Mathematical Formulation and Numerical Simulation of the Mechanical Behavior of Ceramic/Metal (TiB/Ti) FG Sheets Subjected to Spherical Indenter

The main motivation for the present work is to provide an improved description of the response of Functionally Graded (FG) structures under a spherical indenter, considering material nonlinearities. This is achieved through the implementation of elastoplastic material behavior using integration points to avoid the division of the structure into multiple layers. The current paper proposes a numerical investigation into the mechanical response of functionally graded materials (FGMs) in contact with a rigid hemispherical head indenter. The numerical model considers both the Mori–Tanaka model and self-consistent formulas of Suquet to accurately model the smooth variation of material properties through the thickness of the elastoplastic FG material. The model execution involves a UMAT user material subroutine to implement the material behavior into ABAQUS/Standard. The user material UMAT subroutine is employed to introduce material properties based on the integration points, allowing for an accurate representation and analysis of the material’s behavior within the simulation. The developed numerical model is validated through a comparison with experimental results from the literature, showing a good correlation that proves the efficiency of the proposed model. Then, a parametric study is conducted to analyze the effect of the indenter dimension, the indentation depth and the gradient index on the indentation force, the contact pressure evolution, von Mises equivalent stress and equivalent plastic strain distributions located on the vicinity of the contact zone. The results showed that the elastoplastic response of TiB/Ti FG plates is significantly influenced by the gradient index, which determines the properties of the FG composite through the thickness. These results may help development engineers choose the optimal gradation for each industrial application in order to avoid contact damage.