Proportional Specimen Resistance Model Research Articles

Analysis of the Indentation Size Effect in the Microhardness Measurements inB6O

The Vickers microhardness measurements of boron suboxide (B6O) ceramics prepared by uniaxial hot-pressing was investigated at indentation test loads in the range from 0.10 to 2.0 kgf. Results from the investigation indicate that the measured microhardness exhibits an indentation load dependence. Based on the results, we present a comprehensive model intercomparison study of indentation size effects (ISEs) in the microhardness measurements of hot-pressed B6O discussed using existing models, that is, the classical Meyer's law, Li and Bradt's proportional specimen resistance model (PSR), the modified proportional specimen resistance model (MPSR), and Carpinteri's multifractal scaling law (MFSL). The best correlation between literature-cited load-independent Vickers microhardness values, the measured values, and applied models was achieved in the case of the MPSR and the MFSL models.

Indentation Load-Size Effect in Al2O3 — SIC Nanocomposites

Indentation Load-Size Effect in Al2O3 — SIC Nanocomposites The indentation load-size effect (ISE) in Vickers hardness of Al2O3 and Al2O3 + SiC nanocomposites has been investigated and analysed using Meyer law, proportional specimen resistance (PSR) model and modified proportional specimen resistance (MPSR) model. The strongest ISE was found for alumina. Both the PSR and MPSR models described the ISE well, but the MPSR model resulted in slightly lower true hardness values for all materials investigated. No evidence of the effect of machining stresses on the ISE has been found.

Micromechanical and thermal behaviour of gel grown pure- and sodium-modified copper tartrate crystals

Abstract Results regarding micromechanical characteristics of gel grown pure- and sodium-modified copper tartrate crystals, bearing composition CuC 4 H 4 O 6 ·3H 2 O, (Cu) 0.77 (Na) 0.23 C 4 H 4 O 6 ·3H 2 O and (Cu) 0.65 (Na) 0.35 C 4 H 4 O 6 ·H 2 O, as obtained on using indentation induced hardness testing technique are reported. Thermal behaviour of these crystals in the temperature ranging from room temperature (∼25 °C) to about 600 °C is also reported. Pure copper tartrate crystals are found to be thermally more stable than the sodium-modified ones. Dependence of Vickers’ hardness number H v on load ranging from 0.049 to 2.94 N on two different planes for all the three compositions is analyzed. It is shown that after initial rise in the value of H v , the same achieves saturation at a load of 0.49 N. Modification of copper tartrate crystal by introducing sodium in its lattice brings about a change in the micromechanical characteristics. The saturation value of H v decreases with increase in the concentration of sodium ions. The results on (0 0 1) and (1 1 1) planes for both pure and modified copper tartrate crystals suggest hardness anisotropy. Relative difference of hardness between the two planes and yield strength for both pure and modified copper tartrate crystals is worked out. The experimental results are analyzed for applicability of Meyer’s law and Proportional Specimen Resistance Model. It is suggested that the experimental results indicating reverse ISE phenomenon may be explained in terms of the existence of a distorted zone near the crystal–medium interface. The integral method of Coats and Redfern approximation applied to the thermoanalytical data suggests “Random Nucleation Model” for the reaction kinetics of these crystals. Non-isothermal kinetic parameters such as activation energy, frequency factor and order of reaction are calculated.

Mechanical Response of KDP Single Crystal Using Nanoindentation Technique

Mechanical properties of potassium dihydrogen phosphate(KH2PO4,KDP) single crystal at the nano scale are one of important factors for probing its ultraprecision machining technology. Nanoindenting tests on(001) crystallographic plane and the tripler plane of KDP single crystal at room temperature are investigated by using nanoindentation tester with a standard Berkovich indenter with its tip radius around 50 nm.The results show that the nanohardness H and elastic modulus E exhibit significant peak load dependence. And the nonlinear proportional specimen resistance of normal load versus contact depth is responsible for the observed size dependence of H and E by Meyer's law and the modified proportional specimen resistance(MPSR) model. Furthermore,according to the of Raman spectral analysis,the nonlinear amplitude of them is influenced greatly by the surface residual stress of the processed sample. Moreover,pop-in events are also observed in load-displacement curves,which are closely correlated to the transition from elasticity to plasticity of the examined single crystals.

Indentation Size Effect for the Hardness of Refractory Carbides

This study measured the Vickers hardness of the sintered refractory carbides B4C, Mo2C, NbC, TiC, V8C7, W2C, WC, WC–SiC, and ZrC over a wide range of test forces between 0.49 and 196 N. The results showed an indentation size effect (ISE), with hardness values that increased with decreasing test force for the carbides. The test force dependence of the hardness was analyzed by the proportional specimen resistance (PSR) model. The value of the a1 term that reflects the elastic resistance in the model was obtained for the carbides and compared with their measured elastic, shear, and bulk moduli. It was not clear what type of modulus related strongly to the a1 term. There was a strict correlation between the hardness at an infinite test force and at a test force of 9.8 N. However, the hardness at a test force of 0.49 N a little poorly reflected the hardness at an infinite test force. The hardness at low test forces must be corrected using the a1 value in comparing it with the hardness at a test force of 9.8 N recommended for the Vickers hardness test by the Japanese Industrial Standard.

Micromechanical behaviour of gel grown pure and doped potassium hydrogen tartrate single crystals

AbstractMicromechanical characteristics of (001) and (111) planes of gel grown pure, sodium‐ and lithium‐doped potassium hydrogen tartrate single crystals as revealed by indentation induced technique are described. The indentation size effect (ISE) exhibited by the crystals is explained on application of proportional specimen resistance (PSR) model and the analytical law of Hays and Kendall. The load independent values of Vickers hardness of (001) and (111) planes of these crystals as indicated by indentation experiments and computed on the basis of PSR model and the analytical law are shown to be in good agreement. The doping by sodium or lithium results in the increase in hardness of potassium hydrogen tartrate crystals. The crystals exhibit hardness anisotropy. The values of yield strength of each plane of both pure and sodium and lithium doped potassium hydrogen tartrate single crystals are estimated using appropriate equations.

Effect of impurities on the microhardness of borax decahydrate

Microhardness of borax decahydrate single crystals grown from pure and impure borax solutions was measured. It was found that the microhardness of borax decahydrate crystals showed clear load dependence. The results obtained from Meyer Law indicated that Meyer index was found to be less than 2. The microhardness measurements were also evaluated according to the PSR (proportional specimen resistance) model to analyze normal ISE and measured microhardness values were converted to load-independent microhardness. The variation of these load independent microhardness values with different types and concentrations of impurities was determined and found that the microhardness of borax decahydrate crystals was strongly affected by ionic impurities. Based on microhardness measurements it was observed that radial and lateral cracks occurred during the measurements. The dependence of these crack lengths on applied load and fracture toughness was investigated by some empirical equations. Crystal surface stresses were evaluated using an empirical equation and it was determined that tensile stresses were effective on the microhardness of borax decahydrate crystals.

The role of friction to the indentation size effect in amorphous and crystallized Pd-based alloy

The role of friction between the indenter and the test specimen in amorphous and crystallized Pd40Cu30Ni10P20 alloy was investigated through instrumented nanoindentation under unlubricated and lubricated conditions. It was found that the reduction of hardness with the increasing penetration depth, i.e., the indentation size effect (ISE), becomes milder in the lubricated test than that in the unlubricated measurement. The important role of friction that related to the surface area to volume (S/V) was discussed in terms of the proportional specimen resistance (PSR) model and energy dissipation.

Microhardness studies of nanocrystalline lead molybdate

Nanocrystalline lead molybdate (PbMoO 4) of four different grain sizes were synthesized through chemical precipitation technique and the grain sizes and crystal structure are determined using the broadening of X-ray diffraction patterns and transmission electron microscopy. The microhardness of nanocrystalline lead molybdate (PbMoO 4) with different grain sizes were measured using a Vicker's microhardness tester for various applied loads ranging from 0.049 to 1.96 N. The microhardness values showed significant indentation size effect at low indentation loads. The proportional specimen resistance model put forward by Li and Bradt and energy balance model put forward by Gong and Li were used to analyze the behaviour of measured microhardness values under different indentation loads. The microhardness data obtained for samples of different grain sizes showed grain size dependent strengthening obeying normal Hall–Petch relation. The dependence of compacting pressure and annealing temperature on microhardness of the nanostructured sample with grain size of ∼18 nm were also studied. The samples showed significant increase in microhardness values as the compacting pressure and annealing time were increased. The variation of microhardness of the material with pressure of pelletization and annealing time are discussed in the light of change of pore size distribution of the samples.

AFM studies of microindented GaN and InGaN

The microhardness characteristics of GaN and GaN/InGaN films epitaxially grown on (0001) sapphire have been investigated using Vickers and Knoop indenters. The variation of H V and H K follows a reverse type of indentation size effect (reverse ISE). The microhardness results have also been analyzed using Meyer's law, Hays–Kendall approach and Proportional specimen resistance (PSR) model. The effect of N + implantation on the microhardness of GaN has also been studied. The implanted sample is more resistant to plastic penetration than the unimplanted one and it is found that implantation enhances the surface hardness. Detailed AFM studies around the indented regions of the GaN and GaN/InGaN give the nature and behavior of the deformation on the surface.

Microhardness of laser ablated alumina coating on Ti-6Al-4V

Alumina coated on Titanium alloys find wide tribological applications due to the improvement in hardness of substrate. This paper presents the effect of deposition of alumina by pulsed laser ablation on Vickers hardness of Ti-6Al-4V substrate. Nd: YAG laser of wavelength 1064nm is used with sintered alumina disc as target for ablation. The variation of Vickers microhardness with load in Ti-6Al-4V shows indentation size effect. Proportional Specimen Resistance (P.S.R) model is applied to separate load -independent hardness from the load -dependent hardness. Composite hardness of Alumina coated Ti-6Al-4V is measured for different laser processing conditions. The film hardness has been separated from the composite hardness of the film-substrate system by the use of an approach based on the law of area of mixtures model taking into an account of ISE, due to proportional specimen resistance of the material to indentation. Film hardness of different films produced by varying the target — substrate distance is presented. As the film thickness increases its hardness decreases as compared to bulk hardness. These studies will be useful in the selection of appropriate coating thickness and substrate hardness to achieve a required composite hardness in the design and production of wear-resistant parts of engineering devices.

Dynamic hardness and elastic modulus calculation of porous SiAlON ceramics using depth-sensing indentation technique

Interest in characterizing the mechanical properties of porous materials at micro-/nanometer scales has increased due to recent development of micro-/nanosystems. Depth-sensing indentation (DSI) systems, also referred to as nanoindentation, are strong tools for performing indentation measurements. The load-displacement curves of SiAlON-based porous ceramics were measured under different peak load (200–1800 mN). The most commonly used Oliver–Pharr method was used to analyze the unloading segments of these curves. The experimental results revealed that the dynamic hardness ( H d) and reduced elastic modulus ( E r) exhibit peak-load dependence, i.e., indentation size effect (ISE). Such peak-load dependence requires calculation of the load-independent hardness ( H LI) and elastic modulus ( E r). The experimental hardness data were analyzed using Meyer's law, Hays–Kendall's model, the proportional specimen resistance (PSR) model, and the modified PSR (MPSR) model. As a result, the modified PSR model is found to be the most effective one for H d determination of these SiAlON ceramics.

Dynamic hardness and reduced modulus determination on the (001) face ofβ-Sn single crystals by a depth sensing indentation technique

In this work, the creep behaviour ofβ-Sn single crystals having different growth directions under different peak indentation testloads (10, 20, 30, 40, and 50 mN) was investigated at room temperature during indentationtests. It was found that a ‘nose’ appears in the unloading segment of the applied indentationtest load–penetration depth curve. When a ‘nose’ occurs, the apparent unloading stiffnessSu, definedas dP/dh, is negative and the reduced modulus can no longer be calculated from theOliver–Pharr method (Oliver and Pharr 1992 J. Mater. Res. 7 1564). The ‘nose’disappears when the load hold before unload is lengthened. The correction term due tothe creep is the ratio of indenter displacement rate at the end of the load holdto unloading rate (Feng and Ngan 2002 J. Mater. Res. 17 660; Tang and Ngan2003 J. Mater. Res. 18 1141). Besides, the effect of creep on contact-depthmeasurement is considered. Removal of creep effects in both contact-area and contactstiffness measurement leads to satisfactory prediction of the dynamic hardness(Hd) and reducedmodulus in β-Sn single crystals. The experimental results reveal that the measured hardness values exhibita peak-load dependence, i.e. an indentation size effect (ISE). Such peak-load dependence isthen analysed using the Meyer law, the Hays–Kendall approach, the proportional specimenresistance (PSR) model, the modified PSR (MPSR) model, and the Nix–Gao model.As a result, the modified PSR model is found to be the most effective one forHd determinationof β-Sn single crystals.

Analysis of ISE in dynamic hardness measurements of β-Sn single crystals using a depth-sensing indentation technique

The dynamic indentation tests on (001) plane β-Sn single crystals having different growth directions under different peak indentation test load (10, 20, 30, 40, and 50 mN) has been investigated. The experimental results reveal that the measured hardness values exhibit a peak-load dependence, i.e., indentation size effect (ISE). Such peak-load dependence is then analyzed using the Meyer's law, the Hays–Kendall's approach, the Elastic/Plastic Deformation model, the Proportional Specimen Resistance (PSR) model, and the Modified PSR (MPSR) model. As a result, Modified PSR model is found to be the most effective for dynamic hardness determination of β-Sn single crystals.

Transport, microstructure and mechanical properties of Au diffusion-doped Bi-2223 superconductors

We have investigated the effect of the Au-diffusion on the mechanical and transport properties of the (Bi,Pb) 2Sr 2Ca 2Cu 3Oy (Bi-2223) superconducting samples with different annealing times of 10, 20 and 50 h. The samples are prepared by the conventional solid-state reaction method in the polycrystalline bulk form. Doping of Bi-2223 was carried out by means of Au diffusion during sintering from an evaporated Au film on pellets. The experimental works in this study consist of dc electrical resistivity and critical current density measurements for electrical and superconducting properties, microhardness measurements for mechanical properties, powder X-ray diffraction (XRD) for phase analyses (phase ratio) and lattice parameters, and scanning electron microscopy (SEM) for microstructure examination. These measurements showed that Au-doping, in comparison with the undoped samples, increased the critical transition temperature, critical current density and enhanced formation of high- T c phase. Additionally, microhardness and grain size were also improved with increasing amount of diffusion. Moreover, the diffusion-annealing time decreased the number and size of voids and increased the transition temperature. The experimental results of microhardness measurements were analyzed using the Kick's law, modified proportional specimen resistance (MPSR) model and the Hays–Kendall (HK) approach. Kick's law did not give useful knowledge of the origin of the indentation size effect. It was observed that the load independent microhardness values were determined based on the MPSR and HK models, and found to be similar with each other. The possible reasons for the observed enhancement in transport and mechanical properties due to Au diffusion are discussed.

Influence of x‐irradiation on indentation size effect and formation of cracks for [Ky(NH4)1‐y]2ZnCl4 mixed crystals

AbstractThe effects of x‐beam irradiation with different doses on microhardness and its related physical constants on [Ky(NH4)1‐y]2ZnCl4 mixed crystals with concentrations, y equals 0.000, 0.232, 0.644, 0.859 or 1.000 has been studied. The tests were performed for x‐doses from 0.2 kGy up to 1.6 kGy for loads from 20 to 160 g. The variation of hardness on (010) faces of orthorhombic [Ky(NH4)1‐y]2ZnCl4 mixed crystals with load were studied. The experimental results showed that, the hardness decreased as the x‐doses increased. Variation of the microhardness follows the normal ISE trend for low x‐doses and un‐irradiated crystals, then follows the reverse ISE trend for high x‐doses. Analysis of the experimental results revealed that: the radial cracks length, indentation size and applied indentation load are mutually related, and these dependences related with fracture mechanics are the basis of Meyer's empirical law. Indentation size effect (ISE) can be explained satisfactory by Hays‐Kendall's approach and proportional specimen resistance model. Brittleness of two cracks system are applicable for characterizing cracks around indentation impression (i.e. radial cracks) and another is (lateral cracks) for [Ky(NH4)1‐y]2ZnCl4 mixed crystals, crystals in the load range 60 – 160 g. It is shown that indentation induced microhardness decreases, whereas the length of radial cracks induced on indentation increases with the increase of x‐doses. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanical characterization for β-Sn single crystals using nanoindentation tests

Depth-sensing nanoindentation tests were made on β-Sn single crystals having different growth directions. The indentation load-displacement curves of the samples were obtained under different peak loads ranging from 10 to 50 mN. The most commonly used Oliver–Pharr method was used to analyze the unloading segments of these curves. It was found that the dynamic nanohardness ( H d) and reduced elastic modulus ( E r) exhibited significant peak load dependence. The observed size dependence of the H d was rationalized using classical Meyer's law, Proportional Specimen Resistance (PSR) and the Modified Proportional Specimen Resistance (MPSR) model. Reduced elastic modulus-indentation test load curves exhibited distinct transition to a plateau of constant E r. It can be concluded that the transition in such curves correspond to the intrinsic E r value of the examined materials. The examined single crystals also exhibit pop-in phenomenon attributed to the onset of dislocation nucleation activity underneath the indenter.

Influence of firing temperature on mechanical properties on roofing tiles

In the ceramic roofing tile manufacturing, absence of good mechanical properties, such as strength and hardness, leads to reject production of both green and fired tiles. We evaluated the effects of firing temperatures on bending strength and Vickers hardness in fired ceramic roofing tiles from kaolinite and illite-carbonate clay materials. The separately designed ceramics samples were shaped by dry pressing at 25 MPa, and then fired at 960 and 1050 °C following exposures to freezing/thawing cycles. The aim was to compare the bending strength and Vickers hardness, before and after cycling. The results showed that Vickers hardness HV5 and bending strength increased with increasing firing temperatures. For cycling specimens and firing temperature used, the values of hardness and bending strength were always lower. For the tile samples, where the low load hardness was evaluated, we also analysed the indentation size effect (ISE). The results followed the same pattern for samples obtained after freezing and thawing. The best correlation between measured values and available mathematical models was achieved with the modified proportional specimen resistance model. The most reliable results for the roofing tiles examined were achieved for the load independent hardness, H LIH when Vickers hardness measurements were HV0.5 and HV1.

Microhardness of Hg 1− xMn xTe

The microhardness of Hg 1− x Mn x Te has been investigated by means of Vickers measurements. First, the Hg 0.93Mn 0.07Te single crystal was measured at the applied load varying from 15 to 200 g. The results show that the microhardness decreases with the load increasing from 32.8 to 29.7 kgf mm −2. The Meyer's law, Hays–Kendall approach and proportional specimen resistance (PSR) model were used to analyze this phenomenon. However, the microhardness of Hg 1− x Mn x Te with variant x value from 0 to 0.26 was found to depend on the concentration strongly, which increases from 26 kgf mm −2 for x = 0–50 kgf mm −2 for x = 0.26. The results are explained using the elastic interaction of solid solution hardening theory.

Measurement of Vickers hardness on ceramic floor tiles

In this paper, Vickers macro- and micro-hardness of ceramic floor tiles samples made from two types of clay materials, kaolinite and illite–carbonate raw materials, were presented. The samples, designed separately, from both types of clay materials were shaped by dry pressing at 25 MPa, then fired at 960 and 1050 °C in laboratory conditions and exposed to freezing/thawing cycles with the aim to compare the hardness before and after cycling and correlate it to their microstructure. The results showed that Vickers macrohardness increases with the increasing of the firing temperature, although the expected microstructure is not achieved. The results obtained after freezing and thawing follow the same trend. In addition, the indentation size effect (ISE) in the case of low-load hardness testing was analysed. It should be noticed that the samples based on illite–carbonate clay material after the freezing/thawing cycles showed an unexpected increasing of hardness. The obtained results might be the consequence of the calcium silica hydrates formation during cycling treatment, causing a different behaviour of this kind of systems under low-loading. The ISE was described through the application of the Mayer's law, proportional specimen resistance (PSR) model and modified PSR model. The best correlation between measured values and used models was achieved in the case of modified PSR model. The most reliable results for the load independent hardness, H LIH, were obtained in the case of Vickers hardness measurement HV1.