3.5 Summary
4.1.2 Effects of indentation speed
Chapter 4. Results and Discussion of MD Simulations 54
(a) (b) (c)
Figure 4.7: Surface imprint after unloading in (a)h001i, (b)h110i, (c)h111idirection.
(a) (b)
Figure 4.8: (a) Hardness, and (b) reduced modulus for loading inh001i, h110i, and h111idirection.
is the weaker direction for the pure Al as a result both the hardness and the reduced modulus are lower. The hardness for other two directions are comparable while the reduced modulus for theh111i direction is higher than h001i direction of loading.
Chapter 4. Results and Discussion of MD Simulations 55
(a) (b)
(c)
Figure 4.9: Load-displacement curves for different speeds during indentation in (a) h001i, (b)h110i, and (c)h111idirection.
the curves obtained for 10 m/s and 50m/s indentation velocity. However, the computa- tional time required for 10 m/s is 5 times higher than that required for 50 m/s. So, for the subsequent simulations shown in this thesis, unless otherwise mentioned, they are carried out for speed of 50 m/s.
Fig. 4.10 shows the variation of dislocation density with the indentation speed for different crystallographic orientations. For h001i and h110i directions, the dislocation density is significantly lower for higher velocities while the pattern is opposite in the h111idirection. It is also observed that before yielding dislocation density is highest for
Chapter 4. Results and Discussion of MD Simulations 56
(a) (b)
(c)
Figure 4.10: Variation of dislocation density for different speed during indentation in (a)h001i, (b)h110i, (c)h111idirections.
1000 m/s velocity but after yielding there is no clear observable trend.
4.1.2.2 Effects on formation of dislocation loops
The formation of dislocation loops for different indentation speed is shown in the Fig.
4.11. From the figure, it can be depicted that there are formations of two Shockley-partial pair inh001idirection at low speed (10 m/s) which repels each other and send each other away. If the speed is increased up to 100 m/s, similar pattern in the dislocation loop formation prevails. At much higher speed (1000 m/s), there are some blunting effects.
Chapter 4. Results and Discussion of MD Simulations 57
(a) 10 m/s (b) 50 m/s (c) 100 m/s (d) 1000 m/s
(e) 10 m/s (f) 50 m/s (g) 100 m/s (h) 1000 m/s
(i) 10 m/s (j) 50 m/s (k) 100 m/s (l) 1000 m/s
Figure 4.11: Dislocation formation at the maximum loading position for different speeds during indentation in (a) h001i, (b)h110i, (c)h111idirection.
The loops do not propagate as much as in case of lower speed. The pattern for h110i direction is quite different from the h001i direction of indentation. Here, at low speed it can be seen that there are formations of the prismatic loop which becomes separated from the main loop and moves towards the bottom surface. At 50 and 100 m/s speed, the dislocation loops are formed along the edge of the indenter. Shockley partial type dislocation loops are mainly visible. At 1000 m/s, the dislocation loops are not fully formed. It seems that they are arrested inside the materials for this higher speed. Similar trend is found for theh111idirection of indentation. At low speed the dislocation loops are formed. Here cross slip are more prominent and there are many partial dislocation loops with cross slip. At 1000 m/s, the loops are not fully formed and make a lock in their way.
4.1.2.3 Effects on hardness and reduced modulus
In Fig. 4.12, the variation of hardness and reduced elastic modulus in different directions are shown with indentation velocity where it is observed that the hardness increases with velocity significantly. Though the dislocation density is low forh001iandh110idirections at higher velocity, the hardness of the materials is higher. The dislocation patterns in the
Chapter 4. Results and Discussion of MD Simulations 58
(a) (b)
Figure 4.12: Variation of (a) hardness and (b) elastic modulus with indentation velocity on different loading directions.
higher speed are quite different from the low speed. At high speed the dislocation loops lock each other and make it harder for the indenter to penetrate inside the materials.
The hardness value is lower for theh110idirection compare to the other direction as the total dislocation inside the material is less. The reduced modulus also shows a similar pattern. However, the reduced modulus increases significantly for theh111i direction at the high speed.
4.1.2.4 Effects on von Mises stress distribution
Fig. 4.13 shows the von Mises stress distribution during the indentation at different speed and at different stage (mid depth, full depth, and unloading) of indentation in h001i direction. It can be seen from the Fig. 4.13(a) that the stress distribution is more or less symmetric in the mid loading position. The value of the von Mises stress generally increases with the indentation speed. At maximum loading (Fig. 4.13b), the stress distribution is symmetric for 100 and 1000 m/s but at low speed of 10 and 50 m/s it shows non-symmetric pattern. After the unloading, the maximum residual stress is seen for the 1000 m/s indentation speed. Similarly, the von-Mises stress distributions forh110i direction are shown in Fig. 4.14 for different indentation speed. Results show similar trend as in case of h001i direction.
However, the stress distribution for h111i direction is completely different from the other two directions as shown in Fig. 4.15. For this case, the symmetric pattern of the stress distribution at the mid-loading position is broken down at the maximum speed of 1000 m/s. Also, at maximum loading, for all the speed the stress distribution is
Chapter 4. Results and Discussion of MD Simulations 59
(a) 10 m/s (b) 50 m/s (c) 100 m/s (d) 1000 m/s
(e) 10 m/s (f) 50 m/s (g) 100 m/s (h) 1000 m/s
(i) 10 m/s (j) 50 m/s (k) 100 m/s (l) 1000 m/s
Figure 4.13: Von Mises stress distributions (a-d) at 0.75 nm loading , (e-h) at 1.5 nm loading, (i-l) completely unloading during indentation inh001idirection.
non-symmetric. This is due to the dislocation formation and propagation in different slip plane inside the materials. Moreover, there are significant amount of residual stress after unloading for different speeds inh111i direction of the indentation.
4.1.2.5 Effects on surface imprint
The surface imprint for different indentation speeds and loading directions is shown in Fig. 4.16. It is observed that at 1000 m/s, the surface imprint is more flat compared to the other indentation speed with comparatively less pile ups of the material. In h111i direction, the materials are more spreaded on the surface compare to the other two directions.
Chapter 4. Results and Discussion of MD Simulations 60
(a) 10 m/s (b) 50 m/s (c) 100 m/s (d) 1000 m/s
(e) 10 m/s (f) 50 m/s (g) 100 m/s (h) 1000 m/s
(i) 10 m/s (j) 50 m/s (k) 100 m/s (l) 1000 m/s
Figure 4.14: Von Mises stress distributions (a-d) at 0.75 nm loading , (e-h) at 1.5 nm loading, (i-l) completely unloading during indentation inh110idirection.