Predicting Box Compression Strength

Predicting Box CompressionStrengthRoman Popil, Ph.D.Senior Research ScientistGeorgia Tech/IPSTAtlanta, GA.Roman@gatech.edu404 894 97221

How to calculate BCT from componentproperties from medium and linerboard compressionstrengths (SCT or RCT), we can calculate theexpected edge compression strength (ECT) ofcorrugated board From corrugated ECT, bending stiffness, caliper,box perimeter, the BCT can be calculated using:a) Simplified McKee equation (typical)b) Full McKee equation (more accurate )2

Simplest and quickest way to estimate BCT“Maltenfort” equal deformation model for ECT:ECT C 2 SCTliner SCTmedium C 0.7Take-up factor for themedium 1.42 for CfluteSimplified McKee equationfor box compression (easybut not accurate) :BCT (lbs ) C ECT h ZC 5.87Box footprintperimeter (in)Corrugated boardcaliper (mils/1000)3

For better accuracy, use the McKeeequation in full formThis is the equation with constants fitted by McKee et al. using 1963 dataBCT 2.028𝐸𝐶𝑇 0.746 𝐷𝑀𝐷 𝐷𝐶𝐷0.254 0.492𝑍PerimeterThis is the Geometric Mean of the MD and CD bending stiffnesses ( flexural rigidity)The form of the equation is derived from principles regarding the buckling ofa plate under vertical compression :BCT C 𝐸𝐶𝑇 𝒃The best agreement with the data is obtained when this equation is used and thea fit is made to calculate the constant C and exponent b for a given set of similarboxes, the empirical constant(s) are actually functions of panel rigidity and size,McKee et al., also assumed a square box footprint for simplicity.4

Four point bending stiffness method is usedfor DMD and DCD(Actually, the simpler3 point methodmight be betterbecause then this isaffected by shearwhich lowers whenboard is crushed !!)For the panel buckling term in the McKee equation,calculate the geometric mean bending stiffness: 𝐷𝑀𝐷 𝐷𝐶𝐷This term arises from the formula for the “critical buckling load” (aka Pcr)for a simply supported vertically loaded (solid) panel (ex Marsh 1954,FPL) and neglects transverse shear.5

Which is the best way to predict BCT ? RCT or SCT ?Which relates better to ECT ?What problems occur at low basis weights ?How do converting operations affect the BCTprediction ? Which McKee equation to use ?6

Box performance is predicted based on strengthof the components of the board:Whitsitt1983, IPCRelatedECT toRCT:(1) ECT 0.8 * (RCT1 RCT2 αRCTMed) 12For linerboards 42 lb/msf(2) ECT 1.27 * (RCT1 RCT2 αRCTMed) - 6For linerboards 42 lb/msfFigure 1) Whitsitt Relationship of ECT to Composite Ring CrushDifferent equations fordifferent basisweights why?.7

RCT is supposed to predict BCT BCT testRCT measures a combination of buckling and compression failurethe former is a function of board caliper.8

Short Span Compression (SCT) shouldReplace Ring Crush (RCT)1.Short span compression is an easier, quicker and cheapertesting method, is available in automated systems, worksfor all basis weights – RCT does not track basis weight !2. The science behind SCT is sound and established:results correlate with basis weight, refining, fiber quality –RCT is affected by bending and edge rolling leads tomisleading conclusions3. SCT correlates directly with ECT, BCT, box lifetime – RCTcorrelates differently at basis weight classes4. Using SCT instead of RCT makes good sense – rest of theworld thinks so too !!9

SCT is replacing RCT since 1980’s SCT and RCT testing worldwide: USA– Some are using only RCT– other only SCT– Some both, SCT on low basis weight and RCT onhigh basis weight Europe– SCT dominating Asia– RCT almost only Australia– Moving from RCT to SCT10

Manual lab testing is being replaced byautomated “one-touch” reel strip testingRCT is unavailable as a test moduleHowever, SCT, basis weight and TSO usually arefor linerboard mill installations, so 11

The Short Span Compression Test is SCTSTFI SVENSKA TRÄFORSKNINGSINSTITUTET (transl. - SwedishForest Products Research Laboratory) , a part of the RoyalInstitute of Technology in Stockholm Sweden, now renamedas “Innventia AB”)the SCT test method wasdeveloped by Christer Fellersin the late 1970’s as part ofhis PhD at S.T.F.I.,L&W was the 1st tocommercialize the methodThe short span compression test isnot “STFI” (aka “stiffy” (!))Christer gets a Tappi award from Jeffrey Suhling (Auburn12U.)

Short span compression has been shown in the publishedliterature to be a correct measure of compression strengthRCTIncreased buckling for lightweights decreasesRCT with density13Christer Fellers’ slide from Inventia, Sweden

SCT works because over the 0.7 mm shorttest span, there is no bendingShows that specificSTFI (SCT) isindependent ofbasis weight and isa property of thefiber consolidation“Euler” bucklingcurves go as1/(length)214

Real compressive failure ismarked by materialbreakdown and occurs whenthe column height prohibitsbucklingWhen testing a strip, the crease isoften hard to see – looks likenothing has happened15

SCT replacing RCTSCT tracks basis weight, RCT does not and is 1/2 SCT, but error barsare smaller for RCTfrom Popil Tappi PaperCon 201016

Examples of RCT not increasing with other properties as expectedabound in the literatureSCTECTIPC, Whitsitt 1985RCTECT increased in accordance with SCT results.RCT predicted an ECT decrease.17

SCT and RCT comparisonNote the differencebetween STFI andRCT (about 2 X)Why is that ? Bothare supposed to bethe same property !!At very high basisweights (90#) andcalipers, get slip:more surfacecompression –(could increaseclamping pressure)18

Comparison of various compression tests – effect of basisweightExcerpted from:Malstrom, L&W handbook19

Slide from: Christer Fellers, STFI20

This data set shows the only way to change SCTis to change the furnish and beating of fiberskraftsoftwoodHardwood21

Effects of Processes on Compressive strength using SCTExcerpted from“Paper Physics” byNiskanen22

Measuring SCT on the same sample on 2 different labs, anexample, IPST Paper Analysis lab dataA mill measured the same sample 150times in an attempt to improveaccuracy !Std.dev.Millmeasuredvaluen 150 !!c.i.18.42 0.93 (5%)19.41 1.25 (6.4%)Error bars in c.i. decrease as 1/ n, Tappi standard is n 10Overlapping error bars (n 20) indicate no significant difference, butthis high variability (cv %) is bad for quality control23

RCT vs SCT for quality control – “real life” examples46# liner, same mill, same machine, different reelsRCT says Sample G H, I SCT says they are all equal in strength24

RCT vs SCT for quality control – “real life” examples 2Same mill, same product, different reel numbers Error bars are 95% confidence interval about the average values from 10measurements, so for RCT can say D E, C,B,A For SCT can say D E & C. Reels D and B are within statisticalagreement25

But the variation in SCT 7%, is still too high forquality control, why so ?160 mm15mmStrip width is about 2 flocs wideSCT tests a length only 0.7 mmlong across 1 - 2.5 flocs along thestrip length.Mass formation cv% 6 – 8% , SCT is proportional to mass, mass isproportional to modulus, thereforeSCT variation is inevitable !!26

Back to BCT, Assumptions in the simplifiedMcKee – why it is better to use the full form(“b” exponent forms hereensure units correctness)Bending stiffness measurement may not be available so For a corrugated board the bending stiffness is approximatedas a sandwich beam:𝐷𝑀𝐷,𝐶𝐷 𝐸𝑀𝐷,𝐶𝐷 𝑡ℎ2t2hThe medium contributes to D lessthan 5% : 𝐸𝑀𝐷 𝑡ℎ2 𝐸𝐶𝐷 𝑡ℎ2 22𝐸𝐶𝐷 22𝑡 2 ℎ4 𝐸𝐶𝑇 ℎ2The last assumption draws a linear correlation between CDtensile stiffness of the liners ECD and ECTMicrograph by Roman Skuratowicz, Corn Products27

Simplified McKee equation derivationApproximate the bending stiffness to be proportional to ECT times board calipersquared :Note: Measurement of Dis more sensitive to boardcrush than caliper hAssume the typical b ¾ C ’ 𝐸𝐶𝑇 3/4𝐸𝐶𝑇 ℎ21/4Z1/2Chalmers’ DST (gainingpopularity) measures MDtwisting stiffness (bytwisting board strips)which is also a sensitiveindicator of crush damage 𝐶 ′ ECT ℎ𝑍Crushed board recovers caliper but not loss in D, therefore loss inpredictive accuracy in BCT when not measuring bending stiffness28

A box under vertical compressiondLWNote how thepanels bulgeoutwardwhenever d ishigh enoughNote the interflute patternedbuckling of the linerboardsThe McKee equation assumer panel buckling (bulging) . For thiscondition to occur, the boxes have to be high enough to allowthis:d 2 x (L W)/7 or d Z/7Otherwise: BCT C’ECT x Z29

Corrugated board, ECT basics and problemsZDCDLinerboard single-faceFluted mediumDirection assignmentsfor corrugated boardMDLinerboard double-faceECT test clamping fixtures (T 839)“Neck down” sample cutter (T 838)ECT is prone to artifactdepending on type of boardand method of sample prepRolled edgeOK, middlecreaseBowingliners30

Comparison of different ECT methods,lab made A flute boardsT 838 “neckdown” method has the best agreement with predicted ECTfor all samples32

Clamp ECT can produce low results forcrushed or lightweight board33

Video studies at IPST have characterizedinterflute buckling during ECTExperimentalset-upWhen buckling occurs, we can have a better predictor than:34

How to fit the McKee equation constants:1. Get BCT, ECT , Bending stiffness DMD and DCD and perimeter Z data for aset of similar boxes of interest. At least 6 data points are required coveringa range of BCT values. Enter as data in separate columns into Excel.2. Keep values for the McKee C and b in a separate area of the spreadsheet.3. Assume the usual McKee constants for C 2.028 and b 0.75, calculate ina separate column the predicted McKee BCT using:4. Calculate in a separate column, ΔBCT the absolute value ofthe differences between actual and predicted McKee BCT’s.5. Calculate the sum of the ΔBCT errors in a separate cell.6. Use Excel Solver function to Minimize the sum ΔBCT error by changingthe cells containing the McKee C and b function returns new C and b .35

Fitting the McKee constants to improve prediction,an exampleExcel Solver function window pop-up menu tominimize the sum of errors by fitting McKee C and bSpreadsheet set-up with raw data and McKeepredicted BCT’s1A2345 Sample ID678 Box 19 Box 210 Box 311 Box 412 Box 513 Box 614 Box 715 Box 816 Box 917 Box 101819BCDEFGHBCTlbsECTlb/inD MDlb -inD CDlb .0097.3283.811.6563.9840.75161.6536.2958.89sum of errors IJMcKee C 1.87028McKee b 0.791213original .41833.37907.23953.05McKee fit constants kept in thesecells , start with 2.028 and b 0.75 , these become changed bySolverabsolute value of differencebetween predicted and actualBCT values ABS(predicted -McKee prediction is calculatedusing the constants in the box :McKee pred. J 1*C7 J 2*(SQRT(D7*E7) (1 J 2)*F7 (2* J 2-1))576.088575736

Summary: Predicting BCT Best to use the SCT of liners and medium , calculate the“Maltenfort” ECT, plug in Tappi board Caliper h andperimeter Z into standard McKee BCT formula Better to include Bending Stiffness D of board, useMcKee full form equation, and check Maltenfort ECT withactual values, (there can be ECT problems at small orhigh basis weights, low pin adhesion values etc.) Use box and board data to fit McKee equation constantsC and b for the best predictive model for sets of similarstyle boxes37

Thank you!Send: testing samples, inquiries of interest, to Roman@gatech.edu404 894 9722500 10th St NW., Atlanta, GA., 30332“serving the paper industry since 1929 to survive is to do research, butto thrive is to implement ”38

8 Box 1 956 42 141 94.0 48 924.25 31.75 759.31 9 Box 2 1150 56 135 90.0 48 1150.00 0.00 931.97 10 Box 3 1100 47 136 90.7 48 1002.68 97.32 818.72 11 Box 4 975 48 163 108.7 48 1058.81 83.81 870.27 12 Box 5 967 44 148 98.7 48 968.65 1.65 795.85 13 Box 6 836 41 136 90.7 48 899.98 63.98 739.01