Determination of Paper Cross- Section Stress-Strain Properties with - PowerPoint PPT Presentation

Determination of Paper Cross- Section Stress-Strain Properties with Zero/Short-Span Testing Warren Batchelor 1 and Bo Westerlind 2 1 Australian Pulp and Paper Institute, Dept of Chemical Engineering, Monash University, Australia 2 SCA 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) 100 1000 6000 90 Force, (N/cm) 80 3000 70 0 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Displacement, µ m 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 100 3000 90 80 1000 6000 70 Force, N/cm 60 0 50 40 30 20 10 0 0 20 40 60 80 100 Displacement, µ m 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 � Load on sample, F L Tensile force � Applied by friction, at F L Clamping Pressure, P c two jaws over Normal Force, N distance, S � Displacement during test comes from F L /2 slippage under both 0 jaws S F L = S � Span is µ 2 P F L /2 c � µ : coefficient of friction N Batchelor, Westerlind 2001 Gullichsen Colloquium

� Non-linear � Linear-elastic behaviour � Average strain depends on stress- � Average strain is strain curve equivalent to load, � Concept of a F L , applied over residual span is then span, S meaningless � S is then the residual span Strain as a function of 1 / 2 ∆  µ G 2 P position under the jaw j c =   F ε L E   Elastic-plastic   p Linear-elastic ∆ G : Jaw displaceme nt j E : Paper elastic p modulus S

Non-linear behaviour � Consider general case ε = K ( F ) � Paper: stress-strain characterised by � Displacement is then given by ( x is distance from jaw edge) F / 2 uP L c ∫ ∆ = G 2 K ( F ( x )) dx j 0 � Problem: only determine stress-strain properties by knowing them in first place! 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 G length, l G G ∆ G ε = Overall strain : G Batchelor, Westerlind 2001 Gullichsen Colloquium

Short span theory Assumption s   ∆ 32 G G   = − − F E 1 ( 1 c ) G < 1 ) 0 . 7 l ( 0 ) L p  π  9 G l   0 2) Random orientatio n F force (measured) L 3) All fibres crossing both E paper cross - section elastic modulus p jawlines contribute G t est span l average load - bearing element length 0 ∆ G displaceme nt from straining span of G = c 1, long fibres, perfectly bonded = 0, unbonded Batchelor, Westerlind 2001 Gullichsen Colloquium

Load-displacement curves 0-300 micron spans, Bleached kraft (B), 1000 PFI revs refining 100.00 90.00 80.00 70.00 Force (N/cm) 60.00 50.00 v 40.00 0 microns 50 microns 30.00 101 microns 159 microns 20.00 300 microns 10.00 0.00 0 20 40 60 80 100 Displacement ( µ m) Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 1000 PFI revs beating 140 120 Tensile index (kNm/kg) 100 80 60 50 micron span 40 101 micron span 159 micron span 20 300 micron span 0 0 5 10 15 20 25 30 35 Strain (%) 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  −  ∆ 32 G G = F E 1 c   L p π 9 G   l ( 0 )   = c 1, unbonded ≈ 0, long fibres, perfectly bonded Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), Unrefined 120 100 Tensile index (kNm/kg) 80 60 40 50 micron span 101 micron span 20 159 micron span 300 micron span 0 0 5 10 15 20 25 Strain (%) Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 1000 PFI revs beating 140 120 Tensile index (kNm/kg) 100 80 60 50 micron span 40 101 micron span 159 micron span 20 300 micron span 0 0 5 10 15 20 25 30 35 Strain (%) Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 3000 PFI revs beating 160 140 Tensile index (kNm/kg) 120 100 80 60 50 micron span 40 101 micron span 159 micron span 300 micron span 20 0 0 10 20 30 40 Strain (%) Batchelor, Westerlind 2001 Gullichsen Colloquium

Stress-strain curves determined from subtraction, Bleached kraft (B), 6000 PFI revs beating 160 140 Tensile index (kNm/kg) 120 100 80 60 50 micron span 101 micron span 40 159 micron span 300 micron span 20 0 0 5 10 15 20 25 30 35 Batchelor, Westerlind 2001 Gullichsen Colloquium Strain (%)

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µ m span curves, bleached kraft (B) 160 140 Tensile index (kNm/kg) 120 100 80 60 Unrefined 40 1000 PFI revs 3000 PFI revs 6000 PFI revs 20 0 0 5 10 15 20 25 Strain (%) Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µ m span curves, once dried, bleached kraft (C) 160 140 Tensile index (kNm/kg) 120 100 80 60 Unrefined 40 1000 PFI revs 3000 PFI revs 6000 PFI revs 20 0 0 5 10 15 20 25 Strain (%) Batchelor, Westerlind 2001 Gullichsen Colloquium

Effect of refining on Cross-section Stress-strain curves determined from subtraction, 300 µ m span curves, unbleached kraft (A) 180 160 Tensile index (kNm/kg) 140 120 100 80 60 Unrefined 1000 PFI revs 40 3000 PFI revs 20 6000 PFI revs 0 0 5 10 15 20 25 Strain (%) 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 Batchelor, Westerlind 2001 Gullichsen Colloquium