strain at large shrinkage is approximately the following:
At small shrinkage or moderate wet strain levels, breaking strain equals the constant in Eq. 11. This therefore reflects the effects of furnish and wet pressing indicated above in Figures 2 and 3. Analysis of fibre orientation effects 6 shows that fibre orientation does not alter Eq. 1 other than by changing the shrinkage potential of paper. For a given drying shrinkage, papers with different fibre orientation still have the same breaking strain.
Figure 4. Breaking strain vs. drying shrinkage or wet strain for unbleached kraft (triangles) and groundwood pulp (squares)) at a low and high level of beating (open and closed symbols, respectively) using the same samples as in 6 Figure 3 in Elastic constants and their measurement.