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

/ 18

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

2

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.

/ 18

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

3

/ 18

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.

C

C

C

C

C

C

C

C C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

potential auxetic molecule

microporous expanded PTFE

UHMWPE

4

auxetic foamconventional foam

macroscopic auxetic material

/ 185

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

/ 18

Page, TREND (1969)

SEM, Copy Paper

6

Paper as an out-of-plane auxetic material

/ 18

N Stenberg (2002)

Machine Direction

Sample: uncoated paperboardt0 = 458 ± 10 μm

7

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

/ 188

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

/ 18

Copy Paper

Filter Paper

9

/ 18

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

/ 1811

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

/ 1812

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

/ 1813

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

/ 1814

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

/ 1815

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)

/ 1816

Olov E. Ohrn, Svensk papperstidning, 1965, 68(5), 141-149Deformation mechanism

/ 18

𝑙2 = 𝑑2 + 𝑥02

𝑑𝑧 = 𝑑 − 𝑑2 − 2𝑥0. 𝑑𝑥 − 𝑑𝑥2

𝑙2 = (𝑑 − 𝑑𝑧)2+(𝑥0+𝑑𝑥)2

For d = 30 μm, x0 =100 μm

17

/ 1818

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 ?