Presentation for Paper Physics conference 1999 Webusers.monash.edu.au/~batchelo/Downloads/Batchelor Paper...Title Microsoft PowerPoint - Presentation for Paper Physics conference 1999

Presented at 1999 Paper Physics Conference San Diego

Determination of LoadDetermination of Load--Bearing Bearing Element Length in Paper using Element Length in Paper using Zero/Short Span Tensile TestingZero/Short Span Tensile Testing

Warren BatchelorAustralian Pulp and Paper Institute

Dept of Chemical EngineeringMonash University


IntroductionIntroduction

Paper strengthEffect of drying treatmentDefects in fibresLoad-bearing element


LoadLoad--bearing elementbearing element

NOT a fibreFibres can be made up of many elementsJoined by kinks etc

Properties:Length, lCross sectional area, CYoung’s modulus, E


Test and Sample DimensionsTest and Sample Dimensions

Lsheet

Wsheet

WJ

G

Jaw

1

Jaw

2θ

A=LsheetWsheet


ProbabilitiesProbabilities

Single load-bearing element in sheet, length, l, angle: P1: probability that element is gripped by Jaw 1P2: probability of element gripped by Jaw 2 if also gripped by Jaw 1

Assumption: Wsheet, Lsheet, Wj much greater than l.

θ

sheet

j

sheet WW

LlP θcos

1 =

lGP / cos12 θ−=


Short span testShort span test

G

l

G

GG ∆+

GG∆

=ε :strain Overall


Load on single fibreLoad on single fibre

curl plane ofout todue load bearingnot fibres offraction is where

coscos2)1(

or is fibre oriented located,randomly by on contributi Average

cos

isdirection loadingin component and

cos

is jawsboth spanning fibreon force , strain,At

)/(cos

0 34

21

3

2

1

c

lGjcav

f

f

f

f

dlG

AlW

ECfF

PPF

ECF

ECF

θθθπ

ε

θε

θε

ε

∫−

−−=

=

=


bonding fibre-fibre Non orientatio Random 7.0sAssumption

(2) 932

83)1(

:obtainexpansion seriesTaylor Use

(1) 1247arccos

83

11212)1(

get gIntegratin

2

23

lG

GlA

WECfF

lG

lG

lG

lG

lG

AlW

ECfF

jcav

jcav

<

−−=

−−+

−

−−=

πε

πε


Comparison between equations 1 and 2Comparison between equations 1 and 2

Approximate limit for accuracy of Taylor’s series approximation

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1G/l

Forc

e (a

rbitr

ary

units

) Full function (Eq 1)

Taylor seriesexpans ion (Eq2)


( )

−

−=

GGCGE

GlGCGEA

WfGIGF j

c

)()(932

)()()(83 )1)((,

π

εε

Total forceTotal force

For gap, G, if have I(G) load bearing elements with

then the total force, F, is

where is the average of the I(G) elements

π9/32Gl >

)()()( GlGCGE


Average length of elementsAverage length of elements

Assumptions:)0( )0()0()0()0()0( lCElCE ≈

lGGGlGCGE << if oft independen )( ,)()(

0

),(

)0,(932)0(

=

−=

G

frac

frac

dGGdF

Fl

ε

ε

π


Validity of AssumptionsValidity of Assumptions

Furnish Relativenumberof fibres

EC L )0()0()0( lCE )0( )0()0( lCE K

Hardwood 0.5 1.0 0.6 0.9 0.875 0.9720.5 1.5 0.8

Hardwood & 0.8 1.0 0.5 1.2 0.96 0.8softwood 0.2 2.0 2.0

)0()0()0()0( )0()0( lCEKlCE =

Major assumption:Test: artificial distributions of fibre propertiesResult: K<1 (always) if longer fibres are stiffer

)0( )0()0()0()0()0( lCElCE ≈


Experimental MethodExperimental MethodFive samples

Unbleached Eucalypt NSSC pulp*

E. globulus kraft pulp- Laboratory pulped, oxygen bleached to kappa no. 17.9*

Unbleached brown mixed waste pulp for packaging grades*

Unbleached P. Radiata kraft pulp #1*

Unbleached P. Radiata kraft pulp #2, 45 kappa**

* Refigerated for up to 1 year before making handsheets.**Collected from pulp mill brown-stock washer. Handsheets made immediately.


ExperimentsExperiments

Handsheet preparationBritish Standard Handsheet machineNot refined in PFI mill

Zero/short span testsPulmac zero span testerSpan: 0.0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 mm

Fibre length measurementsKajaani FS 200

Sheet tensile strength


3 Drying Conditions3 Drying Conditions

1. Make handsheets; air-dry under restraintLabelled never/air dried

2. Make handsheets; air dry under restraint; reslush; make handsheets; air dry under restraint

Labelled air/air dried

3. Make handsheets; oven dry without restraint; reslush; make handsheets; air dry under restraint

Labelled oven/air dried


ResultsResults

Zero/short span measurementsPlotted with residual span of 0.2 mm

Tensile strengthFits of data to obtain load-bearing element lengthComparison with measured fibre length


Zero/short span results:Zero/short span results:NSSC EucalyptNSSC Eucalypt

0102030405060708090

100

0 0.2 0.4 0.6 0.8 1

True Span (mm)

Tens

ile in

dex

(Nm

/g)

Never/Air DriedAir/Air DriedOven/Air Dried


Zero/short span results:Zero/short span results:E. globulus kraft pulpE. globulus kraft pulp

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1

True Span (mm)

Tens

ile in

dex

(Nm

/g)



Zero/short span results:Zero/short span results:waste paperwaste paper

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1

True Span (mm)

Tens

ile in

dex

(Nm

/g)



Zero/short span results:Zero/short span results:P. radiata kraft pulp #1P. radiata kraft pulp #1

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1

True Span (mm)

Tens

ile in

dex

(Nm

/g)



Zero/short span results:Zero/short span results:P. radiata kraft pulp #2P. radiata kraft pulp #2

020406080

100120140160180

0 0.2 0.4 0.6 0.8 1

True Span (mm)

Tens

ile in

dex

(Nm

/g)

Never/Air Dried Air/Air DriedOven/Air Dried


Sheet tensile strength under different Sheet tensile strength under different drying conditionsdrying conditions

0

10

20

30

40

50

60

70

NSSC Waste Eucalyptkraft

Pine #1 Pine #2

Tens

ile in

dex

(Nm

/g)



Fits to zero/short span dataFits to zero/short span data

QuadraticLinear (full data set)Linear (restricted data set)No residual span

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1Gap (mm)

Tens

ile In

dex

(Nm

/g)

mm 74.0)0( =l

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1Gap (mm)

Tens

ile In

dex

(Nm

/g) mm 02.1)0( =l

60

70

80

90

100

110

120

130

140

0 0.2 0.4 0.6 0.8 1Gap (mm)

Tens

ile In

dex

(Nm

/g)

mm 02.2)0( =l

60708090

100110120130140150160

0 0.2 0.4 0.6 0.8 1Gap (mm)

Tens

ile In

dex

(Nm

/g)

mm 32.1)0( =l

NSSC Eucalypt- Air/Air dried Pine kraft #1- Air/Air dried


Never/Air Dried Air/Air DriedQuad-ratic

Linear(0-0.4mm)

Linear Quad-ratic

Linear(0-0.4mm)

Linear

Euc NSSC 0.61 0.82 0.97 0.74 0.90 1.02Euc kraft 0.67 0.92 1.04 0.79 1.00 1.02

Waste 0.63 0.82 1.26 0.73 0.90 1.26Pine #1 1.00 1.19 1.97 1.33 1.32 2.02Pine #2 0.89 1.29 1.69 1.26 1.21 1.83

Oven/Air DriedQuad-ratic

Linear(0-0.4mm)

Linear

Euc NSSC 0.69 0.86 0.99Euc kraft 0.74 0.96 1.02

Waste 0.75 0.92 1.23Pine #1 1.75 1.82 1.88Pine #2 1.24 1.50 1.71

Load-bearing elementlengths (mm) determinedby different fitting methods


Effect of residual spanEffect of residual span

Never/Air Dried Air/Air Dried Air/Oven DriedResidual0.2 mm

NoResidual

Residual0.2 mm

NoResidual

Residual0.2 mm

NoResidual


Waste 0.63 0.57 0.73 0.67 0.75 0.65Pine #1 1.19 0.97 1.32 1.10 1.82 1.59Pine #2 1.29 1.07 1.21 0.99 1.50 1.28

Average load-bearing element lengths (mm) from fitting zero/short span data using different residual spans


Never/Air Dried Air/Air DriedArithme-

tic(FS 200)

Load-bearingelement length

(fit)

Lengthweighted(FS 200)

Arithme-tic

(FS 200)


(fit)



Waste 0.61 0.63 1.14 0.63 0.73 1.17Pine #1 1.23 1.19 2.19 1.27 1.32 2.21Pine #2 1.56 1.29 2.43 1.56 1.21 2.43

Oven/Air DriedArithme-

tic(FS 200)


(fit)


Euc NSSC 0.63 0.69 0.81Euc kraft 0.57 0.74 0.71

Waste 0.59 0.75 1.10Pine #1 1.18 1.82 2.15Pine #2 1.56 1.50 2.43

Comparison of loadComparison of load--bearingbearingelement length (mm) with element length (mm) with

arithmetic and lengtharithmetic and lengthweighted fibre lengths (mm)weighted fibre lengths (mm)


ConclusionsConclusions

Load-bearing element length approximately the same as arithmetic fibre length for these pulpsDrying treatment- no effect on average load-bearing element length


AcknowledgementsAcknowledgements

Daniel Ouellet, Paprican and University of British Columbia Pulp and Paper CentreRussell Allan, Amcor Research and Technology CentreGlenda Spencer, Michael Briggs and Geoff Ennis for assistance with the experimentsFunding from the Commonwealth Government of Australia through the Cooperative Research Centre for Hardwood Fibre and Paper Science

Documents

Presentation for Paper Physics conference 1999 Webusers.monash.edu.au/~batchelo/Downloads/Batchelor Paper...Title Microsoft PowerPoint - Presentation for Paper Physics conference 1999