Numerical and experimental studies on single point diamond turning of brittle and ductile materials

Abstract

The results were used to validate the developed FEM-IPT model and to investigate the effect of process parameters such as speed, feed and depth of cut on the surface roughness. It is believed that the developed integrated approach will be useful in predicting the surface roughness of the shop floor before the actual machining runs are performed.

Acknowledgements

81 3.21 Spherical nanoindentation of SiC showing an irregular stress field 82 3.22 Repetitive nanoindentation using a spherical indenter with nm depths 83 3.23 P-h graph for cyclic nanoindentation of silicon carbide with a spherical indenter 84 4.1 Overview of the work done to obtain the DBT thickness 88 4.2 Sch ematic of the developed numerical plunge cutting model 89. 98 4.9 Schematic representation of sliding and sticking regions at the chip-tool interface 98 4.10 Schematic representation of boundary conditions applied to tool and workpiece 99 .

List of Tables

List of Abbreviations

List of Symbols

Single Point Diamond Turning (SPDT)

It uses ultra-sharp poly or single crystal diamond tools to produce components with surface finishes on the order of Aº [Davis et al. According to Davies et al. 2003), the single crystal diamond turning experiments were first reported by Jesse Ramsden in 1779.

SPDT of Brittle Materials

As the depth of cut increases, so does the stress field and cracks form from defects. The literature reports plunge cutting experiments to determine the critical depth of cut of brittle materials.

Figure 1.2 Schematic of ductile regime machining [Redrawn from Blake and Scattergood (1989)]

Motivation for the Present Research Work

Understanding the effect of process parameters of SPDT on its performance parameters such as machining forces and surface roughness is important for improving the product quality and process efficiency. This thesis aims to understand the ductile regime machining by identifying the critical depth of transition and thereby predicting the machining force and surface roughness to optimize the process conditions for improving process efficiency and product quality.

Organization of the Thesis

It should be noted that the investigation of the effect of crystal orientation, tool wear, thermal and vibration is beyond the scope of this study. It is expected that the knowledge gained from the present numerical and experimental studies will be useful for researchers and industrial engineers to perform efficient, high-quality SPDT operations.

Chapter 4 presents finite element method based numerical simulations of plunge cutting of silicon and silicon carbide to study the ductile to brittle transition. Various output parameters

Then, simulations were performed on Al6061-T6 workpiece material to compare the surface roughness obtained with FEM-IPT technique with that of experimental results. A study on the influence of process parameters such as speed, feed and depth of cut on the surface roughness was presented.

Conventional Machining of Brittle Materials
Single Point Diamond Turning (SPDT)
Process Parameters of SPDT

Machining Parameters
Cutting Tool Geometry

Ductile Regime Machining of Brittle Materials

Ductile to Brittle Transition (DBT)
Nanoindentation
Plunge Cut

Performance Parameters

Machining Forces
Surface Finish

Numerical Modeling and Simulation of SPDT Process
Discussions
Objectives of the Present Research Work
Motivation and Objectives of Present Work
Overview of the Present Work
Nanoindentation and Computation of Mechanical Properties
Numerical Simulation of Nanoindentation for the Determination of Mechanical Properties

Selection of Solution Methodology
Development of FEM based Nanoindentation Model

The depth of cut (d) is the immersion length of the cutting tool inside the workpiece along the axial direction of the tool. Additionally, none of the literature attempted to determine the ductile to brittle transition thickness.

Figure 2.1 Schematic of Single Point Diamond Turning Machine

Idealize the body into ‘e’ finite elements

It should be noted that, after the indentation process, the surface of the workpiece material (i.e., location of interest) is free from the hydrostatic stresses. It is therefore convenient to use von-Mises stress to determine the various stresses and pressures of the nano-indentation simulation because it also does not include hydrostatic stress. It is also worth mentioning that the starting pressure is determined at the interface of indenter and workpiece, which still cannot be determined during the actual (physical) experiments.

The calculated pressures are compared with the hardness of the workpiece material (in relation to a possible HPPT or stress-induced amorphization). In dynamic problems, the field variables such as displacements, velocities, strains, stresses, and strain are all time dependent.

Assume the displacement model of an element ‘e’ as

Step 3: Derive the element characteristic (stiffness and mass) matrices and characteristic (load) vector. The strain can be expressed as

Computation of Young’s Modulus and Hardness from Load-Displacement Plot This section presents the methodology to compute the Young’s modulus and hardness

Computation of Elastic Modulus
Computation of Hardness
A Case Study

Experimental Validation of FEM based Nanoindentation Simulation

Experimental Validation of Nanoindentation of Silicon Carbide
Experimental Validation of Nanoindentation of Silicon

Study of Ductile to Brittle Transition (DBT) using Nanoindentation

Determination of DBT
Validation of DBT with Published Experimental Results

Numerical Study on the Effect of Residual Stress on DBT during Repetitive Indentation
Summary
The Need
Overview of the Present Work
Overview of the Process Model Development
Numerical Simulation of Plunge Cutting Process of Silicon

Governing Equations
Geometric Modeling
Material Model and Properties
Damage and Failure Models
Chip Separation Criterion
Finite Element and Meshing
Arbitrary Lagrangian Eulerian (ALE) Method
Contact Algorithm
Boundary Conditions
Solution Methodology
Post Processing

Results and Discussion

Determination of Critical Depth of Cut

The lower surface of the indenter and the upper surface of work materials formed a contact pair in the present numerical model. The contact radius can be found from the depth of the contact circle hc. In the present case, we have found that 1/3 of the data points give good results while calculating Young's modulus and hardness.

After validating the model, we analyzed the critical indentation depth, i.e. transition from ductile to brittle and phase-changing pressures. In the following, the details of the model development are given in the following sections. The details of the Drucker-Prager material model have already been presented in Section 3.4.2 (D) of Chapter 3.

According to these studies, the change in specific cutting energy can be used to determine the ductile-to-brittle transition phenomenon in the plunge cutting process.

Figure 3.6 Schematic of 2D axisymmetric indentation simulation model

Comparison of Methods used to Determine Critical Depth of Cut during Plunge Cutting Simulation

From the above analyzes of the critical depth of cut, a comparative analysis of all the three methods viz. From the table, it can be observed that in the case of a tool with an inclined angle of -30°, the critical depths of cut obtained from the analysis of the surface profile are higher than the experimental results [Yan et al. The critical depth of cut obtained from the force analysis was found to be much closer to the experimental values.

In addition, similar trends in the variation of transition depths were observed for tools with rake angles of 0 and -25 degrees in all three methods. There are no experimental transition depth values available in the literature for the validation for 0º and −25º inclination angle.

Numerical Simulation of Plunge Cutting of Silicon Carbide

For reference, Jacob et al. 2005) reported a transition depth or critical depth of cut of 70 nm for 6H-SiC in fly cutting experiment. 2018) also reported a critical undeformed chip thickness of 50 nm during the plunge cutting experiment of 6H-SiC with -30 rake angle, 10. From the overall analysis it is observed that study of variation of machining force provides results close to the experimental results for –30º rake angle tool.

It is also important to mention that the critical undeformed chip thickness obtained from nanoindentation simulation (Chapter 3) gives higher critical depth of cut compared to plunge cutting. Therefore, a lower value of critical undeformed chip thicknesses or ductile to brittle transition thicknesses is obtained during plunge cutting simulation.

Figure 4.20 Variations of the cutting and thrust forces during a single plunge cut using 0º rake angle tool

Summary

The criterion for initiation of the first brittle fracture was used to determine the critical depth of cut. In the second part, the variation of machining forces as a function of depth of cut was analyzed to determine the critical depth of cut. It was seen that with the increase in the depth of cut, the fluctuation/frequency of the force becomes more prominent in the brittle region than in the ductile region.

Furthermore, the work was extended by performing a simulation for silicon carbide and the critical depth of cut was determined. The analysis showed that the evaluated critical depth of cut was approximately 65 nm for rake angles of 0, –25 and –30.

The Need

Details of the development of a submicron level orthogonal cutting process that captures ductile deformation leading to material separation have been elaborated. A comparative study was also carried out into the effect of material models for silicon and silicon carbide. No literature has been reported on the study of the influence of material models during numerical simulation of the SPDT process of brittle material.

The present work was carried out to assess the ability of the developed numerical model to predict responses such as machining forces, chip morphology and stress during nanometric machining process of silicon and silicon carbide using the diamond tool. In addition, the effect of the extreme rake angle on the cutting force was also analyzed.

Overview of the Process Model Development

Patten and Jacob (2008), and Carroll and Strenkowski (1988) justified the comparison of the experimental results with 2D simulation results. Parametric studies were carried out for obtaining the optimum process conditions to obtain minimum machining force. The overview of the work carried out in this chapter is illustrated in Figure 5.2.

Case studies were conducted to analyze crack propagation, elastic recovery/spring back effect, roughness/plowing effect, and chip morphology. An integrated analysis using the finite element method (FEM) and response surface methodology (RSM) and full factorial analysis (FFA)) was performed for the prediction of machining forces and optimization of process parameters.

Figure 5.2 Overview of the work carried out in this chapter

Development of Numerical Model for SPDT using Finite Element Method

Material Model and Properties
Governing Equations
Element and Meshing
Contact Algorithms
Boundary Condition
Post Processing

In plunge cutting, the workpiece is held firmly and the tool is given an oblique movement to the surface of the workpiece as shown in Figure 5.4 (b). The detail of the Drucker-Prager material model has already been described in previous section 3.4.2 (D) of Chapter 3. This was verified from the observations of continuous chip formation and the structure of the generated surface.

During machining simulations, large deformation of the workpiece material occurs and the material is said to have failed when it loses its load carrying capacity. Other regions of the cutting tool were coarse meshed to increase the computational efficiency of the simulation.

Figure 5.3 Input and output parameters from finite element simulation of machining 5.3.1 Model Definition and Assumptions

Results Analysis

In FE machining studies, the results such as displacement, force, temperature, stress, surface profile or other fundamental variables from the simulation can be evaluated once the simulation is completed. To obtain the specified output results, variables must be selected from the field output and history output module prior to the simulation. All the data and results will be saved in a file with .ODB file extension during the simulation and can also be transferred to another system for analysis.

The following sections describe the extraction of force values and chip contour plots during machining simulations.

Numerical Simulation and Experimental Validation of SPDT of Silicon Carbide After the extraction of responses, the experimental validation of the responses

Study on Quantitative Crack Propagation using JC and DP Material Models
Parametric Analysis of SPDT of Silicon Carbide using FEM and Full Factorial Analysis
Full Factorial Design
Analysis of Results and Discussion
Confirmation Simulations
Multi-Objective Optimization of Machining Forces using FFA

From the plots it can be observed that the depth of cut greatly affects the shear strength. The interaction effects of tool rake angle and depth of cut on cutting force are shown in Figure 5.24 (a). It can be seen that the cutting force values are low at low depth of cut.

147 It can be seen that the depth of cut has the most significant influence on the pressure force. It can also be noted that increasing the depth of cut increases the compressive force value.

Figure 5.7 Comparison of cutting force for JC and DP model for set 1

Numerical Simulation and Experimental Validation of SPDT of Silicon

Experimental Validation of Machining Simulation of Silicon
Formation of Chips during SPDT of Silicon
Ploughing/Rubbing
Parametric Analysis of SPDT of Silicon using Response Surface Methodology After the validation of our developed model for silicon, parametric analysis has been
Response Surface Methodology
Parametric Analysis of SPDT of Si using FEM and RSM
Analysis of Results and Discussion

It can be seen that the cutting force increases with the increase in negative rake angle and decreases with the increase in cutting speed. It is observed that the cutting force increases with the increase in depth of cut. However, increasing the rake angle up to 30 nm depth of cut shows no significant effect on the cutting force value.

However, when the depth of cut is high (i.e. ≥ 30 nm), the cutting force increases with the increase of the negative rake angle. The effective rake angle of the cutting tool becomes more negative when the edge radius is greater than the depth of cut.