determination of load-bearing element length in paper ...batchelo/downloads...warren batchelor...
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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
Presented at 1999 Paper Physics Conference San Diego
IntroductionIntroduction
Paper strengthEffect of drying treatmentDefects in fibresLoad-bearing element
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
Test and Sample DimensionsTest and Sample Dimensions
Lsheet
Wsheet
WJ
G
Jaw
1
Jaw
2θ
A=LsheetWsheet
Presented at 1999 Paper Physics Conference San Diego
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−=
Presented at 1999 Paper Physics Conference San Diego
Short span testShort span test
G
l
G
GG ∆+
GG∆
=ε :strain Overall
Presented at 1999 Paper Physics Conference San Diego
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
∫−
−−=
=
=
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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)
Presented at 1999 Paper Physics Conference San Diego
( )
−
−=
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
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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 ≈
Presented at 1999 Paper Physics Conference San Diego
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.
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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)
Never/Air DriedAir/Air DriedOven/Air Dried
Presented at 1999 Paper Physics Conference San Diego
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)
Never/Air DriedAir/Air DriedOven/Air Dried
Presented at 1999 Paper Physics Conference San Diego
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)
Never/Air DriedAir/Air DriedOven/Air Dried
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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)
Never/Air DriedAir/Air DriedOven/Air Dried
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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
Presented at 1999 Paper Physics Conference San Diego
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
Euc NSSC 0.61 0.57 0.74 0.62 0.69 0.57Euc kraft 0.67 0.57 0.79 0.65 0.74 0.62
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
Presented at 1999 Paper Physics Conference San Diego
Never/Air Dried Air/Air DriedArithme-
tic(FS 200)
Load-bearingelement length
(fit)
Lengthweighted(FS 200)
Arithme-tic
(FS 200)
Load-bearingelement length
(fit)
Lengthweighted(FS 200)
Euc NSSC 0.63 0.61 0.81 0.63 0.74 0.81Euc kraft 0.57 0.67 0.71 0.57 0.79 0.71
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)
Load-bearingelement length
(fit)
Lengthweighted(FS 200)
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)
Presented at 1999 Paper Physics Conference San Diego
ConclusionsConclusions
Load-bearing element length approximately the same as arithmetic fibre length for these pulpsDrying treatment- no effect on average load-bearing element length
Presented at 1999 Paper Physics Conference San Diego
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