Elastoplastic Indentation Response of Sigmoid/Power Functionally Graded Ceramics Structures

Functionally graded materials (FGMs) are increasingly used in tribological systems due to their tailored mechanical properties. Prior research has shown that FGMs can reduce stress concentrations and improve wear resistance. However, the indentation response of FGMs with sigmoid or power gradation remains understudied. This gap motivated the development of computational and empirical models to better understand their elastoplastic behavior. Existing studies often focus on uniform or linear gradation, leaving nonlinear gradation unexplored. The need for accurate modeling of indentation under spherical rigid punches is clear. No prior work had resolved the effect of gradation function and index on contact mechanics. This study addresses those limitations by integrating modified TTO models with finite element analysis.

The study aimed to develop a model to predict the elastoplastic indentation response of functionally graded ceramics. It focused on the influence of gradation function and index on mechanical behavior. The goal was to provide a tool for engineers to optimize FGM design for tribological applications. The model integrates computational and empirical approaches for better accuracy. It considers bilinear hardening and uses a modified TTO model for property evaluation. The study also aimed to validate the model against experimental data. The research sought to clarify how gradation affects contact pressure and deformation. This work fills a gap in understanding nonlinear gradation effects in FGMs.

The study used a modified Tamura-Tomota-Ozawa (TTO) model to evaluate effective material properties. A finite element procedure was developed to simulate indentation with a rigid spherical punch. The gradation function was modeled using power law and sigmoid functions. Contact pressure, displacement, and deformation were calculated numerically. Bilinear hardening was incorporated into the material model. Mesh convergence and solution stability were verified. Empirical equations for permanent deformation were derived from simulation results. The model was validated against experimental indentation data for accuracy.

The model predicted contact pressure, horizontal displacement, and permanent deformation under indentation. Sigmoid gradation reduced stress concentrations compared to power law. Higher gradation indices increased contact pressure and deformation. Bilinear hardening significantly affected the plastic deformation profile. The empirical forms for permanent deformation matched simulation results closely. Mesh convergence was achieved with a fine element size. Von Mises stresses peaked at the indentation center for both gradation types. The model successfully captured the influence of gradation function and index on mechanical response.

The study demonstrated that gradation function and index strongly influence indentation response. Sigmoid gradation offers better stress distribution than power law. The modified TTO model accurately predicted effective material properties. Bilinear hardening is essential for modeling plastic deformation. The empirical forms for permanent deformation align with simulation results. The model provides a reliable tool for FGM design optimization. Engineers can use this approach to select optimal gradation parameters. The findings support the use of nonlinear gradation in tribological applications.