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.     

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.     

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%.     

Double cantilever beam fracture toughness measurement method for glass

A simple method of measuring Mode I fracture toughness, K_IC, of glass using the double cantilever beam (DCB) geometry is presented. An inert atmosphere is created at the crack tip to prevent subcritical crack growth and enable “pinning” the crack while the specimen is loaded to failure. This was achieved experimentally using liquid toluene or a glovebox with dry argon. K_IC values measured by this method showed good agreement with published literature values for selected glasses. Applicability of the analytical stress intensity factor solution based on crack length, crack front curvature, and the height of the crack guiding groove are confirmed through experimental data and finite element analysis. The experimentally observed crack front curvature, which leads near the edges for small groove heights and leads in the center for larger groove heights, is predicted from the geometry of the DCB specimen for a linear elastic solid through finite element modeling.     

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.     

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.     

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.     

Hardness, Toughness, and Scratchability of Germanium–Selenium Chalcogenide Glasses

Ge–Se chalcogenide glasses are characterized by relatively low hardness (0.39–2.35 GPa) and low fracture toughness (0.1–0.28 MPa·m^1/2). Actually, the hardness of chalcogen-rich glasses is low enough so that the brittleness parameter, B = H / K _c , is lower than that of silicate glasses. Whereas hardness and Young's modulus increase with increasing germanium contents, fracture toughness follows a trend similar to that of the density and exhibits a maximum for the Ge₂₀Se₈₀ composition, which corresponds to the rigidity percolation threshold. Optical microscopy and atomic force microscopy observations suggest that the indentation deformation proceeds by a localized shear deformation phenomenon. Glasses in the chalcogen-rich region behave viscoelastically at room temperature. As a consequence, an increase of the loading time results in a decrease of hardness and toughness.     

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.     

Surface Damage Resistance of Gel-Derived Oxycarbide Glasses: Hardness, Toughness, and Scratchability

Gel-derived oxycarbide glasses have atomic network structures similar to that of vitreous silica glass but with carbon-rich regions consisting of CSi₄ tetrahedra and C–Si–O bonds finely dispersed in the glass. Therefore, oxycarbide glasses exhibit the so-called anomalous hardness behavior, similar to silica-rich glasses, with a substantial densification–strain component beneath the indenter. However, the role of carbon is twofold: on the one hand, the covalently bonded carbon atoms slightly affect the behavior, similar to the way network modifiers affect the behavior of silicate glasses, and favor a normal indentation behavior; and on the other hand, the free carbon, forming turbostratic graphite domains, provides easy crack initiation sites and low-energy fracture paths. Almost concentric shear steps and microcracks, which follow the turbostratic graphite domains, are observed after indentation. The ultimate coalescence of the microcracks produces Hertzian-type cone cracks.     

Adaptation of the chevron‐notch beam fracture toughness method to specimens harvested from diesel particulate filters

The apparent fracture toughness of a porous cordierite ceramic was estimated using a large specimen whose geometry was inspired by the ASTM‐C1421‐standardized chevron‐notch beam. Using the same combination of experiment and analysis used to develop the standardized chevron‐notch test for small, monolithic ceramic bend bars, an apparent fracture toughness of 0.6 and 0.9 MPa√m were estimated for an unaged and aged cordierite diesel particulate filter structure, respectively. The effectiveness and simplicity of this adapted specimen geometry and test method lends itself to the evaluation of (macroscopic) apparent fracture toughness of an entire porous‐ceramic, diesel particulate filter structure.     

Comment on “Lubauer J,Lohbauer U,Henrich M,Munz M,Lube T,Belli R. Intricacies involving the evaluation of fracture toughness obtained by the surface-crack-in-flexure method. J. Am. Ceram. Soc., 2022;105(12) 7582–7599”

We have evaluated over fifty materials using small semi–elliptical controlled surface flaws with the Newman–Raju factors. Although occasionally there were nuances and peculiarities, the results were sound and comparable to other methods. So, despite the lengthy discussions and numerous plots in Lubauer et al.’s paper, what is evident is that if one simply follows the guidelines in ASTM C 1421 and the other standards for most ceramics including the SL200B sintered silicon nitride, and polish off the recommended 4.5 to 5 h material, one will obtain the correct results. Excessive indentation forces and excessive material removal to obtain sharp corner, shallow surface cracks are unwise. Removing more than 5 h should only be done to remove lateral cracks. In such cases the Strobl et al. solutions may be useful. These solutions are an interesting alternative to the reputable Newman–Raju factors, but much more experience and verification is needed before they can be accepted. They and the extension of their analysis for precrack angles χ < 70° need to be vetted in a major engineering journal.     

New method for extracting fracture toughness of ceramic materials by instrumented indentation test with Berkovich indenter

Applying finite element analysis, a method is proposed for evaluating fracture toughness of ceramic materials by instrumented indentation with Berkovich indenter. The crack-tip K_I (Stress intensity factor) of Berkovich-produced crack is numerically calculated by using virtual crack closure technique, in particular, three kinds of crack pattern, i.e., radial crack, transition crack and half-penny crack are identified and their crack fronts meet the equi-K_I requirement. The validity of the proposed method is verified by instrumented indentation tests on standard SRM2100 (Si₃N₄) and CRM156 (Fused Silica) samples. Comparison with six representative conventional indentation methods indicates that the proposed method has advantages including wide application range, high accuracy and applicability to different crack patterns. Additionally, it’s revealed that the conventional indentation fracture toughness formulae derived from Lawn-Evans-Marshall formula tend to exhibit larger test error when applied to materials of relatively high indentation work ratio W_e/W_t.     

Temperature dependent fracture toughness model for whisker-reinforced ceramic matrix composites

A temperature dependent fracture toughness model for whisker-reinforced ceramic matrix composites was developed in this study, which considers the effects of matrix fracture toughness, residual thermal stress, crack bridging, crack deflection, and their temperature dependence. Its predicted results were compared with the fracture toughness of six types of whisker-reinforced ceramic matrix composites at different temperatures, and good agreement between predicted results and experimental results is obtained. Furthermore, based on this model, we systematically analyzed the effects of the volume fraction and aspect ratio of whisker, Young's modulus of matrix and whisker, thermal expansion coefficient difference, stress-free temperature, the ratio between the fracture energy of matrix and that of interface, on their temperature dependent fracture toughness for the first time. Finally, insights and suggestions which could help to optimize and improve the composite fracture toughness at different temperatures are provided.     

Artificial Intelligence-based determination of fracture toughness and bending strength of silicon nitride ceramics

Two mechanical properties, fracture toughness (K_IC) and bending strength (σ), of silicon nitride (Si₃N₄) ceramics were determined from their microstructural images via convolutional neural network (CNN) models. The Si₃N₄ samples used for database were fabricated using various kinds of sintering additives under different process conditions. In total, 330 data sets were prepared and used for building the CNN models for artificial intelligence-bassed determination of the two mechanical properties and testing the determination accuracy of the trained models. The determination coefficients (R²), which were used as accuracy indices, were approximately 0.85 for K_IC and 0.92 for σ. Although both the R² values were relatively high, the lower value for K_IC suggests that it is influenced more by what is little obtained from the microstructural information, such as grain-boundary characteristics. Furthermore, gradient-weighted class activation mapping, which can visualize which parts of the image the CNN models focus on, showed that the trained models determined the two mechanical properties based on correct recognition of the microstructural difference among the images.     

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.     

Enhanced fracture toughness in nonstoichiometric magnesium aluminate spinel through controlled dissolution of second phase alumina

Dissolution of Al₂O₃ particles into a MgAl₂O₄ (spinel) matrix is accompanied by a volumetric expansion that is predicted to lead to a compressive stress field upon cooling, resulting in a promising microstructure for enhanced toughening of transparent spinel. This study explores the conditions to form such a microstructure by hot‐pressing powders of Al₂O₃ and spinel, at temperatures that promote dissolution of the Al₂O₃. Tough, particulate‐reinforced composites were formed under lower temperatures and shorter times, but single phase, cubic spinel was formed at 1700°C for 10 hours. The single phase spinel made in this way exhibited a toughness of 2.26 ± 0.17 MPa√m, significantly higher than the equivalent nonstoichiometric spinel made by traditional methods, 1.72 ± 0.06 MPa√m. X‐ray diffraction measurements revealed lattice parameter changes consistent with the dissolution of Al₂O₃ into spinel. Mechanics modeling reveals that toughening arises due to the volume expansion as Al₂O₃ dissolves into the spinel matrix.     

Elastic properties and fracture toughness of SiOC-based glass-ceramic nanocomposites

Four different SiOC glass ceramics were synthesized and their fracture toughness (K_Ic) and fracture surface energy (γ) were assessed by means of the single-edge precracked beam (SEPB) method. In addition, the elastic moduli were measured and the Vickers indentation behavior (hardness and microcracking) was characterized. In particular, the dependence of K_Ic on the free carbon content and on the fraction of crystallized nanoparticles (SiC, ZrO₂, HfO₂) was investigated. An increase in K_Ic, from about 0.73 to 0.99 MPa √m is observed as the free carbon content is increased from less than 1 to 12 vol%. The addition of Hf and Zr (resulting in 4.5 to 7.8 vol% HfO₂ and ZrO₂ nanoparticles) was found to increase K_Ic to an extent similar to the free carbon content. Moreover, predicted K_Ic values, assuming that the crack travels through all phases accounting for their respective volume fractions, disrupting the weakest links within the structural units, are in agreement with the experimental values.     

Fracture toughness enhancement via sub-micro silver-precipitation in silica glass fabricated by spark plasma sintering

Sub-micro silver (Ag) precipitated in silica (SiO₂) glass was prepared via spark plasma sintering (SPS), and the microstructure, mechanical properties, and thermal conductivity were investigated. The in situ formation of Ag sub-micro particles through decomposition of silver nitrate (AgNO₃) was homogeneously distributed within the SiO₂ matrix. By precipitation of Ag particles, larger steady-state creep deformation and plastic deformation were observed owing to the ductility of the Ag particles. Moreover, crack bridging and pull-out of Ag particles were observed during crack propagation. As a result, the fracture toughness of SiO₂ glass improved with increasing Ag content. The sample with 1.4 vol% Ag sintered at 1200°C showed the highest toughness value of 2.15 ± 0.2 MPa m^1/2. Larger Ag particles in the samples sintered at higher temperatures tend to deform easily, resulting in larger ductility. In addition, incorporation of Ag particles improved thermal conductivity.