Elastoplastic characterization of rolled C11000 copper sheets via a coupled calibration methodology: Experiments, modeling, and simulation

Abstract

A comprehensive study of the post-necking response of materials is a relevant aspect in many metal-forming applications. For this purpose, the proposal of a suitable constitutive model to describe the elastoplastic response, an adequate material characterization, and the rise of numerical simulation as a feasible tool in the control and design of parts subjected to plastic deformation are key aspects that have to be addressed. In this context, to characterize the elastoplastic behavior of rolled C11000-H2 99.90% pure copper sheets, a constitutive model accounting for appropriate yield criterion function (Cazacu-Plunket-Barlat 06, named CPB06) and hardening law (modified Voce) is presented. In this material, the necking formation is produced at low levels of strain (5% approximately in a tensile test). The 3D stress state that develops afterward is a critical aspect that must be considered when developing an adequate characterization of this material. Therefore, there is a need to formulate an effective and robust strategy to determine the model parameters. In this regard, a coupled calibration procedure is proposed, using a combined experimental-analytical-computational approach. To calibrate the model parameters, this methodology is used with experimental results of proportional loading paths corresponding to uniaxial tensile tests carried out in seven in-plane directions, along with the equibiaxial condition via hydraulic bulge tests. Then, uniaxial tensile tests under non-proportional loading paths, with specimens previously pre-strained along the rolling direction of the sheets to two levels, both beyond the ultimate tensile strength (UTS) zone: 0.07 and 0.14, are used subsequently to evaluate the performance of the model previously calibrated. The reasonably good experimental-numerical agreement in the material response for these last cases successfully validated the proposed characterization methodology.