Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

ANISOTROPY OF INTERNAL STRESS RELATED TO PAPER SURFACE ROUGHENING
Toshiharu Enomae
Assistant Professor
Graduate School of Agricultural and Life Science
The University of Tokyo
Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657
JAPANKiyoshi Sasaki
Graduate student
Graduate School of Agricultural and Life Science
The University of Tokyo
Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657
JAPANBong-Yong Kim
Associate Professor
College of Agriculture
Kyungpook National University
1370, Sankyuk-Dong, Buk-Gu, Taegu 702-701
Korea

Fumihiko Onabe
Professor
Graduate School of Agricultural and Life Science
The University of Tokyo
Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657
JAPAN

ABSTRACT
Release of internal stress has been referred to as one of the causes for surface roughening of paper. However,occasionally drying-induced stress is not corresponding to the roughening of the sheet. The authors assumed thatroughening is not caused by release of in-plane internal stress built in drying, but of transverse internal stress built intransverse processes such as calendering and wet-pressing. The analytical procedure of Kubát for determining
in-plane internal stress was attempted to apply to the transverse compressive mode to determine the transverse
internal stress. A straight-line portion was found at higher initial stresses in the plots of relaxation speed per unit
logarithmic time versus initial stress (Kubát’s plot). The slope and the offset of this straight-line portion were variedwith the forming process the sheet subjected. The initial stress at a relaxation speed of 25 N/log(s) was defined as anindex of transverse internal stress. Consequently, the greater the calendering, wet-pressing and beating, the higher
the transverse internal stress (the slower the relaxation). But, the amount of loaded calcium carbonate did not affectit. The transverse internal stress had influence on surface roughening of paper, but the relationship was observed tobe different between the papermaking processes. Besides, the transverse internal stress was likely to be associatedwith apparent sheet density depending on the fiber source and the way of sheet making. The authors considered thatthe degree of fiber collapse and viscoelasticity are closely related to the transverse internal stress.

INTRODUCTION
Surface roughening of paper in water-based processes like pigment coating and off-set printing has been considered
to occur due to fiber rising and puffing[1], recovery (ribbon-to-tube) of fiber shape, interfiber debonding, fiberswelling and relaxation of internal stress[2]. Internal stress is generally defined as stress built in fibers or the fiber
network during restrained drying and remaining there even after removal of the drying tension. That’s why it is also
termed dried-in stress, built-in stress, frozen-in stress and residual stress. Residual stress is generally conceived as
being within elastic behaviors. Sasaki et al [3, 4] calculated and measured a residual stress distribution in curved
laminated wood beams within the elasticity limit. But, he suggested the deviation of the observed stress from thecalculated ones seemed to be caused by the relaxation of the residual stresses. Johanson and Kubát et al [5, 6]
proposed a method to measure internal stress in paper by stress relaxation measurements (details will be discussed

later) and showed that the level of internal stress was varied with drying tension and that it relaxed by exposing
1Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

paper to water or high humidity. Without tension, paper shrinks during drying. Drying shrinkage of paper, a contrary
concept of internal stress, affects its physical properties as suggested by Kimura[7]. He reported that, in tensile test,
paper elongated until failure by a length (additionally to that of the unshrunk sheet) almost equal to the length thepaper shrank during drying. Where and how is internal stress built in paper? Microcompression[8] at fiber crossings
probably play a roll. Fiber twisting[9] caused by hydrogen bondings between fibrils running at an angle may also
contribute.
However, it is doubtful that such internal stress due to drying tension is directly related to surface roughening.
Additon[10] showed that exposure to 97 % relative humidity for one week hardly changed surface properties ofhandsheets from never-dried hardwood kraft pulp; gloss seemed to decrease moderately, but it was not significant;
PPS roughness did not change (thickness increased by up to 2 %); internal stress measured according to Kubát's
method decreased by 24 to 38 % depending on the beating degree. The author obtained a similar results forcommercial bond paper; as a result of the same exposure, it did not show any significant change in gloss or PPS
roughness, but a large decrease in internal stress of 33 %. Those are examples of internal stress reduction without
surface roughening. Sasaki et al [11] showed that soaking commercial fine paper in water and redrying it reduced its
smoothness as internal stress decreased. When the water-treated paper was calendered to an equivalent level to thatof the original paper and subjected to the same water treatment again, smoothness was reduced as much as was thatof the original paper while internal stress was unchanged. This is an example of surface roughening without internal
stress reduction.
Internal stress mentioned so far is all connected to in-plane tension during drying. Internal stress must be anisotropic
because the inducing stress applied to the material is anisotropic. So, it is natural to think that compressive force, as
in calendering, likewise should build internal stress in the transverse direction of paper. Engström suggested that
precalendering compressed fiber flocs in the basepaper and they expanded on coating with the larger coat weightvariance, implying the more roughening than for uncalendering. To measure transverse internal stress, Kubát's
method was attempted in the compressive mode. Differences found in stress relaxation curves in the compressivemode between differently processed sheets were interpreted and discussed.
THEORY
In-plane internal stress (Kubát’s method)
Kubát et al [5] proposed a unique method to determine in-plane internal stress based on the hypothesis ofstress-aided thermal activation[12]. According to it, in-plane internal stress is determined as follows: For stressrelaxation curves obtained for various target stresses in a tensile mode, the rate of stress relaxation to logarithmic
time after the target stress was reached are calculated for each curve; plots between the relaxation speed and theinitial (target) stress usually gives two rectilinear portions; The intercept of a rectilinear relationship at higher initialstresses in extension on the initial stress axis represents the in-plane internal stress of the specimen. Figure 1
illustrates these calculation processes.
Transverse internal stress
The same procedure was utilized for the compressive mode, empirically. Details will be explained in Results andDiscussion.
Transverse internal stress seems to be generally connected with fiber collapse. Robertson[13] stated that fiber
collapse is produced by wet-pressing and that frozen-in stress maintaining the fiber collapse is developed duringdrying. Reswelling of the dried fibers is dependent on the frozen-in stress in the way that bonding within the cellwall is dissolved wherever forces tending to restore the original shape of the fiber assert themselves. The recovery,2

Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

however, is incomplete if the frozen-in stress have relaxed by time, temperature and plasticization. Here, it should be
noted that compressive stress relaxation in the compressive mode is different from frozen-in stress relaxation
mentioned by Robertson.
Forseth et al[14] showed that mechanical pulp fibers that collapsed in calendering regain their tubular shape whenmoisture releases the pressure-induced stresses. The author revealed that the fiber shape recovery affected surface
roughening and that the effect increased with cell wall thickness.
Enomae et al[15,16] examined freeze-dried kraft fibers from a handsheet after soaking in water, after defibering,after beating and compared to fibers from a reslushed lap pulp and the never-dried pulp. There were no mechanicalactions that perfectly recovered the tube-like shape, but only beating carried out to the reslushed lap pulp did for avery small proportion of the fibers. The work concluded that in the case of kraft fibers, shape recovery is not asignificant contribution to the roughening process.
EXPERIMENTAL
Samples
Tables 1 and 2 summarize attributes of the samples used to examine effects of calendering, wet-pressing, beating
and filler loading. For calendering effects, machine-made wood-containing paper consisting of a 15/40/45 ratio ofsoftwood kraft/GWD/TMP was used. The paper with a moisture content of ca. 8 % was supercalendered
off-machine on a laboratory scale at two levels of linear pressure, 29 and 49 N/m. For wet-pressing, beating andfiller (calcium carbonate) loading effects, handsheets were prepared from bleached hardwood kraft pulp. For the
beating series, the freeness was 639, 460 and 260 ml CSF for unbeaten, 5000 and 20000 revolutions, respectively.
Neither filler nor chemicals was added to the furnish of the wet-pressing or beating series. The pulp for filler loading
was beaten for 5000 revolutions in PFI mill. Calcium carbonate used was PC (Shiraishi Kogyo Kaisha. ltd., Hyogo,
Japan). All the handsheets were prepared according to TAPPI test method unless stated in the table.
Smoothness
Smoothness was measured using Oken type smoothness tester (Asahi Seiko co. ltd., Chiba, Japan). As an axis title,"Bekk smoothness" was used because the principle is identical to that of Bekk smoothness. However, it is pressure
depression of the former room from which air is sent out that is measured with a water column manometer in Oken
tester. The pressure depression is converted to time required to draw 10 ml of air at a pressure of 49.3 kPa, which isthe definition of Bekk smoothness. Additionally, the length of air travel through the gap in the radial direction is 1
mm, while it is ca 17.8 mm for Bekk. This reduces a proportion of air permeating paper to the other side. In figures,the cube root of Bekk smoothness was plotted, because this dimension is equivalent to an inverse of Parker
Print-Surf roughness[17].
Stress relaxation in compressive mode
In a compressive test, 7 to 9 sheets were stacked so that the total basis weight were ca. 480 g/m2 (actually 444 to 590
g/m2). A stack of sheets was inserted between the load cell and the cross bar head of a tensile tester UTM-III-100(Orientec co. ltd., Tokyo, Japan). To obtain even stress distribution, the compressed area was reduced by placing acoin-shaped piece of steel between the top sheet and the cross bar head. So, the compressed area was 707 mm2.
Figure 2 illustrates how to set the sheet stack. The compressing speed was constant at 0.667 mm/s.

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

RESULTS AND DISCUSSION
Load-compression curve of stacked paper sheets
Figure 3 shows an example of the load-compression curve. After a rapid increase in compressive load, thecompressing was stopped and the load kept measured for 120 s. The slope of load decrease plotted against
logarithmic time was linear after ca. 0.5 s. Logarithmic time law[4] approved in the tensile mode of paper can apply
to the compressive mode. Slopes of the load decrease, namely, relaxation speed, for varied initial stresses were
measured and the relation between them (Kubát's plot) consisted of two linear portions, also as well as found in thetensile mode.
Calendering effect on transverse internal stress
Figure 4 shows the relaxation speed versus the initial stress, what we call Kubát’s plot in the compressive mode.
Every relationship traced a steep rectilinear slope at lower initial loads and then a gentle rectilinear slope at higher
ones. The steep slope did not necessarily go through the origin, but intersected the relaxation speed axis at a positive
value. Those characteristics resembles those of Kubát’s plot in the tensile mode, though the relations are all reversed
as seen by comparison to Figure 1. Calendered sheets showed lower relaxation speeds than uncalendered ones. But,
the calendering effect seemed to be equivalent between at 29 kN/m and at 49 kN/m. Water treatment, that is, soaking
in water for 1 day and redrying, shifted the three relationship upward, namely, in the direction of increasing
relaxation speeds, to an almost common relationship . According to Kubát’s theory for the tensile mode, theintercept of the later rectilinear slope in extension on the initial stress axis is interpreted as an in-plane internal stress.
This is possible because every slope is in parallel and has a constant gradient of ca. 0.1, irrespective of in-planeinternal stress level. However, the corresponding slope in the compression mode, namely, the gentle rectilinear slope
showed a fairly different gradient for the water-treated sample from those unsoaked. For the present, we defined theinitial load with the relaxation speed equal to 25 N/log(s) in the gentle slope ranging from 294 to 687 N (30 to 70kgf) or in its extension as an index of the transverse internal stress. The transverse internal stress so defined aretabulated also in Table 2. The value of 25 N/log(s) does not have a special meaning but close to the mean value ofthe measured range. Even for the tensile mode, the slopes empirically determined are not always in parallel
accurately, so a shift distance at certain relaxation speed can be more reasonable to estimate a change in in-planeinternal stress. The gradient of the gentle slope was attempted to the analysis, but did not result in a systematic
relation.
Wet-pressing effect on transverse internal stress
Figure 5 shows a Kubát's plots for the handsheets of the wet-pressing series. It is clearly shown that the stronger the
wet-pressing, the lower the relaxation speed. Based on the transverse internal stress defined in the above section, it
followed that wet-pressing increased the transverse internal stress. Water application decreased the transverse
internal stress except for 49 kPa for 1 min. This suggests that the network and fiber structures formed at the lowest
level of wet-pressing seems not to have been changed by soaking and drying. For the other two higher levels, thereductions in transverse internal stress were much less than those for the calendered wood-containing papers.
Beating effect on transverse internal stress
Figure 6 shows a Kubát's plot for the handsheets of the beating series. The higher the beating degree, the higher thetransverse internal stress. It was interesting that the unbeaten sample shows one straight line throughout the fullrange of initial load. This implies that the transverse stress of uncollapsed fibers relaxed in an invariable manner
throughout the range. Water application overall tended to reduce transverse internal stress. The unbeaten sample

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

with the lowest transverse internal stress showed a fairly large reduction by water application, which is different
from the case of the least wet-pressed sample. Generally, beating increases flexibility of fibers in water andcontributes to formation of intra- and interfiber bondings. Wet-pressing assists, in particular, interfiber bondings. For
the unbeaten sample intermediately wet-pressed, the fibers are considered to recover a little to tube-like shape bywater application, lowering the relaxation speed. For the least wet-pressed sample intermediately beaten, in contrast,
the fiber shape is considered to be hardly changed by water application [15], keeping the relaxation speed. However,the shape of the fibers should be confirmed in other study.
Filler loading effect on transverse internal stress
Figure 7 shows a Kubát's plot for the handsheets of the filler loading. The three relationships were all similar andslight differences seem to be within experimental errors. It was found that filler loading did not affect transverse
internal stress. This finding suggests that fewer interfiber bondings due to a larger amount of filler loading are notrelated to the transverse internal stress. Collapse of fibers and resulting fiber stiffness, rather, determines thetransverse internal stress. The unloaded sample was equivalent to intermediately beaten and intermediately
wet-pressed ones shown in other figures, but the total basis weight of the tested stack was higher for the unloaded
sample. This is the reason for a lower transverse internal stress for it. For the present, experiments of water
application have not been made with this series.
Relationship between transverse internal stress and smoothness
Values of transverse internal stress for all the samples used are listed in Table 2. It is considered that, for theconditions used, beating had the largest effect on increasing transverse internal stress. Then, calendering, the second,
and wet-pressing, the last though the values are not exactly corrected based on basis weight. Figure 8 shows therelationship between transverse internal stress and the cube root of the mean smoothness of the two sides. The lines
connecting every two points shows changes caused by water application. The point on the lower-left side always
denotes a value after water application. For all of the kraft handsheets except the filler loading series (left out
because of the higher total basis weight), the higher the transverse internal stress, the higher the smoothness. The
calendered wood-containing paper also shows the same tendency, but the smoothness was lower than those of thekraft handsheets at equivalent transverse internal stresses. Furthermore, the reduction of transverse internal stress
was much larger than those of the kraft handsheets. In the case of mechanical pulp the shape recovery,
ribbon-to-tube, of fibers are generally considered to be a main cause for surface roughening[14]. From thisstandpoint, this shape recovery by water application may have a strong influence on reduction in transverse internal
stress.
Figure 9 shows index of transverse internal stress versus apparent sheet density for every sample used in this work.
Past literature taught that a procedure of compression of a fiber network structure was well formulated with regard3
to density as shown[18] in Equation (1):(1)
ρ 3 − ρ 0 = MP N
, where ρ, ρ0 and P are the density, the density under no pressure and the pressure, respectively. M and N are
constants. Historically, a similar equation applied to water saturated pulp[19] and a wool fiber mass[20]. Other
modified formula was also tried to paper board[21]. For kraft handsheets and post-water application calendered
wood-containing paper, transverse internal stress are related to apparent density as all the data points fall on thesame curve. Only the data points for pre-water application calendered wood-containing paper do not meet thisrelation. Certain different mechanism should have worked with those samples.
Behavior of paper in compressing process
What was occurring during the compressing process and during the stress relaxation process? It was assumed as5Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

follows: Initially, small interfiber voids made by relaxation right after wet-pressing and calendering were being
filled with adjacent fibers again[22]. At the same time, fibers were becoming bent and incompletely collapsed fibers
were moreover collapsing. At higher loads, inter-lamella or inter-fibrillar voids in fiber walls were collapsing.
During the relaxation process, in addition to fibers packing, fiber bending, fiber collapse and fiber wall collapse that
all continued to occur, viscous deformation - viscose flow of the material comprising fibers toward less-stressed
portions - was presumably proceeding.
Yanagida[23] divided the hot-pressing process in forming a particle board into several stages; packing of apart chipelements with mutual collisions and frictions; resistance of the packing; bending, buckling and compressive
deformation of individual elements; and in-plane expansion of the board. The stages were clearly distinguished for
an element-aligned structure, but unclear for a random structure. The author found the last stage above ca. 9.8 MPa,
while the maximum of the stress in this work was up to ca. 0.97 MPa. So, only deformation of the packing level andelement level (namely, the fiber level in the case of paper) should be involved in the compressive stress relaxation inthis work.
Jackson and Ekström measured relative compression (total compression at maximum pressure to initial paper
thickness ratio) and relative expansion (elastic recovery after pressure removal to the total compression) for various
kinds of paper. Their results showed that beating reduced the relative compression, the effect of clay filling on thecompressibility was negligible, coating suffered heavy reduction in the compressibility, and overdrying at 100 ºC
reduced the compressibility. They considered that a stiffening of the cell wall caused a reduction in the relative
compressibility but an increase in its elastic recovery. The compressive stress relaxation in this work harmonizedwell with their results as, for example, beating reduced the relaxation speed because it is a phenomenon resulting
from both compression and expansion. They stated that there is some relationship between surface smoothness andcompressibility characteristics, it is important to realize that this relationship will be different among papers fromdifferent pulping processes. Paper with high transverse internal stress are commonly composed of highly collapsed
fibers by beating, wet-pressing and calendering. Such a sheet has little intrafiber void (lumen) to allow viscose flow
for relaxation. Particularly, beating makes fibers stiff, resulting in less pliability. So, those transversely operated
processes increased transverse internal stress. In comparison in relation to smoothness between fiber sources,
mechanical fiber or chemical fiber, there was other limitations involved. One was machine-made and the other was
hand-made. Besides, the comparison must be made for the same papermaking process. More exact interpretationneeds further researches.
CONCLUSIONS
A new concept was proposed that what dominates surface roughening is not in-plane internal stress built in drying,
but transverse internal stress built in transverse processes such as calendering and wet-pressing.
The analytical procedure of Kubát proposed for in-plane internal stress was attempted to apply to the transverse
compressive mode to determine the transverse internal stress. A straight-line portion was found at higher initialstresses in the plots of relaxation speed per unit logarithmic time versus initial stress (Kubát’s plot). The slope andthe offset of this straight-line portion were varied with the process the sheet subjected. The initial stress at arelaxation speed of 25 N/log(s) was defined as an index of transverse internal stress for convenience, though
theoretical consideration is further needed. Consequently, the greater the calendering, wet-pressing and beating, thehigher the transverse internal stress (the lower the relaxation speed). But, the amount of loaded calcium carbonate
did not affect it. The transverse internal stress had influence on surface roughening of paper, but the relationship wasobserved to be different between the papermaking processes. Besides, the transverse internal stress was likely to be
associated with apparent sheet density depending on the fiber source and the way of sheet making. The authors

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

considered that the degree of fiber collapse and viscoelasticity are closely related to the transverse internal stress.
AKNOWLEDGMENT
The authors thank Mr. S. Kaneko and Mr. T. Sato, Hokuetsu paper mill, Japan for supplying the machine-madepaper and for the calendering operations. This research was partially supported by the Ministry of Education,
Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists, 08760158, 1996.
REFERENCES
1.
2.

Leslie, F., "Development of a laboratory method for fibre roughening", Paper Technology 33(10): 11-13(1992)
Skowronski, J., "Surface roughening of pre-calendered basesheets during coating", J. Pulp Paper Sci. 16(3):J102-110(1992)
3. Sasaki, Y., Okuyama, T. and Kikata, Y., "Determination of the residual stress in a cylinder of inhomogeneous
anisotropic material (I, II)", Mokuzai Gakkaishi Vol. 27(4):270-276, 277-282(1981)
4. Sasaki, Y., Tsuzuki, K. and Adachi K., "Stress analyses of curved laminated-wood beams considering theresidual stresses (I, II)", Mokuzai Gakkaishi Vol. 37(7):661-667(1991), Vol. 37(8):694-701(1991)
5. Johanson, F and Kubát, J., "Measurements of stress relaxation of paper", Svensk Papperstidn. 67((20):822-832(1964)
6. Johanson, F., Kubát, J. and Pattyranie, C., "Internal stresses, dimensional stability and deformation of paper",Svensk Papperstidn. 70(10): 333-338(1967)
7. Kimura, M., Researches on paper structure and mechanical properties, Ph.D. thesis, Tokyo Institute ofTechnology, 67-75(1996)
8. Page, D. H. and Tydeman, P. A., Formation and structure of paper, ed.by Bolam, F., Tech. Sect. BPBMA,
London, p397-413(1962)
9. Higgins, H. G. and McKenzie, A. W., Appita 16, 145(1963)
10. Additon, D. L., "The effect of internal stress on paper roughening", Ms. thesis of University of Maine, 54-56(1996)
11. Sasaki, K., Enomae, T. and Onabe, F., "Internal stress in paper concerning surface roughening", Sen-i Gakkai
Preprints, Soc. Fiber Sci. Tech., Japan: G-87 (1996)
12. Kubát, J. and Rigdahl, M., "Activation volumes for flow processes in solids", Materials Sci. and Eng.
24:223-232(1976)
13. Robertson, A. A., "Some observations of the effects of drying papermaking fibers", Pulp Paper Mag. Can.
65(3): T162-168(1964)
14. Forseth, T. and Helle, T., ”Effect of moistening on cross-sectional details of calendered paper containing
mechanical pulp”, J. Pulp Paper Sci. 23(3), J95-100 (1997)
15. Enomae, T. and LePoutre, P., "Observation of the swelling behavior of kraft fibers and sheets in theenvironmental scanning electron microscope", Nordic Pulp and Paper Research Journal, 13 no.4:14-18(1998).
16. Enomae, T. and Lepoutre, P., "Paper surface structural changes caused by water at the fiber level", Proceedingsof PTS Symposium, Munich, Germany, 10E(1998)
17. Enomae, T. and Onabe, F., "Characteristics of Parker Print Surf roughness as compared with Bekk Smoothness",
Sen'i Gakkaishi, 53(3): 86-95 (1997).
18. Han, S. T., "Compressibility and permeability of fibre mats", Pulp Paper Mag. Can., 70(9): 65-77(1969)
19. Wilder, H. D., "The compression creep properties of wet pulp mats", Tappi 43(8): 715-722(1960)
20. van Wyk, C. M., "Note on the compressibility of wool", J Textile Inst 37: T285-T292(1946)
21. Osaki, S., Fujii, Y. and Noritsuka, K., "Compressive properties of paper in Z-direction -theoretical consideration- ", Japan Tappi Journal 34(5): 367-374(1980)
22. Osaki, S. and Fujii, Y., "On the Z-direction compressive elasticity of paper ", Japan Tappi Journal 32(8):476-484(1978)

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

23. Yanagida, M., Nishimura, T. and Ando, N., "Behavior of wood chip elements in hot-pressing the wood chipmatte", Abstracts of the 48th annual meeting, Japan Wood Res. Soc., Tokyo, 295(1998)

Process

Fiber source

Sheet-making

Composition

Condition

Calendering

Wood-containingMachine-madeSoftwood kraft/
GWD/TMP=15/40/45

Uncalendered
29 kN/m supercalendered
49 kN/m supercalendered

Wet-pressing

Wood-freeHandsheet

Hardwood kraft 100 %49 kPa for 1 min
343 kPa for 5 min
686 kPa for 20 min

Beating

Wood-freeHandsheet

Hardwood kraft 100 %Unbeaten, 639 ml CSF
5000 rev. PFI,460 ml CSF
20000 rev. PFI, 260 ml CSF

Filler loading

Wood-freeHandsheet

Hardwood kraft 100 %Unloaded
10 % to dry pulp
30 % to dry pulp

Table 1

Furnish and process of paper samples used.

Process

Calendering

Wet-pressing

Beating

Fillerloading

Transverse
internal stressindex, N

Condition

Numberof sheets

Total basis
weight,g/m2

Uncalendered(soaked & dried)

8
8

586
591

1087
1240

0.540
0.477

649
372

29 kN/m(soaked & dried)

8
8

581
589

989
1184

0.588
0.497

766
364

49 kN/m(soaked & dried)

8
8

588
597

941
1202

0.624
0.497

743
376

49 kPa, 1 min(soaked & dried)

8
8

493
487

946
970

0.521
0.502

401
397

343 kPa, 5 min(soaked & dried)

8
8

447
444

752
808

0.595
0.550

555
505

686 kPa, 20 min(soaked & dried)

8
8

445
448

689
749

0.647
0.598

698
623

Unbeaten(soaked & dried)

7
9

491
465

1059
1045

0.463
0.446

345
288

5000 rev. PFI(soaked & dried)

7
8

453
444

765
808

0.592
0.550

521
505

20000 rev. PFI(soaked & dried)

7
7

448
444

620
645

0.722
0.689

867
722

Unloaded
10 % to dry pulp
30 % to dry pulp

8
8
8

522
549
545

849
894
899

0.615
0.614
0.606

407
399
441

8

Stack
Apparent
thickness, µm density, g/cm3

Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

Table 2 Physical properties of samples used and transverse internal stress defined as an initial load at 25 (N/log(s))
of relaxation speed.

9Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

Stress relaxation curves

Stress relaxation curves
on a log scale
16

16
14

Kubat's plot: initial load vs.
relaxation speed
2.0

14time t12

10

time tLoad, kgf

Load, kgf

10
8

time t

8

6

6

4

4
Initial load vs.
Relaxation speed

time t
2

2

0

0
0

Fig.1

10

20 30 40
Time(T), s

Relaxation speed, -kgf/(log s

12

50

1.5
Internal stress(load) 2.14 kgf
1.0

0.5

0.0
0.01

0.1

1

10

100 1000Time(t), s [log scale]

Procedure to determine internal stress in tensile mode by Kubat's method.

φ 30×5 mm

8 sheets

Load cellFig. 2

Schematic diagram of sheet stacking in the compressive tester.

10

0 2 4 6 8 10 121416
Initial (maximum) load, kgf

Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

Linear Scale

Log Scale

800

800

600

600

Load, N800
Blow-up
600

400

400

400
200

200

200

0
-8 -6 -4 -2 0 2
0

0
-50

0

50

100

150

0.01

Time, sFig. 3

0.1

1

10

100

Time, sLoad-compression curve and procedure to determine relaxation speed of compressive stress.

50
Uncalendered
29 kN/m
49 kN/mRelaxation speed, -N/log(s)40Uncal. soaked & dried
49 kN/m soaked & dried
29 kN/m soaked & dried

30

20

10

0
0

200

400

600

800

Initial load, N
Fig. 4

Fig. 4 Relaxation speed of compressive stress vs. initila load (Kubat's plot)
Relaxation speed of compressive stress vs. initial load (Kubát's plot) for wood-containing sheets
for wood-containing sheets variously supercalendered.
variously supercalendered.

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

50
49 kPa, 1 min
343 kPa, 5 min
686 kPa, 20 min
49 kPa, 1 min, soaked & dried
343 kPa, 5 min, soaked & dried
686 kPa, 20 min, soaked & dried

Relaxation speed, -N/log(s)

40

30

20

10

0
0

200

400

600

800

Initial load, N
Fig 5.

Fig speed
5. Relaxation
speed ofstresscompressive
vs. initialplot)load for(Kubat'splot) variously
Relaxationof compressive
vs. initialstressload (Kubát's
handsheetsforhandsheets
variously
wet-pressed.
wet-pressed.

50

Unbeaten
Unbeaten, soaked & dried
5000 rev.
5000 rev., soaked & dried
20000 rev.
20000 rev., soaked & dried

Relaxation speed, -N/log(s)

40

30

20

10

0
0

200

400

600

800

Initial load, N

Fig. 6Fig.
6 Relaxation
speed stressof compressive
stress(Kubát's
vs. initial
loadfor(Kubat'splot)of different
Relaxation
speed
of compressive
vs. initial loadplot)
handsheetsforhandsheetsofdifferent
revolutions
inbeating.
revolutions in beating.
12Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

50
Unloaded
10 % loaded to dry pulp
Relaxation speed, -N/log(s)4030 % loaded to dry pulp

30

20

10

0
0

100

200

300

400

500

600

700

800

Initial load, N
Fig. 7 Relaxation speed of compressive stress vs. initial load
Relaxation speed of compressive stress vs. initial load (Kubát's plot) for handsheets loaded with
(Kubat's plot) for handsheets loaded with calcium carbonate.
calcium carbonate.

Fig. 7

Cube root of Bekk smoothness, s1/3

5
Wet-pressing, 49 kPa for 1 min
Wet-pressing, 343 kPa for 5 min
Wet-pressing, 686 kPa for 20 min
Beating, Unbeaten
Beating, 5000R
Beating, 20000R
Calendering, Uncal.
Calendering, 29 kN/m
Calendering, 49 kN/m

4

3

2

1

0
0

200

400

600

800

1000

Transverse internal stress, N
Fig.8 Relationshipbetweentransverse
stressbydeterminedby Kubat's
Fig.8 Relationshipbetween transverse
internal
stressinternal
determined
Kubát's method
and Bekk smoothness.
method and Bekk smoothness.
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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

1000

Transverse internal stress, N

800

600

Wet-pressing, 49 kPa for 1 min
Wet-pressing, 343 kPa for 5 min
Wet-pressing, 686 kPa for 20 min
Beating, Unbeaten
Beating, 5000R
Beating, 20000R
Calendering, Uncal.
Calendering, 29 kN/m
Calendering, 49 kN/m

400

200

0
0.4

0.5

0.5

0.6

0.6

0.7

0.7

0.8

Apparent density, g/cm3
Fig.9

Fig.9 Relationshipbetweeninternaltransverse
internal
stress determinedby Kubat's
Relationshipbetween transverse
stressdeterminedby Kubát's method
and Apparent sheet
method and Apparent sheet density.
density..

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Proceedings of Tappi advanced coating fundamentals symposium, Tappi press, Atlanta, USA, 133-145(1999)

15