Chapter 4
Dynamic Mechanical Testing Application of Polymer Development to Constrained-Layer Damping 1
2
Rodger N. Capps and Linda L. Beumel 1
Naval Research Laboratory, P.O. Box 568337, Orlando, FL 32856-8337 TRI/TESSCO, 9063 Bee Caves Road, Austin, TX 78733-6201
Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: May 1, 1990 | doi: 10.1021/bk-1990-0424.ch004
2
Viscoelastic materials are widely used for acoustic attenuation, isolation of continuous vibration, and shock mountings. The properties of these materials are dependent upon temperature and frequency of excitation, molecular structure of the base polymer, and chemical cross-linking systems and fillers. This paper describes a transfer function technique for the measurement of the frequency-dependent Young's modulus and loss tangent. Algorithms for time-temperature superposition are also discussed. It is then shown how the results of such measurements can be used in the selection of viscoelastic materials and fillers in the design of constrained-layer damping structures. Comparisons of mathematical modeling and experimentally determined damping are given for some of the chlorobutyl formulations discussed. Viscoelastic materials are widely used for acoustic attenuation, isolation of continuous vibration, and shock mounting for damping of transient disturbances. For example, elastomers are commonly found in automotive engine and body mounts; load-bearing pads for machinery, railroad rails, and bridges; and constrained-layer damping treatments for decreasing structure-borne noise in airplanes and ships. In particular, constrained-layer damping is becoming increasingly important in naval applications. The engineering property that is of interest for most of these applications, the modulus of elasticity, is the ratio of unit stress to corresponding unit strain in tension, compression, or shear. For rigid engineering materials, unique values are characteristic over the useful stress and temperature ranges of the material. This is not true of natural and synthetic rubbers. In particular, for sinusoidal deformations at small strains under essentially isothermal conditions, elastomers approximate a linear viscoelastic 0097-6156/90/0424-0063S06.00/0 © 1990 American Chemical Society
In Sound and Vibration Damping with Polymers; Corsaro, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
64
SOUND AND VIBRATION DAMPING WITH POLYMERS medium i n mechanical behavior. The dynamic mechanical properties of elastomeric materials are dependent upon a number of factors, including the frequency of excitation, temperature, molecular structure of the base polymer, and chemical cross-linking systems. Additionally, r e i n f o r c i n g f i l l e r s such as the various types of carbon black w i l l s i g n i f i c a n t l y a l t e r both the physical properties and v i s c o e l a s t i c behavior of elastomeric materials. Under c y c l i c deformations, the s t r a i n w i l l lag the stress with a phase angle, 6, that i s between 0 and ir/2 radians. The complex e l a s t i c modulus describing the behavior of the material consists of r e a l and imaginary components. The r a t i o of imaginary to r e a l i s the tangent of the phase angle, 6 and i s commonly denoted as the loss factor or loss tangent. I t i s a measure of the mechanical hysteresis or i n t e r n a l damping of the polymer. This quantity i s of considerable interest f o r many v i b r a t i o n control applications.
Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: May 1, 1990 | doi: 10.1021/bk-1990-0424.ch004
y
The design of vibration control structures and selection of materials for use i n them requires a accurate determination of the v i s c o e l a s t i c properties of the polymers used. The modulus that i s appropriate for consideration w i l l depend upon the geometry and boundary conditions found i n the vibration control structure. A number of commercial and "home brew" instruments have been devised for the measurement of v i s c o e l a s t i c properties of elastomers. Most of these measure either the Young's modulus and loss tangent, or shear modulus and loss tangent. Many of the commercially available instruments suffer the disadvantage that they operate only at r e l a t i v e l y low frequencies which may be inappropriate for certain applications. This paper describes a transfer function technique for the measurement of the frequencydependent Young's modulus and loss tangent. Techniques f o r timetemperature superposition are also discussed. I t i s then shown how the r e s u l t s of such measurements can be used i n the selection of v i s c o e l a s t i c materials i n constrained-layer damping treatments. Comparisons of mathematical modeling and experimental r e s u l t s are given f o r some constrained-layer damping assemblies. MEASUREMENT METHOD A block diagram of the automated measurement system (1) i s shown i n Figure 1. The p r i n c i p l e of measurement i s based upon measuring the t r a n s m i s s i b i l i t y of a mass-loaded rod with high i n t e r n a l damping undergoing longitudinal sinusoidal excitation (2-4). The sample i s harmonically excited using discrete frequency excitation and a locki n analyzer i s used to measure the transfer function (amplitude r a t i o and r e l a t i v e phase of the free and driven ends). I t can be shown (2-5) that the displacement solution of the equation of motion i n the bar can be separated into a pair of coupled transcendental equations r e l a t i n g the experimentally measured transfer function to the e l a s t i c modulus and loss tangent i n the bar. They can be unambiguously solved by Newton's method at the + 90 degree phase crossing points i n the transfer function. The seed values of the modulus and loss tangent can then be used at frequencies other than resonance to obtain a family of frequency dependent modulus and loss
In Sound and Vibration Damping with Polymers; Corsaro, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
4. CAPPSANDBEUMEL
65
Dynamic Mechanical Testing
Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: May 1, 1990 | doi: 10.1021/bk-1990-0424.ch004
tangent curves at each experimental temperature of measurement (4,5). These are then stored on floppy disks f o r further processing. For l i n e a r v i s o e l a s t i c behavior, the i n t e r r e l a t e d dependence upon frequency and temperature of the behavior of polymers subjected to a p e r i o d i c a l l y varying stress can be expressed through the w e l l known time-temperature superposition p r i n c i p l e (6). The c r i t e r i a for i t s application have been discussed by Ferry (6). This technique can be used to superimpose modulus curves covering a limited frequency range at d i f f e r e n t temperatures into an extended frequency curve at a single reference temperature. The amount of horizontal frequency s h i f t required to superimpose a storage or loss modulus curve measured at some temperature T onto another curve at a reference temperature T i s expressed i n terms of a s h i f t factor, a™, which may be viewed as either being equal to the r a t i o of the s h i f t e d frequency to the reference frequency f , or the r a t i o of relaxation times for an elastomer at some temperature T and a temperature T which i s a c h a r a c t e r i s t i c temperature f o r the material under consideration. The modulus, E' , and loss tangent that one would observe at a reference temperature, T , r e l a t i v e to an experimentally measured modulus and loss tangent at some temperature, T, are given by Q
Q
Q
Q
E ' ( f , T ) = (T 0
. />/T
0
. p) . E ( f a , T )
0
T
(la)
and tan
