STRESS RELAXATION

'Stress relaxation' describes how polymers relieve stress under constant strain. Because they are viscoelastic, polymers behave in a non-linear, non Hookean, fashion. This non-linearity is described by both stress relaxation and a phenomenon known as creep (deformation), which describes how polymers strain under constant stress.
Viscoelastic materials have the properties of both viscous and elastic materials and can be modeled by combining elements that represent these characteristics. Models like the Maxwell Model predict behavior akin to a spring (elastic element) being in series with a dashpot (viscous element), while the Kelvin-Voigt Model places these elements in parallel. Though Maxwell can predict stress relaxation it is fairly poor at predicting creep. Voigt, on the other hand, is good for predicting creep but rather poor at predicting stress relaxation. The most accurate of the viscoelastic models is the Standard Linear Solid Model, which combines the characteristics of both Maxwell and Voigt to display both creep and stress relaxation (See Viscoelasticity).
The following image shows the response of a Standard Linear Solid material to a constant stress, $sigma\_0$, over time from $t\_0$ to a later time $t\_f$. For times greater than $t\_f$ the load is removed. The curvature of the model represent the effects of both creep and stress relaxation.
$E\_1$ and $E\_2$ refer to the spring constants of the elastic elements of the model.

'Stress relaxation calculations can differ for different materials:'
To generalize, Obukhov uses power dependencies [2]:
:
★ )(1^{1-n})]}
where $sigma\_0$ is the maximum stress at the time the loading was removed (t
★ ), and n is a material parameter.
Vegener et al. use a power series to describe stress relaxation in polyamides [2]:
:$$
sigma(t)= sum_{mn}^{} { A_{mn} [ln(1+t)]^m (epsilon'_0)^n}
To model stress relaxation in glass materials Dowvalter uses the following [2]:
:$$
sigma(t) = rac { 1 }{ b }
★ log {rac{10^{lpha}(t-t_n)+1}{10^{lpha}(t-t_n)-1}}
where is a material constant and b and $t\_n$ depend on processing conditions.
'The following non-material parameters all affect stress relaxation in polymers '[2]:

★ Magnitude of initial loading

★ Speed of loading

★ Temperature (isothermal vs non-isothermal conditions)

★ Loading medium

★ Friction and wear

★ Long-term storage

Contents

See also

References

See also

★ Creep

★ Viscoelasticity

★ Standard Linear Solid Model

★ Maxwell material

★ Kelvin-Voigt material

References

★ 1. Meyers and Chawla. "Mechanical Behavior of Materials" (1999) ISBN 0-13-262817-1

★ 2. T.M. Junisbekov. "Stress Relaxation in Viscoelastic Materials" (2003) ISBN 1-57808-258-7

★ 3. Fung YC. ''Biomechanics'', 2nd ed. Springer-Verlag, New York (1993). ISBN 0-387-97947-6