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.     

Cracking analysis of HVOF coatings under Vickers indentation

The fracture strength of five HVOF coatings, which are made of hard metals, Tribaloy alloy, and superalloys, respectively, coated on 1018 low carbon steel substrate, is studied under Vickers indentation, associated with FEA stress computation. The cross sections of the coating specimens are examined on a Hitachi Model S-570 scanning electron microscope (SEM), which investigates the quality and measures the geometry of the coatings. The mechanical properties of the coatings and the substrate are determined in the cross sections using the nano-indentation technique. The cracking behavior of the coatings under different indentation loads is investigated using a Vickers hardness tester. Three-dimensional finite element analysis (FEA) simulation of the Vickers indentation test is conducted to determine the stress fields in the coating/substrate systems in order to understand the fracture mechanisms of the coatings under the indentation loads using the ABAQUS software package. The FEA stress results are in good agreement with the experimental observation of Vickers indentation.     

A quantitative analysis of the indentation fracture of fused silica

It is unclear how the densification of fused silica influences the damage of its precision optics subjected to machining. This paper presents a quantitative analysis of the indentation fracture of fused silica involving densification with the embedded center of dilation (ECD) model. The Hertzian stress field and the ECD-induced stress field were superposed to provide the overall stress distribution in the loading stage. A new method was established to accurately determine the strength of the ECD-induced stress field with densification effects. With the aid of the ECD model, the starting locations, initiation stages and initiation sequence of crack morphologies were predicted by analyzing the stress fields. To quantitatively study the initiation of conical cracks in fused silica, the strain energy release rate was calculated by linear elastic fracture mechanics (LEFM). The predicted minimum threshold load leading to conical cracking was consistent with the measured values.     

Crack propagation during Vickers indentation of zirconia ceramics

A quarter finite element model of 3 mol% yttria stabilized tetragonal zirconia polycrystal (3Y-TZP) ceramics undergoing Vickers indentation was established to simulate the evolution of stress and the propagation of cracks inside a sample. The indentation experiment was carried out on the Micro Vickers Hardness Tester. The results of the geometric characteristic parameters, such as the indentation diagonal half-length a, the crack length c and the maximum indent depth h_m, from the indentation simulation and experiment were similar. The types of indentation cracks under various loads were determined according to the Lawn-Evan model, which exactly correspond to the simulation results. In addition, the propagation of indentation cracks was discussed based on the maximum principal stress contour plots at various stages, and the conclusions were verified by the indentation analysis model proposed by Yoffe. As a result, the model developed in this paper can be used in indentation studies to solve the related problem.     

Effect of the phase transformation on fracture behaviour of fused silica refractories

In this paper, the influence of phase transformation on the properties and fracture behaviour of fused silica refractory was investigated. The virgin fused silica refractory is amorphous, and possible failure is attributed to the propagation of a single crack in the structure. Due to the crystallization and phase transformation of low-/high- temperature cristobalite subpolymorphs occurring during the heat treatment, microcracks are formed especially in the matrix and at the grain boundary. This microcracking enables the development of sizable fracture process zone, which is responsible for the increase of specific fracture energy even with the decrease of strength. Therefore, the heat-treated specimens exhibit lower brittleness and higher strain tolerance before failure compared with the virgin fused silica refractory. All of these properties represent a better thermal shock resistance. Furthermore, microcracking causes a characteristic temperature dependence of Young’s Modulus due to phase transformation and partial crack closure at increased temperatures.     

Morphology evolution of Vickers indentation in fused silica glass etched by atmospheric pressure plasma jet

Nondestructive machining of optical components and smoothing of surface/subsurface damage generated by pre-processing is a major challenge for ultra-tight machining. The study analyzes the crack change during smoothing by quantitative layer-by-layer removal of Vickers indentations through atmosphere pressure plasma jet; the indentation change process is modeled and analyzed using Level Set Method (LSM) simulation. The results show that plasma jet processing can smooth the subsurface damage of fused silica optical components, and the LSM simulation verifies that the processing of cracks in fused silica components by plasma jet is dominated by each isotropic etching, and there are also each anisotropic etching during the change of cracks; and the depth of adjacent cracks can be judged by the moving direction of adjacent crack boundaries.     

Statistical evaluation of nano-structured hydroxyapatite mechanical characteristics by employing the Vickers indentation technique

In this study, the mechanical characteristics of hydroxyapatite (HA) against the Vickers indenter under different loads were investigated. For this purpose, the HA powders were first synthesized by a one-pot solvothermal method. The powders were then subjected to consolidating by the spark plasma sintering (SPS) method for mechanical evaluation. Characterization methods used in this study included X-rays diffraction, field emission scanning electron microscopy, transmission electron microscopy, inductively coupled plasma, energy dispersive X-ray spectroscopy, and Vickers indentation technique. The findings of this study showed that the morphology of the synthesized powders by solvothermal method were rod-shaped and nanometer-sized. As the applied load increased to 2 N, the elastic modulus increased but the hardness did not change much. At a constant force, the contact depth increased with decreasing elastic modulus and hardness. Also, increasing contact depth increased the stiffness and contact area. The results of this study will be useful for investigating the mechanical properties of HA based materials.     

Differences in indentation and wear behaviors between the two sides of thermally tempered soda lime silica glass

Thermal tempering is an industrial process widely used to make soda lime silica (SLS) glass panels stronger and tougher. During the tempering process, the upper and bottom sides of the glass may experience different cooling rates, and thus, their properties could be different. This study characterized changes in surface composition and subsurface glass network structures as well as indentation and wear resistance properties of the air- and tin-sides of 6-mm-thick SLS window panels faced toward the upper and sliding roller sides during thermal tempering. The results showed that although the chemical and structural differences detected with X-ray photoelectron spectroscopy and specular reflection infrared spectroscopy are subtle, there are large differences in nanoindentation behaviors and mechanochemical wear properties of the SLS glass surface. The findings of this study provide further insights into the performance difference between the air- and tin-sides of the SLS glass panel treated with thermal tempering.     

高密度熔融石英水口的研制

从理论上分析了提高熔融石英水口质量的途径。试验结果表明：以优选的颗粒级配和ＮＰＳ复合助剂，采用国内现有工艺，可生产出体积密度１．９３—１．９７ｇ／ｃｍ３、耐压强度５０—８０ＭＰａ的高密度熔融石英水口。     

Finite elements based approaches for the modelling of radial crack formation upon Vickers indentation in silicon nitride ceramics

By having superior properties silicon nitride ceramics can be considered as the state-of-the-art material in the bearing industry. Vickers indentation of this material is typically accompanied by formation of cracks visible on surface. Two Finite Elements models are developed in the current work: the first model is based on fracture mechanics and the second on cleavage stress criterion. Plastic behavior of silicon nitride is included in the modeling, and since little is known on the plasticity of this material, the Drucker-Prager model (used for non-metallic materials) along with the classical J₂-plasticity are explored. The results of the fracture mechanics based model correlate well with experimental results in terms of surface crack length. The numerical results in terms of the morphology of the indented zone (including cracks and plastic zone) are provided by the stress criterion based model, and these results correlate well too, with the experimental data.     

Sharp indentation stress fields in fused silica: Finite element analysis and Yoffe analytic model

The closed-form Yoffe analytic model (1982), which superimposes two linear-elastic stress fields, was developed as a first approximation to quantify the mechanical response of silicate glasses to sharp indentation. However, a detailed study with both experimental validation and numerical verification has yet to be published. This paper presents such a study, wherein experimental observation of crack systems in fused silica and numerical results from finite element analysis (FEA) are used to demonstrate the limitations of this analytic superimposition model. Specifically, analytic stress fields deviate from FEA numerical results and are inconsistent with several commonly observed crack systems. In contrast, FEA generated stress fields are entirely consistent with experimentally observed crack systems. Upon further investigation, it was found that the analytic model, with one tunable parameter, could not be adjusted to correlate with FEA and experimental evidence.     

Gel-casting of fused silica based core packing for investment casting using silica sol as a binder

A novel approach for the fabrication of core packing via silica sol gel-casting is described. Concentrated slurry dispersed in silica sol with high solid loading but low viscosity is successfully prepared at about pH 10.2. In situ consolidation of the slurry is realized through adjustment of NH₄Cl concentration to control the gelation time of the slurry. High compaction and uniform green body is obtained by gel-casting technology without de-airing process. The results from flexural strength tests show that wet gel bodies with 0.5 wt.% calcium aluminate obtained by silica sol gel-casting have exceptionally high strength, which are responsible for the integrity of core packing during autoclaving.     

Microstructure and mechanical properties of boron nitride nanosheets-reinforced fused silica composites

In order to overcome intrinsic brittleness and poor mechanical properties of fused silica (FS), boron nitride nanosheets (BNNSs) as a novel reinforcement were employed for fabrication of BNNSs/fused silica composites. BNNSs with micron lateral size were homogeneously dispersed with FS powder using a surfactant-free flocculation method and then consolidated by hot pressing. The flexural strength and fracture toughness of the composite with the addition of only 0.5 wt.% BNNSs increased by 53% and 32%, respectively, compared with those of pure FS. However, for higher BNNSs contents the improvement in mechanical properties was limited. Microstructural analyzes have shown that the toughening mechanisms are combinations of the pull-out, crack bridging, and crack deflection mechanisms.     

Spherical indentation for brittle fracture toughness evaluation by considering kinked-cone-crack

This work aims at evaluating the fracture toughness of brittle materials by spherical indentation. The cone-cracking is simulated by the extended finite element method (XFEM) in Abaqus. The formation of a kinked-cone-crack is observed when the indenter comes into (second) contact with the surface part outside the ring-crack. The effects of friction, Poisson’s ratio and cone-crack kinking on the Roesler’s constant κ_c are analyzed. Based on numerical results, the Roesler’s method for evaluating the fracture toughness is enhanced by considering kinked-cone-crack. By performing systematic XFE analyses, a database for enhanced Roesler’s constant κ_c | _kink is provided for the fracture toughness evaluation of brittle materials. Finally, the proposed method is verified by conducting spherical indentation tests on soda-lime glass specimens.     

Preparation and properties of fused silica ceramics by Isobam spontaneous coagulation casting

By surface modification with APTMS, spontaneous coagulation casting (SCC) of fused silica based on Isobam was achieved and the possible coagulation and molding mechanism is proposed. Through the interaction between the polar groups on the Isobam molecular chain and the incorporated –NH₂ groups on the surface of the silica particles, Isobam molecular chains were adsorbed on the surface of particles, which initiate the formation of flocs and the solidification of the suspension. The addition of dispersant TMAH results in the hydrolyzation of Isobam, forming more –COO^–, which effectively improves the fluidity and stability of the suspension. Then the zeta potential, rheological properties and coagulation behavior of the suspension were systematically investigated and the fused silica suspension with high solid content (up to 52 vol%), low viscosity and good coagulation properties were prepared at 1.8 wt% TMAH and 0.5 wt% Isobam dosage. After sintering at 1260 °C for 4 hours, the fused silica ceramics (50 vol% solid content) shows a high bending strength of 61.59 MPa, the lowest dielectric loss tanδ of 8.46×10^-4 and the dielectric constant of 3.72. Thus, this work provides a simple and effective method for preparing fused silica and other ceramics with negative surface charge by Isobam SCC.     

On the determination of the film hardness in hard film/substrate composites using depth-sensing indentation

The main difficulty in the mechanical characterisation of thin films using depth-sensing indentation is the determination of the relative substrate and film contributions to the measured properties of the film/substrate composite. In this study, a three-dimensional numerical simulation of the Vickers hardness test is used to study the influence of the substrate and film mechanical properties on the composite's behaviour under depth-sensing indentation. The particular case of hard films on soft substrates is analysed. In order to understand the behaviour of the composite, a study of the plastic strain distribution under indentation of several composites is performed. A methodology to determine the relative film hardness, i.e. H_F/H_S ratio, is proposed. The methodology is successfully verified using fictitious and real composite materials.     

Mechanisms of microstructural deformation governing Vickers hardness in phase-separated calcium aluminosilicate glasses

The impact of microstructure on hardness in phase-separated calcium aluminosilicate glasses is investigated. Changes in hardness are governed by microstructure deformations that occur during indentation. Phase separation leads to decreased hardness due to the incongruent yielding of the droplet and matrix phases. Moreover, the deformation of microstructures possessing dilute, spherical droplets did not have a significant impact on hardness. Microstructures characterized by concentrated, acicular droplets were found to deform through a process of droplet coalescence. This process absorbs additional energy during yielding and results in glasses that deform through droplet coalescence possessing improved hardness.     

Indentation densification of fused silica assessed by raman spectroscopy and constitutive finite element analysis

Inelastic deformation of anomalous glasses manifests in shear flow and densification of the glass network; the deformation behavior during indentation testing is linked strongly to both processes. In this paper, the indentation densification field of fused silica is investigated using depth-resolved Raman spectroscopy and finite element simulations. Through affecting the size of the indent, the normal load and the Raman laser spot size determine the spatial sampling resolution, leading to a certain degree of structural averaging. For appropriate combinations of normal load (indent size) and laser spot diameter, a maximum densification of 18.4% was found at the indent center. The indentation behavior was modeled by extended Drucker-Prager-Cap (DPC) plasticity, assuming a sigmoidal hardening behavior of fused silica with a densification saturation of 21%. This procedure significantly improved the reproduction of the experimental densification field, yielding a maximum densification of 18.2% directly below the indenter tip. The degree of densification was found to be strongly linked to the hydrostatic pressure limit below the indenter in accordance to Johnson's expanding cavity model (J. Mech. Phys. Solids, 18 (1970) 115). Based on the good overlap between FEA and Raman, an alternative way to extract the empirical correlation factor m, which scales structural densification to Raman spectroscopic observations, is obtained. This approach does not require the use of intensive hydrostatic compaction experiments.