Rubber Seals : Stress Relaxation Model

Rubber material is classified as viscoelastic material that mechanical behavior depends on the time and temperature. The decreasing of stress in the rubber material while under the constant deformation, is one of the most important characteristics. Because rubber material is used as a rubber seals to prevent leakage of fluids such as rubber gaskets O-Ring, etc. Stress decreasing through the critical value during operation resulting in the leakage of fluid. The decreasing of stress in rubber material, while under the constant deformation is called stress relaxation of the rubber material.

Materials model

Linear viscoelastic model was developed to describe the behavior of rubber material such as Maxwell model , Kelvin-Voigt model as Figure 1.

Fig.1 Linear viscoelastic model

Equations of motion of Kelvin-Voigt model and Maxwell model is shown in equation (1) and (2), respectively.

Solution of equation (1) and (2) can be expressed as Figure 2, which showed that Maxwell's model can simulate the behavior of stress relaxation, while the Kelvin-Voigt model for the simulation is not consistent with the behavior of stress relaxation. Thus, in the modeling of stress relaxation behavior of rubber material is used Maxwell's model .

Fig.2 Response of Maxwell’s Model and Kelvin-Voigt Model

Generally Maxwell's model can not easily predict the behavior of stress relaxation of rubber material which is very accurate. It has developed the Generalized Maxwell’s model, which consists of a maxwell’s model to a simple parallel, as shown in Figure 3.

Fig.3 Generalized Maxwell’s model

Solution of the Generalized Maxwell’s model is described in a pronie’s series is shown in Equation 3.

We can describe the solution of the Generalized Maxwell’s model in the form of a relaxation of shear modulus in the rubber material, as shown in equation (4).

When

G0 is the shear modulus at time t = 0.

gi is a coefficient of pronie’ series order i

ti is the relaxation time order i.

To develop a rubber compound to analyze the behavior of rubber material or rubber products. Stress relaxation testing of rubber material in order to determine coefficient of Pronie series, this is what the design engineer will be doing before design rubber seals etc.

Relate topic

Rubber seals : Seal Friction

Stress relaxation

Rubber seals : Analyze the effectiveness of the rubber seals using Finite element method.