PSI - Issue 43

Kevin Blixt et al. / Procedia Structural Integrity 43 (2023) 9–14 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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parameter for copper is set to a Cu = 3.615Å and for carbon to a C = 3.57Å, and the masses to m Cu = 63.55u and m C = 12.01u, respectively. The system was relaxed with the thermal boundary and the workpiece atoms governed by the canonical ensemble (NVT). The temperature was linearly ramped from 30K to 293K during 30000 timesteps, with timestep Δt = 5fs, whereafter the system was held at 293 K for additionally 10000 timesteps. After relaxation the Newtonian atoms in the workpiece were set to follow the microcanonical ensemble (NVE). This makes it possible to determine the temperature induced in the workpiece by the cutting operation alone by subtracting the kinetic energy due to the centre-of-mass velocity from the average kinetic energy calculated in LAMMPS and convert this to temperature T i for atom i with mass m i and velocity v i , averaged over 300 timesteps as proposed by Zhen et al. (2014): 1 2 ∑ 2 = 3 2 =0 (1) with k B the Boltzmann constant. The temperature was spatially averaged over the n atoms within the distance 4 a Cu from atom i . Thermal conductivity between the tool and the workpiece was neglected. The force at the tool calculated as the sum of the interatomic forces for all tool atoms from the workpiece, and the force vector was averaged over 800 timesteps to reduce instantaneous fluctuations. As a measure of the plasticity the centrosymmetry parameter ( CSP ) according to Kelchner et al (1998) was used: = ∑ | + + 2 | 2 2 =1 (2) Here and + 2 are the vectors from the central atom to the N /2 pairs of opposite nearest neighbours with N = 12 for FCC crystals. The CSP is less than about 3Å 2 for purely elastic deformations. 4. Results and discussion 4.1. Chip formation The chip geometry depends on cutting depth, cutting velocity and tool geometry. In general, the deeper the cut, the thicker the chip and the smaller the tool radius the larger the pileup in front of the tool as illustrated in Figs 2a)-c) for the [100] orientation. For large enough tool radius, the tool mainly compresses the work piece material and only a small pileup is formed. One observation is that chip formation by folding can occur as illustrated in Fig. 3. First a pileup is created by the advancing tool (Fig. 3I) and a chip form and grows (Fig. 3II). As the chip gets large enough, it bends over (Fig. 3III) and forms a thicker chip (Fig. 3IV), and the process is repeated. This effect is enhanced with an increase in cutting velocity. Folding does not occur for small enough tool radii since the chip in this case raises backwards, over the tool, and the chip length increases. The crystallographic orientation also impacts the process significantly. Figures 4a)-c) show the CSP for the [100], [110] and [111] orientations, respectively, at corresponding positions. As seen, the orientation is crucial for the spread of plasticity. The green CSP -lines follow preferred slip planes, and the patterns suggest the emergence of grain structures as is more clearly seen in Fig. 5 which is close-up of Fig. 4b). The left part of Fig. 5 shows the activated slip planes as in Fig. 4b) and the right part is the result of a DXA analysis provided by OVITO, showing sectioning of the wake material into what appears to be a grain structure. This was most clearly seen for the [110] and the [111] orientations. Another observation is that the pileup is the smallest for the [100] direction and the largest for the [111] orientation, which also forms the largest chip. This is related to the dislocation patterns in front of the tool, where the [100] orientation shows fewer number of activated slip planes but a larger uplift of the surface ahead of the tool as compared to the [111] orientation. Thus, there seems to be a competition between surface uplift and chip formation.