Process of Identifying Stress Fields from Strain Fields in the Specimen with a Hole

The paper is focused on the process of identifying stress fields from strain fields in the specimen with a hole. The experiment was realized on the specimen with a hole made from anisotropic material. The main attention is paid to the analysis of deformation in the areas of stress (near the hole). That geometry generates a heterogeneous strain field which has been measured during the test using a digital image correlation system. The advantage of using heterogeneous strain fields in the identification procedure is that a complex state of stress-strain can be analyzed at the same time. On the other hand the stress field cannot be directly computed from the test and a suitable identification procedure has to be developed. Here, the virtual fields method (VFM) adapted for plastic strain has been used to identify the hardening behaviour and the anisotropy of the material. The values obtained by the VFM have been compared with the results coming from a standard identification made with uniaxial tensile tests. 1. Introduction In sheet metal forming an anisotropic behaviour of sheet metals is often observed when they undergo plastic deformation. Such anisotropy is due to the rolling process which introduces anisotropy in the texture of the material. The correct identification of the plastic behaviour of anisotropic sheet metal is a very important aspect that has to be taken into account in order to enhance the results of the numerical models. Traditionally the identification is carried out using uniaxial tensile tests performed at different directions respect to the rolling one. However in recent years, thanks to the development in the full-fields measurement techniques, more complex specimens which generate heterogeneous stress-strain fields can be used to study the behaviour of the material during the plastic flow. The parameters can be then identified using for instance an inverse approach which includes the finite element (FE) updating [1–3]. Another identification procedure is the virtual fields method (VFM) [4] which has been successfully applied in many applications, including elastoplasticity [5, 6] and large strain plasticity [7]. The paper is focused on the process of identifying stress fields from strain fields in the specimen with a hole [8–10]. The main attention is paid to the analysis of deformation in the areas of stress (near the hole) [11–14]. The displacement and strain fields were measured using a stereocorrelation technique and the results have been used to identify the parameter with VFM. The Hill48 yielding criterion and the Swift