1、UDC 678.4.074 : 620.178.324 DEUTSCHE NORM March 1990 DIN Determination of viscoelastic pro pe rt es of e I asto m e rs 53 513 on exposure to forced vibration at non-resonant frequencies Prfung von Kautschuk und Elastomeren: Bestimmung der visko-elastischen Eigenschaften von Elastomeren bei erzwungen
2、en Schwingungen auerhalb der Resonanz _ Supersedes January 1983 edition. In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comma has been used throughout as the decimal marker. See Explanatory notes for connection with Internationa
3、l Standards IS0 2856 : 1981 and IS0 4664: 1987 published by the Inter- national Organization for Standardization (ISO). 1 Scope and field of application This standard specifies a method of determining the visco- elastic (dynamic) properties of elastomers when exposed to forced vibration (.e. oscilla
4、tions) at non-resonant frequen- cies. The viscoelastic characteristics thus established can be used to predict the probable behaviour of rubber, such as is used in tyres, machine components (e.g. seals and clutches) or in vibration isolators (e.g. spring suspension systems, shock absorbers), under c
5、onditions of periodic (Le. sinusoi- dal) strain. The method permits the dynamic properties to be measured under known conditions, .e. known frequency and (stress or strain) amplitude. Measurement of the variation of these properties as a function of temperature can be contin- ued until well into the
6、 glass transition range,and in most cases down to a temperature at which the modulus of elasticity has increased by a factor of five. For measurements of variations as a function of temper- ature down to temperatures in the energy elasticity range (cf. DIN 53 545), the torsion pendulum test method s
7、pecified in DIN 53 445 may be employed, this method being based on free, damped oscillations with decaying amplitude and, gen- erally, variable frequencies. 2 Concepts 2.1 Stress and strain When tests are carried out on the basis of forced vibration, a distinction is to be made between a stress tm w
8、hich is con- stant (designated mean stress) and a time-variable stress of amplitude ra (designated stress amplitude). For sinusoidal excitation with a frequencyf, the stress, 7, at any given instant is defined by the following equation (cf. figure 1): (1 1 where r, is the mean stress; ta is the stre
9、ss amplitude; w is the angular frequency (w = 2rrf); t is the time. t = 7, + ta . sin wt The strain material at any given instant in the linear range (.e. generally for small sa values), which is independent of the magnitude of t, is given by the following equation: (2) where y, is the mean strain;
10、ya is the strain amplitude; 6 is the loss angle. y = ym + ya sin (wt - ) The time-variable component of a strain of amplitude ya (designated strain amplitude), therefore, has the same frequency as the stress, but lags behind this by the loss angle, . Note. The definitions of stress and strain given
11、here for the shear case apply analogously to extension (cf. sub- clause 2.2). Continued on pages 2 to 8 DIN 53 513 Engl. Price group Beuth Verlag GmbH. Berlin, has the exclusive right of sale for German Standards (DIN-Normen). 04.91 Sales No 0107 COPYRIGHT DIN DEUTSCHES Institut Fur Normung E.V.- En
12、glishLicensed by Information Handling ServicesPage 2 DIN 53 513 4 Time, t -0- Time, t Figure 1. Stress-time and strain-time diagrams 2.2 Loss factor and complex modulus To enable the viscoelastic behaviour of a material under con- ditions of dynamic strain to be defined, two characteristics must be
13、specified, suitable parameters for this purpose being the mechanical loss factor and the complex (dynamic) modu- lus. The loss factor is defined as where 6 or (6lw) specifies the amount by which thestrain lags behind the stress (cf. figure 1). Depending on the type of load imposed, a distinction is
14、to be made between the dynamic shear modulus, IG*l, and the dynamic normal modulus (or complex Youngs modulus), IE“I (for extension or compres- sion). The former, is a measure of the shear strength of a test piece under oscil- lation conditions and is the absolute value of the complex shear modulus
15、(cf. DIN 53 535). The dynamic normal modulus (or absolute complex normal modulus) is given by: where u denotes stress and c denotes strain (extension or compression). It is a measure of the dynamic tensile or com- pressive strength of a test piece under oscillation conditions and is the absolute val
16、ue of the complex normal modulus (cf. The definition of the loss factor defined by equation (3) applies equally to shear and extension. 2.3 Damping Damping is the dissipation of mechanical energy by conver- sion into heat during dynamic deformation of a test piece. The d = tan (3) IG“I = tJy, (4) IE
17、“I = U,/ in the case of extension of cylindrical test pieces, the apparatus shall be capable of measuring the force or strain or of keeping it constant while impressing a known mean strain or a sinusoidal strain on the test piece. The apparatus shall be equipped for measuring not only the amplitudes
18、 of force and strain, but also the damping, or the loss angle between force and strain calculated from it, and it shall permit conditioning of the test piece as described in subclause 6.2. A specimen test apparatus is shown below (cf. figure 3). con- sisting of an adjustable eccentric and a force an
19、d strain meas- uring system. Test pieces are subjected to a mean force or mean strain which is constant with time by suitable adjust- ment of the eccentric position, the rotation of the eccentric producing deformation cyclically at a frequency of 10 Hz. 1 Test piece being sheared 4 Adjustable eccent
20、ric 2 Temperature measuring point 5 Force measuring device 3 Conditioning housing 6 Device for measuring displacement Figure 3. Diagrammatic representation of a specimen test apparatus COPYRIGHT DIN DEUTSCHES Institut Fur Normung E.V.- EnglishLicensed by Information Handling ServicesPage 4 DIN 53 51
21、3 For shearing conditions. where the mean force is zero, force F shall be plotted against the deflection of the test piece, s (cf. figure 4). The loss factor, tan 6. can be calculated from the area enclosed by the ellipse, using equation (17), the complex shear modulus, IG*I, being calculated from e
22、quation (16). Figure 4. Force-displacement diagram for shearing conditions For extension conditions, the amplitudes of the change in test piece length, La, and the mean test piece length, L, shall be measured. Plotting F against L, as shown in figure 5, yields an ellipse. The area enclosed by this e
23、llipse and its slope can again be used to calculate 6 and IEY using equations (20) and (25) respectively. rr, ai 2 O LL 5.2 Test pieces for shear measurements Test pieces shall preferably be square in cross section, with a bo/Lo ratio of 4, and have a thickness, LO, of 4 mm and an edge length, bo, o
24、f 16 mm. Under no circumstances shall the thickness of the test piece be less than 3 mm or more than 7mm. An arrangement of two sandwich-typg test pieces (cf. figure 6) has proved satisfactory. Lo Lln Extension, L Figure 5. Force-displacement diagram for extension conditions Figure 6. Test piece ass
25、embly for shear measurements 5.3 Test pieces for extension measurements Test pieces shall preferably be cylindrical in shape, with a diameter, do, of 10 mm and a length. LO, of 10 mm, so that the do/Lo ratio is equal to unity (cf. figure 7). Test piece / Plate with thermocoude 5 Test pieces and test
26、 piece assemblies 5.1 General Use of parallelepipedic and cylindrical test pieces is recom- mended, test pieces with a high do/Lo or bo/Lo ratio being used for shear measurements and test pieces with a low if it does, the duration of the test shall be reduced or testing performed at smaller amplitud
27、es. If the object of the test is to obtain reproducible results under standard conditions, measurements shall be made at 70 OC (cf. DIN 53 535). 6.2.2 Measurement with steady temperature rise (case 2) For determining the temperature-dependence of the visco- elastic characteristics, it has proved exp
28、edient to increase the temperature steadily from its lowest to its highest value. The test piece shall be cooled as rapidly as possible to the lowest temperature, preferably at a rate of 10 to 20 OC per minute, with the mean strain or mean force being applied, in the case of extension measurements,
29、while the test piece is still at ambient temperature: following that, the test piece shall be conditioned for 10 minutes at the lowest temperature, initially without application of dynamic stress. Once dynamic stress lias been applied, the temperature shall be increased at a rate of 1 OC per minute
30、and the viscoelastic characteris- tics measured as described in subclause 6.3 every 2 OC or 5 OC, the measurements being made as soon as the sensors in the metal plates referred to in subclause 6.2.1 reach the re- quired temperature. The upper and lower temperature limits shall be stated in the test
31、 report. 6.3 Determination of viscoelastic characteristics 6.3.1 Determination of the complex shear modulus, IG:,T, and loss factor, tan 6 Measurements shall be made at a frequency of 10 Hz in com- pliance with the specified conditioning schedule (cf. sub- clause 6.2). The shear strain amplitude sha
32、ll be kept constant during measurement, the recommended amplitude ya being 0,06 k 0,006: y -sa LO a- where sa is the deflection and LO, the specimen thickness. From the associated force amplitude, Fa, measured the shear stress and the complex shear modulus are obtained. The factor 2 in equation (16)
33、 allows for two test pieces being combined in a sandwich-type assembly. tan 6 shall be determined from the area of the ellipse in the force-displacement diagram (cf. figure 4), which is equivalent to A, (cf. subclause 2.3), to be calculated from the following equation: This equation enables sin 6 to
34、 be calculated and hence, tan 6. Note. The area A, is related to the specific energy loss, CV, A,= W.Vo (18) For the sandwich-type assembly, the volume is given by: A, = n Fa sa sin 6 (17) defined in subclause 2.3, as follows: Vo = 2 (Ao Lo) (19) 6.3.2 Determination of the complex normal modulus, lE
35、:I, and tan 6 under compression Measurements shall be carried out at a frequency, j, of 10 Hz in compliance with the specified conditioning schedule (cf. subclause 6.2). During measurement, the mean test piece length, L, and the amplitude, La, shall be kept constant and the associated forc- es F, an
36、d Fa measured, or alternatively, F, and F, shall be kept constant and the corresponding values of L, and La measured. In the first case, L, should be 8,O mm and La 0,2 mm for a Shore A hardness of 35 to 80. COPYRIGHT DIN DEUTSCHES Institut Fur Normung E.V.- EnglishLicensed by Information Handling Se
37、rvicesPage 6 DIN 53 513 For test pieces of the type described in subclause 5.3, these values are equivalent to a mean extension, E, of 20 %and an extension amplitude, .za, of 2 Yo. In the second case, F, should be 60 N and Fa, 40 N; for a test piece of the type described in subclause 5.3, these valu
38、es are equivalent to a mean stress, u, of about 0,75MPa and a stress amplitude, ua, of about0,5 MPa. If the Shore A hardness of the test piece is below 50, F, and Fa shall be reduced so that the mean extension does not exceed 20 %.lhe stress, u, and the complex normal modulus, IE*I, both expressed i
39、n MPa, shall be calculated from the following equations on the basis of the dimensions of the unstressed test pieces, as fol- lows: (20) IE“I = Ea . Lo La Ao where Fa is the force amplitude, in N; La is the amplitude of the change in length, in mm: Lo is the length of the unstressed test piece, in m
40、m; Ao is the cross-sectional area of the unstressed test piece, in mm2; lhe mean stress, u, and the stress amplitude, u, are to be calculated from the following equations: 0, =- (21) Ao o - Fa a- AO (22) lhe strain, E, and E, (both dimensionless), is obtained from the following equations: (23) - L,
41、- Lo -La LO E, - Lo (24) a- where L, is the mean test piece length, in mm. lhe absolute damping. A, shall be determined from the area of the ellipse in the force-displacement diagram (cf. figure 5). From the equation: sin 6 and tan 6 can be calculated. In addition to the complex normal modulus, it i
42、s also possible to calculate a static modulus from u,: E=% (26) A, = TIF,. La. sin 6 (25) XI is the strain in the dynamometer; X2 is the strain in the test piece plus that in the dyna- mometer: La is the corrected strain amplitude of the test piece. 6.3.3 Determination of the limiting temperature Fo
43、r the purpose of characterizing the glass transition behav- our. DIN 53 545 recommends that the limiting temperature, TL. down to which the behaviour is entropy-elastic should be established, preferably by way of measurement of the com- plex modulus. This temperature is defined as that tempera- ture
44、 at which ICY exceeds the value at (23 f 2) OC by a factor L, the preferred value of which is 5 (or alternatively 2,10, 20, 50, 100); the limiting temperature is then designated, for example, as T,. Note. It should be noted that the limiting temperature is a function of the test conditions and, if t
45、he procedure described in DIN 53 513 is adopted, in particular a function of the frequency. A decrease in frequency results in a corresponding lowering of the limiting temperature. If the material being examined is not to be stressed at 10 Hz in its subsequent application, it may be advisable to car
46、ry out the test at a lower fre- quency (e.g. 1 Hz). For static applications, the Geh- mann test specified in DIN 53 548 shall be used. 7 Test report The report shall refer to this standard and include the follow- ing particulars. COPYRIGHT DIN DEUTSCHES Institut Fur Normung E.V.- EnglishLicensed by
47、Information Handling ServicesDIN 53 513 Page 7 a) Test piece details: - type and description of elastomer tested; - formulation of mix and vulcanization conditions, if - method of test piece preparation (moulded or cut); - type of elastomer-metal bond (cemented or vulcan- - any significant details o
48、f pretreatment. - brief descripition of test apparatus; - type of stressing (shear or extension); - test frequency, f, in Hz; - type of conditioning (case 1 or 2); - test temperature, in OC (in case 1 only); - minimum and maximum test temperature, in OC (in - strain amplitude (ya or e,) or stress am
49、plitude (7, or u,), - mean strain, E, or mean stress, u,. in MPa (for meas- known; ized); b) Test conditions: case 2 only); in MPa; urement under extension conditions only). c) Test results: - number of test pieces; - test piece dimensions: LO, in mm, and Ao, in mm2, and - absolute complex shear modulus, IG“I, or absolute complex normal modulus IE“I, in MPa; - loss factor, tan ; - if measurements to establish the temperature-depend- ence have been made (conditioning case 2): graph of IG“I or IErl and of tan 6 as a function of temperature; - l
