Fracture of silicate glasses: Microcavities and correlations between atomic-level properties

We use large-scale simulations to investigate the dynamic fracture of silica and sodium-silicate glasses under uniaxial tension. The stress-strain curves demonstrate that silica glass is brittle whereas the glasses rich in Na show pronounced ductility. A strong composition dependence is also seen in the crack velocity which, for the strain rate considered, is on the order of 1800 m/s for glasses with low Na concentration and decreases to 650 m/s if the concentration is high. We find that during the fracture of Na-rich glasses very irregular cavities as large as 3–4 nm form ahead of the crack front, indicating the presence of nanoductility in these glasses. Before fracture occurs, the local composition, structure, and mechanical properties are heterogeneous in space and show a strong dependence on the applied strain. Further analysis of the correlations between these local properties allows to obtain a better microscopic understanding of the deformation and fracture of oxide glasses and how the local heating close to the crack tip, up to several hundred degrees, permits the structure to relax.

Figure 1

(a) Stress-strain behavior of the $\mathrm{NS}x$ glasses. Note that because of the periodic boundary conditions in the tensile direction, the elastic waves generated by the fracture will bounce back and forth between the two surfaces. This explains the small oscillations in the stress-strain curves after fracture. (b) Crack velocity $v_c$ (filled symbols) and the ratio between $v_c$ and the estimated Rayleigh wave speed $v_R$ (open symbols, right scale).

Figure 2

Strain rate dependence of the stress-strain curve and the crack velocity for (a) the silica and (b) the NS3 glass. The circle in the graphs indicates the point where the strain rate is switched from a constant value of 0.5/ns to the values shown in the legend. Also included in the graphs are the velocities of the crack front.

Figure 3

Failure strain vs ${\mathrm{Na}}_2\mathrm{O}$ concentration for the glasses with different geometry. The glasses with free surface are from this work. The results for bulk glasses from a previous simulation work [10] and the experimental results for glass fibers [51] are also included for comparison.

Figure 4

Number density (left scale) and number of the voids (right scale) in the unstrained samples vs the radius of the probing sphere, $R$. In the search of voids, the examined samples are slabs of dimensions $20\mathrm{nm}\times 30\mathrm{nm}\times 50$ nm. The green dashed line represents $N_{\mathrm{void}}=0.5$, i.e., with 50% probability to find only one void with size $R$ in the unstrained sample. Error bars are standard error of the mean over the six fracture simulations.

Figure 5

[(a) and (b)] Snapshots showing the empty space during the fracture of silica (a) and NS3 (b) glasses (sample size $20\times 30\times 50{\mathrm{nm}}^3$). A notch is introduced on the top surface to initiate the fracture. Color coding is based on the coordinate in the $y\mathrm{direction}$. Movies of the fracture process can be found in Ref. [73]. [(c) and (d)] Stress-strain curves corresponding to the fracture of the two glasses. The red circles indicate the strains at which the snapshots in (a) and (b) are shown. [(e) and (f)] The total number (left scale) and volume of voids (right scale) during fracture of the two glasses. The red circles highlight the specific strain points shown in the snapshots of (a) and (b).

Figure 6

(a) Strain dependence of the ratio between the total volume of the voids (in ${\mathrm{nm}}^3$) and the number of voids for different compositions. Note that only a ratio larger than 0.286 ${\mathrm{nm}}^3$ indicates the presence of nontrivial voids, i.e., the ones that grow during deformation. The strain rate is 0.5/ns. (b) Strain dependence of the ratio between the volume (in ${\mathrm{nm}}^3$) and the number of voids for two different strain rates. Note that only values larger than 0.286 ${\mathrm{nm}}^3$ indicate the presence of nontrivial voids, i.e., the ones that grow during deformation.

Figure 7

Enlarged view of the largest void found at $\varepsilon =0.196$ for the fracture of a NS3 glass.

Figure 8

Maps of various local properties during fracture of silica glass (a) and NS3 glass (b). These maps are shown for the middle plane of the simulation box in the direction orthogonal to the crack front. Note that the color range for the same property may not be the same.

Figure 9

Distribution of various local properties in NS3 at various values of the strain. (a) Atomic number fraction of Na (left/bottom axis) and O-Si coordination number (right/top axis). (b) Atomic shear strain ${\eta }^{\mathrm{Mises}}$. (c) Atomic tensile stress. (d) Kinetic temperature $T$. Note that for this analysis the layers, $\approx$2.5 nm in thickness, near the free surfaces of the sample were not taken into account for calculating the distributions. In (b)–(d), “FP” denotes the failure point.

Figure 10

Spearman's correlation coefficient, $r_s$, between various local properties of the NS3 glass, see labeling of curves for details. The vertical dashed lines indicate the failure point (i.e., at maximum stress). Error bars are standard error of the mean of 10 planes that are evenly spaced orthogonal to the direction of the crack front, i.e., orthogonal to the $x$ axis.