investigation of sample-size effects on in-plane … of sample-size effects on in-plane tensile ......

Investigation of sample-size effects on in-plane tensile testing of paperboard Anton Hagman and Mikael Nygårds

KEYWORDS: Size dependency, Paperboard, In-plane,

Tensile test, Speckle photography

SUMMARY: The impact of sample size on in-plane

strain behavior in paperboard was investigated, with the

aim to explore the differences between local and global

properties in paperboard, and try to pinpoint the

mechanisms behind such differences. The local properties

are of interest in converting as well as for future 3D

forming of paperboard. It is important to identify

differences in behavior between local and global

properties since most paperboards are evaluated against

the latter. The methods used for evaluation were tensile

tests in controlled environment and speckle photography.

The results show that there is a difference in strain

behavior that is dependent of the length to width ratio of

the sample, that this behavior cannot be predicted by

standard tensile tests and that it depends on the board

composition. The speckle analysis revealed that the

behavior is a result of the activation of strain zones in the

sample. These zones are relatively constant in size and

therefore contribute differently to total strain in samples

of different size.

ADDRESSES OF THE AUTHORS: Anton Hagman

([email protected]), Mikael Nygårds ([email protected]),

KTH, BiMaC Innovation, Hållfasthetslära, Osquars backe

1, 10044 Stockholm Sweden

Corresponding author: Anton Hagman

In testing of papers large test specimens are often used in

standards. Hence, global properties that have a tendency

of measuring the weakest point in the paper are

characterized. These ''global'' properties may vary from

local properties due to papers heterogeneous nature. The

global properties represent, at least in tension, the

weakest local properties for strength and the average

properties for local strain. Therefore they often suffice to

predict the quality of the paper. But in some cases, e.g.

during converting, the behavior diverge from what is

predicted by the global properties, since the operations

carried out only affect a small part of the board being

converted. An example is a fold that affects a short but

wide area of the paper, compared to the standard

sample’s long and slender geometry.

When it comes to failure in tension it is often caused by

local deformation in a weak spot, such as a defect or an

area with lower density. Such local deformations are

often occurring at fiber-length scale or smaller.

If such local behavior can be identified at an early stage

it can be used or avoided. This would be of interest for

converting or to improve 3D forming methods.

There are indications that denser parts or flocks in paper

can indirectly cause failure, since they are stiffer and

therefore force nearby weaker parts of the paper to higher

local strains (Niskanen 1998, Norman 1965).

Experiments on paper with different strip lengths,

performed by Malmberg (1964), showed that an increase

in strip length cause a decrease in strip strength and

stretchability (lower stress and strain at break),

furthermore the Young's modulus increased. As an

example the strain at break in the cross direction

decreased from 8.73 % to 7.09 % when the strip length

was changed from 50 mm to 200 mm for copy paper.

These experiments were conducted on newspaper, copy

paper, and kraft liner. The decrease in stress at break was

attributed to weakest link behavior by Niskanen (1998).

Furthermore Tryding (1996) briefly mentions a relation

between strain and the sample width to length ratio in

paperboard. A change of width to length ratio from ~0.3

to 3 resulted in a change in strain at failure from 0.025 to

0.055 for a 120 g/m2 paperboard.

Some experiments using different imaging techniques to

collect strain data on paper has been conducted, examples

are; Lyne and Bjelkhagen (1981) who use laser

spectrometry to study the effects of clamping, Choi et al.

(1991) who show that photo spectrometry can be used on

paper and, Weins et al. (1998) who focus on the strain

behavior around the notches in a double edge notched

tension (DENT) sample to investigate fracture behaviors

of paper. All these studies were carried out on copy

paper.

A more recent study was performed by Considine et al.

(2005) who made a good overview of previous literature

on local strain field behavior, before setting out to

characterize the strain fields using speckle photography.

They concluded that speckle is an effective way to

examine local strains in fibrous networks. In their work

they found that there is a transition point between

homogeneous and heterogeneous strain behavior

although they didn’t correlate this transition to any

special event.

Korteoja et al. (1996) made a study, also referenced by

Considine, in which they detected micro damage in

silicone treated papers. The damage was detected as lines

in the strained paper. The damage occurred at less than

half of the failing strain, when the stress strain curve

became non linear. The lines propagated in diagonal

directions. There were few lines detected in samples

strained in the machine direction. In a later study

Korteoja et al. (1998) correlated the microscopic damage

behavior from the previous study to local strains using

speckle. Ostoja-Starzewski and Castro (2003) cross-

correlated the formation and strain field using finit

element simulations, concluding that the higher the basis

weight, the higher local stiffness and strength of the

paper.

The aim of this study was to examine how the sample

geometry affects the tensile properties of multiply

paperboard using speckle photography and regular tensile

tests. Apart from rectangular samples, notched samples

PAPER PHYSICS

Nordic Pulp and Paper Research Journal Vol 27 no.2/2012 295

were also studied in an attempt to even further localize

the properties. The advantage with such a small sample,

i.e. the nick, is that it is held by its natural surroundings,

i.e. not tightly clamped. The disadvantage is the problem

of distinguishing between effects in the nick and effects

caused by the surrounding board.

Materials and Methods The experiments were conducted on three different

multiply paperboards. Two of them are 5 ply boards

(board B and C), from the same mill, made to match the

same specifications but with a different fiber composition

in the different layers (and slightly different grammage).

The third board (board A) is a 3 ply board from another

mill. Descriptions of the different boards can be found in

Table 1.

The boards were tested in four different sets of samples.

Set 1 and 2 had constant length (10 mm resp. 25 mm)

with varying width (50, 25, 15, 10, 5 and 2.5 mm). Set 3

had constant width (15 mm) and varying length (100, 50,

25 and 10 mm). Set 4 had notched samples with a notch

length (Ln) of 0.9 mm and a varying nick width (Wn) of 5,

2.5, 0.8 and 0.2 mm, as shown in Table 2. Table 2 also

contains the measurements for Set 5, in which board B

was tested at different strain rates. A sketch of a notched

sample can be seen in Fig 1.

The notched samples had a clamping length Lc of 40

mm and a width Ww of 15 mm. All samples had

approximately 10 mm excess material that was clamped.

All five sets were conducted in a controlled environment

(23°C and 50% RH) using a tensile test machine (MTS)

with displacement controlled piston movement (speed

0.25 mm/s for set 2, 3, 4 and 0.4 mm/s for set 1). A

complementary set, Set 5, was made with one of the

boards to determine the effect of the difference in relative

strain rate. In this set three different lengths (100, 25 and,

10 mm) was tested at three different strain rates (25 % s-1

,

1-4 % s-1

, and 0.25 % s-1

). The data for the middle set was

taken from earlier sets, and therefore varied a bit (1 % s-1

for the 25 mm long samples, and 4 % s-1

for the 10 mm

long samples). For Set 1, 2 and 5, a 1 kN load cell was

used, for Set 4 a more sensitive 500 N load cell was used.

In Set 1 and 2 four samples of each size were tested. For

the notched samples in Set 4, six samples per size were

used. All sizes were tested in both machine direction

(MD) and cross direction (CD). In addition to this Set 4

was also tested in the 45°-direction.

The samples in Set 1, 2, 3 and 5 where cut using

standard paper cutters (guillotine and rotary). The

samples in Set 4 were first cut into 15 mm wide strips of

appropriate length. Nicks were produced in the strips by

grinding two opposite 0.9 mm wide notches in the middle

of the strip. The notches were ground using a rotating

diamond plated cutting wheel. The strips were ground

five or six at a time, with two sacrificial strips on either

side. The samples were made with four different target

nick widths Wn= 0.2, 0.8, 2.5 and 5.0 mm. The final

width differed a bit between individual samples.

A batch of notched samples (Wn = 5 mm) with a printed

speckle pattern was also made. The pattern was printed

on the paperboard in a standard laser printer before the

samples was ground in the same way as above. The

samples where then loaded in tension in a tensile testing

machine (Instron), while being recorded by speckle

equipment (Aramis). These tests were performed in the

MD and CD directions and outside controlled climate.

Furthermore unnotched specimens of different sizes were

tested and photographed.

All samples tested in controlled climate were carefully

investigated such that no slipping had occurred in the

clamps. However, the clamps used for the speckle tests

were smooth and the risk of slippage was therefore

higher. Nevertheless any slipping could easily be

observed from the stress-strain curve which would then

form a “saw-tooth” pattern, and thus be controlled for.

Strain mapping was displayed using both a continuous

and a discretized scale, the latter made it possible to

estimate zone sizes compared to the sample size. This

was done by examining the percentage of the different

discreet strain levels, using image analysis in Matlab.

Furthermore the strain profile, along straight lines parallel

to the samples, was examined. The lines chosen were

representative for the whole sample, i.e. they had the

same development as the whole sample with regard to

mean, minimum, maximum and deviation of the strain.

The mentioned quantities for both lines and the sample as

a whole, was calculated directly in the Aramis software.

Table 1 Properties of the different boards used.

Board # ply Thickness [mm]

Grammage [g/m2]

Density [kg/m3]

A 3 0.31 210 677

B 5 0.35 220 628

C 5 0.33 230 657

Table 2 Sample dimensions for the different sets.

Set Width Ww [mm]

Length Lc [mm]

Nick- width Wn [mm]

1 50, 25, 15, 10, 5, 2.5 10 -

2 50, 25, 15, 10, 5, 2.5 25

3 15 100, 50, 25, 15, 10, 5

-

4 15 40 5, 2.5, 0.8, 0.2

5 15 100, 25, 10 -

Fig 1. Sketch of notched samples with the measurements used in Table 2 defined. F shows the direction of applied force during testing. Ln is the length of the notch.

PAPER PHYSICS

296 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012

Fig 2. Stress strain curves for board B - set 1. Constant length (10 mm) with varying widths. Dashed lines indicate CD samples and solid lines MD samples. In this graph a representative sample for each length has been selected for clarity.

Fig 4. Stress strain curves for board B - set 2. Constant length (25 mm) varying widths. Dashed lines indicate CD samples and solid lines MD samples. In this graph a representative sample for each length has been selected for clarity.

Results and discussion Tensile tests in controlled climate

Using the force-displacement curves, stress-strain curves

were calculated using the length, width and thickness of

the samples. These calculations were performed for Set 1,

2, 3 and 5. For Set 4, only the stress was calculated. An

attempt to calculate the strain was made, but showed too

small correspondence to the strains measured with

speckle results to be deemed useful. Fig 2-Fig 4 show typical stress-strain curves for board

B Set 1, 2 and 3. Typical stress-displacement curves for

notched samples of board B (Set 4) can be found in Fig 5.

From the stress-strain curves, for Sets 1, 2 and 3 for

board B, it seems that the yield point and the plastic

hardening varied for different sample sizes. The yield

point seems to correlate to the hardening. This behavior

also correlates to the strain at break, i.e. early yield,

decreased hardening and increasing strain at break goes

hand in hand. From this it might be inferred that the same

mechanism that increases the strain at break also plays a

role for the yield point and the hardening behavior. If this

mechanism could be identified, it could be possible to

predict final strainability of a sample already at, or right

after yielding. Such a mechanism is proposed further

Fig 3. Stress strain curves for board B - set 3. Constant width (15 mm) varying lengths. Dashed lines indicate CD samples and solid lines MD samples. In this graph a representative sample for each length has been selected for clarity.

Fig 5. Stress strain graph for board B - set 4. Notched samples (Nw: 5-blue, 2.5-green, and 0.8-black, 0.2-red). Dashed lines indicate CD samples and whole lines MD samples. In this graph a representative sample for each length has been selected for clarity.

down based on the speckle analyzes. From the curves it is

still apparent that the main difference in strainability

between the different sample sizes occurred in the

“plastic” regime. This is consistent with observations

made by Korteoja et al. (1996).

All three board types display the same kind of behavior

for sets 1, 2 and 3. That is, a fairly constant stress at break

for all length to width ratios. A drastic increase in strain

at break occurs when the length to width ratio decreases

below 1. The different sets have the same behavior not

only qualitatively but also quantitatively (i.e. the curves

do not only look the same, they also have roughly the

same magnitude). The absolute strain increase is similar

in both CD and MD, causing a larger relative strain

increase for MD samples. This can be seen in Fig 6,

where the strain at break has been plotted as function of

length/width ratio for board B. In Fig 7 and Fig 9 the

corresponding behaviors for boards A and C can be seen.

The change in strain for Set 1 and 2 shows that wider

samples result in an increasing strain at break. This

phenomenon will be revisited and explained further

down, using reasoning based on the speckle analysis.

PAPER PHYSICS


Fig 6. Strain at break plotted against length/width ratio for board B. Red markings notched sample (Wn= 5 mm).

Fig 7. Strain at break plotted against length/width ratio for board C. Red markings notched sample (Wn = 5 mm).

Fig 8. Boards from Set 1 compared to each other. The different boards show the same behavior in MD. In CD the strain for board C is much more influenced by the sample size then the other boards.

Fig 9. Strain at break plotted vs length/width ratio for board A.

Fig 10. The effect of strainrate on strain at break for board B, lengths 10, 25 and, 100 mm. Rates 0.25, ~2 and, 25 % s-1.

Fig 11. Boards from Set 2 compared to each other. All boards show the same behavior in both CD and MD.

PAPER PHYSICS


Fig 12. Boards from Set 3 compared to each other. The different boards show the same behavior in MD. In CD the strain for board C is much more influenced by the sample size then the other boards.

The results from Set 5, as seen in Fig 10, shows that the

impact of the difference in relative displacement speed on

strain at break was small compared to the difference due

to the length of the sample.

In Figs 8, 11 and 12 comparisons between the different

boards for the different sets are made. The behavior in

MD was almost identical for board B and C, while board

A had the same sort of behavior but with an overall lower

strain. In CD, all boards show the same trends, but board

A had an equal or higher strain than board B. Both other

boards were superseded by board C which had a more

rapid increase in strain as the length to width ratio

decreased.

From the comparison between boards it was obvious

that boards that seem to be equal in a standard test have

quite different local properties (as seen for Set 3 in Fig 12

or Set 1 in Fig 8. This indicates that changes made to

improve standard test results might have a negative effect

for the local properties and thus have an unintended

effect on converting or forming of the board. As stated

above this effect was exclusively seen in CD. The reason

for this can partly be found in the speckle pictures where

the strain distribution was much more homogeneous in

MD than in CD for short wide samples. Another

interesting aspect of these graphs was the difference

between the boards. A comparison between board B and

C shows that the denser board has “better” local

properties.

Speckle analysis

In Fig 13 and Fig 14 speckle images of samples with size

100 x 50 mm2 in MD respectively CD can be seen. The

measured area on the samples was smaller than the whole

sample (~80x45 mm2) and represents the strain state prior

to break.

Strain zones or streaks can be seen cross the samples. In

these zones the strain was much larger than in the rest of

the sample. The zones were much more prominent in

samples pulled in CD, where they form approximately 5

mm wide streaks corresponding to a few fiber lengths

(compare to the grids in figures Fig 13 and Fig 14 which

have 10x10 mm2 cells). These streaks are party wise

diagonal across the sample, this is once again consistent

with previous observations (Korteoja et al. 1996). In the

MD tested samples, the streaks are more diffuse, but

zones clearly appear. The streaks became noticeable, in

both directions, when the sample started to show a

“plastic” behavior. For the shortest samples the streaks

were most diffuse. The perpendicular strain was also

largest in areas corresponding to the strain streaks seen in

the straining direction.

The exceptions were some of the short wide samples,

e.g. 25x50 mm2 and 10x50 mm

2, where a concave strain

pattern was observed. This pattern only occurred in

samples strained in MD. It was suspected to be the result

of pull of slightly skew fibers that are clamped in one

end, with the other end pulling in the edge areas where

there were shorter fibers and perhaps more loosened

bonds. The effect would be cancelled out towards the

middle of the sample.

Fig 13. Strain distribution in part of a 100x50 mm2 MD sample just prior to break. Each grid square is 10 by 10 mm.

PAPER PHYSICS


Fig 14 Strain distribution in part of a 100x50 mm2 CD sample just prior to break. Each grid square is 10 by 10 mm.

The strain streaks can explain the increase in strain at

break for shorter wider samples. As the samples become

shorter the streaks occupy a larger portion of the sample.

Fig 15 and Fig 16 show a discretized strain distribution

for the different samples sizes prior to break. Fig 17 and

Fig 18 show how much of the sample that is covered by

strain zones, for MD and CD respectively. In these

graphs an area with a local strain over 2.1 resp. 4.2 % is

considered to be a strain zone (i.e. the parts of Fig 15 and

Fig 16 that is yellow or red). For the CD samples it is

clear that shorter samples have a larger amount of strain

zones than long samples of the same width. It is also clear

that wider sample has a larger part of the total area

strained than narrow samples of the same length. In the

narrower samples there is just one such zone, and in the

wider samples there are more than one. The zones are of

roughly the same size in all samples, thus occupying a

relatively larger part of the sample per zone for smaller

samples. The MD samples behave differently, the relative

zone area increases with shorter samples, but it is only for

the longest samples that the wider sample has an

increased zone area. For the 10 and 25 mm long samples

the relative zone area decreases for wider samples.

Fig 15. MD samples of different sizes with discretised strain distributions. From top left: 10x50, 10x15, 25x50, 25x15, 100x50 and 100x15 mm2. Note that the size scale is only approximate between the samples.

A possible reason for this is that the perpendicular strain

behaves differently in these samples, as mentioned above.

While a wide sample increases the possibility for a

starting point for such a zone, it also decreases the

possibility for that zone to immediately cross the whole

sample, making it possible for other parts of the sample

to elongate.

One arguable explanation for these zones can be derived

from the arguments of Norman (1965); due to the

inhomogeneity of the board, there are stronger and

weaker parts. The stronger parts force the weaker parts to

deform. Korteoja et al (1996) related damage streaks to

fibers oriented transverse to the straining direction. They

also point out that the site of failure often can be spotted

before the actual break.

One possible explanation is that interfiber bonds in the

weaker parts are broken and the fibers start to align in the

straining direction. This further weakens the zone

compared to the rest of the sample. As mentioned above

the strain streaks start to form when the stress strain curve

becomes nonlinear. This is also consistent with Korteojas

findings. An example of this can be found in Fig 19

where the strain distribution in the beginning of the

nonlinear region is displayed, for the same 100x50 CD

PAPER PHYSICS


Fig 16. CD samples of different sizes with discretised strain distributions. From top left: 10x50, 10x15, 25x50, 25x15, 100x50 and 100x15 mm2. Note that the size scale is only approximate between the samples.

sample as in Fig 14. A visual comparison between the

samples shows great similarity of the zones in the

different time steps (note the different scales). In Fig 21

the strain profile along the line indicated in Fig 19 is

displayed. The strain profiles at different time steps are

displayed along with the same lines normalized against

the mean strain along the line in each step. Finally a

somewhat simplistic comparison is made between the

strain profiles along the line at different time steps. The

graph simply shows how the peaks and valleys of the line

are positioned compared to the profile just before

breaking. This is done by seeing which parts of the line

that is respectively above and below the mean strain of

the line. The blue lines in the graphs are for profiles

captured in the non linear part of the stress strain curve

and the red line is in the linear part. It is apparent from

the graphs and Fig 19 that the zones form at an early

stage, which is consistent with beginning/increasing

inter-fiber bond breakage. The same behavior was

observed for the other sample sizes in CD and a

somewhat lesser degree in MD.

Fig 17. Relative area of samples that is covered by strain zones for different CD samples. Parts of sample with local strain above 4.2% are considered to be strain zones.

Fig 18. Relative area of samples that is covered by strain zones for different MD samples. Parts of sample with local strain above 2.1% are considered to be strain zones.

The early occurrence of the strain zones suggests that it

is the zones that are responsible for the differences in

hardening and yield behavior between different sample

sizes. The zones appear to have a different modulus than

the rest of the sample, at least if the stress in the sample is

considered to be uniform. Simulations made by Korteoja

et al. (1996) support this interpretation. If the zones have

a different modulus than the rest of the sample, it is not

farfetched to reason that they also have a different

hardening behavior. This is supported by the behavior of

the standard deviation of the strain, shown in Fig 20 and

Fig 22, as the mean strain increases the variation in the

sample increases. This increase is fairly linear in the CD

samples and more exponential in the MD samples. These

differences would change the overall behavior of the

sample based on the relative area of the zones. This

would explain the differences in the stress strain curves,

mentioned earlier. The possibility for the zones to be

detected with high accuracy at an early stage in the non

linear region (as suggested by the graphs), should be

interesting from an engineering viewpoint. If the zones

can be detected by some other technique that does not

PAPER PHYSICS


Fig 19. The strain distribution in a 100x50 mm2 CD sample (same Fig 16) in the beginning of the non linear part of the stress strain curve. The blue line indicates where the strain profiles in Fig 21 are taken. The Z+ seen in the top of the picture is indicating the viewing direction in the Aramis-software.

Fig 20. Standard deviation of the strain in all measuring points on the whole sample plotted against the mean strain for the whole sample (as measured by speckle) for each measuring step. CD samples.

require a printed pattern or other destructive interference

with the paper sheets (i.e. a thermo-camera), then maybe

the weak zones can be strengthened or the strong zones

weakened, and in such a way increase the overall strain

performance of the sheet.

No apparent damage can be seen on the surface of the

sample until just prior to break, which might infer that the

damage zone process is mainly happening in the middle

layer. In the paperboards the top ply contains a larger

amount of softwood fines, than the bulky middle plies. It

can therefore sustain a higher strain than the bulk layer.

This would explain why converted paperboard can

sustain the high strains on the outside of a fold without

Fig 21. Top: Strain profiles along the line indicated in Fig 19, at different times during straining. Top line is just prior to break, the red line is taken when the sample is still in the linear region. Middle (top): Strain profiles normalized with mean strain for the whole line. Middle (bottom): Stress strain curve with sample times marked. Bottom: Position of peaks and valleys at different times compared to top line.

Fig 22. Standard deviation of the strain in all measuring points on the whole sample plotted against the mean strain for the whole sample (as measured by speckle) for each measuring step. MD samples.

apparent damage. A question that arises is if the final

failure was due to a drop in load bearing in the middle

layer, or because of increased damage in the top and or

bottom layers.

Notched samples

The stress was plotted against total sample displacement

instead of strain for Set 4. This was done since the

speckle samples showed that the strain situation in the

samples was rather complicated (see Figs 23 and 24).

PAPER PHYSICS


Fig 23. Speckle image for notched CD sample of board B. The strain distribution is superimposed over the original camera picture.

Fig 24. Speckle image for notched MD sample of board B. The strain distribution is superimposed over the original camera picture.

What can be concluded is that the stress at break was

quite constant for the samples and that the total

displacement for the samples decreased with decreasing

notch width. A strain measure can be estimated from the

speckle results, and this is close to the maximum strain of

the samples with width to length ratio > 1.

Samples oriented 45° from the machine direction were

also tested. The results from those tests show that these

samples behave more like the CD samples when it comes

to stress, and more like the MD samples with regard to

displacement, i.e. it follows the direction with lower

values.

Furthermore, wide nicks showed a more brittle

behavior, i.e. the stress-displacement curve dives abruptly

without a trailing tail, for all directions.

The speckle analysis of samples with 5 mm wide

notches shows that the strain was not contained within

the notch; it spreads into the full width parts of the

sample. In CD the strain seems to be focused quite close

to the notch, see Fig 23. In MD the strain spreads deeper

into the full width part, see Fig 24. The difference in

behavior can be attributed to the difference in fiber

direction. The fact that the board was stretched in other

parts of the sample rather than at the notch, explains how

a large total displacement can occur without extreme

strains. It is also worth noting that the strain zone had a

Fig 25. Close up on notched MD sample during crack-propagation. Board B. Cracks can be seen propagating from both sides of the nick.

Fig 26. Nicked MD samples after testing, board B. From left to right: 5, 2.5 ,0.8 and 0.2 mm nickwidth.

Fig 27. Nicked CD samples after testing, board B. From left to right: 5, 2.5 ,0.8 and 0.2 mm nickwidth.

PAPER PHYSICS


triangular and/or half circle shape in both directions. This

zone is more triangular in MD while being more circular

in CD. This indicates that there might be a relationship

between notch width and zone length, which would

explain why less wide notches can withstand smaller

displacements. The less brittle break of the less wide

samples further supports this, since a shorter strained

zone outside the sample was unable to store the same

amount of elastic energy, which in turn would make the

break less abrupt.

No damage zones or streaks can be seen in or around

the nicks. This is logical since the nicks are smaller than

the zones and therefore relatively homogeneous. When

the stress in the sample was increased to a point where

bonds began to break, the whole sample broke apart. This

was supported by the tensile curve which had a smoother

transition from elastic to plastic part in the nicked

samples. A possible reason for this is that the “plasticity”

in nicked samples was only due to movements, e.g.

straitening, of free fiber segments that can occur without

the breaking of bonds, while the curve for larger samples

gets a sharper transition due to the activation of the

damage behavior. The lack of zones also explains why

the yield and hardening behavior of the stress strain

curves differs from the behavior seen for unnotched

samples. Once again it should be noted that the speckle

analysis only shows the strains in the top layer of the

board.

The cracks that appeared in the nicks often started in the

corners of the notch, which was not surprising since

stress concentrations were expected there. The crack-path

then varies, often going partly diagonally, and sometimes

propagating out of the nick (the crack always starts and

ends in the nick). For both CD and MD samples the crack

path becomes straighter with narrower nicks. As can be

seen in Fig 25 the cracks in the notched samples can start

on both sides simultaneously, and drives a small strain

field in front of them. Worth noting was that the cracks

and the strain field was smaller than the nick length,

which made it possible to dismiss that the notches

behaved as crack tips. The cracks in the nicks often

propagated from the corners of the notch where stress

concentrations where to be expected.

Fig 26 and Fig 27 show the separated cracks of tested

nicked samples. In these pictures pulled out fibers can be

seen in both MD and CD samples. This indicates that the

whole nick had been activated during the stretching and

that fiber bonds rather than fibers have been broken.

Conclusions There was an effect on the strainability caused by the size

of the tested sample. This effect was related to the length

to width ratio of the sample, and was caused by strain

streaks in the sample. The strain of each individual streak

is fairly constant which means that the number of streaks

and their part of the whole length determines the final

strain at break of a sample. A wider sample reduces the

risk of streaks crossing the sample and thus increases the

overall maximum strain of the sample. These strain

streaks were caused by a damage behavior in weaker

spots in the board and needed a certain amount of space

to be activated. Apart from the strain at break the weak

streaks affect the yield and hardening behavior of the

sample. The zones are detectable at an early stage using

speckle analysis.

Among the board qualities that were tested, the strain

ability of the top layer seems to be significantly higher

than that of the whole sample as such. Furthermore

denser boards showed better local properties i.e. higher

maximal strains.

Acknowledgements

The authors would like to thank the department of solid mechanics at KTH and BiMaC Innovation for financial support. Furthermore the authors would like to thank Innventia for access to their climate laboratory. A special thanks to Sune Karlsson (Innventia) and Veronica Wåtz (KTH, Solid Mechanics) for sharing their expertise.

Literature

Choi, D., Thorpe, L.J, Hanna, R.B. (1991): Image analysis of measure strain in wood and paper, Wood Sci. Technol., 25, pp. 251-262.

Considine, J.M., Scott C.T., Gleisner R., Zhu J.Y. (2005): Use of digital image correlation to study the local deformation field of paper and paperboard, 13th Fund. Res. Symp. Cambridge, 2005.

Korteoja, M.J., Lukkarinen, A., Kaski, K., Gunderson, D.E., Dahlke, J.L, Niskanen, K. (1996): Local strain fields in paper, Tappi J, 79(4), 217.

Korteoja, M.J., Niskanen, K., Kortschot M.T., Kaski, K.K., (1998): Paperi Puu, 80(5),364.

Lyne, M.B., Bjelkhagen, H. (1981): The Application of Speckle Inteferometry to the Analysis of Elongation in Paper and Polymer Sheets, Pulp Paper Can., 82(6), pp. TR29-TR35.

Malmberg, B. (1964): Remslängd och töjningshastighet vid spänningtöjningsmätningar på papper, Svensk Papperst., 67(17), pp. 690-692.

Niskanen, K. (1998): Paper physics, Fapet, Helsinki, pp. 140,171-173.

Norman, R.J. (1965): Dependence of sheet properties on formation and forming variables, Consolidation of the paper web. Trans. IIIrd Fund. Res. Symp. Cambridge, 1965, pp. 269-298.

Ostoja-Starzewski, M., Castro, J. (2003): Random formation, inelastic response and scale effects in paper, Phil. Trans. R. Soc. Lond. A, 361, pp. 965-985.

Tryding, J. (1996): In-Plane fracture of paper. Ph. D. Thesis Lunds Universitet, Lund, Sweden.

Wiens, M., Göttsching, L., Dalpke, B. (1998): Quantifizierung lokaler Verformungen von Papier mit Hilfe einer neuen Meßtechnik, Das Papier, 11, pp. 649 - 654

PAPER PHYSICS


investigation of sample-size effects on in-plane … of sample-size effects on in-plane tensile ......

Documents