1、AMERICAN NATIONAL STANDARDSINGLE CANTILEVER BEAMMETHOD FOR MEASURINGTHE DYNAMIC MECHANICALPROPERTIES OF VISCOELASTICMATERIALSAccredited Standards Committee S2, Mechanical Vibration and ShockStandards SecretariatAcoustical Society of America120 Wall Street, 32nd FloorNew York, New York 10005-3993ANSI
2、 S2.23-1998ANSIS2.23-1998Reaffirmed by ANSI August 22, 2012 Reaffirmed by ANSI July 5, 2007 Reaffirmed by ANSI July 31, 2002 The American National Standards Institute, Inc. (ANSI) is the na-tional coordinator of voluntary standards development and the clear-ing house in the U.S. for information on n
3、ational and internationalstandards.The Acoustical Society of America (ASA) is an organization of sci-entists and engineers formed in 1929 to increase and diffuse theknowledge of acoustics and to promote its practical applications.American National StandardSingle Cantilever Beam Method for Measuringt
4、he Dynamic Mechanical Propertiesof Viscoelastic MaterialsSecretariatAcoustical Society of AmericaApproved 22 June 1998American National Standards Institute, Inc.AbstractThis Standard defines a method for measuring the dynamic mechanical properties of viscoelastic materialsusing a cantilever beam tec
5、hnique. The dynamic mechanical properties are expressed in terms of thefrequency dependence of Youngs modulus and loss factor at a given reference temperature. The Standardprovides information for constructing such equipment and analyzing the results obtained.ANSI S2.23-1998AMERICAN NATIONAL STANDAR
6、DS ON ACOUSTICSThe Acoustical Society of America (ASA) provides the Secretariat for AccreditedStandards Committees S1 on Acoustics, S2 on Mechanical Vibration and Shock,S3 on Bioacoustics, and S12 on Noise. These committees have wide represen-tation from the technical community (manufacturers, consu
7、mers, and general-interest representatives). The standards are published by the Acoustical Society ofAmerica through the American Institute of Physics as American National Stan-dards after approval by their respective standards committees and the AmericanNational Standards Institute.These standards
8、are developed and published as a public service to providestandards useful to the public, industry, and consumers, and to Federal, State,and local governments.Each of the Accredited Standards Committees operating in accordance with pro-cedures approved by American National Standards Institute (ANSI)
9、 is responsiblefor developing, voting upon, and maintaining or revising its own standards. TheASA Standards Secretariat administers committee organization and activity andprovides liaison between the Accredited Standards Committees and ANSI. Afterthe standards have been produced and adopted by the A
10、ccredited StandardsCommittees, and approved as American National Standards by ANSI, the ASAStandards Secretariat arranges for their publication and distribution.An American National Standard implies a consensus of those substantially con-cerned with its scope and provisions. Consensus is established
11、 when, in thejudgment of the ANSI Board of Standards Review, substantial agreement hasbeen reached by directly and materially affected interests. Substantial agreementmeans much more than a simple majority, but not necessarily unanimity. Consen-sus requires that all views and objections be considere
12、d and that a concertedeffort be made towards their resolution.The use of American National Standards is completely voluntary. Their existencedoes not in any respect preclude anyone, whether he or she has approved thestandards or not, from manufacturing, marketing, purchasing, or using products,proce
13、sses, or procedures not conforming to the standards.NOTICE: This American National Standard may be revised or withdrawn at anytime. The procedures of the American National Standards Institute require thataction be taken periodically to reaffirm, revise, or withdraw this Standard.Standards Secretaria
14、tAcoustical Society of America120 Wall Street, 32nd FloorNew York, New York 10005-3993USATelephone: 11 212 248 0373Telefax: 11 212 248 0146E-mail: asastdsaip.orgInternet: http:/asa.aip.org 1998 by the Acoustical Society of America. This Standard may not be reproduced inwhole or in part in any form f
15、or sale, promotion, or any commercial purpose, or any purposenot falling within the provisions of the Copyright Act of 1976, without prior written permissionof the publisher. For permission, address a request to the Standards Secretariat of theAcoustical Society of America.ContentsPageForeword . ii0
16、 Introduction 11 Scope, purpose, and applications 11.1 Scope . 11.2 Purpose . 11.3 Applications . 12 Informative references 13 Definitions . 13.1 Youngs modulus . 13.2 Loss factor 13.3 Time-temperature superposition 13.4 Shift factor . 13.5 Glass transition temperature . 14 Test apparatus . 24.1 Ele
17、ctromechanical driver 24.2 Force sensor 24.3 Displacement sensor . 24.4 Clamping system . 24.5 Environmental chamber . 24.6 Computer . 25 Operating procedures . 35.1 Sample preparation and mounting 35.2 Calibration and measurement 35.3 Temperature cycle 36 Analysis of results 36.1 Modulus and loss f
18、actor . 36.2 Time-temperature superposition 46.3 Data presentation 5Figure1 Schematic diagram of test apparatus . 2iForewordThis Foreword is for information only, and is not a part of ANSI S2.23 - 1998 AmericanNational Standard Single Cantilever Beam Method for Measuring the Dynamic MechanicalProper
19、ties of Viscoelastic Materials.This Standard was developed under the jurisdiction of Accredited Standards Com-mittee S2, Mechanical Vibration and Shock, which has the following scope:Standards, specifications, methods of measurement and test terminology in thefields of mechanical vibration and shock
20、 and condition monitoring and diagnos-tics of machines, but excluding those aspects which pertain to biological safety,tolerance, and comfort.At the time this Standard was submitted to Accredited Standards Committee S2,Mechanical Vibration and Shock, for approval, the membership was as follows:D. J.
21、 Evans, ChairR. F. Taddeo, Vice ChairA. Brenig, SecretaryAcoustical Society of America D.J.EvansR. F. Taddeo (Alt.)Boyce Engineering International . M.P.BoyceC. Meher-Homji (Alt.)Bruel (2) force rating: .12 N;(3) peak displacement: 64 mm.4.2 Force sensorTypically, the complex force required to displ
22、acethe beam is inferred by measuring the magnitudeand phase of the current driving the electrome-chanical driver. The following specifications apply:(1) frequency range: 0.01 Hz to 50 Hz;(2) resolution: , 0.5 %.4.3 Displacement sensorA non-contacting sensor, typically an eddy currenttype, with the f
23、ollowing specifications shall be usedto measure the specimen complex displacement,magnitude and phase:(1) frequency range: 0.01 Hz to 50 Hz;(2) resolution: , 0.5 %.4.4 Clamping systemOne end of the specimen is clamped rigidly to aframe using the attached end block (See Sec. 5.1).The driven end block
24、 is clamped into a fixtureactuated by an electromechanical driver via a driveshaft.NOTE The stiffness and frequency range specifi-cations for these instruments vary depending on thespecimen dimensions and the desired elastic modu-lus range. However, the following example specifica-tions are provided
25、 for reference:Youngs modulus range: 0.1 MPa to 3 GPa;stiffness range: 90 N/m to 15 MN/m;frequency range: 0.01 to 50 Hz.While in the past, it was common not to use endblocks, their use has been found necessary in orderto obtain reproducible and reliable results.4.5 Environmental chamberAn environmen
26、tal chamber is required to cool thetest sample to a temperature below room tempera-ture, maintain this temperature until the samplehas reached equilibrium, then be capable of in-creasing the temperature of the sample in incre-ments typically of 5 C. The chamber shall be ca-pable of operating over th
27、e temperature rangefrom 280 C to 70 C and be controllable within0.5 C.NOTE The required temperature range is appropri-ate for a viscoelastic material having a glass transi-tion temperature greater than 245 C. Materials withlower glass transition temperatures will require alower starting temperature
28、point. Some materials aresensitive to humidity. It may be desirable to pre-con-dition the sample at a known humidity and to controlor at least record the relative humidity in the cham-ber.4.6 ComputerA computer is required to automate the data ac-quisition and analyses. The computer should beeasy to
29、 program and operate.Figure 1 Schematic diagram of test appa-ratus.ANSI S2.23-19982 1998 Acoustical Society of America5 Operating procedures5.1 Sample preparation and mountingTest specimens are typically cut from a sheetmolded or cast to the desired thickness using asmall band saw or razor. It has b
30、een found thatmachining specimens from a thicker sample oftenaffects the properties of the material. Specimensshould be uniform along each axis, and the endsshould be square to promote adhesion to the endblocks. The dimensions of the specimen dependon the specific instrument and specimen stiffness.A
31、 typical specimen is 12 6 0.5 mm by 10 60.5 mm by 3 6 0.25 mm. A caliper or micrometeris used to determine the average dimensions ofthe specimen, measured at three locations alongeach axis.5.1.1 Specimen end block. Steel or aluminumend blocks are attached to the ends of the speci-men for clamping pu
32、rposes. The actual dimen-sions of the end block vary with the clamp configu-ration, but typical dimensions for the abovespecimen are 11.0 6 0.2 mm by 6.4 6 0.2 mm by4.0 6 0.2 mm.5.1.2 Specimen preparation. The specimen isbonded to the end blocks using a rigid adhesive.The elastic modulus of the adhe
33、sive shall begreater than that of the specimen and shall bestable over the experimental temperature range.Epoxy, urethane, and cyanoacrylate adhesiveshave all been used successfully. Prior to bonding,the end blocks shall be cleaned with denaturedalcohol or other degreaser to promote adhesion.After t
34、he adhesive has cured, excess adhesiveshall be carefully removed, taking care to avoidcutting the specimen or damaging the end blockbond.5.1.3 Specimen mounting. The specimen shallbe mounted in the clamping fixture as shown infigure 1. The specimen shall be placed in the fix-ture so that the clamps
35、touch only the end blocks.The clamps shall be tightened to a torque of atleast 0.4 N-m.5.2 Calibration and measurementThe first step in the procedure shall be to deter-mine the complex stiffness of the driver suspen-sion by making measurements with no specimenin place. Measurements shall be made bot
36、h withand without an end block (which serves as anadded mass) at low and high frequencies, typically1 Hz and 30 Hz. The measurements shall be re-peated ten times at each condition and averaged.A new determination shall be made on a daily ba-sis.Once the instrument stiffness has been deter-mined, mea
37、surements shall be made with thespecimen mounted as specified in 5.1. Force isapplied to the specimen at the discrete frequen-cies, typically 0.3 Hz to 30 Hz, and temperaturesselected for the evaluation. A fixed displacement,typically 64 mm, shall be used.5.3 Temperature cycleMeasurements are made t
38、ypically over the rangefrom 250 C to 50 C, using the following thermalcycle:(1) cool the test specimen, mounted in the testapparatus, to 250 C;(2) after reaching 250 C, hold the specimen atthis temperature for at least 15 minutes beforemaking any measurements;(3) after each set of measurements, incr
39、easethe temperature by no more than 5 C;(4) allow a minimum of six minutes to elapseafter the air temperature has reached the newequilibrium temperature before making the nextmeasurement.6 Analysis of results6.1 Modulus and loss factorThe basic principle of operation of the single can-tilever beam a
40、pparatus is to determine the forceneeded to induce a measurable displacement ofthe specimen. As the magnitude of the displace-ment depends on the modulus of the specimen,this value may be calculated by relating force todisplacement with the following equations 1:F sinvt! 5 Md2xdt21Sg 1S9v1kE9vDdxdt1
41、 S81 kE8!x (1)where:F is peak force applied to the specimen (N);x is axial displacement (m);ANSI S2.23-19983 1998 Acoustical Society of Americav 5 2pf is angular frequency (rad/s);M is vibrating system mass (kg);E 8,E 9 are real and imaginary components ofYoungs modulus of the specimen (Pa);S 8,S 9
42、are real and imaginary components ofthe system stiffness (Pa);g is viscous damping, largely air, of thesystem;k 5 w(t/l )3/(112(11s)(t/l )2) is samplegeometry factor (m);w is specimen width (m);t is specimen thickness (m);l is specimen length (m);s is Poissons ratio of specimen.Defining the complex
43、Youngs modulus asE * 5 E81iE95 E811ih! (2)the solution of Equation 1 yields the elastic andloss moduli, E8 and E9, respectively, as:kE85 K cosb 1 Mv22S8(3)kE95 K sinb 2S92vg (4)whereb is phase lag between stress and strainincluding both material and test appara-tus components;K 5 F/x is effective st
44、iffness of the speci-men evaluated at peak values;h 5 E 9/E8 is loss factor of specimen.NOTE The loss factor, h, is sometimes referred toas the tan d of the material.6.2 Time-temperature superpositionProduce a reduced frequency plot of the modulusand loss factor data in the following manner:(1) make
45、 graphical plots of modulus as a func-tion of base 10 logarithmic frequency for eachtemperature;(2) select as the reference temperature T0thetemperature for which the modulus has thegreatest frequency slope;(3) keeping the data at T0fixed, shift the modu-lus data for the other temperatures, in se-qu
46、ence, along the logarithmic frequency axisuntil each plot partially overlaps the previousdata. Obtain the best fit of the overlap by mini-mizing the sum of the squares of the differencesbetween sets of data at different temperatures.The magnitude of the shift required at each tem-perature is known a
47、s the shift factor aT;NOTE The modulus is chosen to be shifted ratherthan the loss factor because the modulus is mea-sured more accurately and has less scatter than theloss factor.(4) shift the loss factor data using the same shiftfactor that was determined for the modulus;NOTE A material for which
48、the above time-temperature superposition is applicable is calledthermorheologically simple. A material which fails tosuperimpose, due to multiple transitions or crystallin-ity for example, is thermorheologically complex.(5) the resulting plots of modulus and loss factoras a function of shifted logar
49、ithmic frequency atreference temperature T0are known as mastercurves and span a wider range of frequencythan measured;NOTE For a typical viscoelastic material, theshifted frequency range is from about 1025Hz to1010Hz.(6) plot the Napierian logarithm of the shift fac-tor, ln aT, as a function of temperature. Fit thisdata to the WLF equation 2:ln aT52c10T2T0!c201T2T0!(5)where c10and c20are constants for a givenpolymer and subscript zero refers to the refer-ence temperature T0at which the equation isevaluated;(7) the master curves at reference
