Mechanical and elastic properties of fine-grained polycrystalline scandia and erbia as determined by indentation techniques

The Young's moduli, E, and nanoindentation, NI, stress-strain curves of fine-grained scandia, Sc₂O₃, and erbia, Er₂O₃, were determined using spherical indenters with radii of 1.4 μm and 5 μm. The Young's moduli measured with the spherical indenters, were comparable to those measured by a Berkovich tip, and by ultrasound. This work further validates the use of S vs. a plots to measure the Young's moduli of polycrystalline ceramics. A major advantage of using this technique is the possibility of determining NI stress-strain curves and concomitant yield points, apparent strain hardening rates, etc. for the first time. Both the elastic moduli and the yield stresses were affected by the degree of surface polishing and tip size. The most reproducible and reliable results were obtained with the sharper nanoindenter and the best surface finish. The Vickers hardness and indentation fracture toughness values extracted from the Vickers indentations are comparable to the literature results.     

Geometrical Effects in Elastic/Plastic Indentation

A general analysis of elastic/plastic indentation fracture for an arbitrary-shaped indenter is presented. The analysis is based on the observation that the residual indentation stress field provides the driving force for crack formation. After establishing that the influences of indenter geometry and load on the residual field are completely characterized by the volume of the indentation, a relation between the extent of radial cracking, the indentation volume, and the material properties is derived. Predictions of the analysis are examined by comparing calculated load/crack-length relations for two specific indenter geometries (Vickers pyramid and sphere) with experimental measurements in ZnS. For Vickers indentation the crack length is proportional to (load)^2/3, whereas for spherical indenters the variation of crack length with load is nearly linear.     

Comment on hardness definitions

The different definitions of hardness and elastic modulus as obtained using indentation with conical (also Vickers and Berkovich) or spherical indenters are compared and relationships that permit a conversion and an assessment of the differences are derived. A comparison to experimental data is given.     

氧化气氛下热处理对SiC/h-BN复相可加工陶瓷性能的影响

采用热压烧结制备h-BN体积含量分别为30%和40%的可加工SiC/30%h-BN和SiC/40%h-BN复相陶瓷,并在不同温度和氧化气氛下对复相陶瓷样品进行热处理。测试了预制Vickers压痕的复相陶瓷样品在热处理前后的强度和表面硬度,并通过X射线衍射和扫描电子显微镜等研究了复相陶瓷表面成分和显微结构的变化。结果表明:氧化气氛下的热处理可恢复陶瓷在加工时由表面损伤降低的强度,1100℃热处理2h的陶瓷效果最佳。经1100℃热处理2h后,带压痕的SiC/40%h-BN复相陶瓷的强度恢复到389.81MPa,表面硬度从6.11GPa提高10.48GPa。SiC和h-BN的高温氧化行为是强度恢复和表面硬度升高的主要原因。     

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.     

A technique for measuring stresses in small spatial regions using cube-corner indentation: Application to tempered glass plates

Vickers indentation cracks have been used to estimate residual stress in materials; however, a high threshold load for cracking limits the smallest spatial region for stress measurement. Cube-corner indenters have a lower included angle, and their sharpness leads to lowered cracking thresholds enabling stress measurement in small spatial regions. Cube-corner indentations on tempered glass plate and on annealed soda-lime-silica glass revealed that crack surface traces on the tempered material were significantly smaller. Cracks were found to be quarter-penny shaped as opposed to half-penny/radial for Vickers indentation. Using an appropriate stress-intensity factor and a stress-intensity factor superposition approach, surface stresses in the tempered plate were calculated. The stresses were in good agreement with those determined using well-established Vickers indentation approach; however, the spatial region sampled is 6–10 times smaller. An estimate of the smallest spatial region at which a particular stress may be measured using this technique is presented.     

Experimental Measurement of Residual Stress Field around Sharp Indentation in Glass

A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.     

Relation of Load to Radial Crack Length for Spherical Indentations in Hot-Pressed ZnS

Hot-pressed ZnS was indented by spherical indenters of various radii. The relation of the load (P) and radial crack length ( c_r ) was better modeled by Pαic_r^½ , where d_i is the indentation diameter, than by Pαc_r^3/2 .     

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.     

Elastoplastic Indentation on Heat-Treated Carbons

A Vickers indenter, as an efficient mechanical microprobe, was applied to carbon materials heat-treated at temperatures in the range 880°–2600°C. The plasticity of the carbon materials, which was enhanced by increasing the heat-treatment temperature (HTT), was assessed from the relation between the indentation load, P , and the penetration depth, h . Using the concept of the true hardness, H , as a measure of plasticity and the experimental estimate of the H -value, the plasticity of the carbon materials was examined as a function of their crystallographic parameters. The residual impression of the carbons at HTT > 1800°C was hardly visible on the indented surface after unloading, because of the nearly complete elastic recovery of the indented surface, yielding a very unique indentation P – h hysteresis in the loading/unloading cycle. The microscopic processes associated with this unique elastic recovery during unloading are discussed here in relation to the reversible slip of the dislocation-network structures on the graphitic basal planes.     

Characterisation of indentation microstructures for porous SOFC cathodes

In this study, high-resolution focused ion beam sectioning assisted with SEM imaging was used to study the indentation microstructures of porous bulks and films of a solid oxide fuel cell cathode material (La_0.6Sr_0.4Co_0.2Fe_0.8O_3-δ) sintered at different temperatures. The crack morphologies and pore-filling densification caused by crushing of particle networks were studied in details. Analysis showed distinct permanent deformation mechanisms of the indentation microstructures between porous bulks and films. Whilst remarkable porosity gradient was found for the porous films under both Berkovich and spherical indenters, the porous bulks were found to behave more like dense materials. Results also showed that radial cracks induced by Berkovich indentation on the bulks could not generate observable pop-in/pop-out events in the loading-unloading curves. However, when indenting with the spherical indenter on a thick film, the shear sliding of the particle networks immediately under the indenter could cause phenomenal disruption in the loading unloading curves shown.     

Analyzing indentation behavior of LaGaO3 single crystals using sharp indenters

In this work, the mechanical properties of (1 0 0) and (0 0 1) oriented LaGaO₃ single crystals have been studied using sharp indenters. Vickers hardness values for both the (1 0 0) and (0 0 1) samples were found to be in the same range (8 GPa). The values for the indentation fracture toughness (K_R) from Vickers indentation on the (1 0 0) samples were determined to be 0.8 ± 0.2 MPa m^1/2. Different crack lengths, implying a strong anisotropy in the indentation fracture toughness values, were observed in the two mutually perpendicular directions in the indentations on the (0 0 1) samples. These measurements led to estimates of 0.5 ± 0.1 and 1.3 ± 0.3 MPa m^1/2 for the two different sets of cracks on the (0 0 1) samples. In situ nanoindentation inside the SEM using a cube-corner indenter has also been used for studying the indentation fracture response of these samples.     

Fabrication of Hard and Strong α/β-Si3N4 Composites With MgSiN2 as Addivitives

α/β-Si₃N₄ composites with various α/β phase ratios were prepared by hot pressing at 1600°–1650°C with MgSiN₂ as sintering additives. An excellent combination of mechanical properties (Vickers indentation hardness of 23.1 GPa, fracture strength of about 1000MPa, and toughness of 6.3 MPa·m^1/2) could be obtained. Compared with conventional Si₃N₄-based ceramics, this new material has obvious advantages. It is as hard as typical in-situ-reinforced α-Sialon, but much stronger than the latter (700 MPa). It has comparable fracture strength and toughness, but is much harder than β-Si₃N₄ ceramics (16 GPa). The microstructures and mechanical properties can be tailored by choosing the additive and controlling the heating schedule.     

Use of Spodumene in the Processing of Alumina-Matrix Ceramics—Influence on Microstructure and Mechanical Properties

A study has been conducted on the microstructural character, phase assemblage, and selected physical properties of liquid-phase-sintered (LPS) aluminas processed from formulations containing β-spodumene, Li₂O·Al₂O₃·4SiO₂. Assessments were made using density data, SEM imaging, XRD analysis, Vickers indentation testing, and Young's modulus measurements. The results indicate that using β-spodumene to develop LPS alumina ceramics provides materials containing a mix of crystalline β-spodumene and glassy material which are comparable in mechanical performance to currently available commercial debased alumina ceramics.     

Processing and Properties of TiB2 with MoSi2 Sinter-additive: A First Report

The densification of non-oxide ceramics like titanium boride (TiB₂) has always been a major challenge. The use of metallic binders to obtain a high density in liquid phase-sintered borides is investigated and reported. However, a non-metallic sintering additive needs to be used to obtain dense borides for high-temperature applications. This contribution, for the first time, reports the sintering, microstructure, and properties of TiB₂ materials densified using a MoSi₂ sinter-additive. The densification experiments were carried out using a hot-pressing and pressureless sintering route. The binderless densification of monolithic TiB₂ to 98% theoretical density with 2–5 μm grain size was achieved by hot pressing at 1800°C for 1 h in vacuum. The addition of 10–20 wt% MoSi₂ enables us to achieve 97%–99%ρ_th in the composites at 1700°C under similar hot-pressing conditions. The densification mechanism is dominated by liquid-phase sintering in the presence of TiSi₂. In the pressureless sintering route, a maximum of 90%ρ_th is achieved after sintering at 1900°C for 2 h in an (Ar+H₂) atmosphere. The hot-pressed TiB₂–10 wt% MoSi₂ composites exhibit high Vickers hardness (∼26–27 GPa) and modest indentation toughness (∼4–5 MPa·m^1/2).     

Micromechanical properties of Dy3+ ion-doped (LuxY1-x)3Al5O12 (x = 0, 1/3, 1/2) single crystals by indentation and scratch tests

Three kinds of Dy³⁺ ion-doped (Lu_xY_1-x)₃Al₅O₁₂ (x = 0, 1/3, 1/2) single crystals fabricated by the Czochralski method with 4 at.% Dy³⁺ ion doping were investigated by indentation and scratch techniques under Vickers, Knoop, Berkovich, and spherical indenters to understand the influence of Lu ion on micromechanical properties and fracture behavior of Y₃Al₅O₁₂ (i.e. YAG for x = 0) single crystals. The largest (or smallest) values of hardness, elastic modulus, and fracture toughness were found for x = 1/3 (or 1/2). The indentation size effect was explained by four different models with the Hays-Kendall approach being the most suitable one to determine the true hardness. Fracture toughness values of YAG crystals obtained by the Vickers hardness method agreed with those obtained by scratching with a spherical indenter based on linear elastic fracture mechanics.     

Comparison of the Elastic–Plastic Indentation Response of MgAl2O4, AlON,and AlN

Contact damage in the form of localized cracking and inelastic deformation is of concern in the utilization of ceramics and is often studied using hard indenters; an approach that has spawned the field of indentation mechanics. This approach was taken in the current work to study the penetration resistance at low strain rates of four candidate ceramic armor materials: MgAl₂O₄ with two grain sizes, AlON and AlN. Spherical indentation was chosen as this allows the elastic–plastic behavior to be studied and the indentation stress–strain curves to be determined. To further quantify these data, the elastic and plastic indentation work contributions were measured. On empirical grounds, it was postulated that the area under the indentation stress–strain curves, termed the indentation strain energy density, was related to the total indentation work could be used to quantify the penetration resistance. As a test of this hypothesis, it was shown that the total indentation work correlated with the strain energy density and acted over a volume similar to that of the stress field. A simple figure of merit, derived from the indentation strain energy density, was suggested as a means to quantify the penetration resistance of materials at low strain rates and to identify the material parameters that control this process.     

Fracture toughness of glasses and hydroxyapatite: A comparative study of 7 methods by using Vickers indenter

Numerous methods have been proposed to estimate the indentation fracture toughness Kic for brittle materials. These methods generally uses formulæ established from empirical correlations between critical applied force, or average crack length, and classical fracture mechanics tests. This study compares several models of fracture toughness calculation obtained by using Vickers indenters. Two optical glasses (Crown and Flint), one vitroceramic (Zerodur) and one ceramic (hydroxyapatite) are tested. Fracture toughness and hardness are obtained by using instrumented Vickers indentation at micrometer scale. Young's moduli are obtained by instrumented Berkovich indentation at nanometer scale. Fracture toughness is calculated with models involving crack length measurements, and by models free of crack length measurements by considering critical force, chipping, pop-in. Finally, method based on the cracking energy, commonly employed for coated materials is also used.The aim of this work is to compare seven methods, which enable the facture toughness determination, on four brittle materials. To do so, it was necessary to determine some specific constant in the case of Vickers tip use.On the one hand, results show that methods using crack length, critical force, edge chipping or pop-in lead to comparable results, and the advantages and drawbacks are highlighted. On the other hand, the indentation energy method leads to underestimated results of about 20%.     

Recommendations for Determining the Hardness of Armor Ceramics

It is empirically known that an armor ceramic should be as hard or harder than the projectile it intends to defeat. Quasi-static indentation testing is one of the most widely utilized techniques for determining the hardness of armor ceramics. Hardness measurements can also be used to generate other property values that may be relevant to ballistic performance (fracture toughness, elastic properties, and even the yield strength). While the indentation methodologies are simple and straight forward, the resultant hardness values for ceramic materials can be influenced by the indenter geometry, indentation load, loading rate, specimen surface finish, and microstructure. This presentation will summarize the results of a study to determine the hardness of a variety of armor-grade ceramics with different indenter geometries (Vickers and Knoop) over a range of indentation loads (0.98-98 N) and discuss the implications for armor ceramics. The resulting data strongly indicate that the best means of determining the hardness of armor ceramics is the use of 19.6-N Knoop indentations.     

Non-Hall-Petch hardness dependence in ultrafine fibrous MgAl2O4-MgO eutectic ceramics fabricated by the laser-heated floating zone (LFZ) method

MgAl₂O₄-MgO eutectic ceramics were fabricated by the laser-heated floating zone (LFZ) method with various growth rates to assess its possible beneficial effect on microstructural aspects and mechanical properties. It was determined that the growth rate optimizing the microstructure and mechanical properties is 750 mm/h; below this value, coarsening of the fibrous microstructure takes place with a degradation of these properties. In the extreme case of 50 mm/h growth rate, the presence of undesirable transverse cracks was unavoidable. Thanks to the high growth rate of 750 mm/h, ultra-fine fibrous microstructure MgAl₂O₄-MgO eutectic ceramics can thus be fabricated with greater hardness (15.5 GPa from Vickers indentation and 22 GPa from nanoindentation) and flexural strength (?345 MPa). It is reported that hardness scales with the interfiber spacing λ according to a law of the type lnλ/λ, contrary to the assumed Hall-Petch-like dependence. This proposed law can be explained in terms of dislocation hardening induced by the MgO fibers.