Cellulose (2020) 27:6961–6976
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Table 1 Foaming parameters for the trial points
TP1–TP10
TP11 (LBG)
Diameter of the cylindrical foaming tank (cm)
32
16
Mixing speed (rpm)
3000
3500
Initial volume of the pulp suspension (l)
6.8
0.93
Fibre consistency in pulp suspension before foaming (%) 2
2.7
Air content after foaming (%)
58–62 (SDS) 56–63 (PVA blend)
63
SDS concentration (%)
0.12
0.06
PVA concentration (%)
0.1 (6–88) and 0.5 (28–99)
–
Mould dimensions (cm)
42 9 42
9.8 (diameter)
Density adjustment
Pressing of wet foam ? rewetting and pressing Pressing of wet foam
The furnish composition of TP1–TP6 are specified in Table 2 and TP7–TP11 in Table 3
Fig. 5 Photographs of the foam-formed materials, a 100% unrefined NBSK foamed with PVA (TP4) and b refined NBSK and hemp foamed with SDS (TP3), see Table 2. The sawn material pieces are of size 30 9 30 9 20 mm
Theoretical analysis
become high enough to trigger a sudden (buckling) failure in a fibre segment. Because of the inherent heterogeneity of the fibres, their failures can deviate significantly from the classical Eulerian buckling. Besides buckling of the whole segment, a localized failure in a fibre wall is possible as well (Ma¨kinen et al. 2020). In any case, if such a failure happens, the stress is re-distributed quickly to other resisting regions. Thus, the development of local deformations can be quite heterogeneous. Ketoja et al. (2019) derived simple equations for a situation where free fibre segments buckle (with critical load proportional to the inverse square of segment length) and describe the stress-compression behaviour. Their theory assumed exponentially
The analysis of the experimental results is based on the following postulates on relevant mechanisms: (1) under compressive load, deformation of very porous material begins with bending of surface and other slender fibre segments (Subramanian and Picu 2011) and closing up of the largest voids and gaps of the material. (2) Gradually, at higher strains, local axial stresses build up (Subramanian and Picu 2011), especially in regions where a fibre or several of them resist bending. This resistance may be caused by the local orientation of fibres, their geometry (e.g. large cross-sectional area), internal stresses or by high local network density. (3) At certain points, the stress can
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