Numerical study on the surface morphology evolution and hardness during the spherical indentation of copper with plastic behavior described by different stress-strain relationships

• Published in: International journal of solids and structures Vol. 252; p. 111817
• Main Authors: de Santana, Ézio Carvalho, Misiolek, Wojciech Z., Costa, André L.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2022
• Subjects: Brinell hardness; Constitutive laws; Finite element; Pile-up and sink-in effects; Strain hardening; Constitutive laws; Pile-up and sink-in effects; Brinell hardness; Strain hardening; Finite element
• ISSN: 0020-7683
• DOI: 10.1016/j.ijsolstr.2022.111817

•New FEM-based two-steps compression-indentation simulations are applied.•A mathematical model linking Meyer’s law and pile-up is described.•Brinell hardness and pile-up/sink-in agree remarkably well with experimental data.•Results support Copper as a Voce-type hardening material. Spherical indentation on flat surfaces of metallic materials is a very simple and useful test for evaluating mechanical properties. FEM-based simulations have been extensively employed to study pile-up and sink-in effects during indentation process for materials which have plastic behavior described by Hollomon’s power law, where the strength coefficient K is calculated by the continuity condition. In the present numerical study, the stress-strain data of OFHC copper was fitted by three relationships: Voce, Hollomon and continuity-based Hollomon. Then sequential simulations of frictionless compression and ball-indentation tests were carried out, resulting in indentation load-depth curves of workpieces at different hardening levels. These load-depth curves were analyzed to determine the Meyer’s index, the pile-up/sink-in effects, and the Brinell Hardness of each workpiece. The results were compared to literature models and experimental data. The different mechanical behaviors of the Voce- and Hollomon-driven materials during indentation were explained on basis of competition between elastic and plastic deformations along the process. When using Voce’s relationship, the simulated Hardness Brinell curve agreed perfectly with experimental data obtained by Tabor (1951) for annealed and work-hardened copper, and the predicted sink-in for annealed copper agreed very well with experimental data from Campbell et al. (2018). The numerical and mathematical model proved be consistent and results indicate that plastic behavior of copper under indentation test is better described by the three-parameters Voce’s hardening law.