Residual stresses in amorphous materials

Real polymeric materials are viscoelastic bodies. In a purely elastic material stresses a(t) are proportional to deformations e(t), and the coefficient of proportionality is Young s modulus E, i.e., at any time t 

Stresses in viscoelastic materials remember deformation prehistory and so are not an unambiguous function of instantaneous deformations however, they may be expressed by a functional. For a linear viscoelastic material, the relationship between stresses and deformations 

One method for overcoming this difficulty is to introduce the modified (or reduced) time t which allows the use of integral relationships with different arguments. The definition of modified time is based on the principle of time-temperature superposition. This is the usual way to generalize temperature-dependent functions using the argument 

The most popular and widely used formula for the function aT(T) is the Williams-Landel-Ferry equation, which is quite adequate for amorphous polymers above the glass transition temperature  

The temperature dependence of the relaxation times introduced into mechanical equations by means of Eq. (2.93) was used to calculate the residual stresses in cooling amorphous polymers. 

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