Evaluation of the tensile stress-strain properties in the thickness ...
Evaluation of the tensile stress-strain properties in the thickness ...
Evaluation of the tensile stress-strain properties in the thickness ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Evaluation</strong> <strong>of</strong> <strong>the</strong> <strong>tensile</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> <strong>properties</strong> <strong>in</strong> <strong>the</strong><br />
<strong>thickness</strong> direction <strong>of</strong> paper materials<br />
Orlando Girlanda* and Christer Fellers, STFI-Packforsk AB, Stockholm, Sweden<br />
KEYWORDS: Z-direction strength, Stress <strong>stra<strong>in</strong></strong> <strong>properties</strong>,<br />
Delam<strong>in</strong>ation, Stra<strong>in</strong> at failure, Elastic moduli<br />
SUMMARY: The <strong>stress</strong>-<strong>stra<strong>in</strong></strong> <strong>properties</strong> <strong>of</strong> paper <strong>in</strong> <strong>the</strong> <strong>thickness</strong><br />
direction were characterized by means <strong>of</strong> a custom-built<br />
apparatus. A specific procedure was used for fasten<strong>in</strong>g <strong>the</strong><br />
paper to metal blocks by photo-mount<strong>in</strong>g tissue. The effects <strong>of</strong><br />
<strong>the</strong> penetration <strong>of</strong> <strong>the</strong> adhesive <strong>in</strong>to <strong>the</strong> paper were quantified.<br />
The performance <strong>of</strong> <strong>the</strong> apparatus was <strong>the</strong>n <strong>in</strong>vestigated. F<strong>in</strong>ally<br />
<strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> <strong>properties</strong> were characterized for handsheets<br />
made <strong>of</strong> bleached <strong>the</strong>rmo mechanical pulps and bleached chemical<br />
pulps with different ref<strong>in</strong><strong>in</strong>g levels.<br />
ADDRESS OF THE AUTHORS: Orlando Girlanda (orlando.<br />
girlanda@stfi.se) *Present address: orlando.girlanda@polymtl.ca<br />
Christer Fellers (c.fellers@ stfi.se): STFI-Packforsk AB, Box<br />
5604, SE-114 86 Stockholm, Sweden.<br />
Correspond<strong>in</strong>g author: Christer Fellers<br />
The mechanical <strong>properties</strong> <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction <strong>of</strong><br />
paper are important for <strong>the</strong> performance <strong>in</strong> a number <strong>of</strong><br />
convert<strong>in</strong>g operations such as creas<strong>in</strong>g, bend<strong>in</strong>g, pr<strong>in</strong>t<strong>in</strong>g,<br />
and plastic coat<strong>in</strong>g. The knowledge <strong>of</strong> strength, elastic<br />
modulus, <strong>stra<strong>in</strong></strong>-s<strong>of</strong>ten<strong>in</strong>g behavior <strong>in</strong> tension and<br />
compressibility <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction, also called<br />
Z-direction, are needed for a comprehensive description<br />
<strong>of</strong> <strong>the</strong> performance <strong>of</strong> <strong>the</strong> material <strong>in</strong> <strong>the</strong>se operations.<br />
In spite <strong>of</strong> its importance, few publications deal with<br />
<strong>the</strong> evaluation <strong>of</strong> <strong>the</strong> entire <strong>tensile</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curve <strong>in</strong><br />
<strong>the</strong> <strong>thickness</strong> direction (Stenberg et al. 2001; Van Liew<br />
1974). The reason for this is likely <strong>the</strong> <strong>in</strong>tr<strong>in</strong>sic difficulty<br />
<strong>of</strong> test<strong>in</strong>g a th<strong>in</strong>, uneven, porous, fibrous and compressible<br />
material such as paper with sufficient precision and<br />
test<strong>in</strong>g time efficiency.<br />
Some aspects <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> behavior <strong>in</strong> terms <strong>of</strong><br />
elastic modulus are treated <strong>in</strong> several publications listed<br />
<strong>in</strong> Table 1. The elastic modulus has been characterized<br />
ei<strong>the</strong>r by evaluat<strong>in</strong>g <strong>the</strong> slope <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curve<br />
(Stenberg et al. 2001; Van Liew 1974) or by us<strong>in</strong>g an<br />
ultrasonic technique (Berger and Baum 1985; Fleischman<br />
et al. 1982; Mann et al. 1980; Waterhouse et al. 1987).<br />
Ano<strong>the</strong>r aspect is <strong>the</strong> strength <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction<br />
<strong>of</strong> paper, <strong>of</strong>ten characterized by <strong>the</strong> Z-directional <strong>tensile</strong><br />
test. The test piece is fastened by means <strong>of</strong> double adhesive<br />
tape onto two solid plane platens on which <strong>tensile</strong><br />
<strong>stress</strong> is <strong>the</strong>n applied. The maximum <strong>stress</strong> is recorded<br />
and def<strong>in</strong>ed as <strong>the</strong> Z-directional <strong>tensile</strong> strength. For this<br />
measurement standards such as Tappi (1989) and SCAN<br />
(1998) are available.<br />
When <strong>the</strong> deformation <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction <strong>of</strong><br />
paper is measured, it is advantageous to use a stiff adhesive.<br />
A prerequisite is also to consider <strong>the</strong> effects <strong>of</strong> <strong>the</strong><br />
adhesive penetration <strong>in</strong>to <strong>the</strong> porous network <strong>of</strong> paper and<br />
<strong>the</strong> stiffness <strong>of</strong> <strong>the</strong> adhesive itself (Stenberg et al. 2001;<br />
Van Liew 1974). In <strong>the</strong>ir experiments with wheel delam<strong>in</strong>ation<br />
tests, <strong>in</strong> which double adhesive tape is used, Naito et<br />
al. (1995) and Lundh and Fellers (2004) observe changes<br />
<strong>of</strong> <strong>the</strong> paper <strong>properties</strong> due to <strong>the</strong> <strong>in</strong>fluence <strong>of</strong> tape at a<br />
grammage <strong>of</strong> approximately 50-60 g/m 2 . In <strong>the</strong>ir <strong>in</strong>terlam<strong>in</strong>ar<br />
shear measurements, <strong>in</strong> which photo mount<strong>in</strong>g tissue is<br />
used, Byrd et al. (1975) estimate <strong>the</strong> penetration <strong>of</strong> photo<br />
mount<strong>in</strong>g tissue <strong>in</strong>to a l<strong>in</strong>erboard <strong>in</strong> <strong>the</strong> order <strong>of</strong> 7 microns<br />
correspond<strong>in</strong>g to approximately 5 g/m 2 .<br />
The mechanical <strong>properties</strong> <strong>of</strong> paper <strong>in</strong> <strong>the</strong> <strong>thickness</strong><br />
direction are ma<strong>in</strong>ly <strong>in</strong>fluenced by <strong>the</strong> number and<br />
strength <strong>of</strong> <strong>the</strong> fiber-to-fiber bonds, <strong>the</strong> stiffness <strong>of</strong> <strong>the</strong><br />
fibers and <strong>the</strong> fiber strength <strong>in</strong> <strong>the</strong> transverse direction. A<br />
comprehensive review <strong>of</strong> <strong>the</strong> results presented <strong>in</strong> literature<br />
on this subject can be found <strong>in</strong> Uesaka et al. (2002).<br />
S<strong>in</strong>ce <strong>the</strong> fiber-fiber bond <strong>properties</strong> are difficult to<br />
determ<strong>in</strong>e with precision, density is <strong>of</strong>ten used for rank<strong>in</strong>g<br />
<strong>the</strong> effects <strong>of</strong> pulp<strong>in</strong>g and papermak<strong>in</strong>g parameters<br />
on <strong>the</strong> mechanical performance paper along <strong>the</strong> <strong>thickness</strong><br />
direction (Andersson and Mohl<strong>in</strong> 1980; Fleischman et al.<br />
1982; Koubaa and Koran 1995; Waterhouse et al. 1987;<br />
Waterhouse 1991). For this reason, <strong>the</strong> comparison between<br />
different sheet <strong>properties</strong> was performed <strong>in</strong> <strong>the</strong> present<br />
<strong>in</strong>vestigation us<strong>in</strong>g handsheet density.<br />
The resistance <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction <strong>of</strong> a handsheet<br />
is also <strong>in</strong>fluenced by <strong>the</strong> entanglement <strong>of</strong> <strong>the</strong> fiber<br />
network. Paper can be regarded as a layered material<br />
because fibers lay manly parallel to <strong>the</strong> MD-CD plane.<br />
However measurements on paper test pieces show that<br />
<strong>the</strong>re are a number <strong>of</strong> fibers pass<strong>in</strong>g from one layer to <strong>the</strong><br />
o<strong>the</strong>r (Aaltio 1960; Hasuike et al. 1992). These fibers can<br />
Table 1. Paper material <strong>properties</strong> <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction measured by different authors.<br />
Material Elastic Method Failure Apperent Basis<br />
modulus <strong>stress</strong> density weight<br />
MPa MPa kg/m 3<br />
g/m 2<br />
Van Liew<br />
(1974)<br />
Western<br />
Hemlock<br />
bleached<br />
sulfite pulp<br />
140-560 Z-<strong>tensile</strong><br />
strength<br />
test<br />
0.55<br />
0.95<br />
840-950 240-523<br />
Mann et al.<br />
(1980)<br />
Milk carton<br />
stock<br />
39 Ultrasonic<br />
technique<br />
- 780 520<br />
Fleischmann<br />
et al.(1982)<br />
Western<br />
S<strong>of</strong>twood<br />
bleached<br />
kraft pulp<br />
30-300 Ultrasonic<br />
technique<br />
- 400-850 400<br />
Berger and L<strong>in</strong>erboard 29 Ultrasonic - 691 263-286<br />
Baum<br />
(1985)<br />
technique<br />
Waterhouse<br />
et al. (1987)<br />
Unbleached<br />
sou<strong>the</strong>rn<br />
p<strong>in</strong>e<br />
263-426 Ultrasonic<br />
technique<br />
- 790-1071 212-230<br />
Commercial<br />
l<strong>in</strong>erboard<br />
45.9 Ultrasonic<br />
technique<br />
- 723 207<br />
Waterhouse Unbleached 70-210 Ultrasonic - 487-796 312-290<br />
(1991) sou<strong>the</strong>rn<br />
p<strong>in</strong>e<br />
technique<br />
Stenberg et Chemical 3.86 Arcan - 864* 267<br />
al. (2001) bleached<br />
kraft pulp<br />
device<br />
*) Structural density<br />
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 49
<strong>in</strong>fluence <strong>the</strong> mechanical <strong>properties</strong> <strong>of</strong> paper when<br />
test<strong>in</strong>g th<strong>in</strong> paper sheets (Byrd et al. 1975). The irregular<br />
<strong>thickness</strong> <strong>of</strong> paper and irregular mass distribution also causes<br />
non-uniform <strong>stra<strong>in</strong></strong> distributions over <strong>the</strong> area <strong>of</strong> <strong>the</strong><br />
test pieces as po<strong>in</strong>ted out by Van den Akker (1952). These<br />
aspects became more relevant for th<strong>in</strong>ner test pieces.<br />
The aim <strong>of</strong> <strong>the</strong> present paper was to develop a test<strong>in</strong>g<br />
procedure for <strong>the</strong> measurement <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong><br />
<strong>properties</strong> <strong>in</strong> <strong>the</strong> Z-direction <strong>of</strong> paper enabl<strong>in</strong>g <strong>the</strong> extraction<br />
<strong>of</strong> <strong>the</strong> Z-directional <strong>tensile</strong> strength, <strong>stra<strong>in</strong></strong> at break<br />
and elastic modulus for paper. The penetration <strong>of</strong> adhesive<br />
and its <strong>in</strong>fluence on <strong>the</strong> performance <strong>of</strong> paper <strong>in</strong> <strong>the</strong><br />
<strong>thickness</strong> direction were def<strong>in</strong>ed. A selected number <strong>of</strong><br />
papers were tested. The relations between <strong>the</strong> mechanical<br />
<strong>properties</strong> and <strong>the</strong> paper structure, <strong>in</strong> terms <strong>of</strong> structural<br />
density, were obta<strong>in</strong>ed.<br />
Material and Methods<br />
Materials<br />
One <strong>the</strong>rmo mechanical pulp (TMP) and one chemical<br />
pulp were tested. The pulps were ei<strong>the</strong>r unbeaten or<br />
beaten <strong>in</strong> an <strong>in</strong>dustrial ref<strong>in</strong>er to different CSF levels,<br />
Table 2. Handsheets were made accord<strong>in</strong>g to SCAN-C<br />
26:76 with <strong>the</strong> exception that <strong>the</strong> grammage <strong>of</strong> <strong>the</strong> tested<br />
handsheets varied from 10 g/m 2 to 300 g/m 2 . Key <strong>in</strong>-plane<br />
mechanical <strong>properties</strong> for 180 g/m 2 sheets are given <strong>in</strong><br />
Table 2. Structural <strong>thickness</strong> and structural density were<br />
evaluated by SCAN-P88:01 and <strong>in</strong>-plane <strong>tensile</strong> <strong>properties</strong><br />
by ISO 1924-3.<br />
Table 2. Materials used <strong>in</strong> <strong>the</strong> present <strong>in</strong>vestigation and <strong>the</strong>ir <strong>in</strong>-plane <strong>properties</strong><br />
for 180 g/m 2 handsheets.<br />
Pulp CSF Structural In-plane In-plane Stra<strong>in</strong><br />
ml density <strong>tensile</strong> <strong>tensile</strong> at<br />
kg/m 3<br />
<strong>in</strong>dex stiffness break<br />
kNm/kg <strong>in</strong>dex<br />
MNm/kg<br />
%<br />
TMP 1<br />
Unbeaten s<strong>of</strong>twood<br />
TMP 2<br />
325 407 38 4.3 2.1<br />
Beaten s<strong>of</strong>twood<br />
Chem1<br />
Bleached chemical pulp,<br />
210 484 47 5.0 1.6<br />
mix <strong>of</strong> birch, eucalyptus and<br />
s<strong>of</strong>twood, lightly beaten<br />
Chem2<br />
Bleached chemical pulp,<br />
538 682 50 6.5 3.4<br />
mix <strong>of</strong> birch, eucalyptus and<br />
s<strong>of</strong>twood, highly beaten<br />
236 871 73 8.3 3.6<br />
Methods<br />
Preparation <strong>of</strong> <strong>the</strong> paper for test<strong>in</strong>g<br />
The handsheet was fastened to circular 10 cm 2 metal<br />
platens by means <strong>of</strong> a photo mount<strong>in</strong>g tissue (Be<strong>in</strong>fang<br />
ColorMount ® adhesive). The sum <strong>of</strong> platens, adhesive<br />
and paper is referred to as <strong>the</strong> test piece. The adhesive<br />
and <strong>the</strong> paper are henceforth referred to as <strong>the</strong> sandwich.<br />
The test piece was first subjected to 0.23 MPa pressure<br />
at 110°C <strong>in</strong> a hot air oven. After one hour cur<strong>in</strong>g time,<br />
50 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007<br />
<strong>the</strong> test piece was removed from <strong>the</strong> oven and conditioned<br />
under pressure at 23°C and 50% RH. The condition<strong>in</strong>g<br />
time was set to at least 12 hours which was found<br />
adequate to obta<strong>in</strong> <strong>the</strong> equilibrium <strong>of</strong> moisture content.<br />
Additionally bare handsheets underwent <strong>the</strong> same procedure<br />
<strong>in</strong> order def<strong>in</strong>e <strong>the</strong> change <strong>of</strong> <strong>the</strong> <strong>thickness</strong> due to<br />
<strong>the</strong> applied <strong>stress</strong>. The structural <strong>thickness</strong> <strong>of</strong> <strong>the</strong> handsheets<br />
after press<strong>in</strong>g, named thandsheet, and <strong>the</strong> grammage <strong>of</strong><br />
<strong>the</strong> handsheet, whandsheet, were used to determ<strong>in</strong>e <strong>the</strong> structural<br />
density <strong>of</strong> <strong>the</strong> pressed handsheets, which is written as<br />
whandsheet<br />
ρ = handsheet<br />
t<br />
[1]<br />
handsheet<br />
The sandwich consisted <strong>of</strong> three areas, which could be<br />
delimited by imag<strong>in</strong>ary horizontal planes, as shown <strong>in</strong><br />
Fig 1. After cur<strong>in</strong>g, <strong>the</strong> handsheet was penetrated by <strong>the</strong><br />
adhesive on both upper and lower surface. The mix area<br />
consisted both <strong>of</strong> <strong>the</strong> adhesive left outside <strong>of</strong> <strong>the</strong> paper<br />
and <strong>the</strong> part <strong>of</strong> <strong>the</strong> paper penetrated by <strong>the</strong> adhesive. The<br />
<strong>stress</strong>-<strong>stra<strong>in</strong></strong> <strong>properties</strong> <strong>of</strong> <strong>the</strong> paper calculated <strong>in</strong> <strong>the</strong><br />
present <strong>in</strong>vestigation referred to <strong>the</strong> center part <strong>of</strong> <strong>the</strong><br />
handsheet, not penetrated by <strong>the</strong> adhesive.<br />
Fig 1. Schematic picture <strong>of</strong> <strong>the</strong> structure <strong>of</strong> <strong>the</strong> test piece and adhesive penetration<br />
<strong>in</strong>to a handsheet with def<strong>in</strong>itions <strong>of</strong> three <strong>thickness</strong>es.<br />
Procedure for <strong>the</strong> measurement <strong>of</strong> adhesive penetration<br />
<strong>in</strong>to <strong>the</strong> handsheets, two-handsheets technique<br />
The evaluation <strong>of</strong> <strong>the</strong> mechanical <strong>properties</strong> <strong>in</strong> <strong>the</strong> <strong>thickness</strong><br />
direction required an estimation <strong>of</strong> <strong>the</strong> penetration<br />
grammage, which was <strong>the</strong> quantity <strong>of</strong> <strong>the</strong> handsheet<br />
affected by <strong>the</strong> adhesive.<br />
The penetration grammage was assessed by test<strong>in</strong>g<br />
two-handsheets sandwiches for each pulp type. Two<br />
handsheets with equal grammage were piled, pressed<br />
toge<strong>the</strong>r and fastened each on one surface to <strong>the</strong> platens<br />
by perform<strong>in</strong>g <strong>the</strong> already described preparations<br />
procedures. The two-handsheets sandwich was subjected<br />
to a <strong>tensile</strong> <strong>stress</strong> by <strong>the</strong> same experimental set up used<br />
for <strong>the</strong> measurements <strong>of</strong> <strong>the</strong> mechanical <strong>properties</strong> <strong>of</strong> <strong>the</strong><br />
paper. The grammage <strong>of</strong> <strong>the</strong> two handsheets was varied <strong>in</strong><br />
order to obta<strong>in</strong> different degrees <strong>of</strong> adhesive penetration.<br />
As long as <strong>the</strong> grammage <strong>of</strong> two handsheets was higher<br />
than <strong>the</strong> penetration grammage, no separation force was<br />
expected. As soon as <strong>the</strong> grammage <strong>of</strong> <strong>the</strong> handsheets<br />
was lower than <strong>the</strong> penetration grammage, <strong>the</strong> opposite<br />
adhesive layers could make contact and consequently a<br />
separation force was measured. The separation force was<br />
likely to <strong>in</strong>crease as <strong>the</strong> grammage <strong>of</strong> <strong>the</strong> handsheets was<br />
reduced. The penetration grammage, w penetration, was defi-
ned as <strong>the</strong> <strong>in</strong>tercept at zero force <strong>in</strong> a plot relat<strong>in</strong>g <strong>the</strong><br />
separation force to <strong>the</strong> s<strong>in</strong>gle handsheet grammage.<br />
Thickness def<strong>in</strong>ition <strong>of</strong> <strong>the</strong> constituents<br />
The comb<strong>in</strong>ed effect <strong>of</strong> adhesive penetration and nonrecoverable<br />
compression did not allow <strong>the</strong> direct<br />
evaluation <strong>of</strong> <strong>the</strong> <strong>thickness</strong> <strong>of</strong> <strong>the</strong> mix, t mix, and <strong>of</strong> <strong>the</strong><br />
<strong>thickness</strong> <strong>of</strong> <strong>the</strong> paper, t paper. An <strong>in</strong>direct assessment <strong>of</strong><br />
<strong>the</strong>se quantities was <strong>the</strong>refore necessary. The only measurable<br />
quantity was <strong>the</strong> sandwich <strong>thickness</strong>, t sandwich. This<br />
measurement, required ad hoc prepared test pieces.<br />
Alum<strong>in</strong>um sheets were placed between <strong>the</strong> platens and<br />
<strong>the</strong> adhesive so that <strong>the</strong> sandwich could be easily removed<br />
from <strong>the</strong> platens. The <strong>thickness</strong> <strong>of</strong> <strong>the</strong> sandwich<br />
could be determ<strong>in</strong>ed after remov<strong>in</strong>g <strong>the</strong> alum<strong>in</strong>um sheets<br />
from <strong>the</strong> sandwich. The <strong>thickness</strong> <strong>of</strong> <strong>the</strong> paper (see Fig 1<br />
for its geometrical def<strong>in</strong>ition) was calculated for each<br />
tested grammage as <strong>the</strong> difference between <strong>the</strong> <strong>thickness</strong><br />
<strong>of</strong> <strong>the</strong> handsheet after press<strong>in</strong>g and <strong>thickness</strong> <strong>of</strong> paper<br />
penetrated by <strong>the</strong> adhesive, Eqs (2)-(4). In Eq (2) <strong>the</strong><br />
penetration grammage and <strong>the</strong> density <strong>of</strong> <strong>the</strong> pressed<br />
handsheets for each grammage are used.<br />
Eq (2) can also be written us<strong>in</strong>g Eq (1) as<br />
⎛ 2w<br />
t = t ⎜1−<br />
paper handsheet ⎜<br />
⎝ w<br />
penetration<br />
handsheet<br />
The <strong>thickness</strong> <strong>of</strong> <strong>the</strong> mix could <strong>the</strong>n by calculated as<br />
t<br />
mix<br />
t − t<br />
=<br />
2<br />
sandwich paper<br />
Description <strong>of</strong> <strong>the</strong> test<strong>in</strong>g apparatus<br />
A schematic draw<strong>in</strong>g <strong>of</strong> <strong>the</strong> test<strong>in</strong>g apparatus is shown <strong>in</strong><br />
Fig 2. The rod was first screwed onto <strong>the</strong> test piece.<br />
Successively, <strong>the</strong> test piece and <strong>the</strong> rod were screwed<br />
onto <strong>the</strong> load cell. These actions were performed without<br />
subject<strong>in</strong>g <strong>the</strong> sandwich to undesired load<strong>in</strong>g. The rod<br />
was f<strong>in</strong>ally secured to <strong>the</strong> connector by <strong>the</strong> upper p<strong>in</strong>.<br />
Three sensors, fastened to <strong>the</strong> upper platen and displaced<br />
at 120 degrees from each o<strong>the</strong>r, measured <strong>the</strong><br />
displacement between <strong>the</strong> lower and <strong>the</strong> upper platen.<br />
The load<strong>in</strong>g was performed by means <strong>of</strong> a MTS servohydraulic<br />
test<strong>in</strong>g mach<strong>in</strong>e. The load was applied under<br />
displacement control <strong>in</strong> order to enable <strong>the</strong> measurement<br />
<strong>of</strong> <strong>the</strong> post-peak behavior <strong>of</strong> <strong>the</strong> material. The load was<br />
transferred to <strong>the</strong> rod via a universal jo<strong>in</strong>t system,<br />
consist<strong>in</strong>g <strong>of</strong> a connector, an upper and lower p<strong>in</strong>s<br />
cross<strong>in</strong>g each o<strong>the</strong>r. The po<strong>in</strong>t contact between <strong>the</strong> p<strong>in</strong>s<br />
avoided <strong>the</strong> bend<strong>in</strong>g moment caused by possible<br />
misalignments between <strong>the</strong> centre <strong>of</strong> <strong>the</strong> test piece and<br />
<strong>the</strong> po<strong>in</strong>t where <strong>the</strong> force is applied.<br />
The value <strong>of</strong> <strong>the</strong> Z-directional <strong>tensile</strong> strength obta<strong>in</strong>ed<br />
with <strong>the</strong> test<strong>in</strong>g apparatus was compared to <strong>the</strong> value<br />
obta<strong>in</strong>ed by a commercial apparatus follow<strong>in</strong>g SCAN<br />
P80:98. The latter method used tape to fasten <strong>the</strong> test<br />
pieces to <strong>the</strong> metal platens.<br />
⎞<br />
⎟<br />
⎠<br />
[2]<br />
[3]<br />
[4]<br />
Fig 2. A schematic draw<strong>in</strong>g <strong>of</strong> <strong>the</strong> test<strong>in</strong>g apparatus.<br />
Elaboration <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> data<br />
The data collected dur<strong>in</strong>g <strong>the</strong> experiments were <strong>the</strong><br />
displacements between <strong>the</strong> two platens measured by <strong>the</strong><br />
sensors and <strong>the</strong> correspond<strong>in</strong>g applied force measured by<br />
<strong>the</strong> load cell. The displacement at <strong>the</strong> centre <strong>of</strong> <strong>the</strong> test<br />
piece was calculated from <strong>the</strong> sensors measured displacements,<br />
as expla<strong>in</strong>ed <strong>in</strong> Appendix I. The displacement at<br />
<strong>the</strong> centre <strong>of</strong> <strong>the</strong> circular test piece, called δ sandwich, was<br />
taken as representative for <strong>the</strong> deformation <strong>of</strong> <strong>the</strong> whole<br />
sandwich. The elastic modulus <strong>of</strong> <strong>the</strong> sandwich was evaluated<br />
by a l<strong>in</strong>ear regression <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curves.<br />
The <strong>thickness</strong> <strong>of</strong> <strong>the</strong> sandwich t, <strong>the</strong> <strong>in</strong>stantaneous force<br />
F and <strong>the</strong> tested area A were used for <strong>the</strong> determ<strong>in</strong>ation<br />
<strong>of</strong> <strong>the</strong> elastic modulus accord<strong>in</strong>g to Eq (5).<br />
E<br />
sandwich<br />
= δ<br />
F<br />
sandwich<br />
A t<br />
sandwich<br />
The displacement <strong>of</strong> <strong>the</strong> mix, δ mix, was determ<strong>in</strong>ed by<br />
assum<strong>in</strong>g a l<strong>in</strong>ear elastic behavior <strong>of</strong> <strong>the</strong> mix us<strong>in</strong>g Eq 6<br />
where <strong>the</strong> elastic modulus <strong>of</strong> <strong>the</strong> mix was obta<strong>in</strong>ed from<br />
<strong>the</strong> slope <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curve <strong>of</strong> handsheets which<br />
were completely penetrated by <strong>the</strong> adhesive.<br />
The displacement <strong>of</strong> <strong>the</strong> paper was calculated as <strong>the</strong><br />
difference between <strong>the</strong> displacement <strong>of</strong> <strong>the</strong> sandwich and<br />
<strong>the</strong> displacement <strong>of</strong> <strong>the</strong> mix:<br />
Consequently <strong>the</strong> <strong>stra<strong>in</strong></strong> <strong>in</strong> paper was calculated as<br />
The value <strong>of</strong> <strong>the</strong> elastic modulus <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction<br />
<strong>of</strong> paper was determ<strong>in</strong>ed by comb<strong>in</strong><strong>in</strong>g <strong>the</strong> elastic<br />
[5]<br />
F<br />
δmix mix<br />
E A t = [6]<br />
mix<br />
δ = δ −2 δ<br />
paper sandwich mix<br />
[7]<br />
ε<br />
paper<br />
⎛<br />
δ<br />
δ<br />
⎜<br />
paper ⎝<br />
= =<br />
t<br />
paper<br />
sandwich<br />
F<br />
E A t − 2<br />
t paper<br />
mix<br />
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 51<br />
mix<br />
⎞<br />
⎟<br />
⎠<br />
[8]
modulus <strong>of</strong> <strong>the</strong> sandwich and <strong>the</strong> elastic modulus <strong>of</strong> <strong>the</strong><br />
mix accord<strong>in</strong>g to Eq (9), by substitut<strong>in</strong>g Eqs (5) and (6)<br />
<strong>in</strong>to (7),<br />
E<br />
paper<br />
Results<br />
F<br />
A t = = paper<br />
δ<br />
⎛<br />
paper t<br />
⎜<br />
⎝ E<br />
The test<strong>in</strong>g procedure presented <strong>in</strong> this paper was developed<br />
for <strong>the</strong> measurement <strong>of</strong> <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curve <strong>in</strong> <strong>the</strong><br />
Z-direction <strong>of</strong> paper from which <strong>the</strong> extraction <strong>of</strong> <strong>the</strong> Zdirectional<br />
<strong>tensile</strong> strength, <strong>stra<strong>in</strong></strong> at break and elastic<br />
modulus for paper was possible. A selected number <strong>of</strong><br />
handsheets were tested and <strong>the</strong> relations between <strong>the</strong><br />
mechanical <strong>properties</strong> and <strong>the</strong> paper structure, <strong>in</strong> terms <strong>of</strong><br />
structural density, were <strong>in</strong>vestigated. A summary <strong>of</strong> all<br />
<strong>the</strong> results is given <strong>in</strong> Appendix II.<br />
The analysis started by study<strong>in</strong>g <strong>the</strong> change <strong>in</strong> <strong>thickness</strong><br />
<strong>of</strong> <strong>the</strong> handsheets due to <strong>the</strong> press<strong>in</strong>g sequence<br />
(Table 3). The TMP handsheets showed a permanent<br />
deformation after <strong>the</strong> press<strong>in</strong>g, whereas no change was<br />
observed for <strong>the</strong> chemical handsheets.<br />
The penetration <strong>of</strong> <strong>the</strong> Photo Mount<strong>in</strong>g Tissue adhesive<br />
<strong>in</strong>to <strong>the</strong> handsheets was <strong>the</strong>n determ<strong>in</strong>ed by <strong>the</strong><br />
“two-handsheets” technique. Fig 3 shows <strong>the</strong> data for <strong>the</strong><br />
chemical pulp 1. The behavior was representative for all<br />
<strong>the</strong> <strong>in</strong>vestigated handsheets. The straight l<strong>in</strong>e is <strong>the</strong> l<strong>in</strong>ear<br />
fit to <strong>the</strong> data. The extrapolated value to zero-strength<br />
gave <strong>the</strong> penetration grammage <strong>in</strong>to one handsheet. The<br />
results <strong>in</strong> terms <strong>of</strong> penetration grammage for all <strong>the</strong><br />
<strong>in</strong>vestigated papers are summarized <strong>in</strong> Table 4.<br />
52 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007<br />
t<br />
sandwich<br />
paper<br />
sandwich<br />
2 t ⎞<br />
mix<br />
[9]<br />
−<br />
E<br />
⎟<br />
⎠<br />
Table 3. Density after press<strong>in</strong>g and change <strong>in</strong> <strong>thickness</strong> <strong>of</strong> <strong>the</strong> handsheets due to press<strong>in</strong>g.<br />
Measurements were performed at 23°C and 50% RH.<br />
mix<br />
TMP 1 TMP 2 Chem 1 Chem 2<br />
Grammage Density Change Density Change Density Change Density Change<br />
g/m 2<br />
kg/m 3<br />
% kg/m 3<br />
% kg/m 3<br />
kg/m 3<br />
80 444 17 514 10 666 - 862 -<br />
100 448 15 515 7 687 - 849 -<br />
120 472 13 533 9 686 - 856 -<br />
180 459 8 540 10 682 - 885 -<br />
240 465 8 539 8 678 - 879 -<br />
300 491 12 542 9 680 - 882 -<br />
Average 463 12 530 9 682 - 871 -<br />
Fig 3. Z-directional <strong>tensile</strong> strength versus grammage for one handsheet tested by<br />
<strong>the</strong> “two-handsheet” technique.<br />
Table 4. Penetration <strong>of</strong> <strong>the</strong> adhesive <strong>in</strong>to <strong>the</strong> handsheets. The penetration <strong>thickness</strong><br />
was evaluated by Eq (1).<br />
Pulp Penetration<br />
g/m 2<br />
The penetration grammage was approximately 20 g/m 2<br />
for all <strong>the</strong> <strong>in</strong>vestigated handsheets while <strong>the</strong> penetration<br />
<strong>thickness</strong> varied depend<strong>in</strong>g on <strong>the</strong> density <strong>of</strong> <strong>the</strong> handsheet,<br />
Fig 4.<br />
Based on <strong>the</strong> results <strong>in</strong> Table 4, <strong>the</strong> Z-strength tests for<br />
<strong>the</strong> evaluation <strong>of</strong> <strong>the</strong> elastic modulus <strong>of</strong> <strong>the</strong> mix were<br />
performed on 40 g/m 2 handsheets, us<strong>in</strong>g Eq (5). The<br />
elastic modulus for <strong>the</strong> adhesive was also evaluated us<strong>in</strong>g<br />
<strong>the</strong> custom built apparatus. The results are given <strong>in</strong><br />
Table 5 and plotted as function <strong>of</strong> density <strong>in</strong> Fig 5.<br />
mm<br />
TMP1 19.7 0.054<br />
TMP2 19.5 0.042<br />
Chem1 19.5 0.029<br />
Chem2 20.7 0.022<br />
Fig 4. Penetration depth versus density for <strong>the</strong> handsheets tested by <strong>the</strong> “twohandsheets”<br />
technique.<br />
Table 5. Elastic modulus for <strong>the</strong> mix and <strong>the</strong> adhesive performed<br />
on 40 g/m 2 sheets.<br />
Material E, MPa<br />
TMP 1 33<br />
TMP 2 61<br />
Chem1 230<br />
Chem2 302<br />
Adhesive 1600<br />
Fig 5. Relation between elastic modulus for <strong>the</strong> mix and handsheet density.
Test<strong>in</strong>g speed<br />
Paper material and adhesives exhibit a visco-elastic<br />
behavior, i.e. <strong>the</strong>ir response <strong>in</strong> terms <strong>of</strong> strength will<br />
change depend<strong>in</strong>g on <strong>the</strong> test<strong>in</strong>g speed. Rate dependency<br />
was not addressed <strong>in</strong> this paper. However <strong>the</strong> purpose<br />
was to test <strong>the</strong> material <strong>in</strong> a time w<strong>in</strong>dow <strong>in</strong> which <strong>the</strong><br />
<strong>stra<strong>in</strong></strong> rate had negligible <strong>in</strong>fluence on <strong>the</strong> material <strong>properties</strong>.<br />
The <strong>in</strong>fluence <strong>of</strong> <strong>the</strong> <strong>stra<strong>in</strong></strong> rate was studied for<br />
120 g/m 2 paper sheets prepared with chemical pulp 2.<br />
Two different test<strong>in</strong>g speeds were used, 0.025 mm/s and<br />
0.0025 mm/s. The mean times to break were respectively<br />
6.7 and 66 seconds. No <strong>in</strong>fluence on <strong>the</strong> Z-directional<br />
<strong>tensile</strong> strength was found. The tests <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g part<br />
<strong>of</strong> <strong>the</strong> article were <strong>the</strong>refore performed at 0.0025 mm/s<br />
speed.<br />
Stress <strong>stra<strong>in</strong></strong> curves<br />
Fig 6 presents four typical <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curves for 300<br />
g/m 2 , one for each type <strong>of</strong> pulp studied <strong>in</strong> <strong>the</strong> present<br />
<strong>in</strong>vestigation. The curves were calculated by Eq (8). The<br />
elastic moduli presented <strong>in</strong> this <strong>in</strong>vestigation were obta<strong>in</strong>ed<br />
by l<strong>in</strong>ear regression <strong>of</strong> <strong>the</strong> Z-directional <strong>stress</strong>-<strong>stra<strong>in</strong></strong><br />
curves. The limit at which l<strong>in</strong>earity was good approximation<br />
varied depend<strong>in</strong>g on <strong>the</strong> pulps. For TMP <strong>the</strong> elastic<br />
moduli were calculated up to 50% <strong>of</strong> <strong>the</strong> strength. For<br />
chemical pulp <strong>the</strong> calculation limit was set to 80% <strong>of</strong> <strong>the</strong><br />
strength.<br />
Fig 6. True <strong>stress</strong>-<strong>stra<strong>in</strong></strong> curves for <strong>the</strong> <strong>in</strong>vestigated handsheets.<br />
Sheets prepared from chemical pulps were stiffer than <strong>the</strong><br />
ones made <strong>of</strong> mechanical pulps. TMP was characterized<br />
by a <strong>stra<strong>in</strong></strong> at break around 8%, whereas <strong>stra<strong>in</strong></strong> at break<br />
for chemical pulp ranged from 1.4% to 1.8%. The postpeak<br />
behavior changed drastically for different pulps. For<br />
chemical pulp 2 <strong>the</strong> post-peak behavior was unstable at<br />
any grammage. For chemical pulp 1, post peak <strong>in</strong>stability<br />
was also present for low grammage handsheets, but for<br />
higher grammage <strong>the</strong> failure was stable. For TMP<br />
handsheets <strong>the</strong> failure was always stable.<br />
Z-directional <strong>tensile</strong> strength<br />
In Figs 7 to 10 <strong>the</strong> Z-directional <strong>tensile</strong> strength is shown<br />
as a function <strong>of</strong> grammage. The strength values are<br />
obta<strong>in</strong>ed us<strong>in</strong>g two different techniques, i.e. measurements<br />
performed by <strong>the</strong> custom built apparatus us<strong>in</strong>g<br />
adhesive, and data measured us<strong>in</strong>g double adhesive tape.<br />
Fig 7. Grammage versus Z-directional <strong>tensile</strong> strength plot for TMP1 obta<strong>in</strong>ed<br />
us<strong>in</strong>g two different test<strong>in</strong>g methods.<br />
Fig 8. Grammage versus Z-directional <strong>tensile</strong> strength plot for TMP2 obta<strong>in</strong>ed<br />
us<strong>in</strong>g two different test<strong>in</strong>g methods.<br />
Fig 9. Grammage versus Z-directional <strong>tensile</strong> strength plot for chemical pulp 1<br />
obta<strong>in</strong>ed us<strong>in</strong>g two different test<strong>in</strong>g methods.<br />
Fig 10. Grammage versus Z-directional <strong>tensile</strong> strength plot for chemical pulp 2<br />
obta<strong>in</strong>ed us<strong>in</strong>g two different test<strong>in</strong>g methods.<br />
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 53
Fig 11. Density versus Z-directional <strong>tensile</strong> strength <strong>in</strong> a semi-logarithmic plot. Fig 12. Elastic modulus versus grammage for <strong>the</strong> TMP handsheets.<br />
The Z-directional <strong>tensile</strong> strength <strong>of</strong> TMP handsheets<br />
could be regarded as constant down to a grammage <strong>of</strong><br />
approximately 60 g/m 2 . For lower grammages <strong>the</strong> Zdirectional<br />
<strong>tensile</strong> strength <strong>in</strong>creased drastically. For <strong>the</strong><br />
chemical pulps <strong>the</strong> strength gradually <strong>in</strong>creased with<br />
decreas<strong>in</strong>g grammage. A steep <strong>in</strong>crease was also observed<br />
after <strong>the</strong> 60 g/m 2 limit.<br />
The strength measured with double adhesive tape was<br />
<strong>in</strong>dependent <strong>of</strong> grammage, with <strong>the</strong> exception <strong>of</strong> low<br />
grammages, where tape penetration <strong>in</strong>fluenced <strong>the</strong><br />
measurements. When strong chemical pulp was tested,<br />
<strong>the</strong> failure did not occur <strong>in</strong> <strong>the</strong> paper but <strong>in</strong> <strong>the</strong> <strong>in</strong>terface<br />
between tape and paper. On <strong>the</strong> o<strong>the</strong>r hand, when test<strong>in</strong>g<br />
TMP, <strong>the</strong> failure occurred always <strong>in</strong> <strong>the</strong> paper.<br />
Fig 11 presents <strong>in</strong> a logarithmical scale all <strong>the</strong> results<br />
<strong>in</strong> terms <strong>of</strong> Z-directional strength <strong>in</strong> function <strong>of</strong> <strong>the</strong><br />
structural density. A straight l<strong>in</strong>e fit was performed to <strong>the</strong><br />
data.<br />
The elastic modulus was calculated from Eq (9). The<br />
results are presented <strong>in</strong> Figs 12 and 13. The straight l<strong>in</strong>es<br />
correspond to <strong>the</strong> mean value <strong>of</strong> <strong>the</strong> elastic modulus evaluated<br />
for papers with different grammage. The elastic<br />
modulus was essentially <strong>in</strong>dependent <strong>of</strong> grammage.<br />
The relation between elastic modulus and density was<br />
also considered. In order to illustrate <strong>in</strong> <strong>the</strong> same graph<br />
<strong>the</strong> full range <strong>of</strong> elastic modulus for <strong>the</strong> different pulps a<br />
logarithmical scale on <strong>the</strong> y-axis was used <strong>in</strong> Fig 14. A<br />
straight l<strong>in</strong>e fit was performed to <strong>the</strong> data.<br />
Fig 15 presents <strong>the</strong> variation <strong>of</strong> <strong>stra<strong>in</strong></strong> at break as function<br />
<strong>of</strong> grammage. It was observed that <strong>stra<strong>in</strong></strong> at break<br />
<strong>in</strong>creased for lower grammage handsheets both for TMP<br />
and chemical pulps. It was also observed that <strong>stra<strong>in</strong></strong> at<br />
break was significantly higher for TMP handsheets.<br />
Fig 16 shows <strong>the</strong> results for <strong>stra<strong>in</strong></strong> at break as a function<br />
<strong>of</strong> density. Density had a small <strong>in</strong>fluence on <strong>the</strong><br />
<strong>stra<strong>in</strong></strong> at break <strong>of</strong> chemical pulps. TMP seemed to be<br />
slightly more sensitive to small variations <strong>of</strong> density,<br />
s<strong>in</strong>ce a decrease <strong>in</strong> density caused an <strong>in</strong>crease <strong>in</strong> <strong>the</strong><br />
<strong>stra<strong>in</strong></strong> at break.<br />
Discussion<br />
The custom-built experimental set-up was designed to<br />
allow for <strong>the</strong> measurement <strong>of</strong> <strong>the</strong> Z-directional <strong>stress</strong><strong>stra<strong>in</strong></strong><br />
curves <strong>of</strong> handsheets. The first set <strong>of</strong> tests measured<br />
<strong>the</strong> adhesive penetration <strong>in</strong>to <strong>the</strong> handsheet with<br />
54 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007<br />
Fig 13. Elastic modulus versus grammage for <strong>the</strong> chemical pulps handsheets.<br />
Fig 14. Elastic modulus versus density for <strong>the</strong> <strong>in</strong>vestigated handsheets.<br />
Fig 15. Stra<strong>in</strong> at break versus grammage for <strong>the</strong> <strong>in</strong>vestigated handsheets.
Fig 16. Stra<strong>in</strong> at break versus density for <strong>the</strong> <strong>in</strong>vestigated handsheets.<br />
vary<strong>in</strong>g structural density. This was a prerequisite for a<br />
more precise evaluation <strong>of</strong> <strong>the</strong> deformation <strong>of</strong> paper. The<br />
results <strong>in</strong> terms <strong>of</strong> elastic moduli showed that when<br />
evaluat<strong>in</strong>g <strong>the</strong> <strong>stra<strong>in</strong></strong> related <strong>properties</strong>, <strong>the</strong> <strong>in</strong>fluence <strong>of</strong><br />
<strong>the</strong> adhesive could not be neglected even for higher<br />
grammages. Byrd et al. (Byrd et al. 1975) apply an<br />
adhesive similar to <strong>the</strong> one used <strong>in</strong> <strong>the</strong> present study, but<br />
<strong>the</strong>y assume that <strong>the</strong> adhesive has an <strong>in</strong>f<strong>in</strong>ite stiffness.<br />
This might be a reason for <strong>the</strong>ir calculated adhesive<br />
penetration which is significantly lower than <strong>the</strong> one<br />
presented <strong>in</strong> this paper.<br />
A large discrepancy was found between <strong>the</strong> Z-directional<br />
<strong>tensile</strong> strength measured us<strong>in</strong>g adhesive and double<br />
adhesive tape. This was not unexpected s<strong>in</strong>ce <strong>the</strong> strength<br />
results for <strong>the</strong> chemical pulps lie on <strong>the</strong> border or outside<br />
<strong>the</strong> recommended measurement range accord<strong>in</strong>g to<br />
SCAN P80:98. Consequently, reliable Z-directional<br />
strength values for strong papers can only be obta<strong>in</strong>ed by<br />
ensur<strong>in</strong>g a paper-adhesive bond<strong>in</strong>g which is stronger than<br />
<strong>the</strong> paper itself.<br />
A possible drawback for <strong>the</strong> presented method is <strong>the</strong><br />
densification <strong>of</strong> TMP dur<strong>in</strong>g <strong>the</strong> press<strong>in</strong>g process, which<br />
might have an effect on <strong>the</strong> mechanical <strong>properties</strong>.<br />
However, <strong>the</strong> strength results obta<strong>in</strong>ed with commercial<br />
apparatus did not differ, <strong>in</strong> <strong>the</strong> range <strong>of</strong> <strong>the</strong> acceptable<br />
grammages, from <strong>the</strong> ones obta<strong>in</strong>ed by <strong>the</strong> custom built<br />
apparatus.<br />
The chosen pressure ensured a sufficient penetration <strong>of</strong><br />
<strong>the</strong> glue and sufficient bond<strong>in</strong>g between <strong>the</strong> glue and<br />
paper. In <strong>the</strong> future, a reduction <strong>of</strong> <strong>the</strong> cur<strong>in</strong>g time<br />
obta<strong>in</strong>ed by us<strong>in</strong>g more suitable glue comb<strong>in</strong>ed with a<br />
decrease <strong>of</strong> <strong>the</strong> cur<strong>in</strong>g pressure may be <strong>the</strong> way to avoid<br />
<strong>the</strong> densification.<br />
The decrease <strong>in</strong> Z-directional <strong>tensile</strong> strength for<br />
<strong>in</strong>creas<strong>in</strong>g grammage observed for <strong>the</strong> chemical pulps<br />
can be expla<strong>in</strong>ed by <strong>the</strong> Weak L<strong>in</strong>k Theory. Handsheets<br />
with higher grammages present a higher number <strong>of</strong><br />
distributed defects trigger<strong>in</strong>g failures at lower <strong>stress</strong>es.<br />
On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> Z-directional <strong>tensile</strong> strength for<br />
TMP sheets rema<strong>in</strong>ed constant over <strong>the</strong> range <strong>of</strong> <strong>the</strong><br />
acceptable grammages. One explanation might be that<br />
<strong>the</strong> defect sensitivity is related to <strong>the</strong> density <strong>of</strong> <strong>the</strong> fiber<br />
network. The adhesive penetration does not allow test<strong>in</strong>g<br />
grammages less than 60 g/m 2 . Test<strong>in</strong>g <strong>of</strong> th<strong>in</strong>ner paper<br />
may require a ref<strong>in</strong>ement <strong>of</strong> <strong>the</strong> technique.<br />
In l<strong>in</strong>e with <strong>the</strong> previous results on <strong>the</strong> subject, it was<br />
shown that density caused an exponential <strong>in</strong>crease <strong>in</strong><br />
both Z-directional <strong>tensile</strong> strength and <strong>the</strong> elastic<br />
modulus for <strong>the</strong> tested material. It is likely that <strong>the</strong> f<strong>in</strong>es<br />
cause <strong>the</strong> <strong>in</strong>crease <strong>of</strong> strength for <strong>the</strong> beaten pulps but<br />
less <strong>in</strong>fluence on <strong>the</strong> Z-directional elastic modulus is<br />
expected. The magnitude <strong>of</strong> <strong>the</strong> elastic modulus is <strong>in</strong><br />
agreement with <strong>the</strong> previous literature data. With regard<br />
to <strong>the</strong> fiber shape, two ma<strong>in</strong> concurrent structural factors<br />
<strong>in</strong>fluenc<strong>in</strong>g <strong>the</strong> Z-directional elastic modulus <strong>of</strong> paper<br />
can be identified. A consequence <strong>of</strong> <strong>in</strong>creas<strong>in</strong>g density is<br />
a lower free fiber segment length correspond<strong>in</strong>g to higher<br />
resistance to bend<strong>in</strong>g for s<strong>in</strong>gular fibers. This phenomenon<br />
may have positive effect on <strong>the</strong> Z-directional elastic<br />
modulus <strong>of</strong> paper. The fiber collapse, caused by beat<strong>in</strong>g,<br />
on <strong>the</strong> o<strong>the</strong>r hand, reduces <strong>the</strong> <strong>thickness</strong> <strong>of</strong> <strong>the</strong> fiber and<br />
<strong>the</strong>refore <strong>the</strong> bend<strong>in</strong>g stiffness <strong>of</strong> <strong>the</strong> s<strong>in</strong>gle fiber drops.<br />
This fact is likely to be detrimental to <strong>the</strong> elastic moduli<br />
<strong>of</strong> paper.<br />
S<strong>in</strong>ce <strong>the</strong> elastic modulus <strong>in</strong>creases with density, <strong>the</strong><br />
negative effect <strong>of</strong> fiber collapse seems to be negligible<br />
over reduction <strong>of</strong> <strong>the</strong> free fiber length.<br />
Conclusions<br />
·<br />
·<br />
·<br />
·<br />
·<br />
A method for <strong>the</strong> measurement <strong>of</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong> <strong>properties</strong><br />
<strong>of</strong> paper <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction was developed.<br />
The measurements were applicable for grammages<br />
over approximately 60g/m 2 .<br />
The paper <strong>properties</strong> were highly dependent on <strong>the</strong><br />
density. Higher density caused an exponential <strong>in</strong>crease<br />
<strong>in</strong> Elastic modulus, Z-directional strength, and a<br />
reduction <strong>of</strong> <strong>the</strong> <strong>stra<strong>in</strong></strong> at break<br />
The presented technique should help <strong>in</strong>creas<strong>in</strong>g <strong>the</strong><br />
knowledge <strong>of</strong> <strong>the</strong> relationship between <strong>the</strong> network<br />
structure and <strong>the</strong> mechanical <strong>properties</strong> <strong>of</strong> paper.<br />
The collected data may be used as a first approximation<br />
for model<strong>in</strong>g purposes <strong>of</strong> convert<strong>in</strong>g processes<br />
and end use performance.<br />
Acknowledgments<br />
The f<strong>in</strong>ancial support <strong>of</strong> <strong>the</strong> Surface Treatment Program at Karlstad University is<br />
acknowledged. The authors wish to thank <strong>the</strong> STFI-Packforsk partner companies<br />
participat<strong>in</strong>g <strong>in</strong> <strong>the</strong> Research Cluster ‘Eng<strong>in</strong>eered Paperboard’.<br />
Appendix I. F<strong>in</strong>d<strong>in</strong>g <strong>the</strong> displacement <strong>in</strong> <strong>the</strong> center <strong>of</strong><br />
<strong>the</strong> test piece.<br />
The aim <strong>of</strong> such calculation is to determ<strong>in</strong>e <strong>the</strong> displacement<br />
<strong>in</strong> <strong>the</strong> middle <strong>of</strong> <strong>the</strong> test piece. The displacement<br />
field <strong>of</strong> <strong>the</strong> all <strong>the</strong> po<strong>in</strong>ts <strong>in</strong> <strong>the</strong> test piece can be<br />
described as a plane <strong>in</strong> space, s<strong>in</strong>ce <strong>the</strong> test piece is<br />
rigidly connected to plane platens. The centre <strong>of</strong> <strong>the</strong> test<br />
piece is taken as <strong>the</strong> orig<strong>in</strong> <strong>of</strong> <strong>the</strong> coord<strong>in</strong>ate system. The<br />
displacements can be considered as <strong>the</strong> Z-coord<strong>in</strong>ates <strong>in</strong><br />
<strong>the</strong> space. The sensors yield <strong>the</strong> values <strong>of</strong> <strong>the</strong> dis-<br />
Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007 55
placements along <strong>the</strong> <strong>thickness</strong> direction <strong>in</strong> three<br />
different po<strong>in</strong>ts outside <strong>the</strong> test piece. The displacements<br />
<strong>of</strong> all po<strong>in</strong>ts belong<strong>in</strong>g to <strong>the</strong> same plane are given by<br />
ax + by + cz + d =0. [A1.1]<br />
The unknowns <strong>in</strong> <strong>the</strong> Eq (1) are <strong>the</strong> three cos<strong>in</strong>e directors<br />
a /d b /d c /d. The unknowns can be evaluated by substitut<strong>in</strong>g<br />
<strong>of</strong> <strong>the</strong> coord<strong>in</strong>ates three sensors <strong>in</strong>to Eq (1), be<strong>in</strong>g <strong>the</strong><br />
position <strong>in</strong> <strong>the</strong> x-y plane <strong>the</strong> x i,y i coord<strong>in</strong>ates and z i <strong>the</strong><br />
displacement along <strong>the</strong> <strong>thickness</strong> direction:<br />
⎡−1⎤<br />
⎡x<br />
y z ⎤⎡a<br />
d⎤<br />
1 1 1<br />
⎢ ⎥ ⎢ ⎥⎢<br />
⎥<br />
⎢−1⎥<br />
= ⎢x<br />
y z<br />
2 2 2⎥⎢bd⎥<br />
⎢<br />
⎣−1⎥<br />
⎢<br />
⎦ ⎣x<br />
y z ⎥⎢<br />
⎥<br />
3 3 3⎦⎣cd⎦<br />
The deformation <strong>of</strong> <strong>the</strong> centre <strong>of</strong> <strong>the</strong> test piece z center was<br />
determ<strong>in</strong>ed by substitut<strong>in</strong>g <strong>the</strong> coord<strong>in</strong>ate <strong>of</strong> <strong>the</strong> centre<br />
x center=0 and y center =0 <strong>in</strong>to (A1.1)<br />
z<br />
center<br />
−c<br />
=<br />
d<br />
Appendix II<br />
56 Nordic Pulp and Paper Research Journal Vol 22 no. 1/2007<br />
[A1.2]<br />
[A1.3]<br />
Table AII:1. Experimental results <strong>of</strong> Z-directional strength, elastic modulus and <strong>stra<strong>in</strong></strong> at break<br />
for <strong>the</strong> tested pulps.<br />
Grammage Z-directional 95% Z-directional 95% Elastic 95% Stra<strong>in</strong> 95%<br />
kg/m 2<br />
<strong>tensile</strong> CI <strong>tensile</strong> strength CI Modulus CI at break CI<br />
strength kPa (tape) kPa MPa %<br />
TMP1<br />
100 197 14 188 12 7.1 2.8 12.5 2.1<br />
120 215 33 204 17 7.9 3.7 10.5 0.8<br />
180 233 11 225 5 9.5 2.1 9.3 1.1<br />
240 220 10 215 9 7.7 2.2 8.7 0.7<br />
300 220 10 232 11 9.4 1.0 8.3 1.0<br />
TMP2<br />
80 335 42 323 16 13.3 3.7 12.6 0.8<br />
100 353 16 312 17 16.7 2.5 10.2 0.5<br />
120 384 17 328 46 19.6 3.7 9.0 0.8<br />
180 400 15 344 18 19.6 2.8 8.2 0.4<br />
240 375 15 352 27 16.01 2.7 8.4 0.4<br />
300 332 12 354 7 13.6 2.1 8.4 0.7<br />
Chem1<br />
80 777 99 442 3.2 62 26.7 2.7 1.2<br />
100 699 36 424 17.7 67 15.7 2.4 0.4<br />
120 655 7 409 8.9 91 14.6 2.0 0.6<br />
180 611 8 505 14 73 18.9 2.2 0.2<br />
240 550 11 484 5 73 9.5 1.7 0.1<br />
300 529 8 488 10 71 11.3 1.4 0.2<br />
Chem2<br />
80 1946 38 717 7.3 188.6 75.9 2.8 1.2<br />
100 1936 29 716 6.2 169.0 26.6 3.4 0.4<br />
120 1916 39 719 7.6 217.3 62.5 2.6 0.6<br />
180 1833 53 688 19 203.4 25.4 2.0 0.2<br />
240 1781 24 683 14 205.5 31.8 1.9 0.1<br />
300 1693 37 683 11 206.0 16.9 1.8 0.2<br />
Literature<br />
Aaltio, E.A. (1960): Studies on <strong>the</strong> Z-orientation <strong>in</strong> Paper, Svensk Papperstidn<strong>in</strong>g,<br />
(3) 58-61.<br />
Andersson, M. and Mohl<strong>in</strong>, U.-B. (1980): Z-strength <strong>of</strong> mechanical pulps,<br />
Paperi Puu, 62(10) 583-586.<br />
Berger, B.F. and Baum, G.A. (1985): Z-direction <strong>properties</strong>: <strong>the</strong> effects <strong>of</strong> yield<br />
and ref<strong>in</strong><strong>in</strong>g, Eighth Fundamental Research Symposium, Oxford, V. Punton, pp.<br />
Byrd, V.L. Setterholm, V.C. and Wichmann, J.F. (1975): Methods for measur<strong>in</strong>g<br />
<strong>the</strong> <strong>in</strong>terlam<strong>in</strong>ar shear <strong>properties</strong> <strong>of</strong> paper, Tappi, 58(10) 132-135.<br />
Fleischman, E.H. Baum, G.A. and Habeger, C.C. (1982): A study on <strong>the</strong> elastic and<br />
dielectric anisotropy <strong>of</strong> paper, The role <strong>of</strong> fundamental research <strong>in</strong> papermak<strong>in</strong>g,<br />
Transactions <strong>of</strong> <strong>the</strong> symposium, Cambridge, 1981. 115-118.<br />
Hasuike, M. Kawasaki, T. and Murakami, K. (1992): <strong>Evaluation</strong> Method <strong>of</strong> 3-D<br />
Geometric Structure <strong>of</strong> Paper Sheet, J. Pulp Paper Sci. 18(3) J114-J120.<br />
Koubaa, A. and Koran, Z. (1995): Measure <strong>of</strong> <strong>the</strong> <strong>in</strong>ternal bond strength <strong>of</strong><br />
paper/board, Tappi J. 78(3) 103-111.<br />
Lundh, A. and Fellers, C. (2004): A method for determ<strong>in</strong>ation <strong>of</strong> delam<strong>in</strong>ation<br />
toughness <strong>in</strong> different positions <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction <strong>of</strong> paperboard, Nord.<br />
Pulp Paper Res. J. 19(2) 224-228.<br />
Mann, R.W. Baum, G.A. and Habeger, C.C. (1980): Determ<strong>in</strong>ation <strong>of</strong> all n<strong>in</strong>e<br />
orthotropic elastic constants for mach<strong>in</strong>e-made paper, Tappi, 63(2) 163-166.<br />
Naito, T. Nishi, K. and Kawano, Y. (1995): Delam<strong>in</strong>ation resistance <strong>of</strong> paper,<br />
1995 International Paper Conference, Niagara-on-<strong>the</strong>-lake, ON. pp.125-130.<br />
SCAN (1998): P80:98 Paper and Board, Z-directional <strong>tensile</strong> strength,<br />
Stenberg, N. Fellers, C. and Östlund, S. (2001): Measur<strong>in</strong>g <strong>the</strong> <strong>stress</strong>-<strong>stra<strong>in</strong></strong><br />
<strong>properties</strong> <strong>of</strong> paperboard <strong>in</strong> <strong>the</strong> <strong>thickness</strong> direction, J. Pulp Paper Sci. 27(6) 213-<br />
221.<br />
Tappi (1989): Standard T 541 om, Internal bond strength <strong>of</strong> paperboard ( Zdirection<br />
<strong>tensile</strong> ).<br />
Uesaka, T. Retula<strong>in</strong>en, E. Paavila<strong>in</strong>en, L. Mark, R. E. and Keller, S. (2002):<br />
Determ<strong>in</strong>ation <strong>of</strong> fiber-fiber bond <strong>properties</strong>, New York.<br />
Van Den Akker, J.A. (1952): Instrumentation studies. LXIX. General discussion <strong>of</strong><br />
<strong>the</strong> measurement <strong>of</strong> <strong>the</strong> adhesion and cohesion, Tappi, 35(4) 155A-162A.<br />
Van Liew, G. P. (1974): The Z-direction deformation <strong>of</strong> paper, Tappi, 57(11) 121-<br />
124.<br />
Waterhouse, J. Stera, S. and Brennan, D. (1987): Z-direction variation <strong>of</strong> <strong>in</strong>ternal<br />
<strong>stress</strong> and <strong>properties</strong> <strong>in</strong> paper, J. Pulp Paper Sci. 13(1) 33-37.<br />
Waterhouse, J.F. (1991): The failure envelope <strong>of</strong> paper when subjected to comb<strong>in</strong>ed<br />
out-<strong>of</strong>-plane <strong>stress</strong>es, International Paper Physics Conference, Kona, Hawaii,<br />
USA., pp. 629-640.<br />
Manuscript received August 30, 2006<br />
Accepted November 10, 2006