List of Symbols
3.1 Motivation and Objectives of Present Work
45 CHAPTER 3 A STUDY ON DUCTILE REGIME MACHINING USING NUMERICAL
SIMULATIONS OF NANOINDENTATION 3.0 Scope
This chapter primarily focuses upon the study of ductile regime machining of brittle materials during single point diamond turning with the help of finite element simulation of nanoindentation. Initially, an overview of the work carried out in this chapter is presented. A study on ductile behavior and transition from ductile to brittle regions that occur during the nanoindentation process of brittle materials viz. silicon (Si) and silicon carbide (SiC) has been carried out. Details of the development of the finite element based model of nanoindentation in terms of assumptions, governing equations, model geometry, material behavior modeling, damage model, meshing, surface contact modeling, boundary conditions, and solution methodologies are presented. After the development, a comparison with published experimental results is presented. Effects of various process conditions and parameters on responses are studied and presented in detail.
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instrument, fluctuation of machining force and specific cutting energy during unit removal of material can be studied.
Ductility of a material can be defined as the extent to which materials can be deformed permanently without fracture. All materials exhibit the property of ductility, no matter how brittle they are. Glass exhibits perfectly brittle at macroscale whilst it undergoes plastic deformation at the micro scale [Xi et al. (2005)]. Over the past two decades, extensive and eminent research works have been carried out on the evaluation of plastic deformation of hard and brittle materials like glass and ceramics through indentation, scratching, scribing, grinding and machining. The hypothesis of ductile-mode machining of brittle materials has emerged from the indentation of brittle materials. Researchers noted that indentation of brittle material with a very small depth of indentation by a sharply pointed diamond indenter leaves some irreversible deformation zone without any fracture [Lawn and Evans (1977, 1980), Marshall and Lawn, (1986)]. It was also reported that if the brittle material is processed with cutting condition below a critical depth of cut, plastic flow occurs and a crack free machined surface can be obtained [Puttick et al. (1989)]. Brittle materials such as silicon and silicon carbide may behave like ductile materials at ambient conditions if sufficient contact pressures are applied, i.e., above 9-16 GPa for silicon [Cheong and Zhang (2000), Domnich et al.
(2000), Domnich and Gogotsi (2001), Cai et al. (2007b)] and 30-60 GPa for silicon carbide [Chang and Cohen (1987), Patten et al. (2005), Patten and Jacob (2008)]. These findings may be useful in smoother and crack-free machining of brittle materials. Significant literature is reported on measurement and analysis of residual stresses in the indentation zone [Scattergood and Blake (1990), Bifano et al. (1991), Blackley and Scattergood (1991), Leung et al. (1998), Patten and Jacob (2005)]; however, very scant literature is available on in-situ measurement of contact pressures. Thus, it was found to be worthy and interesting research direction on understanding the ductile regime machining mechanism by using in-situ measurement and analysis of contact pressures in the nanoindentation process.
The main objective of this chapter is to understand; study and investigate the ductile-to- brittle transition, i.e., to identify the critical depth where the transition from ductile to brittle occurs by carrying out finite element simulations of nanoindentation. For brittle materials, nanoindentation finds a very important and useful technique as it is capable of finding physical parameters which are difficult to obtain from general tensile/compression tests. It provides nanometric displacement to the tip of the indenter and records a very small load value (of the order of mN) with a high degree of precision. The capital cost involved in nanoindentation instrument is very high in comparison to that of conventional micro hardness testing instruments.
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47 Although the experimental study is regarded as defining methodology to study and analyze any problem, it is very difficult to obtain the in-situ information about the stress and pressure developed, temperature profile, and displacement underneath the indenter during physical experiments. Therefore, use of numerical techniques such as finite element method (FEM), finite volume method (FVM) can be thought to be simple, easy and economical alternatives to costly, tedious and time-consuming physical experiments. By using numerical techniques, one can carry out simulations of nanoindentation process by mimicking and analyzing the actual process while performing the indentation. Thus, it was thought worthy to develop a numerical model for two-dimensional nonlinear dynamic explicit analysis of nanoindentation of brittle materials for various sets of process conditions.
In this work, FEM-based simulations of nanoindentation of silicon and silicon carbide have been carried out by using spherical indenter. In the case of nanometric machining, the depth of cut is very small, the tool becomes blunt, and the workpiece is compressed underneath the tool edge. This phenomenon can be characterized as a loading process of the indentation process. Due to the compressive force experienced by the workpiece, the brittle material changes its phase from brittle to ductile. Thus, the main interest of this work is to study the occurrence of ductile onset of brittle material by carrying out finite element based numerical simulations of nanoindentation and plunge cut simulations. The present study has been carried out to achieve the following objectives.
To explore nano-mechanical responses during static nanoindentation of brittle materials such as silicon (Si) and silicon carbide (SiC).
To assess the feasibility of modeling and simulation of a hardness test using the finite element method.
To derive basic mechanical properties of Si and SiC from the FEM based model and simulated results.
To validate the results predicted by the proposed methodology by using the published experimental load-displacement graphs.
To examine the occurrence of ductile onset of brittle material by measuring the in-situ contact pressures.
To obtain the critical transition depth of cut and to study the insights of ultra-precision machining of SiC.
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