1.1 (a) A schematic setup for the nanoindentation test (Alaboodi and Hussain (2017)), (b) typical load-displacement curve of nanoindentation. List of Figures xii 4.28 Load-displacement curves for indentation in different grain sizes of poly-.
Nanomaterials and Its Properties at Nanoscale
Nanoindentation not only predicts material properties, but also provides insight into the plastic behavior of materials at the nanometer scale. The properties of the material can be even hundreds of times better at the nanometer compared to its bulk structure.
Nanoindentation
This point is considered the yield point of the material and the material exhibits plastic behavior after this pop-in event. Since the material experiences yielding and irreversible transformation, the unloading curve does not follow the loading curve.
Applications of Nanoindentation
When the final indentation depth is reached, the indentation remains idle for a few moments and then the unloading process begins. As the indentation moves in the opposite direction, the material also follows the indentation to release its residual stress, and after a certain time, the surface of the indentation breaks with the surface of the material, which creates a permanent impression of the indentation on the surface of the material as can be seen. from some examples shown in Fig.
Dislocations During the Nanoindentation
This stress field can significantly alter the plane of dislocation motion and cause dislocation pinning. Therefore, the dislocation mechanism within the alloy material where solute atoms are present is very complex in nature.
Aluminium and Its Alloys
Generally, the percentage of Mn in the alloy varies up to 5% and this type of alloy is used in radiators, air conditioner condensers, heat exchangers, piping systems, etc. In Al-Znalloy, the percentage of Zn can vary up to 8% and these alloys have higher strength, so they are widely used in aerospace technology.
Motivation of the Present Work
Like the bulk alloys, alloys can also be fabricated at nanoscale, and this type of nanoscale alloy of Al has improved material properties, which have numerous applications in nanotechnology, such as support and assemblies for nanoelectronics, lightweight structure, etc. These MD simulations are able to predict the elastic and plastic behavior of the materials during this process;.
Objectives of the Present Study
To the best of the author's knowledge, there is still a lack of atomistic study of nano-indentation in aluminum alloy and finding its mechanical properties at the nanoscale. The underlying mechanism of dislocations nucleation, propagation and interaction with each other and how this contributes to the plasticity of the material will also be investigated for Aland's alloys.
Thesis Outline
Verkhovtsev et al. (2013) studied nanoindentation in Ti crystal using MD simulation and studied the effect of indenter shape. Lu et al. (2009) studied the nanoindentation in F e using a hemispherical and pyramidal indenter and found that the shape of the indenter has a significant influence on the behavior of the nanoindentation.
Finite Element Study of Nanoindentation
Spearot and Sangid (2014) reviewed the plastic deformation process in polycrystalline materials and proposed how the grain boundary interacts with the dislocations. 2015) investigated the grain boundary effects for different crystallographic orientations of Åland suggested that the presence of a grain boundary requires higher strain to indent.
Summary
- Basic concepts
- Integration algorithm
- Temperature and pressure control
- Boundary conditions
- Inter-atomic potential
- Advantages and limitations of Molecular Dynamics (MD)
From this process it is possible to extract all the information about thermodynamic properties of interest. Molecular Statics is a modified version of molecular dynamics where the atoms are considered at zero temperature.
Molecular Dynamics Modeling of Nanoindentation
- Problem definition
- Simulation methodology
- Mechanical properties calculation
- Hardness and reduced modulus
- Von Mises stress calculation
- Dislocation density
- Validation of the Molecular Dynamics approach
- Validation of inter-atomic potential
- Validation with Hertz contact theory
- Visualization of results
For the hardness and indentation modulus calculation, the Oliver-Pharr (Oliver and Pharr, 2004) method was followed to use the data from the unloading portion of the load-displacement curve. Since the critical depth of the indentation is found, it is now possible to calculate the critical contact area using the following expressions (Oliver and elastic modulus of the indenter and the substrate.
However, the Hertz theory of contact stress is only applicable up to the elastic limit of the material.
Molecular Dynamics Modeling of Tensile Simulations
Problem definition
Simulation methodology
Calculation of tensile properties
Finite Element Method
- Axi-symmetry modeling of nanoindentation using FEM
- Software implementation
- Preprocessing
- Simulation
- Post processing of the results
- Grid independency study
- FEM code validation
Of the two available modules (ABAQUS-Standard and ABAQUS-Explicit module), the ABAQUS-Standard module is used for the current work because the indentation problem is modeled as a quasi-static problem (time effects are not taken into account). The first region is taken as 5 nm by 5 nm and a very fine mesh is used as this is the main contact area of the indenter and the substrate. First, the nodal forces and displacements for the indenter reference point are calculated.
The modeling of nano-indentation is performed considering the problem as axisymmetric problem and the dimension of the substrate was 2mm × 2mm.
Summary
Effects of crystallographic orientation on nanoindentation
- Effects on P-h curves and dislocation density
- Effects on formation of dislocation loops
- Effects on von Mises stress distribution
- Effects on surface imprint
- Effects on hardness and reduced modulus
In the discharge curves, the load gradually decreases and returns to the starting point with an imprint of the indentation on the material surface after the indentation depth of 0.5 nm. Partial dislocations are more energetically favorable compared to the perfect form of dislocation and create a stacking fault inside the materials. 4.3, the formation and evolution of dislocation loops for different indentation depths is shown for loading in the h001i direction.
It is clear from the figure that the stress distribution is symmetric for the h001i direction at the middle position of the indenter load at the maximum load depth, the symmetric pattern of this distribution is distributed, which significantly changes the dislocation behavior.
Effects of indentation speed
- Effects on P-h curves and dislocation density
- Effects on formation of dislocation loops
- Effects on hardness and reduced modulus
- Effects on von Mises stress distribution
- Effects on surface imprint
For h001i and h110i directions, the dislocation density is significantly lower for higher velocities, while the pattern is opposite in the h111i direction. Although the dislocation density is low in higher velocity directions, the hardness of the materials is higher. At high speed, the dislocation loops lock each other and make it more difficult for the indentation to penetrate the materials.
This is due to dislocation formation and propagation on different slip planes within the materials.
Effects of indentation depth
- Effects on P-h curves
- Effects on formation of dislocation loops
- Effects on hardness and reduced modulus
For this direction, there are no dislocation formations at 0.5 nm indentation, and as the depth increases, dislocation loops form along the edge of the spherical indenter. With further indentation depth, these partial dislocation loops form in the prismatic shape, which move towards the bottom of the substrate. For theh111i direction, dislocation loops are formed at the 1 nm depth, and all the loops show a cross-slip type dislocation behavior.
However, with greater indentation depth, the dislocation loops spread across the material, so they require less energy to propagate.
Effects of indenter size
- Effects on P-h curve
- Effects on formation of dislocation loops
- Effects on hardness and reduced modulus
- Effects on von Mises stress distribution
It can also be observed that with the increase in the size of the indentation, the number of dislocation loops also increases. With a larger indenter, the contact area of the indenter increases and the critical indentation depth after unloading decreases. The reduced modulus also shows an increasing trend with indentation size as the critical indentation depth decreases.
The von Mises stress distribution is shown for different indentation sizes at mid-load position (indentation depth =0.75 nm), maximum load depth and after unloading for h001i, h110 and h111i directions, respectively in Fig.
Indentation in Polycrystalline Aluminium
- Effects on P-h curves
- Effects on hardness and reduced modulus
- Effects on von Mises stress distribution
- Effects on surface imprint
Among the three polycrystalline curves, the strength is found to be maximum for the smallest grain size (4.98 nm). It is evident that as the grain size increases, the stiffness of the material decreases. It can be found that the reduced modulus is maximum for grain size of 5.70 nm and minimum for grain size of 7.17 nm.
On the other hand, for the largest grain size, there are fewer grains.
Nanoindentation of Al-Mg Alloy
- Effects on P-h curves and dislocation density
- Effects on formation of dislocation loops
- Effects on hardness and reduced modulus
- Effects on von Mises stress distribution
- Effects on surface imprint
It is observed from the figure that for h001i direction, with the increase of alloying element, the dislocation loops are increased. The dislocation networks become more dispersed throughout the material with the higher percentage of M g addition. For h111i direction, the dislocation loops are found to be reduced with the higher percentage of the solvated atomM g.
It is observed that with a higher percentage of the alloying element, the clustering phenomenon becomes more obvious.
Nanoindentation of Al-Cu Alloy
- Effects on P-h curves and dislocation density
- Effects on formation of dislocation loops
- Effects on hardness and reduced modulus
- Effects on von Mises stress distribution
- Effects on surface imprint
The dislocation loops produced at the maximum strain position for different percentages of Cu are shown in Fig. For 1 and 2% Cu addition, some blunt fronts in dislocation loops are visible, but for the other Cu percentages, the dislocation loops are able to propagate. Reduced modulus in the h110i direction is lower than the h001i direction for the different percentages of Cu addition.
The step-up effect is more prominent for the pure Al in all directions of loading.
Comparison Between P-h Curves of Al and Its Alloys
Tensile Loading on Al and Its Alloys Nanowire
Stress-strain curves are used to obtain the material's plastic properties, which are further used for the nanoindentation simulation in the Finite Element Method. 4.48 the stress-strain curves are shown for different percentages of M g and loading in different directions. The maximum breaking strain and strength is achieved for the 2% M g addition and for the pure Al the breaking load is lower.
Here the ultimate stress is higher for the pure Al and the elongation at break is higher for the 1% M g alloy.
Summary
Effects on P-h curves
Similar results are obtained from MD simulations and the force is minimal for pure Al in this direction. For this alloy, the indentation force and critical depth decrease with increasing percentage of M g. It is found that the indentation force is maximum and critical depth is minimum for 10% Al-Cualloy.
In the h111i direction, the indentation force is maximum for the 0% Al-Cualloy alloy, but for this direction the critical depth is minimum for the 10% Al-Cu alloy.
Effects on von Mises stress distribution
5.1, the load-displacement curve obtained by FEM simulations for AlandAl−M gallium is shown for indentation in different directions h001i, h110i and h111i. In the h111i direction, the 0% Al−M g alloy shows the highest force and critical indentation depths, and the results are also comparable to other M g percentages. 5.2 shows the load-displacement curves for the Al-Cu alloy for different loading directions.
In the direction, the strain increases with the addition of Cu and the critical depth also decreases with the higher percentage of Cu.
Effects on hardness and reduced modulus
It can be seen from the figure that the hardness increases with the increase of Cu percentage for h001i direction while for h111i it first decreases to 2% of Cu and then increases again. Again for h110i direction the value of the hardness shows no specific trend with the change of Cu percentages.
Comparison of FEM Results with MD Results
Comparison between P-h curves of MD and FEM
It is observed that the MD and FEM results are again in good agreement for this potential. For the h001iandh111i directions, the load-displacement curves for MD and FEM are in good agreement. In all three directions, the critical indentation depth is slightly larger in the FEM than in the MD results.
Results and discussion of FE simulations 102 Table 5.1: Comparison of hardness and reduced modulus for Al−M galloy at different percentages of Mg and at different loading directions obtained by MD and FEM.
Comparison between hardness and reduced modulus of MD and
Summary
FEM nanoindentation simulations are performed to reduce the computational time, and the obtained results are compared with the MD simulation results. MD can correctly predict the elastic and plastic deformation for nanoindentation, and the load-displacement curves obtained by MD agree well with the theoretical framework of Hertz contact stress theory. The hardness and reduced modulus of the materials also increase with larger indentation radius.
In this way, both the simulation time and cost can be reduced with trivial sacrifice of the accuracy in the results obtained from the MD.
Future Research Scopes
Molecular dynamics investigations of mechanical behavior in monocrystalline silicon due to nanoindentation at cryogenic temperatures and room temperature. Molecular dynamics simulation of incipient plasticity of nickel substrates of different surface orientations during nanoindentation. Molecular dynamics simulation on bursting and arrest of stacking faults in nanocrystalline Cu under nanoindentation.
Dislocation Nucleation and Interaction during Nanoindentation in Single Crystalline Al and Cu: Molecular Dynamics Simulations.
