A numerical study of indentation using indenters of different geometry
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Chen Wei-min Division of Engineering and Scientific Research, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Liang Nai-gang and Wang Ling-Dong State Key Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China (Received 28 May 2003; accepted 22 August 2003)
Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic–plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load–displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3° in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.
I. INTRODUCTION
In recent years, microindentation and nanoindentation have become a standard test in investigating the mechanical properties of various new types of surface materials. As a principal tool, application of the finite element method (FEM) to simulate the indentation process plays an important role in interpreting the experimental phenomena and in providing much insight and detailed data for a better description of material properties. In their studies, Bhattacharya and Nix1,2 and Laursen and Simo3 had to replace the standard Vickers and Berkovich indenters by a conic indenter to reduce the problem from three-dimensional (3D) to more tractable two-dimensional (2D). Even so, due to the limited computer performance of the time, it still would take 1 to 2 days to solve such a finite element problem with 400 to 2000 four-node-rectangular elements on a supercomputer. Although this artifice greatly reduced the work load, certain new problems arise, such as (i) how well can the fine stress–strain field around the tip of a non-conic indenter be simulated by a cone, and (ii) how to determine the semiapex angle of the cone to ensure that the load–displacement curve of the 3D indenter is sufficiently well simulated. The clarification of problems such as these ultimately determines the usefulness of the 2D axial symmetrical simulation. J. Mater. Res., Vol. 19, No. 1, Jan 2004
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In the work of Bhattacharya and Nix1,2 and Laursen and Simo,3 the apex angle of the cone was taken to be 136°, which is the included angle of a Vickers indenter (see Fig. 3). This choice leads to a displaced volume (defined as the volume bounded by the lateral surface and the base area) versus depth of indentation relation that very closely emulates that of either the Vickers or the Berkovich indenters. Sun et al.4 and Bolshakov et al.5 substituted the Be
