7 92
M. Nygårds
Fig. 1 The failure criterion plotted for a 400 μm paperboard with different normal and shear failure stresses. In bending the paperboards will fail in the z -position, where the normal- ized stress is maximal
Results
such as density, fiber orientation, and fiber length to predict strength and stiffness. Since paperboard is orthotropic the geometrical mean strength is often calculated from the strength in the machine direction (MD) and cross-machine direction (CD) [18],
Properties of free‑laid plies
Paperboards from a series of trial productions have been split- ted (Fortuna [8] to free-lay the top, middle, and bottom plies. About 100 paperboards with various properties was used in the study. The paperboards were selected to have variation in the different plies to represent the limits with respect to density, fiber orientation etc. within each layer. The plies have been characterized with respect to physical properties and tensile tests to measure density, degree of anisotropy, strength, and stiffness within each layer. The in-plane tensile properties were measured using ISO 1924-2, while the ZD tensile test was measured using ISO 15754. Normally the variation of strength is about 10% when whole paperboard is tested, which is due to the inhomogeneous fiber structure that can have density vari- ations. When free-laid plies are tested, the strength variation is about the same. However, the splitting procedure is also a source of variation, since thickness of the free-laid plies can vary between splits. The aim here has been to try to position the splitting position to the middle of the interface. However, the interface has a thickness of 10–20 mm, hence some fibers from the neighboring ply will still be found on the free-laid ply. The variation of strength properties would then be about 10% and is the main reason to the variations seen in Figs. 2, 3, 4, 5. The data will be used to formulate simplified models that can be used to make qualitative analytical predictions, in these we will not consider variation at this time. Of interest will be to identify the importance of papermaking parameters
0 =
(19)
b MD
b
..
CD
In this work several paperboards have been tested, a differ- ent feature between the paperboards was the fiber orientation. From tensile testing of paperboards with different fiber orienta- tion it was established that as the MD/CD strength ratio varied; in fact, the tensile strengths in MD and CD were invariant, see Fig. 2, where the top, middle, bottom plies have the same behavior as the whole paperboard. The strength of a paperboard in arbitrary direction was expressed as
(20)
= 0 A ,
where A is the degree of anisotropy, which by rearranging Eq. (19) the strengths in MD and CD can be expressed as
� 𝜎 b 𝜎 b � 𝜎 b 𝜎 b
≥ 1
A = ⎧⎪ ⎨⎪ ⎩
𝜎 b
MD
MD
for MD, where
𝜎 b
(21)
CD
CD
,
𝜎 b
CD
MD
for CD, where
< 1
𝜎 b
MD
CD
where σ 0 is the strength of an isotropic sheet, at b MD b CD = 1 . At this stage it can be concluded that the Eqs. (20–21) can be
1 3
Made with FlippingBook Online newsletter maker