Strength by liaoqinmei



This article describes results of 2-layer stratification of through air dried, creped and
uncreped (flat) sheets on a slow speed (40 fpm) pilot paper machine, using two different,
"strong and weak" model systems, one consisting of refined and unrefined NSWK the
other NSWK and Eucalyptus. The study dealt with the effects of BW, composition, and
layer orientation on creped and uncreped (i.e. flat) strength, density, bulk, and water
absorptive capacity. Surprisingly, stratification showed no benefit in improving density-
related properties; stratified sheets had the same density, bulk, and water absorptive
capacity as homogeneous sheets of similar strength and composition. However, compared
to the homogeneous controls, stratification altered the strength of the creped web. The
direction of the change depended on the orientation of the layers; the drier side layer lost
30% more, while the air side 30% less than the unstratified homogeneous control.

These findings would most likely apply to the more popular 3-layer stratification.
Furthermore, they imply that stratification would not improve any other
density-related tissue product properties, like, for instance, sheet flexibility and bulk
softness. However, the findings do not contradict the well-known overall softness and
economic benefits of 3-layer stratification. The article also shows how to compare
products of different Basis Weight using corrected Breaking Length and corrected
Bulk/BW, since these properties are not BW-independent.


In the last 2 decades stratification has become widespread as a technique for making
premium grade tissue. The use of three different layers has provided considerable
economic benefit by allowing cheaper furnish to be placed in the middle layer, and also
afforded a means for increasing the product softness, or at least surface smoothness,
through the use of superior furnish components in the outer layers. These benefits, while
seldom documented systematically in the Literature, are intuitively obvious. It is,
however, by no means clear how stratification affects other important properties, like
strength, cushioniness, flexibility, bulk, and water absorptive capacity.

The present work as undertaken to quantify the effect of stratification on strength, bulk,
water absorptive capacity, and density, at a wide range of Basis Weights and at different
layer orientations. To reduce the number of variables the study was restricted to 2-layer
stratification using two different, "strong and weak" model systems, one consisting of
refined and unrefined NSWK the other NSWK and Eucalyptus. The study was carried out
on a slow speed (40 fpm), through air dried (TAD) pilot paper machine. Since the TAD
method allowed the easy removal of the sheet before creping, both creped and uncreped
(flat) sheets could be studied separately.

The present work utilizes several seldom-used testing methods and calculating
procedures. Instead of apparent density, based on product thickness, it uses true density,
determined by the oil saturation method. Since oil only penetrates into the basic portion
of the sheet, it is not influenced by the pattern imparted by creping. This method, aside
from being more accurate, allows comparison between creped and uncreped sheets. The
second novel method relies on the use of "-corrected Breaking Length" to compare
strength at different BWs. Regular BL tacitly assumes that the TS-BW relationship is not
only linear but the two variables are directly proportional to each other. Its calculation
simply divides TS by BW. Since, as has been found by several researchers (xx) and is
very clear from this work that there is a considerable BW-intercept (dubbed the -value),
ignoring it in the usual BL calculating procedure leads to considerable error when
comparing products of different BWs. The concept of -corrected BL takes this fact into
consideration and requires that the -value be subtracted from the appropriate BW before
BL is calculated. Similarly, Bulk does not directly proportional to BW, something
implicitly assumed when Bulk/BW is used to compare products at different BWs.
Bulk/BW in fact is highly dependent on BW. The BW-intercept (dubbed the -value) for
the Bulk-BW relationship is extremely high. The concept of -corrected Bulk/BW takes
this fact into consideration and requires that the -value be subtracted from the
appropriate BW before Bulk/BW is calculated. These calculating procedures allow
comparison of properties for the wide BW range and layer composition in the study.
While the results may not be immediately comparable to other works, the extra accuracy
of these procedures is a compensation.

Experimental Procedure.

The runs have been carried out on a 14 in wide pilot paper machine in a trough air dried
mode at 50 fpm, employing 2 layer stratification and a model furnish of "strong" and
"weak" components. Two different systems have been studied, a refined and unrefined
Irving pulp (as the strong and weak components, respectively), and an Irving-Santa Fe
Eucalyptus system. The experimental conditions are shown in Tables 1-4.

Results and Discussion.

Tensile Strength-Basis Weight for homogeneous sheets.

As mentioned above, the study was carried out on 2 different model furnish systems, both
modeling mixtures of a strong and a weak furnish. The first such system consisted of a
refined and unrefined Irving pulp, to stand for the strong and weak components. The
second system utilized a refined Irving pulp for the strong, and an unrefined Santa Fe
Eucalyptus as the weak component. The test results for the first system are given in
Tables 1 and 2, for the second in Tables 3 and 4. Since the findings for both systems were
surprisingly similar, I will be discussing exclusively the first system.

Uncreped sheets.

Strength-BW data for the 3 different homogeneous sheets, 100% strong, 100% weak, and
50-50 mixture are shown in Figure 1. As can be seen, for all 3 compositions tensile
strength vary linearly with Basis Weight. The relation, however, is not direct
proportionality; there is a considerable x-intercept, in accordance with several other
researchers who noticed that (1,2)…The relationship has the form:

Equ.1 GMT=a*(BW-)

Where "a" is the slope, a  is the intercept.

I shall be referring to this intercept as the "" value. It probably represent the minimum
BW required to form a coherent load-bearing layer. It is especially important for tissue
weight sheets for which failure to take it into account can lead to considerable error when
using the BW-normalized strength, or Breaking Length. The concept assumes that the
slope of the relationship is constant for all points, and the line goes through the origin. In
this article, I will use the real slope, or the "-corrected Breaking Length", which is
obtained by subtracting the -value for each composition from Basis Weight. Hence:

Equ. 2 BL =(GMT)/(BW-)

As can be seen, "a" from equation 1 is the BL. This value now is, of course,
BW-independent and can be used to characterize the furnish strength. While the most
commonly used unit for BL is meters, in this article, for ease of handling and comparison,
I will use mixed units, in which GMT is in oz/in and BW in lbs/ream. The conversion to
meter is easy; multiplying by 658.42 will yield meters. I am sure the wisdom of my usage
will become obvious. In the rest of the article BL will mean
BL in mixed units (mu).

As can be seen, there are 3 distinct lines for the 3 compositions. All cut the axis at
approximately 5 lbs/ream. Since all 3 compositions contain the same fiber, one would
expect the same -value. By and large this is so, the regression values are 5.19, 4.25, and
5.08 for the strong, weak, and 50-50 mixture, respectively. The corresponding BL's (the
actual slopes) are BLs = 4.99 mu, BLw 1.77 mu, and BLm 3.47 mu (where the subscipts
"s", "w" and "m" refer to the strong, weak, and mixed compositions, respectively. The
ratio of BLs between the strong and weak furnish, (BLs)/ (BLw) is 4.99/1.77, or 2.81. It
should be pointed out that the weight average law of mixing applies quite well, the
calculated BL for the 50-50 mixture is 3.38 mu. This compares quite well with the actual
number of 3.47 mu.

Creped sheets.

Figure 2 shows the same relationship for the creped sheets. Once more, the 3 distinctly
different lines are obtained for the 3 compositions. The -values are 3.43, 5.03, and 5.68.
These should be closer to each other and maybe slightly higher than the corresponding
uncreped values, but the data is not adequate to yield greater accuracy. Therefore I have
used these values to calculate the BLs. They are 2.45 mu, 0.44 mu, and 1.36 mu. For the
mixture, the weight average law predicts a BL of 1.44 vs. the actual value of 1.36, a fairly
good agreement. Interestingly, strength breakdown due to creping has changed the ratio
of BLs between the strong and weak furnish from 2.81 to 5.57. In other words, strength
loss in creping was higher in the weak component. Before leaving this section, I would
like to point out the difference between the conventional, uncorrected BL and -corrected
BL, using the conditions for the mixed composition. These only vary in BW, hence they
should have the same BL. Conventional BL values are 594, 695, and 742 for the 3 BWs.
The corresponding BL values are 878, 912, and 890. Obviously, the latter are far more
constant for all BWs.

Tensile Strength-Basis Weight for stratified sheets.

50-50 strong-weak mixtures.

In the original series of runs, the 50-50 furnish mix was run in at 3 different BWs in 2
different layer orientation, strong layer on top (strong-weak, designated as "s-w") and
weak layer on top (weak strong, designated as "w-s"). The data for these is given in Table
1, (Run Numbers 10, 14, 17, 18, 22, and 25). When TS-BW was plotted, somewhat
surprisingly there was a considerable difference between the 2 orientations, the s-w line
was well above of the w-s line; I had expected that the 2 orientation would be similar to
each other, and to the 50-50 homogeneous sheets. Owing to the experimental design, the
2 orientations were run on different days. Despite all efforts, the strength of the 2
furnishes changed from one day to the next, casting some doubt as to the validity of these
findings. To be absolutely certain, the 2 series were rerun on the same day at 4 different
BWs (Runs 25-32), and tested in duplicates. The results for these are shown in Figures 3
and 4 for the uncreped and creped series. Figure 3 shows the tensile strength-BW
relationship for the uncreped sheets. The data points fall on two distinct lines for the 2
orientation. This time without a doubt the s-w line was above that of the w-s line. The BL
for the former (calculated using weighted average of the -values) was 3.92, the latter
3.42, a 15% difference in favor of the s-w orientation. Even more surprising, this
difference became more magnified for the creped sheets, as shown in Figure 4. The two
orientations fall on 2 distinct lines. BLws was 1.92 mu, while BLsw was 1.2 mu, a
difference of 58% While not shown in a graph form, the curves for the 2 series were quite
similar to those found for the original, suspect ones (Run Numbers 10, 14, 17, 18, 22, and
25). Obviously the difference is real. I have found no immediately obvious explanation
for the difference between the uncreped points. For now accepting it as it is, there is still
the extra widening of the gap during creping to account for.

Clearly, the weight average law cannot explain the difference, since the overall
composition for the two orientations is the same. One way to explain the difference is to
assume that the layer against the drier side loses strength differently than the air side. If
the magnitude of the different "extra strength loss" (ESL) for the 2 cases were known, the
weight average law would still apply. The following is a description of such an approach.
Let's assume that the layers against the drier side breaks down to a strength level which is
different than the strength of the pure components (i.e. BLs and BLw). Using subscripts
"d" and "a" for air-and-drier side, we can set up the following equations:

Equ. 2: BLsd =BLs *ESLd
Equ. 3: BLwd =BLw *ESLd

Equ. 3: BLsa =BLs *ESLa

Equ. 4: BLwa =BLw *ESLa

The terms BLsd ,BLwd ,BLsa ,BLwa are the "true" strengths of the different layers, and can
now be used to calculate total strength, suing the weight average law:

Equ 5: BLsw = 0.5*BLsa + 0.5*BLwd

Equ 6: BLws = 0.5*BLwa + 0.5*BLsd

Solving the above equations we obtain the following final results:

ESLd = 0.725, and ESLa = 1.435. This means that when a layer is against the drier side,
its strength will be 27.5% less (i.e. 100-72.5%) than that of the 100% pure component
creped homogeneously, while any air side layer will be 43.5% higher than that of of the
100% pure component creped homogeneously.

To show that these are the correct values, let us use real numbers:

BLswcalc = 0.5*2.44*1.44+0.50.44*0.725 , which yields BLswcalc=1.91, which is identical
to the value obtained for BLsw. Similarly,

BLwscalc = 0.5*2.44*0.725+0.50.44*1.435, which yields BLwscalc=1.2 , which is identical
to the value obtained for BLsw.

The above treatment, somewhat simplistically assumed that the 2 different layers break
down uniformly within each layer, hence only one number for the drier side and one for
the air side. In practice, there is most likely a gradient of breakdown. Furthermore, it
ignored the 15% difference, already existing between the uncreped sheets. Still, the
success of these to explain the discrepancy is heartening. It should also be clear that the
values for ESLd and cannot be entirely ESLw arbitrary. To see this, let us try to apply the
above values to a homogenous case, assuming that they can be thought of as consisting of
2 layers, one air side and one drier side. Using such a procedure for BLs

BLscalc = 0.5*1.99*0.725+ 0.5*1.99*1.435 we obtain BLscalc = 2.174, compared with the
actual value of 1.99 for BLs. The error is about 8 %. Had I used the pair of values 0.7 and
1.3 for ESLd and ESLa there would have been perfect agreement between the calculated
and real values for the homogeneous case. Thus it can be concluded that for the particular
paper machine used the drier side layer will lose about 30% more than that of the 100%
pure component creped homogeneously, while any air side layer will be 30 % higher than
that of the 100% pure component creped homogeneously. Undoubtedly, these values will
be different for different paper machine, but the direction of the differences will be the

One further point emerges from the above discussion. Since there is a difference between
drier and air side strength, actually probably a gradient, this means that for a
homogeneous sheet, and probably for most stratified as well, there is also a density
gradient. And since the drier side layer is most likely weaker, its density will also be

Strength-density relationships.

We have seen that there can be a change in the tensile strength-BW relationship between
homogeneous and stratified sheets of the same composition. While this is of considerable
theoretical interest, an even more important question is whether stratification can alter the
important strength-related tissue properties. Since bulk, water absorptive capacity, and
some components of softness (bulk softness, possibly flexibility, but not surface softness)
all depend inversely on density, it is instructive to compare the BL-density relationship of
homogeneous and stratified sheets. Figures 5 and 6 shows such relationships respectively
for uncreped and creped sheets for all compositions. As may be seen in both Figures,
there is an excellent correlation between BL and density; all points fit the regression lines
extremely well. Furthermore, all points, homogeneous and stratified, are so close to the
regression line that the only conclusion that can be made is that stratification does not
affect the BL-density relationship, for a given strength, both homogeneous and stratified
sheets have the same density.

Interestingly, and somewhat surprisingly, as can be seen by comparing Figure 5 and 6,
the creped and uncreped lines are fairly similar, at the same density they yield about the
strength for the uncreped and creped sheets. This means that creping does not affect the
basic sheets structure. These same two conclusion may be drawn from the unit water
absorptive capacity (UWA)-strength relationship, which will be discussed in the next

It should be pointed out that, while the strength-density is generally a linear relationship
when strength is varied by a constant method, refining in this instance, it is by no means
necessary that the same relationship should hold for different compositions, nor even
when strength is changed by breakdown during creping. The fact that it is the case for
refined and unrefined pulp merely means that by changing the ratio of strong and weak
components, we vary strength as well. It is not clear why creping breakdown should also
be along the line.

Water absorptive capacity-strength relationships.

As mentioned above, unit water absorptive capacity (UWA) depends inversely on
density, hence directly on Breaking Length. Figure 7 shows the UWA-BL relationship for
both uncreped and creped sheets. As has been the case for the density there is an
excellent correlation between BL and UWA; all points fit the regression lines extremely
well. Furthermore, all points, homogeneous and stratified, are so close to the regression
line that the only conclusion that can be made is that stratification does not affect the BL-
UWA relationship.

As for the strength-density relationships, at the same strength water absorptive capacity is
quite similar for the creped and uncreped sheets; in fact there is a slight advantage for the
uncreped sheets. This shows that creping does not affect the underlying sheet structure by
de-densification, though it obviously imparts shaped bulk and stretch.

Bulk-strength relationships.

It may be recalled that the tensile strength-BW relationship was described by a linear
relationship as given by equation 1 as GMT = a*(BW-), which means that GMT is
directly proportional to BW. Actually, a somewhat similar relationship exists for
TWA-BW relationship. TWA is not directly proportional to BW, there is a y-intercept.
However its value is so small that it could be neglected for the purpose of this work. One
can, however not neglect a similar intercept for the Bulk-BW relationship. The
relationship is shown in Figure 8. While the relationship is linear, it shows an extremely
pronounced y-intercept, Bulk0. Its value is 135, 160.3, and 137 TMI Bulk units
respectively for strong, weak, and 50-50 mixture. This intercept means that for the strong
furnish, the Bulk at zero BW would be 135. Conventional Bulk/BW calculation,
however, implicitly assumes that the intercept is zero, hence when used to compare
sheets of different BWs it is in error. This can be seen, for instance, by looking at the
strong series. The only difference among the 3 conditions is BW. The density of these
points is quite constant. The conventional Bulk/BW values for the 3 conditions are 16.96,
11.5 and 10.07. Clearly, we cannot use conventional Bulk/BW values for comparisons
across BWs. To see how correct comparison may be obtained, we can use the same
thought process as for BL. The actual Bulk-BW relationship has the form:

Equ. 3 Bulk-c = b*BW, or

Equ. 4 Bulk=b*(BW+), where "b" is the slope and  is the BW intercept.

Bulk is now directly proportional to (BW+). We can call Bulk/(BW+) as -corrected
Bulk/BW, or (Bulk/BW). Clearly, Bulk/(BW+) is now independent of BW. To see this,
let's calculate Bulk/BW again for the 3 strong points, using the appropriate -value of
-31.62 (the BW-intercept in Figure 8. We obtain 4.82, 4.21, and 4.28, fairly constant
values. This not surprising, since the Bulk-intercept at zero BW may be thought of as the
contribution of shaped Bulk to total bulk. Subtracting this amount from actual Bulk
figures yields basic, weight-bearing, water-absorbing Bulk, and the corresponding
Bulk/BW is counterpart of density. If density is constant, so should be Bulk/BW. In fact,
while not shown in graphical form, there is an excellent correlation between corrected
Bulk/BW and density. In the rest of the discussion Bulk/BW will mean (BW+). Plotting
it against BL (-corrected) we can compare homogeneous and stratified products for all
BW range. This is shown in Figure 9 for creped strong, weak, 50-50 homogeneous, and
50-50 strong-weak and weak-strong stratified sheets. For the stratified sheets the average
of all 3 homogeneous -values for used in the calculations. As can be seen, stratified and
homogeneous sheets fall on the same line, showing that stratification has no benefit in
Bulk generation.


The present study, using 2-layer stratification and the simplest possible furnish system of
the same refined and unrefined furnish has shown no advantage for stratification for
water absorptive capacity, bulk, or density. There is no particular reason to believe that
using the far more widespread 3-layer stratification, or different type of furnish
components would alter these conclusions. However, the findings do not contradict the
well-known overall softness and economic benefits of 3-layer stratification.
Figure 1





         0           5            10              15   20   25   30   35   40
             dat a points fo r strong
             regression line for st rong
             dat a points fo r weak
             regression line for weak
             dat a points fo r 50-50 mixture
             regression line for 50-50 mixt ure
Figure 2



  Tensile Strength



                           0            5             10           15        20        25   30   35   40
                                                                        Basis Weight
                               data points for strong
                               regression line for strong
                               data points for weak
                               regression line for weak
                               data points for 50-50 mixture
                               regression line for 50-50 mixture
Figure 3



  Tensile Strength





                           0           5            10           15        20        25   30   35   40
                                                                      Basis Weight
                               data points for strong-weak
                               regression line for strong-weak
                               data points for weak-strong
                               regression line for weak-strong
Figure 4



  Tensile Strength




                          0           5             10           15        20        25   30   35   40
                                                                      Basis Weight
                              dat a point s for strong-weak
                              regression line for st rong-weak
                              dat a point s for weak-st rong
                              regression line for weak-st rong
Figure 5



  Breaking Length, m





                              0      0.05      0.1     0.15      0.2     0.25        0.3        0.35   0.4   0.45   0.5   0.55   0.6
                                                                                Density, g/cc
                                  data points for strong (homogeneous)
                                  data points for weak (homogeneous)
                                  data points for 50-50 mixture (homogeneous)
                                  all data points
                                  regression line for all points
Figure 6



  Breaking Length, m




                              0      0.05      0.1      0.15      0.2      0.25          0.3        0.35   0.4   0.45   0.5   0.55   0.6
                                                                                    Density, g/cc
                                  dat a point s for strong (h omogeneous)
                                  dat a point s for weak (ho mogeneous)
                                  dat a point s for 50-50 mixt ure (ho mogeneous)
                                  all dat a point s
                                  regression line for all point s
Figure 7




  UWA g/g





                0        0.05        0.1        0.15       0.2    0.25   0.3   0.35   0.4   0.45   0.5
                                                                 BL, m
                    dat a point s for crep ed sheets
                    regression line for creped sheet s
                    dat a point s for uncrep ed sheets
                    regression line for uncreped sheet s
Figure 8

                                                 Bulk vs. BW                  600








               40           30         20   10        0        10   20   30    40
                    St ron g
                    Regression Line
                    50-50 Mix
                    Regression lin e
                    Regression Line
Figure 9





  Bulk/BW, TMI units






                            0        200        400   600   800          1000          1200   1400   1600   1800   2000
                                                                  Breaking Length, m
                                Regression Line
                                50-50 strong-weak
                                50-50 weak-strong

Homogenous sheets, using "strong" component as an example:

(BL)s =(GMT)/(BW-s),

[(Bulk/BW)]s =(GMT)/(BW-s),

Stratified sheets of any composition, using "s/w" as an example:

(BL) s/w =(GMT)/(BW-[s* fs, + w* fw]),

Stratified sheets for 50-50 composition only:

[(Bulk/BW)] s/w =(Bulk)/{BW-[(s+ m +m)/3]}

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