Evaluation of the elastic-plastic properties of TiN coating by nanoindentation technologies using FEM-reverse algorithm

Highlights

• The elastoplastic properties of TiN coatings were investigated by FEM-Reverse algorithm.

• The sensitivity of the parameters of Swift and Voce models to the load-displacement curve is analyzed.

• A mixed Swift-Voce model is used to capture the elastoplastic properties of a thick TiN coating.

• The predicted stress vs. strain curves from Swift, Voce and Swift-Voce models are consistent in a small strain range.

Abstract

Various methods have been employed to extract the elastoplastic properties of coating materials. In this work, the Levenberg-Marquardt optimization algorithm is integrated with the finite element (FE) analysis, and different hardening models are utilized to characterize the elastic plastic mechanical properties of the coating materials. Based on load-displacement curves obtained from different models such as the Swift unsaturated model and the Voce saturation model, it can be optimized to obtain a set of material properties. The sensitivity of the model parameters of the load-displacement curve is analyzed. The elastoplastic properties of the nanoindentation curve of TiN coating are extracted. The results show that yield stress, elastic modulus and the initial stage of the stress-strain curve can be impressively consistent, but are less accurate when it comes to large strain ranges.

Introduction

The working environment of the engine is very harsh, facing a high temperature, high speed, fatigue and other issues [[1], [2], [3], [4]]. This puts more stringent requisitioned on the design of the coating. In order to obtain more excellent coatings, it is feasible to design coatings using traditional experiments which are time consuming and costly. However, the combination of numerical simulation and experiment can explain the internal mechanism more deeply. For example, Shahed et al. [5]. compared the elastoplastic performance and fracture behavior of the coating system through nanoindentation experiment and simulation. The mechanical properties of the coating are indispensable when using public finite element method [6,7]. In previous studies, only the elastic properties of coatings are emphasized, but plastic properties are equally essential [8,9]. Therefore, it is necessary to calibrate the elastoplastic properties of the coatings. The elastic modulus and hardness of the material can be calculated through the load-displacement curve [9]. DAO et al. [10]. established a reverse analysis algorithm based on the dimensionless function, which can extract the elastoplastic properties of the pure and alloyed engineering metal from the indentation data. Through nanoindentation simulation and nonlinear programs, material parameters can be reversed and calculated, and the equivalent replacement of the nanoindentation model indenter can effectively simplify the model and reduce the calculation cost [11,12]. J.J. Kang et al. [13]. Used a non-linear least-squares optimization to successfully extract a unique set of four elastic-plastic material properties (E, n, σ, and n) of the power-law material, based on a single target load-displacement indentation curve. Nima and Iman [14] used non-linear global optimization approach, fully integrated with FE analysis to characterize the elastoplastic properties of the film. K. Bobzin et al. [15]. combined nanoindentation and simulation to obtain the plastic flow curves of CrN, AlN and CrN/AlN-multilayer coatings. Recently, Kenta Goto et al. determined the plastic parameters of A5052 aluminum alloy based on the reverse optimization technology of a single indentation. Kenta Goto et al. [16] proposed a method based on a single indentation to calibrate the material parameters, both three-dimensional information of an indentation mark and a load-displacement curve are involved. The found that the parameter, the maximum pile-up height normalized by the maximum indentation depth, are highly sensitive to the experimental variations. Thus, it can be chosen as a suitable parameter for inverse estimation. Similarly, Wang et al. [17] proposed a method to determine the anisotropic plastic properties of materials based on statistical Bayesian inference and the spherical indentation experiment. Only residual imprint mapping is used in their parameters identification process, while not the entire indentation loading history. The authors found that the anisotropic material parameters estimated by indentation and uni-axial tests show good agreement. However, research objects in these papers are common alloys or metal materials, which plastic properties can be closely approximated by a power-law description. For coatings with uncertain material constitutive models, such as TiN coating, there are few studies. Therefore, this paper uses FEM-reverse algorithm to study the elastoplastic properties of TiN coating.

In this paper, TiN coating is prepared by a physical vapor deposition method using titanium alloy as substrate. The mechanical properties and load-displacement curve of the coating are tested by nanoindentation. Through finite element method (FEM) and Levenberg-Marquardt optimization algorithm, different hardening models are utilized to characterize the elastoplasticity of the coating. Compared and analyzed the optimization results, what's more, the influences of the parameters of the hardening models on the consequences are explored.