Determination of Mechanical Moduli of Polymeric Materials by Biaxial Tensile Testing

Abstract

Poisson's ratio and Young's modulus are two important material constants for isotropic elastic materials, but there are usually very difficult problems regarding Poisson's ratio since high accuracy is required for its measurement. And also, for orthotropic elastic materials it is required that these material constants will be determined in line with the respective principal structure direction.In this paper, we describe the methods of measuring Young's moduli and Poisson's ratios for isotropic elastic material and orthotropic elastic materials using biaxial tensile tester. For isotropic elastic materials the Young's modulus and Poisson's ratio can be measured by strip biaxial testing, where the stretch ratio is variable to the axis of X1 and the stretch ratio to the axis of X2 is kept in unity. And the material constants are given by the following equations.E=1/e1σ1(σ12-σ22)ν=σ2/σ1where E is Young's modulus, ν is Poisson's ratio, σ1, σ2 are stress to the axis of X1, X2 and e1 is strain to the axis of X1. For orthotropic elastic materials these material constants are measured by three operations, that is, the strip biaxial tensile testings where the extension direction is selected to 0°(Lateral), 90°(Transverse) and 45°from one of structure principal axis. And the material constants are given by the following equations.EL=1/eL(σL-σTσL'/σT') ET=1/eT(σT'-σL'σT/σL)νLT=σL'/σT'ET/EL and GLT=σθ1/eθ1-EL(1+2νTL)+ET/4(1-νLTνTL)where EL, ET are Young's moduli of lateral and transverse directions respectively, νLT is Poisson's ratio, GLT is shearing modulus, σL, σT are stresses in lateral and transverse axis and eL, eT are the strains. And the prime means the case of transverse direction tensile, and suffix θ1 indicates the case of 45°direction tensile.