Furnish and papermaking effects on tensile strength
Tensile strength has the same units as elastic modulus, i.e., the breaking force per cross-sectional area is given in units of MPa. However, usually it is expressed as force per specimen width in kN/m or as the tensile index in units of Nm/g, obtained by dividing the strength per width by grammage. In older literature, breaking length in units of km was used in place of the tensile index. Breaking length tells how long a piece of paper can be before its own weight causes tensile failure.
It would naturally be most interesting to analyse tensile strength data against fracture energy and damage width in order to relate the observations to changes in fibre and bond properties. Unfortunately, fracture energy or damage width values have not been measured until very recently. However, in line with the earlier emphasis on elastic modulus, we observe that the experimental observations on tensile strength T are considerably simplified when we consider elastic breaking strain, εel = T/E, i.e., tensile strength divided by elastic modulus. Figures 1–3 show εel vs. density for the same cases whose elastic modulus we discussed before. Within experimental accuracy, the values of εel and E are linearly dependent on density when only one parameter such as beating varies.
Figure 1. Elastic breaking strain of bleached kraft pulp handsheets of different grammages.
Figure 2. Elastic breaking vs. density when varying beating. Each line connects the data for one wood species, pulp type and fixed wet pressing level.
Figure 3. Elastic breaking strain vs. density when wet pressing varies. Each line connects the data for one wood species, pulp type and fixed beating level.
When only wet pressing or grammage varies, as in Figures 1 and 3, the elastic breaking strain is almost constant. It increases by only 0.05–0.1% for every 100 kg/m3 increment in density. The mechanical properties of fibres should remain constant in this case, so that the slight variation in εel is all that the effect of changes in inter-fibre bonding can have on εel.
Beating (Figure 2) influences the elastic breaking strain much more than wet pressing or grammage. The change is approximately 0.4% for every 100 kg/m3 increment in density. Like the elastic modulus, the curves for εel are independent of furnish and wet pressing, except a shift in the density scale. It seems obvious that changes in the furnish and its beating alter the strength properties of both bonds and fibres. Beating may simultaneously lead to changes in bond strength and in fibre properties such as curl, length and strength. The improvement in bonding with increasing beating is also seen as a reduction of the light scattering coefficient, Figure 4. The bonds formed between well-beaten fibres should tolerate more stretching than bonds between lightly-beaten fibres.
Figure 4. Light scattering coefficient vs. tensile strength when beating and wet pressing vary for softwood kraft and groundwood pulps 3.
The changes in tensile strength with increasing beating of chemical pulp or refining of mechanical pulp come partly from increasing fines content. Figure 5 shows the result when adding two kinds of fines to a long-fibre fraction. When adding fines, paper density also increases, but elastic modulus is insensitive to the type and content of the fines. Fines therefore seem to alter only bond strength and not the sheet structure. Figure 5 shows that when adding mechanical pulp fines, the usual link between tensile strength and light scattering co-efficient no longer holds.
Figure 5. Tensile strength and elastic breaking strain vs. density (a) and tensile strength vs. light scattering coefficient (b) for different additions of kraft and TMP fines to unbeaten kraft long fibres. The effect of a 1.2% starch addition is shown in (b)4.
The drying-induced internal stress state of inter-fibre bonds affects the elastic breaking strain of paper, although clear changes occur only at high levels of shrinkage, close to the maximum shrinkage, as indicated in Figure 6. High drying stress and low drying shrinkage or even moderate wet strain give brittle bonds 4 and therefore low elastic breaking strain. When compared at a constant, non-zero drying shrinkage, different beating levels and furnish types do not affect εel considerably.
Figure 6. Elastic 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).
High drying shrinkage gives low elastic modulus. Tensile strength therefore increases with decreasing shrinkage. The opposite trends of elastic modulus and elastic breaking strain can lead to a maximum in tensile strength at small wet strains 6.
In machine-made papers, drying shrinkage and fibre orientation determine the anisotropy of tensile strength. The MD/CD ratio of tensile strength is similar to that of elastic modulus. In the centre of a web, the MD/CD ratio of tensile strength is usually equal to the elastic modulus ratio, as shown in Figure 7. The elastic breaking strain appears to be isotropic in that case. At the edges of a web, the modulus ratio is higher than the strength ratio.
Figure 7. MD/CD ratio of elastic modulus vs. MD/CD tensile strength ratio in machine-made copy papers for the centre of the web (a) and edges (b). Symbols refer to different paper machines (KCL, unpublished).
Pulp mixtures
Chemical pulp is added to mechanical pulp in order to improve the mechanical properties of paper. As pure furnishes, chemical pulps usually give higher tensile strength and elastic modulus than mechanical pulps, and a corresponding improvement is seen when adding chemical pulp to a mechanical pulp. Since the properties of pure components can be measured separately, general insights into the mechanical properties of paper can in principle be obtained by analysing binary mixtures.
The properties of pulp mixtures usually change in a non-linear manner as a function of the mixing ratio. Figure 8 illustrates this for the addition of springwood kraft fibres to a TMP furnish. The tensile index increases only if the kraft content exceeds 30%. The addition of summerwood kraft causes a decrease in tensile strength. The specific elastic modulus shows a similar but not quite as strong a variation in the two cases, Figure 8(b).
Figure 8. Tensile index (a) and specific elastic modulus (b) vs. the furnish mixture of TMP and springwood or summerwood kraft pulp 7.
Considerable variability exists in the minimum consistency of chemical pulp that is necessary for an improvement in a given mechanical property of paper. The threshold consistency typically varies between 20% and 50%, but it may also be so small that even slight amounts of added chemical pulp can have a positive effect 8. Paper density (Figure 9) reveals that a lot but still not all of the non-linear variation comes from changes in bonding. When mixing fibres of different flexibility, the density of the network may be limited by the stiffer furnish component, as the more flexible component may conform to the structure defined by the stiffer component. The degree of fibre collapse may also depend on the mixing ratio, leading to non-linear dependence of inter-fibre bonding on the mixing ratio 9.
Figure 9. Density (a) and light scattering coefficient (b) vs. furnish mixture for handsheets of TMP and springwood or summerwood kraft pulp. The same samples as in Figure 8 7.
The tensile strength of a pulp mixture also relates to its stress-strain curve. If one ignores the possible complications of load sharing, the curve for a mixture should be equal to a properly weighted mean stress of the two components for the common strain. Then one only needs to determine where the failure point lies on the mean value curve. With some additional assumptions, this approach gave very accurate predictions for the tensile strength and breaking strain of various mixtures when the same properties of the pure pulps were known 8. However, Fig. 10 gives a counterexample where the mean stress assumption fails, as the separation between the curves is not linearly proportional to the mixing ratio.
Figure 10. Load-elongation curves of beaten softwood kraft and groundwood at kraft mass fractions of 0, 10, 40, 60 and 100% (KCL, unpublished).
A main use of fracture toughness and tear strength measurements is in evaluating the efficiency of reinforcement chemical pulps in improving the runnability of printing papers made from mechanical pulp. Figure 11 illustrates the reinforcement effect when softwood kraft pulp was added to pressure groundwood (PGW). The critical value of the J-integral and the in-plane and out-of-plane tear energy all increase when replacing the mechanical pulp with kraft pulp, but in a different manner.
Figure 11. Critical value of the J-integral, Jc, indexed with grammage (black diamonds), in-plane tear index (white squares), and out-of-plane tear index (asterisks) vs. kraft pulp content added to PGW handsheets (KCL, unpublished).
