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.     

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.     

Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.     

Effect of Nonstoichiometry on Fracture Toughness and Hardness of Yttrium Oxide Ceramics

This work deals with the changes in mechanical properties of yttrium oxide ceramics induced by nonstoichiometry. The maximum fracture toughness, K_lc, is observed at the stoichiometric composition. For an oxygendeficient ceramic, a decrease of K_lc is observed from 3.5 to 2.3 MPa.m^1/2. On the other hand, the Vickers hardness seems to be less dependent on stoichiometry. These results are discussed in the frame of the evolution of the Y-O bond with the stoichiometry. They set in particular the problem of the role of electrostatic energy stored in a brittle material containing charged defects in the energy balance controlling crack propagation.     

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.     

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.     

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.     

Hardness and Fracture Toughness of Pressureless-Sintered Boron Carbide (B4C)

This is a companion work to our previous study on the pressureless sintering of boron carbide (B₄C). The Vickers hardness and indentation fracture toughness of B₄C compacts were measured after various sintering heat treatments. Increases in hardness and decreases in indentation fracture toughness as the grain size decreased in sintered B₄C were attributed to the effects of more rapid strain hardening associated with dislocation pileups at grain boundaries.     

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.     

Hardness and Fracture Toughness of SiC-Particle-Reinforced MoSi2 Composites

The indentation technique has been used to evaluate the hardness and fracture toughness of SiC-reinforced MoSi₂ composites made by hot-pressing. It is seen that the toughness increases with increasing indentation crack length (under increasing load) and a probable mechanism responsible for this behavior is described. It is also observed that there is an optimum volume fraction of SiC particles for which the maximum fracture toughness of the composite can be achieved.     

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.     

Indentation Behavior of Ion-Exchanged Glasses

Indentation fracture mechanics was extended to include the effect of a thin layer of residual stress on the identation strength of brittle materials. The proposed theory was used to predict the residual stress values for an ion-exchanged glass. For flaws placed before the exchange, considerable strengthening was observed, but the value of the surface stress predicted was considerably underestimated. For flaws placed after the exchange, there was no strengthening and the value of the surface stress was predicted to be zero. The failure of the indentation analysis indicates that it has to be modified for accurate stress determination. Thin layers of residual stress were found to retard the initiation of surface damage, but their influence on the strength after damage initiation was minimal.     

Processing, Fracture Toughness, and Vickers Hardness of Allylhydridopolycarbosilane-Derived Silicon Carbide

Bulk specimens of precursor-derived silicon carbide (SiC) suitable for mechanical-property measurements were prepared from allylhydridopolycarbosilane (AHPCS), which is a commercially available, hyperbranched polycarbosilane. Crack-free pellets were obtained by cold-pressing mixtures of finely ground, 1000°C pyrolyzed, "AHPCS-SiC" with neat AHPCS, followed by pyrolysis to 1000°C and ten subsequent reinfiltration/pyrolysis steps with the neat liquid AHPCS. Then, these pellets were heat-treated to 1200°, 1400°, and 1600°C, followed by additional reinfiltration/pyrolysis cycles to the final respective maximum temperatures. This fabrication process simulated the production of the matrix phase for ceramic-matrix composites via successive infiltration/pyrolysis cycles. The density of the material processed at these temperatures, measured via the Archimedes method, was 2.3, 2.5, 2.6, and 2.9 g/cm³, respectively, and the average open porosities of the samples were 2, 0.2, 1, and 9 vol%, respectively. The fracture toughness was measured using the single-edge V-notched-beam method, and the hardness was measured via Vickers indentation. The samples had an average toughness of 1.40 ± 0.08, 1.65 ± 0.09, 1.67 ± 0.07, and 1.46 ± 0.08 MPa·m^1/2 for the samples that were treated at 1000°, 1200°, 1400°, and 1600°C, respectively. The Vickers hardness for these samples, measured at a load of 1000 g, was 12 ± 1, 13 ± 2, 11 ± 1, and 9 ± 1 GPa, respectively.     

Effects of an Electric Field on the Fracture Toughness of Poled Lead Zirconate Titanate Ceramics

Compact tension tests and indentation-fracture tests have been conducted to study the effects of an applied electric field on the fracture toughness ( K _{I C} ) of poled commercial lead zirconate titanate (PZT) ceramics. The experimental results show that an applied electric field, either parallel or antiparallel to the poling direction, considerably reduces the K _{I C} value of the PZT ceramics. The reduction in K _{I C} for a negative field is larger than that for a positive field of the same strength. The failure mode in the PZT ceramics is basically transgranular, insensitive to the applied electric field.     

Mechanical Properties of Monoclinic Zirconia

Fracture toughness and fracture strength data are presented for the first time for monoclinic zirconia. An undoped nanocrystalline zirconia powder was sintered at 1100°C and yielded a theoretical density of more than 90% with a grain size of about 150 nm. The surface crack in flexure (SCF) technique was deemed most suitable for nanocrystalline materials. Measurements of Young's modulus and the determination of the fracture origin are also provided.     

Third-Harmonic Generation from Some Chalcogenide Glasses

Third-order optical nonlinear susceptibilities (χ⁽³⁾) of some high-refractive-index chalcogenide glasses were evaluated from third-harmonic generation. Compared with oxide glasses whose χ⁽³⁾ has been known, χ⁽³⁾ of the present glasses was higher by an order of magnitude. The addition of selenium drastically increased χ⁽³⁾. The highest χ⁽³⁾ was 1.4 × 10^–11 esu, being comparable with those of high-χ⁽³⁾-organic compounds. Further, χ⁽³⁾ generally increased with increasing density in the present glasses.     

Crack-Shape Effects for Indentation Fracture Toughness Measurements

Various methods to measure fracture toughness using in-dentation precracks were compared using soda-lime glass as a test material. In situ measurements of crack size as a function of applied stress allow both the toughness K_c and the residual-stress factor χ to be independently determined. Analysis of the data showed that stress intensity factors based on classical half-penny crack shapes overestimate toughness values and produce an apparent R -curve effect. This is due to a constraint on crack shape imposed by primary lateral cracks in soda—lime glass. Models based on elliptical cracks were developed to account for the crack-shape effects.     

Modeling of Rigidity Percolation and Incipient Plasticity in Germanium–Selenium Glasses

We compute the bulk and surface structures of glasses in the germanium–selenium (Ge–Se) system using Monte Carlo simulations and our previously derived set of ab initio potentials. We investigate the elastic response of the Ge–Se glasses under a flat "micro"-indentation and incipient plasticity under a spherical nanoindentation. The glasses with a high average coordination number (〈 m 〉>2.4) display structural frustration owing to an excess of bond constraints, leading to permanent densification from both types of indentations. The glasses with a low average coordination number (〈 m 〉<2.4) exhibit a large number of floppy modes, enabling continuous shear flow. According to the Phillips theory of topological constraints, the ideal glass former is one in which the number of constraints exactly equals the number of degrees of freedom (GeSe₄, where 〈 m 〉=2.4). In both types of indentation simulations, we find that the GeSe₄ glass structure is most resistant to distortions of its basic structural unit.     

Mixed-Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al₂O₃. Multiaxial fracture mechanics of the Al₂O₃ ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness K _Ic, the mode III fracture initiation toughness is 2.3 times higher than K _Ic. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.