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

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