Hardness and elastic properties of Bi2O3-based glasses

The hardness and elastic properties of 20PbO · xBi₂O₃ · (80 – x)B₂O₃ glasses with x = 20–60 were evaluated through usual Vickers indentation and nanoindentation tests. The glass transition temperature (T _g = 295–421°C), Vickers hardness (H _v = 2.9–4.5 GPa), true hardness (H = 1.5–3.8 GPa) and Young's modulus (E = 24.4–72.6 GPa) decreased monotonously with increasing Bi₂O₃ content. This compositional trend demonstrates that the strength of Bi–O chemical bonds in these glasses is considerably weak compared with B–O bonds and plastic deformations under indentation loading occur easily. The elastic recovery after unloading was about 45% for the glasses with x = 20–50, and the Poisson's ratio was 0.27 for the glass with x = 20. The fracture toughness was evaluated to be 0.37–0.88 MPam^1/2 from the values of H _v and E, and it was proposed that not only weak Bi–O bonds but also boron coordination polyhedra (BO₃ or BO₄) and their arrangements affect on crack formation. From the temperature dependence of Vickers hardness up to the glass transition region, it was suggested that the glasses with high Bi₂O₃ contents belong to the category to fragile glass-forming liquids.     

Scaling functions in conical indentation of elastic-plastic solids

Summary The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young’s modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young’s modulus E and Poisson’s ratio ν are known.     

Mechanical and elastic properties of transparent nanocrystalline TeO2-based glass-ceramics

Mechanical and elastic properties of transparent TeO₂-based glass-ceramics (15K₂O · 15Nb₂O₅ · 70TeO₂) consisting of nanocrystalline particles (each particle size: 40–50 nm) and showing optical second harmonic generation were evaluated by means of usual Vickers indentation and nanoindentation tests. The precursor glass has Vickers hardness H _v of 2.9 GPa, Young's modulus E of 54.7 GPa, the fracture toughness K _c of 0.25 MPam^1/2 and Poisson's ratio of 0.24. The transparent nanocrystalline glass-ceramic heat-treated at 420°C for 1 h has H _v = 3.8 GPa, E = 75.9 GPa and K _c = 0.34 MPam^1/2, and the opaque glass-ceramic heat-treated at 475°C for 1 h has H _v = 4.5 GPa, E = 82.9 GPa and K _c = 0.68 MPam^1/2, demonstrating that poor mechanical and elastic properties of the precursor TeO₂-based glass are improved through sufficient crystallization. The fracture surface energy, brittleness and elastic recoveries (about 44%) after unloading (the maximum load: 30 mN) of transparent nanocrystalline glass-ceramics are almost the same as those of the precursor glass, implying that the interaction among nanocrystalline particles is not so strong.     

Determination of mechanical properties of thermally grown oxide on Fecralloy by nano-indentation

Nano-indentation was used to measure the mechanical properties of the thermally grown oxide (TGO) on a Fecralloy substrate. Due to the influence both of the substrate and the indenter size effect (ISE), the measured hardness and Young's modulus of the TGO system decreased with increasing indentation depth. Models were proposed to determine the mechanical properties of the TGO with consideration of both the substrate effect and the ISE. In addition, the ratio of hardness to Young's modulus (H/E) can be related to the ratio of irreversible work to total work (W_ir/W_t) during the indentation process.     

Microhardness properties of 4-methoxy benzaldehyde N-methyl 4-stilbazolium tosylate

The mechanical properties of crystals are evaluated by mechanical testing which reveals certain mechanical characteristics. The fastest and simplest type of mechanical testing is hardness measurement. The Vickers and Knoop microhardness studies have been carried out on 4-methoxy benzaldehyde N-methyl 4-stilbazolium tosylate crystals grown by a slow evaporation technique over a load range of 10-100 g. The Vickers hardness number (H_v) and the Knoop microhardness number (H_k) were found to increase with the increase in load. The Meyer's index number ‘n’ was calculated from H_v. The Young's modulus was calculated using the Knoop hardness values. Hardness anisotropy has been observed in accordance with the orientation of the crystal.     

Microhardness studies in gel-grown ADP and KDP single crystals

Microhardness studies were carried out on (100) faces of gel-grown ADP and KDP single crystals. Slip lines were observed on (100) face of ADP crystal at the corners of the impressions. Microcracks around the indentation were found on (100) face of KDP crystal from 10g load which spread out as the load increased. Vickers hardness numberH _v decreased with increase in load. ΔH _v at 50g load for solution-grown crystals and gel-grown crystals (present case) was determined. Work hardening indexn for both ADP and KDP crystals was less than 2 showing soft-material characteristics. Using Wooster’s empirical relation, values of C₁₁ from hardness were calculated and found to be close to the reported ones. The work was done under a research project sanctioned by the Council of Scientific and Industrial Research (CSIR), New Delhi.     

Significant Change in Mechanical Properties of YBa2Cu3O7−x Bulk Superconductors Diffused with Sn Nanoparticles

Mechanical behavior of YBa₂Cu₃O_7?x (Y123) superconductors exposed to Sn nanoparticles diffusion is determined by the way of Vickers microhardness (H _v ) conducted at different applied loads (0.245N≤F≤2.940 N). Load dependent microhardness, load independent microhardness, elastic modulus, and yield strength values are estimated from the microhardness curves. Unpredictably, the findings of the H _v values reveal that the undiffused sample and Sn diffused sample prepared at 500 ^°C exhibit reverse indentation size effect (RISE) behavior while the other samples obey indentation size effect (ISE) nature. Further, we extract the load independent (true) microhardness using the Meyer’s law, proportional specimen resistance (PSR), elastic/plastic deformation (EPD), Hays–Kendall (HK) approach and indentation-induced cracking (IIC) model, and compare the true hardness with the apparent hardness.     

Production and characteristics of glass-ceramics derived from manganese crust tailings

Glass-ceramics have been produced via vitrification from manganese crust tailings with over 23% reduction in tailings volume. The crystalline behaviour of parent glass and glass-ceramics were investigated using DTA, TGA, XRD, and SEM/EDS. XRD analysis revealed that the major crystalline phase was iron manganese oxide. The Vickers microhardness (H _v) was 9.74 MPa, the indentation strength (K _c) was 1.88 Mpa m^1/2, and elastic modulus (E) was 140 MPa. The properties of the glass-ceramic compared well with known research and industrial glass-ceramic materials. Results suggest that manganese crust tailings have potential to be vitrified into useful, marketable glass-ceramic materials.     

Microhardness studies on 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST)

The Vickers and Knoop microhardness studies were carried out on the (001) face of 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST) crystals grown by the slope nucleation technique. The Vickers microhardness number (H_v) and the Knoop microhardness number (H_k) were found to dwindle with increasing load. The Meyer's index number (n) and hardness were calculated from H_v. The fracture toughness, brittle index and yield strength were calculated. The Young's modulus was calculated using the Knoop hardness value.     

Some physical properties and Vickers hardness measurements of Fe diffusion-doped Bi<Subscript>1.8</Subscript>Pb<Subscript>0.35</Subscript>Sr<Subscript>1.9</Subscript>Ca<Subscript>2.1</Subscript>Cu<Subscript>3</Subscript>O<Subscript>y</Subscript> superconductors

In this study we have investigated the influence of iron diffusion and diffusion-annealing time on the mechanical and the superconducting properties of bulk Bi_1.8Pb_0.35Sr_1.9Ca_2.1Cu₃O_y superconductors by performing X-ray diffraction (XRD), scanning electron microscopy (SEM), Vickers hardness, dc resistivity (ρ-T) and critical current density (J_c) measurements. The samples are prepared by the conventional solid-state reaction method. Doping of Bi-2223 was carried out by means of iron diffusion during sintering from an evaporated iron film on pellets. Then, the Fe layered superconducting samples were annealed at 830 °C for 10, 30 and 60 h. The mechanical properties of the compounds have been investigated by measuring the Vickers hardness (H_v). The mechanical properties of the samples were found to be load dependent. The load independent Vickers hardness (H₀), Young’s modulus (E), yield strength (Y), and fracture toughness (K_IC) values of the samples are calculated. These all measurements showed that the values of the Vickers hardness, critical current density, and critical transition temperature and lattice parameter c increased with increasing Fe doping and diffusion-annealing time.     

Elastic properties and Vickers hardness of optically transparent glass-ceramics with fresnoite Ba2TiSi2O8 nanocrystals

Optically transparent glass-ceramics (40BaO-20TiO₂-40SiO₂ (mol%)) consisting of nonlinear optical fresnoite Ba₂TiSi₂O₈ (BTS) nanocrystals (diameter: 100-200 nm) are fabricated, and their elastic properties and deformation behavior are examined as a function of the volume fraction (f) of BTS nanocrystals using cube resonance and Vickers indentation techniques. The elastic properties such as Young's modulus (E) increases linearly with increasing the volume fraction of nanocrystals, e.g., E = 84 GPa for f = 0% (glass) to E = 107 GPa for f = 54.5%. The Vickers hardness (H_v) and indentation fracture toughness (K_c) increase from 5.0 to 6.0 GPa for H_v and 0.48 to 1.05 MPa m^−1/2 for K_c with increasing the volume fraction (from f = 0% to f = 54.5%), but they do not change linearly against the volume fraction of nanocrystals. It is suggested that BTS nanocrystals themselves induce a high resistance against deformation during Vickers indenter loadings.     

Correlation between hardness and elastic moduli of the covalent crystals

From a statistical manner, we collected and correlated experimental bulk (B), shear (G), Young’s modulus (E), and ductility (G/B) with Vickers hardness (H_v) for a number of covalent materials and fitted quantitative and simple H_v–G and H_v–E relationships. Using these experimental formulas and our first-principles calculations, we further predicted the microhardness of some novel potential hard/superhard covalent compounds (BC₂N, AlMgB₁₄, TiO₂, ReC, and PtN₂). It was found that none of them are superhard materials (H_v ? 40 GPa) except BC₂N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/superhard materials.     

A comprehensive study on mechanical properties of Bi1.8Pb0.4Sr2MnxCa2.2Cu3.0Oy superconductors

This study manifests the crucial change in the mechanical performances of Bi_1.8Pb_0.4Sr₂Mn_xCa_2.2Cu_3.0O_y superconductor samples (x = 0, 0.03, 0.06, 0.15, 0.3 and 0.6) prepared by conventional solid-state reaction method by use of Vickers microhardness (H_v) measurements carried out at different applied loads, (0.245 N ≤ F ≤ 2.940 N). Load dependent microhardness, load independent microhardness, Young’s (elastic) modulus and yield strength values being account for the potential technological and industrial applications are evaluated from the hardness curves and compared with each other. It is found that the H_v, elastic modulus and yield strength obtained decrease (increase) with the enhancement of the applied load for the undoped (doped) samples. Surprisingly, the results of the H_v values illustrate that the samples doped with x = 0.03, 0.06, 0.15, 0.3 and 0.6 exhibit reverse indentation size effect (RISE) feature whereas the pure sample obeys indentation size effect (ISE) behavior. Furthermore, the experimental results are examined with the aid of the available methods such as Meyer’s law, proportional sample resistance model (PSR), elastic/plastic deformation (EPD), Hays–Kendall (HK) approach and indentation-induced cracking (IIC) model. The results inferred show that the hardness values calculated by PSR and EPD models are far from the values of the plateau region, meaning that these models are not adequate approaches to determine the real microhardness value of the Mn doped Bi-2223 materials. On the other hand, the HK approach is completely successful for the explanation of the ISE nature for the pure sample while the IIC model is obtained to be the best model to describe the hardness values of the doped materials exhibiting the RISE behavior. Additionally, the bulk porosity analysis for the samples reveals that the porosity increases monotonously with the increment in the Mn inclusions inserted in the Bi-2223 system, presenting the degradation of the grain connectivity.     

Instrumented and Vickers Indentation for the Characterization of Stiffness,Hardness and Toughness of Zirconia Toughened Al_2O_3 and SiC Armor

Instrumented and Vickers indentation testing and microstructure analysis were used to investigate zirconia toughened alumina(ZTA) and silicon carbide(SiC).Several equations were studied to relate the Vickers indentation hardness,Young's modulus and crack behavior to the fracture toughness.The fracture in SiC is unstable and occurs primarily by cleavage leading to a relatively low toughness of 3 MPa m~(1/2),which may be inappropriate for multi-hit capability.ZTA absorbs energy by plastic deformation,pore collapse,crack deviation and crack bridging and exhibits time dependent creep.With a relatively high toughness around 6.6 MPa m~(1/2),ZTA is promising for multi-hit capability.The higher accuracy of mediar equations in calculating the indentation fracture toughness and the relatively high c/a ratios above 2.5suggest median type cracking for both SiC and ZTA.The Young's modulus of both ceramics was most accurately measured at lower indentation loads of about 0.5 kgf,while more accurate hardness and fracture toughness values were obtained at intermediate and at higher indentation loads beyond 5 kgf respectively.A strong indentation size effect(ISE) was observed in both materials.The load independent hardness of SiC is 2563 HV,putting it far above the standard armor hardness requirement of 1500 HV that is barely met by ZTA.     

Microhardness studies on nonlinear optical L-alanine single crystals

Vickers and Knoop microhardness tests were carried out on grown L-alanine single crystals by slow evaporation technique over a load range of 10–50 g on selected broad (2 0 3) plane. Vickers (H _v ) and Knoop (H _k ) microhardness for the above loads were found to be in the range of 60–71 kg/mm² and 35–47 kg/mm², respectively. Vickers microhardness number (H _v ) and Knoop microhardness number (H _k ) were found to increase with increasing load. Meyer’s index number (n) calculated from H _v shows that the material belongs to the soft material category. Using Wooster’s empirical relation, the elastic stiffness constant (c ₁₁) was calculated from Vickers hardness values. Young’s modulus was calculated using Knoop hardness values. Hardness anisotropy has been observed in accordance with the orientation of the crystal.     

Mechanical characterization of Ti-added MgB2/Cu superconducting wires using Vickers hardness test

The Ti-added (0%, 5%, and 10%) MgB₂/Cu superconducting wires were prepared by the powder-in-tube (PIT) method. Mechanical properties of the samples were then characterized by using a dynamic ultra-microindentation experimental technique. We observed that the sink-in effect is significant in our samples. So, the loading–unloading (P–h) curves were analyzed by the displacement approach to indentation. It was found that hardness (H) and the effective elastic modulus (E) values increased with added Ti. In addition, these values showed peak load dependence (i.e. indentation size effect (ISE)).     

The determination of tensile properties from hardness measurements for Al-Zn-Mg alloys

The correlations between tensile properties (yield strength, ultimate tensile strength and uniform strain) and indentation hardness are studied for two types of Al-Zn-Mg alloys. The reasons why Tabor's equations do not well fit the experimental data when the strain-hardening coefficient is larger than 0.3 are discussed. New equations for the determination of tensile properties from hardness measurements are theoretically derived and found to be in excellent agreement with the experimental data for Al-Zn-Mg alloys. The equations areT _u=(H _v/c ₂)[4.6(m–2)] ^m–2 and _y=(H _v/C ₂)^{1-(3–m> )} +25 (m–2), whereT _u and _y are ultimate tensile strength and yield strength,H _v is Vicker's hardness number,m is Meyer's hardness coefficient,E is Young's modulus,c ₂ is a constant about 2.9 in magnitude. In these equationsT _u, _y,H _v andE are all expressed in kg mm^–2.     

Elastic recovery at hardness indentations

The mechanics of hardness indentation are considered. On the basis of a cycle in which the loading is elastic-plastic and the unloading (and subsequent reloading) elastic, an expression is derived for the relative depth recovery of the impression as a function of hardness/modulus,H/E. Experimental observations on indented surfaces of selected materials, mostly ceramics, using a tilting procedure in the scanning electron microscope to measure the residual depths, confirm the predicted trends. The analysis offers a simple means of characterizing the deformation properties of materials and should provide a basis for evaluating a range of contact-related properties, particularly surface damage phenomena in sharp-particle impact.     

Indentation testing of nuclear-waste glasses

The fracture properties of several nuclear-waste glasses were determined by indentation techniques. The fracture toughness,K _Ic, was calculated from the measurement of radial cracks around Vickers diamond indentations as a function of applied load, and the results agree quite satisfactorily with values obtained by the Hertzian indentation technique. The fracture toughness of the waste glasses containing simulated fission products ranged from 0.9 to 1.1 MN m^–3/2 in air, with slightly higher values measured in dry nitrogen. The hardness was also obtained from the Vickers indentations and the ratioH/E was determined from the elastic recovery of Knoop diamond indentations. The values ofE deduced fromH andH/E were within 15% of values measured by ultrasonic tests. The results along with the limitations of the different techniques are discussed in detail.Supported by the US Department of Energy.