Determination of Rheological Parameters of Polyvinylchloride at Different Temperatures

The paper proposes the method of determining the relaxation constants of the material included in the nonlinear equation of Maxwell-Gurevich. We performed the processing of relaxation curves of recycled polyvinylchloride (PVC) at different temperatures and investigated the effect of temperature on the value of the relaxation parameters. For each parameter, we have chosen empirical formula describing its dependence on temperature.


Introduction
For polymers of mesh and linear structure, the connection between the creep strain and stress is set by nonlinear equation of Maxwell-Gurevich [1]. In the case of a uniaxial stress state, it has the form [2]: , K w H w f t (1) where İ* -highly elastic deformation, f -stress function, K -relaxation viscosity.
The stress function and relaxation viscosity are calculated as follows: 0 ; exp .
f f E m

Solution of Problem
We consider the method for determining the rheological parameters using the relaxation curves and establish the dependences of each parameter on the temperature on the example of recycled PVC. The results of tests on the stress relaxation of the PVC at a relative deformation İ = 3%, taken from [3], are given in table 1.
The total deformation İ, which in the process of relaxation remains constant, is the sum of the elastic and highly elastic deformation: where E -instantaneous modulus of elasticity. Since in the initial moment of time there is no highly elastic deformation, then we can immediately find the value of E: If we know the modulus of elasticity, we can determine the highly elastic deformation at each time: Differentiating (5) with respect to time, we get: Next, the function ı(t) must be numerically differentiated with respect to t, to find the value v t H wH w at any moment of time. To do this, we use the method of undetermined coefficients. At the end of relaxation process, the growth rate of highly elastic deformation is equal to zero. Using this condition we can obtain the value of E f : Expression (8)

Results and Discussion
From the tests on stress relaxation, we can define all the parameters in the equation of Maxwell-Gurevich. The results of processing of experimental data are summarized in table 2.
where T -temperature in degrees centigrade. Dependence of high elasticity modulus on temperature can be approximated as follows: The relationship between the initial relaxation viscosity and temperature is accurately approximated by an exponential dependence: It is necessary to note that for polymers PMMA and EDT dependences of the initial relaxation viscosity on temperature are also exponential [4].
The magnitude of the velocity modulus at a temperature from 20 to 60 degrees is approximately constant and at 70 degrees slightly decreases. It is proposed to approximate ( ) m T by a linear function:

Fig. 5. Theoretical and experimental relaxation curves
The solid lines on Figure 5 show relaxation curves calculated on the basis of the Maxwell-Gurevich law and dependencies (9) -(12). The triangular markers correspond to the experimental values of the stress. At T = 20 , 30 and 60 agreement with the experimental data is very good, at the rest values of temperature -is satisfactory.

Conclusions
Determination of the viscoelastic properties of materials is a primary and a very important component in the design of structures made of polymers and composite materials based on polymers. The paper presents a simple method of determining the characteristics using the experimental data on the stress relaxation at various temperatures. Usage as a physical law of Maxwell-Gurevich equation (generalized equation of Maxwell) is due to the numerous studies of authors in the field of analysis of polymeric structures in the different modes [5 -10].

Acknowledgement
Scientific work is realize under support of Ministry education and science Russian Federation (grant of President Russian Federation No14.Z57.14.6545-SS) (