j ： numbers assigned to other copper atoms inside the cut-off radius other than a certain copper atom affected by the Morse force of cutter
4. RESULT AND DISCUSSION
4.3 Analysis on the Numerical Values of Equivalent Strain and Equivalent Stress in Nanocutting State
For the cutting model of copper material with point-defect concentration of 0.1%, it cut to the 5,000th step to observe the distribution trend of equivalent strain and equivalent stress. The diagrams of equivalent strain and equivalent stress when the cutting reached the 5,000th step are shown in Fig. 5. The maximum numerical value of equivalent strain produced when using sharp diamond cutter for cutting was around 1.0, and the maximum numerical value of equivalent stress was around 3.7 GPa. The maximum numerical value of equivalent strain produced when using the round-edge diamond cutter with nose radius of 10Α for cutting was around 0.9, and o the maximum numerical value of equivalent stress was around 3.5 GPa.
(a) Equivalent strain (b) Equivalent stress (c) Equivalent strain (d) Equivalent stress Fig. 5 Diagram of distribution trend of (a) equivalent strain, and (b) equivalent stress of the
cutting of copper material by the sharp diamond cutter, (c) Equivalent strain and (d) Equivalent stress by the round-edge diamond cutter with nose radius of 10Å , the cutters all with rake angle of 10o and copper material with point-defect concentration of 0.1%
at the 5000th feed step
For the cutting model of copper material with point-defect concentration of 0.5%, it cut to the 5,000th step to observe the distribution trend of equivalent strain and equivalent stress. The diagrams of equivalent strain and equivalent stress when the cutting reached the 5,000 step are shown in Fig. 6. The maximum numerical value of equivalent strain produced when using sharp diamond cutter for cutting was around 0.6, and the maximum numerical value of equivalent stress was around 3.3 GPa. The maximum numerical value of equivalent strain produced when using the round-edge diamond cutter with nose radius of 10 Å for cutting was around 0.5, and the maximum numerical value of equivalent stress was around 3.1 GPa.
(a) Equivalent strain (b) Equivalent stress (c) Equivalent strain (d) Equivalent stress Fig. 6 Diagram of distribution trend of (a) equivalent strain, and (b) equivalent stress of the
cutting of copper material by the sharp diamond cutter, (c) Equivalent strain and (d) Equivalent stress by the round-edge diamond cutter with nose radius of 10Å , all cutters with rake angle of 10o and copper material with point-defect concentration of 0.5%
Having synthesized the above results, it can induce Table 2. When the copper material has a higher defect concentration, the values of the produced equivalent stress and strain are smaller.
The possible reason is that the copper material with point defect would be filled up by other atoms of copper. As a result, the deformation of element of the copper material with point defect is not as great as the deformation of the perfect crystal copper material, and the numerical value of equivalent strain and stress of the copper material with point defect is smaller than that of perfect crystal copper material. Besides, it is observed that the equivalent strain and equivalent stress acquired by using the diamond cutter with a rake angle of 10o for cutting have an island-shaped distribution trend on the rake face of diamond cutter, whereas the equivalent strain and equivalent stress acquired by using the round-edge diamond cutter with nose radius of 10Å for cutting have an island-shaped distribution trend at the round edge of the nose radius of diamond cutter.
Table 2: Numerical value of equivalent stress produced when copper materials with different defect concentrations is being cut
Sharp diamond cutter with a
rake angle of 10o 10Å round-edge diamond cutter
Copper material Maximum numerical value of
equivalent stress (GPa) Maximum numerical value of equivalent stress (GPa) Point-defect concentration of 0% 3.8 3.7
Point-defect concentration of 0.1% 3.7 3.5 Point-defect concentration of 0.5% 3.3 3.1 5. CONCLUSIONS
This paper develops a quasi-steady molecular statics nanocutting model to simulate the nanocutting of copper material with point defect in order to observe the effects of point defect on cutting action, cutting force, equivalent strain and equivalent stress. The quasi-steady molecular statics nanocutting model used by this paper is the calculation of the trajectory of each atom to solve directly the equilibrium equation of Morse force in X direction and Y direction, and the use of Hooke-Jeeve searching method in engineering optimization to find the displacement position of copper atom. After that, according to the displacement of copper atom, nanoscale equivalent strain and equivalent stress are employed to analyze the distribution trend of equivalent strain and equivalent stress. According to the above nanocutting simulation results, the following phenomena are drawn:
(1). During the simulation of nanocutting action, when the diamond cutter cuts the copper material with point defect, the copper workpiece would be jostled as affected by the Morse force of diamond cutter, and the place of point defect would be filled up. Therefore, at the same feed steps, the chip length of the copper material with point defect would be made shorter than that of perfect crystal copper material.
(2). Regarding the calculation of horizontal cutting force and normal cutting force, it is found that point defect exists, thus acquiring the numerical values of horizontal cutting forces and normal cutting force are different on the perfect crystal copper material and on the copper material with point defect. Especially before the cutting reaches the defected place, there is quite a great difference of horizontal cutting force and normal cutting force among the different point-defect materials. Generally speaking, for the cutting of copper material with point defect, the horizontal cutting force at the place around the point defect is smaller than the horizontal cutting force on perfect crystal copper material. Using different diamond cutters for cutting would also produce different results. When sharp diamond cutter is used to cut the copper materials with the different point defect concentrations, there will be a more obvious difference of horizontal cutting force among them, but with no obvious
difference of normal cutting force among them. Nevertheless, when round-edge diamond cutter is used for cutting, no matter horizontal cutting force or normal cutting force, an obvious difference will be caused.
(3).The numerical value of equivalent stress produced by using round-edge diamond cutter to cut the copper materials with different defect concentrations is smaller than the numerical value of equivalent stress produced by using sharp diamond cutter.
6. ACKNOWLEDGEMENTS
The authors thank National Science Council (grant number NSC-96-2221-E-011-106-MY3) supporting this research.
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Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis ESDA2010 July 12-14, 2010, Istanbul, Turkey
ESDA2010-25139
MEASUREMENT SIMULATION MODEL AND QUALITATIVE ANALYSIS OF