Proportional Specimen Resistance Model Research Articles

Load-Independent Hardness and Indentation Size Effect in Iron Aluminides.

In this paper, an iron-aluminide intermetallic compound with cerium addition was subjected to Vickers microhardness testing. A full range of Vickers microhardness loadings was applied: 10, 25, 50, 100, 200, 300, 500, and 1000 g. Tests were conducted in two areas: 0.5 mm under the surface of the rolled specimen and in the center. The aim was to find the optimal loading range that gives the true material microhardness, also deemed load-independent hardness, HLIH. The results suggest that in the surface area, the reverse indentation size effect (RISE) occurred, similar to ceramics and brittle materials, while in the center, indentation size effect (ISE) behavior was obtained, more similar to metals. This clearly indicated an optimal microhardness of over 500 g in the surface region and over 100 g in the central region of the specimen. Load dependencies were quantitatively described by Meyer's law, proportional specimen resistance (PSR), and the modified PSR model. The modified PSR model proved to be the most adequate.

Investigations on theoretical models describing the load-indentation size dependence for (001), (010), (101), (1̄1̄1) and (1̄11) faces of triglycine sulphate

Ferroelectric triglycine sulphate (TGS) single crystals were grown by slow evaporation technique over a period of 30–40 days. The Vickers microhardness studies have been carried out on (001), (010), (101), ([Formula: see text][Formula: see text]1) and ([Formula: see text]11) faces of the TGS crystal. The as-grown (001) face and (010) face with the ferroelectric phase were used to study the temperature dependence of hardness. The indentation size effect (ISE) described using the five theoretical models viz., Meyer’s law, Hays–Kendall, elastic/plastic deformation (EPD), proportional specimen resistance (PSR) and modified PSR model has been investigated on all the crystal faces under study. The experimental results show that the modified PSR model is more accurate at generating load-independent hardness data and also for explaining the origin of ISE.

Effect of strain rate on the hardness of relaxor ferroelectric PMN-0.32PT single crystals

The relaxor ferroelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) has been considered to be a potential choice for high performance actuators and sensors owing to their ultrahigh electromechanical properties. Recent experiments have shown that the hardness and indentation fracture toughness of PMN-PT varies with load and loading direction. However, it is not clear from these studies that how the loading rates would affect the indentation response of these materials. Therefore, nanoindentation experiments at different strain rates are performed on [001] and [011] oriented poled PMN-0.32PT single crystals. Results show that the hardness, H decreases with increase in strain rate. This behavior is in contrast to the trend reported for PMN-PT single crystal in the recent past. The indentation size effect (ISE) is noticed in both the orientation for all the strain rates. In order to analyze the observed ISE, various mechanistic models are used such as Meyer's law, Hays-Kendall (H-K) model, proportional specimen resistance (PSR) model, and modified PSR (MPSR) model. The analysis of nanoindentation data using MPSR model satisfactorily describes the ISE in terms of resistance offered by the specimen to indenter penetration, the interface friction, and surface residual stress.

Anisotropic Deformation Behavior and Indentation Size Effect of Monocrystalline BaF2 Using Nanoindentation.

In this study, our objective is to investigate the anisotropic deformation behavior and the indentation size effect (ISE) of monocrystalline barium fluoride (BaF2) using nanoindentation experiments with a diamond Berkovich indenter. BaF2 is known for its anisotropy, which results in significant variations in its mechanical properties. This anisotropy poses challenges in achieving high processing quality in ultra-precision machining. Through our experiments, we observed numerous pop-in events in the load-displacement curves, indicating the occurrence of plastic deformation in BaF2 crystals, specifically in the (100), (110), and (111) orientations; these pop-in events were observed as the indentation depth increased to 56.9 nm, 58.2 nm, and 57.8 nm, respectively. The hardness-displacement and elastic modulus-displacement curves were obtained from the tests exhibiting the ISE. The nanoindentation hardness of BaF2 is found to be highly dependent on its crystallographic orientation. Similarly, for BaF2 in the (100) orientation, the range is from 2.43 ± 0.74 and 1.24 ± 0.12 GPa. For BaF2 in the (110) orientation, the values range from 2.15 ± 0.66 to 1.18 ± 0.15 GPa. For BaF2 in the (111) orientation, the values range from 2.12 ± 0.53 GPa to 1.19 ± 0.12 GPa. These results highlight the significant influence of crystallographic orientation on the mechanical properties of BaF2. To better understand the ISE, we employed several models including Meyer's law, the Nix-Gao model, the proportional specimen resistance (PSR) model, and the modified PSR (mPSR) model, and compared them with our experimental results. Among these models, the mPSR model demonstrated the best level of correlation (R2>0.9999) with the experimental measurements, providing a reliable description of the ISE observed in BaF2. Our reports provide valuable insights into the anisotropic mechanical characteristics of BaF2 materials and serve as a theoretical guide for the ultra-precision machining of BaF2.

Indentation analysis on L-Glutamic acid doped ZTS single crystal

The primary aim of the paper is to study the mechanical characteristics of L-Glutamic acid doped ZTS crystal. With sizeable merits in high-power lasers, the growth of L-Glu doped ZTS crystals is grown over 25 days and is mentioned briefly in this paper. Different analysis methods were carried out to describe the mechanical characteristics of the crystal. Though, the methods namely Vickers Pyramid number with applied force, Meyer power law, Hays-Kendall’s approach (HK approach), Proportional Specimen Resistance model (PSR model) and Elastic/Plastic deformation model (EPD model) were utilised, and every method indicated the clear trend of RISE behaviour of the crystal. The EPD model proved that it is best in providing the proper description of the grown crystal.

Micro Hardness Study of Macro Wire of Bismuth Samples Using Contact Model

Abstract: The micro-hardness test is often used to pre-determine the mechanical properties of a material. The Vickers method can be used for testing metals, particularly those with extremely hard surfaces. The study of the correlation between applied load and the measured value of the microhardness was carried out for Bismuth wire samples. Bismuth is a semimetal in bulk, it is not a good thermal electrical material. Bismuth nanowires (10nm) have a thermal electric figure while exhibiting semiconductor behaviour. Mechanical characterization is critical for the formation of nanowires made of various materials. The microhardness testing of bismuth wire plate samples was performed on a microscopic scale in this communication. Vicker's number variation is reported. At low indentation test loads, an indentation size effect was observed for Bismuth wire plate samples. For all samples, the variation of microhardness number (Hv) with variable loads is non-systematic. PSR ( Proportional specimen Resistance )Model, MPSR ( Proportional specimen Resistance )Model for the calculation of elastic stiffness constant C11, Wooster’s empirical relations used with obtain hardness data.

Indentation size effect in the hardness measurements of high entropy carbides

The indentation load-size effect was investigated during hardness testing of high entropy carbides with different hardness, applying indentation loads from 50 mN to 10 N. The experimental systems were recently developed (Hf-Ta-Zr-Nb-Ti)C and (Mo–Nb–Ta–V–W)C high-entropy carbides, prepared by ball milling and a spark plasma sintering, with single-phase and high relative density of 99.4% and 99.0%, respectively. The load dependence of hardness was analysed using the traditional Meyer's law, the proportional specimen resistance model and the modified proportional specimen resistance model. The best correlation (R2> 0.99) between the measured values and the used models was achieved using the modified proportional specimen resistance model. This resulted in the so-called load-independent hardness of (Hf-Ta-Zr-Nb-Ti)C and (Mo–Nb–Ta–V–W)C systems 21.96 and 14.81 GPa in the case of analyses for 50 mN–10 N load range and 25.42 GPa and 14.13 GPa in the case of 50 mN–1 N load range, respectively. The different deformation and damage mechanisms detected as a potential reason for the origin of the load-size effect were microcracks at grain boundaries during the micro/macro-indentation and plastic deformation/nanocrack formation at the indents during nano/micro-indentation.

Effect of metastable phase on the crystallization and mechanical properties of MgO-Al2O3-SiO2 glass-ceramics without nucleating agents

Glass-ceramics without nucleating agents usually undergo surface crystallization, which deteriorates the overall performance of the products. In this paper, we evaluated the effects of the metastable MgAl2Si3O10 crystalline phase on the crystallization behavior of a MgO–Al2O3–SiO2 (MAS) glass without nucleating agents and mechanical properties of the glass-ceramics obtained. The results demonstrated that the precipitation of metastable MgAl2Si3O10 crystallites promotes the crystallization mechanism transformed from surface crystallization into volume crystallization with two-dimensional crystal growth. Furthermore, the grain size of MgAl2Si3O10 near the surface of the prepared glass-ceramics was larger than that of MgAl2Si3O10 inside, which helps to generate compressive stress and improves its mechanical properties. The glass-ceramics containing metastable MgAl2Si3O10 phase exhibited an enhanced hardness in the range of 7.6 GPa–9.5 GPa for indentation loads ranging from 2.94 N to 98 N, and indentation size effect behavior was observed in Vickers hardness tests of both MAS glass and glass-ceramics. The load-independent hardness values for MAS glass and glass-ceramics were reliably evaluated by the modified proportional specimen resistance (MPSR) model of 7.1 GPa and 7.6 GPa, respectively, with a high correlation coefficient of more than 0.9999. This work reveals the unexploited potential of the metastable phase in improving the crystallization ability and mechanical properties of glass-ceramics.

Nanoindentation responses of black anodic coating on additively manufactured Al–10Si–Mg alloy

The present work reveals the variation of nanomechanical properties (nanohardness-H and modulus-E) of black anodic coating on additively manufactured Al–10Si–Mg alloy. The plan-section of the coating has mud-crack-like morphology with various nano/micro-pores, micro-channels, and irregularities. In contrast, the cross-section possesses a compact morphology with minimum surface/sub-surface defects like micro-cracks or irregularities. The H and E are derived from nanoindentation experiments using Berkovich tip at loads 10–50 mN. The nanomechanical properties are higher across the cross-section than the plan section of the coating, attributing to the difference in morphology between the plan- and the cross-sections. Due to characteristic porosities, defects, and nano/micro-cracks in the anodic coating, Weibull statistical analysis has been employed to rationalize the scatter in nanoindentation-based data. For both plan and cross-sections, the H and E values decrease as the indentation load increases from 10 to 50 mN, confirming the indentation size effect (ISE). The well-established Meyer's law, Hays–Kendall approach, elastic recovery model, proportional specimen resistance (PSR) model and the modified PSR model have been used to thoroughly analyze the ISE characteristics.

Indentation size effect in steels with different carbon contents and microstructures

Indentation Size Effect (ISE) in steels having a wide spectrum of carbon (C) concentrations (wt-%) 0.002 (interstitial-free), 0.07 (microalloyed), 0.19 (low carbon), 0.32 (medium carbon), and 0.7 (high carbon), and microstructures were investigated using Vickers micro-hardness tester. A decrease in micro-hardness with increasing load, i.e. ISE, is observed in all the samples except microalloyed steel. The empirical relations, such as the Nix and Gao model, Minimum Resistance model, and Proportional Specimen Resistance (PSR) model, were used to determine the load-independent or true hardness values. Nix and Gao model was adopted to determine the plastically deformed zone (PDZ) size under the indenter and subsequently correlated with ISE in the materials. It is observed that ISE is absent when the PDZ size becomes comparable to or larger than the grain size of the material.

Size effect and anisotropy in cold rolled Zr-base bulk metallic glasses during nanoindentation

A series of instrumented nanoindentation tests have been performed in control loading rate mode on Zr52.5Cu18Ni14.5Al10Ti5 (VIT105) and Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 (VIT106A) as-cast and various cold rolled samples to investigate the indentation size effect (ISE) in three perpendicular planes i.e., rolling-width (RW), normal-rolling (NR) and normal-width (NW) planes at peak loads in the range of 50 mN - 500 mN. The hardness, reduced modulus and dynamic hardness have reduced with the increase of indentation depth in NR, RW and NW planes. The as-cast and cold rolled BMGs exhibit normal ISE for NR, RW and NW planes. The size effect has been analyzed using power law, Nix-Gao model, and proportional specimen resistance model suggesting that dynamic mechanical softening and the friction between the indenter and specimen are the underlying reasons behind the observed ISE.

Microindentation response of relaxor ferroelectric PMN-0.32PT single crystal

The relaxor ferroelectric 0.68Pb(Mg1/3Nb2/3)O3-0.32PbTiO3 (PMN-0.32PT) which lies near the morphotropic phase boundary (MPB) composition has gained attention in the recent past due to its excellent electromechanical properties. The devices made of these materials are often subjected to contact forces which may lead to domain switching/phase-transformation resulting in poor electromechanical properties and sub-standard performance. This has encouraged researchers to understand their deformation behavior under contact loading such as indentation. The indentation experiments on other relaxor ferroelectric materials reported the indentation size effect (ISE) in the hardness, though mechanistic reasons for this behavior are not well understood. In addition, the ISE in the relaxor ferroelectric PMN-0.32PT has not been investigated in detail till now. Therefore, Vickers micro-indentation experiments are performed on [001] poled PMN-0.32PT single crystals. The results show that these crystals exhibit a strong ISE. Further, the load-independent hardness of these crystals is found to be 4.85 ± 0.05 GPa which is in agreement with the previously reported values. The XRD analysis performed on indented surface suggests indentation induced phase transformation which is further confirmed by Raman spectroscopy. It is found that the ISE in PMN-0.32PT single crystals can be satisfactorily described by proportional specimen resistance (PSR) model, but not by modified PSR model. Thus, it is concluded that the ISE in poled PMN-0.32PT single crystals can be attributed to the combined effect of resistance offered by the specimen to indenter penetration, the interface friction, and the polarization-rotation induced phase transition below the indenter.

Effect of Indentation Load on Nanomechanical Properties Measured in a Multiphase Boride Layer.

The study investigated the dependence of the indentation load on nanomechanical properties for a gas-borided layer produced on Inconel 600-alloy. During the measurements, the indentation load range from 10 mN to 500 mN was used. Three types of tested areas, differing in the concentration of chromium, were examined. The increase in chromium concentration was accompanied by an increase in indentation hardness and Young’s modulus. Simultaneously, the increase in the indentation load resulted in a decrease in the indentation hardness and Young’s modulus, for each type of the tested area. The presence of the indentation size effect was analyzed using four models: Meyer’s law, Hays and Kendall model, Li and Bradt model, Nix and Gao model. For all tested areas, good agreement with the Meyer’s law was obtained. However, areas with a higher chromium concentration were more susceptible to indentation size effect (ISE). The proportional specimen resistance (PSR) model was used to describe the plastic-elastic behavior of the tested materials, as well as to detect the presence of ISE. It was found that the increase in chromium concentration in the tested area was accompanied by a greater tendency to elastic deformation during nanoindentation.

Investigation of indentation size effect and R-curve behaviour of Li2O–SiO2 and Li2O–2SiO2 glass ceramics

Indentation size effect (ISE) and R-curve behaviour of Li2O-SiO2 and Li2O-2SiO2 glass ceramics are investigated using micro-indentation and indentation-strength (IS) techniques, respectively. Vickers micro-indentations were applied on both materials at the load of 0.10-19.6N to determine the load influence on the measured hardness. For the IS-measured fracture toughness, the load ranged from 1.96 to 19.6N. The hardness decreased with increasing load by 20% and 18% on Li2O-SiO2 and Li2O-2SiO2 glass ceramics, respectively, indicating the ISE behaviour on both materials. The fracture toughness increased with the load by 27% and 59% on Li2O-SiO2 and Li2O-2SiO2 glass ceramics, respectively, signifying the R-curve behaviour. The ISE behaviour of both materials was analysed using the Meyer's, Hays-Kendall (HK), proportional specimen resistance (PSR), Nix-Gao (NG), modified PSR (MPSR) and elastic plastic deformation (EPD) models while the R-curve behaviour was analysed by the fractional power law. The Meyer's index of both materials was less than 2, strongly confirming the ISE existence. The HK, PSR and NG models were only suitable to determine intrinsic Vickers hardness for Li2O-2SiO2 glass ceramic while the MPSR and EPD models were successful for both materials. The fractional power law gave higher R-curve steepness for Li2O-2SiO2 than Li2O-SiO2 glass ceramics. Also, material and brittleness indices predicted, respectively, higher quasi-plasticity and better machinability for Li2O-2SiO2 than Li2O-SiO2 glass ceramics indicating superior performance in the former to the latter. Finally, this study presents a new significant insight into the micro-mechanisms of fracture tolerance behaviour of these glass ceramics which is critical to their functional performance as structural ceramics.

Experimental and theoretical investigation of the mechanical characteristics of sillenite compound: Bi12GeO20

The present study reports the mechanical and elastic characteristics of Bi12GeO20 (BGO) compound by experimental nanoindentation measurements and density functional theory (DFT) calculations. X-ray diffraction pattern of BGO was plotted and revealed diffraction peaks were associated with Miller indices of cubic crystalline structure with lattice constant of a = 10.304 Å. Two- and three-dimensional representations of Young’s modulus, linear compressibility, shear modulus and Poisson’s ratio were presented according to DFT calculations. The calculated elastic constants pointed out the mechanically stable and anisotropic behavior of the BGO. The hardness and Young’s modulus ranges of the BGO calculated from DFT studies were found as 3.7–6.3 GPa and 61.7–98.9 GPa, respectively. Hardness and Young’s modulus of BGO single crystal were also obtained by analyzing force-dependent nanoindentation experimental data. It was observed that hardness and Young’s modulus decrease with increase of load in the low applied loads and then reaches saturation in the high applied loads. This behavior is known as indentation size effect. True hardness value was determined from proportional specimen resistance model as 4.1 GPa. The force independent region presented the Young’s modulus as 114 GPa.

Elastic-plastic deformation behavior of sapphire M-plane under static loading using nano-indentation

Elastic-plastic response of M-plane single crystal sapphire was explored via a nano-indenter with a Berkovich tip. Elastic-plastic transition was observed with eight different points (ranging from 0.30 to 0.55 mN) subject to respective peak load. Mechanical properties i.e., Oliver-Pharr hardness and elastic modulus were also determined in the onset elastic and elastic-plastic regions. Stable value of elastic modulus estimated from Oliver-Pharr nanoindentation experiments was around 430 ± 15.0 GPa. However, Oliver-Pharr hardness in purely elastic and elastic–plastic (ISE) regions was approximately 2.19 and 2.0 times greater than the non-ISE hardness values respectively. Values of hardness in the non-ISE region were also in compliance with the depth independent hardness calculated through Nix-Gao and proportional specimen resistance models. Additionally, principal stresses and maximum shear stress were estimated on pop-in burst using Hertzian contact theory. Values of the critical resolved shear stress (CRSS) and maximum possible shear strength were also calculated at the first pop-in burst. Moreover, plastic zone size enhanced 1.36 times by shifting of critical load from 0.30 to 0.55 mN. Multiplication of Schmid factor and interplanar spacing indicated two slip systems i.e., prism {011‾1‾} <101‾1‾> and pyramidal {112‾0} <1‾100>, which are verified in the Transmission electron microscopy (TEM) images. Estimated values of maximum contact pressures at respective critical loads were much lower in comparison to phase transformation pressure of sapphire. Maximum tensile stress was also calculated using Hertzian contact theory relations. Obtained value of maximum tensile strength was 3.58 times lower than cleavage fracture stress at the first pop-in.

Analysis of indentation size effect (ISE) in nanoindentation hardness in polycrystalline PMN-PT piezoceramics with different domain configurations

Piezoelectric materials contain microstructural features (e.g., domain walls, interdomain spacing, and grain size) that span across several length scales, i.e., few nm in the case of interdomain wall spacing to several μm in case grain sizes. Recent experimental findings indicated that the domain configurations have more influence on the hardness of these materials than the grain size. In this study, nanoindentation experiments are conducted on polycrystalline PMN-PT (a relaxor ferroelectric material) with a focus to investigate the influence of domain configurations on the indentation size effect (ISE) in hardness, H. Different domain configurations are achieved by selectively annealing the as poled samples above and below the Curie temperature. Nanoindentation hardness is obtained in the load range of 1–5 mN with the maximum penetration depth well below the grain size of the samples. The experimental results reveal that all the samples, albeit to a different order, exhibit strong Reverse Indentation Size Effect (RISE) and normal ISE in H. The observed ISE is then analyzed using classical Meyer's law, the proportional specimen resistance (PSR) model and modified PSR (mPSR) model. The critical analysis of nanoindentation data reveals that the PSR model provides a satisfactory understanding of the genesis of RISE and ISE considering the elastic resistance of test material and frictional resistance at indenter facet/test material.

Analysis of micro indentation hardness of thiourea added L-histidine crystals (TLH)

Vickers microhardness analysis was carried out to identify the mechanical stability of the thiourea added L-histidine crystals (TLH) which were grown by slow evaporation solution growth technique at room temperature with different indentation loads. Indentation size effect (ISE) was investigated by analyzing the theoretical models. The microhardness values of the single crystal were calculated by using Meyer Law, proportional specimen resistance model, elastic/plastic deformation model and the Hays–Kendall (HK) approach. The results show that the HK approach is the most successful model to explain the deformations in the TLH single crystal. It is concluded that the RISE is a result of the specimen cracking during the indentation.

Load effect on the mechanical behaviour of zirconia-reinforced lithium silicate glass ceramics

The mechanical behaviour of pre-crystallized and crystallized zirconia-reinforced lithium silicate glass ceramics (ZLS) using micro-indentation techniques is reported. Vickers micro-indentations were conducted on these materials at the load of 0.245 N–9.8 N and 4.9 N–9.8 N to determine the load effect on the hardness and fracture toughness, respectively. The hardness increased with the load by 78.2% (ANOVA, p < 0.05) and 163% (ANOVA, p < 0.05) on pre-crystallized and crystallized ZLS, respectively, indicating the occurrence of the reverse indentation size effect (RISE) on both materials. The fracture toughness increased with the load by 20% and 12.3% on pre-crystallized and crystallized ZLS, respectively. Hardness data of both materials were analyzed using the Meyer's, indentation-induced cracking (IIC), proportional specimen resistance (PSR), modified PSR, Hays–Kendall and elastic plastic deformation (EPD) models. The Meyer's and IIC models described the RISE behaviour of both materials satisfactorily. The PSR, Hays–Kendall and EPD models provided consistent load-independent hardnesses while the modified PSR model gave erratic load-independent hardnesses for both materials. The continuum model provided intrinsic compressive yield strengths of both materials which were consistent with those obtained from the EPD model and the Tabor relation, implying the EPD model as the most successful. The brittleness index predicted better machinability for crystallized ZLS than pre-crystallized ZLS. Finally, the variations of hardness and fracture toughness with load might account for the different micro-material removal mechanisms in the sharp abrasive machining of these materials.

Au katkılı YBCO süperiletkenlerin kırılma tokluğu ve kırılganlıkları

In this work, the effect of Au addition on some mechanical properties of YBCO superconductors are analyzed. Five different samples (undoped, 1%, 5%, 15% and 20%) were prepared using the conventional solid state reaction method. The experimental results of the microhardness measurements are used to obtain the yield strength, Young’s modules, fracture toughness and brittleness index. These mechanical properties mentioned above are extracted by using the proportional specimen resistance (PSR) model. The mechanical properties of the samples were found to be load dependent. The yield strength, Young’s modules, brittleness index and fracture toughness values increase with decreasing test load and decreases with increasing Au content. The possible reasons for the observed degradation in the mechanical properties due to Au addition are discussed.