ME 8883 Physical Properties of Paper MeasurementTear Strength testTear strength theoryTear strength theoryTear strength theoryTear resultsTear strength detailReporting tear resultsPaper elastic constants digressionBursting test theoryBurst test theoryBurst testsBurst testsME 8883 Physical Properties of Paper Tear Burst Fold1ME 8883 Physical Properties of Paper MeasurementTear, Burst, FoldME 8883 Physical Properties of Paper Tear Burst Fold2ME 8883 Physical Properties of Paper Tear Burst Fold3Tear Strength test• test measures the energy to propagate an existing crack throughpaper, the path it takes is often variable especially in the CD• not clear how the test relates to end-use: resistance to tearing of the pages of a book when turned ? Press room belief: Elmendorf tear is an indicator of runnability (web breaks) • 63 mm specimen length in the test direction, secured by 2 clamps, slit is made with knife leaving 43 mm to tear in the test • Tear measures the rupture of fibers along the tearing line and the pulling out of fibers that cross the tearing line• fiber pull-out requires more work than breaking a fiberME 8883 Physical Properties of Paper Tear Burst Fold4Tear strength theoryThe total work tear work T is:fiberaoutpulltoworkaverageWfiberabreaktoworkaverageWfibersoutpulledofnumbernbrokenfibersofnumbermnWmWTfrfr−−−−+=• fiber strength enters as Wr, fiber length contributes as:1. number of fibers crossing tear line is proportional to fiber length2. fiber rupture occurs when # of fiber-to fiber bonds > fiber strengthME 8883 Physical Properties of Paper Tear Burst Fold5Tear strength theory• Shallhorn and Karnis (1979, 1994) assumed that fiber pull-out is resisted by frictional forcesfibersofstrengthtensilelrWfailsomesobondedtightlyarefibersifButlengthfiberlradiusfiberrareasurfacefiberperforcefrictionallrWffffrff−=−−−=στσπτπτ2234212/:12/ME 8883 Physical Properties of Paper Tear Burst Fold6Tear strength theoryNiskanen et al (1996) : Bonds open in random sequence competing with fiber rupture so fracture energy per fiber dependon the fraction of broken fibers Nf()2:mod:4/:4/,0lim1ln4ffffdebondffffdebondfrdebondfdebondrflTelShalhornthewithdiasgreesthisNotelWTthenlLNfibersstrongofittheInNlNLdebondingfiberforenergyWrupturefiberforenergyWdebondedlengthfiberaverageLWLWNTα=→→−=−−−+=ME 8883 Physical Properties of Paper Tear Burst Fold7Tear resultsME 8883 Physical Properties of Paper Tear Burst Fold8Tear strength detailME 8883 Physical Properties of Paper Tear Burst Fold9h∆dFhgmW ×=∆=Center of mass of pendulum at test startCenter of massThe Elmendorf tear tester measures the amount of work done to tear precut plies of a specimen, the change in height of the pendulum after it “tears” through the specimen is detected and converted to a tear strengthME 8883 Physical Properties of Paper Tear Burst Fold104 plies for handsheets, newsprint, copy paper16 plies for very light papers2 plies for linerboardME 8883 Physical Properties of Paper Tear Burst Fold11Enter number of plies tearingActuate sample clampRelease pendulum when readyReadout in mN is adjusted for the number of plies enteredME 8883 Physical Properties of Paper Tear Burst Fold12Pneumatic clampCreate a notch in the bottom of the sample with the knife prior to releasing the pendulumME 8883 Physical Properties of Paper Tear Burst Fold13Electrically operated punch for tear samples CD tear specimensME 8883 Physical Properties of Paper Tear Burst Fold14After the pendulum is released the tearing force is displayed in mNME 8883 Physical Properties of Paper Tear Burst Fold15ME 8883 Physical Properties of Paper Tear Burst Fold16Reporting tear resultsME 8883 Physical Properties of Paper Tear Burst Fold17Paper elastic constants digressionRecall Hooke’s law for an orthotropic solid with 3 planes of symmetry (e.g. paper):Recall this is the stiffness matrix and we measure the stiffnesses directly using ultrasonicsME 8883 Physical Properties of Paper Tear Burst Fold18ME 8883 Physical Properties of Paper Tear Burst Fold19velocityshearplaneinVCDinvelocitysoundVMDinvelocitysoundVVGVEVE12221121212211222222211221111)1()1(ρννρννρ=−=−=calipersoftweightbasistcalipersoftVVCijijij=∆==ρρ2So we can approximate C11as: 11211211119.0)1( CCE ≈−=ννME 8883 Physical Properties of Paper Tear Burst Fold20The constants and combinations from ultrasonic measurements can be correlated to standard physical tests:•C11 MD tensile strength•C22 CD tensile strength• C33 ZD tensile strength, internal bond strength•C11 + C22 Bursting strength• C11 + C55 Flutability• C22 + C44 Combined board performanceBurst test is a combined property testSchematic of the burst test conceptME 8883 Physical Properties of Paper Tear Burst Fold21ME 8883 Physical Properties of Paper Tear Burst Fold22Bursting test theoryConsider a paper membrane distended into a spherical sector:In-plane strain:Arc:In 1DME 8883 Physical Properties of Paper Tear Burst Fold23Burst test theoryh is the thickness of the membrane, assume spherical revolution, then Pressure behind the distended membrane: In-plane stresses Taylor series expansion…ME 8883 Physical Properties of Paper Tear Burst Fold24Burst test theorySquare root of distension Sum of in-plane stressesME 8883 Physical Properties of Paper Tear Burst Fold25{}{}11212212111222122122222221111221111111EEEEννενεννσενεννσ=+−=+−=Use the above relationships into the pressure behind a membrane expression:12212112211212111/16ννννψεψ+++==vEahPMD and CD tensile strengths, s –MD stretch at failure, R diaphragm curvatureAlso : Burst test theoryME 8883 Physical Properties of Paper Tear Burst Fold26Burst testsFor thick samples, there is a bending component in the stresses, so there is a difference in felt and wire side burst test values especially more so in laminated sheetsME 8883 Physical Properties of Paper Tear Burst Fold27ME 8883 Physical Properties of Paper Tear Burst Fold28Burst testsME 8883 Physical Properties of Paper Tear Burst Fold29“CA” type Mullen for testing handsheets and paper up to 100 psi. Calibration foils are 30, 65 and 110 psi Hydraulic sample clamp actuated by moving rings down Electronic display of max burst pressure in psiNote:After burst you mustpull the lever back to neutral, otherwise the diaphragm will burst !!Rubber diaphragm bulges outward as glycerin gets pumped into the chamberME 8883 Physical