A new characterisation method for rubber

Abstract

This paper deals with the mechanical characterisation of elastomeric materials. An original method is proposed to identity the material parameters. It consists of performing only one heterogeneous mechanical test, measuring the displacement/strain field using suitable Digital Image Correlation software and applying an inverse method, namely the Virtual Fields Method, to process the resulting displacement/strain maps. For this purpose, a new apparatus was designed to be adapted to a conventional tensile machine. This apparatus enables us to obtain simultaneously uniaxial tension, pure shear and equibiaxial tension, using only one sample. The heterogeneity of the kinematic fields induced by the test is first discussed in relation to two criteria. The main features of the identification method are then presented, and results provided by a test performed on an elastomeric material are discussed in the context of hyperelasticity.

Introduction

The behaviour of rubber-like materials is generally modelled in the framework of hyperelasticity. Numerous constitutive relations are available in the literature and have recently been compared in the work of Marckmann et al. [1]. However, the identification of the material parameters that govern the constitutive equations is still a difficult task. Classically, three homogeneous tests are considered to identify constitutive parameters, namely uniaxial tensile (UT), pure shear (PS) and equibiaxial tensile (ET) [2], [3], [4]. In practice, the constitutive parameters that are identified with these three types of test differ from one test to another. A trade-off between these three sets of values has to be found to obtain parameters which can be considered as intrinsic. This approach derives from the strong assumption of homogeneity of the kinematic fields induced by each test. Moreover, the sample geometry is different for each homogeneous test.

In the present work, a new approach is developed. It consists of performing only one heterogeneous test, which simultaneously generates the three types of strain states mentioned above as well as the intermediary states. With regard to a recent study by the authors [5], the challenge here resides in using a conventional uniaxial tensile machine to generate a heterogeneous strain state. For this purpose, the sample geometry and loading conditions are defined beforehand by numerical investigations. To generate UT, PS and ET, a new apparatus was designed to be adapted to the uniaxial testing machine. Two specific criteria are defined to discuss the heterogeneity induced by the test. From an experimental point of view, kinematic fields are provided by a Digital Image Correlation (DIC) code suitable for large strains: CORRELI^LMT [6]. Finally, the constitutive parameters are identified using an inverse method, namely the Virtual Fields Method, which is extended to the case of finite deformations.