Physical Testing of Paper

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Renewable Bioproducts Institute (formerly IPST) Georgia Institute of Technology 50 10th St. N.W., Atlanta, Georgia, U.S.A. 2

In this talk, we’ll cover : • • • •

Basic paper physics, all you need to know A quick look at a few basic tests How the tests all tie together A few useful models

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Paper structure

Paper can be thought of a conglomeration of pine straw clumps on a millimeter scale , paper is thus inherently non-uniform .

In cross section, paper is a stack of tubes, many are collapsed.

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Paper Structure

Laser confocal shot torn edge 40 X

Same as left but 2 lighting up a single layer

Same paper but a different spot

Paper as a mass of fettucine !

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3 Principle Directions, Paper and Board

Introducing Stiffness or Elastic Modulus E: EMD > ECD >> EZD 6

Moisture effects: hysteresis

1. Samples for testing should always be preconditioned at 20% RH

2. Then, conditioned at 50% RH and tested at 50% RH

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Moisture effects: strength properties

When conditioning samples takes too long , for intra-lab comparison of specs and reproducibility , use the correction: đ?‘şđ?’•đ?’“đ?’†đ?’?đ?’ˆđ?’•đ?’‰đ?&#x;“đ?&#x;Ž% đ?‘šđ?‘Ż = đ?‘şđ?’•đ?’“đ?’†đ?’?đ?’ˆđ?’•đ?’‰ (%đ?‘´) Ă— %đ?‘´ Ă— . đ?&#x;Žđ?&#x;• + đ?&#x;Ž. đ?&#x;’đ?&#x;• 8

Paper variability and the need for testing Samples taken from Front or Back positions show greater CD variation than those near the Center

Variability increases when testing pieces on a smaller scale e.g. SCT vs RCT, or 15 mm wide strips vs 25 mm wide strips.

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The Tensile Test Tells All Load cell measures F

l w Cross head moves down distance ∆l 10

Tensile test tells all

Define tensile stiffness Sb , using values from the tensile test:

đ?‘†đ?‘?

∆đ??š Ă— đ?‘™ = đ?›Ľđ?‘™ Ă— đ?‘¤ 11

Elastic Modulus E, from Tensile Testing 1) For both MD and CD orientation, where t is the sheet “caliper�*:

đ??¸đ?‘€đ??ˇ,đ??śđ??ˇ Ă— đ?‘Ą = đ?‘†đ?‘?đ?‘€đ??ˇ,đ??śđ??ˇ 2) Defining strain Îľ : đ?œ€đ?‘€đ??ˇ,đ??śđ??ˇ

3) Stress Ďƒ, is Force/Area

4) Hooke’s law

∆đ?‘™đ?‘€đ??ˇ,đ??śđ??ˇ = đ?‘™đ?‘€đ??ˇ,đ??śđ??ˇ

đ?œŽđ?‘€đ??ˇ,đ??śđ??ˇ

đ??¸đ?‘€đ??ˇ,đ??śđ??ˇ =

∆đ??šđ?‘€đ??ˇ,đ??śđ??ˇ = đ?‘Ą Ă—đ?‘¤

đ?‘†đ?‘? đ?‘€đ??ˇ,đ??śđ??ˇ đ?‘Ą

đ?œŽđ?‘€đ??ˇ,đ??śđ??ˇ = đ?œ–đ?‘€đ??ˇ.đ??śđ??ˇ 12

Elastic Modulus of Paper • E is principally governed by the fiber modulus which is determined by species, fiber length • E appears as the dominant factor in the theory for tensile strength T (Page equation) and compression stress Ďƒ (Shallhorn Gurnagul) 1 đ?&#x;? đ??śđ?‘¤ = + đ?œŽđ?‘? đ??ˆđ?’?

2đ?›źđ??¸đ?‘“ đ?‘Ą 3

đ?œŒđ?‘“ −1 đ?œŒ

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Shallhorn Gurnagul SCT model 13

Compression and Tension Relation to Modulus

Modulus E is the same in Tension and Compression, and EMD ~ 1.5 - 2 x ECD 14

Modulus and Tensile Strength Unaffected

by Bonding Page and Seth experiments 1981

~ Âą 12 % about Control

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Compression Strength Follows Modulus

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Example: Modulus and Corrugated Board Pin Adhesion

Pin adhesion test

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Tensile Stiffness in Bending: Paper

Bending stiffness D : đ??¸đ?‘Ą Ă— đ?‘Ą 2 đ??ˇ= 12 18

Tensile Stiffness in Bending: Board

“Sandwich� beam approximation:

đ??¸ ∙ đ?‘Ą ∙ â„Ž2 đ??ˇ= 2

t – liner caliper h – board caliper E – liner modulus

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Tensile Stiffness in Bending: Boxes Vertical load

McKee equation for BCT failure load: BCT = C(ECT)3/4{(DMD x DCD)1/2}1/4 x Z1/2 = C(ECT)3/4 {(EMDth2/2 x ECDth2/2)1/2}1/4 x Z1/2 = C’(ECT)3/4 (E x t) ¼ (h x Z)1/2

= 5.87 ECT x √(h x Z)

E x t = Sb of liners is assumed to be proportional to board ECT

Usual simplified McKee equation

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Tensile Stiffness in Ultrasonics

đ?œŒđ?‘˝

đ?&#x;?

Ď â€“ density = Basis weight/caliper = β/t V2 – sound velocity squared aka “specific stiffnessâ€?

Tensile stiffness is related to specific stiffness:

đ?‘†đ?‘?

đ?›˝ 2 = đ??¸đ?‘Ą = đ?œŒđ?‘‰ đ?‘Ą = đ?‘‰ đ?‘Ą = đ?›˝đ?‘‰ 2 đ?‘Ą 2

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Ultrasonic Tensile Stiffness in Ring Crush

+ RCT

V2

SCT

Buckling load for a cylinder:

A proposed “McKee” equation for RCT:

+ Model for RCT:

The data fit: 22

Example: Ultrasonic tensile stiffness correlates with CMT and SCT

CMT

Ultrasonic Tensile Stiffness (N/mm) x 103 23

Models for End-use: Writability

= Bristow wheel emulating handwriting

Top printed side

Applying a swath of aqueous ink

Bottom unprinted side

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Challenge: Quantify and Relate Showthrough to Physical Properties

= Underside show-through

Tappi method colorimeter

CIE L*a*b* values

Show-though quantified as difference in unprinted and printed: ∆đ?‘Ź =

đ?‘łâˆ—đ?’– − đ?‘łâˆ—đ?’‘

đ?&#x;?

+ đ?’‚∗đ?’– − đ?’‚∗đ?’‘

đ?&#x;?

+ đ?’ƒâˆ—đ?’– − đ?’ƒâˆ—đ?’‘

đ?&#x;?

Seek a regression predictive model of the form:

ΔE = a1x1 + a2x2 + ...+ anxn + b 25

Physical Properties and Show-through

+ Contact Angle Cobb water absorption Air permeability

?..

Surface roughness (stylus)

Hercules size (HST)

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Show-through Analysis Using Excel LINEST multiple regression analysis, retain significant terms, optimize r2: ΔE = - 0.0312 x (HST) + 0.170 x (contact angle) + 2.60 x (angle rate) + 7.86 x (Cobb30/β -10.3

This model is used to evaluate candidate commercial papers for 27 notebooks

Summary • Elastic Modulus, “E” is key to understanding the interrelationships between: – Compression and Tension strengths – Burst – Bending stiffness

• “E” can be measured from tensile testing and sonic (speed of sound) testing • Physical testing of paper is necessary for wood fiber based products – and gives me (and a few others) a job !!

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E is key…

E is key It’s the modulus, you see It is there, for you and me It’s good for tension Nice for compression, And deserves, your attention !

Thank you for your Attention !!

Questions, Comments, to:  Roman@gatech.edu 29