Measurement of Fibre Stress- - Measurement of Fibre Stress Strain Properties with Strain Properties with Zero/Short- -Span Testing Span Testing Zero/Short Warren Batchelor 1 and Bo Westerlind 2 1 Australian Pulp and Paper Institute, Dept of Chemical Engineering, Monash University, Australia 2 SCA Research, Sundsvall, Sweden
Introduction 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
Our work Our work � Goal: measure stress-strain properties of fibres in sheet � 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. � Each curve average of 24 tests
Experimental- - pulps pulps Experimental � 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)
Measurements Measurements � Sheets formed by teflon drying with heated drum � Low level of restraint � PFI refining: 1000, 3000 and 6000 revs (for pulps A,B,C) � Zero/short span measurements � 0, 50, 100, 150 and 300 micron spans � Tests conducted dry � Standard laboratory tests for strength, fibre length etc.
‘Raw Raw’ ’ Force Force- -displacement curves for a displacement curves for a ‘ bleached kraft pulp (B) for different bleached kraft pulp (B) for different refining levels (PFI revolutions) 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
Problem: Where is test start Problem: Where is test start point? 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
Effect of PFI refining (revs) on bleached kraft pulp Effect of PFI refining (revs) on bleached kraft pulp (B). Curves corrected to remove load take up (B). Curves corrected to remove load take up effects 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
Force- -displacement curves for five pulps displacement curves for five pulps Force beaten to 3000 PFI revs beaten to 3000 PFI revs 120 100 unbleached kraft Once dried bleach Force, N/cm 80 Bleached kraft 60 TMP 54 ml CSF 40 TMP 120 ml CSF 20 0 0 20 40 60 80 Displacement, µ m
Residual span 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 load- displacement to stress-strain.
Zero span test- - theory theory Zero span test � 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 F L /2 µ 2 P c � µ : coefficient of N friction
� Non-linear � Linear-elastic behaviour � Average strain depends on stress- � Average strain is strain curve equivalent to load, � Concept of a residual F L , applied over span is then span, S meaningless � S is then the residual span Strain as a function of 1 / 2 ∆ position under the jaw µ G 2 P ε j c = F L Elastic-plastic E p Linear-elastic ∆ G : Jaw displaceme nt j E : Paper elastic p modulus S
Non- -linear behaviour linear behaviour Non � 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!
Short span test test- - theory theory Short span + ∆ G G length, l G G ∆ G ε = Overall strain : G
Load- -bearing element bearing element Load � NOT a fibre � Fibres can be made up of many elements � Joined by kinks etc � Properties: � Length, l � Cross sectional area, C � Young’s modulus, E
Short span theory Short span theory Assumption s − ∆ 32 G G = F E 1 c L p G < 1 ) 0 . 7 l ( 0 ) π 9 G l ( 0 ) 2) Random orientatio n F force (measured) L 3) All fibres crossing both E paper elastic modulus at very small span p jawlines contribute G t est span l ( 0 ) average load - bearing element length ∆ G displaceme nt from straining span of G = c 1, unbonded ≈ 0, long fibres, perfectly bonded
New method New method � Summary so far.. � Measure load-displacement from zero, short span tests � Zero span test- need stress-strain curve to convert displacement to strain. � Short span test- displacement is sum of displacements under the jaw (zero-span test) and free span between jaws. � New method: � For same force, subtract zero-span displacement from short-span displacement to give displacement due to free span. Convert to strain.
Load- -displacement curves 0 displacement curves 0- -300 micron 300 micron Load spans, Unbleached kraft (A), 6000 PFI revs spans, Unbleached kraft (A), 6000 PFI revs refining refining 120 Span 0 50100 150 300 100 Force, N/cm 80 60 40 20 0 0 50 100 150 200 Displacement, µ m
Stress- -strain curves determined from strain curves determined from Stress subtraction, Unbleached kraft (A), 6000 PFI subtraction, Unbleached kraft (A), 6000 PFI revs beating revs beating 120.0 100.0 Force, N/cm 80.0 60.0 50 40.0 100 150 20.0 300 0.0 0 10 20 30 40 Strain, %
Method limitations Method limitations � Minimum span is 0.15 mm (150 microns) � Shorter spans- curves too close together, errors high � Effect of span on stress-strain?? � Need to maximise term in brackets by � Long, straight fibres � Well beaten: low 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
Stress- -strain curves determined from strain curves determined from Stress subtraction, Unbleached kraft and bleached subtraction, Unbleached kraft and bleached kraft, 6000 PFI revs beating kraft, 6000 PFI revs beating 120 100 Force (N/cm) 80 60 40 Unbleached 20 Bleached 0 0 5 10 15 20 25 Strain (%)
Conclusions Conclusions � Load-displacement curves measured for several pulp types � New method developed to use short and zero-span measurements to obtain stress- strain curves � An unbleached kraft sample, heavily refined- breaking strain of 20%, considerable plastic deformation
Acknowledgements Acknowledgements � SCA Research for funding this research � Anneli Neumann and Ulrika Sedin � Sheet making and standard lab tests � Sten Larsson � Data acquisition � Rickard Boman � Matlab programming
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