1School of Science, China University of Mining and Technology, Beijing 100083, China 2State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China 3State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China 4Institute of Defense Engineering, AMS, PLA, Beijing 100036, China
We investigate the mechanical and microstructural changes of the densified silica glass under uniaxial loading-unloading via atomistic simulations with a modified BKS potential. The stress–strain relationship is found to include three respective stages: elastic, plastic and hardening regions. The bulk modulus increases with the initial densification and will undergo a rapid increase after complete densification. The yield pressure varies from 5 to 12 GPa for different densified samples. In addition, the Si–O–Si bond angle reduces during elastic deformation under compression, and 5-fold Si will increase linearly in the plastic deformation. In the hardening region, the peak splitting and the new peak are both found on the Si–Si and O–O pair radial distribution functions, where the 6-fold Si is increased. Instead, the lateral displacement of the atoms always varies linearly with strain, without evident periodic characteristic. As is expected, the samples are permanently densified after release from the plastic region, and the maximum density of recovered samples is about 2.64 g/cm3, which contains 15 % 5-fold Si, and the Si–O–Si bond angle is less than the ordinary silica glass. All these findings are of great significance for understanding the deformation process of densified silica glass.
* Project supported by the National Natural Science Foundation of China (Grant Nos. 51727807 and 11875318), Beijing Institute of Technology Research Fund Program for Young Scholars, and Yue Qi Young Scholar Project in CUMTB.
Cite this article:
Yi-Fan Xie(谢轶凡), Feng Feng(冯锋), Ying-Jun Li(李英骏)†, Zhi-Qiang Hu(胡志强), Jian-Li Shao(邵建立)‡, and Yong Mei(梅勇)§ Mechanical and microstructural response of densified silica glass under uniaxial compression: Atomistic simulations 2020 Chin. Phys. B 29 108101
Aij/J
Bij/m−1
Cij/J⋅m6
aij/(J/m2)
bij/(J/m)
cij/J
O–O
2.225 × 10−16
2.760 × 1010
2.804 × 10−77
1.510 × 102
−7.925 × 10−8
1.100 × 10−17
Si–O
2.884 × 10−15
4.873 × 1010
2.139 × 10−77
3.413 × 102
−9.361 × 10−8
3.925 × 10−18
Si–Si
0.0
0.0
0.0
0.0
0.0
0.0
Table 1.
Values of Aij, Bij, Cij, and aij, bij, cij are taken from Refs. [27,31].
3-fold Si/%
4-fold Si/%
5-fold Si/%
6-fold Si/%
S1
0
98.94
1.01
0
S2
1.06
96.55
1.87
0.01
S3
1.05
94.87
3.53
0.04
S4
1.06
90.49
7.77
0.18
S5
1.04
84.26
13.67
0.53
Table 2.
The proportions of 3-fold, 4-fold, 5-fold, and 6-fold Si atoms of S1–S5.
Fig. 1.
Normal stress (a) and maximum shear stress (b) as a function of strain for different silica glass samples (S1–S5). Three stages are displayed, and hardening tendency increases with initial densification.
Fig. 2.
Pressure-density relation for silica glass samples: present study compared with the experiments. Curves S1–S5: under uniaxial compression; circle and triangle: hydrostatic experimental data obtained by Meade et al.[38] and Sato et al.;[39] square and pentagon: shock experimental data obtained by Renou et al.[21] and Sugiura et al.[41] Yield pressure of densified silica glass ranges from 5 to 12 GPa. All curves converge at 12 GPa.
Fig. 3.
Density as a function of pressure for S1 during uniaxial loading-unloading. Densification and hysteresis are both shown. A, B, C, D and E correspond to strains of 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. The solid line represents the loading path, and the dotted lines are the unloading paths.
Fig. 4.
RDFs of Si–O (a) Si–Si (b) O–O (c) for S1 at different strains. RDFs of Si–O (d) Si–Si (e) O–O (f) for glass unloaded from different strains. The arrows indicate the change of the peak position. The RDFs of the unloaded sample are consistent with the initial state.
Fig. 5.
BADs of Si–O–Si (a) O–Si–O (b) for S1 at different strains. BADs of Si–O–Si (c) O–Si–O (d) for glass unloaded from different strains. The arrows indicate the change of the peak position. The Si–O–Si bond angle of silica glass unloaded from the inelastic region becomes smaller.
Fig. 6.
Si–O coordination number curves of S1 at different strains. The average coordination number of Si–O increases with strain from 4 to around 6.
Fig. 7.
(a) Fractions of 4-fold, 5-fold, 6-fold coordinated Si atoms versus strain. Pink atoms: Si, blue atoms: O in the insert figure). Here 5-fold Si increases linearly with strain in plastic region and 6-fold Si increases mainly in hardening region. (b) Color micrographs of Si atoms according to the coordination number CN color bar. The figure only includes Si atoms. The cutoff distance for coordination is set to 2.4 Å.
Fig. 8.
(a) Average atomic displacement as a function of strain, and (b) microstructure of atoms in X–Y plane at different strains according to the R(i) color bar. The law of atomic lateral diffusion during uniaxial compression is shown.
Fig. 9.
The density of recovered glass at 0 GPa as a function of the maximum strain reached. Results for all the samples are displayed.
Fig. 10.
Density as a function of pressure for S3 (a) and S5 (b) during uniaxial loading-unloading. Solid and hollow triangles represent the hydrostatic experimental data on compression and decompression obtained by Sato et al.[42].
Fig. 11.
BADs of Si–O–Si (a) O–Si–O (b) for the initial state, 0.3 strain, unloaded state of S5. The arrows indicate the change of the peak position. The Si–O–Si bond angle becomes smaller.
4-fold Si/%
5-fold Si/%
6-fold Si/%
S5
84.26
13.67
0.53
0.3 strain
10.58
53.37
34.88
0.3 strain_unload
81.93
15.89
0.66
Table 3.
The proportions of 4-fold, 5-fold, and 6-fold Si atoms of the initial state, 0.3 strain, and unloaded state of S5.
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