3.5 Summary
4.1.1 Effects of crystallographic orientation on nanoindentation
4.1.1.1 Effects on P-h curves and dislocation density
Crystallographic orientations have significant impact on the material properties as the atomic positions are different for different orientations. For the FCC material likeAl, Cu, etc., most common orientation for loading in nanoindentation is the h001i crystallo- graphic direction. Along with this direction, h110i and h111i directions are also inves- tigated in this study. In Fig. 4.1(a) the load displacement curves are shown for three different loading direction (h001i, h110i and h111i) of nanoindentation. It can be seen from the figure thath111i direction of loading shows the maximum force corresponding to the yield point as well as the highest indentation depth. The yield point (where the load drops with the displacement) is considered where the plasticity is introduced inside the material during the loading. For h001i and h110i direction the yield point is around displacement of 0.6 nm and for h111i direction yield point is found at displace- ment of 0.8 nm. The indentation force increases smoothly up to the elastic limits and after that there are some fluctuations in the load displacement curves which results from the dislocation nucleation and interaction. When the loading process is completed at
Chapter 4. Results and Discussion of MD Simulations 49 maximum indentation depth of 1.5 nm, the unloading process starts. In the unloading curves the load drops gradually and returns to the initial point with an impression of the indenter on the material surface after the indentation depth of 0.5 nm. The fluctuation in the load-displacement (P −h) curve can be further explained from the Fig. 4.1(b) where the dislocation densities are shown with indentation depth. From the figure, it can be seen that the dislocation density initiate at the same place where the yielding occurs. For h111i direction, the dislocation density curve jumps at slightly later than h001i and h110i direction. There are some initial dislocation in h111i direction which is basically produced during the equilibration process of the indentation which will be further explained in a future section.
In Fig. 4.2, contributions of different types of dislocations on the total dislocation of the materials are represented. In the Fig. 4.2(a), the dislocation analysis forh001idirection of indentation are shown. The dominant type of dislocation for this direction is Shockley partial dislocation. Partial dislocations are more energetically favorable compared to the perfect type of dislocation and create a stacking fault inside the materials. During the propagation in FCC metals, the perfect dislocation is dissociated into two partial dislocations which require less energy to move compare to the perfect dislocation. These partial dislocations are called ”Shockley partials” and they can glide as their burger vector lies in the stacking fault plane. On the other hand, partial dislocation whose Burger’s vector is not parallel to the fault plane, so that it can only diffuse and not glide, is termed as ”Frank partials.” However, the fluctuations in the P −h curve can be explained as it can be seen that some other dislocations interact with the partial dislocations and total dislocation density remains constant in the range of 0.8-1.0 nm indentation depth. In the regime of 1.0-1.5 nm depth of indentation, a sudden jump is observed in dislocation due to the fact that some dislocation locks themselves during the interaction of partial and Hirth dislocation. These dislocations are also get multiplied by loop formation. Moreover, it is evident that some other (Frank partials and Stair-rod type) dislocations still form in the high plastic zone of indentation (1 to 1.5 nm). Similar trend can be found forh110idirection indentation and for this direction of loading, there are less amount of lock formation. Here also, Shockley partial is the dominant type of dislocation. Similarly in case ofh111i orientation, the Shockley partial dislocation is the dominant mode of dislocation as depicted in 4.2(c).
Chapter 4. Results and Discussion of MD Simulations 50
(a) h001i (b)h110i
(c)h111i
Figure 4.2: Contribution of different types of dislocation on the total dislocation with displacement of the indenter
4.1.1.2 Effects on formation of dislocation loops
In Fig. 4.3, the formation and evolution of dislocation loops for different indentation depth are shown for loading in h001i direction . Form the figure, it can be seen that when the indenter is pushed inside the materials, the {111} h110i slip system becomes activated. As a result, the dislocations are produced along the primary slip plane and form a shape like a pyramid. Basically, this tetrahedron forms a dislocation lock. When the indenter penetrates further, at the higher force, this lock breaks down and an emis- sion of partial type of dislocation is observed. These partials create a stacking fault zone which is further enhanced in size due to the further indentation depth. During the unloading process these loops annihilate themselves and keep a trace of the initial tetrahedron inside the materials.
The dislocation formation in h110i direction is quite different from the h001i direction (see Fig. 4.4). Here, the dislocations are emitted from the edge of the indenter and there are two symmetric partial formation at the initial stage of loading which further
Chapter 4. Results and Discussion of MD Simulations 51
(a) 0.550 nm (b) 0.675 nm (c) 1.00 nm
(d) 1.10 nm (e) 1.50 nm (f) after unloading
Figure 4.3: Formation of dislocation loops at different displacement during indenta- tion inh001idirection
(a) 0.625 nm (b) 0.8 nm (c) 1.175 nm
(d) 1.3625 nm (e) 1.5 nm (f) unloading
Figure 4.4: Formation of dislocation loops at different displacement during indenta- tion inh110idirection
propagate and form a cylinder like pattern. Unlike h001i direction, in h110i direction, dislocation just moves downward and try to form a prismatic loop. When the unloading is performed, some of the loops still remain as shown in Fig. 4.4(f) .
In Fig. 4.5, formation of the dislocation loops during the indentation inh111idirection is presented where it can be observed that there are cross slip formations in this case.
It is well known that when there are energy barrier for dislocation in a particular slip plane, dislocation changes its direction on the other energetically favorable slip plane by gliding along the cross slip plane. So, it is obvious that the dislocation is thwarted more frequently inh111idirection of indentation and it is no exception that this direction will
Chapter 4. Results and Discussion of MD Simulations 52
(a) 0.750 nm (b) 0.950 nm (c) 1.150 nm
(d) 1.338 nm (e) 1.50 nm (f) unloading
Figure 4.5: Formation of dislocation loops at different displacement during indenta- tion inh110idirection
show higher load in theP−hcurve. After unloading, there are some distinct dislocation loops which stay within the materials.
4.1.1.3 Effects on von Mises stress distribution
The von Mises stress distribution signifies the stress anisotropy inside the materials and this stress field distribution has significant impacts on the material failure behavior. In Fig. 4.6, von Mises stress distributions are shown for h001i h110i and h111i directions at the mid position of loading, maximum loading, and for unloading. From the figure, it is clearly observed that the stress distribution is symmetric for h001i direction at mid loading position of the indenter at the maximum loading depth, the symmetric pattern of this distribution is distributed which changes the behavior of dislocation significantly. After the unloading, there is almost no residual stress on the substrate for this direction. Similar pattern can be seen for the h110i and h111i directions of indentation. However, there are some residual stresses exist after the unloading of these directions of indentation.
4.1.1.4 Effects on surface imprint
The surface imprint is a very important parameter for the indentation simulations. The reminiscent surface imprint after the unloading process of indentation can be directly
Chapter 4. Results and Discussion of MD Simulations 53
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 4.6: Von Mises stress distribution in (a-c)h001i, (d-f)h110i, (g-i)h111idirec- tions at mid loading, max loading and unloading.
verified by the experiment. In experiment, this surface imprint plays a critical role as the experimentalist directly measures the critical depth of indentation from microscopic image from this imprint. In Fig. 4.7, the surface imprints after indentation in different directions are shown. It is clear from the figure that different directions of indentation create different types of surface imprint. In all case, the pile up nature of the indentation surface is conspicuous. It is evident from the figure that the h111i direction surface imprint is comparatively more flat in nature while theh110idirection shows more depth in the residual imprint due to lowest dislocation density and hardness.
4.1.1.5 Effects on hardness and reduced modulus
The value of the hardness and the reduced modulus are shown in Fig. 4.8for different loading directions. From the figure, it is evident that both the hardness and the reduced modulus are lowest for the h110i direction of loading. The crystal direction of h110i
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.