Deformation mechanisms of SiC reinforced nanocomposites under indentations

Size: px

Start display at page:

Download "Deformation mechanisms of SiC reinforced nanocomposites under indentations"

Miles Greene
6 years ago
Views:

1 Deformation mechanisms of SiC reinforced nanocomposites under indentations Mark Apicella, Youping Chen, and Liming Xiong Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA INTRODUCTION Silicon Carbide (SiC) nanoparticles pose as an important material because of their impeccable hardness. SiC is widely used to reinforce components in composites. Recently, it has been mainly used in armor systems. The objective of this research is to find an optimized design of SiC reinforcement. This is done by observing the strongest SiC nanoparticle in terms of shape and size and by observing various failures at the Si/SiC interface. SiC is a very important material for armor systems, currently. In general, ceramics have been used in armor systems for the last half century for personal and vehical protection. 4 In a Review of Ceramics for Armor Applications, they compare SiC to boron carbide. 5 Boron carbide is used for personal armor; however, it has tested below expectations for more tenacious threats, especially when compared to SiC. 5 The reason for this is that boron carbide undergoes amorphization under high applied dynamic pressure, when SiC does not. 5 Molecular Dynamics (MD) simulation was used to aid in the calculations of the SiC nanoparticles hardness by running nanoindentation simulations. MD simulation shows how materials deform at the nano and at the atomic scale. The program LAMMPS was used to run these MD simulations. LAMMPS is a very successful program that has a wide variety of applications. For instance, it can provide information such as stress fields locations or such as physical properties of materials after applied shear stress. 2 COMPUTATIONAL SET-UPS AND METHODOLOGY In order to identify the deformation mechanisms of SiC nanoparticles and SiC nanoparticle reinforced composites, these materials mechanisms must be observed under indentations. Nanoindentation is an effective way to measure mechanical properties of materials with very small volumes. 1 Molecular dynamics (MD) is a virtual experiment governed by Newton s second law. MD simulation provides the atomic resolution needed to calculate the positions, velocities, and forces of each atom provided by the LAMMPS software. 1

2 Classical molecular dynamics follows a fundamental procedure. First, Newton s second law (F = ma) is integrated. The Velocity Verlet algorithm is used to get the velocity of each atom per time step: v(t t) v(t) 1 [a(t) a(t )] t 2 The Nosé Hoover 3 algorithm is used to produce temperature, pressure, and stress control. The NVT ensemble is also used. Stress, diffusion coefficient, etc. are derived from atomic velocities, positions and forces. For SiC, the Tersoff potential, developed in 1989, is used. Two sets of models were created for this experiment. The first is a set of isolated SiC nanoparticles. The second is a set of SiC reinforced composites. In order to generate the SiC nanoparticles, a perfect diamond crystal structure of SiC with a lattice constant of 4.35 was created. Parameters were created using equations of shapes as inequalities to regulate which atoms had the desired positions. All atoms that did not satisfy these parameters were discarded. The particles were placed onto a substrate with a fixed rigid surface. The surface is perpendicular to the direction of motion of the indenter. This prevents the particle from moving when the indenter is forcing its way upon the particle. The shapes, number of atoms, and dimensions for each model can be found in Table 1. The r corresponds to the radius of either a sphere or the cross section of a fiber, and L is the length of a fiber. For the ellipsoids, a, b, and c correspond to the x, y, and z equatorial radii, respectively. Figure 1 shows a nanosphere with r=2.0 nm. Table 1: Shape, number of atoms, and dimensions for isolated nanoparticles Shape Number of Atoms Dimensions (nm) Sphere 51,816 r=2.0 Sphere 597,947 r=5.0 Sphere 1,212,933 r=10 Fiber 85,012 r=2.0, L=8.0 Fiber 698,769 r=5.0, L=20 Fiber 2,024,939 r=10, L=40 Ellipsoid 55,710 a=3.2, b=2.7, c=2.0 Ellipsoid 642,371 a=7.2, b=6.5, c=5.0 Ellipsoid 1,330,399 a=14.8, b=13, c=10 2

Figure 1: Nanosphere with radius=2.0 nm and 51,816 atoms The SiC reinforced composites are set up similarly. The SiC nanoparticles are placed within a cube made of Si.

3 Figure 1: Nanosphere with radius=2.0 nm and 51,816 atoms The SiC reinforced composites are set up similarly. The SiC nanoparticles are placed within a cube made of Si. To generate this model, the SiC particles were created the same, except that the lattice constant was The Si cube is generated using the same procedure, equations, and inequalities to form the SiC particles. The only difference is that the positions that are normally discarded for SiC particle are the desired positions for the Si cube. This leaves a Si cube with a hole in the shape of the SiC particle in the middle. Combining these two models generates the reinforced composite model. A 0.05 nm gap is left between the Si and the SiC interface by slightly altering the parameters for Si before generating the Si model. Since the SiC lattice constant is 4.20, it will need time to equilibrate in order to expand, fill the gap, and form a natural interface between the Si and SiC. Each Si cube has dimensions 22 nm x 22 nm x 22 nm. Information on these combined models is shown in Table 2. Table 2: Shape and dimensions of nanoparticles within Si matrix, and total number of atoms Shape Number of Atoms Dimensions (nm) Sphere 915,787 r=8.05 Fiber 1,044,817 r=8.05, L=22 Ellipsoid 838,766 a=8.05, b=4.05, c=6.05 3

4 Figure 2: General Si/SiC combined model Figure 3: Si cube reinforced with SiC fiber. Notice gap between Si and SiC Figure 4: Si cube reinforced with SiC sphere 4

Figure 5: Si cube reinforced with SiC ellipsoid After the models were generated, the

The indenter is a rigid sphere with a radius of 500 nm, providing an infinitesimal curvature.

The indenter travels until a phase change is observed within the isolated particles or until the

Figure 6: Model of SiC nanoparticle under indentation RESULTS A.

5 Figure 5: Si cube reinforced with SiC ellipsoid After the models were generated, the nanoindentation process began. The indenter is a rigid sphere with a radius of 500 nm, providing an infinitesimal curvature. The indenter travels at a velocity of 0.05 nm per time step (1 fs). The indenter travels until a phase change is observed within the isolated particles or until the interface between the Si and SiC is adequately deformed. Figure 6: Model of SiC nanoparticle under indentation RESULTS A. Simulation results from SiC nanoparticles Once the simulations are completed, force vs. displacement graphs can be extracted. The force calculated is the force applied by the particle onto the indenter. The displacement corresponds to the displacement of the indenter. The force vs. 5

6 displacement plots for each particle show a similar phenomena. As the displacement increases, the force increases as well. However, there s a range where the force remains almost constant. This indicates a phase change. Each particle undergoes a phase change from a perfect diamond structure to a rocksalt structure, as seen in Figures 7 and 8. Figure 7: Force vs. Displacement graph Notice plateau around 3 nm 6

Figure 8: RDF plots for nanosphere with r=5 nm showing phase change from diamond structure to rocksalt structure The pressure at which the phase change occurs gives

To get the contact area, consider the 3 dimensional equation for each particle s shape.

The indenter s displacement is defined as d, and the distance from the center to the edge of the particle at time step=0 is defined as r.

7 Figure 8: RDF plots for nanosphere with r=5 nm showing phase change from diamond structure to rocksalt structure The pressure at which the phase change occurs gives insight on the hardness of the SiC particle. Since pressure is force divided by area, the contact area must be calculated. To get the contact area, consider the 3 dimensional equation for each particle s shape. The indenter is moving in the negative z direction on the z axis, and the center of each particle is located at the origin. The indenter s displacement is defined as d, and the distance from the center to the edge of the particle at time step=0 is defined as r. For each shape s 3 dimensional equation, the value r d equals z. Now, 2 dimensional equations are given defining the shape that the indenter is contacting. Integrating this will provide the contact area. Below, the various pressures and the procedure for calculating the contact area of a nanosphere are listed. x 2 y 2 z 2 r 2 x 2 y 2 (r d) 2 r 2 A [r 2 (r d) 2 ] P F A 7

Table 3: Required pressure for SiC nanoparticle phase change Shape Number of Atoms Size (nm) Pressure (GPa) Sphere 51,816 r = 2.0 38.8 Ellipsoid 55,710 a = 3.2, b = 2.7, c = 32.5 2.

8 Table 3: Required pressure for SiC nanoparticle phase change Shape Number of Atoms Size (nm) Pressure (GPa) Sphere 51,816 r = Ellipsoid 55,710 a = 3.2, b = 2.7, c = Fiber 85,012 r = 2.0, L = Sphere 597,947 r = Ellipsoid 642,371 a = 7.2, b = 6.5, c = Fiber 698,769 r = 5.0, L = Sphere 1,212,933 r = 10 Still running Ellipsoid 1,330,399 a = 14.8, b = 13.0, c Still running = 10.0 Fiber 2,024,939 r = 10.0, L = 40.0 Still running Unfortunately, the larger models are still running; therefore, no conclusive trend can be determined. However, most models seem to require ~40 GPa to induce a phase change. Experimental results show that SiC changes to a rocksalt structure at ~100 GPa. 6 B. Simulation results from SiC reinforced nanocomposites These models had to first equilibrate before the indentation process could occur. These simulations are also still running. The interface after equilibriation and the slightly deformed interface are shown below for the Si cube reinforced with SiC fiber. Figure 9: Interface after equilibriation of Si cube reinforced with SiC fiber 8

Figure 10: Slight deformation of Si/SiC interface DISCUSSION, SUMMARY & FUTURE WORK Testing SiC nanoparticles hardness indicates that phase transitions from a diamond structure to a rocksalt

More investigation is needed of the deformation mechanisms of SiC nanoparticles with different sizes, geometries, and morphologies.

9 Figure 10: Slight deformation of Si/SiC interface DISCUSSION, SUMMARY & FUTURE WORK Testing SiC nanoparticles hardness indicates that phase transitions from a diamond structure to a rocksalt structure occurs at ~40 GPa. This research also shows the equilibrium interfacial structure within (particle/fiber reinforced) SiC/Si composites. This research still requires much work to be done. More investigation is needed of the deformation mechanisms of SiC nanoparticles with different sizes, geometries, and morphologies. Measurements of the interfacial strength of the SiC particle/fiber reinforced composites will be recorded. Tailoring the interfacial structures or compositions will contribute to the optimization of microstructures of SiC reinforced nanocomposites. ACKNOWLEDGMENTS This work was supported by the REU in Computational Materials Science at the University of Florida. Dr. Youping Chen and her research group aided in the procedure and provided code for the simulations. REFERENCES W. G. Hoover, Phys. Rev. A 31, 1695 (1985). 4 M.J. Normandia, J.C. LaSalvia, W.A. Gooch Jr., J.W. McCauley, and A.M. Rajendran, AMP TIAG 8, 21 (2004). 5 P. G. Karandikar, G. Evans, S. Wong, and M. K. Aghajanian, CESP 29 (2008). 6 M. Yoshida, A. Onodera, M. Ueno, K. Takemura, and O. Shimomura, Phys. Rev. B 48, (1993). 9

Supplementary Materials

Supplementary Materials Atomistic Origin of Brittle Failure of Boron Carbide from Large Scale Reactive Dynamics Simulations; Suggestions toward Improved Ductility Qi An and William A. Goddard III * Materials