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Design considerations and analysis of a complex-modulus apparatus

Equipment has been designed to measure the dynamic properties of viscoelastic materials in shear. Measurements taken with this equipment indicate that the experimental difficulties are not extensive and the results are reliable and consistent

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Abstract

An analytical assessment is made of an apparatus designed for the measurement of the complex shear modulus of viscoelastic materials. It is shown that simple measurements of amplitude ratio and phase angle are sufficient to determine the complex modulus at any point over a wide range of frequency and dynamic strain. Data obtained for butyl rubber and some experimental elastomers are presented.

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Abbreviations

A :

specimen area

b :

specimen thickness

c :

velocity of shear waves in an elastic\(material = \sqrt {G/_\rho } \)

f :

the frequency of vibration

G :

elastic shear modulus

G * :

complex shear modulus=G′+iG″=G 0 exp (iθ)

G′:

storage modulus in shear=G 0 cos θ

G″:

loss modulus in shear=G 0 sin θ

G 0 :

magnitude of the complex shear modulus

θ:

loss angle in shear=arc tan (G″/G′)

i :

\(\sqrt { - 1} \)

Q :

displacement amplitude of lower block

\(\bar Q\) :

displacement amplitude of upper block or free mass

R :

ratio,\(\bar Q/Q\)

u :

displacement in thex direction

W :

weight of the free mass, the center of gravity of which is at the top of the specimen

x, y :

rectangular coordinate axes

ω:

circular frequency=2πf

ϕ:

phase angle between the lower and upper blocks

τ:

shear stress

ϱ:

mass density of the specimen material

\(\dot h\) :
figure 1
H :

\(\left( {\omega ^2 Mb} \right)/A\)

g :

acceleration of gravity=386 in./sec2

k :

\(\frac{\omega }{c} = \frac{\omega }{{\sqrt {G/\rho } }}\)

k * :

\(\frac{\omega }{{\sqrt {G^* /\rho } }}\)

References

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Author information

Authors and Affiliations

  1. Metals and Ceramics Division, Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio

    Richard L. Adkins

  2. Research and Technology Division, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio

    Richard L. Adkins

Authors
  1. Richard L. Adkins
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Adkins, R.L. Design considerations and analysis of a complex-modulus apparatus. Experimental Mechanics 6, 362–367 (1966). https://doi.org/10.1007/BF02327213

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  • DOI: https://doi.org/10.1007/BF02327213

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