Depth Dependence Of Hardness Research Articles

Unusual indentation depth dependent hardness and creep behaviors in NbMoTaW films at the nanoscale

Herein, nanocrystalline NbMoTaW and (NbMoTaW)N thin films were prepared via magnetron sputtering and investigated using nanoindentation creep tests at various indentation loads (P). The hardness (H) of films increases with P, exhibiting an abnormal indentation size effect (ISE). At the same time, with decreasing indentation depth (h), the creep rate and the creep rate sensitivity (m) both increase. Under a critical h (hc) for each film, m sharply increases. The diffusion between the indenter/film interface dominates the creep mechanism at h lower than hc, whereas the dislocation–grain boundary interaction dominates the creep deformation at h higher than hc. The coble creep and lattice diffusion were both excluded as the main deformation mechanism. The escape of screw dislocations to the surface leads to the softening of the film, whereas the pile-up of screw dislocations leads to hardening, explaining the abnormal ISE on H. The effect of residual stress, grain boundary structures, substrate, and impurities are also discussed.

Effect of Fe addition and ion irradiation on surface hardness in zirconium alloys: Experiments and modeling

Exploring the effect of Fe addition and ion irradiation on surface hardness in Zr alloys not only elucidates the strengthening mechanisms of individual alloying elements but also facilitates the assessment of mechanical properties under varying damage levels. In this work, the microstructural variations and surface hardness of Zr and Zr-Fe alloys were examined through Ne+ and Au3+ irradiation experiments. Electron backscatter diffraction (EBSD) characterization suggested the potential of Fe addition in Zr-Fe alloys for grain refinement. Transmission Electron Microscopy (TEM) observations indicated the formation of dislocation loops in irradiated materials, accompanied by a transformation of Zr3Fe particles from a crystalline to an amorphous state. Furthermore, nano-indentation tests were employed to measure the depth-dependent hardness, revealing an augmentation in hardness with increasing Fe content and highlighting noticeable irradiation hardening in Zr alloys. A mechanical model was then developed to theoretically investigate the contribution of diverse hardening mechanisms in ion-irradiated Zr alloys, particularly addressing the impact of non-uniformly distributed defects. Theoretical analysis denoted that the irradiation-induced defects hardening at varying depths follows distinct laws, whereas the precipitation hardening in Zr-Fe alloys was attributed to high-density strengthening particles induced by Fe addition. Moreover, it was determined that the surface hardness is governed by geometrically necessary dislocations (GNDs) and irradiation-induced defects at shallow depths, whereas precipitates and statistically stored dislocations (SSDs) dominate at relatively larger depths.

Assessment of phenomenological models for Indentation Size Effect (ISE) through physically based dislocation density evolution

The depth dependent hardness, referred to as indentation size effect (ISE) has gained considerable attention. ISE is attributed to the strain gradient caused by the inhomogeneous strain distribution beneath the indenter tip. The depth dependence of hardness is phenomenologically accounted using an appropriate length scale parameter. The Unified model is one such model that is built on Nix–Gao’s model and focuses on integrating various length scale parameters resulting from both microstructural and geometrical effects. One aspect of the current work is to assess the applicability of the Unified model to a material like bulk Nickel with a history of cold work. Also, the physics of ISE in metals can be related to the dislocation mean free path influenced by strengthening mechanisms. Past attempts are scarce to quantify the ISE through the microstructure variables. In the present work, an attempt has been made to simulate the nanoindentation test using a dislocation density based constitutive model. The objective of this study is to establish a correlation between the equivalent plastic strain resulting from deep depth indentation (which does not exhibit a size effect) and an equivalent dislocation density. The dislocation density here serves as a state variable that describes the microstructure-dependent mechanical behaviour. The modified KME, a dislocation density-based model, is incorporated as a user subroutine in a commercial finite element solver. It has been proven to accurately predict the indentation behaviour at substantially large depths, which aligns well with the predictions of the Unified model or experimental observations. The good correlation between the value of effective dislocation density and equivalent plastic strain in the plastic zone underneath the indenter assures to extend the use of dislocation density as a state variable to predict ISE.

Irradiation-Hardening Model of TiZrHfNbMo0.1 Refractory High-Entropy Alloys.

In order to find more excellent structural materials resistant to radiation damage, high-entropy alloys (HEAs) have been developed due to their characteristics of limited point defect diffusion such as lattice distortion and slow diffusion. Specially, refractory high-entropy alloys (RHEAs) that can adapt to a high-temperature environment are badly needed. In this study, TiZrHfNbMo0.1 RHEAs are selected for irradiation and nanoindentation experiments. We combined the mechanistic model for the depth-dependent hardness of ion-irradiated metals and the introduction of the scale factor f to modify the irradiation-hardening model in order to better describe the nanoindentation indentation process in the irradiated layer. Finally, it can be found that, with the increase in irradiation dose, a more serious lattice distortion caused by a higher defect density limits the expansion of the plastic zone.

Revealing the temperature-dependent hardening mechanisms of non-uniformly distributed defects for ion-irradiated metals: Experiments and modeling

In this work, an integrated approach including experimental examinations and theoretical modeling was employed to examine the temperature-dependent hardening of structural materials under ion irradiation. Experimental procedures involved the characterization of grain morphology and size distribution by electron backscatter diffraction (EBSD). Irradiation experiments were conducted utilizing high-energy Au-ions at elevated temperatures, with transmission electron microscopy (TEM) employed for observing irradiation-induced defects. Moreover, mechanical properties were assessed through high-temperature nano-indentation tests (HTNIT), revealing the concurrent occurrence of irradiation hardening and high-temperature softening in the considered materials. For theoretical modeling, a mechanistic model was developed to address the depth-dependent hardness. This model innovatively characterized the hardening mechanisms resulting from non-uniformly distributed defects in the irradiated layer while simultaneously incorporating the temperature effect. Calibration of the model demonstrated its capability to elucidate the hardness-depth relationships at different irradiation doses and testing temperatures. Further theoretical analyses indicated distinct evolution laws in irradiation hardening behavior with varying indentation depths, while the increment in temperature accelerated the expansion of the plastic zone, resulting in a moderate indentation size effect (ISE). With increasing indentation depth, the hardening contributions of geometrically necessary dislocations (GNDs) and irradiation-induced defects gradually diminished. At substantial indentation depths, the dominant hardening mechanism was then controlled by statistically stored dislocations (SSDs).

Indentation Depth-Dependent Hardness of Metal-Organic Framework Crystals: The Effect of Local Amorphization Induced by Indentation.

The hardness of metal-organic frameworks (MOFs) is an important mechanical property metric measuring their resistance to the permanent plastic deformation. The hardness of most MOFs measured from nanoindentation experiments usually exhibits the similar unique indentation depth dependence feature, the mechanism of which still remains unclear. In order to explain the effect of the indentation depth on the hardness of MOFs, we conducted nanoindentation simulations on HKUST-1 by using reactive molecular dynamics simulations. Our simulations reveal that the HKUST-1 material near the indenter can transform from the parent crystalline phase to a new amorphous phase due to the high pressure generated, while its counterpart far from the indenter remains in the crystalline phase. By considering the crystalline-amorphous interface in the energy analysis of MOFs, we derived an analytical expression of the hardness at different indentation depths. It is found that the interface effect can greatly increase the hardness of MOFs, as observed in nanoindentation simulations. Moreover, the proposed analytical expression can well explain the indentation depth-dependent hardness of many MOF crystals measured in nanoindentation experiments. Overall, this work can provide a better understanding of the indentation depth dependence of the hardness of MOFs.

Ion-irradiation induced hardening behavior of zirconium alloys: A combination of experimental and theoretical study

This study aimed to investigate the microstructure information and mechanical behavior of ion-irradiated zirconium (Zr) alloys through a combination of experimental measurements and theoretical analysis. Experimental procedures involved Au3+ irradiation of Zr-1.5Sn-0.2Fe-0.1Cr and Zr-1.0Sn-1.0Nb-0.1Fe at 3 displacements per atom (dpa) and 30 dpa. Transmission electron microscopy analysis revealed the formation of precipitates such as Zr(Fe, Cr)2 in Zr-1.5Sn-0.2Fe-0.1Cr, as well as β-Nb and Zr(Nb, Fe)2 in Zr-1.0Sn-1.0Nb-0.1Fe. These precipitates exhibited a transformation from crystalline state to partial or complete amorphization after ion-irradiation. Furthermore, macroscopic mechanical properties of the Zr alloys were characterized by nano-indentation tests, which revealed a significant indentation size effect (ISE) and irradiation hardening behavior. To provide a theoretical understanding of the depth-dependent hardness observed in ion-irradiated Zr alloys, a mechanistic model was developed to address the different expansion rates of the plastic zone in the irradiated and unirradiated region. The results indicated that the ISE phenomenon could be attributed to the reduction in the density of geometrically necessary dislocations (GNDs) caused by the expansion of the plastic zone. In addition, the irradiation hardening behavior primarily resulted from the contribution of irradiation-induced defects. With increasing indentation depth, the dominant hardening mechanisms changed from the contribution of irradiation-induced defects, GNDs and statistically stored dislocations (SSDs) in the irradiated region to SSDs in the unirradiated substrate.

Depth dependence of hardness and reaction in metakaolin‐based geopolymers cured at low humidity

AbstractCompared to metakaolin‐based sodium and potassium geopolymers cured at 20°C/100% relative humidity, geopolymers, which were cured at 20°C/40% relative humidity, were found to have considerable changes in the nanoscale structure and physical properties near the surface due to dehydration that occurred before completely hardening. For low‐humidity samples, the density in a thin near‐surface region was higher than the bulk, while porosity and BET specific surface area were greatly diminished. The microhardness at the exposed surface was low but increased sharply within a small depth before decreasing with depth to a constant value, which depended on the initial water content and charge‐balancing cation. 29Si NMR spectroscopy showed that the extent of reaction also varied with distance from the exposed surface. Both the elevated microhardness and incomplete reaction were detected at distances of up to 1.5 cm from the exposed surface, indicating that premature dehydration can cause microstructural changes over length scales that may be significant in large, ambiently cured 3D‐printed geopolymers. These effects are reduced by the use of sodium rather than potassium as the charge‐balancing cation and by raising the initial water content of the geopolymer, although higher water content caused greater surface deformation during drying.

Modelling the laser surface hardening in a ferrite and pearlite initial microstructure

ABSTRACT The present study explores the microstructure and the depth-dependence of hardness after a single pass laser heat-treatment. The initial microstructure was selected as ferrite and pearlite in different fractions, with the aim of studying low, medium, and high carbon steels. A modification of an existing model is proposed, whereby the cementite dissolution is incorporated to better reflect the microstructure evolution during the rapid thermal cycle. It is found that the predictions under the new paradigm show fair agreement with the experimental data. The new model indicates that the correct estimation of the composition of austenite near the transition zone produces a more accurate prediction of the hardness profile, reducing the overestimation obtained in previous works.

Alternative approach for the growth of a TiB2/TiC multilayer on M2 steel using the duplex method: Cathodic arc physical vapor deposition and cathodic reduction and thermal diffusion boriding

An alternative approach for producing a hard TiB2/TiC multilayer on M2 high-speed steel was introduced by combining cathodic arc physical vapor deposition (CA-PVD) and cathodic reduction and thermal diffusion-based boriding (CRTD-Bor). In this regard, the CRTD-Bor process was applied on CA-PVD Ti-deposited M2 steel and the effects of boriding parameters (i.e., temperatures and durations) on multilayer growth were examined. During boriding, Ti coating on the substrate was converted into Ti-borides on the top surface and a TiC layer was simultaneously formed at the interface of the Ti deposit and the steel matrix. The growth of boride and carbide phases was found to obey the parabolic law. The pre-exponential factors (K0) and the activation energy (Q) values were calculated as 7.50 × 10−9 m2/s and 146.10 kJ/mol for TiB2 growth and 1.81 × 10−7 m2/s and 187.31 kJ/mol for TiC formations, respectively. Additionally, empirical equations for estimating the thicknesses of TiB2 and TiC layers were derived. The penetration depth-dependent hardness measurements revealed the TiB2 layer hardness as 41 ± 5 Gpa, which decreased gradually toward the TiB region (24 ± 2 GPa) and fell to 13 ± 1 GPa in the Ti-rich area. The hardness then increased to 20 ± 1 GPa with the contribution of the TiC layer adjacent to the substrate. This multilayer coating exhibited −5.5 to −4.5 GPa compressive stress and good adhesions (HF1) to the substrates. Also, the results of tribological tests indicated a sevenfold increase in wear resistance under dry sliding conditions.

Microstructure-informed prediction and measurement of nanoindentation hardness of an Fe-9Cr alloy irradiated with Fe-ions of 1 and 5 MeV energy

Hardening of Fe-9%Cr alloys exposed to irradiation with Fe2+ ions of two different energies, 1 and 5 MeV, is investigated using nanoindentation. The limited penetration depth of the ions causes steep damage gradients in the near-surface volumes of the irradiated samples. This damage gives rise to graded microstructures resulting in depth-dependent irradiation hardening. Nanoindentation integrates the depth-dependent hardness over the indentation plastic zone. Our study combines quantitative analysis of the ion-irradiated microstructures with the determination of the full depth dependence of irradiation hardening. The microstructure-informed model incorporates direct experimental evidence revealed by a former investigation using cross-sectional scanning transmission electron microscopy. For both ion energies, the observed microstructures consist of dislocation loops with band-like distributions and are concluded to be the dominant source of the measured irradiation-induced hardening. The model predictions are found to be in reasonable agreement with the as-measured nanoindentation response. The comparison of hardening predictions with different kinds of superposition rules of hardening contributions suggests linear superposition as the most appropriate selection under the present conditions. The possible transferability of these results to neutron irradiation is also discussed.

Growth and mechanical properties of Nb[sbnd]Cr carbide coatings on graphite by TRD technique

Niobium‑chromium (NbCr) carbide coatings were deposited on graphite using the thermo-reactive deposition and diffusion (TRD) technique. The microstructure, hardness, and coefficient of thermal expansion were characterized to search for the optimal treatment parameters for hard and adherent coatings on graphite. The growth rate increased with treatment temperature for fixed treatment duration and remained constant at a constant temperature for about 6 h. The coatings were found to consist of alternating Nb and Cr layers, and this interesting multilayer structure might be explained by the thermodynamics of oxide reduction and carbide formation reactions. Compared to the single-carbides layer, the hardness of the complex coatings increased from about 2500 HV to above 3000 HV, and displayed a smaller gradient of the depth-dependent hardness from the coating to the substrate. The variation of coefficient of thermal expansion of the samples with temperature was similar to that of the graphite substrate at temperatures from 40 to 450 °C. These results showed the effectiveness of the TRD method for synthesizing hard and adherent carbide coatings on graphite, and for other coating/substrate systems with sharply dissimilar mechanical properties.

A hardening model considering grain size effect for ion-irradiated polycrystals under nanoindentation

In this work, a new hardening model is proposed for the depth-dependent hardness of ion-irradiated polycrystals with obvious grain size effect. Dominant hardening mechanisms are addressed in the model, including the contribution of dislocations, irradiation-induced defects and grain boundaries. Two versions of the hardening model are compared, including the linear and square superposition models. A succinct parameter calibration method is modified to parametrize the models based on experimentally obtained hardness vs. indentation depth curves. It is noticed that both models can well characterize the experimental data of unirradiated polycrystals; whereas, the square superposition model performs better for ion-irradiated materials, therefore, the square superposition model is recommended. In addition, the new model separates the grain size effect from the dislocation hardening contribution, which makes the physical meaning of fitted parameters more rational when compared with existing hardness analysis models.

Revealing the hardening mechanisms of ion-irradiated nanostructured multilayers/substrate systems: A theoretical model

In this work, a mechanistic model is proposed for modeling the depth-dependent hardness of ion-irradiated nanostructured multilayers/substrate systems. Four dominant hardening mechanisms during the whole nanoindentation process are systematically analyzed, which include the indentation size effect (ISE) induced by geometrically necessary dislocations (GNDs), irradiation hardening determined by irradiation-induced defects, substrate effect and interface hardening existing within the multilayers. Thereinto, the former three are determined by the average density of dislocations and defects within the plasticity affected region (PAR), and are noticed to be affected by both the indentation depth and existing interface between the film and substrate layer. By considering the interface effect on both the geometrical shape and expansion ability of the PAR, the hardness-depth relation of ion-irradiated nanostructured multilayers/substrate systems is explicitly deduced at four different stages. Based on this model, the evolution of related microstructures in the film and substrate can be quantitatively analyzed, which involves the PAR, and average density of irradiation-induced defects and GNDs. The rationality and accuracy of the proposed model are validated by comparing the theoretical results with the experimental data, including two types of unirradiated systems (the YSZ/Al2O3 multilayers/Si substrate and W/Si system) and an ion-irradiated YSZ/Al2O3 multilayers/Si substrate system. The proposed model offers a promising way to qualitatively analyze other mechanical properties of ion-irradiated nanostructured multilayers/substrate systems.

Big Data Nanoindentation and Analytics Reveal the Multi-Staged, Progressively-Homogenized, Depth-Dependent Upscaling of Rocks’ Properties

This paper presents a newly observed phenomenon of upscaling of rocks’ properties using big data nanoindentation and analytics involving Gaussian mixture modeling (GMM), leading to characterizing the cross-scale mechanical properties of four shales and one sandstone. A large number (i.e., ~ 500) of statistical indentation measurements to depths of 6–8 μm were performed on each rock, resulting in continuous depth-dependent hardness and Young’s modulus data from unknown phases, which were then segmented at various depths to extract an array of discretized subdatasets. Two-dimensional GMM of each subdataset yields the number, fraction, and properties of mechanically distinct phases, and re-assembly of these results leads to clearly discernible property-depth curves. Such improved data analytics consisting of data segmentation, GMM deconvolution, and re-assembly enables the transformation of a massive number of chaotic curves from unknown phases into a few discernible lines corresponding to identified phases, from which the mechanical properties of individual phases are accurately determined at relatively small depths. With increasing depth, initially unique mechanical properties of individual phases undergo multistage merging at the intermediate mesoscale and progressively homogenize into a unified value at large depths or macroscale (e.g., > ~ 5 μm), which is regarded as the bulk rock’s properties. More importantly, such depth-dependent transition and progressive merging and homogenization actually manifest the micromechanics of nanoindentation on a heterogeneous composite, including the indentation surround effect and rock’s microstructure (e.g., sizes and spacings of different solid particles and their properties). Compared to different micromechanical upscaling models, this newly developed big data indentation technique and pertinent data analytics enable more accurate, multi-parameter, and cross-scale characterization of highly heterogeneous materials and explicitly uncover the multi-staged, progressively-homogenized, depth-dependent upscaling of elasticity from individual constituents at the nanoscale to merged virtual interface phases at the mesoscale and to bulk material at the macroscale.

NANOINDENTATION OF HYDROGEN ENRICHED Zr-1Nb ZIRCONIUM ALLOY NUCLEAR FUEL CLADDINGS

Zirconium alloys are being commonly used as a material of choice for nuclear fuel claddings in water cooled nuclear reactors for decades due to their good corrosion resistance and low neutron absorption. However, the increasing operation conditions of next generation nuclear reactors (Gen-V) in terms of higher temperatures, pressures and higher neutron flux requires evaluation of further Zr cladding usability. The embrittlement of Zr claddings due to hydrogen pickup from reactor coolant is one of the issues for its potential use in Gen-IV reactors. Nanoindentation is an effective tool for analysis of the change of mechanical properties of hydrogen enriched Zr claddings from localised material volume. Zirconium alloy Zr-1Nb (E110) with experimentally induced hydrides was analysed by the means of nanoindentation. Zirconium hydrides were formed in the material after exposure in high temperature water autoclave. The optimized methodology of surface preparation suitable for nanoindentation is described and the resulting surface quality is discussed. The nanoindentation measurements were performed as an array of 10x10 indents across areas with hydrides. Depth dependent hardness and reduced modulus values measured by nanoindentation were compared between the material with no hydrogen content, low hydrogen content (127 ppm H) and high hydrogen content (397 ppm H). Complementary microhardness measurements at HV 0.1 were performed on all materials for bulk material hardness comparison.

On the crystallographic anisotropy of plastic zone size in single crystalline copper under Berkovich nanoindentation

Aiming at revealing plastic deformation mechanisms of nanoindentation tests, we investigate the crystallographic orientation-influenced indentation size effect in the Berkovich nanoindentation tests of single crystalline copper, by using the nonlocal crystal plasticity finite element approach and specifically designed experiments. In our simulation model of nanoindentation, a new geometrically necessary dislocation density-based crystal plasticity model is proposed, and the utilized model parameters are calibrated by fitting the measured load-displacement curves of indentation tests. Then the size of plastic zone of indentation tests is defined by the surface pile-up profile, i.e. the diameter of a circle consisting of material points with half of maximum pile-up height. It is found that the modified plastic zone model incorporated with the newly developed scaling factor provides good predication of the indentation depth-dependent hardness of single crystalline copper.

New ultra-high temperature nanoindentation system for operating at up to 1100 °C

In this work a new ultra-high temperature (UHT) nanoindentation system for testing at up to 1100 °C is presented. The system is capable to perform indents from small scale up to large indentation depths due to the combination of a 1 N actuator and a frame stiffness of >1·106Nm even at 1100 °C. Dynamic testing allows a continuous determination of the contact stiffness (CSM) and thus also the depth-dependent hardness and indentation modulus. Low drift rates can be achieved by an independent tip and sample heating. Operating the nanoindenter inside a scanning electron microscope (SEM) equipped with a high temperature backscattered electron (BSE) detector opens the possibility of in-situ observations, as high vacuum minimizes oxidation effects. The HT capability of the system is demonstrated on three reference materials: fused silica, molybdenum assessing the change in modulus with increasing temperature using constant strain rate tests (CSR). The creep response of single crystalline Ni has been assessed by strain rate jump (SRJ) as well as a step-load and hold creep (SLH) method. The resulting modulus, hardness as well as the strain rate sensitivity from RT up to 1100 °C are in good accordance with literature data, highlighting the applicability of the system.

Microstructural investigation of irradiation damage behavior of proton irradiated Zr-1 wt.% Nb fuel cladding alloy

In the present study the irradiation damage behavior of Zr-1 wt.% Nb fuel cladding alloy was investigated using X-ray diffraction (XRD), positron annihilation lifetime spectroscopy (PALS), transmission electron microscopy (TEM) and nano-indentation. The samples were irradiated at two different fluences of 5 × 1016 p/cm2 and 1 × 1018 p/cm2 using proton beam of 3.5 MeV energy at room temperature. SRIM calculation showed an inhomogeneous damage distribution as a function of proton penetration depth with maximum damage at a depth of 68 μm. XRD analysis revealed variation in the microstructural parameters of irradiated samples after proton irradiation. PALS showed formation of open volume defects in the irradiated samples and a clustering tendency of the same with irradiation. The formation of <a>− and <c>− type dislocation loops and needle-shaped precipitates upon irradiation was demonstrated by TEM. The depth dependent hardness of the irradiated samples evaluated from nano-indentation technique was found to follow the damage distribution predicted by SRIM simulation.

Structural and Mechanical Characterization of Platinum Thin Films Prepared Electrochemically on ITO/Glass Substrate

We report the structural characterization and nanomechanical properties of platinum (Pt) thin films prepared through facile electrochemical synthesis. The Pt thin films were coated onto indium tin oxide (ITO)/glass substrates by two-electrode electrochemical deposition at room temperature. They were characterized using X-ray diffraction, scanning electron microscopy, and atomic force microscopy for structural and morphological analyses. Indentation depth-dependent hardness and elastic modulus of the prepared films were analyzed using the nanoindentation technique. Furthermore, the mechanical properties of the ITO/glass substrates were also investigated to understand the influence of the substrate on the film properties. The prepared films showed reasonable mechanical and structural properties suitable for device applications. Finally, the photoconductivity effect of the prepared Pt film was also studied to determine its suitability for device applications. The Pt film was also coated on Cu plates to check substrates effects on this electrochemical deposition, and found that the Cu plates produced well adherent smooth films.