Dynamic Modulus - Viscoelastic Stress-strain Phase-lag

Viscoelastic Stress-strain Phase-lag

Viscoelasticity is studied using dynamic mechanical analysis where an oscillatory force (stress) is applied to a material and the resulting displacement (strain) is measured.

• 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 ( radian) phase lag.
• Viscoelastic materials exhibit behavior somewhere in between that of purely viscous and purely elastic materials, exhibiting some phase lag in strain.

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

• Strain:
• Stress:

where

=2πf where f is frequency of strain oscillation,

is time,

is phase lag between stress and strain.