A new scheme for computational modeling of conical indentation in plastically graded materials
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In this paper, a new scheme has been proposed for the computational modeling of conical indentation in plastically graded materials. Based on the new scheme and the work of Dao et al. [Acta Mater. 49, 3899 (2001)], and taking the example of conical indentation with an indenter whose tip apex angle is ⳱ 70.3°, an analytical expression to predict the loading P − h curve for the indentation of plastically graded materials has been presented. A reverse algorithm has further been established to determine the plastic properties of a plastically graded surface. The existence, uniqueness, and stability of the solution to the inverse problem have been systematically investigated. The current work can be applied to the evaluation or optimization of various plastically graded surfaces.
I. INTRODUCTION
Plastically graded materials are usually produced during surface treatments such as case hardening of steels, ion implantation, laser surface treatments, shot peening, and other surface preparation methods. Plastically graded materials show significantly different performance characteristics when compared with traditional plastically homogenous materials. From the viewpoint of surface engineering, this gradual variation in plastic properties, if properly controlled, can lead to significant improvement in the behavior of structures. For example, a gradation in the yield limit will have a marked effect on the contact fatigue behavior of the structures.1 Detailed information about the scientific and technological significance of surface treatments in creating plastically graded materials can be found in Ref. 2. At present, much work is still needed to quantitatively evaluate the properties of a plastically graded surface. Indentation tests have been used extensively to assess the mechanical properties of materials. Many theoretical and numerical models have been proposed to extract various material properties by using the loading and unloading P − h curves obtained from the indentation test. Oliver and Pharr3 have proposed a successful method for obtaining the hardness and Young’s modulus from the loading and unloading P − h curves. By using dimensional analysis and the finite element method, Cheng and Cheng4,5 have derived several very useful scaling relationships for conical indentation
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0239 J. Mater. Res., Vol. 19, No. 6, Jun 2004
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in elastic–perfectly-plastic solids and elastic–plastic solids with work-hardening. These relationships provide new insight into the shape of indentation curves and are also useful as a guide to finite element computation of conical indentation. Giannakopoulos and Suresh6 have proposed a systematic framework to obtain elastic plastic properties from the P − h data, but their results are mainly based on small deformation finite element analysis. Recently, Dao et al.7 carried out a comprehensive computational study to identify the extent to which elasti
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