factors influencing the stress-strain curve of paper
DESCRIPTION
a power point presentation of my Msc. dissertation.TRANSCRIPT
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TOPIC: FACTORS INFLUENCING THE STRESS-STRAIN CURVE OF PAPER
Presented by:ALEX NYARKO
Supervisor:Dr. W. Sampson
School of Materials, The University of Manchester.
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BACKGROUND
Fig 1-Cellulosic fibre network
(micrograph of paper autoflourescing under
ultraviolet illumination, credit: Richard Wheeler)
http://kleunerteachingspring2012.wordpress.com/2012/03/18/cb-notes-chapter-8/ [ accessed: 27/03/12]
Fig 2- Fourdrinier paper machine
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Cellulose microfibrils fibrils cellulosic fibres
Fig 3- Sublayers of fibre wall
Fibres are bound together by Lignin, with Hemicelluloses aiding in the development of fibre-to-fibre bonds.
Primary wall
Secondary wall
Hubbe M. (2012). Mini-Encyclopaedia of Papermaking Wet-End Chemistry: Fibres. URL:http://www4.ncsu.edu/~hubbe/FIBR.htm [accessed: 27/03/12]
CONT…
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Fig 4-3-D visualizations of four paper samples produced using a synchrotron X-ray microtomography. The size of each sample is (700 x 700 x 35 μm3 )
du Roscoat, S. R., Decain M., Thibault X., Geindreau C. & Bloch J. F. (2007). Estimation of microstructural properties from synchrotron X-ray microtomography and determination of the REV in paper materials. Acta Materialia, 55, pp.2841-2850.
CONT…
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0 0.5 1 1.5 2 2.5 30
0.01
0.02
0.03
0.04
0.05
0.06
0.07
STRESS-STRAIN CURVE OF PAPER
STRAIN
ST
RE
SS
/N
Elastic section
Plastic behaviour
Yield Threshold
CONT…
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CONT… PIVOTAL LITERATURE FINDINGS
Seth and Page (1981): A marked semblance in the shape of the stress-strain curves of the samples, and consequently suggested the reality of a constant shape factor for the stress-strain curve of paper.
El. Hosseiny (1994): Geometric similarity between all stress-strain curves of paper with each being obtained from a master curve, depending on the values of its stress and strain
Seth R.S and Page D.H. (1981): in The role of fundamental research in paper making (ed. J. Brander), 412-452, London, Mechanical Engineering Publications
El-Hosseiny.F. (1994). The Effect of Sheet Densification on the Shape of its Stress-Strain curve. J. Pulp Pap Sci , 20 (12), 366-370
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OBJECTIVE To probe the existence of a consistent shape factor which
gives rise to the constant shape of the stress-strain curve of paper
Specific objectives include:A. To investigate the load-elongation behaviour of
anisotropic industrially manufactured paper samples.
B. To investigate the relationship between the tensile energy absorption (TEA) , load and strain.
C. To investigate the extent to which the behaviours in objectives A and B are affected by the anisotropy of the sheet.
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EXPERIMENTAL PROCEDURE & EQUIPMENT
•10 different types of machine-made paper were tested:
•Samples were conditioned and tested at 23°C room temperature and 50% relative humidity.
• ‘Chartam’ Tracing paper• Arjo wiggins Laid paper
‘Courier’ • Arjo wiggins wove ‘send
me’ • Arjo wiggins office/printing
and writing
• Arjo wiggins Laid ‘conqueror’
Combination of hardwood &
softwood fibres
• Security Paper – Portals delarueCotton Fibres
• News Print• Xerox Office paper• Lyreco Standard Office
Paper
Recycled fibres
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Thickness measurements
• Messmer Dead weight Micrometer
Zero Span Tensile testing
• Pulmac Zero Span Tester
• 10 strips each of 9 cm x 2cm
• Measured in MD and CD
• Samples clamped at 70 psi
Long Span Tensile testing
• Instron 5564 Tensile tester & Series 9 software
• 10 strips each of 15cm x 1.5cm, 10cm between clamping jaws
• Testing conducted in: MD and CD, at increasing fibre angle orientation of 15° interval, and three different strain rates.
CONT…
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RESULTS
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400 GRAPH 1: AVERAGE TEA VRS AVERAGE FAILURE LOAD X EXTENSION OF MD AND CD TESTS
breaking load/N x extension/m
TE
A/J
y = 0.733xR2 = 0.993
MD: Col-ouredCD: Gray-scale
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20 40 60 80 100 120 140 160 1800
20
40
60
80
100
120GRAPH 2: AVERAGE TEA VRS AVERAGE FAILURE
LOAD X EXTENSION FOR EACH FIBRE ANGLE ORIENTATION
breaking load/N x extension/mm
TE
A/J
y = 0.726xR2 = 0.960
MD
Office pa-per: Col-oured Tra-cing paper: Black
CD
Incre
asing fibre
angle
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0 50 100 150 200 250 300 3500
50
100
150
200
250
GRAPH3: AVERAGE TEA VRS AVERAGE BREAKING LOAD X EXTENSION AT STRAIN RATES : 1mm,
10mm&100mm/min
breaking load/N x extension/mm
TE
A/J y = 0.729x
R2 = 0.984
1mm/min: black10mm/min:red100mm/min:orange
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The ratio (K) of the work to failure/Tensile energy absorption (TEA) to the product of the extension and breaking load was between 0.64-0.78.
K of MD ~ 0.6 and CD ~ 0.75.
• This indicates the constant shape factor K, and shape for the stress-strain curves of paper.
stress
strain
0.6 ≤ K ≤ 0.78
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12
3
4
5
6
7
8
9
10
11
121314
15
16
17
18
19
20
21
22
23
24
25
0
0.5
1
Polar Chart: variation of K with fibre angles
tracing paper
MD
CD
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Though the constant shape factor of the stress-strain curve of paper has been established and quantified yet,
0 0.5 1 1.5 2 2.5 3 3.50
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09 GRAPH 4: STRESS-STRAIN CURVE OF TRACING PAPER IN MD
strip 1
strip 2
strip 3
strip 4
strip 5
strip 6
strip 7
strip 8
strip 9
strip 10
strain
stress/N
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Cont...Using Mathematica version8, curves could be
scaled into a ‘Master curve’.
0.0 0.5 1.0 1.5 2.0 2.5 3.00.00
0.02
0.04
0.06
0.08
0.10
GRAPH 5: STRESS-STRAIN CURVE OF TRACING PAPER IN MD (obtained from
Mathematica)
ST
RE
SS
/N
STRAIN
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SUMMARY El Hossieny, Seth and Page suggested the constant
shape of the stress-strain curve of paper.
Concept was further investigated by tensile testing and analysing data from 10 dissimilar machine-made paper.
Ratio, K, between TEA and product of extension and breaking load showed a constant behaviour at all testing conditions.
Stress-strain curves can be obtained from a single “master curve”.
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CONCLUSION
The shape of the stress-strain curve of paper is constant, with the ratio, K, of the area beneath the curve to the boundary region of the curve being 0.6 ≤ K ≤ 0.78.
K is independent of fibre angle orientation, strain rate and isotropy of the paper.
THANK YOU
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REFERENCES1. Sampson W.W. (2009). Materials properties of paper as
influenced by its fibrous architecture. International Materials Reviews, 54 (3), 134, 143. doi : 10.1179/174328009X411154
2. Page D.H. (1969). A Theory for the Tensile Strength of Paper. Tappi J, 52 (4), 674
3. Sjostrom. E. (1993). Wood Chemistry, fundamentals and applications (2nd Edition) London, England: Academic Press, Inc.
4. Hubbe M. (2012). Mini-Encyclopaedia of Papermaking Wet-End Chemistry: Fibres. URL:http://www4.ncsu.edu/~hubbe/FIBR.htm [27/03/12]
5. El-Hosseiny.F. (1994). The Effect of Sheet Densification on the Shape of its Stress-Strain curve. J. Pulp Pap Sci , 20 (12), 366-370.
6. Seth R.S and Page D.H. (1981): in The role of fundamental research in paper making (ed. J. Brander), 412-452, London, Mechanical Engineering Publications.
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Average TEA vs. product of Average breaking load and Average extension for sample sheets tested in the MD, showing error bars at 95% confidence level
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Average TEA vs. product of Average breaking load and Average extension for sample sheets tested in the CD, showing error bars at 95% confidence level