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Batchelor, Westerlind 2001 Gullichsen Colloquium

Determination of Paper Cross- Section Stress-Strain Properties with Zero/Short-Span Testing

Warren Batchelor1 and Bo Westerlind2

1Australian Pulp and Paper Institute, Dept of Chemical

Engineering, Monash University, Australia

2SCA Graphic Research, Sundsvall, Sweden

Batchelor, Westerlind 2001 Gullichsen Colloquium

Introduction

Stress-strain behaviour of fibres- large factor in sheet mechanical properties Measurement?

Single fibre tests?

⌧Many tests ⌧Representative of fibres in sheet?

Zero span test

⌧Tensile test at zero span- no gap between jaws ⌧Measure of mechanical properties of fibres in the sheet ⌧Normally only measure breaking load

Batchelor, Westerlind 2001 Gullichsen Colloquium

Our work

Goal: measure stress-strain curve of fibres in sheet = the sheet cross-section stress-strain curve. Method: Pulmac zero/short span tester with additional instrumentation.

Kaman Corp. capacative transducer- measure jaw separation Continuous measurement of load during test. Thus can measure load-displacement during test Need method to convert displacement to strain.

Batchelor, Westerlind 2001 Gullichsen Colloquium

Experimental- pulps

A: Never dried unbleached kraft (SCA’s Östrand mill) B: Never dried bleached kraft (SCA’s Östrand mill) C: Once dried bleached kraft

Free dried from pulp B:, reslushed and formed into handsheets

D: TMP, 120ml CSF, (SCA’s Ortviken mill) E: TMP, 54ml CSF, (SCA’s Ortviken mill)

Batchelor, Westerlind 2001 Gullichsen Colloquium

Measurements

Sheets formed by teflon drying with heated drum

Low level of restraint

PFI refining: 1000, 3000 and 6000 revs Zero/short span measurements

0, 50, 101, 159 and 300 micron spans Tests conducted dry

Each curve shown here is average of 24 tests

Batchelor, Westerlind 2001 Gullichsen Colloquium

Zero Span ‘Raw’ Force-displacement curves for a bleached kraft pulp (B) for different refining levels (PFI revolutions)

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 Displacement,µm Force, (N/cm) 1000 6000 3000

Batchelor, Westerlind 2001 Gullichsen Colloquium

Problem: Where is test start point?

Load take up effects at start of test

Dependent on level of drying restraint

Solution used:

Determine point of maximum slope of curve Extrapolate gradient to determine displacement at 0 N force Subtract extrapolated displacement from measured

Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of PFI refining (revs) on bleached kraft pulp (B). Curves corrected to remove load take up effects

10 20 30 40 50 60 70 80 90 100 20 40 60 80 100

Displacement, µm Force, N/cm

1000 3000 6000

Batchelor, Westerlind 2001 Gullichsen Colloquium

Residual span

Fibres held in place by friction under the jaw clamping pressure. Requires a finite distance from jaw edge to work, and also depends on force at any point in the test. Residual span not known Need method to convert measured displacement to strain.

Batchelor, Westerlind 2001 Gullichsen Colloquium

Zero span test- theory

Normal Force, N

N

Tensile force

FL FL/2 S FL/2

Load on sample, FL Applied by friction, at two jaws over distance, S Displacement during test comes from slippage under both jaws Span is µ: coefficient of friction

Clamping Pressure, Pc

c L

P F S µ 2 =

Linear-elastic behaviour

Average strain is equivalent to load, FL, applied over span, S S is then the residual span

Non-linear

Average strain depends on stress- strain curve Concept of a residual span is then meaningless

modulus elastic Paper : nt displaceme Jaw : 2

2 / 1 p j p c j L

E G E P G F ∆        ∆ = µ

ε S

Linear-elastic Elastic-plastic Strain as a function of position under the jaw

Batchelor, Westerlind 2001 Gullichsen Colloquium

Non-linear behaviour

Consider general case

Paper: stress-strain characterised by

Displacement is then given by (x is distance from jaw edge) Problem: only determine stress-strain properties by knowing them in first place!

∫

= ∆

c L

uP F j

dx x F K G

2 /

)) ( ( 2 ) (F K = ε

Batchelor, Westerlind 2001 Gullichsen Colloquium

New method

For same force, subtract zero-span displacement from short-span displacement to give displacement due to free span. Convert to strain. How is this strain related to span at span of zero (cross-section strain)?

Use short span theory

Batchelor, Westerlind 2001 Gullichsen Colloquium

Short span test- theory

G length, l G

G G ∆ +

G G ∆ = ε : strain Overall

Batchelor, Westerlind 2001 Gullichsen Colloquium

Short span theory

unbonded 0, bonded perfectly fibres, long 1,

• f

span straining from nt displaceme length element bearing

• load

average span est t modulus elastic section

• cross

paper (measured) force 9 32 ) 1 ( 1 = = ∆ ∆         − − = c G G l G E F G G l G c E F

p L p L

π

contribute jawlines both crossing fibres All 3) n

• rientatio

Random 2) ) ( 7 . ) 1 s Assumption l G <

Batchelor, Westerlind 2001 Gullichsen Colloquium

Load-displacement curves 0-300 micron spans, Bleached kraft (B), 1000 PFI revs refining

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 20 40 60 80 100

Displacement (µm) Force (N/cm)

0 microns 50 microns 101 microns 159 microns 300 microns

v

Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 1000 PFI revs beating

20 40 60 80 100 120 140 5 10 15 20 25 30 35

Strain (%) Tensile index (kNm/kg)

50 micron span 101 micron span 159 micron span 300 micron span

Batchelor, Westerlind 2001 Gullichsen Colloquium

Method limitations

Minimum span is 0.15 mm (150 microns)

Shorter spans- curves too close together, errors high

Effect of span on stress-strain distribution in z- direction? Maximise accuracy of subtraction by

Long, straight fibres Well beaten: high value of c- reduces effect of fibres not bridging between jaws

bonded perfectly fibres, long 0, unbonded 1, ) ( 9 32 1 ≈ = ∆         − = c G G l G c E F

p L

π

Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), Unrefined

20 40 60 80 100 120 5 10 15 20 25

Strain (%) Tensile index (kNm/kg) 50 micron span 101 micron span 159 micron span 300 micron span

Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 1000 PFI revs beating

20 40 60 80 100 120 140 5 10 15 20 25 30 35

Strain (%) Tensile index (kNm/kg)

50 micron span 101 micron span 159 micron span 300 micron span

Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 3000 PFI revs beating

20 40 60 80 100 120 140 160 10 20 30 40

Strain (%) Tensile index (kNm/kg)

50 micron span 101 micron span 159 micron span 300 micron span

Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 6000 PFI revs beating

20 40 60 80 100 120 140 160 5 10 15 20 25 30 35

Strain (%) Tensile index (kNm/kg)

50 micron span 101 micron span 159 micron span 300 micron span

Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µm span curves, bleached kraft (B)

20 40 60 80 100 120 140 160 5 10 15 20 25

Strain (%) Tensile index (kNm/kg)

Unrefined 1000 PFI revs 3000 PFI revs 6000 PFI revs

Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µm span curves, once dried, bleached kraft (C)

20 40 60 80 100 120 140 160 5 10 15 20 25

Strain (%) Tensile index (kNm/kg)

Unrefined 1000 PFI revs 3000 PFI revs 6000 PFI revs

Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µm span curves, unbleached kraft (A)

20 40 60 80 100 120 140 160 180 5 10 15 20 25

Strain (%) Tensile index (kNm/kg)

Unrefined 1000 PFI revs 3000 PFI revs 6000 PFI revs

Batchelor, Westerlind 2001 Gullichsen Colloquium

Conclusions

New method developed to use short and zero- span measurements to obtain stress-strain curves An unbleached kraft sample: increasing cross- section strain at breaking and increasing breaking stress with refining An bleached never-dried sample and a bleached once-dried sample: decreasing strain at break, increasing breaking stress with refining

Batchelor, Westerlind 2001 Gullichsen Colloquium

Acknowledgements

SCA Research for funding this research Anneli Neumann and Ulrika Sedin

Sheet making and standard lab tests

Sten Larsson

Data acquisition

Rickard Boman, Tomas Unander

Matlab programming