deconstructing the auxetic behavior of...
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Deconstructing the auxetic behavior of paper Prateek Verma
Dr. Anselm Griffin
Dr. Meisha Shofner
Advisers
IPST Executive Conference
14th March, 2014
Paper Science and Engineering Fellow
Materials Science and Engineering
Georgia Institute of Technology
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Poisson’s Ratio
laterally shrink
laterally expand
x
y
y
xy
x
x: longitudinal direction
y: lateral direction
isotropic anisotropic
νxy -1 ~ +0.5 no limitation
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What are auxetic materials?
G. N. Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel, Nat. Mater., vol. 10, no. 11, pp. 823–37, Nov. 2011.
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R. J. Young, Introduction to Polymers. Chapman and Hall: London New York, 1983.K. E. Evans, M. A. Nkansah, I. J. Hutchinson, S. C. Rogers, Nature, 1991, 353, 124.
L. J. Gibson, M. F. Ashby, G. S. Schajer, C. I. Tobertson, Proc. R. Soc. London A, 1982, 382, 25.
unit cell of α-cristobalite fully stretched & compressed
Auxetic Structure
re-entrant honeycomb
Certain types of
Minerals
Skins
Arteries
Bones
…have been found to be auxetic
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J. B. Choi, R. S. Lakes, J. Mater. Sci. 1992, 27, 4678, B. D. CaddockK. E. Evans, J. Phys. D: Appl. Phys. 1989, 22, 1877.
K. E. Evans et al., Nature, 1991, 353, 124.
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C C
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potential auxetic molecule
microporous expanded PTFE
UHMWPE
4
auxetic foamconventional foam
macroscopic auxetic material
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Some applications
S. Jayanty, J. Crowe, and L. Berhan, Phys. status solidi, vol. 248, no. 1, pp. 73–81, Jan. 2011.A. Alderson, Chem. Ind, no. May, 1999.http://home.um.edu.mt/auxetic, http://gilbert13.co.uk/auxbowl.html
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Page, TREND (1969)
SEM, Copy Paper
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Paper as an out-of-plane auxetic material
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N Stenberg (2002)
Machine Direction
Sample: uncoated paperboardt0 = 458 ± 10 μm
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Cross Direction
Sample: uncoated paperboardt0 = 458 ± 10 μm
Ohrn(1965)
Thickness Variations of Paper on Stretching, Olov E. Ohrn, Svensk papperstidning, 1965, 68(5), 141-149Out-of-plane Poisson’s ratios of Paper and Paperboard, Nordic Pulp and Paper Research Journal (2002)
Previous reports
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Copy Paper 105±2 75
Paperboard 270±2 220
Bamboo Paper 433±7 295
Cotton Paper 190±3 120
Filter Paper 178±4 85
Glassine Paper 52±2 48
Handsheet SW 542±26 220
Handsheet HW 586±28 210
PET Film 144±2 152
Thickness(μm)
Grammage(gm-2)
Material selection
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Copy Paper
Filter Paper
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Sample size10 cm x 2 cm
Instron 5566, 10 kN load cell
Rate: 0.5 mm/min (paper)1.0 cm/min (NWs)
Reported thickness at center of sample*
5 samples of each type
*thickness was measured using Mitutoyo micrometer 369-350 at 20-25 kPa
Measuring thickness vs. length
10
Experimental setup
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Results (paper)
103
104
105
106
107
108
109
110
10.00 10.03 10.05 10.08 10.10
Th
ick
nes
s (μ
m)
Length (cm)
268
272
276
280
284
288
292
296
10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35
Th
ick
nes
s (μ
m)
Length (cm)
Machine direction present, anisotropic Marked increase in thickness, ν < -2.0 Similar production sequence for both Pulping, bleaching, paper
machine, calendaring
Copy paper Paperboard
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Results (paper)
174
176
178
180
182
10.00 10.04 10.08 10.12 10.16
Th
ick
nes
s (μ
m)
Length (cm)
49
50
51
52
53
54
6.00 6.02 6.04 6.06
Th
ick
nes
s (μ
m)
Length (cm)
Random fiber orientation (filter paper) Filter Paper: Moderate increase in thickness before break, made from
cotton fibers Glassine Paper: Ordinary (+ve) Poisson’s ratio – super-calendering
Filter paper Glassine paper
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Results (paper)
187
189
191
193
195
10.00 10.05 10.10 10.15 10.20 10.25
Th
ick
nes
s (μ
m)
Length (cm)
425
428
431
434
437
440
10.00 10.02 10.04 10.06 10.08 10.10 10.12
Th
ick
nes
s (μ
m)
Length (cm)
Machine direction present, anisotropic Cotton Paper: Moderate increase in thickness before break Bamboo Paper: Near zero Poisson’s ratio
Cotton paper Bamboo paper
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Results (paper)
510.0
530.0
550.0
570.0
590.0
610.0
630.0
10.00 10.05 10.10 10.15 10.20
Th
ick
nes
s (μ
m)
Length (cm)
550
570
590
610
630
10.00 10.02 10.04 10.06
Th
ick
nes
s (μ
m)
Length (cm)
Random wet-laying of fibers under hydrostatic pressure Largely negative Poisson’s ratios, ν < -4.0 No paper machining, calendaring orientation or compression Close to a cellulose random fiber network
Handsheet SW Handsheet HW
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Sample Name
Poisson’s
ratio *
Copy paper -3.3
Paperboard -1.1
Bamboo Paper 0.1
Cotton Paper -0.3
Filter paper -0.3
Glassine paper 1.2
Handsheet SW -4.8
Handsheet HW -3.8
PET Film 0.5
P. Verma, M. L. Shofner, and A. C. Griffin, “Deconstructing the auxetic behavior of paper,” Phys. Status Solidi B, published online, Oct. 2013.
*calculated from linear fit ofelastic region
Results (paper)
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Olov E. Ohrn, Svensk papperstidning, 1965, 68(5), 141-149Deformation mechanism
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𝑙2 = 𝑑2 + 𝑥02
𝑑𝑧 = 𝑑 − 𝑑2 − 2𝑥0. 𝑑𝑥 − 𝑑𝑥2
𝑙2 = (𝑑 − 𝑑𝑧)2+(𝑥0+𝑑𝑥)2
For d = 30 μm, x0 =100 μm
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Task 1Handsheetpossibilities
Changing pulp type
Varying stock concentration
Varying compressive forces?
Possibility of making non-cellulosic paper?
Task 2Imaging (SEM)
Identification of structural features
Task 3Cross Direction Tests
For all representative samples
Lower value of νanticipated
Task 4Geometrical model
To consider effect of
Fiber properties (elasticity)
Network properties (grammage, density)
Modeling random layout of fibers
Future work
Thank you!
Questions ?