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Precision Engineering
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352 Models for Ductile Mode Machining of Brittle Materials
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Fracture mechanics predicts that even brittle solids can be machined by the action of plastic flow, as is the case in metal, leaving crack-free surfaces when the removal process is performed at less than a critical depth of cut [41] This means that under certain controlled conditions, it is possible to machine brittle materials, such as ceramics and glass, by using single-point diamond tools so that the material is removed by plastic flow, leaving a smooth and crack-free surface It has been reported that an almost 100% ductile mode machining is possible when machining hard materials using a well-defined geometry of single-point single crystal diamond tools on a rigid ultra-precision turning machine [43] The ductile regime is realized on the machined component that exhibits a mirror-like finish with a nanometric roughness, with crack-free smooth surfaces and a continuous ribbon chip generation during turning Although ductile mode cutting can be achieved through the application of this advanced technology, the rapid tool wear continues to present problems In order to overcome these problems, multi-point cutting (grinding) becomes more economic especially when machining hard and brittle materials Ultra-precision surface grinding making use of Electrolytic In-process Dressing (ELID) provides for in-process dressing of the wheel achieving almost 100% ductile surfaces with a mirror-like finish without the need for subsequent polishing when grinding optical glasses and silicon-based materials With conventional grinding machines, less than 90% ductile mode grinding is achievable because of lack of in-process dressing and therefore requires subsequent polishing Several models have been put forward to explain the ductile mode theory in real machining processes Blackley and Scattergood [41] and their colleagues Bifano and Fawcett [43] proposed the critical depth of cut and feed rate concept for ultra-precision machining as shown in Figure 338
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Fig 338: Blackley and Scattergood s model on ultra-precision machining showing on the left the 3-D view of a
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diamond tool cutting material and on the right a cross-sectional view of the tool and the workpiece [41]
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Mechanics of Materials Cutting
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An initial model was developed based on indentation fracture mechanic analysis According to Scattergood, fracture initiation plays a central role for ductile-regime machining A critical penetration depth, dc, for fracture initiation was derived by Blackley and Scattergood [41] as follows:
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K E (31) dc = b c H H where Kc is the fracture toughness, H is the hardness and E is the elastic modulus b is a factor that will depend upon geometry and process conditions such as the tool rake angle and coolant The left portion of Figure 338 shows a round nosed diamond tool moving through the workpiece, and Figure 338 (right) shows a projection of the tool perpendicular to the cutting direction Using the critical depth concept, fracture damage will get initiated at the effective cutting depth, dc (tc dc on the right side of Figure 338) and will propagate to an average depth, yc , as shown If the damage does not continue below the cut surface plane, ductile regime conditions are achieved The cross feed, f, determines the position of dc along the tool nose Larger values of f make dc to move closer to the centreline of the tool It is important to note that when ductile regime Fig 339: Evidence of subsurface damage [47] conditions are achieved, material removal still occurs by fracture The model proposed in Figure 338 (right) was verified by interrupted tests and the following relationship was obtained [41]: As per sine s law
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sin a sin b sin c = = A B C
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Applying this law to the cutting geometry,
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(32)
sin ( + ) = sin ( + ) sin = R f R
Precision Engineering
Fig 340: Tool workpiece interface showing subsurface damage
so that
sin ( + ) =
R sin f
Applying the trigonometric identity,
sin ( + ) = sin cos + cos sin
So we can write
sin cos + cos sin =
R sin f
Multiplying both sides by
1 cos R sin f
sin + cos tan =
f f sin + cos tan = tan b R R f f sin = tan 1 cos R R
Mechanics of Materials Cutting Therefore, tan b = From fig
( f R ) sin 1 ( f R ) cos
(33)
a = 90 q sin a = sin (90 q) = cos q cos a = sin q tan b =
and Since f/R <<< 1
( f R ) cos 1 ( f R ) sin
tan b = ( f/R) cos q From equation (33) and the aforementioned triangle in Figure 341, lets X = f/R sin b = cos b =
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