Indentation of transversely isotropic power-law hardening materials: computational modelling of the forward and reverse problems

Abstract

Using a combination of dimensional analysis and large deformation finite element simulations of triple indentations of 120 materials, a framework for capturing the indentation response of transversely isotropic materials is developed. By considering 4800 combinations of material properties within the bounds of the original set of 120 materials, forward algorithms that predict the indentation response of materials and reverse algorithms that predict the materials' elastic and plastic properties from experimentally measured indentation responses are formulated for both longitudinal and transverse indentations. Issues of accuracy, reversibility, uniqueness and sensitivity within the context of the indentation of transversely isotropic materials are addressed carefully. Using 1400 combinations of material properties, it is demonstrated that there is perfect reversibility between the material properties and their indentation responses as predicted by the forward and reverse algorithms. On average, the differences between the results of the finite element analysis and those predicted by the forward algorithms for longitudinal or transverse indentations are less than 1%, thus demonstrating the high accuracy and uniqueness of the forward analysis. For longitudinal and transverse indentations, the reverse algorithms provide accurate results in most cases with an average error of 3 and 6%, respectively. A sensitivity analysis with a ±2% variation in the material properties in the forward algorithm and ±2% variation in the indentation responses in the reverse algorithms demonstrated the robustness of the algorithms developed in the present study, with the longitudinal indentations providing relatively less sensitivity to variability in indentation responses as compared to the transverse indentations.

Nanoindentation study of electrodeposited Ag thin coating: An inverse calculation of anisotropic elastic-plastic properties

“…The current method uses a single Berkovich indenter indenting in the two orthogonal directions to quantify the coating anisotropy. Since no significant elastic modulus anisotropy is obtained for the coating in this study, an isotropic elastic formulation could potentially be used instead of Equation (1) in the inverse method [36,56]. Indeed, the results indicate that the actual anisotropic indentation responses are more dominant by the plastic parameters rather than the elastic ones.…”

“…With these observations, the thin Ag coating was assumed as a transversely isotropic material for which the mechanical property is isotropic in the plane parallel to the coating surface. To describe the elastic-plastic behaviors of a transversely isotropic material, simplified constitutive equations based on Hill's criterions for yielding was adopted and the details were described in previous studies [11,36]. Here, we briefly review the constitutive relations.…”

“…In Equation 1, five independent elastic constants ( , , , and ) can then fully describe the elastic properties of a transversely isotropic material. The five independent constants are further simplified [11]: the Poisson's ratio is approximated as 0.3 for metallic materials [36], and the average of the two out-of-plane Poisson's ratio is taken to be equal to the in-plane Poisson's ratio:…”

“…However, for the purpose of coating performance analyses, elastic-plastic properties in addition to hardness are required. Although many inverse algorithms have been developed to extract elastic-plastic properties for isotropic materials [32][33][34][35] from nanoindentation load-depth (P-h) curves, few methods have been proposed to estimate coating properties [11,36,37] because the large number of the anisotropic elastic-plastic parameters will render nonunique solutions.…”

“…For relatively thick coatings or bulk materials [11,36], different inverse methods have been proposed to estimate the elastic-plastic properties with multi-indentations. For example, Nakamura and Gu [11] proposed a simplified transversely isotropic elasticplastic model for the atmospheric-plasma sprayed NiAl coating with a thickness of ~290 m, and estimated the corresponding elastic-plastic parameters with dual-indenter: a Berkovich and a spherical indenter.…”