Download the book, free !! contact roman@gatech.edu, also available in paperback from Amazon
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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. 9
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 !! 28
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