Viscoelastic measurement techniques

Viscoelastic materials have a relationship between stress and strain which depends on time or frequency. Anelastic solids represent a subset of viscoelastic materials: they have a unique equilibrium configuration and ultimately recover fully after removal of a transient load. Internal friction refers to the dissipative response of a material when subjected to a sinusoidal deformation. All materials exhibit viscoelastic response; elasticity or spring-like behavior does not exist in real materials but is an approximate description of materials for which the viscoelastic effects are small enough to ignore. Viscoelasticity is of interest in the context of understanding physical processes such as molecular mobility in polymers, and of phase transformations, motion of defects, alloying atoms in crystalline solids. Viscoelasticity is also used in the design of materials and devices for a variety of purposes including earplugs, vibration abatement, reduction of mechanical shock, instrument mounts, and control of rebound and rolling resistance. The loss angle d is the phase angle between stress and strain during sinusoidal deformation in time. The loss angle or the loss tangent tan d as a measure of damping or internal friction in a linear material is advantageous in that it is clearly defined in terms of observable quantities. Tan d depends on frequency, and it is customary to plot it on a logarithmic frequency scale. A factor ten ratio in frequency is referred to as a decade. Tan d is also the ratio of the imaginary part G9 to the real part G8 of the complex modulus G*[G81iG9. The quality factor Q associated with the width of resonant peaks @see Eq. ~3!# is given for small d by Q'tan d. If vibration in a resonating system is allowed to decay with time due to material viscoelasticity after removal of the excitation, one may define the log decrement L in terms of amplitudes A1 and A2 of successive cycles as L