Densification effects on the fracture in fused silica under Vickers indentation

This study investigates the effects of densification on the deformation and fracture in fused silica under Vickers indentation by both the finite element analysis (FEA) and experimental tests. A refined elliptical constitutive model was used, which enables us to investigate the effects of the evolution of yield stress under pure shear and elastic properties with densification. The densification distribution was predicted and compared with experiments. The plastic deformation and indentation stress fields were used to analyze the initiation and morphology of various crack types. The formation mechanism of borderline cracks was revealed for the first time. This study reveals that the asymmetry of the densification distribution and elastic-plastic boundary significantly influences the cracking behavior. Under the Vickers indentation, conical cracks have the largest penetration depth. When these cracks emerge from a region far from the impression, they extend with constant radii to form circles on the sample surface. Otherwise, they tend to be initiated at the centers of the indenter-material contact edges before propagating towards the impression corners with increasing radii. Therefore, the borderline cracks consisting of successive partial conical cracks can form at a low load and makes them the first type of crack to appear.     

A critical evaluation of indentation crack lengths in air

An extensive overview is presented of Vickers indentation crack lengths in ceramics in air. Measurement of such crack lengths is one of the most common and powerful assessments of the fracture properties of ceramics and the overview provides a critical evaluation of observed behavior as functions of material type and indentation load, and an extensive basis for comparison of results from new materials and analyses. The overview considers single crystals, polycrystals, transforming materials, glasses, and multiphase materials, including cermets, glass-ceramics, and tooth enamel. The coverage extends over structural and electronic ceramics, including oxides, carbides, nitrides, and titanates. The data are presented in a single format for ease of interpretation in terms of idealized indentation fracture and for inter-material comparisons; most data are unique to this work, but the results of selected studies from the published literature are included. The overview considers the precision and accuracy of crack length measurements and demonstrates a simple quantitative evaluation and ranking scheme for ceramic fracture based on load-adjusted crack length and cracking susceptibility. Indentation hardness and cracking threshold are also determined and related to the susceptibility. Material toughness is related to cracking susceptibility by fracture mechanics analyses: typical crack length measurements in air are shown to provide estimates of inert toughness with a relative uncertainty of ±50%.     

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.     

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.     

Lateral cracks during sliding indentation on various optical materials

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂–Al₂O₃–P₂O₅–Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅–Al₂O₃–K₂O–BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 µm conical, and 200 µm conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.     

Competitive effects of free volume,rigidity, and self-adaptivity on indentation response of silicoaluminoborate glasses

Lithium aluminoborate glasses have recently been found to feature high resistance to crack initiation during indentation, but suffer from relatively low hardness and chemical durability. To further understand the mechanical properties of this glass family and their correlation with the network structure, we here study the effect of adding SiO₂ to a 25Li₂O–20Al₂O₃–55B₂O₃ glass on the structure and mechanical properties. Addition of silica increases the average network rigidity, but meanwhile its open tetrahedral structure decreases the atomic packing density. Consequently, we only observe a minor increase in hardness and glass transition temperature, and a decrease in Poisson's ratio. The addition of SiO₂, and thus removal of Al₂O₃ and/or B₂O₃, also makes the network less structurally adaptive to applied stress, since Al and B easily increase their coordination number under pressure, while this is not the case for Si under modest pressures. As such, although the silica-containing networks have more free volume, they cannot densify more during indentation, which in turn leads to an overall decrease in crack resistance upon SiO₂ addition. Our work shows that, although pure silica glass has very high glass transition temperature and relatively high hardness, its addition in oxide glasses does not necessarily lead to significant increase in these properties due to the complex structural interactions in mixed network former glasses and the competitive effects of free volume and network rigidity.     

The fracture toughness of inorganic glasses

Measuring the fracture toughness (K_Ic) of glasses still remains a difficult task, raising experimental and theoretical problems as well. The available methods to estimate K_Ic are reviewed, with emphasis on their respective advantages and drawbacks. In view of our current understanding, this analysis gives precedence to the SEPB method. The ultimate glass strength, the critical flaw size, and the indentation load for the onset of crack initiation are discussed, in the light of the fundamentals of fracture mechanics and classical background regarding the mechanics of brittle materials. Analytical expressions were further proposed to predict the fracture energy and fracture toughness of glasses from different chemical systems from their nominal compositions. The theoretical values were compared with the experimental ones, as obtained by self‐consistent methods when available. The agreement observed in most cases suggests that measured K_Ic values correspond to the crack propagation regime (as opposed to the crack initiation threshold), and supports previous investigations in glasses and ceramics, which showed that a crack tip is nearly atomically sharp in these materials (but for metallic glasses). Some ideas to design tougher glasses are finally presented.     

The impact of densification on indentation fracture toughness measurements

The fracture toughness was measured by the Vickers indentation method and by chevron notch for a series of xCaO-xAl₂O₃-(100 − 2x)SiO₂ glasses. As the silica content was increased, the fixed ξ value Vickers indentation fracture toughness (IFT) values increased, while the chevron notch values decreased. Glasses with higher silica contents deform with more densification and less shear when indented with a Vickers tip, thus resulting in reduced residual stress in the region surrounding the indent. The reduction in residual stress for high silica glasses results in less median/radial crack extension and unreasonably high Vickers IFT values. This indicates that a fixed ξ value of 0.016 is not appropriate for the glasses in this series. By repeating the IFT method with a sharper 110° four-sided pyramidal diamond indenter, it is demonstrated that indentation toughness and chevron notch toughness values now trend in the same direction and are in good agreement with a fixed ξ value of 0.0297. With the sharper indenter tip, the densification component to the deformation is substantially reduced for all glass types such that it no longer has such a prominent influence on the residual stress field. This result suggests that a fixed ξ value IFT method may be appropriate for all glass types if a sharper indenter tip is substituted in the place of the Vickers tip.     

Determining the Toughness of Ceramics from Vickers Indentations Using the Crack-Opening Displacements: An Experimental Study

Recently, a method for evaluating the fracture toughness of ceramics has been proposed by Fett based on the computed crack-opening displacements of cracks emanating from Vickers hardness indentations. To verify this method, experiments have been conducted to determine the toughness of a commercial silicon carbide ceramic, Hexoloy SA, by measuring the crack-opening profiles of such Vickers indentation cracks. Although the obtained toughness value of K _o= 2.3 MPa·m^1/2 is within 10% of that measured using conventional fracture toughness testing, the computed crack-opening profiles corresponding to this toughness display poor agreement with those measured experimentally, raising concerns about the suitability of this method for determining the toughness of ceramics. The effects of subsurface cracking and cracking during loading are considered as possible causes of such discrepancies, with the former based on direct observations of lateral subsurface cracks below the indents.     

Indentation cracking and deformation mechanism of sodium aluminoborosilicate glasses

Developing less brittle oxide glasses is a grand challenge in the field of glass science and technology, as it would pave the way toward new glass applications and limit the overall raw material usage and energy consumption. However, in order to achieve this goal, more insight into the correlation between the chemical composition and material properties is required. In this work, we focus on the mechanical properties of quaternary sodium aluminoborosilicate glasses, wherein systematic changes in glass chemistry yield different resistances to indentation crack initiation. We discuss the origin of the composition dependence of indentation cracking based on an evaluation of the deformation mechanism taking place during the indentation event. To this end, we use a simple metric, the extent of indent side length recovery upon annealing, to quantify the extent of reversible volume deformation. Finally, we also compare the compositional trend in crack initiation resistance to that in crack growth resistance (fracture toughness), showing no simple correlation among the two.     

Cracking and the Indentation Size Effect for Knoop Hardness of Glasses

The Knoop hardnesses of five glasses decreased with increasing load in accordance with the classic indentation size effect (ISE). At moderate loads, cracking dramatically altered the indentation sizes and the ISE trends in three of the five glasses. Cracked indentations were as much as 10 μm longer than uncracked indentations made under identical conditions. Diagonal length readings must be corrected for optical resolution limitations if low power lenses are used.     

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.     

石英毛细管反应器内双酚A在高温水中的稳定性

引言双酚A(bisphenol A,BPA)是一种重要的有机中间体,是生产聚碳酸酯(PC)树脂及环氧(EP)树脂的主要原料。工业上BPA由苯酚和丙酮缩合而成,现也可通过解聚废弃聚碳酸酯回收得到。聚碳酸酯、环氧树脂作为食品容器或生物材     

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.     

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.     

High temperature fracture toughness and residual stress in thermal barrier coatings evaluated by an in-situ indentation method

High temperature fracture toughness and residual stress are important for the evaluation of TBCs. In this paper, an in-situ high temperature indentation method was originally developed to investigate the high temperature fracture toughness and residual stress in a typical TBC, nanostructured 8?wt% yttria partially stabilized zirconia (YSZ) coating. The cracks caused by in-situ high temperature indentation tests were observed, and high temperature fracture toughness and residual stress were experimentally measured. The fracture toughness was measured to be 1.25, 0.91 and 0.75?MPa*m^1/2 at 25, 800 and 1000?°C, respectively. The residual stress was measured to be ? 131.3, ? 55.5 and ? 45.5?MPa, correspondingly. Moreover, the residual stress and fracture toughness both decrease with increasing environmental temperature. It is also found that the fracture toughness without consideration of residual stress is significantly larger than the intrinsic fracture toughness, which may result from the compressive stress state.     

Thermal expansion and Young's modulus evolution of fused silica and crystalline silica-containing materials

Fused silica bricks (FSBs) with exceptional thermal shock resistance are frequently used to repair localized damage in coke ovens and are hold promising candidates for the efficient construction of new coke ovens. To maximize their utilization, the effects of thermal history on the thermal expansion and Young's modulus evolution of FSBs were investigated in comparison to crystalline silica bricks (CSBs). Due to the gradual phase transformation of fused silica into cristobalite, the thermal expansion of FSBs are sensitive to the thermal cycle; both silica materials exhibit an increase in thermal expansion after five cycles at 1200°C, whereas the thermal expansion of CSBs is five times greater than that of FSBs. When the testing temperature is less than 1000°C, Young's modulus of CSBs is more sensitive to the thermal history, which is caused by phase transformation-induced microcracks. This sensitivity reduces when the testing temperature is 1200°C, as microcracks healed by liquid phase as well as the softening of residual glass phase. By contrast, when the testing temperature is 1200°C, Young's modulus of fused silica specimens is sensitive to the thermal history owing to the microcracks caused by the gradual phase transformation of fused silica to cristobalite.     

Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with vickers indenter

Virtual crack closure technique and elastoplastic finite element method were employed to calculate the stress intensity factors (SIF) of ceramic materials on the tip of both half‐penny crack (HPC) and radial crack (RC) induced by Vickers indenter and the value of fracture toughness (K_IC) was extracted by the design of equi‐SIF contour of HPC and RC crack front. Through dimensional theorem and regressive analysis, a functional relationship between instrumented indentation parameters, crack length of Vickers impression and fracture toughness of ceramic materials was established, thus a novel methodology has been presented for measuring fracture toughness of ceramic materials by instrumented Vickers indentation. Both numerical analysis and experiments have indicated that this methodology enjoys higher measurement precision compared with other available indentation methods. The methodology is universally suitable for HPC, RC as well as transition cracks and capable of determining fracture toughness and elastic modulus in a single indentation test. In addition, it saves the effort of measuring the diagonal length of Vickers impression in case that the impression remains unclear.     

Fracture mechanics properties of fused silicas used for international space station windowpanes

The fracture toughness and slow crack growth (SCG) parameters of a quartz-based silica and a high-purity fused silica were measured as part of a program to review the reliability of the International Space Station windows. The materials exhibit the same fracture toughness (.75 MPa m^1/2 in N₂) and very similar SCG parameters. The literature on fused silica indicates excellent agreement of fracture toughness, but a very wide range of SCG parameters, even from the same institution, with strength-based methods usually yielding a lower power law exponent than direct crack velocity measurements. Use of the exponential function is shown to provide better agreement between test methods, with velocity curves derived from strength tests of bare fiber and polished or ground test specimens paralleling those from wide-range, direct crack velocity observations, implying that constant stress rate tests can predict long lifetime via the exponential function. However, much variation still exists. SCG parameters for soda–lime silicate are much less sensitive to the test method than fused silica. Static load tests and stress intensity measurements resulted in a fatigue threshold of .3 MPa m^1/2 for fused silica.