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What’s important in liner and medium physical properties
Roman Popil, [email protected]
Institute of Paper ScienceGeorgia Tech,
Atlanta
Presentation for a general technical audience, sponsored by AbitibiBowater
Coosa Pines Al,
2
Who is Roman Popil ? •
Georgia Tech/IPST senior research scientist in Atlanta since 2002
•
Principal Investigator of Engineered Packaging research consortium program
•
Manager of IPST Paper Analysis lab for contract testing and research –
yes, send those
samples to me !•
Been in paper industry R&D since 1986: MacMillan Bloedel, Honeywell-measurex
•
PhD in plasma physics from the University of British Columbia –
Canadian, eh ?
hmm…
3
Paper Physical Analysis Paper Physical Analysis Testing Services at IPSTTesting Services at IPST
Contact Roman Popil, Ph.D.Lab Manager 404 894 9722
[email protected], seminars, consulting, research…
4
IPST@ GT Paper Analysis Lab
5
What was requested for this seminar
1.
Liner and medium properties how they relate to end-use
2.
The IPST testing lab capabilities
3.
Market rends, use of recycle
4.
Lab equipment for tetsing
6
What you will see in this talk ? Specifically…•
How BCT is related to ECT related to liner and medium compression strength
•
Why caliper and bending stiffness matter as well•
Why RCT is not a good measurement for product optimization
•
How SCT is better for product optimization•
How to use the SCT for product development
•
Some basic paper physics for background •
How the TSI with BW and SCT can be used to predict RCT anyway (if you must have RCT)
•
How to implement in an Autoline to predict RCT
7
Why measure compression strength of medium or linerboard ?
A warehouse of stacked boxes, the customer wants the boxes to remain stacked and protect the contents
Linerboard shows a buckling pattern from vertical applied load
ECT creep test
BCT creep test
Strains increase until box panels buckle, fold and collapse –
stacks topple
What happens instead….
8
United States Rule 41 –
since 1991 certificastion
for shipping containers
•
Old rule–
Burst(Mullen)–
Why ??
•
alternative rule–
ECT –
much better
The requirement for ECT allows reduction in basis weight my increasing the strength of the board
9
What’s going on out there ???
Reports typical values
Reports guaranteed values
Scandinavia 1 Scandinavia 2 Spain Germany
Basis weight Basis weight Basis weight Basis weight
Moisture Moisture Moisture Moisture
Caliper Caliper
SCTCD (STFI) SCTCD (STFI) SCTCD (STFI) SCTCD (STFI)
SCTMD (STFI)
Tensile stiff. MD Tensile stiff. MD
Tensile stiff. CD Tensile stiff. CD
Burst Burst Burst Burst
Cobb Cobb Cobb Cobb
Scott bond Scott bond
ZDT
Pick resistance
Air permeance Air permeance Air permeance
Roughness Roughness
Friction Friction
Scandinavia 1 Scandinavia 2 Spain Germany
Basis weight Basis weight Basis weight Basis weight
Moisture Moisture Moisture Moisture
Caliper Caliper
SCTCD (STFI) SCTCD (STFI) SCTCD (STFI) SCTCD (STFI)
SCTMD (STFI)
Tensile stiff. MD Tensile stiff. MD
Tensile stiff. CD Tensile stiff. CD
Burst Burst Burst Burst
Cobb Cobb Cobb Cobb
Scott bond Scott bond
ZDT
Pick resistance
Air permeance Air permeance Air permeance
Roughness Roughness
Friction Friction
Tests on liners medium
10
Country RequirementBelgium Burst, FCTDenmark Burst, PunctureFEFCO Burst, ECT ,Puncture France Burst, ECTItaly Burst, FCTSouth-East Asia Burst, Basis weightSweden Burst, ECT, FCTSwitzerland Burst, ECTUSA,Canada Burst, ECT, basis weightUnited Kingdom Burst, FCTJapan Thickness, ECT,FCT
Tests on corrugated board
11
Corrugated board weight trend
From the magazine: Solutions! February 2006
143#
122#
102#
12
Compression strength is a key property for box performance
Box compression is predicted by the McKee (1963) equation:
ZDDECTCBCT CDMD4/14/3 ))(
Board edge compression strength
board bending stiffness Box perimeter
BCT in lbs
ECT in lb/in
D’s in lb-in
Z = box (length + width) x 2 in inches
13
ECT is related to liner and medium compression strengths
)2(" mediumliner SCTSCTCECT
Compression strength of linerboard
Board take-up factor (length of medium to liner)
C flute 1.42
B flute 1.25
A flute 1.50
Compression strength of medium
14
ECT Methods: Clamp vs
Neckdown vs
Waxed Edge
Sumitomo and Emerson ECT clamps, 200 grit sandpaper on jaw faces, 10 psi pressure from spring clamps, we measure 5 psi –
is that ok ?
References on T 839: Schampfer
10, 15, Eriksson 40
L&W neckdown ECT sample cutter, localizes compressive failure
References: Koning
23, Frank, 38, Eriksson 40
15
Bending stiffness of corrugated board
2
2boardlinerliner htE
D
Board caliper Liner modulus
Liner caliper
linerliner tEstrengthtensilelinerboard
16
Measurement of transverse shear stiffness of board
•
using the IPST torsion pendulum tester also requires 4 point measurement of board bending stiffness
•Ensis Papro “DST”
tester measures the twisting frequency of 4 x 1”
board specimens
•Both methods require cutting and mounting of samples
17
How do we measure loss of transverse shear from crushing ?
•
developed at IPST from 1st
principles, calibrated output using weights
•
damped twisting motion of a board is analyzed by a computer program to find the twisting stiffness
•
bending stiffnesses of the test specimen are found by 4 point L&W tester
•
the transverse shear stiffness is calculated using an equation
•
Ensis Papro (New Zealand) also has developed a similar dynamic twist tester
IPST torsion pendulum
18
Box performance depends on the strength of the components
•
Historically, strength of board and components has been measured by:
•
Mullen burst•
Ring Crush
•
Short Span Compression Test (SCT)•
Edge Crush test (waxed method) also clamp method
19
Other alternatives to measure transverse shear:
BQM from XQ Innovations Australia, measures the resonant frequency of a board vibrated along the MD, -
no sample prep required, one button press provides a number in seconds
The measured area of the board must not have anything underneath it.
MD
20
Hydraulic sample clamp actuated by moving rings down
Rubber diaphragm bulges outward as glycerin gets pumped into the chamber
Electronic display of max burst pressure in psi
Note:
After burst you must
pull
the lever back to neutral, otherwise the diaphragm will burst !!
“CA”
type Mullen for testing handsheets and paper up to 100 psi. Calibration foils are 30, 65 and 110 psi
21
Ctrl+9 to start a new measurement
“PF2”
Spec no. 1 or 100
L&W Burst tester for linerboard, Calibration foils are 110 and 160 psi
22
The line of the burst will often be along the MD
23
Burst measures a combination of properties
From theory considerations the pressure to burst a sheet is proportional to:
MD and CD tensile strengths, s –
MD stretch at failure, R diaphragm curvature
24
Burst is dependent on many factors
25
SCT and RCT testing worldwide
•
USA –
Some are using only RCT
–
other only SCT–
Some both, SCT on low basis weight and RCT on high basis weight
•
Europe–
SCT dominating
•
Asia–
RCT almost only
•
Australia–
Moving from RCT to SCT
26
TestsBasis
Weight Hard
Caliper Density
(g/m2) (microns) (g/cm3) md cd Ex (GPa) Ey (Gpa) Vxy Vyx G (Gpa)Roll 96048 14# med 65.82 144.24 0.46 0.33 0.13 4.16 1.74 0.18 0.42 0.98Roll 96044 16# med 78.16 162.74 0.48 0.55 0.17 4.7 1.13 -0.03 -0.13 0.96Roll 96038 18# med 86.36 175.6 0.49 0.79 0.28 4.42 1.71 0.14 0.36 1.03Roll 96033 20# med 94.58 183.65 0.51 0.94 0.36 4.41 2.05 0.17 0.37 1.14Doug C 26# med 125.25 252.9 0.5 2.03 0.8 1.85 4.31 0.32 0.14 1.08Roll 99004 33# med 162.69 329.6 0.49 4.23 2.11 3.64 2.05 0.18 0.32 1.07
42# Liner A 203.97 293.26 0.7 9.31 4.61 7.13 3.54 0.17 0.33 1.94
42# Liner B 209.54 294.22 0.71 8.46 2.95 7.04 2.34 0.05 0.016 1.63
42# Liner C 211.78 318.84 0.67 11.42 3.66 6.46 2.59 0.14 0.34 1.55
2 pt L&W (mNm) In-plane Ultrasonic velocities data
Some typical properties for linerboard/ medium set
Density of medium is 0.5 g/cm3
Density of linerboards are 0.7 g/cm3
Bending stiffness
27
TestsSTFI lbf/in
(cd only) Taber units in mN-m
MD Slope (N/mm)
CD Slope (N/mm)
MD Ten.Stiff (N/mm)
CD Ten.Stiff (N/mm) md cd md cd
Roll 96048 14# med 63.606 26.723 445.336 187.124 6.04 1.66 0.73 0.162846 0.071613Roll 96044 16# med 86.484 24.94 605.6 174.643 6.8 2.82 0.93 0.276642 0.091233Roll 96038 18# med 75.5 23.057 529.48 161.583 7.96 3.53 1.43 0.346293 0.140283Roll 96033 20# med 81.783 27.492 573.532 192.661 8.8 4.52 2.15 0.443412 0.210915Doug C 26# med 112.549 41.728 788.64 292.429 13.55 12.38 6.43 1.214478 0.630783Roll 99004 33# med 130.31 60.093 912.764 421.027 19.82 26.79 14.1 2.628099 1.38321
42# Liner A 194.91 88.752 1365.885 622.111 27.12 53.56 31.65 5.254236 3.104865
42# Liner B 182.951 61.354 1281.896 429.92 22.47 50.87 17.96 4.990347 1.761876
42# Liner C 191.789 70.67 1343.845 495.546 23.36 61.03 23.6 5.987043 2.31516
Instron (tensile) dataBending Stiffness
(Taber Unit) (gmf-cm)
Some properties of linerboard/medium
Virgin unbleached 42# softwood kraft80/20 virgin/recycle
28
Box performance is predicted based on strength of the components of the board
Figure 1) Whitsitt Relationship of ECT to Composite Ring Crush
Whitsitt 1983, IPC
Related ECT to RCT:
(1)
ECT = 0.8 * (RCT1 + RCT2 + αRCTMed
) + 12
For linerboards > 42 lb/msf
(2)
ECT = 1.27 * (RCT1 + RCT2 + αRCTMed
) -
6
For linerboards < 42 lb/msf
Different equations for different basis weights…hmmm…
29
ECT predictive models based on SCT are simpler
7.0
2
C
SCTSCTCECT mediumliner
87.5
CZtECTCBCT
Simplified McKee equation for box compression:
Take-up factor for the medium ~ 1.42
for C flute
Corrugated board caliper
Box footprint perimeter
30
But…the linerboard industry still sells by the Ring Crush spec
•
manual measurement, cannot be automated
•
requires accurate cutting of sample –
can’t easily do handsheets
• handling of the sample
•
measurement of sample caliper and selection of the correct fixture insert
•
it is actually a combination of compression and…
•
bending failure, this is not good for optimization programs
Ford Highland Park plant –
Model T magneto assembly line
31
Ring Crush method
Sample and holder between compression platens –
what could go wrong ??
32
By golly, you’re right
!!
These results are absolutely ridiculous
!!
Ohh…let’s just send the report out anyway –
ha,ha.ha!!
The trouble of RCT measurement…
RCT measurement is prone to many types of errors…some can be human
…
33
The RCT vs SCT “debate”For RCT:
1.
Frank, Benjamin (Tappi J., Sept. 2007) RCT has lower coefficient of variation, correlation with ECT is better because:
a) test occurs over a larger test piece more averaging, smaller variability
b) Bending occurs in ECT and box failure
Against RCT:
2.
Seth, Fellers etc., SCT is the intrinsic compression strength of
the linerboard,
3.
Variability is inherent in the linerboard due to contaminants, defects, formation
4.
SCT is more easily optimized through wet end deification, furnish changes or refining
5.
RCT is not available on in-line automated testing machines.
6.
RCT requires more sample preparation and handling.
34
RCT is supposed to predict BCT
BCT test
35
Then which way is the length of the test strip for CD and MD tests ?
Can you cut the strips exactly along MD or CD, should they be together or spread apart, how far apart is good enough, what do you do for small handsheets ?
36
Cutter for 15 mm wide 4 inch span samples
However, parallel edges not so critical for SCT can use a ratchet cutter for consecutively adjacent strips handy for handsheet samples
37
Got to use a different cutter for ring crush though…
Both look the same –
need to read the small label !
38
Ring Crush
Samples are 6 inches long and 12.5 mm (1/2”) wideUse different center “island”
inserts depending on the caliper for the specimen
39
I don’t know about you, but I am wearing gloves to protect my nice new nail job !
Gloves ?? Nah…What for ?!
Calm cool technicians required with dry hands
40
IPST data ex Mike Schaepe I sure hope you like my
data !
What’s this ??
41
Short Span Compression Test is SCT
•
STFI = SVENSKA TRÄFORSKNINGSINSTITUTET (Swedish Forest Products Research Laboratory , now renamed “Inventia”)
Test method was developed by Christer Fellers in the
late 1970’s
The short span compression test is not “STFI”
Christer gets another award from Jeffrey Suhling
42
Fun Fact (from a student presentation
)•
Compression tests are all called *CT, e.g. FCT, ECT, BCT, but SCT is rather new…
•
Many call the short span compression test SCT as “STFI”, pronounced “stiffy”
•
Why is this a bad
idea ??•
Answer: ________
Unfortunately, I can see your “STFI”
is way down today…
Ahem.. um, ah…
my what
?!!!..
43
Corrugated medium comparison – SCT and RCT
ECTSCT
RCT
ECT increased in accordance with SCT results.RCT predicted ECT decrease.
Conclusion:SCT is better suited for low grammage corrugated medium than RCT.
IPC, Whitsitt 1985
44
Note the difference between STFI and RCT (about 2 X)
At very high basis weights and calipers, get slip: more surface compression
SCT and RCT comparison
45
Effect of grammage and density
RCT
Christer Fellers’
slide
Increased buckling for lightweights decreases RCT with density
46
Sample strip
Pressurized clamps prevent slipping
CD
0.7 mm gap between clamping jaws
47
The L&W SCT On-board test sample moisture correction is available, based on resistance measurement requires calibration that is furnish dependent –
unused at IPST since all samples are conditioned
Instrument is checked periodically using a selected standard paper sample kept in a drawer with its data history for instant comparison
For mill QC use –
samples must be conditioned to 50% RH equilibrium…fastest way cut 6”
x 15mm strips, place in microwave oven for 10 seconds, hang separated strips in a draft for ~ 2 hours, then
test
Simple strip insertion, one button operation
Strip edge parallelism not critical
48
After many years of service…Thermal dot matrix printer dots fades,
rollers wear out
Green LED read-out fades,
missing dots
Keyboard button contacts become
erratic or fail
Unit must be in a conditioned lab, if taken into humid environments (e.g. mill floor) electronics will be affected
49
Shows that specific STFI is independent of basis weight and is a property of the fiber consolidation
SCT works because over the 0.7 mm test span there is no bending
Euler buckling curves
50
Real compressive failure is marked by material breakdown and occurs when the column height prohibits buckling
When testing a strip, the crease is often hard to see –
looks like nothing has happened
51
STFI or SCT (Short Span Compression Test) is considered to be the intrinsic compression test strength for linerboard –
this is how you can understand
what affects it through a “Page equation”
model for SCT:
Note the dependence on fiber modulus (fibril angle,species)
and sheet density (wet pressing)
Can affect this by low consistency
refining
52
Effects of Processes on Compressive strength using SCT
Excerpted from “Paper Physics”
by Niskanen
53
Shows the only way to change SCT is to change the furnish and beating level of fibers
Recall the Shallhorn Gurnagul model for SCT…
Graphs excerpted from the Handbook of Physical Testing
Using SCT
54
Ring Crush is affected by the bending stiffness and the caliper of the test specimen so is not a true compression test
Note the dependence on Taber and caliper in this empirical relationship
Note that Taber is a bending stiffness measurement
Tappi Journal 1998
55
Why the bending stiffness of linerboard mattersVideo observation of ECT tests show:a) No out-of-plane buckling at higher basis weightsb) Slight buckling at low basis weights for A and C flute boards
Schaepe and Popil2006
Buckling of linerboard
facings occurs in A and C flute, more so for lightweights
56
We can calculate the buckling load for linerboard using MD and CD Bending Stiffness
Taber has historically been used for 2 point bending stiffness of liners and medium, Taber measures bending moment
M not stiffness EI/b !
We did a lot of work with an L&W 2 point stiffness tester, a more straightforward design, cross calibrated instruments with stainless steel shims.
From linear elasticity theory, the conversion factor from Taber moment M to stiffness D is:
67.13
M
bLM
bEID
This means that Taber x 1.67 bending stiffness !!
57
Wet pressing increases SCT but lowers bending stiffness
12/3EtD
As density increases SCT increases but bending stiffness goes down
what is going on is that the caliper decreases lowering D
STFI vs density
200 gsm: y = 24.501Ln(x) + 42.411R2 = 0.9949
300 gsm y = 40.655Ln(x) + 61.97R2 = 0.9999
160 gsm: y = 12.587Ln(x) + 25.411R2 = 0.9895
100 gsm: y = 10.107Ln(x) + 19.315R2 = 0.954
5
10
15
20
25
30
35
40
45
50
0.35 0.45 0.55 0.65 0.75 0.85 0.95
Density gsm
STFI
lb/in
Lab data using kraft handsheets pressed to various densities
58
Wet pressing increases SCT but lowers bending stiffness
0
5
10
15
20
25
30
35
40
0.35 0.45 0.55 0.65 0.75 0.85
Density (g/cm3)
Geo
met
ric m
ean
bend
ing
stiff
ness
(mN
-m)
10 gsm150 gsm200 gsm300 gsm 12/3EtD
As density increases SCT increases but bending stiffness goes down
what is going on is that the caliper decreases lowering D
59
Wet pressing increases density increases SCT but decreases
bending stiffness
12
3EtD
For linerboard: Modulus increases with wet pressing from increased bonding
Linerboard caliper
ESCT
60
3
4
5
6
7
8
9
0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
Density (g/cm3)
ECT
(kN
/m)
100 gsm160 gsm200 gsm
Predicting ECT for handsheets using SCT and bending stiffness relationships to determine the ECT as a function of density for handsheets for various basis weights as specified.
More buckling occurs with increased wet pressing so this limits ECT
The ECT buckling model is used to predict the optimum liner density for ECT
The ECT buckling model predicts the optimal density for 160 gsm liner single wall C flute to be 0.75 g/cm3
Note the Peak ECT occurs here
61
How can RCT and SCT be related ? (current IPST ongoing research)
•
RCT is a combination of bending and compression failure
•
SCT is compression failure only•
McKee reasoning for plate failure as a combination of compression and bending takes the empirical form:
)1(`)()( bb loadBucklingstrengthnCompressioloadfailurenCompressio
Related to the bending stiffness which depends on the structure e.g, round tube, plate, flute shape, etc.
62
Buckling load for a thin walled tube:
rtE
cr
)1(3 2
r = 24.2. mm
t = 0.3 mm
l
= 6 mm
“E x t ” is tensile stiffness
For this formula to hold need to fit one half wave into the tube height:
mmtrml 7.472.1
Yep, specimen is high enough to buckle -
so we can use this formula for buckling of the RCT sample
From Timoshenko and Gere:
63
We can get a measure of the ring buckling load using the L&W TSI
By measuring the speed of sound in paper, basis weight and the caliper we can estimate the tensile stiffness
The tensile stiffness is directly proportional to the buckling load of a thin walled tube.
This can all be done instantly and automatically…
64
Combining measurements to predict RCT
The Autoline for linerboard will have SCT, caliper, basis weight, and a TSI –
these measurements can be combined to fit an RCT model, the model can be programmed into the Autoline software to provide a
calculated estimated equivalent value for RCT …
But first let’s review a few concepts before we see how to do this…
65
MD
ZD
CD
Paper consists of 50 to 30% air and a network of bonded fibers aligned predominantly along the MD –
machine direction
Fibers: former wood cells, typically 1 –
3 mm long, 50 microns wide
PAPER STUCTURE - OVERSIMPLIFIED
SEM surface
SEM x-section
For box making applications, only CD compression is considered
66
Paper as a 3D spring:
CDCDCD E MDMDMD E
In 1D we have Hooke’s law for the Force F to move a spring distance x
F = k x
For a 3D solid slab such as paper, we have by analogy, (actually a good physical analogy is the common cellulosic cleaning sponge) the pressure or stress
σ
required to displace the solid by a strain ε
for each principal direction:
ZDZDZD E
The E’s here are the elastic moduli for each of the 3 directions
The ε’s are the strains i.e. relative changes in displacement : ∆ℓ
/ ℓ
0
67
To a good approximation:
E’s and sound speed
22112
2
22112
2
)1(
)1(
CDCDCD
MDMDMD
VVE
VVE
Moduli (MD or CD) = apparent density x velocity squared
We can measure the speed of sound propagating along the plane of
the sheet using a pair of transducers:
timeVolts
Transmitted pulse Received pulse
?
68
Bimorph “paddle”
transducers apart for “far”
readingClose up of transducers for “near”
reading in shear mode, transducers are rotated for longitudinal mode
IPC 1970’s Robot Arm difference method technique
From successive pairs of measurements a 2 distances get Poisson ration, and shear modulus –
15 minutes per test
Measuring sound speed in paper
69
IPST Robot Arm – from the 1980’s
4 user selectable measuring stations
Robot arm end effector rotates for polar plots
Takes an hour for a 2 degree resolution plot
You know, I’d rather not wait an hour
for just one polar plot, thanks !!
A typical lab tech’s response
Lars Ingman
marketed a version through “Robotest”
Sonisys
now has an updated version called “UTI”
70
L&W TSI comes to the rescue
8 pairs of transducers fixed distance, head comes down at a higher pressure for basis weights > 100 gsm
Polar plot and V2 produced in 6 seconds but:
Might be influenced by low density and high roughness to produce
underestimates of V2
So…correlation of V2
from TSI vs tensile stiffness has to be verified for particular sample sets
71
L&W TSI measures VCD2
= TSI_CD
CDTSIBWtVt
BWtVtECD _22
For the buckling load part in the RCT model we need E x tThis is the same as:
So the buckling load in an RCT model becomes:
CDTSIBWCrtE
cr _)1(3 2
With C’’
being constant since r and the Poisson ratio’s do not change appreciably
72
Modeling RCT in terms of combined compression and
buckling strengths
bb EtSCTCRCT 1)()(•Based on McKee reasoning for the compression strength of a plate
but instead replacing the buckling load of a plate by that for a thin cylindrical ring (e.g. Roark’s formulas) where:
•Pcr is the buckling load for a ring is proportional to Et
•Et = tensile stiffness ( modulus E times sheet thickness t) = constant x (v2) x basis weight
•Can get v^2 ( specific stiffness) from L&W TSI output
• so…
can now get an RCT value by measuring SCT, BW and TSI_CD
The model for ring crush is proposed as:
73
Ultrasonic tensile vs Instron N/mm
y = 1.7524x - 73.305R2 = 0.9829
0
200
400
600
800
1000
1200
1400
0 200 400 600 800 1000
Series1Linear (Series1)
This shows that TSI * BW = Et when E x t is measured by the Instron as tensile stiffness
TSI x
BW
(N
/mm
)
Instron tensile stiffness (N/mm)
Ultrasonically measured values are always higher than mechanical equivalents
74
IPS
T in
-pla
ne s
peci
fic s
tiffn
ess
(km
/s)2
TSI index
TSI vs IPST V^2
y = 1.0821x - 0.1875R2 = 0.9782
2
4
6
8
10
12
14
2 3 4 5 6 7 8 9 10 11 12
Series1Linear (Series1)
Sample ID
42 lb kraft liner
33 lb medium
26 lb medium
56 lb liner WC
16 lb medium
18 lb medium
OCC 42lb liner
20 lb medium
3m mylar
yellow copy
inkjet mylar
WAM 33#
blotter
TSI checkout with IPST Robot
CD valuesMD values
Correlation looks ok for a variety of various liners medium, copy paper and plastic film
75
C = 0.349467355b = 0.362403921
STFI (lb/in)) Ring Crush (lb) ET Model error^218.6 61.48 688.8574233 65.02243389 12.54883787
22.43 76.06 837.696652 78.83173899 7.68253705622.069 101.15 1066.474227 91.41300701 94.8090325230.813 118.4 1172.550736 109.5963138 77.5048899231.231 122.4 1350.911968 120.5385411 3.46502940433.467 129.6 1378.359952 125.192706 19.4242404446.08 158.41 1640.9707 157.1106897 1.688207376
35.829 126.49 1421.312619 130.8608967 19.1047379153.631 161.49 1652.173551 166.7145053 27.2954553226.209 98.46 1136.489074 101.3153034 8.15275758840.786 160.2 1556.65121 145.3418956 220.763265321.702 74.34 875.2949972 80.10608446 33.2477300634.443 125.36 1285.666476 121.0113364 18.9108747816.051 61.98 680.5922305 61.16781024 0.659652228.64 98.77 1063.086323 100.264588 2.233793158
22.178 87.82 961.1309916 85.70075308 4.49120749914.288 39 661.461174 57.58578752 345.431497717.155 65.7 882.722197 73.96061475 68.237756097.539 15.15 281.03 26.46449812 128.01786768.599 21.9 331.8952 30.86274479 80.33079429.981 25.47 394.284 36.35707584 118.5284204
14.975 44.99 534.2069 51.11413764 37.505061822.193 74.09 747.9719 73.05644945 1.068226737
1331.101873 sum error RSQ= 0.980453481
model:
RCT = (STFI)^b(Et)^(1-b)
Et = TSIxBW
C = 0.35, b = 0.36
q38
This is the spreadsheet analysis using Excel “Solver”
to fit the model RCT = C x (SCT)b
x (Et)(1-b)
i.e., a “McKee”
style equation for RCT using a combination of compression strength (SCT) and buckling load ( ~ Et which in turn, is TSI x BW)
Data is for a series of linerboards and medium of a wide range of basis weights
64.036.0 )()(35.0 CDTSISCTRCT
Model to calculate an equivalent RCT
Got data ? Send it to me to analyze ! [email protected]
76
Ring Crush vs SCT
y = 3.591x - 1.3082R2 = 0.9371
y = 0.8825x + 12.246R2 = 0.9805
0
50
100
150
200
250
0 50 100 150 200
SCT (lb/in) or 0.35 SCT.36(TSI).64
Rin
g C
rush
(lb/
6 in
) Ring Crush (lb)
Bending model
Linear (Ring Crush(lb))Linear (Bendingmodel )
This shows that the r2
improves from 0.94 to 0.98 if we use a non-linear bending model for RCT: the value is that we get a better prediction for RCT using SCT, BW and TSI_CD
MSE linear = 2.26 lbs
MSE bending model = 1.59 lbs
64.036.0 )()(35.0 CDTSISCTRCT
77
Will this always work ?•
If just using Et = D x (TSI_CD) x BW the assumption of stiffness being proportional to failure may not hold if:
1.
stress-strain curve is changed by increased or decreased ductility of paper
2.
addition of filler, starch, impregnation with polymer, radical change in fiber species
Compression load
Compression Displacement
TSI_CD
RCT 1 –
linerboard
RCT 2 –
waxed linerboard
RCT –
refined linerboard
Comparable
stiffnesses but different failure loads can occur…
78
Relevance to Industry, you, me, the world and everything else..
Current requirement to address the manufacture of recyclable boxes for food and produce transport meeting FDA specs must be produced locally –demand cannot decline with a growing population.
Chinese corrugated production volume surpassed US already in 2008Overseas product and shipping containers are not a threat to this market: food transport and packaging
Mullens here are bogus
Doublewall BC box for furniture shipping Single wall B flute box for
PC monitor
79
Corrugated is not going away
Thank you:Abitibi-Bowater
Awwright !!Let’s make boxes !!
Yeeaahh!!
Hasta la Vista, RCT
!!
Questions, problems, testing, research…
80
Thank you
“serving the paper industry since 1929…to survive is to do research, to thrive is to implement…”
