Kang, JiJun
(2013)
Determination of elastic-plastic and visco-plastic material properties from instrumented indentation curves.
PhD thesis, University of Nottingham.
Abstract
Instrumented indentation techniques at micro or nano-scales have become more popular for determining mechanical properties from small samples of material. These techniques can be used not only to obtain and to interpret the hardness of the material but also to provide information about the near surface mechanical properties and deformation behaviour of bulk solids and/or coating films. In particular, various approaches have been proposed to evaluate the elastic-plastic properties of power-law materials from the experimental loading-unloading curves. In order to obtain a unique set of elastic-plastic properties, many researchers have proposed to use more than one set of loading-unloading curves obtained from different indenter geometries.
A combined Finite Element (FE) analysis and optimisation approach has been developed, using three types of indenters (namely, conical, Berkovich and Vickers), for determining the elastic-plastic material properties, using one set of ‘simulated’ target FE loading-unloading curves and one set of real-life experimental loading-unloading curves. The results obtained have demonstrated that excellent convergence can be achieved with the ‘simulated’ target FE loading-unloading curve, but less accurate results have been obtained with the real-life experimental loading-unloading curve. This combined technique has been extended to determine the elastic and visco-plastic material properties using only a single indentation ‘simulated’ loading-unloading curve based on a two-layer viscoplasticity model.
A combined dimensional analysis and optimisation approach has also been developed and used to determine the elastic-plastic material properties from loading-unloading curves with single and dual indenters. The dimensional functions have been established based on a parametric study using FE analyses and the loading and linearised unloading portions of the indentation curves. It has been demonstrated that the elastic-plastic material properties cannot be uniquely determined by the test curves of a single indenter, but the unique or more accurate results can be obtained using the test curves from dual indenters.
Since the characteristic loading-unloading responses of indenters can be approximated by the results of dimensional analysis, a simplified approach has been used to obtain the elastic-plastic mechanical properties from loading-unloading curves, using a similar optimisation procedure. It is assumed that the loading-unloading portions of the curves are empirically related to some of the material properties, which avoids the need for time consuming FE analysis in evaluating the load-deformation relationship in the optimisation process. This approach shows that issues of uniqueness may arise when using a single indenter and more accurate estimation of material properties with dual indenters can be obtained by reducing the bounds of the mechanical parameters.
This thesis highlights the effects of using various indenter geometries with different face angles and tilted angles, which have not been covered previously. The elastic-plastic material parameters are estimated, for the first time, in a non-linear optimisation approach, fully integrated with FE analysis, using results from a single indentation curve. Furthermore, a linear and a power-law fitting scheme to obtain elastic-plastic material properties from loading-unloading indentation curves have been introduced based on dimensional analysis, since there are no mathematical formulas or functions that fit the unloading curve well. The optimisation techniques have been extended to cover time-dependent material properties based on a two-layer viscoplasticity model, has not been investigated before.
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