5.5 Numerical Simulation and Experimental Validation of SPDT of Silicon Carbide After the extraction of responses, the experimental validation of the responses
5.5.2 Study on Quantitative Crack Propagation using JC and DP Material Models
In this section, a quantitative analysis of crack propagation has been carried out to study the crack propagation mechanism and chip morphology during machining of silicon carbide. Figure 5.12 shows the crack initiation and its propagation during machining of silicon carbide using DP material model. It can be observed that the initiation of crack occurs after 1.95 μs (Figure 5.12 (b)). After 0.05 μs, the crack reaches to the top surface and a chip generates. During this process the crack travels a distance of 1.043 μm from point 1 to 2. The shear angle noted to be of 35 (approx.).
Figure 5.12 Crack propagation of silicon carbide with Drucker-Prager material model at (a) 1.5μs, (b) 1.95 μs, (c) 1.99 μs and (d) 2.0 μs
1.5 µs (250thframe) 1.95 µs (325thframe)
2.0 µs (334thframe)
35
1 2
Initiation of crack
Crack propagation
Secondary crack
Top surface Top surface
1
2
1
Tool
Workpiece
1.998 µs (333thframe)
(a) (b)
(c) (d)
Workpiece
Workpiece Workpiece
Tool
Tool Tool
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Figure 5.13 Crack propagation of silicon carbide with Johnson-Cook material model at (a) 1.5 μs, (b) 2.19 μs, (c) 2.4 μs and (d) 2.77 μs
Figure 5.13 shows the propagation of crack during simulation of machining of SiC using JC model. It can be seen that the initiation of crack occurs after 2.19 μs (Figure 5.12 (b)). After 0.576 μs, the crack reaches to the top surface and a chip is formed. During this process, the crack travels a distance of 1.052 μm from point 1 to 2 at an angle of 35 (approx.). From above observations, it can be verified that JC material model represents ductile material mode of cutting whereas the DP material model represents brittle behavior.
This can be justified by analyzing the time taken to propagate the crack from point 1 to 2. It can be seen that the JC model takes more time (0.576 μs) to propagate the crack as compared to that of DP model (0.05 μs) for same process conditions and tool geometry. The depth of cut and shear angles are same for both the cases, therefore the crack length is found to be same in both cases. The longer crack propagation time indicates that the material is getting deformed plastically. This is very analogous to the tensile test of ductile material; in which the material elongates and takes considerable time till it breaks. While, in case of brittle materials, the material breaks within a short duration without showing any noticeable plastic deformation.
To verify the conclusion that JC model predicts the ductile behavior, the chip morphologies were studied for both the JC and DP models. Figures 5.14 and 5.15 show the progression of workpiece deformation and chip formation for JC and DP material models. It can be seen that, long and connected chips are formed during SPDT of SiC using JC material
35
1 2
Initiation of crack
Secondary crack
Crack propagation
Top surface Top surface
1
1
Tool
Workpiece
(a) (b)
(c) (d)
Workpiece Workpiece
Tool
Tool Tool
2.19 µs (365thframe)
2.40 µs (400thframe) 1.5 µs (250thframe)
2.766 µs (461thframe)
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Figure 5.14 Contour plot of equivalent von-Mises stress with the formation of a continuous chip (0° rake angle, 5° clearance angle and 100nm depth of cut)
Figure 5.15 Contour plot of equivalent von-Mises stress with the formation of a brittle chip.
(0° rake angle, 5° clearance angle and 100 nm depth of cut)
Figure 5.16 shows optical microscopic image of the ductile chip obtained during the experimental cutting of SiC [Mariayyah (2007)]. The process conditions used were cutting speed of 0.8 m/s, depth of cut of 25 nm and feed rate of 25 nm/rev. The diamond tool was having a planar rake angle of −25 and a clearance angle of 10 and cutting edge radius of 50 nm. The formation of chips predicted by our model using JC is similar to the experimental results reported. The experimental results are reported for a very small depth of cut i.e. 25 nm, which can be considered to be less than critical depth of cut.
Ductile chips
Brittle chips
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Figure 5.16 Optical microscopic image of the ductile chip during experimental cutting of SiC [Mariayyah (2007)]
The formation of brittle chips during SPDT of SiC can be understood by using basic five stages. These are: (a) dynamic loading, (b) crack initiation, (c) crack propagation, (d) chip formation and (d) Formation of surface and sub-surface damage. Figure 5.17 shows the stages.
Figure 5.17 Five essential stages in the brittle material removal
Figure 5.17 (a) The tool touches the work piece, the impact between the tool and workpiece induces a stress field.
Figure 5.17 (b) The workpiece starts deforming due the compressive stress exerted by the tool. Due to the induced stress, a crack nucleation begins immediately and propagates as the machining process progresses. Since the deformation is more along the tool side of the chip, a localized plastic deformation zone is first formed in front of the tool and above the cutting edge. Then, an internal
Workpiece
Tool Cutting direction
(a) Dynamic loading and induced stress field
Workpiece
Cutting direction
Tool
Grains Crack initiation
(b) Crack initiation
Workpiece
Tool Cutting direction Crack propagation
Workpiece
Tool
(c) Crack propagation
(d) Chip formation
Workpiece
Tool Surface damage
Sub-surface damage (e) Formation of surface and
sub-surface damage Induced stress
Machined chip Fractured chip
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Figure 5.17 (c) The internal crack propagates and reaches the free surface and material is separated by fracture. Sometimes, a free surface crack also initiates during the deformation process and propagates toward the cutting edge to form a chip.
Figure 5.17 (d) The material shears strongly along the crack surface. Sometimes two cracks join together and discontinuous fractured chips are formed subsequently. The chips that formed due to the shearing of material are termed as machined chips. Fragments formed without any direct contact to tool face are called fractured chips.
Figure 5.17 (e) The brittle fracture not only forms the cracks but also creates sub-surface damage to the machined surface.
Figure 5.18 Stages of chip formation during SPDT machining of SiC
To verify the above stages, in the present work, a detail analysis has been carried out.
Figure 5.18 shows the various stages of chip formation and sub-surface damage. Figure 5.18 (a) shows the contour plots of stresses induced on the workpiece due to the impact of the tool.
Crack is initiated at the workpiece near to the tool tip (Figure 5.18(b)) and as the tool proceeds, the stress continues to develop and the crack grows and at last propagates to the free surface. This forms the chips (Figure 5.18 (c)). As a result two types of chips are obtained viz.
machined chips of larger size and fractured chips of smaller size (Figure 5.18 (d)). Figure 5.18 (e) shows the formation of machined surface with surface damage that occurred due to brittle fracture. From the above observations, it can be stated that our model is able to successfully simulate the SPDT machining of brittle materials and numerical results are fairly matching with the available published experimental results. After the validation of the developed model, a parametric analysis of machining forces using full factorial design has been carried out. This is presented in the next section.
Workpiece
Tool
(a) Dynamic loading and induced stress field
Workpiece Cutting
direction Tool Crack initiation
(b) Crack initiation
Workpiece
Tool
Cutting direction Crack propagation
Workpiece Tool
(c) Crack propagation
(d) Chip formation
Workpiece Tool Surface damage
(e) Formation of surface and sub-surface damage Induced stress
Machined chip Cutting direction
Fractured chip
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5.5.3 Parametric Analysis of SPDT of Silicon Carbide using FEM and Full Factorial