Identification of the Plastic Behaviour in the Post-Necking Regime Using a Three Dimensional Reconstruction Technique

Abstract

Nowadays a wide number of constitutive models are available to describe the plastic behaviour of metals at large deformations including anisotropy, strain rate effect, kinematic hardening etc. Often the main limitation to the practical applicability of a model resides in the difficulty of experimentally identifying the constitutive parameters. At large deformations the identification can become very complicated because of the occurrence of instabilities, e.g. localized necking or buckling, which create a complex three-dimensional stress and strain state inside the specimen. In these cases, the identification problem is usually tackled by Finite Element Model Updating where a numerical model of the test is built up and the parameters are iteratively varied to achieve the best agreement with the experiments. Recently it has been demonstrated that the Virtual Fields Method (VFM) can be successfully adopted to solve the identification problem using three dimensional displacement data [Rossi and Pierron, Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields, Comp. Mech., 2011]. This paper presents the first experimental validation of this approach. It deals with the identification of plastic constitutive parameters at large strains looking at the post-necking behaviour of a notched specimen. The experiment consisted in a tensile test performed on a notched specimen obtained from a 3 mm thick sheet of 316L stainless steel. An experimental procedure has been developed to reconstruct the volume deformation history of the specimen during the test. A set of four cameras, two for each side of the specimen, has been used to measure the displacement field on the two faces at the same time using Digital Image Stereo-Correlation. The adopted spatial resolution is good enough to describe the out-of-plane movement which takes place at the surface after the occurrence of necking. Starting from the surface measurements, the volume displacement field inside the specimen has been reconstructed using a non-linear volume interpolation. The procedure as well as the reliability of the reconstruction process is described in the paper. Finally, the three dimensional displacement field is used to identify the parameters of a plastic constitutive model using the VFM. The anisotropy of the sheet metal is also taken into account. The main outcome of the paper is to illustrate that it is possible to retrieve the three dimensional deformation history of a specimen in the post-necking region using surface measurements and that these data can be quantitatively used to identify the constitutive model.