Basic studies in biaxial tensile tests

Abstract

Biaxial tensile experiments are an increasing test alternative of thin‐walled specimens to characterize the material behavior under mechanical agencies. This is mainly driven by digital image correlation systems to obtain information about the surface deformation. However, it is not as simple as a tensile test since we can only measure the deformation in a region on the specimen and not the stress state. The latter aspect of stress determination is discussed as well. In this article, we address several basic questions. First: can we obtain a homogenous strain state in cruciform‐like specimens? In this sense the shape will be discussed and a measure of homogeneity is introduced for proofing whether homogeneity can be guaranteed. Second: how can we reach large strains in the center of the specimens? This is connected to the specimen's geometry (arm reinforcement, slots, thinning of center, …). Furthermore, we discuss the problem of material parameter identification using biaxial tensile test information, which is connected to the concept of identifiability using finite elements. This is discussed at the simplest constitutive model, namely linear isotropic elasticity. Thus, the overall goal is connected to a critical review on biaxial experiments using cruciform specimens. The test materials are polymers.

Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

“…First, we carried out experiments using a biaxial testing device, see [33] for more details and references. We chose a natural rubber according to [5].…”

“…Horizontally, a displacement is applied which is four times larger than in the vertical direction (in order to ensure identifiability of the parameters, see the discussion in [33]). The displacement rates of the clamps are horizontallyu h (t) = 0.004, 0.01, 0.1, 1 mm s −1 .…”

“…In this context, the physical meaning of the parameters becomes questionable. This was mentioned in [4,7] for the general case in parameter identification, and studied in solid mechanics in [25,33,71]. Since this is only a local concept in the solution found by some optimizer, it is merely an indicator (so far, however, it appears to be quite a useful indicator).…”

“…With regard to the findings of a unique identification of the material parameters in biaxial experiments from [33], one approach is to apply a much larger deformation in one direction than in the other direction. We define a four times larger displacement in vertical direction, see Fig.…”

From Experiment to Material Parameter Identification

“…numerically generated, unperturbed data by the model) is a method of choice to find out whether identifiability is given, see [18,19]. Even for very simple models and tests, for example, equibiaxial tensile test for linear, isotropic elasticity, it turns out that identifiability of the parameters in principal is not given, [19]. The concept of identifiability has both an impact on the experiment and its loading paths as well as on the constitutive modeling process itself.…”