Machinery's Handbook, 31st Edition
DUCTILE REGIME MICROMACHINING 1173 on the tool rake face. These specific directions and planes are called slip systems. Soft materials such as copper and aluminum have more slip systems, therefore, are easier to be machined compared to harder materials such as steel with fewer slip systems. The directional Miller index is the coordinate of a vector representing the atom sliding direction. In Fig. 13a, if the atom slides from C to G (also the same as sliding from O to D), then this vector with corresponding coordinates are given by: CG OD x x,y y,z z D O D O D O = = − − − = 6 @ [0, 0, 1] or [001] direction Similarly, if an atom slides from B to A (or C to O) then the Miller direction is: BA CO x x,y y,z z or direction O C O C O C = = − − − = 6 6 6 @ @ @ 0, − 1, 0 010 The Miller plane represents the planes that intersect with the coordinate system. The plane DEFG in Fig. 13a, congruent with OABC, intersects the z-axis while parallel with the x and y axes. The Miller index for this plane is represented by the inverse of the axis intersection: , , , , x y z 1 1 1 1 1 1 1 0,0,1 001 Plane DEFG intercept intercept intercept or plane ∞ ∞ = - - - = = a a ^ ^ k k h h The plane EGCA in Fig. 13b, congruent with DFBO, intersects the x and y axes while parallel with z axis. The Miller index for this plane is: , , , , 1 1 1 1 1 1 1 1,1,0 110 Plane EGCA or plane ∞ = = = a a ^ ^ k k h h 1 x y z intercept intercept intercept - - - The plane DCA in Fig. 13c, congruent with BEG, intersects all the x, y, and z axes. The Miller index for this plane is: , , , , 1 1 1 1 1 1 1 1,1,1 111 Plane DCA or plane = = = a a ^ ^ k k h h 1 1 x y z intercept intercept intercept - - - Miller Index Nomenclature: In both direction and plane Miller indices, any minus sign is written on top of the number, for example [111], and all commas are omitted for simplicity. Square brackets “[ ]” are used to indicate a specific direction, and pointed brackets “< >” are used to indicate a family of directions with similar geometries. For example, the <100> family has 12 directions similar to [100], [001], …, which are all the edges of the cube in Fig. 13a. Parentheses “( )” are used to indicate a specific plane, and curly brackets “{ }” are used to indicate a family of planes with similar geometries. For example, the {100} family has 6 planes similar to (100), (001), …, which are all the surfaces of the cube in Fig. 13a. Introduction.— The concept of ductile-regime machining has been investigated since the 1960s for amorphous brittle materials such as glasses. Silicon, germanium, and glasses have become strategic materials that are widely used to fabricate intricate com- ponents in microelectronics, optical, defense industries, and recently as micro optical- electrical-mechanical systems. Silicon and other brittle materials are known for their low machinability unless they are machined in the ductile-regime conditions. When utilized at the optimal machining conditions, only minimum effort is required for the subsequent etching, grinding, or polishing to remove the damaged subsurface. This section summa- rizes the theory and provides practical guidance for ductile regime machining. Theory.— The mechanism of ductile-regime machining has been studied by many re- searchers. Using a fracture mechanics approach, it can be shown that there is a threshold below which the ductile regime prevails: (12) d A H E H K fracture energy plastic flow energy c c 2 = = a a k k
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