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ME 883 Physical property measurements - Lecture 3Tensile StrengthPaper load elongation curvesPaper on a microscopic scale is an agglomeration of bonded fibersUltrasonic measurementsUltrasonic measurementsLoad- elongation curveCalculations from the load displacement curveDerivation of Tensile stiffness modulus relationshipNotes on tensile strengthSome useful unit conversionsDepending on your sample size you may have to do 4 inch span tests rather than 7 inchTappi method is very specific about sample cutting – use this cutter for 1” wide samplesCutter for 15 mm wide 4 inch span samplesEnable IEEE 488 interface run up Series IX software, select the right tensile test for your set-up in Methods e.g. tensile 05Proceed to go to the test screen after you are satisfied with the test method parameters, you start the tensile test from thiThe L&W Alwetron is customarily used for 4 inch span handsheetsAlwetron useME 8883 Physical propoerties paper - tensile1ME 883 Physical property measurements - Lecture 3Tensile StrengthMechanics Overview Tensile tests – their significance and use Interpretation and analysis of the load displacement curve Equipment pragmaticsME 8883 Physical propoerties paper - tensile2Mechanics Overview (101) Study of the deformation and failure behavior of materials, the concepts of stress and strain and the relationship between them are key to describing that behavior.Typical tension test:Screws supporting the cross head turn increasing the force distributed over the sample cross section area A.Force divided by area is the stress:σ = F/AThe displacement l of the stressed sample normalized to the dimension prior l0to stress is the strainε = (l – l0)/l0ME 8883 Physical propoerties paper - tensile3Elastic Behavior•Material Response is instantaneous•Loading and unloading path are the same•All deformation energy is stored in the material•Deformation is completely recoverableεσE=Hooke’s lawIdealized case, in one dimension ÎA more realistic stress strain curve can be like this, Area contained in by the curve in the return path is referred to as the hysteresisME 8883 Physical propoerties paper - tensile4Paper load elongation curvesNewsprint has mechanical fibers in the furnish, shorter, more lignin, less bondingKraft is all chemical pulp, longer fibers, better binding, especially with beating which beating fibrillationWhen dealing with solids, stresses in one direction can lead to components of stress in other directions, similarly strains in one direction will affect strain in another direction ME 8883 Physical propoerties paper - tensile5ME 8883 Physical propoerties paper - tensile6ME 8883 Physical propoerties paper - tensile7ME 8883 Physical propoerties paper - tensile8Paper on a microscopic scale is an agglomeration of bonded fibersME 8883 Physical propoerties paper - tensile9If you cut a specimen form a roll of paper, be aware that the paper has three principal directions1,13,32,2ME 8883 Physical propoerties paper - tensile10Hooke’s law for an orthotropic solid i.e. paper For paper, we are mostly concerned with C11 – MD tensileC22 = CD tensileC33 = out of plane compressibilityC44, C55 = out of plane shearME 8883 Physical propoerties paper - tensile11Ultrasonic measurements CDinvelocitysoundCMDinvelocitysoundCwhereCECEyxyyxx)1()1(2112221122ννρννρ−=−=Ultrasonic measurementsl2-D Plane Stress⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧xyyyxxxyyyxxQQQQQγεετσσ66221212110000126621121121122112222221121111111GQEQEQEQ=−=−=−=υυυυυυυ22211112EEυυ=ME 8883 Physical propoerties paper - tensile12ME 8883 Physical propoerties paper - tensile13From Cox Model)2(161)46(161)46(1612661221222111avEQQaavEQaavEQffffff−==+−=++=We measure Q’s in ultrasonics22V1EQρν=−=There is confusion in the literature on this. Some think the3-D stress state stiffness, C, is involved. THIS IS INCORRECTNote this is an ideal case and only holds in a loose senseME 8883 Physical propoerties paper - tensile14E11= EMD~ C11E22= ECD~ C22E33= EZD~ C33Mechanical tests measure the stiffnesses in the principal directions as indicatedME 8883 Physical propoerties paper - tensile15Shear properties we measure using the ultrasonic devices in 351 and 336Out of plane ZD-MD shear stiffness C44Out of plane ZD-CD shear stiffness C55In-plane MC CD shear also known as G12ME 8883 Physical propoerties paper - tensile16Tensile strength test definitions• clamp strips of paper 15 or 25 mm wide between 2 jaws of an extensometer, subject the strips to a specified rate of strain• Tensile strength N/m – force required to break the specimen, expressed per meter width• Tensile Index Nm/g = tensile strength (N/m)/grammage (g/m2) a characteristic of the material• Breaking length m = length in meters of hanging a paper strip which can support its own weight = 102X tensile index• Elongation at break % = extension at break expressed as a percentage of the gauge length (free span between clamps) • Tensile energy absorbed (TEA) J/m2= amount of work done to break the specimen, calculated form the area under the load-elongation curve and the area of the test stripME 8883 Physical propoerties paper - tensile17Load- elongation curveLoadElongation∆F∆lTensile stiffness,Modulus of elasticity from the linear slopeFmaxME 8883 Physical propoerties paper - tensile18Calculations from the load displacement curvetTSEelasticityofModuluslblFTSstiffnessTensilellElongationwbFindexTensile=∆∆=∆=×=,,00maxstiffnesstensileTSelasticityofModulusEtestpiecetheoflengthoriginallpaperforambiguoustestpiecetheofthicknessttestpiecetheofwidthbweightbasistheiswwhere=====0)!!(ME 8883 Physical propoerties paper - tensile19Derivation of Tensile stiffness modulus relationshiptElblFxyTScurveelongationloadofslopetheisTSwidthunitperstiffnessTensileltblFlAlFEstrainandstressofsdefinitionbyELawsHookeFrom×=∆×=∆∆=∆××=∆===000:,::'εσεσRemember that for “t” we must use either “soft” caliper or mechanical equivalent caliper !!ME 8883 Physical propoerties paper - tensile20Notes on tensile strength• tensile strength depends on fiber strength but mostly on degree of bonding between fibers• faster rate of elongation results in higher tensile strength, log relationship with rate• CD tensile strength for machine paper is about half that in the MD, use 25 mm strip width, 7 inch gap for paper samples, for handhsheets have to use 15


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