Chapter IV: Compression of solid benzene
4.6 Molecular Dynamic (MD) simulations
COMPRESSION OF SOLID BENZENE Section: 4.6
Figure 4.11: Scatterplot showing the evolution of stiffness of unbursted benzene.
COMPRESSION OF SOLID BENZENE Section: 4.6
Figure 4.12: Comparison between experimental and MD simulated compressions of benzene crystals before and after compression.
making a surface mesh from the full atomic models with the Ovito software package.
Yield stress was defined as the maximum contact pressure, and flow stress was defined as the average contact pressure between the onset of large-scale propagation of phase transition and 40% strain. Yield stress was defined as such because this appears to be the first point in which the simulated crystals showed any plastic deformation. Shear strain was found by calculating the local transformation matrix between the current and reference atomic configurations [6].
Figure 4.12 shows that there is good qualitative agreement between the experi- ments and simulations. The shape of the crystal after agrees quite well between experiments and simulations. The mechanical signatures varied between these two methodologies, but the densified top layer appears to be consistent between the two.
Atoms of an amorphous phase are present in this layer in the simulations, and we observe a change in secondary electron contrast in this layer in the SEM.
Computed compressions of a nanometer-sized orthorhombic benzene single crystal reveal that the deformation is confined near the indenter tip up until a point in which there is a large-scale propagation of a phase transition or amorphization region throughout much of the crystal. The simulations were done to measure the impact of temperature, crystal size, and compression direction on the mechanical properties of single-crystalline benzene.
COMPRESSION OF SOLID BENZENE Section: 4.6
Figure 4.13: Relationships between stress and stiffness with loading direction col- ored by temperature and particle size represented by data point size.
A typical simulation is shown in Figure 4.13. From these plots we can see that three different regimes have emerged for this compression of a 20 nm crystal at 10 K along the[0 1 0]direction.
The deformation during compression may be broken up into phases based on the behavior of the contact pressure versus displacement plots. For the[0 1 0]and[0 1 1] loading directions, there is initially a directional relationship as the contact region is becoming amorphous and small deformation is observed throughout the rest of the crystal. After yielding occurs, there is a slightly inverse relationship between contact pressure and displacement as there is a large-scale phase propagation throughout the crystal. Especially evident in the simulations of larger crystals loaded in the [0 1 0] direction, and possibly also for the smaller crystals, is the appearance of a third region in which the contact pressure increases with increased strain and the loading stiffness becomes much higher.
During the loading process, the shear strain of atoms in the amorphization and phase transition regions remain relatively constant, which suggests that they are no longer load bearing, and serve only to transfer the applied load further down into the crystal.
The regions of the crystal below this layer are characterized by small deformations having shear strain that varies from 0 to 0.5, suggesting that this part of the crystal is actually load bearing.
COMPRESSION OF SOLID BENZENE Section: 4.7 We do not see a strong dependence of mechanical properties over the range of tem- peratures studied. Yield stress decreases with increased crystal size, while unloading stiffness increases with increased crystal size. There is only slight dependence on deformation direction, which suggests low anisotropy and lends itself to be a fair comparison to the experiments of compressions in unknown crystal directions. The results from the MD simulations are summarized in Figure 4.14.
No significant bulging of the cuboids was observed during any of the tests, so it was assumed that all of the densifying was done in the same direction as the uniaxial compressive load. However, the simulations showed that the crystal’s volume remained approximately constant, but the amount of material that would go in to bulging would be so low that it would be very difficult to observe in the SEM.
The relatively constant stiffness throughout the loading suggests that the deformation mechanism is largely localized, so it is always acting on relatively pristine benzene, thus the behavior remains constant throughout the whole test. The only difference is that there is a continually growing “crust” of densified, non-load bearing, material directly underneath the indenter that artificially increases the contact area by an amount that is difficult to quantify.
Loading and unloading stiffness from the simulations are about three orders of mag- nitude lower than experiments, which, given that the size of the samples measured were almost around three orders of magnitude smaller, is expected. The simulation stress values are one order of magnitude lower than experiments, which is harder to reconcile. One might consider this difference to be attributed to the larger proportion of amorphous to crystalline regions of the entire sample given that the simulated samples are much smaller. However, the simulated yield stress decreases as sample size increases from 10 to 30 nm height of the crystal. It is possible that the combi- nation of the bulging and slight increase of contact area from the densified top layer lead to an overestimation of contact pressure in the experimental results.