Hays Kendall Approach Research Articles

Experimental and theoretical modelling of Vickers, Knoop microhardness and laser damage threshold studies on Ca0.9Nd0.1Ti0.9Al0.1O3 single crystals grown by optical floating zone technique

Vickers and Knoop microhardness studies were done on the (200) face of Ca0.9Nd0.1Ti0.9Al0.1O3 crystals grown by optical floating zone technique for various loads ranging from to 0.24–9.8 N. Various important mechanical properties such as Vickers hardness, Knoop hardness, Young's (elastic) modulus, yield strength, stiffness constant which accounts for various industrial applications were determined. The Indentation Size Effect (ISE) were observed for the grown crystal, four different models such as Meyer's law, Hays-Kendall (HK) model, proportional sample resistance (PSR) model, elastic/plastic deformation model (EPD) were used to determine the true hardness values. Among these four mechanical analysis models, HK approach seemed to be the best model to describe the mechanical properties of the grown crystal. The variation of microhardness number for different orientations showed the presence of microhardness anisotropy in the grown crystal. Laser damage threshold for the grown crystal was found to be 2.49 GWm−2.

Degeneration of mechanical characteristics and performances with Zr nanoparticles inserted in Bi-2223 superconducting matrix and increment in dislocation movement and cracks propagation

This study explains the role of Zr concentration level on mechanical characteristics and performance belonging to the bulk Bi-2223 superconducting materials by means of standard Vickers microhardness (H v ) measurements at different applied loads in the range of 0.245–2.940 N and evaluated theoretical calculations. The experimental measurement results obtained display that the mechanical performances regress with the increment of the Zr addition level due to the increased artificial disorders/damages/breaks/voids/cracks and irregular grain orientation distribution. In other words, the Zr addition accelerates both the dislocation movement and especially the cracks/voids propagation of as a consequence of the decrement in the Griffith critical crack length, being one of the most striking points deduced from this work. These vital findings are also favored by the extracted parameters of Young’s modulus, yield strength, fracture toughness and brittleness index. Nevertheless, it is found that every sample studied exhibit typical indentation size effect (ISE) behavior due to the production of the elastic and plastic deformations simultaneously in the system. Moreover, the load dependent microhardness values are theoretically analyzed with the aid of six available models such as six available approaches: Meyer’s law, proportional sample resistance model, modified proportional sample resistance model, elastic/plastic deformation, Hays–Kendall (HK) and indentation-induced cracking model for the first time. The results obtained show that the HK approach exhibits perfectly performance on the analysis of the mechanical characteristics of the superconducting materials exhibiting ISE behavior whereas the other models are inadequate to explain the load independent mechanical characteristics of the Bi-2223 system added by the Zr nanoparticles.

Enhancement of local microstructural distortions, boundary weak-interactions and crucial defeats performed via Bi+3/La+3 partial substitution in the Bi-2212 matrix

This exhaustive study examines not only the decrement in characteristic two-stage (pairing and coherence) transitions but also the characteristic variation of the mechanical performance with the partial substitution level of homovalent La nanoparticles on Bi sites in the Bi-2212 crystal structure with the aid of the detailed dc resistivity (ρ-T), bulk density, Vickers microhardness (Hv) experimental findings and evaluated theoretical calculations. The experimental results obtained show that both the electrical and superconducting properties being responsible for the potential technological and industrial applications degrade consistently with the increment of the La inclusions in the Bi-2212 superconducting matrix. In fact, the crucial characteristics disappear completely after the critical dopant value of x = 0.20 as a result of the full deformation between the Bi-2212 planes and grain boundaries. In other words, the excess La impurities lead to the disorder and hole localization (filling) problem in the system due to the normal-state electrical resistance transition from the truly-metallic state to the disordered metallic state, and the electrical and superconducting properties demolish totally due to the metal to insulator transition (MIT). In this paper, we focus only on the (Bi,La)-2212 materials exhibiting superconducting behavior to reveal granular superconducting nature of Bi1.6-xLaxPb0.5Sr2.0Ca1.1Cu2.1Oy. As for the theoretical values deduced from the resistivity curves, temperature derivatives of the sample resistivities (dρ/dT) confirm characteristic two-stage transitions in all the samples prepared and both the pairing (bulk genuine) and coherence transitions tend to suppress with the increase of the La inclusions inserted in the Bi-2212 superconducting core as a consequence of the presence of the increased structural inhomogeneities (distribution of oxygen) and grain boundaries. Moreover, Percolation model confirms that the decrease in the coherence transitions with the dopant level is explained with the enhancement of Josephson coupled energy and the degradation of coupling probability. The existence of the relationship between microstructure and strength of interaction between the grains is also confirmed by the bulk density and porosity surveys. As for the load dependent microhardness parameters deduced from Vickers measurements, the pure sample exhibits the Indentation Size Effect (ISE) behavior whereas the La nanoparticles inserted in the Bi-2212 superconducting system make the materials present Reverse Indentation Size Effect (RISE) feature. This is attributed to the fact that the local structural distortions and boundary weak-interactions between the superconducting grains enhance dramatically with the La doping. In other words, plastic (irreversible) deformation becomes a much more dominant character in the materials as a result of the loss of the elastic recovery. At the same time, we analyze the microhardness experimental findings with the aid of the available models such as Meyer's law, proportional sample resistance (PSR), modified PRS (MPSR), Elastic–Plastic Deformation (EPD), Hays–Kendall (HK) and Indentation-Induced Cracking (IIC) approach for the first time. The results determined show that HK approach is found to be the best descriptor to examine the mechanical performance of the pure sample, showing ISE nature while the IIC model is observed to be the most successful model in understanding the mechanical properties of the Bi-site La substituted Bi-2212 superconducting compounds, obeying RISE nature.

Preparation, structural and micromechanical properties of (Al/Mg) co-doped ZnO nanoparticles by sol–gel process

Zn0.90Mg0.10−xAlxO (x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.10) nanoparticles were prepared by using sol–gel technique. The effects of Al and Mg doping on the structural and mechanical properties were investigated by using X-Ray diffraction (XRD), scanning electron microscopy (SEM) and digital micro-hardness tester, respectively. The grain size, a and c lattice parameters and morphology of nanoparticles were characterized by XRD and SEM measurements. The grain sizes of Al/Mg co-doped ZnO nanoparticles were also calculated by Scherrer–Warren equation. a and c lattice parameters are calculated from XRD peaks. According to the results it was observed that the grain sizes increased with increasing the Al doping. c lattice parameter partially decreased with Al doping. The experimental results of hardness measurements were analyzed using Meyer’s law, proportional specimen resistance model, elastic/plastic deformation model, and Hays–Kendall (HK) approach. It was observed that HK approach is the most successful model for the micro-hardness analysis of Al/Mg co-doped ZnO materials.

Decrement of crack propagation in bulk Bi-2223 superconducting ceramics with Sn-diffusion annealing temperature

The effect of Sn diffusion at different annealing temperature on the Bi1.8Pb0.4Sr2.0Ca2.1Cu3.0Oy superconducting materials is performed with the aid of Vickers microhardness (H v ) measurements at different applied loads in the range of 0.245–2.940 N. The measurement results observed show that all the samples exhibit typical indentation size effect behavior, meaning that both the elastic and plastic deformations play dominant role on the inorganic structures owing to the presence of the elastic recovery. Likewise, the mechanical characteristics increase with the Sn additives as a consequence of improvement of the local structural distortions and boundary weak-links between the grains. Furthermore, the increased Sn inclusions in the crystal lattice make the cracks propagate slower than before. This may be related to the fact that the Sn particles prefer to accumulate throughout the grain boundaries (defect locations) similar to the propagation of the cracks in the materials. In other words, the ductility (nondirectional interactions) of the ceramics tends to improve with the increment in the Sn concentration level in the crystal lattice as a consequence of the enhancement of the tensile strength, fracture toughness and especially Griffith critical crack length values. Hence, the mechanical flexibility takes place rapidly in the crystal structure. Moreover, the hardness measurements allow us to discuss the load dependent and independent microhardness, elastic modulus, yield strength and fracture toughness parameters. At the same time, the experimental data of the Vickers hardness are studied by the available models regarding Meyer’s law, proportional sample resistance model, elastic–plastic deformation model and Hays–Kendall (HK) approach for the first time. According to the results obtained, the load dependence of Vickers microhardness is fitted with the HK approach rather than the other methods. Based on the electrical and superconducting results observed before, it is to be mentioned here that the significant improvement of electrical performance may contribute to enhancement in mechanical characteristics.

Significant change in micro mechanical, structural and electrical properties of MgB2 superconducting ceramics depending on argon ambient pressure and annealing duration

In this study, the effects of different Ar pressure (vacuum, 0, 10 and 20 bar) and different annealing times (0.5 and 1 h) on microstructural, mechanical and superconducting properties of the bulk superconducting MgB2 are investigated. The samples are produced using the solid state reaction method. X-ray diffraction and scanning electron microscopy measurements are performed for phase formation, crystal structure, lattice parameters, particle size analysis, grain orientations, grain connectivity, and surface morphology of MgB2 samples. The superconducting properties are studied by dc resistivity measurements. In this study we have focused on microhardness measurements to investigate the mechanical properties. Vickers microhardness test is employed for determination of mechanical properties of the samples. The experimental microhardness results are analyzed by Meyer’s law, proportional sample resistance model, elastic–plastic deformation model, Hays Kendall (HK) approach, and indentation induced cracking (IIC) model. HK approach is identified as the most appropriate model for MgB2 superconducting samples exhibiting the indentation size effect behavior; for the other samples that have reverse indentation size effect behavior IIC model is appointed as the most appropriate model.

Microhardness studies of sulfamic acid single crystal

Vicker's microhardness study of (100), (010) and (001) faces of a non-linear optical crystal sulfamic acid have been reported. Single crystals of sulfamic acid have been grown by slow evaporation method. The load dependence of the Vickers microhardness of sulfamic acid crystal were investigated and analyzed from the stand point of various theoretical models. Crystal samples in a, b and c-axes exhibit reverse indentation effect which is best described by Meyer's law, Hays-Kendall's approach and proportional specimen resistance (PSR) models. The negative values of load dependent quantities in Hays-Kendall's approach and PSR model suggest that the origin of indentation size effect is associated with the process of relaxation of indentation stresses.

Effect of Zn content on microstructure and mechanical performance in Bi1.8Sr2Ca2Cu3.2−xZnxO10+δ glass ceramic

In this study, we have investigated the effects of Zn doping on structural and mechanical properties of Bi1.8Sr2Ca2Cu3.2−xZnxO10+δ ceramic samples with x = 0.0, 0.1, 0.5, 1.0. The prepared samples were characterized by using scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), X-ray powder diffractometer (XRD) and static microhardness indenter. Surface morphology, orientation of grains and elemental composition analysis of the samples were investigated by SEM and EDS measurements, respectively. Texturing and lattice parameters a, b and c were determined from the XRD measurements. In this work we focused on Vickers microhardness measurements in order to characterize the mechanical properties. Experimental results of Vickers microhardness measurements were analyzed by using Meyer’s law, the elastic/plastic deformation model, proportional sample resistance model (PSR), modified PSR model, Hays–Kendall (HK) approach and indentation induced cracking (IIC) model. According to the obtained results, HK approach is the most suitable model for the CZn00 sample showing indentation size effect behavior and IIC Model is the most suitable model for the CZn01, CZn05 and CZn10 samples showing reverse indentation size effect behavior.

Investigation on superconducting properties of GdBa2Cu3O7−δ added with nanosized ZnFe2O4

The effect of nanosized ZnFe2O4, prepared by Co-precipitation method, on GdBa2Cu3O7−δ superconductor was studied. Therefore, superconducting samples of type (ZnFe2O4)xGdBa2Cu3O7−δ, 0.0⩽x⩽0.1wt.%, were prepared by the conventional solid-state reaction technique. Moreover, nanosized ZnFe2O4 was characterized using X-ray powder diffraction (XRD), transmission electron microscope (TEM) and magnetic hysteresis measurements. The results revealed that a nanosized ZnFe2O4 was achieved with average grain size 9nm and a super-paramagnetic hysteresis. On the other hand, the superconducting samples were characterized and investigated through XRD, scanning electron microscope (SEM), electrical resistivity, ac magnetic susceptibility and Vickers microhardness. XRD results showed that the volume fraction of Gd-123 phase increases as x rises from 0.0 to 0.06wt.% while the SEM results showed that the grain connectivity between the grains increases with increasing x. The superconducting transition temperature Tc, determined from electrical resistivity and ac magnetic susceptibility, increases up to x=0.06wt.%, and then it decreases. Moreover, electric field–current density (E–J) characteristic curves were measured at 77K. An improvement of the critical current density was obtained with x increase up to 0.06wt.%. Furthermore, the Vickers microhardness data were analyzed using Meyer’s law, Hays–Kendall approach, elastic/plastic deformation model and proportional specimen resistance model. The results indicated that Vickers microhardness number HV increases as x increases and it exhibits a normal indentation size effect. Moreover, the proportional specimen resistance model is found to be the best model to verify the experimental load independent Vickers microhardness values.

Physical and Mechanical Properties of GdBa2Cu3O7−δ Added with Nanosized CoFe2O4

Superconductor samples of type (CoFe2O4) x GdBa2Cu3O7−δ , 0.0≤x≤0.1 wt.%, were synthesized by the conventional solid-state reaction technique. The prepared samples were investigated using X-ray diffraction (XRD), scanning electron microscope (SEM), electrical resistivity, AC magnetic susceptibility, and Vickers microhardness. Phase examination by XRD indicated that the orthorhombic structure of Gd-123 is not affected by nanosized ferrite CoFe2O4 addition, whereas the volume fraction of Gd-123 increased with x up to 0.01 wt.%. Morphological investigations by SEM revealed that the porosity among grains decreased as x increased from 0.0 to 0.1 wt.%. The superconducting transition temperature T c was estimated from electrical resistivity and the AC magnetic susceptibility measurements. A reduction in T c was observed as x increased from 0.0 to 0.1 wt.%, consisting with the effect of adding magnetic impurities to HTSCs. Room temperature microhardness measurements were carried out at different applied loads (0.5–10 N) for the study of the mechanical performance of the studied samples. The experimental results were analyzed using Meyer’s law, Hays–Kendall approach, elastic/plastic deformation model, and proportional specimen resistance model. The results showed that all the samples exhibited normal indentation size effect, and Vickers microhardness values were increased as nanosized CoFe2O4 addition increased. The analysis showed that the proportional specimen resistance model is the best model for computing the load-independent microhardness values of our samples.

Deformation of Mechanical Properties and Failure Behavior of Hays–Kendall Approach in Bi-2223 Superconducting Core After Eu Inclusions

Mechanical features of Bi1.8Pb0.4Eu x Sr2Ca2.2Cu3O y superconductor samples (x=0, 0.01, 0.03, 0.05, 0.07, 0.1, and 0.3) are elaborated by traditional solid-state reaction route. The deformation of the mechanical properties belonging to the Bi-2223 crystal structure by Eu impurities with the aid of Vickers hardness (H v ) measurements are conducted at different indentation loads from 0.245 N to 2.940 N for the first time. Further, the H v values extracted from experimental results are investigated using five different models so as to demonstrate the role of Eu addition on Bi-2223 samples. Based on these results, we observed that the undoped sample reveals the indentation size effect (ISE) feature, whereas the Eu-doped Bi-2223 superconducting core demonstrates the reverse indentation size effect (RISE) nature. Additionally, it is attained that the models (Meyer’s law, EPD, and PSR) fail to determine the estimate of the microhardness with the applied load. Nonetheless, the HK approach is observed to be superior to other models for the pure sample showing the ISE feature, while the IIC model is found to be the most successful model for the explanation of the mechanical characteristics of the Eu impurities in Bi-2223 bulk ceramics obeying RISE nature.

Improvement of the Nature of Indentation Size Effect of Bi-2212 Superconducting Matrix by Doped Nd Inclusion and Theoretical Modeling of New Matrix

Neodmium (Nd) inclusions at different stoichiometric ratios (x=0.0, 0.001 %, 0.005 %, 0.01 %, 0.05 %, 0.1 %) are doped in the Bi-2212 superconducting samples and the samples obtained are subjected to the sintering process at 840 ∘C constant temperature for 72 hours. The effect of Nd doping on the structural and mechanical properties of prepared samples is investigated by the standard characterization measurements. XRD and SEM measurements are performed to obtain information about surface morphology, phase ratios, lattice parameters and particle size. Moreover, Vickers microhardness (H V ) measurements are exerted to investigate the mechanical properties of the all samples in detail. It is found that all the properties given above retrogress with the increase of the Nd concentration in the Bi-2212 superconducting core. However, the ISE nature of the materials improves systematically. Additionally, the experimental results of microhardness measurements are analyzed using Meyer’s law, PSR, MPSR, EPD models and HK approach. The results show that Hays–Kendall approach is determined as the most successful model.

Structural and mechanical properties of ZnMgO nanoparticles

This study reports the effect of annealing temperature on the structure and mechanical properties of Zn0.95Mg0.05O bulk samples by using digital Vickers microhardness tester, X-ray diffraction analysis, scanning electron microscopy and electron dispersive X-ray measurements. The samples were prepared using Zn and Mg based alkoxed by the sol–gel technique and annealed at various temperatures (500, 600, 700 and 800°C). Vickers microhardness, elastic modulus, yield strength and fracture toughness values of Zn0.95Mg0.05O bulk samples were separately calculated and compared with each other. The experimental results of hardness measurements were analyzed using Meyer's law, Proportional Specimen Resistance (PSR) and Elastic/Plastic Deformation (EPD) models and Hays–Kendall (HK) approach. Finally, it was seen that HK approach is the most successful model for the microhardness analysis of these materials.

Microstructure and size effect in ultrafine (Ti0.705Fe0.295)100−xSnx (0⩽x⩽4at.%) composites

Abstract The effect of Sn addition on the microstructure evolution in ultrafine lamellar (Ti0.705Fe0.295)100−xSnx (0 ⩽ x ⩽ 4 at.%) eutectic composites and size effect during Vickers microhardness measurements at load in the range of 0.049 N and 19.61 N have been studied. The hardness of all the lamellar composites with varying Sn content decreases with increase of applied load pointing the existence of normal indentation size effect (ISE). The load dependence microhardness values have been analysed using existing models such as, Meyer’s law, depth dependence hardness model, proportional specimen resistance model (PSR), modified PSR model, Hays-Kendall approach, and elastic–plastic deformation model. Furthermore, the load dependent microhardness has been correlated with the dislocation density, microstructure length-scale, and ISE. The microscopic mechanisms of ISE and strain hardening behaviour in lamellar eutectic composite have been explored.

Structural and mechanical characterization of Bi1.75Pb0.25Sr2Ca2Cu3−xSnxO10+y superconductor ceramics using Vickers microhardness test

In this work we investigated the role of Sn doping on mechanical and structural properties of Bi1.75Pb0.25Sr2Ca2Cu3−xSnxO10+y (x = 0.0, 0.1, 0.3 and 0.5) superconducting ceramic material. All samples were fabricated with glass ceramic method. The prepared samples were characterized by using scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), X-ray powder diffractometer (XRD) and static microhardness indenter. Surface morphology, orientation of grains, and elemental composition analysis of the samples were made by SEM and EDS measurements, respectively. Texturing and lattice parameters a and c were determined by XRD measurements. Load dependent and load independent microhardness, elastic modulus, yield strength and fracture toughness were obtained by hardness measurements. In this work we focused on Vickers microhardness measurements in order to characterize the mechanical properties of our samples. Experimental results of Vickers microhardness measurements were analyzed by using Meyer’s law, the elastic/plastic deformation model, proportional sample resistance model (PSR), modified PSR model and Hays-Kendall (HK) approach. From these analyses, HK approach was determined as the most successful model describing the mechanical properties of our samples. Finally in this study, the changes on the mechanical and microstructural properties of Sn doped Bi-2223 superconductors and their possible reasons were also discussed in detail.

Zr diffusion coefficient and activation energy calculations based on EDXRF measurement and evaluation of mechanical characteristics of YBa2Cu3O7−x bulk superconducting ceramics diffused with Zr nanoparticles

Abstract This study reports two main mechanisms on the YBa 2 Cu 3 O 7 − x bulk superconductor for the researchers: (I) determination of the diffusion coefficient and activation energy of Zr nanoparticles in the YBa 2 Cu 3 O 7 − x matrix over the annealing temperature range of 500–945 °C by means of the energy dispersive X-ray fluorescence (EDXRF) technique, and (II) change of the mechanical performances belonging to the YBa 2 Cu 3 O 7 − x bulk superconducting materials by Zr inclusions with the aid of Vickers microhardness (H v ) measurements performed at various indentation loads (0.245 N ≤ F ≤ 2.940 N) for the first time. The results obtained from the first part show that the zirconium diffusion coefficient increases dramatically with the enhancement of the diffusion annealing temperature, presenting that at higher temperatures more Zr nanoparticles begin to penetrate into the Y123 matrix. Thus, two different diffusion coefficients (in grains and over grain boundaries) are determined for the Zr individuals in the Y123 materials. The thickness dependences of the Zr diffusion coefficients are defined by the equations D 1 = 1.47 × 10 − 4 exp (− 1.05 eV/k B T) and D 2 = 2.23 × 10 − 3 exp (− 1.03 eV/k B T) in grains and over grain boundaries, respectively. The related activation energies (− 1.05 eV and − 1.03 eV) may be attributed to the relatively slow migration in the former region and rapid migration over the latter region, respectively. In other words, the physical and mechanical properties of the Y123 superconducting samples improve with the Zr additives owing to the elimination of the defects. The second part also indicates that the Zr nanoparticles lead to change in the microhardness characteristic of the Y123 bulk superconductors. Whereas the microhardness parameters such as Vickers microhardness ( H v ), elastic modulus and yield strength of the undiffused sample tend to increase systematically, those of the diffused samples decrease with the enhancement of the applied load, meaning that the former sample shows the reverse indentation size effect ( RISE ) behavior while the latter superconductors exhibit Indentation Size Effect ( ISE ) feature. Additionally, in the second part, the load independent (true) microhardness values are analyzed by Meyer's law, elastic/plastic deformation ( EPD ), proportional sample resistance ( PSR ), indentation-induced cracking ( IIC ) and Hays–Kendall ( HK ) approach. It is found that the three models (Meyer's law, EPD and PSR ) fail to explain the evaluation of the microhardness with the applied load. However, the IIC model is found to be superior to other models for the pure sample exhibiting the RISE behavior, whereas the HK approach is observed to be the most successful model for the description of the mechanical properties of the Zr diffused Y123 bulk superconductors obeying ISE feature. To sum up, it is not wrong to generalize that the IIC model is the best approach for the Y123 superconductor presenting the RISE feature, while the HK approach defines perfectly the mechanical properties of the Y123 materials obtaining the ISE behavior.

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

This study manifests the crucial change in the mechanical performances of Bi1.8Pb0.4Sr2MnxCa2.2Cu3.0Oy 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 (Hv) 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 Hv, 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 Hv 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.

Variation of Mechanical Properties of Cr Doped Bi-2212 Superconductors

This study shows the influence of Cr inclusions on the mechanical properties of Bi1.8Sr2.0Cr x Ca1.1Cu2.1O y (Bi-2212) superconducting samples (x=0, 0.1, 0.3, 0.5, 0.7, and 1) prepared by conventional solid-state reaction route with the aid of the microhardness (H v) measurements. Moreover, some characteristics such as Vickers microhardness, Young’s (elastic) modulus (E) and yield strength (Y), being responsible for the potential technological and industrial applications, are theoretically evaluated from the microhardness curves belonging to the samples and compared with each other. It is found that the load dependent microhardness values decrease nonlinearly as the applied load enhances until 2 N beyond, which the curves shift to the saturation region, confirming that all the samples exhibit the indentation size effect (ISE) nature. Further, the elastic modulus and yield strength values observed reduce with the enhancement of the applied load and Cr inclusions in the Bi-2212 matrix. The experimental findings are also analyzed by Meyer’s law, proportional sample resistance model (PSR), modified proportional sample resistance model (MPRS), elastic/plastic deformation model (EPD), and Hays–Kendall (HK) approach. According to the results obtained, the load independent microhardness values calculated by EPD, PSR, and MPSR models are far from the values of the plateau region; however, the HK approach is the most suitable model for the microhardness calculations of the samples prepared in this study.

Comparative study on indentation size effect, indentation cracks and superconducting properties of undoped and MgB2 doped Bi-2223 ceramics

This study examines the evaluation mechanism of MgB2 doped Bi1.8Pb0.4Sr2(MgB2)xCa2.2Cu3.0Oy (0 ≤ x ≤ 1.0) superconducting ceramics prepared by conventional solid-state reaction method via dc resistivity, X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) and Vickers micro hardness (Hv) measurements. Variation of room temperature resistivity, critical transition temperatures (onset and offset), phase purity, cell parameter, texturing, grain connectivity, surface morphology, crystallinity and H v values of the materials are deduced and compared with each other for the determination of the optimum doping level in the Bi-2223 system. It is found that all the properties given above depend strongly on the MgB2 concentration. From dc resistivity investigations, each sample studied exhibits the superconducting behavior below their variable offset critical temperature values. The maximum onset (T ) and offset (T ) temperatures are found to be about 121.3 and 114.1 K, respectively, for the sample doped with x = 0.05. The minimum T of 118.6 K and T of 109.4 K are observed for the sample doped with x = 1.0. Similarly, XRD and SEM examinations indicate that there is an improvement in the crystal structures and surface morphologies of the superconducting materials with the increment of the MgB2 inclusions in the Bi-2223 system up to x = 0.05 beyond which the crystallinity, grain connectivity and surface morphology start to degrade regularly and in fact reach to the worst structure appearance for the doping level of x = 1.0. Furthermore, the Hv measurement results being analyzed by Meyer’s law, proportional sample resistance (PSR), modified PSR, elastic–plastic deformation model, Hays–Kendall (HK) approach, Indentation-induced cracking model (IIC) allow us to derive the mechanical properties of the superconducting samples for the potential technological and industrial applications. According to the results obtained, HK approach, among the mechanical analysis methods, is determined as the most successful model for the samples (doped with x = 0, 0.1, 0.3, 0.5 and 1.0) exhibiting indentation size effect behavior whereas the IIC model is noted to be superior to other models for the other samples (doped with x = 0.01, 0.03 and 0.005) presenting reverse indentation size effect feature.

Comparative study on mechanical properties of undoped and Ce-doped Bi-2212 superconductors

This study discusses the mechanical performances of Bi1.8Sr2.0CexCa1.1Cu2.1Oy ceramics with x = 0, 0.001, 0.003, 0.005, 0.01, 0.03, 0.05 and 0.1 by way of Vickers microhardness (Hv) measurements performed at different applied loads in the range of 0.245–2.940 N. For the potential industrial applications, the important mechanical characteristics such as Vickers microhardness, elastic modulus, yield strength, fracture toughness and brittleness index values of the samples studied are extracted from the microhardness measurements. All the results obtained indicate that the Vickers hardness, Young’s (elastic) modulus, yield strength, fracture toughness and brittleness index values suppress with the increment of the Ce concentration in the system as a consequence of the degradation in the connectivity between superconducting grains. The decrement in the Hv values with the applied load is attributed Indentation Size Effect behaviour of the samples studied. Moreover, the experimental results of Vickers microhardness measurements are estimated using the 5 different models such as Kick’s law, proportional sample resistance model, modified proportional sample resistance model, elastic/plastic deformation model and Hays–Kendall approach. According to the results obtained from the simulations, Kick’s law is not useful model to obtain information about the origin of the indentation size effect feature of the Ce-doped bulk Bi-2212 superconductors. On the other hand, the Hays–Kendall approach is determined as the most suitable model for the description of the mechanical properties of the superconducting samples. In addition, the bulk porosity analysis for the samples reveals that the porosity increases monotonously with the Ce inclusion in the Bi-2212, leading to the degradation of the grain connectivity.