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

Fig 16. Strain at break versus density for the investigated handsheets.
varying structural density. This was a prerequisite for a
more precise evaluation of the deformation of paper. The
results in terms of elastic moduli showed that when
evaluating the strain related properties, the influence of
the adhesive could not be neglected even for higher
grammages. Byrd et al. (Byrd et al. 1975) apply an
adhesive similar to the one used in the present study, but
they assume that the adhesive has an infinite stiffness.
This might be a reason for their calculated adhesive
penetration which is significantly lower than the one
presented in this paper.
A large discrepancy was found between the Z-directional
tensile strength measured using adhesive and double
adhesive tape. This was not unexpected since the strength
results for the chemical pulps lie on the border or outside
the recommended measurement range according to
SCAN P80:98. Consequently, reliable Z-directional
strength values for strong papers can only be obtained by
ensuring a paper-adhesive bonding which is stronger than
the paper itself.
A possible drawback for the presented method is the
densification of TMP during the pressing process, which
might have an effect on the mechanical properties.
However, the strength results obtained with commercial
apparatus did not differ, in the range of the acceptable
grammages, from the ones obtained by the custom built
apparatus.
The chosen pressure ensured a sufficient penetration of
the glue and sufficient bonding between the glue and
paper. In the future, a reduction of the curing time
obtained by using more suitable glue combined with a
decrease of the curing pressure may be the way to avoid
the densification.
The decrease in Z-directional tensile strength for
increasing grammage observed for the chemical pulps
can be explained by the Weak Link Theory. Handsheets
with higher grammages present a higher number of
distributed defects triggering failures at lower stresses.
On the other hand, the Z-directional tensile strength for
TMP sheets remained constant over the range of the
acceptable grammages. One explanation might be that
the defect sensitivity is related to the density of the fiber
network. The adhesive penetration does not allow testing
grammages less than 60 g/m 2 . Testing of thinner paper
may require a refinement of the technique.
In line with the previous results on the subject, it was
shown that density caused an exponential increase in
both Z-directional tensile strength and the elastic
modulus for the tested material. It is likely that the fines
cause the increase of strength for the beaten pulps but
less influence on the Z-directional elastic modulus is
expected. The magnitude of the elastic modulus is in
agreement with the previous literature data. With regard
to the fiber shape, two main concurrent structural factors
influencing the Z-directional elastic modulus of paper
can be identified. A consequence of increasing density is
a lower free fiber segment length corresponding to higher
resistance to bending for singular fibers. This phenomenon
may have positive effect on the Z-directional elastic
modulus of paper. The fiber collapse, caused by beating,
on the other hand, reduces the thickness of the fiber and
therefore the bending stiffness of the single fiber drops.
This fact is likely to be detrimental to the elastic moduli
of paper.
Since the elastic modulus increases with density, the
negative effect of fiber collapse seems to be negligible
over reduction of the free fiber length.
Conclusions
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A method for the measurement of stress-strain properties
of paper in the thickness direction was developed.
The measurements were applicable for grammages
over approximately 60g/m 2 .
The paper properties were highly dependent on the
density. Higher density caused an exponential increase
in Elastic modulus, Z-directional strength, and a
reduction of the strain at break
The presented technique should help increasing the
knowledge of the relationship between the network
structure and the mechanical properties of paper.
The collected data may be used as a first approximation
for modeling purposes of converting processes
and end use performance.
Acknowledgments
The financial support of the Surface Treatment Program at Karlstad University is
acknowledged. The authors wish to thank the STFI-Packforsk partner companies
participating in the Research Cluster ‘Engineered Paperboard’.
Appendix I. Finding the displacement in the center of
the test piece.
The aim of such calculation is to determine the displacement
in the middle of the test piece. The displacement
field of the all the points in the test piece can be
described as a plane in space, since the test piece is
rigidly connected to plane platens. The centre of the test
piece is taken as the origin of the coordinate system. The
displacements can be considered as the Z-coordinates in
the space. The sensors yield the values of the dis-
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 55