Indentation size effect–crack propagation model and finite element simulation verification for microhardness test of ceramic materials

In this study, an indentation size effect–crack propagation model for hard and brittle materials in microhardness testing was proposed on the basis of the relationship between the size effects in microhardness testing and the generation and propagation of cracks in an indentation area. Results showed that crack length and crack opening angle were the main factors that influenced the size effect. The longer the crack length, the larger the crack opening angle, and the more obvious the size effect. The generation and propagation of cracks in the indentation region of ultrafine-grained Si₂N₂O–Si₃N₄ ceramics during microhardness testing were simulated on ABAQUS finite element software. The distributions of displacement field, strain field, and stress field in the indentation area with the presence of cracks was analyzed, the influence of crack propagation on the elastic recovery of the indentation area was discussed, and the correctness of the size effect–crack propagation model was verified.     

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.     

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.     

Elastoplastic stress–strain relationship of Si2N2O–Si3N4 ultrafine-grained ceramics based on microhardness test and finite element simulation

A method for obtaining the stress–strain relationship of ceramic materials was proposed on the basis of the relationship between the maximum load and the indentation size obtained by microhardness test. The microhardness testing process of Si₂N₂O–Si₃N₄ ultrafine-grained ceramics was simulated using ABAQUS finite element software. The stress–strain relationship curve of the material was obtained by repeatedly modifying and comparing the experimental and simulation results. The hardness testing principle and elastic–plastic theory were comprehensively applied in this work in accordance with the geometrical characteristics of the Vickers diamond indenter. The theoretical formula for calculating the stress–strain relationship of hard and brittle materials using microhardness experimental data combined with finite element simulation was deduced. The elastic–plastic area division principle for calculating yield stress was proposed. The accuracy of the theoretical formula was verified by comparing the theoretical and simulation results.     

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.     

Study on the subsurface damage mechanism of optical quartz glass during single grain scratching

The single grain scratching SPH simulation model was established to study the subsurface damage of optical quartz glass. Based on the analysis of the stress, strain and scratching force during scratching, the generation and propagation of subsurface cracks were studied by combining with the scratch elastic stress field model. The simulation results show that the cracks generate firstly at the elastic-plastic deformation boundary in front of the grain (φ = 28°) due to the influence of the maximum principal tensile stress. During the scratching process, the median crack closes to form the subsurface damage by extending downward, the lateral crack promotes the brittle removal of the material by extending upward to the free surface, and microcracks remain in the elastic-plastic boundary at the bottom of the scratch after scratching. The depth of subsurface crack and plastic deformation increases with rising scratching depth. The increase of scratching speed leads to the greater dynamic fracture toughness, accompanied by a significant decrease of the maximum depth of subsurface crack and the number of subsurface cracks. The subsurface residual stress is concentrated at the bottom of the scratch, and the residual stress on both sides of the scratch surface would generate and propogate the Hertz crack. When the scratching depth is less than 1.5 μm or the scratching speed is greater than 75 m/s, the residual stress value and the depth of residual stress are relatively small. Finally, the scratching experiment was carried out. The simulation analysis is verified to be correct, as the generation and propagation of the cracks in the scratching experiment are consistent with the simulation analysis and the experimental scratching force indicates the same variation tendency with the simulation scratching force. The research results in this paper could help to restrain the subsurface damage in grinding process.     

Quantitative Evaluation by Fractal Analysis of Indentation Crack Paths in Si3N4–SiCw Composites

The crack paths, generated by Vickers indentation in Si₃N₄–SiC_w composites, were analysed from a quantitative point of view, in order to distinguish between the possible toughening mechanisms involved. It was found that the roughness parameter R_L and the fractal dimension D describe the geometrical features of the cracks and evidence the anisotropy of the microstructure, due to the whisker and Si₃N₄β-grain orientation. The relationships found between fracture toughness and these geometrical parameters emphasise the importance of the crack deflection mechanism in improving toughness and provide information on the role played by microstructure in determining the mechanical properties of a composite.     

Crack profiles under a Vickers indent in silicon nitride ceramics with various microstructures

The effect of microstructure on crack morphology under a Vickers indentation was studied using 20 various silicon nitride ceramics including bearing-grade silicon nitrides. The indentation load was decreased from 98 N to 9.8 N and a transition of the crack types from half-penny crack to radial one was observed with both decoration method and serial sectioning technique. All of the indented samples possessed the half-penny cracks at the load of 98 N. The transition of crack profiles in the samples with coarse microstructure occurred when the load decreased from 49 N to 19.6 N, whereas the transition load for the sample with fine microstructure was ～9.8 N. Half-penny cracks were formed regardless of the microstructures when the ratio of the half of crack length to the half of diagonal size of an indentation, c/a, was above ～2. The dependence of the transition load on both Vickers hardness and fracture resistances was analyzed using Pajares's equation.     

Ferroelastic domain switching and R-curve behavior in lead zirconate titanate (Zr/Ti = 52/48)-based ferroelectric ceramics

In this work, ferroelastic domain switching and R-curve behavior in lead zirconate titanate (Nb/Ce co-doped Pb(Zr_0.52Ti_0.48)O₃, ab. PZT-NC)-based ferroelectric ceramics were investigated, using the indentation-strength-in-bending (ISB) method. Firstly, Vickers indentation test examined the notable fracture anisotropy of PZT-NC ceramics between the poling direction and its perpendicular direction, and the crack open displacement (COD) profiles in the two directions were also theoretically calculated from the indentation fracture mechanics. And then two kinds of ferroelastic domain switching modes (in-plane and out-of-plane) were used for explaining such anisotropic propagation behavior of indentation cracks. The subsequent three-point bending test illustrated the dependence of fracture strength on indentation load and the rising crack growth resistance curves (R-curves) in two directions. The resulted R-curves were fitted by the Hill's type Growth Function successfully, giving the reasonable values of crack extension exponential (n), plateau fracture toughness (K_max), and initial fracture toughness (K_ini). The in-plane ferroelastic domain switching was identified as a more significant toughening mechanism for PZT-NC ceramics than the out-of-plane switching due to more switchable domains.     

Mechanical behaviour of partially stabilized zirconia crystals with terbia and ceria additives

Mechanical behaviour of partially stabilized zirconia crystals (PSZC) with terbia and ceria additives was investigated under bending and indentation conditions. Test specimens were oriented along the [010] direction and along the axis of crystal growth. The PSZC bending strength (σ_b) was dependent on the crystallographic orientation of the specimens. The specimen volume subjected to stress influenced the PSZC strength. The highest mechanical characteristics were measured for ceria-doped crystals (σ_b = 1.9 GPa, K_lc = 11.4 MPa m^1/2, E_d = 366 GPa). The failure process was studied on the Vickers indentation, with special emphasis put on the development and propagation of lateral cracks. Anisotropy of lateral cracks in the (100) plane associated with that of the elastic moduli was revealed. At the same time anisotropy of radial cracks and hardness was not found. A new version of the equation to evaluate the fracture toughness (K_c^v) on the Vickers indentation was derived. The K_c^v values calculated by this equation correspond to those (K_lc) obtained by an SENB method.     

Indentation crack profiles of cordierite materials under mechanical and thermal biaxial stresses

The indentation crack profiles under mechanical and thermal stresses of cordierite materials obtained from a commercial powder were studied. Disks were prepared by slip casting and sintering, and they were indented (Vickers; 44.1 N; 15 s) at the center of one of their surfaces to be subjected to flexion in the mechanical test or to a sudden temperature change in the thermal shock test. Indented specimens were fractured in biaxial flexure (BF) or thermal shock (TS) tests. Some indented disks were thermally treated following two different schedules that involve exposures at high temperatures without (T₁) and with a sudden cooling (T₂). These specimens were fractured in biaxial flexure to observe the fracture surfaces. In all specimens (BF, TS, T₁ and T₂), the evolution of the indentation crack profiles was fractographically analyzed by SEM. In order to study the crack shape and the profile evolution, both the length and the depth of the indentation cracks were measured.     

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.     

Comments on “Thermal shock resistance of yttria-stabilized zirconia with Palmqvist indentation cracks” by G. Fargas,D. Casellas,L. Llanes,M. Anglada [J. Eur. Ceram. Soc. 23 (2003) 107–114]

In a recent paper, Fargas et al. [Fargas, G., Casellas, D., Llanes, L. and Anglada, M., Thermal shock resistance of yttria-stabilized zirconia with Palmqvist indentation cracks. J. Eur. Ceram. Soc., 2003, 23, 107–114] make use of the Vickers indentation technique to characterise the thermal shock resistance of brittle materials exhibiting the Palmqvist indentation crack system. They claim that their approach can provide a measurement of Hasselman's R⁗ thermal shock resistance parameter. It is here demonstrated that the obtained parameter is in fact different from R⁗. In parallel, it is shown that a previously developed approach, which is both consistent with the concepts of R⁗ and of the critical quenching temperature difference, ΔT_C, can be used in the case of the Y-TZP ceramics of Fargas et al. This approach also allows an estimation of the maximum thermal stresses and of the coefficient of heat transfer at the fluid–solid interface as a function of the quenching temperature difference.     

Indentation resistance of zirconia ceramics and crystals

Special features of resistance to Vickers indentation exhibited by ZrO₂ ceramics and crystals are investigated. The relation between their behavior in indentation and deformation in static bending is investigated. The anisotropy of lateral cracks in the (001) plane in partially stabilized ZrO₂ crystals is shown to correspond to the anisotropy of their elasticity moduli. New variants of the formulas for evaluating the crack resistance in indentation of zirconia materials, which obey Hooke's law until the moment of failure, are presented. Translated from Ogneupory, No. 3, pp. 2 – 12, March, 1996.     

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.     

Comprehensive understanding of horizontal and vertical crack effects on failure mechanism of lamellar structured thermal barrier coatings

The local spalling induced by the propagation and coalescence of cracks in the ceramic layer is the fundamental reason for the thermal barrier coatings (TBCs) failure. To clarify the effects of horizontal and vertical cracks on the coating failure, an integrated model combining dynamic TGO growth and ceramic sintering is developed. The effects of cracks on the normal and shear stress characteristics are analyzed. The driving force and propagation ability of cracks under different configurations are evaluated. The interaction between horizontal and vertical cracks is explored by analyzing the variation of the crack driving force. The results show that TGO growth causes the ratcheting increase of σ₂₂ tensile stress above the valley, and the σ₁₂ shear stress is on both sides of the peak. Ceramic sintering mainly contributes to the ratcheting increase of σ₁₁ tensile stress. There is minimum strain energy when the horizontal crack extends to the peak. The vertical cracks on the surface of the ceramic layer are easier to propagate through the coating than that of other locations. When the horizontal and vertical cracks simultaneously appear near the valley, they can promote the propagation of each other. The present results can offer theoretical support for the design of an advanced TBC system in the future.     

Microstructure and indentation damage resistance of ZrB2‐20 vol.%SiC ipo‐eutectic composites

Zirconium diboride with 20 vol.% silicon carbide bulk composites were fabricated using directionally solidification (DS) and also by spark plasma sintering (SPS) of crushed DS ingots. During the DS the cooling front aligned the c‐axis of ZrB₂ grains and its Lotgering factor of f_(00l) was high as 0.98. The Vickers hardness was anisotropic and it was high as 17.6 GPa along the c‐axis and 15.3 GPa when measured in an orthogonal direction. On both surfaces, even when using 100 N indentation load, no cracks were observed, suggesting a very high resistance to crack propagation. Such anomalous behavior was attributed to the hierarchical structure of DS sample where the ZrB₂ phase was under strong compression and the SiC phase was in tension. In the SPSed sample, the microstructure was isotropic respect to the direction of applied pressure. Indentation cracks appeared around the indent corners but not emanated from the diagonals, confirming high damage resistance.     

Thermal Shock Resistance of Laminated ZrB2–SiC Ceramic Evaluated by Indentation Technique

In this work, the thermal shock behavior of laminated ZrB₂–SiC ceramic has been evaluated using indentation‐quench method based on propagation of Vickers cracks and compared with the monolithic ZrB₂–SiC ceramic. The results showed that the laminated ZrB₂–SiC ceramic exhibited better resistance to crack propagation and thermal shock under water quenching condition, and the critical temperature difference (ΔT_c) of laminated ZrB₂–SiC ceramic (ΔT_c ≈ 590°C) was much higher than that of monolithic ceramic (ΔT_c ≈ 290°C). The significant improvement in thermal shock resistance was attributed to residual stresses enhancing the resistance to crack growth during thermal shock loading.     

Raman spectroscopy mapping of amorphized zones beneath static and dynamic Vickers indentations on boron carbide

Three-dimensional models of amorphized zones beneath quasistatic and dynamic Vickers indentations on boron carbide were constructed using micro-Raman spectroscopy. The square of amorphized zone depth varied linearly with load and the maximum amorphized area occurred beneath the indentation imprint in accord with the maximum shear stress under Hertzian contact. Reduced measurements of amorphization intensity at loads above 10 N may be due to a loss of subsurface amorphized material through lateral cracks. Utilizing an expanding cavity model with power-law (n = 0.79–0.80) and linear (E_p = 0.39–0.45) strain hardening responses, finite element simulations were conducted to determine the critical values of stress and strain required to cause amorphization. These simulations suggest that amorphization may initiate at von Mises stresses and equivalent plastic strains above 6.6 GPa and 0.026, respectively. These results may be useful for validating computational models of boron carbide under complex loading scenarios (e.g., ballistic impact).     

Toughness measurement and toughening mechanisms of arc ion plating Cr2O3 films treated by annealing

Chromium sesquioxide (Cr₂O₃) films were deposited on Ni-based high-temperature alloy substrates by an arc ion plating technique and then annealed at different temperatures and heating rates. The influence of annealing conditions on the toughness of Cr₂O₃ films was calculated according to spherical indentation tests. The increase in grain size and compressive stress, variety of microstructure and surface morphology, and atom diffusion that resulted from annealing caused toughness variations. The increase in grain size closed micro-cracks along the direction of film growth. Compressive stress and a multi-crystal plane led to cracks caused by indentation that required more energy to break through the film. In the process of indentation, turning, bifurcating, and bridging of cracks on film surface was also able to dissipate energy. Atom diffusion in the process of 1000 °C annealing also played a role in grain boundary toughening. The toughness improvement of Cr₂O₃ film significantly improved friction life.