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

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]