Visco-Elastic Behaviour of Plasticized PVC Sheet under Biaxial Large Deformation

Abstract

In this paper the report is made of the measurement performed of the stress relaxation of plasticized PVC sheet under biaxial large deformation by means of a biaxial tensile tester. It is assumed that the material is an isotropic, homogeneous and incompressible, and the strain energy function W may be described in the following equation.
W=W(I₁, I₂)
The function W can be represented as the function of time t with respect to the stress relaxation. That is
W=W(I₁, I₂, t).
The partial derivatives of the strain energy are given in the following equation as the function of invariants of deformation tensor and time from the theory of continuous media.
∂W/∂I₁(I₁, I₂, t)=1/2H(λ₁²-λ₂²)[λ₁³f₁(t)/λ₁²-λ₁^-2λ₂^-2-λ₂³f₂(t)/λ₂²-λ₁^-2λ₂^-2]
∂W/∂I₂(I₁, I₂, t)=1/2H(λ₂²-λ₁²)[λ₁f₁(t)/λ₁²-λ₁^-2λ₂^-2-λ₂f₂(t)/λ₂²-λ₁^-2λ₂^-2](1)
The force f_i in formula (1) has been measured by the stress relaxation experiment as a function of time t, and ∂W/∂I_i can be obtained by substituting f_i(t) in formula (1).
It is observed that the relation between log(∂W/∂I_i) and log t is approximately expressed as a stright line having slope k. According to the slope of the line ∂W/∂I_i(t) is approximately represented in the following equation as a function of time.
∂W/∂I_i(I₁, I₂, t)=At^-ki
where i=1, 2, A=A (I₁, I₂, t=t₀).
The value of k is not constant for all deformation measured and also for different temperature. Some contour maps representing the surfaces of ∂W/∂I₁ and ∂W/∂I₂ as function of I₁ and I₂ are obtained for this materials at some fixed time t. It follows that the shape of contour map has not been influenced by the time, but it has been remarkably influenced by the temperature.