List of Symbols
2.5 Performance Parameters
2.5.1 Machining Forces
29 was conducted on SiC to verify the analysis of the mechanics, and to estimate the critical undeformed chip thickness according to the proposed mechanics.
Observations:
From the literature review, it was learned that taper or plunge cutting can be used to study the ductile regime machining of brittle materials. This helps in determining the ductile to brittle transition zones thereby identifying the critical depth of cut. This is further helpful in producing crack free surface during machining of brittle materials. In a plunge cutting process, the depth of cut is varied from zero to few hundreds of nm, normally above the critical depth of cut of the workpiece material. A significant literature has been reported on experimental study of plunge cutting of silicon and silicon carbide. However, very scant literature is available on numerical simulation of plunge cutting simulation to determine the ductile to brittle transition of silicon and silicon carbide. A need thus exist to develop a numerical model for quicker and accurate prediction of ductile to brittle transition of silicon and silicon carbide.
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shear force, friction force and normal force component. In the late eighties, Oxley (1989) developed a slip-line theory based model to predict various machining parameters such as chip thickness and tool-chip contact length involved in the metal cutting process.
However, the primary assumption of sharp tool used in Merchant and Oxley’s models cannot be used in SPDT machining [Liu et al. (2004)]. As the depth of cut approaches to nanometric scale, the bluntness associated with the tool tip creates a ‘ploughing’ action rather than shearing, which is the primary mode of chip formation in SPDT process. Therefore, these models cannot be directly applied to determine the machining parameters during SPDT process. This led to the development of newer theories. Researchers have reported various analytical models to predict the machining parameters. Lo-A-Foe et al. (1988) proposed a analytical model based on the model introduced by Dautzenberg and his team to estimate the cutting force and surface profile while machining aluminum and brass using single point diamond turning. Patten et al. (2007) presented an analytical model by extending the existing Lee and Shaffer’s second model to predict the chip thickness, cutting force and thrust force.
Authors validated the developed model for nanometric machining of silicon carbide for the experimental condition of –45º rake angle tool and 50 nm and 250 nm depth of cut.
Literature reports eminent articles on experimental studies on the influence of process parameters on cutting force. Lucca et al. (1991) studied the effect of depth of cut on principal and thrust forces. It was concluded that the principal force becomes small and the thrust force increases as the depth of cut decreases. In case of very low depth of cut (smaller than the cutting edge radius), the effective rake angle changes to negative. Therefore, the material is forced to flow downward below the tool tip due to the edge radius. This causes the thrust force to increase and eventually cross over the cutting force. When the depth of cut increases above the cutting edge radius, shearing of material takes place, and then the thrust force decreases and cutting force increases.
Patten et al. (2005) carried out experimental studies on single crystal 6H-SiC by varying rake angles and depth of cut. Authors observed the ductile removal of SiC when the depth of cut is below 500 nm. This ductile behavior has been confirmed by production of smooth surfaces, formation of ductile chips and phase transformation to metallic state. Bhattacharya et al. (2005) carried out orthogonal ductile machining on polycrystalline SiC (6H) with three different diamond tools (one poly-crystal and two single crystal diamond tools from different manufacturer) having −45º rake angle and 5º clearance angle. Authors studied variation of cutting force and surface roughness with the depth of cut and type of diamond tool. It was reported that ductile regime machining of polycrystalline SiC is possible at depths of cut of 10 TH-2306_10610325
31 and 25 nm. In the subsequent work, Patten et al. (2007) and Patten and Jacob (2008) conducted FEM based 2D numerical simulations using pressure sensitive Drucker-Prager yield criterion. The generated cutting and thrust forces were compared with the experimental results. The results were in good agreement for smaller depths of cut (below the critical depth of cut). However, the simulations were not able to predict the forces where the experiments revealed brittle machining conditions as the model did not include a fracture criterion or brittle material removal mechanisms. Venkatachalam et al. (2009) proposed a predictive model to determine the undeformed chip thickness in micro-machining of single crystal silicon (1 1 1) materials. The comprehensive model includes a force model considering the rounded tool edge radius effect and ploughing. Yan et al. (2009a) carried out submicron-level orthogonal cutting simulation of silicon by using finite element approach. Authors investigated the effects of tool edge radius on cutting force, cutting stress, temperature and chip formation. It was observed that increase in the tool edge radius and a decrease in chip thickness causes a significant increase in the thrust force. The hydrostatic pressure generated in the cutting region also revealed the phase transformations in silicon.
Arif et al. (2013) developed an analytical model to predict the critical undeformed chip thickness for ductile–brittle transition in nano-machining of brittle materials based on specific cutting energy. The results were validated by carrying out the experimental study on silicon and BK7 Glass. The model was used to identify three distinct zones of machining, i.e., ductile-mode, transitional-mode and brittle-mode. Venkatachalam et al. (2015) studied the effect of microstructure on cutting forces and flow stresses in ultraprecision machining of polycrystalline SiC. MD simulations were performed to explore the effect of grain size, grain boundary and crystallographic orientation and found that both cutting force and thrust force increase with the increase in grain size. Goel et al. (2016) carried out MD simulations to study the mechanisms of plasticity during cutting of mono crystalline and polycrystalline silicon using polycrystalline and single crystal diamond tool. It was reported that the direct amorphisation from the pristine crystalline phase, in contrast to HPPT, is the root cause of plasticity in silicon. Moreover, the plasticity in silicon is triggered by large deviatoric stresses rather than the high temperature in the cutting zone. Similarly, Mir et al. (2017) presented numerical studies on surface defect machining (SDM) method in the fabrication of silicon using smooth particle hydrodynamics (SPH) simulation approach. An inverse parametric analysis was carried out to determine the Drucker- Prager (DP) constitutive model parameters of silicon from indentation test simulations. Cutting forces and steady-state chip formation in different defect type simulations were studied. It was revealed that SDM can be effectively
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exploited to attain better surface finish and reduced tool wear in single point diamond turning process.
Observations:
Analysis of machining forces is important in view of the computation of power consumption, machinability study, and prediction of tool failure. Till date, significant experimental works have been reported on understanding of the cutting mechanism and chip formation during machining of silicon and silicon carbide. However, as the machining scale enters from micro to nano regime, it becomes complicated and challenging to study the force, pressure, stress, and roughness during the cutting process. Important numerical research works on SPDT process using molecular dynamics (MD) have been reported to study the insight of the machining process by analyzing stress, chips formation, temperature, and phase change during the machining process. However, experimental validation of MD based results is still difficult due to its very small, i.e., atomic level study domain. Few attempts have been reported on numerical simulations using finite element method. Very scant literature is reported on the influence of various material models on the process performance during numerical simulation of SPDT process of brittle material. Selection of proper material model is essential in obtaining accurate results. Researchers have reported use of various material models such as Johnson-Cook, Johson-Homilquist and Drucker-Prager for modeling of ceramic materials. However, there is no comparative study amongst these material models for machining of Si and SiC is reported till date. Also, scant research work is reported on systematic parametric study based on the numerical simulation of SPDT of Si and SiC.