An Inverse Method for Measuring Elastoplastic Properties of Metallic Materials Using Bayesian Model and Residual Imprint from Spherical Indentation

In this paper, an inverse method is proposed for measuring the elastoplastic properties of metallic materials using a spherical indentation experiment. In the new method, the elastoplastic parameters are correlated with sub-space coordinates of indentation imprints using proper orthogonal decomposition (POD), and inverse identification of material properties is solved using a statistical Bayesian framework. The advantage of the method is that model parameters in the numerical optimization process are treated as the stochastic variables, and potential uncertainties can be considered. The posterior results obtained from the measuring method can provide valuable probabilistic information of the estimated elastoplastic properties. The proposed method is verified by the application on 2099-T83 Al-Li alloys. Results indicate that posterior distribution of material parameters exhibits more than one peak region when indentation load is not large enough. In addition, using the weighting imprints under different loads can facilitate the uniqueness in identification of elastoplastic parameters. The influence of the weighting coefficient on posterior identification results is analyzed. The elastoplastic properties identified by indentation and tensile experiment show good agreement. Results indicate that the established measuring method is effective and reliable.

New Inverse Method for Determining Uniaxial Flow Properties by Spherical Indentation Test

The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way. Current inverse methods mainly rely on extensive iterative calculations, which yield a considerable computational costs. In this paper, a database method is proposed to determine tensile flow properties from a single indentation force-depth curves to avoid iterative simulations. Firstly, a database that contain numerous indentation force-depth curves is established by inputting varied Ludwic material parameters into the indentation finite elements model. Secondly, for a given experimental indentation curve, a mean square error (MSE) is designated to evaluate the deviation between the experimental curve and each curve in the database. Finally, the true stresses at a series of plastic strain can be acquired by analyzing these deviations. To validate this new method, three different steels, i.e. A508, 2.25Cr1Mo and 316L are selected. Both simulated indentation curves and experimental indentation curves are used as inputs of the database to inversely acquire the flow properties. The result indicates that the proposed approach provides impressive accuracy when simulated indentation curves are used, but is less accurate when experimental curves are used. This new method can derive tensile properties in a much higher efficiency compared with traditional inverse method and are therefore more adaptive to engineering application.

Improving the tensile property calculations with plastic zone radius measurements in depth-sensing spherical indentation tests

Depth-sensing spherical indentation tests (SITs) have been widely used in tensile property calculations, but the accuracy and reproducibility of calculations may be significantly influenced by displacement measurement errors. Taking two representative tensile property calculation methods as examples, namely the analytical and numerical methods, the rationale as to why accurate and reproducible tensile property calculations cannot be expected from the depth-sensing SITs was discussed in detail. Subsequently, the proportional limit σ0 calculation from plastic zone radius rp measurements, which was analytically developed in the expanding cavity model (ECM) and experimentally measured by digital image correlation (DIC), was introduced to enhance the accuracy and reproducibility of the two representative methods. Principles for setting the strain threshold εth were established, and factors influencing the σ0 calculation from rp measurements were investigated through the optical system, the friction condition, the hardening behaviors of specimen materials, and the indentation depth. Through finite element calculations, it was proven that tensile property calculations at the existence of displacement measurement errors, particularly the constant error from the origin correction, can be significantly improved with the introduction of rp measurements. Similar findings were also observed in experiments on four metals that exhibited different hardening behaviors.

Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.