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Fracture toughness. SCAN-P 77:95 Accepted Papers and boards. Constant rate of elongation method (1,7 mm/s)

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Acceted 995 Paers and oards racture toughness Constant rate of elongation method (,7 mm/s) 0 Introduction The fracture toughness may e imortant for the rediction of e reaks in the re-inder, in a rinting
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Acceted 995 Paers and oards racture toughness Constant rate of elongation method (,7 mm/s) 0 Introduction The fracture toughness may e imortant for the rediction of e reaks in the re-inder, in a rinting ress or in other situations here in-lane fracture occurs during the manufacture and converting of different aer roducts. This SCAN-test Method descries one ossile measuring and calculation rocedure for determining the fracture toughness. The measuring rocedure consists of to arts; the tensile testing rocedure and the fracture toughness testing rocedure. In the to rocedures, the test san length is 00 mm and the rate of elongation is,7 mm/s. The recommended test iece idth is 5 mm in the tensile testing rocedure and 50 mm, ith a 0 mm notch in the centre of the test iece, in the fracture toughness testing rocedure. The rocedure takes advantage of the high testing rate and the high calculation caacity of modern comuterised tensile testing machines. Note This method is ased on ISO 94-3, hich is an alternative method to ISO 94- (EN ISO 94-) for the determination of tensile roerties. ISO 94-3 differs from ISO 94- in the folloing resects: The tensile stiffness and tensile stiffness index are included. The test san length, i.e. the distance eteen the claming lines, has een changed from 80 mm to 00 mm, irresective of the kind of samle to e tested. The rate of elongation has een increased in order to reduce the testing time and make it ossile to test a larger numer of samles ithin a given time eriod. The calculation rocedure is comlicated and must e comuterized (5.3). rom the tensile test data, a relationshi eteen J-integral value and elongation is estalished. The critical elongation is evaluated from the fracture toughness test data. rom a knoledge of the critical elongation, the critical J-integral value, hich is the fracture toughness, is evaluated. Page Scoe This SCAN-test Method secifies a method for measuring the fracture toughness of aers and oards, using a tensile testing machine oerating ith a constant rate of elongation. The Standard is alicale to all kinds of aer and oard ut not for lo density aers, such as cree aer, or for corrugated fireoard. The theoretical derivation for the calculation of fracture toughness is descried in the Annex. References ISO 87 Paer, oard and uls Standard atmoshere for conditioning and testing and rocedure for monitoring the atmoshere and conditioning of samles (EN 087) ISO 536 Paer and oard Determination of grammage (EN ISO 536) SCAN-P 9 Paers and oard Identification of machine and cross direction ISO 94-3 Paers and oard Determination of tensile roerties Constant rate of elongation method (00 mm/min) (SCAN-P 67) Note SCAN-test has ithdran a numer of test methods and refers instead to the corresonding ISO and/or EN Standards. 3 Definitions or the urose of this Method, the folloing definitions aly: 3. racture toughness, The incremental ork done er notch-length groth, in a test iece containing a notch, hen the test iece is strained to a critical elongation. 3. racture toughness index, The fracture toughness divided y grammage. 3.3 Elongation, δ The increase in length of a test iece. 3.4 Critical elongation, δ c The elongation at the maximum force. Note The definitions of the terms used in the tensile test are given in ISO Princile rom the tensile test data, otained from un-notched test ieces in accordance ith ISO 94-3, a J-integral versus elongation curve is constructed for a notched test iece of a given size. Note The tensile curves in oth machine direction (MD) and cross direction (CD) are needed to otain the J-integral versus elongation curve in any of the to directions. A notched test iece is strained to reak and the critical elongation is determined. The fracture toughness is defined as the J-integral value at the mean critical elongation, igure. J-integral, J/m A δ c h a W δ / δ / Elongation, δ, m igure. rom tensile test data, a J-integral-elongation curve (A) is constructed. The mean critical elongation (δ C ) determines the critical J-integral value, hich is the fracture toughness. 5 Aaratus 5. Tensile testing machine, as descried in ISO The idth of the to clams shall e easy to change eteen 5 mm and 50 mm. Note Building locks can e used instead of changing the clams. In that case, only the clams ith a idth of 50 mm are needed, and to uilding locks are used to centre the 5 mm ide test ieces during the tensile test. To e ale to centre the test iece, each uilding lock shall have a idth of 7,5 mm. Page 3 5. Anti-uckling guide, made for instance of steel or of aluminium, to kee the notched test ieces flat during the test. The guide shall have to arallel, flat and smooth surfaces ith a lo friction, and cover a length of 30 mm and the total idth in the centre of the test iece. Before the fracture toughness test, the smooth surfaces shall e rought into contact ith the test iece ith a force of (0,6 ± 0,) N. The distance shall then e locked and ket locked during the test. 5.3 Comuter, means for numerical calculation of the fracture toughness in accordance ith the equations given in the Annex. 5.4 Device for cutting the test ieces, ith test iece idths of 5 mm and 50 mm. 5.5 Device for making a notch in each 50 mm ide test iece. The notch in each test iece can e made y means of a shar lade, referaly mounted in a unch ress. The notch shall e (0 ± 0,) mm and laced in the centre of the test iece, erendicular to the long edge of the test iece, see igure. 6 Caliration and adjustment of aaratus The aaratus shall e calirated according to instructions given y the manufacturer of the testing aaratus. The test san and the rate of searation of the clams shall e calirated according to ISO Check that the antiuckling guide (5.) is loading the test iece ith a force of (0,6 ± 0,) N y using a knon eight or a force measurement instrument. If necessary adjust the loading force. 7 Samling and rearation of test ieces 7. Samling. The samling rocedure is not covered y this Method. 7. Conditioning. Condition the samles as secified in ISO 87. If the fracture toughness index is to e calculated, determine the grammage of the samles as descried in ISO Prearation of test ieces for the tensile testing. The rearation of test ieces for the tensile test is descried in ISO Prearation of test ieces for the fracture toughness testing. Test ieces for the fracture toughness test are reared in the same ay as for the tensile test. Hoever, the test iece idth for the fracture toughness test is (50,0 ± 0,) mm. Cut a sufficient numer of test ieces to enale at least 0 tests to e made in oth the MD and in the CD. Make a notch in each test iece ith a notch-length of (0 ± ) mm y using the device for making a notch (5.5). Note Several test ieces can e cut simultaneously rovided the test ieces formed fulfil the requirements secified aove and that the test ieces formed give the same results as test ieces cut singly. 8 Procedure and evaluation of results 8. Tensile test. The urose of the tensile test is to construct a reresentative mean force-elongation curve for the MD and CD, from hich the material arameters can e calculated. or the tensile test, follo the instructions given in ISO The test iece idth is 5 mm. Evaluate the nominal elongation, the nominal force and the maximum sloe from the test data otained as follos: igure shos the rincile for calculating roerties from the tensile test. The figure illustrates ho individual curves hich are not reresentative for the material roerties of the samle are deleted efore the construction of the mean curve. our curves are shon to illustrate the rincile. All calculations are to e made from zero elongation of each curve, i.e. the oint here the tangent of the curve, ith a sloe equal to the maximum sloe of the curve, intersects the elongation axis. Note This test, like other mechanical tests, is very sensitive to changes in the moisture content of the test iece. Handle the test ieces carefully and never touch ith the are hand the art of the test iece to e laced eteen the clams. Kee the test iece aay from moisture, heat and other influences that may change its moisture content. Page 4 orce, 9 Calculation N Tangent to the mean curve. The maximum sloe is c 90% of Rejected cu rve. 3 4 δ Τ δ Τ Mean curve δ N Elongation, δ The calculation rocedure to otain the arameters must e comuterized. The theoretical derivation for the calculation of fracture toughness is descried in the Annex. or aer and oard, calculate the results searately for the MD and CD. In order to secify the kind of result reorted, the suffixes MD and CD shall e used to exress MD and CD resectively. As an examle, MD is used for fracture toughness index in the MD,, CD is used for fracture toughness index in the CD. igure. Princile for calculating roerties from the tensile test. δ N c N δ T is the nominal elongation; is the maximum sloe; is the nominal force; is the mean elongation at reak. Calculate the mean elongation at reak, δ T. Delete those tensile curves hich have an elongation at reak less then 90 % of the mean elongation at reak (Curve 4 in igure ). Determine the smallest elongation of the remaining curves. The smallest elongation is named the nominal elongation, δ N, (Curve in igure ). Determine the mean force versus elongation curve y means of the remaining curves (y calculating the mean force at each elongation increment u to the nominal elongation). Determine the nominal force, N, of the mean curve as the force at the nominal elongation. Determine the maximum sloe, c, of the mean curve referaly y linear regression analysis over a numer of force-elongation values. The elongation increment shall then e 0, mm and the linear regression shall contain at least 0 force-elongation values. 8. racture toughness. Make sure that the antiuckling guide (5.) is in function. Ensure that the test iece does not end hen it asses over the to antiuckling guide surfaces. Perform the fracture toughness test using the notched test ieces reared as descried in 7.4 and igure. Test at least 0 test ieces in the MD and 0 in the CD. 9. Tensile testing Tensile data are needed for the evaluation of fracture toughness. To enale strength calculations y means of fracture toughness results, reort tensile stiffness according to ISO 94-3 and arameters and Φ according to equations [A3] and [A8]. 9. racture toughness The fracture toughness, J Ic, is otained from the equation: J Ic here ( β) E h ( ν ν ) h f+ σ0 0 + Φ ( ε ) β ε0 h is the fracture toughness, in joule er metre. The other symols are descried in the Annex. + f [] 9.3 racture toughness index Calculate the fracture toughness index,, from the folloing equation: J JIc 000 Ic here [] is the fracture toughness index, in joulesmetres er kilogram; is the grammage, in grams er square metre. Page 5 0 Reort The test reort shall include reference to this SCAN-test Method and the folloing articulars: (a) () (c) (d) (e) (f) date and lace of testing; identification mark of the material tested; the direction of the test; the test results; the coefficient of variation of the results; any dearture from the rocedure descried in this SCAN-test Method and any other circumstances that may have affected the result. Precision. Reeataility Results from reeated measurements carried out at seven laoratories, under normal laoratory conditions using test ieces from the same gross samle, have a mean coefficient of variation ithin las for fracture toughness index as follos: Paer grade Grammage, g/m Direction Mean fracture toughness index, Jm/kg Mean coeff of variation, % * Kraft liner 00 MD 4,5 9 CD 0,7 6 Nesrint 45 MD 6, CD 4,5 0 Coy aer 80 MD 0,9 0 CD 7,9 4 * The laoratories received a diskette containing the rogram for calculating the coefficient of variation of the fracture toughness.. Reroduciility Seven laoratories tested the same aer and oards. The reroduciility, exressed as coefficient of variation eteen las, for fracture toughness index as as follos: Paer grade Grammage, g/m Direction racture toughness index, Jm/kg Coeff of variation, % Kraft liner 00 MD 4,5 8 CD 0,7 4 Nesrint 45 MD 6, 6 CD 4,5 6 Coy aer 80 MD 0,9 7 CD 7,9 Literature. Wellmar, P., ellers, C., Nilsson,., and Delhage, L. Crack ti characterization in aer (Acceted for ulication in Journal of Pul and Paer Science.) Page 6 Annex Symols and calculation rocedure A. Symols used in the calculations A.. Un-notched test ieces δ δ N δ T N c U k A(E) l E MD E CD α α MD α CD Φ f f E E is the elongation, in metres; is the nominal elongation, in metres; is the mean elongation at reak, in metres; is the force, in netons; is the nominal force, in netons; is the maximum sloe of the mean force versus elongation curve, in netons er metre; is the area under the mean force versus elongation curve, in netonmetres; is a material arameter; is a material arameter; is the anisotroy in tensile stiffness; is the tensile stiffness in MD, in netons er metre (ISO 94-3); is the tensile stiffness in CD, in netons er metre (ISO 94-3); is a material arameter; is a material arameter in MD; is a material arameter in CD; is the test san length, in metres; is a material arameter; is a dimensionless function; is a dimensionless function; is the tensile stiffness erendicular to the loading direction, in netons er metre (ISO 94-3); is the tensile stiffness in the loading direction, in netons er metre (ISO 94-3). A.. Notched test ieces W is the idth, in metres; h is the test san length, in metres; a is the notch length, in metres; δ c δ o νν (0,93) σ c β β σ 0 ε 0 V J V β CV J is the critical elongation, in metres; is the zero elongation, in metres; is the roduct of the Poisson s ratios in MD and CD; is the critical stress, in netons er metre; is a arameter, in metres; is the mean value of the arameter β, in metres; is the reference stress, in netons er metres; is the reference strain, in metres er metre; is the fracture toughness, in joules er metre; is the fracture toughness index, in joulemetres er kilogram; is the variance in fracture toughness, in (joule er metre); is the variance of the arameter β, in square metres; is the coefficient of variation of the fracture toughness, as a ercentage; is the grammage, in grams er square metre. The calculation and the evaluation rocedures are comlicated and must e comuterized. The aove symols are used in the theoretical derivation for calculation of the fracture toughness. Page 7 A. Calculation rocedure A.. Work of elongation Calculate y numerical integration, for the mean force versus elongation curve, the area U under the curve from zero elongation u to the nominal elongation, δ N, igure and equation [A]: δ N U ( δ) d δ 0 [A] A.. Material arameters it the mean force versus elongation curve from zero elongation u to the nominal elongation to equation [A] y calculating the material arameters and k from equations [A3] and [A4]: δ + k c c N N δ N c U N NδN + c δn N k c N c [A] [A3] [A4] A..3 Anisotroy, arameters and functions in MD and CD Calculate the anisotroy in tensile stiffness, A(E), from the folloing equation: Calculate the material arameter Φ in MD and CD according to the folloing equation: When MD is the test direction, use α α MD When CD is the test direction, use α α CD ( )( ) Φ k l α α α + 0, 94 [A8] Calculate the dimensionless functions f and f according to the folloing equations: f 09, E 0567, E [A9] f 05, + 05, tanh( 006, ) [A0] Note The functions f and f have een determined y using finite element analysis and aly only to this test iece geometry. or other geometries, ne calculations have to e made. A..4 racture toughness Record the force-elongation curve for each test iece, igure 3. Determine the zero elongation, δ o, i.e. the oint here the tangent of the curve, ith a sloe equal to the maximum sloe of the curve, intersects the elongation axis. Determine for each test iece the critical elongation. orce, N AE ( ) E MD E [A5] CD Calculate the folloing material arameters: When the test direction is MD, use the folloing equation: α MD 093, [A6] AE ( ) When the test direction is CD, use the folloing equation: α CD ( ) 093, AE [A7] δ o δ c Elon gation, m igure 3. orce-elongation curve for a fracture toughness test iece. δ o δ c is the zero elongation; is the critical elongation. Page 8 Determine for each test iece, the critical stress, σ c, y numerical inversion of the folloing equation: δc νν ν ν σ σ c h h c + Φ [A] E E Calculate for each test iece the arameter, β, from the folloing equation: h β ( ν ν ) E σ c Calculate the mean value, β, of the arameter β. [A] Calculate the reference stress, σ 0, from the folloing equation: A..5 Error estimation The error in the fracture toughness value consists of to factors, the error in the mean force versus elongation curve and the error in the critical elongation. Assuming that the error in this curve is negligile, the error in the fracture toughness is estimated in the folloing ay: Calculate the variance, V β, and mean value, β, of the arameter β. Estimate the variance of the fracture toughness from the folloing equation: VJ 4 h β E h f + Φ σ0 ( ) ( ε0 ) ν ν β + β f V 0 h β ε [A5] σ 0 ε0 E ( ν ν ) [A3] Calculate the coefficient of variation, CV J, of the fracture toughness, as a ercentage, from the equation: Note or aers, the reference strain, ε 0, is set to e 0,003, a value that is not critical for to the calculated fracture toughness. inally, calculate the fracture toughness, J Ic, from the folloing equation: CVJ VJ 00 [A6] JIc J Ic ( β) h E ( ν ν ) h + σ + Φ ( ε ) f β f ε0 h [A4] Method SCAN-test Methods are issued and recommended y KCL, PI and STI-Packforsk for the ul, aer and oard industries in inland, Noray and Seden. Distriution: Secretariat, Scandinavian Pul, Paer and Board Testing Committee, Box 5604, SE-4 86 Stockholm, Seden.
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