1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 11093-7:2011Paper and board Testing ofcoresPart 7: Determination of flexural modulusby the three-point methodBS ISO 11093-7:2011 BRITISH STANDARDNational forewordThis Brit
2、ish Standard is the UK implementation of ISO 11093-7:2011.It supersedes BS ISO 11093-7:1997 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee PAI/11, Methods of test for paper, board and pulps.A list of organizations represented on this committee can beob
3、tained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. BSI 2011ISBN 978 0 580 68907 9ICS 85.060; 85.080.30Compliance with a British Standard cannot confer immunity fromlegal obligati
4、ons.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 October 2011.Amendments issued since publicationDate Text affectedBS ISO 11093-7:2011Paper and board Testing of cores Part 7:Determination of flexural modulus by the three-point methodPapi
5、er et carton Essais des mandrins Partie 7: Dtermination du module de flexion par la mthode trois points ISO 2011Reference numberISO 11093-7:2011(E)Second edition2011-09-15ISO11093-7INTERNATIONAL STANDARDBS ISO 11093-7:2011ISO 11093-7:2011(E)COPYRIGHT PROTECTED DOCUMENT ISO 2011All rights reserved. U
6、nless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester.ISO
7、 copyright officeCase postale 56 CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyrightiso.orgWeb www.iso.orgPublished in Switzerlandii ISO 2011 All rights reservedBS ISO 11093-7:2011ISO 11093-7:2011(E)Contents PageForeword iv1 Scope 12 Normative references .13 Terms and defini
8、tions .14 Principle .15 Apparatus 25.1 Test-piece support 25.2 Measuring device 25.3 Load 36 Test piece .46.1 Sampling 46.2 Test-piece size 46.3 Conditioning .47 Procedure 47.1 General .47.2 Positioning of bearings and measuring device 57.3 Application of loading 57.4 Determination .58 Calculation o
9、f the flexural modulus .59 Estimation of required force .610 Test report .6Bibliography .7 ISO 2011 All rights reserved iiiBS ISO 11093-7:2011ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of prepa
10、ring International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in l
11、iaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.The main task of
12、technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.Attention is d
13、rawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights.ISO 11093-7 was prepared by Technical Committee ISO/TC 6, Paper, board and pulps.This second edition cancels and rep
14、laces the first edition (ISO 11093-7:1997), which has been technically revised. The following amendments have been made compared with ISO 11093-7:1997:a) adaptation to editorial rules for International Standards;b) as the effect of transverse frame on deflection is so low with usual reel core measur
15、ements that it can be neglected given the usual variation in materials, the Timoshenko factor has been deleted along with the corresponding equation.ISO 11093 consists of the following parts, under the general title Paper and board Testing of cores : Part 1: Sampling Part 2: Conditioning of test sam
16、ples Part 3: Determination of moisture content using the oven drying method Part 4: Measurement of dimensions Part 5: Determination of characteristics of concentric rotation Part 6: Determination of bending strength by the three-point method Part 7: Determination of flexural modulus by the three-poi
17、nt method Part 8: Determination of natural frequency and flexural modulus by experimental modal analysis Part 9: Determination of flat crush resistanceISO 11093-7:2011(E)iv ISO 2011 All rights reservedBS ISO 11093-7:2011INTERNATIONAL STANDARD ISO 11093-7:2011(E)Paper and board Testing of cores Part
18、7:Determination of flexural modulus by the three-point method1 ScopeThis part of ISO 11093 specifies a method for the determination, by the three-point method, of the flexural modulus of cylindrical paper and board cores which meet the following criteria: internal diameter: 50 mm to 350 mm; minimum
19、wall thickness: 0,05 internal diameter, but not less than 10,0 mm; minimum length of core: 10 internal diameter, but not less than 1 000 mm.If the flexural modulus has to be used for the calculation of a paper cores natural frequency, ISO 11093-82applies instead of this International Standard.2 Norm
20、ative referencesThe following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 11093-1, Paper and board Testi
21、ng of cores Part 1: SamplingISO 11093-3, Paper and board Testing of cores Part 3: Determination of moisture content using the oven drying method3 Terms and definitionsFor the purposes of this document, the following terms and definitions apply.3.1flexural modulusEmaterial property which, together wi
22、th core dimensions, describes the resistance of the core to traction or bending deflection4 PrincipleIn order to determine the flexural modulus, a static bending test is conducted on the test piece. The test piece is considered as a “beam” and the classic beam theory for the deflection of “slender b
23、eams” is applied. During the test, the test piece is supported at its ends and loaded transversally by a load applied by a hanging weight. Special measures are undertaken to avoid permanent deformation of the test piece and to ensure the validity of the equation, used for calculation.The flexural mo
24、dulus is calculated as described in Clause 8. ISO 2011 All rights reserved 1BS ISO 11093-7:20115 Apparatus5.1 Test-piece supportThe test piece is supported at each end by two rolls arranged like a vee, referred to as the lower bearings (see Figure 1). The angle between the two rolls shall be 120 2.
25、The diameter a of the rolls shall be (30 1) mm. The width b shall be large enough to allow the test piece to rest on the lateral surface area of the rolls. At an angle of 120, the theoretical minimum value of b is half the outer diameter D of the core.Dimensions in millimetresFigure 1 Schematic draw
26、ing of the bearings5.2 Measuring deviceThe measuring device consists of two rolls arranged like a vee, referred to as the upper bearings, a support bar on which the upper bearings are mounted, and a displacement gauge. The lower and upper bearings are arranged with mirror-image symmetry. The measuri
27、ng device is placed on the test piece.The change in deflection f of the test piece is measured in the direction of the applied force using a displacement gauge (see Figure 2).If a material-testing machine is used to apply the load (see 5.3), it may also be used to measure the deflection of the test
28、piece. It shall be accurate to 0,01 mm.The tolerances of the distances and the force F are defined in Clause 7.ISO 11093-7:2011(E)2 ISO 2011 All rights reservedBS ISO 11093-7:2011Dimensions in millimetresKey1 lower bearing2 upper bearing3 test piece4 support bar5 dial gaugeF load (force)L0length of
29、test piece, length of paper coreL centre-to-centre distance of the lower bearingsl centre-to-centre distance of the upper bearingsFigure 2 Schematic drawing of the measuring set-up5.3 LoadThe magnitude of the load to be used in the test can be estimated using Equation (2). The load F is applied to t
30、he test piece by a belt loaded with hanging weights. The width of the belt shall be approximately 50 mm (see Figure 3). The belt shall have an opening to allow the shaft of the displacement gauge to rest on the test piece.ISO 11093-7:2011(E) ISO 2011 All rights reserved 3BS ISO 11093-7:2011Figure 3
31、Schematic drawing of the loading systemAlternatively, the load can be applied by a testing machine capable of applying the load using a displacement rate of (10 0,1) mm/min and measuring the load to an accuracy of 0,1 N.6 Test piece6.1 SamplingSamples shall be taken in accordance with ISO 11093-1.6.
32、2 Test-piece sizePrepare at least five test pieces such that their lengths L0are 10 times the internal diameter of the paper or board core. If the calculated length is less than 1 000 mm, the test piece length shall be (1 000 2) mm.6.3 ConditioningIn practice, the test piece shall be dried such that
33、 the moisture content measured in accordance with ISO 11093-3 shall be equal to that specified for the lot.7 Procedure7.1 GeneralCarry out the test under the same atmospheric conditions as those used to condition the test piece.The cores outer and inner diameter, D and d respectively, shall be deter
34、mined with an accuracy of 0,1 mm.ISO 11093-7:2011(E)4 ISO 2011 All rights reservedBS ISO 11093-7:20117.2 Positioning of bearings and measuring deviceThe length of the test piece L0shall be determined with an accuracy of 1 mm. The test piece shall be centred on the lower bearings with a tolerance of
35、2 mm.Position the lower bearings such that their centre-to-centre distance L is 300 mm less than the length of the test piece L0and the upper bearings such that their centre-to-centre distance l is 600 mm less than the length of the test piece, each with an accuracy of 2 mm.The centres of the lower
36、and upper bearings, and the positions of the displacement gauge and the application of force in the direction of the test pieces axis shall be centred with respect to the centre of the test piece to an accuracy of 2 mm.The displacement gauge is positioned centrally on the test piece. The displacemen
37、t gauge is vertically attached on a support bar. The deflection is measured on the upper side of the test piece.7.3 Application of loadingApply the load F by hanging an appropriate weight on the belt which is placed at the midpoint of the measuring length L of the test piece (see Figure 3). The hang
38、ing weight shall be applied slowly.Alternatively, the loading can be applied in a material-testing machine. The loading rate (rate of advance) shall be 10 mm/min.The load shall be such that the deflection f is between 0,20 mm and 0,70 mm (see Clause 9).7.4 DeterminationIf the load is applied by a ha
39、nging weight, within 2 s after application of the loading, the deflection recorded by the displacement gauge shall be read. If the load is applied by a material-testing machine, determine the load required to produce a deflection f between 0,20 mm and 0,70 mm. By applying the values F, L, l and f to
40、 be used in Equation (1), the flexural modulus for each test piece shall be calculated.Repeat 7.2 to 7.4 for additional test pieces.8 Calculation of the flexural modulusThe flexural modulus E, or Youngs modulus, is calculated according to Equation (1), which is developed from the bending theory for
41、slender beams.EFl L lf D d=( )( )2 3324 4pi(1)whereF is the applied transversal load on the test piece, expressed in newtons; the load shall be positioned in such a way that the deflection f lies between 0,20 mm and 0,70 mm;L is the centre-to-centre distance of the lower bearings, expressed in milli
42、metres;l is the centre-to-centre distance of the upper bearings, expressed in millimetres;f is the difference, expressed in millimetres, between the loaded and unloaded deflection measured in the direction of the applied load;D is the external diameter of the core, expressed in millimetres;d is the
43、internal diameter of the core, expressed in millimetres.ISO 11093-7:2011(E) ISO 2011 All rights reserved 5BS ISO 11093-7:2011The flexural modulus shall be specified in newtons per square millimetre, to the nearest integer.EXAMPLE F = 200 N, L = 1 700 mm, l = 1 400 mm, f = 0,54 mm, D = 106 mm, d = 76
44、 mm.The calculation using Equation (1) gives: E = 6 136 N/mm2.9 Estimation of required forceOn the assumption of a deflection of about 0,5 mm and an assumed flexural modulus Eass, the required load F, in newtons, can be approximately calculated using Equation (2):F ED dl L l 320 534 42pi,( )( )ass(2
45、)whereEassis the assumed value for the flexural modulus, expressed in newtons per square millimetre;D, d, L and l are defined after Equation (1).EXAMPLE Eass= 6 000 N/mm2, L = 1 700 mm, l = 1 400 mm, D = 106 mm, d = 76 mm.The calculation using Equation (2) gives: F 181 N.10 Test reportThe test repor
46、t shall include the following information:a) a reference to this part of ISO 11093;b) type and designation of the cores tested;c) place and date of sampling;d) place and date of testing;e) number of test pieces tested;f) measured moisture content;g) core dimensions L0, D and d;h) L, l (actual sizes)
47、, F and f;i) individual and mean values for E;j) whether the load was applied with a hanging weight or a material-testing machine;k) any deviation from this part of ISO 11093 that may have affected the results.ISO 11093-7:2011(E)6 ISO 2011 All rights reservedBS ISO 11093-7:2011Bibliography1 ISO 1109
48、3-2, Paper and board Testing of cores Part 2: Conditioning of test samples2 ISO 11093-8, Paper and board Testing of cores Part 8: Determination of natural frequency and flexural modulus by experimental modal analysisISO 11093-7:2011(E) ISO 2011 All rights reserved 7BS ISO 11093-7:2011ISO 11093-7:201
49、1(E)ICS 85.060Price based on 7 pages ISO 2011 All rights reservedThis page deliberately left blankBSI is the independent national body responsible for preparing British Standardsand other standards-related publications, information and services. It presents the UK view on standards in Europe and at the international level. It is incorporated by Royal Charter.British Standards Institution (BSI)raising standards worldwideBSI Group Headquarters389
