When the uncut chip thickness gradually decreases, removal of the mate- rial takes place across the grains as shown in Figure 3.8. In this case, the typical failure path shown in the figure moves across the grain instead of, along the grain boundary [18]. Resistance offered for the material removal becomes enormous, as the defect density along the path of failure becomes much lesser. Defects like dislocations and vacancies within a grain play a major role in providing the failure path. As the uncut chip thickness value reduces from the micro to the nano level, the defect density becomes lesser and the resistance to the removal of the material increases significantly [19,20]. This resistance to the material removal also affects the tool life and
Typical crack initiation point Direction of
tool movement
Typical material separation path Grain boundary
Grain Tool
FIGURE 3.7
Multigrain mode material removal.
Crack initiation at dislocation Tool
Dislocations
Typical material separation path within
Direction of tool movement
Single grain
FIGURE 3.8
Sub-grain material removal.
causes its deterioration. Figure 3.9 shows a typical graph indicating the cor- relation between uncut chip thickness and the specific cutting energy. At the atomic level of uncut chip thickness, the specific cutting energy is equivalent to the atomic bonding force.
Figure 3.10 shows various regions for a typical cutting process. Regions I, II and III represent the regions corresponding to nano cutting, micro cutting and macro cutting, respectively.
Unlike the single point machining process, the abrasive-based micro- and nano-finishing processes gradually remove only the project- ing peaks, until all of them are smoothed out. Once all the peaks are removed, material removal slows down. Figure 3.11 shows various stages of material removal by a single loosely held abrasive. Figure 3.11a shows the interaction of abrasive particle with the peak of the micro irregular- ity, and Figure 3.11b shows a partially sheared off chip over the peak. In this stage, the abrasive particle and chip are joined due to the secondary bonding force. As the length of shear plane along the cutting path gradu- ally reduces, the material resisting force becomes lesser than the second- ary bonding force existing between the abrasive and chip. Subsequently, it leads to the removal of the chip.
As experimental techniques cannot be applied effectively when uncut chip thickness is at the nanometric level, the molecular dynamics simula- tion (MDS) technique is extensively used to explain the material removal behaviour at the nanometer scale level [21,22]. Figure 3.12a shows a typi- cal molecular dynamic simulation for a tool–work-piece interaction.
There are three types of atomic layer regions, namely, the Newtonian layer, the thermostat layer and the boundary layer. The Newtonian layer atoms follow Newton’s second law of motion under specified pair
Uncut chip thickness (in microns)
Specific cutting energy (in GPa)
0 1 2 3 4 5 6
20 60 100 140 180
Material: Brass Tool nose radius
1.2 microns
Tool: Single crystal diamond
FIGURE 3.9
Effect of uncut chip thickness on specific shear energy.
37 Mechanism of Material Removal
Region III (Base material)
X X X X X X X X X X X X X X X X X X X
X X X X X X X
X X X
Crystal grain void range (>10 μm)
Grain boundary Dislocation (movable) Precipitant
Cavity, crack
Precipitant
II III I
Region I
X X
X X
Dislocation Points defects range (Atomic cluster) [1 nm–0.1 àm]
Vacancy Interstitial
atom Lattice atom
Dislocation range
(0.1 àm–10 àm) Micro-crack range (0.1 àm–10 àm)
X X X X X
X X
X X
Dislocation Precipitant 1 àm
1 àm Region II
Tool
Work
FIGURE 3.10
Macro, micro, and nano cutting regions.
Abrasive Shear plane Work-piece
Possible path of abrasion to get
another chip
Interaction due to secondary bonding force
Chip
Work-piece Work-piece
Abrasive Abrasive
(a) (b) (c)
FV
FC
FC - Cutting force FV - Holding force FIGURE 3.11
Material removal by abrasive particle. (a) Abrasive starts touching the work-piece. (b) Abrasive shearing the peak. (c) Peak sheared as chip.
potential interaction. Whenever two atoms come near to each other, they are subjected to inter-atomic force which is a negative derivative of the pair potential. This force is used to move the atoms. Velocity and position of the atoms are computed using the Verlet algorithm. Thermodynamic aspects are computed by applying conservation of number of atoms, vol- ume and energy of the Newtonian region. During atomic movements, a rise in the local temperature is carried away by the thermostat layer. All atoms in this region will have the same temperature. Atoms in the bound- ary layer region provide fixed boundary condition. Among other factors, MDS helps to visualise and analyse the following:
• Shear plane and chip formation
• Type of crystal
• Temperature
• Phase transformation
• Interaction between two bodies like work material and tool
Figure 3.12b and c show MDS for different ratios of uncut chip thick ness to tool edge radius, when copper and single crystal diamonds are used as work material and tool material, respectively. Similarly, Figure 3.12d and e show MDS for different ratios of uncut chip thickness to tool edge radius or
Boundary atoms ermostat atoms
Work material
Tool
Uncut chip thickness, a = 10 Å
Cutting edge sharpness, r = 0 (Sharp cutting edge), Cu Chip formation due to
shear plane deformation
a/r = 0.5, a = 10 Å, r = 20 Å, Cu Large deformation
No shear plane Adhesion with tool
at rake and flank face
a = 10 Å, r = 0, (Sharp cutting edge), Si Adhesion with rake
and flank face Deformed
layer
Deformed layer
a/r = 0.5
a = 10 Å, r = 20 Å, Si Newtonian atoms
(a) (b)
(c) (d)
(e) FIGURE 3.12
(a) MDS layers; (b) MDS for Cu with sharp tool; (c) MDS for Cu with finite tool sharpness;
(d) MDS for Si with sharp tool and (e) MDS for Si with finite tool sharpness.
39 Mechanism of Material Removal
sharpness, when silicon (Si) and single crystal diamonds are used as work material and tool material, respectively.