Dynamic modulus

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Dynamic modulus is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free or forced vibration tests, in shear, compression, or elongation). It is a property of viscoelastic materials.

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[edit] Viscoelastic stress-strain phase-lag

Viscoelasticity is studied using the dynamic mechanical analysis. Where we apply small oscillatory strain and measure the resulting stress:

  • In purely elastic materials the stress and strain occur in phase, so that the response of one occurs simultaneously with the other.
  • In purely viscous materials, there is a phase difference between stress and strain, where strain lags stress by a 90 degree (π / 2 radian) phase lag.
  • Viscoelastic materials exhibit behavior somewhere in between that of purely viscous and purely elastic materials, exhibiting some phase lag in strain[1].

Stress and strain in a viscoelastic material can be represented using the following expressions:

  • Strain: \varepsilon = \varepsilon_0 \sin(t\omega)
  • Stress: \sigma = \sigma_0 \sin(t\omega + \delta) \, [1]

where

ω is period of strain oscillation,
t is time,
δ is phase lag between stress and strain.

[edit] Storage and loss modulus

The storage and loss modulus in viscoelastic solids measure the stored energy, representing the elastic portion, and the energy dissipated as heat, representing the viscous portion [1]. The tensile storage and loss moduli are as follows:

  • Storage: E' = \frac {\sigma_0} {\varepsilon_0} \cos \delta
  • Loss: E'' = \frac {\sigma_0} {\varepsilon_0} \sin \delta [1]

Similarly we also define shear storage and loss moduli, G' and G''.

Complex variables can be used to express the moduli E and G as follows:

E = E' + iE'' \,
G = G' + iG'' \, [1]

where

i = \sqrt{-1} \,

[edit] See also

[edit] References

  1. ^ a b c d e Meyers and Chawla (1999): "Mechanical Behavior of Materials," 98-103.