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

Evaluation of the tensile stress-strain properties in the
thickness direction of paper materials
Orlando Girlanda* and Christer Fellers, STFI-Packforsk AB, Stockholm, Sweden
KEYWORDS: Z-direction strength, Stress strain properties,
Delamination, Strain at failure, Elastic moduli
SUMMARY: The stress-strain properties of paper in the thickness
direction were characterized by means of a custom-built
apparatus. A specific procedure was used for fastening the
paper to metal blocks by photo-mounting tissue. The effects of
the penetration of the adhesive into the paper were quantified.
The performance of the apparatus was then investigated. Finally
the stress-strain properties were characterized for handsheets
made of bleached thermo mechanical pulps and bleached chemical
pulps with different refining levels.
ADDRESS OF THE AUTHORS: Orlando Girlanda (orlando.
girlanda@stfi.se) *Present address: orlando.girlanda@polymtl.ca
Christer Fellers (c.fellers@ stfi.se): STFI-Packforsk AB, Box
5604, SE-114 86 Stockholm, Sweden.
Corresponding author: Christer Fellers
The mechanical properties in the thickness direction of
paper are important for the performance in a number of
converting operations such as creasing, bending, printing,
and plastic coating. The knowledge of strength, elastic
modulus, strain-softening behavior in tension and
compressibility in the thickness direction, also called
Z-direction, are needed for a comprehensive description
of the performance of the material in these operations.
In spite of its importance, few publications deal with
the evaluation of the entire tensile stress-strain curve in
the thickness direction (Stenberg et al. 2001; Van Liew
1974). The reason for this is likely the intrinsic difficulty
of testing a thin, uneven, porous, fibrous and compressible
material such as paper with sufficient precision and
testing time efficiency.
Some aspects of the stress-strain behavior in terms of
elastic modulus are treated in several publications listed
in Table 1. The elastic modulus has been characterized
either by evaluating the slope of the stress-strain curve
(Stenberg et al. 2001; Van Liew 1974) or by using an
ultrasonic technique (Berger and Baum 1985; Fleischman
et al. 1982; Mann et al. 1980; Waterhouse et al. 1987).
Another aspect is the strength in the thickness direction
of paper, often characterized by the Z-directional tensile
test. The test piece is fastened by means of double adhesive
tape onto two solid plane platens on which tensile
stress is then applied. The maximum stress is recorded
and defined as the Z-directional tensile strength. For this
measurement standards such as Tappi (1989) and SCAN
(1998) are available.
When the deformation in the thickness direction of
paper is measured, it is advantageous to use a stiff adhesive.
A prerequisite is also to consider the effects of the
adhesive penetration into the porous network of paper and
the stiffness of the adhesive itself (Stenberg et al. 2001;
Van Liew 1974). In their experiments with wheel delamination
tests, in which double adhesive tape is used, Naito et
al. (1995) and Lundh and Fellers (2004) observe changes
of the paper properties due to the influence of tape at a
grammage of approximately 50-60 g/m 2 . In their interlaminar
shear measurements, in which photo mounting tissue is
used, Byrd et al. (1975) estimate the penetration of photo
mounting tissue into a linerboard in the order of 7 microns
corresponding to approximately 5 g/m 2 .
The mechanical properties of paper in the thickness
direction are mainly influenced by the number and
strength of the fiber-to-fiber bonds, the stiffness of the
fibers and the fiber strength in the transverse direction. A
comprehensive review of the results presented in literature
on this subject can be found in Uesaka et al. (2002).
Since the fiber-fiber bond properties are difficult to
determine with precision, density is often used for ranking
the effects of pulping and papermaking parameters
on the mechanical performance paper along the thickness
direction (Andersson and Mohlin 1980; Fleischman et al.
1982; Koubaa and Koran 1995; Waterhouse et al. 1987;
Waterhouse 1991). For this reason, the comparison between
different sheet properties was performed in the present
investigation using handsheet density.
The resistance in the thickness direction of a handsheet
is also influenced by the entanglement of the fiber
network. Paper can be regarded as a layered material
because fibers lay manly parallel to the MD-CD plane.
However measurements on paper test pieces show that
there are a number of fibers passing from one layer to the
other (Aaltio 1960; Hasuike et al. 1992). These fibers can
Table 1. Paper material properties in the thickness direction measured by different authors.
Material Elastic Method Failure Apperent Basis
modulus stress density weight
MPa MPa kg/m 3
g/m 2
Van Liew
(1974)
Western
Hemlock
bleached
sulfite pulp
140-560 Z-tensile
strength
test
0.55
0.95
840-950 240-523
Mann et al.
(1980)
Milk carton
stock
39 Ultrasonic
technique
- 780 520
Fleischmann
et al.(1982)
Western
Softwood
bleached
kraft pulp
30-300 Ultrasonic
technique
- 400-850 400
Berger and Linerboard 29 Ultrasonic - 691 263-286
Baum
(1985)
technique
Waterhouse
et al. (1987)
Unbleached
southern
pine
263-426 Ultrasonic
technique
- 790-1071 212-230
Commercial
linerboard
45.9 Ultrasonic
technique
- 723 207
Waterhouse Unbleached 70-210 Ultrasonic - 487-796 312-290
(1991) southern
pine
technique
Stenberg et Chemical 3.86 Arcan - 864* 267
al. (2001) bleached
kraft pulp
device
*) Structural density
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 49

influence the mechanical properties of paper when
testing thin paper sheets (Byrd et al. 1975). The irregular
thickness of paper and irregular mass distribution also causes
non-uniform strain distributions over the area of the
test pieces as pointed out by Van den Akker (1952). These
aspects became more relevant for thinner test pieces.
The aim of the present paper was to develop a testing
procedure for the measurement of the stress-strain
properties in the Z-direction of paper enabling the extraction
of the Z-directional tensile strength, strain at break
and elastic modulus for paper. The penetration of adhesive
and its influence on the performance of paper in the
thickness direction were defined. A selected number of
papers were tested. The relations between the mechanical
properties and the paper structure, in terms of structural
density, were obtained.
Material and Methods
Materials
One thermo mechanical pulp (TMP) and one chemical
pulp were tested. The pulps were either unbeaten or
beaten in an industrial refiner to different CSF levels,
Table 2. Handsheets were made according to SCAN-C
26:76 with the exception that the grammage of the tested
handsheets varied from 10 g/m 2 to 300 g/m 2 . Key in-plane
mechanical properties for 180 g/m 2 sheets are given in
Table 2. Structural thickness and structural density were
evaluated by SCAN-P88:01 and in-plane tensile properties
by ISO 1924-3.
Table 2. Materials used in the present investigation and their in-plane properties
for 180 g/m 2 handsheets.
Pulp CSF Structural In-plane In-plane Strain
ml density tensile tensile at
kg/m 3
index stiffness break
kNm/kg index
MNm/kg
%
TMP 1
Unbeaten softwood
TMP 2
325 407 38 4.3 2.1
Beaten softwood
Chem1
Bleached chemical pulp,
210 484 47 5.0 1.6
mix of birch, eucalyptus and
softwood, lightly beaten
Chem2
Bleached chemical pulp,
538 682 50 6.5 3.4
mix of birch, eucalyptus and
softwood, highly beaten
236 871 73 8.3 3.6
Methods
Preparation of the paper for testing
The handsheet was fastened to circular 10 cm 2 metal
platens by means of a photo mounting tissue (Beinfang
ColorMount ® adhesive). The sum of platens, adhesive
and paper is referred to as the test piece. The adhesive
and the paper are henceforth referred to as the sandwich.
The test piece was first subjected to 0.23 MPa pressure
at 110°C in a hot air oven. After one hour curing time,
50 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007
the test piece was removed from the oven and conditioned
under pressure at 23°C and 50% RH. The conditioning
time was set to at least 12 hours which was found
adequate to obtain the equilibrium of moisture content.
Additionally bare handsheets underwent the same procedure
in order define the change of the thickness due to
the applied stress. The structural thickness of the handsheets
after pressing, named thandsheet, and the grammage of
the handsheet, whandsheet, were used to determine the structural
density of the pressed handsheets, which is written as
whandsheet
ρ = handsheet
t
[1]
handsheet
The sandwich consisted of three areas, which could be
delimited by imaginary horizontal planes, as shown in
Fig 1. After curing, the handsheet was penetrated by the
adhesive on both upper and lower surface. The mix area
consisted both of the adhesive left outside of the paper
and the part of the paper penetrated by the adhesive. The
stress-strain properties of the paper calculated in the
present investigation referred to the center part of the
handsheet, not penetrated by the adhesive.
Fig 1. Schematic picture of the structure of the test piece and adhesive penetration
into a handsheet with definitions of three thicknesses.
Procedure for the measurement of adhesive penetration
into the handsheets, two-handsheets technique
The evaluation of the mechanical properties in the thickness
direction required an estimation of the penetration
grammage, which was the quantity of the handsheet
affected by the adhesive.
The penetration grammage was assessed by testing
two-handsheets sandwiches for each pulp type. Two
handsheets with equal grammage were piled, pressed
together and fastened each on one surface to the platens
by performing the already described preparations
procedures. The two-handsheets sandwich was subjected
to a tensile stress by the same experimental set up used
for the measurements of the mechanical properties of the
paper. The grammage of the two handsheets was varied in
order to obtain different degrees of adhesive penetration.
As long as the grammage of two handsheets was higher
than the penetration grammage, no separation force was
expected. As soon as the grammage of the handsheets
was lower than the penetration grammage, the opposite
adhesive layers could make contact and consequently a
separation force was measured. The separation force was
likely to increase as the grammage of the handsheets was
reduced. The penetration grammage, w penetration, was defi-

ned as the intercept at zero force in a plot relating the
separation force to the single handsheet grammage.
Thickness definition of the constituents
The combined effect of adhesive penetration and nonrecoverable
compression did not allow the direct
evaluation of the thickness of the mix, t mix, and of the
thickness of the paper, t paper. An indirect assessment of
these quantities was therefore necessary. The only measurable
quantity was the sandwich thickness, t sandwich. This
measurement, required ad hoc prepared test pieces.
Aluminum sheets were placed between the platens and
the adhesive so that the sandwich could be easily removed
from the platens. The thickness of the sandwich
could be determined after removing the aluminum sheets
from the sandwich. The thickness of the paper (see Fig 1
for its geometrical definition) was calculated for each
tested grammage as the difference between the thickness
of the handsheet after pressing and thickness of paper
penetrated by the adhesive, Eqs (2)-(4). In Eq (2) the
penetration grammage and the density of the pressed
handsheets for each grammage are used.
Eq (2) can also be written using Eq (1) as
⎛ 2w
t = t ⎜1−
paper handsheet ⎜
⎝ w
penetration
handsheet
The thickness of the mix could then by calculated as
t
mix
t − t
=
2
sandwich paper
Description of the testing apparatus
A schematic drawing of the testing apparatus is shown in
Fig 2. The rod was first screwed onto the test piece.
Successively, the test piece and the rod were screwed
onto the load cell. These actions were performed without
subjecting the sandwich to undesired loading. The rod
was finally secured to the connector by the upper pin.
Three sensors, fastened to the upper platen and displaced
at 120 degrees from each other, measured the
displacement between the lower and the upper platen.
The loading was performed by means of a MTS servohydraulic
testing machine. The load was applied under
displacement control in order to enable the measurement
of the post-peak behavior of the material. The load was
transferred to the rod via a universal joint system,
consisting of a connector, an upper and lower pins
crossing each other. The point contact between the pins
avoided the bending moment caused by possible
misalignments between the centre of the test piece and
the point where the force is applied.
The value of the Z-directional tensile strength obtained
with the testing apparatus was compared to the value
obtained by a commercial apparatus following SCAN
P80:98. The latter method used tape to fasten the test
pieces to the metal platens.
⎞
⎟
⎠
[2]
[3]
[4]
Fig 2. A schematic drawing of the testing apparatus.
Elaboration of the stress-strain data
The data collected during the experiments were the
displacements between the two platens measured by the
sensors and the corresponding applied force measured by
the load cell. The displacement at the centre of the test
piece was calculated from the sensors measured displacements,
as explained in Appendix I. The displacement at
the centre of the circular test piece, called δ sandwich, was
taken as representative for the deformation of the whole
sandwich. The elastic modulus of the sandwich was evaluated
by a linear regression of the stress-strain curves.
The thickness of the sandwich t, the instantaneous force
F and the tested area A were used for the determination
of the elastic modulus according to Eq (5).
E
sandwich
= δ
F
sandwich
A t
sandwich
The displacement of the mix, δ mix, was determined by
assuming a linear elastic behavior of the mix using Eq 6
where the elastic modulus of the mix was obtained from
the slope of the stress-strain curve of handsheets which
were completely penetrated by the adhesive.
The displacement of the paper was calculated as the
difference between the displacement of the sandwich and
the displacement of the mix:
Consequently the strain in paper was calculated as
The value of the elastic modulus in the thickness direction
of paper was determined by combining the elastic
[5]
F
δmix mix
E A t = [6]
mix
δ = δ −2 δ
paper sandwich mix
[7]
ε
paper
⎛
δ
δ
⎜
paper ⎝
= =
t
paper
sandwich
F
E A t − 2
t paper
mix
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 51
mix
⎞
⎟
⎠
[8]

modulus of the sandwich and the elastic modulus of the
mix according to Eq (9), by substituting Eqs (5) and (6)
into (7),
E
paper
Results
F
A t = = paper
δ
⎛
paper t
⎜
⎝ E
The testing procedure presented in this paper was developed
for the measurement of the stress-strain curve in the
Z-direction of paper from which the extraction of the Zdirectional
tensile strength, strain at break and elastic
modulus for paper was possible. A selected number of
handsheets were tested and the relations between the
mechanical properties and the paper structure, in terms of
structural density, were investigated. A summary of all
the results is given in Appendix II.
The analysis started by studying the change in thickness
of the handsheets due to the pressing sequence
(Table 3). The TMP handsheets showed a permanent
deformation after the pressing, whereas no change was
observed for the chemical handsheets.
The penetration of the Photo Mounting Tissue adhesive
into the handsheets was then determined by the
“two-handsheets” technique. Fig 3 shows the data for the
chemical pulp 1. The behavior was representative for all
the investigated handsheets. The straight line is the linear
fit to the data. The extrapolated value to zero-strength
gave the penetration grammage into one handsheet. The
results in terms of penetration grammage for all the
investigated papers are summarized in Table 4.
52 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007
t
sandwich
paper
sandwich
2 t ⎞
mix
[9]
−
E
⎟
⎠
Table 3. Density after pressing and change in thickness of the handsheets due to pressing.
Measurements were performed at 23°C and 50% RH.
mix
TMP 1 TMP 2 Chem 1 Chem 2
Grammage Density Change Density Change Density Change Density Change
g/m 2
kg/m 3
% kg/m 3
% kg/m 3
kg/m 3
80 444 17 514 10 666 - 862 -
100 448 15 515 7 687 - 849 -
120 472 13 533 9 686 - 856 -
180 459 8 540 10 682 - 885 -
240 465 8 539 8 678 - 879 -
300 491 12 542 9 680 - 882 -
Average 463 12 530 9 682 - 871 -
Fig 3. Z-directional tensile strength versus grammage for one handsheet tested by
the “two-handsheet” technique.
Table 4. Penetration of the adhesive into the handsheets. The penetration thickness
was evaluated by Eq (1).
Pulp Penetration
g/m 2
The penetration grammage was approximately 20 g/m 2
for all the investigated handsheets while the penetration
thickness varied depending on the density of the handsheet,
Fig 4.
Based on the results in Table 4, the Z-strength tests for
the evaluation of the elastic modulus of the mix were
performed on 40 g/m 2 handsheets, using Eq (5). The
elastic modulus for the adhesive was also evaluated using
the custom built apparatus. The results are given in
Table 5 and plotted as function of density in Fig 5.
mm
TMP1 19.7 0.054
TMP2 19.5 0.042
Chem1 19.5 0.029
Chem2 20.7 0.022
Fig 4. Penetration depth versus density for the handsheets tested by the “twohandsheets”
technique.
Table 5. Elastic modulus for the mix and the adhesive performed
on 40 g/m 2 sheets.
Material E, MPa
TMP 1 33
TMP 2 61
Chem1 230
Chem2 302
Adhesive 1600
Fig 5. Relation between elastic modulus for the mix and handsheet density.

Testing speed
Paper material and adhesives exhibit a visco-elastic
behavior, i.e. their response in terms of strength will
change depending on the testing speed. Rate dependency
was not addressed in this paper. However the purpose
was to test the material in a time window in which the
strain rate had negligible influence on the material properties.
The influence of the strain rate was studied for
120 g/m 2 paper sheets prepared with chemical pulp 2.
Two different testing speeds were used, 0.025 mm/s and
0.0025 mm/s. The mean times to break were respectively
6.7 and 66 seconds. No influence on the Z-directional
tensile strength was found. The tests in the following part
of the article were therefore performed at 0.0025 mm/s
speed.
Stress strain curves
Fig 6 presents four typical stress-strain curves for 300
g/m 2 , one for each type of pulp studied in the present
investigation. The curves were calculated by Eq (8). The
elastic moduli presented in this investigation were obtained
by linear regression of the Z-directional stress-strain
curves. The limit at which linearity was good approximation
varied depending on the pulps. For TMP the elastic
moduli were calculated up to 50% of the strength. For
chemical pulp the calculation limit was set to 80% of the
strength.
Fig 6. True stress-strain curves for the investigated handsheets.
Sheets prepared from chemical pulps were stiffer than the
ones made of mechanical pulps. TMP was characterized
by a strain at break around 8%, whereas strain at break
for chemical pulp ranged from 1.4% to 1.8%. The postpeak
behavior changed drastically for different pulps. For
chemical pulp 2 the post-peak behavior was unstable at
any grammage. For chemical pulp 1, post peak instability
was also present for low grammage handsheets, but for
higher grammage the failure was stable. For TMP
handsheets the failure was always stable.
Z-directional tensile strength
In Figs 7 to 10 the Z-directional tensile strength is shown
as a function of grammage. The strength values are
obtained using two different techniques, i.e. measurements
performed by the custom built apparatus using
adhesive, and data measured using double adhesive tape.
Fig 7. Grammage versus Z-directional tensile strength plot for TMP1 obtained
using two different testing methods.
Fig 8. Grammage versus Z-directional tensile strength plot for TMP2 obtained
using two different testing methods.
Fig 9. Grammage versus Z-directional tensile strength plot for chemical pulp 1
obtained using two different testing methods.
Fig 10. Grammage versus Z-directional tensile strength plot for chemical pulp 2
obtained using two different testing methods.
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 53

Fig 11. Density versus Z-directional tensile strength in a semi-logarithmic plot. Fig 12. Elastic modulus versus grammage for the TMP handsheets.
The Z-directional tensile strength of TMP handsheets
could be regarded as constant down to a grammage of
approximately 60 g/m 2 . For lower grammages the Zdirectional
tensile strength increased drastically. For the
chemical pulps the strength gradually increased with
decreasing grammage. A steep increase was also observed
after the 60 g/m 2 limit.
The strength measured with double adhesive tape was
independent of grammage, with the exception of low
grammages, where tape penetration influenced the
measurements. When strong chemical pulp was tested,
the failure did not occur in the paper but in the interface
between tape and paper. On the other hand, when testing
TMP, the failure occurred always in the paper.
Fig 11 presents in a logarithmical scale all the results
in terms of Z-directional strength in function of the
structural density. A straight line fit was performed to the
data.
The elastic modulus was calculated from Eq (9). The
results are presented in Figs 12 and 13. The straight lines
correspond to the mean value of the elastic modulus evaluated
for papers with different grammage. The elastic
modulus was essentially independent of grammage.
The relation between elastic modulus and density was
also considered. In order to illustrate in the same graph
the full range of elastic modulus for the different pulps a
logarithmical scale on the y-axis was used in Fig 14. A
straight line fit was performed to the data.
Fig 15 presents the variation of strain at break as function
of grammage. It was observed that strain at break
increased for lower grammage handsheets both for TMP
and chemical pulps. It was also observed that strain at
break was significantly higher for TMP handsheets.
Fig 16 shows the results for strain at break as a function
of density. Density had a small influence on the
strain at break of chemical pulps. TMP seemed to be
slightly more sensitive to small variations of density,
since a decrease in density caused an increase in the
strain at break.
Discussion
The custom-built experimental set-up was designed to
allow for the measurement of the Z-directional stressstrain
curves of handsheets. The first set of tests measured
the adhesive penetration into the handsheet with
54 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007
Fig 13. Elastic modulus versus grammage for the chemical pulps handsheets.
Fig 14. Elastic modulus versus density for the investigated handsheets.
Fig 15. Strain at break versus grammage for the investigated handsheets.

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
·
·
·
·
·
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

placements along the thickness direction in three
different points outside the test piece. The displacements
of all points belonging to the same plane are given by
ax + by + cz + d =0. [A1.1]
The unknowns in the Eq (1) are the three cosine directors
a /d b /d c /d. The unknowns can be evaluated by substituting
of the coordinates three sensors into Eq (1), being the
position in the x-y plane the x i,y i coordinates and z i the
displacement along the thickness direction:
⎡−1⎤
⎡x
y z ⎤⎡a
d⎤
1 1 1
⎢ ⎥ ⎢ ⎥⎢
⎥
⎢−1⎥
= ⎢x
y z
2 2 2⎥⎢bd⎥
⎢
⎣−1⎥
⎢
⎦ ⎣x
y z ⎥⎢
⎥
3 3 3⎦⎣cd⎦
The deformation of the centre of the test piece z center was
determined by substituting the coordinate of the centre
x center=0 and y center =0 into (A1.1)
z
center
−c
=
d
Appendix II
56 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007
[A1.2]
[A1.3]
Table AII:1. Experimental results of Z-directional strength, elastic modulus and strain at break
for the tested pulps.
Grammage Z-directional 95% Z-directional 95% Elastic 95% Strain 95%
kg/m 2
tensile CI tensile strength CI Modulus CI at break CI
strength kPa (tape) kPa MPa %
TMP1
100 197 14 188 12 7.1 2.8 12.5 2.1
120 215 33 204 17 7.9 3.7 10.5 0.8
180 233 11 225 5 9.5 2.1 9.3 1.1
240 220 10 215 9 7.7 2.2 8.7 0.7
300 220 10 232 11 9.4 1.0 8.3 1.0
TMP2
80 335 42 323 16 13.3 3.7 12.6 0.8
100 353 16 312 17 16.7 2.5 10.2 0.5
120 384 17 328 46 19.6 3.7 9.0 0.8
180 400 15 344 18 19.6 2.8 8.2 0.4
240 375 15 352 27 16.01 2.7 8.4 0.4
300 332 12 354 7 13.6 2.1 8.4 0.7
Chem1
80 777 99 442 3.2 62 26.7 2.7 1.2
100 699 36 424 17.7 67 15.7 2.4 0.4
120 655 7 409 8.9 91 14.6 2.0 0.6
180 611 8 505 14 73 18.9 2.2 0.2
240 550 11 484 5 73 9.5 1.7 0.1
300 529 8 488 10 71 11.3 1.4 0.2
Chem2
80 1946 38 717 7.3 188.6 75.9 2.8 1.2
100 1936 29 716 6.2 169.0 26.6 3.4 0.4
120 1916 39 719 7.6 217.3 62.5 2.6 0.6
180 1833 53 688 19 203.4 25.4 2.0 0.2
240 1781 24 683 14 205.5 31.8 1.9 0.1
300 1693 37 683 11 206.0 16.9 1.8 0.2
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Manuscript received August 30, 2006
Accepted November 10, 2006