Download the book, free !! contact roman@gatech.edu, also available - PowerPoint PPT Presentation

Download the book, free !! contact roman@gatech.edu, also available in paperback from Amazon 1

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 3

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. 4

Paper Structure Laser confocal shot, torn edge Same as left but lighting up a single layer 40 X Same paper but a different spot Paper as a mass of fettucine ! 5

3 Principle Directions, Paper and Board Introducing Stiffness or Elastic Modulus E : E MD > E CD >> E ZD 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 7

Moisture effects: strength properties When conditioning samples takes too long , for intra-lab comparison of specs and reproducibility , use the correction: 𝑻𝒖𝒔𝒇𝒐𝒉𝒖𝒊 𝟔𝟏 % 𝑺𝑰 = 𝑻𝒖𝒔𝒇𝒐𝒉𝒖𝒊 (% 𝑵 ) × % 𝑵 × . 𝟏𝟖 + 𝟏 . 𝟓𝟖 8

Paper variability and the need for testing Samples taken from F ront or B ack positions show greater CD variation than those near the C enter 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 F l Δ Define tensile stiffness S b , using values from the tensile test: 𝑇 𝑐 = ∆𝐺 × 𝑚 𝛦𝑚 × 𝑥 11

Elastic Modulus E, from Tensile Testing 1) For both MD and CD orientation, where t is the sheet “caliper”*, tensile stiffness S b : 𝐹 𝑁𝐸,𝐷𝐸 × 𝑢 = 𝑇 𝑐 𝑁𝐸,𝐷𝐸 2) Defining strain ε : 𝜁 𝑁𝐸,𝐷𝐸 = ∆𝑚 𝑁𝐸,𝐷𝐸 𝑚 𝑁𝐸,𝐷𝐸 𝜏 𝑁𝐸,𝐷𝐸 = ∆𝐺 𝑁𝐸,𝐷𝐸 3) Stress σ , is Force/Area 𝑢 × 𝑥 𝑇 𝑐𝑁𝐸,𝐷𝐸 = 𝜏 𝑁𝐸,𝐷𝐸 𝐹 𝑁𝐸,𝐷𝐸 = 4) Hooke’s law 𝑢 𝜗 𝑁𝐸.𝐷𝐸 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 σ (Shallhorn Gurnagul) 2 1 = 𝟐 𝐷𝑥 𝜍 𝑔 + 𝜍 − 1 𝑔 𝑢 3 𝜏 𝑑 𝝉 𝒑 2𝛽𝐹 Shallhorn Gurnagul SCT model 13

Compression and Tension Relation to Modulus Modulus E is the same in Tension and Compression , and E MD ~ 1.5 - 2 x E CD 14

Modulus and Tensile Strength Unaffected by Bonding Page and Seth experiments 1981 ~ ± 12 % about Control 15

Compression Strength Follows Modulus 16

Example: Modulus and Corrugated Board Pin Adhesion Pin adhesion test 17

Tensile Stiffness in Bending: Paper Bending stiffness D : 𝐸 = 𝐹𝑢 × 𝑢 2 12 So, D can be checked using S b and t 18

Tensile Stiffness in Bending: Board “Sandwich” beam approximation: 𝐸 = 𝐹 ∙ 𝑢 ∙ ℎ 2 t – liner caliper h – board caliper 2 E – liner modulus 19

Tensile Stiffness in Bending: Boxes Vertical load McKee equation for BCT failure load: BCT = C(ECT) 3/4 {(D MD x D CD ) 1/2 } 1/4 x Z 1/2 E x t = S b of liners is assumed to be = C(ECT) 3/4 {(E MD th 2 /2 x E CD th 2 /2) 1/2 } 1/4 x Z 1/2 proportional to board ECT = C’(ECT) 3/4 (E x t) ¼ (h x Z) 1/2 = 5.87 ECT x √(h x Z) Usual simplified McKee equation 20

Tensile Stiffness in Ultrasonics 𝜍𝑾 𝟑 ρ – density = Basis weight/caliper = β /t V 2 – sound velocity squared aka “specific stiffness” Tensile stiffness is related to specific stiffness: 𝑇 𝑐 = 𝐹𝑢 = 𝜍𝑊 2 𝑢 = 𝛾 𝑢 𝑊 2 𝑢 = 𝛾𝑊 2 21

Ultrasonic Tensile Stiffness in Ring Crush + RCT V 2 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 β V 2 (N/mm) x 10 3 23

Models for End-use: Writability = Applying a swath of aqueous ink Bristow wheel emulating handwriting Bottom unprinted side Top printed side 24

Challenge: Quantify and Relate Show- through to Physical Properties = Underside show-through Tappi method colorimeter CIE L*a*b* values Show-though quantified as difference in unprinted and printed: 𝟑 + 𝒃 𝒗 𝟑 + 𝒄 𝒗 𝟑 ∗ − 𝑴 𝒒 ∗ − 𝒃 𝒒 ∗ − 𝒄 𝒒 ∗ ∗ ∗ ∆𝑭 = 𝑴 𝒗 Seek a regression predictive model of the form: ΔE = a 1 x 1 + a 2 x 2 + ...+ a n x n + b 25

Physical Properties and Show-through + Contact Angle Cobb water absorption Air permeability ?.. Surface roughness (stylus) Hercules size (HST) 26

Show-through Analysis Using Excel LINEST multiple regression analysis, retain significant terms, optimize r 2 : ΔE = - 0.0312 x (HST) + 0.170 x (contact angle) + 2.60 x (angle rate) + 7.86 x (Cobb 30 / β ) -10.3 This model is used to evaluate candidate commercial papers for notebooks 27

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