GT ME 8883 - ME 8883 Physical Properties of Paper Measurement - Lecure 16 flat crush torsion pendulum

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ME 8883 Physical Properties of Paper MeasurementFlat crush of corrugated boardConcora flat medium crushConcora flat crushFlexible beam compression testerTorsion pendulum introductionCalculation of the twisting stiffness D66Torsion pendulum detailsCalibration procedureTorsion pendulum calibrationME 8883 Physical Properties of Paper MeasurementLecture 16: Corrugated Board Flat Crush and the Torsion PendulumFlat crush of corrugated board• We use 3 x 3” samples having good clean edges• Use the L&W compression tester, measure the peak load, report the peak as psi • Using the Instron compression tester, the load compression curve can be interesting first noted by R.A. Stott 1968LoadCompression testers are set to detect the peak load based on the % “fallback of load, for flat crush thois can be misleading…Hard Caliper Measurements (after 24hours conditioning at Tappi 402) 4.14.34.54.74.95.15.3a flute crushed A crushed Ccaliper (mm)rolling nip set at 70% of uncrushed board caliper C fluteNotice that C flute is not as affected by crushing as A flute boardLoad displacement curves for C crushed -200204060801001201401601802000 0.02 0.04 0.06 0.08 0.1 0.12 0.14Displacement (inches)Load (lbs)2545.954.466.974.7Load displacement curves for C flute boards0501001502002500 0.02 0.04 0.06 0.08 0.1 0.12 0.14Displacement (inches)Load (lbs)107107.5110128.3134.5136.6Note the large first peakLoad-displacement flat crush Crushed board shows a diminished first peak The value of the first peak is called“hardness”Still a large max peak despite crushingLoad displacement curves for crushed A flute boards051015202530354045500 0.02 0.04 0.06 0.08 0.1 0.12 0.14Displacement (inches)Load (lbs)16.61718.1818Load displacement for A flute -200204060801001201401600 0.02 0.04 0.06 0.08 0.1 0.12 0.14Displacement (inches)Load (lbs)7884.588.195.595.5First peak is drastically reduced in crushed boardA flute case is much clearerFirst peak is prominent in an uncrushed boardFlat crush hardness and R551030507090110130A flute Crushed A flute C Flute Crushed C fluteFlat crush lbs010002000300040005000600070008000Transverse shear rigidity N-mFlat crush hardnessTransverse shear rigidityNote the hardness correlates with the transverse shear rigidity measured by the torsion pendulum – more on this later in this lecture….This is also known as the “Concora” medium crush testMedium strips are sent through a Concora fluterThe corrugated medium strips are adhered to a supporting linerboard with double sided tape using a “rack” and “comb”arrangement to ensure good adhesion Samples are tested for flat crush using a flexible beam type compression tester, load is read from a peak beam deflection holding micrometerSamples are prepared and tested 5 to 8 seconds upon emerging from the fluter which is heated to 350 deg FConcora flat medium crush Fluter consists of mating corrugating wheels heated to 350 deg F, strips of medium 0.5 x 6” length along the MD, are passed through the fluterStrips of medium become corrugated exiting hereConcora flat crushImmediately exiting the fluter, the strips are paced in the rack andcomb arrangement and the exposed flute tips are adhered to an adhesive tape strip using the rubber rollerFlexible beam compression testerLoad is measured by a peak holding micrometer gauge, as platen moves downward the deflection in creases then stops momentarily (first peak) then increases and finally starts to decrease stop the test after the second peakTorsion pendulum introduction We are interested in the torsional stiffness of corrugated board, which we will represent as an orthotropic plate. For the plate, we are interested in three curvatures and two transverse shear deformations. The constitutive equation for the plate is written as ⎪⎪⎪⎭⎪⎪⎪⎬⎫⎪⎪⎪⎩⎪⎪⎪⎨⎧⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=⎪⎪⎪⎭⎪⎪⎪⎬⎫⎪⎪⎪⎩⎪⎪⎪⎨⎧xzyzxyyyxxxzyzxyyyxxRRDDDDDQQMMMγγκκκ55446622121211000000000000000000 (1) where the distributed moments and shear forces, κij are the curvatures, γij are the transverse shear strains, Dij’s are the bending stiffnesses, and Rii are the shear rigidities. Equation 1 is the starting basis for calculating the potential effects of transverse shear on box properties The properties of interest for the immediate current discussion are the three shear terms, D66, R44, and R55. For a sandwich structure similar to corrugated board the twisting bending stiffness is approximately 26621thGDxy= (2) where Gxy is the in-plane shear stiffness of the liners, t is the thickness of the liners, and h is the thickness of the sheet.MDCDZDMDZDCDZDLTθTCorrugated board directions There is less resistance to shear in the MD dirctionof corrugated boardSo MD transverse shear rigidity is affected by flute crushingThe twisting motion of corrugated board can be used to determine transverse shear rigidity R55θTk =Torque/angle of rotation = torsion stiffnessThere have been several analytical models in the literature for the prediction of torsional stiffness of corrugated board, we have selected the one proposed by E. Reissner “On Torsion and Transverse Flexure of Orthotropic Elastic Plates”, Journal of Applied Mechanics, 47, pp 855-860, (1980). The plate solution for the torsional problem can be expressed as MDissnerkbRDLbDT=⎟⎟⎠⎞⎜⎜⎝⎛+=2556666Re1214θ (3) where the length of the plate L is assumed to be large compared to the width b and thickness. In our procedure, L is 24 cm and b is 7.6 cm or less.Calculation of the twisting stiffness D662,2,2266222211thGDthEDthEDxyyx≅≅≅where Ex, Ey are the in-plane moduli of the liners and Gxy is the in-plane shear modulus of the liners, D11, D22 in-plane bending stiffness of the combined board and D66 is the combined board twisting stiffness as before. Moreover, Baum et al., ( “Orthotropic elastic constants of paper” Tappi Journal 64, 97-101 (1981)) showed a relationship between the liner in-plane shear modulus and the in-plane moduli to be: yxxyEEG 387.0≅ 221166387.0 DDD ≅Side View of a Generic Sandwich StructureFigure 1corefacescdhtThese can be measured form the four point bending stiffness So:Use L&W 4 point bending stiffness for D11and D22 for corrugated board Get a k(MD) from the torsion pendulumFor k(MD) the boards of length L width b, between clamps are cut along the MD, clamped portions have metal dowels to prevent


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