Atomic-scale mechanisms of densification in cold-compressed borosilicate glasses

Knowledge of the underlying structural response during deformation processes is essential for understanding the macroscopic mechanical response of glass. Here we present results from cold compression-decompression molecular dynamics (MD) simulations of two multicomponent borosilicate glasses, Borofloat^®33 (Boro33) and N-BK7^® (N-BK7). Our results suggest that the densification of these two borosilicate glasses involves different types of structural changes. The fraction of permanent densification can be correlated to the change in intermediate-range structure. By performing Voronoi analysis, we quantify the contributions to densification from different cation types in these two multicomponent borosilicate glasses, finding that 3-coordinated cations facilitate the densification process. Higher-coordinated cations are relatively stable and can even show a slight expansion in their Voronoi volume.     

Plasticity of borosilicate glasses under uniaxial tension

The mechanical response of multicomponent borosilicate glasses has drawn significant attention in the design of damage-resistant glasses. In this work, we investigate the plasticity of two borosilicate glasses, Borofloat^®33 (Boro33) and N-BK7^®, by implementing a uniaxial tension test using molecular dynamics simulations. A bond-switching mechanism is found to be responsible for the plastic response of both glasses and is governed by the increasing rate of non-bridging oxygen (NBO) production during the uniaxial tension. We found that the amount of B⁴OSi⁴ linkages in the glass governs the stress drop after yielding, due to its higher tendency to create NBOs compared to Si⁴OSi⁴. Also, the initial existence of NBOs weakens the critical stress for breaking the B⁴-O bond in B⁴OSi⁴, which in turn lowers the yield strength of the glass. The local atomic constraints are analyzed in the two glasses, and high anti-correlation between the concentration of rigid constraints and plastic deformation is observed.     

Effect of pressurization on the fracture toughness of borosilicate glasses

In this study, hot-compression is applied to two multicomponent borosilicate glasses, Borofloat33 (Boro33) and N-BK7, using molecular dynamics simulations. The effects of pressure on elastic properties, surface energy, and fracture toughness ( are investigated. It is found that the impact on is mainly dominated by the change of Young's modulus under pressure, which is proportional to the relative change in density. Between the two glasses under investigation, can be improved more effectively by the hot-compression process for Boro33, due to its higher concentration of 3-coordinated boron (B³), which facilitates densification via B³ to B⁴ conversion under compression.     

Microhardness and Plastic Deformation of Glasses upon Microindentation

The mechanics of plastic deformation of silicate and polymer glasses upon microindentation of a Vickers pyramid is analyzed. The microhardness characterizes the shear strength of a glass and is determined by the maximum shear stress. For silicate glasses, the microhardness virtually coincides with the yield point (plastic limit), above which the plastic deformation is observed.     

Role of Densification in Deformation of Glasses Under Point Loading

It is proposed as a working hypothesis that the many so-called microplastic effects produced by pressure of hard, sharp points on glasses do not occur by plastic flow, but by densification. An interferometric technique is illustrated, by means of which the existence of densification can readily be demonstrated and its magnitude estimated. It is concluded that the "hardness" number of glasses is best interpreted as a measure of the critical stress for yield by densification; that the hardness number has no necessary relation to tensile strength; and that the technology of glass cutting is dependent on residual stresses associated with densification.     

Structure and disorder in MgSiO3 glasses above megabar pressures via nuclear magnetic resonance: DFT calculations

The structural modifications in oxide glasses under extreme compression may account for the pressure-induced increase in their mechanical toughness and rigidity, rendering potential for technological applications of the compressed glasses. High-resolution solid-state nuclear magnetic resonance has provided a structural information regarding glasses by identifying how nuclear spins behave and interact with nearby elements. However, knowledge of nuclear spins resonance in oxide glasses under extreme pressure above 1 million atmospheres has not been available, making the origins of glass densification illusive. In this article, ab initio calculations of prototypical magnesium silicate glasses quantify how structural changes in glasses affect the nature of nuclear spin interactions at high pressure beyond megabars. The calculated results establish novel correlations between pressure-induced evolution of atomic structures, such as oxygen and cation coordination numbers, bond angle and lengths, and structurally relevant nuclear magnetic resonance parameters for Mg, Si, and O in compressed oxide glasses above megabar pressures. The established correlations highlight that the nuclear spins in glasses can serve as a new indicator to the extreme densification paths. Pressure-induced dispersion in nuclear spin parameters also reveals an overall increase in the topological entropy. This entropy gain may weaken glasses at an elevated pressure conditions, accounting for potential softening of the compressed glasses. The proposed relationships open a new window to the evolution of diverse complex glasses under extreme stress and compression with high-resolution solid-state nuclear magnetic resonance.     

Constitutive Law for the Densification of Fused Silica, with Applications in Polishing and Microgrinding

We discuss a constitutive model describing the permanent densification of fused silica under large applied pressures and shear stresses. The constitutive law is assumed to be rate-independent and uses a yield function coupling hydrostatic pressure and shear stress, a flow rule describing the evolution of permanent strains after initial densification, and a hardening rule describing the dependence of the incremental densification on the levels of applied stresses. Normality, or lack thereof, of the permanent strain increments to the current yield surface in stress space allows for various relative contributions of densification and shear flow in the ensuing deformation. The constitutive law accounts for multiaxial states of stress, since during polishing and grinding operations complex stress states, with large shear components due to friction and abrasion, occur in a thin surface layer due to the action of abrasive particles. We apply the constitutive law in estimating the extent of the densified layer during the mechanical interaction of an abrasive grain and a flat surface under polishing and grinding conditions. The grain is assumed to be spherical and in Hertz contact with the surface, or sharp and in point contact. The effect on the densified depth of stress relaxation due to densification is discussed.     

Transition in deformation mechanism of aluminosilicate glass at high pressure and room temperature

Deformation experiments for 20(MgO or Na₂O)-20Al₂O₃-60SiO₂ glasses were performed in simple shear geometry at 1.5-5 GPa and room temperature. An abrupt change in the thinning rate and the turning of the birefringence azimuth at a shear strain of γ = 1-2 indicate a transition of deformation mechanism from uniaxial compression aided by densification to shear flow in the glasses. The high-dense magnesium aluminosilicate glass showed strain softening controlled by the rearrangement of the tetrahedral network. On the other hand, low-dense sodium aluminosilicate glass deformed by packing-induced flow associated with densification and via the rearrangement of the tetrahedral network at lower and higher strains, respectively. The transition of the deformation mechanism was triggered by the limitations of the densification of the tetrahedral network. The difference of deformation mechanism brought about higher strain in magnesium aluminosilicate glass than sodium aluminosilicate glass at the same stress condition. Easiness of remarkable deformation, which relaxed residual stress, and high deformability contributed to the high ductility of the MgO-aluminosilicate glass.     

Indentation analysis of elastic and plastic deformation of precursor-derived Si–C–N ceramics

Elastic and plastic deformation behavior of precursor-derived Si–C–N ceramics at room temperature under contact loading was investigated using nano- and microindentation experiments. The observed behavior showed striking similarities to that of anomalous silicate glasses and amorphous carbon based films. The elastic deformation was controlled by the overall rigidity of the material microstructure, that evolved with the increase in the network connectivity due to progressive dehydrogenation in the amorphous materials, and the formation and organization of turbostratic graphite and nanocrystalline SiC in the phase-separated materials. The plastic deformation of the amorphous materials displayed anomalous densification inducing appreciable strain hardening, which reduced with progressive phase separation in the materials. The contrasting evolution of elastic and plastic deformation work quantities in amorphous and phase-separated materials indicate that the plastic deformation in former materials was volume deformation-controlled whereas that in the latter materials was interface deformation-controlled.     

Volume relaxation in a borosilicate glass hot compressed by three different methods

The temperature dependence of glass relaxation has been intensively studied; however, the effect of an imposed pressure history on relaxation behavior is poorly understood. In this study, we subjected SCHOTT N-BK7^® borosilicate glasses to isostatic compression in a Paterson press (PP) and a gas pressure chamber (GPC). The pressure ranged from 0.1 GPa to 2 GPa for various dwell temperatures and times near the glass transition region. Comparison with our recent results on the same glass using the piston-cylinder apparatus (PC, 0.5-1.5 GPa) reveals that the density of a glass, which has been quenched from the equilibrium state under high pressure at 2 K/min (pressure quench), increases approximately linearly with increasing pressure up to 2 GPa. Considering the volume recovery results at ambient pressure, we assert that the preceding high-pressure treatment in PC (uniaxial loading) generates a similar isostatic pressure effect on N-BK7 glass as those of PP and GPC treatments. Finally, we verify the previously proposed two-internal-parameter relaxation model on the volume recovery data using the three different compression methods. With a new set of parameters in the model, we can account for the pressure and temperature dependence of volume relaxation even for the samples quenched from nonequilibrium states at high pressure.     

Heats of Solution, Density, and Refractive Index Changes in Sodium Borate Glasses Subjected to High Pressure

The densification produced in sodium borate glasses by pressures to 40 kbars at 25° and 250°C was measured. At a constant temperature and pressure, the densification decreased with increasing alkali content. For specimens pressed at 40 kbars and 250°C, the densification ranged from 14.2% for B₂O₃ to 6.3% for the 33.3 mole % Na₂O composition. Under the same conditions, the refractive index increase ranged from 4.8 to 1.1%, and the decrease of the molar refraction of the oxygen ions ranged from 2.5 to 1.5%. The heats of solution of the pressed glasses were more negative than those of the corresponding unpressed glasses. The heats of solution of both the pressed and unpressed glasses pass through a minimum near 20 mole % Na₂O. A decrease in density was observed at room temperature for all pressed specimens. Electron micrographs were made of two of the pressed specimens. The results could be explained on the basis of a repacking of structural units.     

振动剪切作用下聚合物熔体的非仿射网络结构模型 Ⅱ．非仿射网络结构模型

假设聚合物熔体的缠结网络形变是非仿射的，运用瞬态网络结构原理，采用在本课题第一部分^[1]中所建立的动态速率方程，并对上随体Maxwell本构方程加以修正来建立一个非仿射网络结构模型，利用这一模型来研究振动剪切作用下LDPE熔体的流变行为，研究表明，随着应变振幅和频率的增加，LDPE熔体的剪切应力也增加，同时指出了非仿射网络结构模型的精确变比仿射结构模型有较大提高，这表明在振动力场作用下，网络形变发生了非仿射形变，因此在建立振动力场作用下聚烯烃熔体本构方程时，不能假设其网络是仿射形变的。     

Composition dependent structure and elasticity of lithium silicate glasses: Effect of ZrO2 additive and the combination of alkali silicate glasses

The elasticity and structure of lithium silicate glasses Li₂O·3SiO₂, Li₂O·2SiO₂, and Li₂O·2SiO₂·0.135ZrO₂ were studied at ambient conditions, using both Raman and Brillouin spectroscopies. The conventional nucleating agent, i.e., Zr⁴⁺ caused a more polymerized silicate network, amorphous phase separation before crystallization, and a significant drop in shear, Young's and bulk moduli, though Raman spectra have revealed that the partial substitution of Zr for Si occurred chiefly in the less polymerized Q² species. The compiled data of alkali silicate glasses M₂O–SiO₂ (M = Li, Na, K) showed that each glass displays different M₂O concentrations for getting minimum bulk modulus due to difference in field strength of cations, depolymerization of silicate network, and coordination number of cations. The specific M₂O concentrations for such minima increase with increasing cation size. Different composition dependences of elastic moduli for the glasses having same constituents can be ascribed to different mechanisms for compression and shear deformation.     

Fabrication and characterization of hot-pressed B-rich boron carbide

Boron carbide has a wide solubility range owing to the substitution of B and C atoms in the crystal. In this study, boron carbides with different stoichiometric ratios were prepared using a hot-pressing sintering method, and the influences of the B/C atomic ratio on the microstructures and properties were explored in detail. X-ray diffraction analysis showed that excessive B atoms caused lattice expansion. Raman spectroscopy analysis showed disordered substitution of B atoms in the chains and icosahedra. Analysis of the densification process and microstructure evolution revealed that the addition of B promoted densification, and more stacking faults and twins occurred in B-rich boron carbide, and result in the densification mechanism gradually changes from atomic diffusion mechanism driven by thermal energy to plastic deformation mechanism dominated by the proliferation of dislocation and substructures. The introduction of chemical composition changes by dissolving excessive B into boron carbide further affected the microstructure and consequently the mechanical properties. The Vickers hardness, modulus, and sound velocity all decreased with the increase in B content. Moreover, the fracture toughness improved with increased B content. The flexural strength of the samples was optimised at the B/C stoichiometric ratio of 6.1.     

A finite element study on the effects of densification on fused silica under indentation

The pressure-induced densification significantly affects the deformation and damage behavior of fused silica. This paper presents a finite element analysis (FEA) of the densification and its effects on the deformation in fused silica under indentation. An elliptical constitutive model was refined to consider the influence of densification on elastic properties and its saturation with hydrostatic pressure. By matching the simulated indentation hardness to experiments, the plastic properties of fused silica were more accurately identified. FEA shows that the modified elliptical model can improve the prediction accuracy of the load-displacement curve of Berkovich indentation. As a widely-used reference material, the heavy densification in fused silica dose not influence the calibration accuracy of the tip area function in the Oliver-Pharr method, which provides a theoretical foundation for the use of fused silica as a reference material. With the modified elliptical model, the FEA successfully predicted the geometry of plastic zone, and the extent of elastic recovery and densification, which provided input parameters for the analytical embedded center of dilation (ECD) model of indentation stress field. Results show that the stress fields under a conical indenter predicted by the FEA agreed well with the ECD model.     

Structure-property relations of polyethertriamine-cured bisphenol-A-diglycidyl ether epoxies

The relations between the chemical and physical network structure, the deformation and failure processes and the tensile mechanical properties of polyethertriamine-cured bisphenol-A-diglycidyl ether epoxies are reported for a series of epoxy glasses prepared from a range of polyethertriamine concentrations. Near-infra-red spectroscopy indicates that these glasses form exclusively from epoxide-amine addition reactions. Their T_g exhibits a maximum and swell ratio a minimum at the highest crosslink density. Stress-birefringence studies reveal that these highly crosslinked glasses are ductile and undergo necking and plastic deformation. The plastic deformation initially occurs homogeneously but ultimately becomes inhomogeneous and shear bands develop. Tensile failure occurs in the high strain shear band region. The ultimate tensile strain of these epoxies attains a maximum of 15% for the highest crosslinked glass. Off stoichiometric networks fail at lower strains because such networks inherently contain more defects in the form of unreacted ends. The density, yield stress, tensile strength, and modulus of these glasses all decrease with increasing polyethertriamine concentration as a result of increasing free volume because of the poor packing ability of the amine molecule. A slight minimum is superimposed on this downtrend in density and modulus with increasing amine content at the highest crosslink density because of geometric constraints imposed on segmental packing by the network crosslinks. The ability of these crosslinked glasses to undergo deformation is discussed in terms of the free volume and the crosslinked network topography. Network failure is considered in terms of stress-induced chain scission which is determined by the concentration ad extensibility of the least extensible network segments.     

Hot‐Pressing Kinetics and Densification Mechanisms of Boron Carbide

The hot‐pressing kinetics of boron carbide at different stages in the hot‐pressing process was investigated. Based general densification equation and pore‐dragged creep model, the densification and grain growth kinetics were analyzed as a function of various parameters such as sintering temperature, sintering pressure and dwell time. Stress exponent of n ≈ 3 at the initial dwell stage suggests the plastic deformation may dominates the densification. The further TEM observations and the calculation based on effective stress and plastic yield stress also indicate that plastic deformation may occur and account for the large increase in density at the initial stage of sintering. Calculated grain size exponent of m ≈ 3 suggests that the grain‐boundary diffusion dominates the densification at the final stage. During the final stage of sintering, grain growth may be determined by evaporation/condensation and grain‐boundary migration.     

Indentation Behavior of Soda-Lime Silica Glass, Fused Silica, and Single-Crystal Quartz at Liquid Nitrogen Temperature

In an attempt to elucidate the processes involved in the formation of indentation impressions, Vickers hardness measurements have been made on soda-lime silica glass, fused silica, and crystalline quartz indented at room temperature and 77 K. The hardness of all three materials increases by a factor of ∼2.5 on cooling to liquid nitrogen temperature. High-magnification SEM photographs revealed that the deformation and cracking patterns of the glasses changed strikingly: no shear lines were observed within the indentations, and ring cracking occurred instead of radial/median cracking. In addition, cracking occurs at much higher loads than at room temperature. The hardness results have been explained in terms of volume flow (densification) rather than shear flow (viscous or plastic) for the glasses at low temperature. The quartz crystal, on the other hand, deformed plastically at both room temperature and 77 K. Cracking differences result from changes in both flow and water activity     

Densification mechanism during reactive hot pressing of B4C-ZrO2 mixtures

The densification behaviors of pure B₄C and B₄C-ZrO₂ mixtures were compared during hot pressing. The results showed that in-situ formed ZrB₂ effectively enhanced the densification process of B₄C-ZrO₂ mixtures, more significantly during the intermediate stage. Within the relative density ranging from 0.75 to 0.90, the B₄C-15?wt%ZrO₂ mixture (B15Z) achieved the maximum densification rate as twice much as that of pure B₄C. The stress exponent n>3 indicated plastic deformation was the dominant densification mechanism of B15Z. The viscosities of plastic flow were evaluated using Murray-Rodger-William equation and the viscosity of B15Z was only a quarter of that in pure B₄C. The sintering activation energy was calculated to be 305.9?kJ/mol for pure B₄C and 197?kJ/mol for B15Z, respectively. It was proposed that the lower viscosity of plastic flow and activation energy accelerated the sliding and propagating motions of plastic flow, by which underlain the enhanced densification behaviors of B₄C-ZrO₂ mixtures.