Factors influencing the stress-strain curve of paper.

TOPIC: FACTORS INFLUENCING THE STRESS-STRAIN CURVE OF PAPER

Presented by:ALEX NYARKO

Supervisor:Dr. W. Sampson

School of Materials, The University of Manchester.

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

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…

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…

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…

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

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.

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

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…

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

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

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

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

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

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

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

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”.

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

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.

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

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