Automated dynamic Young’s modulus and loss factor measurements

Automated dynamic Young's modulus and loss factor measurements

Walter M. Madigosky and Gilbert F. Lee

Naval Surface Weapons Center, White Oak, Silver Spring, Maryland 20910 (.Received 20 March 1979; accepted for publication 12 April 1979)

A progressive wave apparatus featuring an automated data processor is described. The apparatus accurately determines the propagation constants of an extensional acoustic wave by exciting one end of a strip of material while the other end is suspended under constant tension. The apparatus is capable of making measurements in the frequency range of 100 Hz to 40 kHz, depending on the extensional wave velocity and attenuation in the material. As illustrations of the technique, measurements were made on three rubber compounds: a polyurethane, a neoprene, and a nitrile rubber. Extensional sound speed, attenuation, modulus, and loss factor were determined over a frequency range of 1-10 kHz and a temperature range of 4ø-47øC. Applying the time-temperature superposition principle to the data, master curves were constructed and WLF shift constants were determined. The apparatus was found to be a fast and reliable method to determine the dynamic viscoelastic constants.

PACS numbers: 43.85.Dj, 43.35.Cg, 43.35.Mr

INTRODUCTION

Progressive wave techniques TM have been widely used to determine the dynamic material constants of rubber compounds. These techniques commonly use a piezoelectric element which contacts lightly on the surface of a test strip. The strip is excited into oscillation by an electromechanical shaker. The element is moved along the surface so that a continuous record is made of the

amplitude level as a function of distance along the test strip at one frequency. From this record, the attenuation is determined. The wavelength is determined between points of equal relative phase along the strip. Since the frequency is known, the propagation velocity is determined. These techniques are difficult to use since the data is taken by hand at each discrete frequency, making the measurements a very time-con- suming process. The element is not only sensitive to the response of the excited strip, but also to the surface roughness and variations introducing nonsystematic er- rors in the measurements.

The purpose of this paper is to describe an advanced progressive wave or string apparatus using an alterna- tive method of obtaining the experimental data. This apparatus features an automated data processor. In contrast to the previous technique, the piezoelectric element (in our case, a phonograph cartridge) is positioned on the surface of the test strip, and the relative attenuation and phase are measured over a frequency range. Then the cartridge is moved to a new position, and the relative attenuation and Phase are measured again. By this method, the effect of surface roughness and variations on the measurements is minimized. The

purpose of the data processor is to initiate and control the frequency scan, data accumulation and data reduc- tion; therefore, on the average, the amount of time spent in obtaining data over the complete frequency range (100 Hz-40 kHz) is approximately 5 min.

I. APPARATUS, METHOD, AND MATERIALS

The string apparatus is used to excite an extensional acoustic wave along a strip of rubber material whose

length is sufficient such that a standing wave pattern was not generated, and whose cross-section dimensions are a small fraction of a wavelength. Thus, all

portions of the cross section experiences a similar deformation at a given time. This deformation is as- sociated with a Young's modulus. The extensional sound speed and attenuation are measured as a function of frequency and temperature. Measurements can be made over a frequency range of 100 Hz-40 kHz. The exact limits of this frequency range are dependent on the attenuation and wave velocity in the material, e.g., at high temperature, the loss per centimeter may be very high, and thus reduce the high frequency range, whereas at low temperature, the loss may be too low to measure at low frequencies.

The string apparatus is shown in schematic form in Fig. 1. An electromagnetic shaker (Bruel & Kjaer Mini-Shaker type 4810) is used to drive a rubber strip at the bottom end while the other top end is suspended under constant tension. The dimensions of the rubber

strip are: length, 60 cm; width, 0.6 cm; and thickness, 0.3 cm. A phonograph cartridge (Micro-Acoustic 2002 E cartridge) is utilized to measure the mechanical response of the vibrating strip. This cartridge was chosen because of good frequency response and tracking capabilities. The shaker, rubber strip, and cartridge are placed in a refrigerator oven.

The shaker is programmed to step piecewise over the

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I COMPUTER II I t--I .aWORK I i ..,o,-r.:., I'-I co'""""." I / ,,,.,,,,,,., I

/ I'Y"'""'"" I // FIG. 1. String apparatus.

345 J. Acoust. Soc. Am. 66(2), Aug. 1979 345

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TABLE I. Physical properties of various rubbers.

Density Shore A (g/cm 3) hardness

Polyurethane 1.072 63 Neoprene 1.32 68 Nitrile 1.132 58

frequency range by a frequency synthesizer (Hewlett- Packard 330B). The source signal is first filtered, then amplified by a 20-W power amplifier (Mcintosh). The purpose of the filter is to lower the source signal level at low frequencies in order to provide a constant output level at the network analyzer. The signal from the cartridge is amplified (Tektronix AM 502 differen- tial amplifier) and then routed to a network analyzer (Hewlett-Packard 3570A). The analyzer measures and digitizes the phase angle and amplitude differences between the reference output signal from the synthesizer and the measured signal from the cartridge. The analog reference and measured signals are displayed on an oscilloscope.

The acquisition of the data is automated with a mini- computer (Hewlett-Packard 9825A calculator). The calculator is programmed to initiate and control the frequency sweep of the frequency synthesizer, and to collect and store data from the output of the network. analyzer in memory when the cartridge is positioned initially at 1 cm above the shaker on the strip. Fifty data points are accumulated in less than 10 s. A spacer under the shaker is then removed such that the distance

between the cartridge and the top of the shaker is in- creased anywhere from 1.5 to 10 cm, and a second set of data are collected. The difference in distance

(length) between the initial and final positions is record- ed in the calculator. The absolute phase angle and

TABLE II. Nitrile rubber recipe.

Hycar 1034-60 100 pts (Goodrich)

United N234 40 pts (Ashland)

Dioctyl Phthalate (DOP) 15 pts (Ashland)

St. Joe 42-41 3 pts (Harwick)

MBTS 1.5 pts (American Cyanamid)

Tire 21-12 MC-TP Sulfur 1.5 pts (Stauffer)

Stearic Acid F-1000 1 pt (Harwick)

AgeRite Stalite 1 pt (Vanderbilt)

Cure 30 rain at 320 øF

163 pts

lO 1o

10 0 I 5 10

FREOUENCY, kHz

12.5 ø

17 ø

41.8 ø 47 ø _

FIG. 2. Young's modulus vs frequency at various temperatures for neoprene rubber.

amplitude are determined from the relative phase angle and amplitude differences, respectively, measured at the initial and final positions for a given frequency. Finally, the sound speed and attenuation or Young's modulus and loss factor are automatically plotted versus frequency on a plotter (Hewlett-Packard 9862A calculator plotter).

Three rubber compounds were chosen for this study. Their physical properties are listed in Table I. The polyurethane rubber, U.S. Polymerics V-356, was obtained commercially. The rubber was prepared in two steps: first, a hydroxy terminated, block copolymer of polyether is reacted with an excess amount of diisocyanate to yield a prepolymer; second, the prepolymer and the excess diisocyanate is cured with a mixture of diols and triols of low molecular weight to yield a crosslinked polyether polyurethane.

A commercially available neoprene (polychloroprene) rubber (MIL R 6855 C class 2)was selected because of its wide use.

A nitrile butadiene copolymer rubber gum stock,

60O

5OO

400

200

lOO

• 170 • 230

1 2 3 4 5 6 7 ß • 9 10 FREQUENCY, kHz

FIG. 3. Extensional sound speed vs frequency for nitrile rubber at various temperatures.

W. M. Madigosky and G. F. Lee: Dynamic Young's modulus 346 J. Acoust. Soc. Am., Vol. 66, No. 2, August 1979 346


7

6

3

2

1

........ 23o

17 ø '

.

FREOUENCY, kHz

FIG. 4. Attenuation vs frequency for nitrile rubber at various temperatures.

B. F. Goodrich Chemical Company Hycar 1034-60, was used to prepare a nitrile rubber using the recipe given in Table II.

As a matter of convenience in shifting the data, measurements were made over the frequency range 1-10 kHz at various temperatures ranging from 4 ø to 47øC.

II. THEORY

The sound speed c and attenuation c• are expressed in terms of the two measured values phase angle P and amplitude A:

c= 360FL/P cm/s, (1) and

• = (A/L) dB/cm, (2)

where F is frequency (Hz), and L (cm) is the length between the initial and final positions of the cartridge.

The real part of Young's modulus E' is calculated from c and r:

E'= pcZ ( 1 -rZ)/( i + rZ) z dyn/cm z , (3)

where p is the density of the rubber strip (g/cmS). The

200 Nn'RILE

100

01 . FREQUENCY, kHz

POLYURETHANE

,

FIG. 5. Extensional sound speed vs frequency for the three rubber compounds.

8 -

7

6

, , .

NEOPRENE•//••E E

2 7 8 , FREQUENCY, kHz

FIG. 6. Attenuation vs frequency for the three rubber compounds.

loss factor 5 is defined as the ratio of the imaginary (E") to real parts and is given by

5 = 2r/(1 - r2),

where

r= aX/[2•T (8.69)]= 6.59 A/P,

and X is the wavelength (cm).

(4)

(5)

Using the modulus and loss factor data, master curves (complete modulus-frequency and loss factor- frequency behavior at a constant temperature) are con'- structed by a shifting procedure. This procedure is based on the principle of time-temperatures superposition. The principle states that measurements made over an accessible frequency scale for several temperatures are the same as one measurement made over

a large frequency range at one temperature. Applying this principle to the data shown in Fig. 2, we observe that shifting the modulus curve at 17øC horizontally to the right results in a superposition with the modulus curve at 25.8øC in the area where the'two curves over-

lap. The new modulus curve at 25.8øC is extended to higher frequencies and to higher modulus values than previously measured at 25.8øC. Continuing this process, a master curve is generated for both the modulus and loss factor.

i øø 25j• 4ø 31ø • 41.8 o- 47 ø-

lr 1 1 5 10

FREOUENCY, kHz

FIG. 7. Loss factor vs frequency at various temperatures for neoprene rubber.

347 J. Acoust. Soc. Am., Vol. 66, No. 2, August 1979 W.M. Madigosky and G. F. Lee: Dynamic Young's modulus 347


J , t, j

-24 -22 -20 -18

FIG. 8. WLF shift plot for neoprene rubber.

20

16

12

8

4

o ";'

-8

-12

-16

-20

10 lo ,

710 J I I I i lO • lO' lO• lO 8 I:REOUmCY,

- lO 1

9

lO-1

FIG. 9. Master curves for the Young's modulus and loss factor at 7"0= 20øC for nitrile rubber.

The amount of shift, that is required, varies with the temperature. The analytic form of this function is given by the WLF equation 5 (Williams, Landel, and Ferry), which relates the amount of horizontal shift required to superimpose a curve measured at a temperature T on- to another curve at a reference temperature To:

log aT= -c•.(T - To)/(c,.+ T - To). (6)

The shift factor a T is equal to the ratio of the shifted frequency f to the reference frequency fo- The constants c] and c 2 are the shift constants which are char- acteristics of the polymer. In order to evaluate the constants c• and c,. from the experimental data, the fol- lowing procedure (modified from Ferry 5) was used. Rearranging Eq. (6),

- - o)/1o -c,. (?)

is obtmined, then a plot of (T- To) vs (T- To)/log a T has a slope equal to -c] and an intercept of -c,..

III. DATA AND ANALYSIS

Typical plots of sound speed and attenuation versus frequency at various temperatures are presented in Figs. 3 and 4 for nitrile rubber. The sound speed increases with increasing frequency and decreasing temperature, while the attenuation increases with increasing frequency and increasing temperature.

A comparison of sound speed and attenuation versus frequency at room temperature (20øC) for the three rubber compounds is illustrated in Figs. 5 and 6.

Typical plots of Young's modulus and loss factor versus frequency at various temperatures are shown in Figs. 2 and ? for neoprene rubber. The modulus in-

TABLE HI. WLF shift constants for various rubber compounds at a reference temperature of 20øC.

c 1 c 2

Polyurethane 5.37 51 Neoprene 4.09 67 Nitrile 9.35 133

creases with frequency and decreases with temperature. The loss also increases with frequency and decreases with temperature. However, at temperatures below 12 ø , the trend reverses.

A typical plot of (T- To) against (T- To)/log a T for neoprene rubber is shown in Fig. 8. A least-squ•re curve fit was applied on the data points. Since a good fit was obtained, there is confidence in the shifted modulus and loss curves. Scatter in the data points would mean the modulus and loss curves are shifted incor-

rectly, either too much to the left or right. Values of cx and c,. at a reference temperature of 20ø(? are listed in Table III.

The master curves for nitrile, neoprene, and polyurethane rubber are presented in Figs. 9, 10, and 11. These master curves span roughly four decades of frequency.

The loss factor curves indicate a transition in each of

the rubber materials. The frequency at which the transition occurs is located by the maximum of these peaks. The peak for the nitrile and neoprene rubbers occurs approximately in the frequency range of 104-105 Hz, whereas the transition for the polyurethane rubber occurs at a much lower frequency (around 10'-Hz). The modulus curves steadily increase with frequency. The magnitude of change of the modulus curves is approximately two decades (10-10 •ø dyn/cm•). It is believed that this transition represents a glass transition.

lO lo

1o"

lO ? I I I I 10' 10 z 16 3 10 4 10"

FREOUENCY, Hz

- 101 i

- 10"

lO -1 lO"

FiG. 10. Master curves for the Young's modulus and loss factor at T O = 20øC for neoprene rubber.

348 J. Acoust. Soc. Am., Vol. 66, No. 2, August 1979 W. M. Madigosky and G. F. Lee: Dynamic Young's modulus 348


lO Io 1 i i i

10 7 I I I I 10 '! 101 10 2 10 3 10 4 10 6 10 e

FREOUENCY, IIz

101

FIG. 11. Master curves for the Young's modulus and loss factor at T O = 20øC for polyurethane rubber.

IV. CONCLUSIONS

The string apparatus described in this paper is shown to be a rapid method to determine viscoelastic constants of rubber material. With practice, a complete master

curve is obtained in about 3 h. This apparatus is also accurate and sensitive to the polymer type. Other data (not presented here) also shows that the apparatus is accurate and sensitive enough to determine small changes in the polymer mix, compounding, curing con- ditions, and aging history.

1W. S. Cramer, "Propagation of stress waves in rubber rods," J. Polym. Sci. XXVI, 57 (1957).

2j. W. Ballou and J. C. Smith, 'q)ynamic measurements of polymer physical properties," J. Appl. Phys. 20, 493 (1949).

3R. S. Witte, B. A. Mrowca, and E. Guth, "Propagation of audiofrequency sound in high polymers," J. Appl. Phys. 20, 481 (1949).

aA. W. Nolle, "Acoustic determination of physical constants of rubber-like materials," J. Acoust. Soc. Am. 19, 194 (1947).

5j. D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York, 1961), 2nd ed., Chap. 11, p. 303.

349 J. Acoust. Soc. Am., Vol. 66, No. 2, August 1979 W.M. Madigosky and G. F. Lee: Dynamic Young's modulus 349


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Automated dynamic Young’s modulus and loss factor measurements