Indentation Size Effect Research Articles

Review of indentation size effect in crystalline materials: Progress, challenges and opportunities

Nanoindentation has been widely utilized for measuring mechanical properties at small scales over the past three decades. Indentation size effect (ISE) is a crucial phenomenon in nanoindentation testing of crystalline materials, which is usually manifested as an increase of hardness with a decrease of indent size. Tremendous efforts have been made to understand ISE with the aim of eliminating its influence on determining the intrinsic mechanical properties. More importantly, ISE is a key phenomenon for exploring the unique deformation mechanisms of crystalline materials at the nanoscale. We critically review the experimental observations of ISE in crystalline materials, focusing on the influences of the indenter geometry and crystal structure. In addition, the mechanistic models proposed for ISE as well as recent findings by numerical simulations are also examined in detail to explore the origins of ISE and identify the unsolved challenges.

Nanoindentation study on early-stage radiation damage in single-phase concentrated solid solution alloys

Concentrated solid solution alloys (CSAs) comprising multiple components have unlocked novel pathways for materials design, particularly in enhancing radiation tolerance. It is imperative to detect early-stage radiation damage in CSAs to gain insights into damage initiation and accumulation mechanisms. In this study, nanoindentation is employed to assess the impact of irradiation on deformation mechanisms in single crystal CSAs, specifically NiCo, NiFe, and NiCoFeCr. It is discovered that pile-up behavior in CSAs significantly affected by irradiation: pile-up induces 10–20 % increase in the contact area before irradiation that is independent of the penetration depth but 20–30 % after irradiation, which substantially affects hardness analyses. Within the context of strain gradient plasticity theory, distinct radiation-induced hardening in three CSAs is interpreted by two components: one is from the radiation-induced defects, and the other is the increase in density of geometrically necessary dislocations (GNDs) associated with indentation size effect (ISE). Quantitative analysis shows that the radiation-induced defects produce obvious hardening in NiFe and NiCoFeCr sample, but not in the NiCo sample. Meanwhile, the irradiation induces a higher GND density in NiCo and NiFe, but not in NiCoFeCr, which is interpreted by the volume change of the plastic zone.

Crystal plasticity framework related to size effect: From single crystal parameters to polycrystalline mechanical properties

Size effect has a significant influence on the accuracy of two key factors of parameters and models in crystal plasticity simulation. This study introduces a parameter identification method that considers the indentation size effect, determining the initial slip resistance of IN625 alloy. Based on the identified parameters and utilizing the integral point traversal method, a grain boundary affected zone (GBAZ), whose strength field related to the distance to the grain boundary (GB) is introduced into the polycrystalline microstructure to represent the hindering effect of GBs on dislocations. This method effectively predicts the Hall-Petch effect and strain hardening behavior of IN625 alloy. The research reveals that dislocation pile-ups primarily concentrate in small grain clusters within the material. In fine-grained microstructures, a large volume fraction of GBs promotes dislocation pile-ups, reducing the mean free path of dislocations, leading to an increase in dislocation multiplication rate, and consequently, enhancing the strain hardening rate. An increase in GBAZ thickness results in a large stress level within the material, accompanied by a decrease in the homogeneity of stress distribution. However, the sensitivity of strain to GBAZ thickness is found to be low. The method proposed in this work holds significant applicative relevance in parameter calibration and prediction the mechanical properties of polycrystalline materials.

Impact of strain rate on the Indentation Size Effect: Evidence of an intimate link between Size effect, Strain Rate and Ductility in Soda-lime Silica glass

Many glasses exhibit the so-called indentation size effect (ISE), where the indentation hardness decreases with the maximum applied force. Here, we seek to uncover the connection between the ISE and strain rate in soda-lime silica (SLS) glass using micro-indentation. Two different loading protocols: constant loading rate (CLR), resulting in a nonlinear strain rate through the depth of indent, and a non-linear loading rate that gives a constant strain rate (CSR) with depth, are used to determine Hardness for six different strain rates and seven peak forces. A modified Bernhardt size effect law is then used to determine the extent of the ISE and load-independent hardness. We show that a small increase in micro-ductility, which can be achieved by either switching from a CLR to CSR protocol or by increasing the applied rates, can greatly reduce the extent of the ISE and slightly reduce the load-independent hardness.

Model for predicting temperature-dependent indentation yield strength and hardness considering size effects

The development of theoretical models to facilitate access to the mechanical properties of materials has been a long-standing pursuit of scholars. In this study, temperature-dependent yield strength models and temperature-dependent hardness models considering indentation size effects were developed under different loading modes (loading to the same displacement or the same load at different temperatures), respectively. Based on the Force-Heat Equivalence Energy Density Principle, the proposed models are free of any adjustable fitting parameters, and the quantitative relationships among temperature, yield strength/hardness, Young's modulus, and indentation load/displacement were successfully captured. All the available 36 groups of experimental data validate the accuracy of the proposed models over a wide temperature range. The yield strength and hardness of metallic materials over a wide temperature range can be easily predicted by using the developed models. Based on the parametric analysis of the models, it has been theoretically clarified for the first time that the two loading modes have opposite indentation size effects for the same material. Although the indentation size effect all decreases gradually with increasing temperature for different loading modes. The influence of loading modes should be noted in future studies where temperature-dependent indentation size effects need to be considered. This work systematically considers the effects of temperature, loading mode, indentation load/displacement, and Young's modulus on the indentation yield strength and hardness, which is important to facilitate the study of the deformation behavior of materials at different temperatures by indentation methods.

Microhardness Variation with Indentation Depth for Body-Centered Cubic Steels Pertinent to Grain Size and Ferrite Content.

For a micro-indentation hardness test with non-destructivity, the Nix-Gao model is widely used to describe tested hardness or microhardness variation with an indentation depth induced by indentation size effect, in which tested hardness approaches the macrohardness when the indentation depth is large enough. Based on an analysis of hardness measurements on 10 body-centered cubic steels with diverse microstructure, this paper proposes an analytical relation between microhardness to macrohardness ratio and the indentation depth by explicitly linking characteristic indentation depth (a data-fitting parameter) to grain size and ferrite volume fraction using two different methods. In addition, the normal distribution theory is incorporated to consider the inevitable scatter of identical measurements resulting from material heterogeneity and machining/testing errors. Results show that the proposed model, with 96% reliability, can effectively predict microhardness variation with the indentation depth and its scatter.

Indentation size effects in hardness of annealed NiB coatings

Indentation size effects in hardness of annealed NiB coatings

Photocatalytic dye degradation, H2 evolution, electrical and mechanical performances of mechano-synthesized multifunctional Bi2Te3 nanoparticles: Effect of milling time and thermal treatment

Bi2Te3 nanoparticles are synthesized by mechanical alloying the Bi and Te powders under the Ar and pressed powdered samples are sintered at 573 K. Rietveld refined XRD patterns, FESEM images and EDX spectra reveal the microstructure, morphology and phase purity of the samples. Bandgaps are obtained from the FTIR spectra and a blue shift with size reduction indicates the size confinement effect. The non Debye type ac conductivity and dielectric constant variations with milling time and sintering are measured. The improved photocatalytic degradation efficiency of the sintered sample (83.59 %) using Rhodamine B dye under visible light elucidates reduced porosity effect. The photocatalytic hydrogen evolution efficiencies of these nanoparticles are measured and a probable mechanism is depicted. The highest H2 generation efficiency (1462.5 μmol g−1h−1) is observed with the sintered sample. Microhardness measurement reveals normal indentation size effect. Empirical correlations among electrical conductivity, microhardness and photodegradation are established for the first time.

EXPLORING STRENGTHENING MECHANISMS OF ULTRAFINE-GRAINED Fe35Mn27Ni28Co5Cr5 HIGH-ENTROPY ALLOY PROCESSED BY SEVERE COLD ROLLING PROCESS

This study describes the strengthening mechanisms of an ultrafine-grained (UFG) Fe35Mn27Ni28Co5Cr5 high-entropy alloy (HEA) processed by severe cold rolling (SCR) process at room temperature. Microstructural evaluations were performed by field emission scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The findings demonstrated that the development of deformation microstructures consisted of a single face-centered cubic (FCC) phase with stretched grains along the rolling direction and lamellar deformation bands after a 90 % reduction in thickness. Using the Nix-Gao model, the dislocation density was determined by measuring the microhardness indentation size effect. The results indicated that an increase in rolling deformation leads to an increase in dislocation density. The dislocation density increased from 2.28 ×109 cm-2 for as-homogenized specimen to 8.65 ×109 cm-2 after 90 % reduction in thickness. The yield strength of the UFG Fe35Mn27Ni28Co5Cr5 HEA was 5.2 times (1155 MPa) higher than that of the as-homogenized state (225 MPa). Finally, an assessment was conducted on the relative contributions of individual mechanisms, such as dislocation and grain refinement, to the strengthening of the Fe35Mn27Ni28Co5Cr5 HEA.

Evolution of fundamental mechanical properties with aliovalent Co/Cu partial substitution and preparation method for Y-123 system

This study investigates the effect of aliovalent Co/Cu replacement and preparation method on fundamental mechanical performance features of YBa2Cu3−xCoxO7−δ (Y-123) ceramic system depending on the crack propagation mechanism by Vickers hardness measurements (Hv) and mechanical investigation models for the first time. All the findings are verified by the scanning electron microscopy (SEM) examinations. Besides, the electron-dispersive X-ray (EDX) technique verifies the successful substitution mechanism. Besides, the Vickers hardness parameters improve systematically with the increment in the Co/Cu partial substitution (serving as a barrier) level due to formation of operable slip systems, ionic bond formations, and decrement of stress-amplified strain fields. Moreover, the Y-123 ceramic produced by solid-state reaction method and molecular weight of 0.20% presents the densest and smoothest surface morphology with the largest particle distributions and well-linked cobblestone-like grains. On the other hand, the Y-123 ceramic compounds produced by the sol–gel method are more sensitive and responsive to the indentation test loads. All the findings are wholly supported by the mechanical performance properties, including the shear modulus, resilience, and degree of granularity. Furthermore, the mechanical models indicate that every compound prepared exhibits the untypical reverse indentation size effect (RISE). Additionally, the modeling studies display that the induced cracking (IIC) approach is found to be the most appropriate method to examine true Vickers hardness parameters in the plateau limit regions. All in all, this comprehensive study reports efficiently exploiting the process–structure–property relationships in Y-123 ceramic material design for physical science and mechanical application fields using the aliovalent partial substitution and preparation condition.

Study of the irradiation hardening of a Fe9Cr ferritic model alloy by nanoindentations

This paper presents a series of Berkovich indentation results obtained on unirradiated and 7.2 MeV proton irradiated specimens of a Fe9Cr model alloy with an equiaxed ferritic microstructure. Using a energy degrader wheel made of 24 aluminum foils of different thickness, a flat damage profile of about 50 μm resulted from the irradiation, allowing to perform indentations within a volume material that is homogeneously irradiated. The indentation size effect on measured hardness was analyzed with a model based on the disloction-slip distance theory built on the concept of combined spatial frequency of all obstacles to dislocation motion. The effects on hardness of the tip-specimen contact size (or penetration depth), dislocation density and mean distance between irradiation defects were quantified and discussed. The irradiation hardening was characterized by the increase of hardness determined at large penetration depths.

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.

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.

High-current gas tungsten arc welding of Ni-base superalloy Haynes 282: correlating heat input with weld profile, microstructure, hardness and indentation size effect

High-current gas tungsten arc welding of Ni-base superalloy Haynes 282: correlating heat input with weld profile, microstructure, hardness and indentation size effect

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.

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).

A super‐hard high entropy boride containing Hf, Mo, Ti, V, and W

AbstractSuper‐hard (Hf,Mo,Ti,V,W)B2 was synthesized by boro‐carbothermal reduction and densified by spark plasma sintering. This composition was produced for the first time as a single‐phase ceramic in the present research. The optimized ceramic had a single hexagonal AlB2‐type crystalline phase with a grain size of 3.8 µm and homogeneous distribution of the constituent metals. The Vickers hardness exhibited the indentation size effect, increasing from 27 GPa at a load of 9.8 N to as high as 66 GPa at a load of 0.49 N. This is the highest hardness reported to date for high entropy boride ceramics.

Size dependence of micro-scale mechanical properties on heavy-ion irradiated tempered-martensitic steel evaluated through nanoindentation and micropillar compression tests

The size dependence of microscale mechanical properties is crucial for evaluating irradiation hardening using nanoindentation and micropillar compression tests. To predict bulk hardness without the indentation size effect in heavy-ion irradiated materials, this study designed a modified Nix–Gao model incorporating the effect of irradiation hardening. The model was used to determine the bulk hardness of irradiated film and unirradiated substrate in tempered F82H martensitic steel irradiated with 10.5 MeV Fe-ion. The bulk hardness of unirradiated F82H predicted from the nanoindentation hardness was consistent with the traditional Vickers hardness obtained using a multiscale hardness relationship. The effects of irradiation conditions and the irradiation damage gradient were also determined by the modified model. In a micropillar compression test performed using micropillars with sizes of 1–8 μm, the flow stress at 8 % plastic strain of the micropillars showed a stable and comparable value with that of a bulk tensile specimen, while the yield stress at 0.2 % strain offset decreased with decreasing pillar sizes. The irradiation hardening calculated using the bulk hardness obtained in the nanoindentation tests and the flow stress determined from the micropillar compression tests at 8 % plastic strain were consistent, as predicted by Tabor's law. These findings prove that the proposed method is effective for assessing the mechanical characteristics of a size-limited region, even on the subsurface of metallic materials exposed to heavy-ion irradiation.

Mechanical properties of Ag-added DyBa2Cu3Oy superconducting melt-textured bulks prepared by the single-direction melt growth method

Ag-added DyBa2Cu3Oy superconducting melt-textured bulks were prepared using the newly developed single-direction melt growth (SDMG) method with different pre-heat-treatment conditions. Clearly distinct microstructures were observed depending on the pre-heat-treatment conditions and thickness of the bulks. Their mechanical properties were evaluated by use of Vickers microhardness measurements at varying applied forces. Vickers microhardness increases with an increase in the applied force for each sample, up to an importantly high value of ∼9 GPa at the saturated region, indicating all the prepared bulks demonstrate the untypical reverse indentation size effect (RISE) performance. In addition, the experimental results found from the saturation regions are examined by the mechanical methods such as Meyer's law, proportional sample resistance model, elastic/plastic deformation, Hays-Kendall (HK) approximation, and indentation-induced cracking (IIC) model. According to the mechanical modelling findings, the HK and IIC models are found as appropriate mechanical models describing the hardness values for all the studied bulks exhibiting RISE feature and the true values are suggested to lie between the estimated values of HK and IIC models.

Orientation-dependent plastic flow in nanoscratching of copper surfaces

The characterization of frictional behavior in ductile metals is a crucial aspect of materials science, as it relates to the plastic deformation of the material. However, due to the intricate dislocation evolution at the submicron/nanometer scale, the isolation of the basic plastic mechanisms remains challenging. In this study, nanoscratching technology is employed to investigate submicron/nanometer-level plastic deformation in individual grains of polycrystalline copper. To achieve this, a crystal plastic constitutive model for copper materials is developed by incorporating geometrically necessary dislocation effects. The calibration of the constitutive model is conducted with great precision and specificity, leveraging mechanical responses, surface accumulation morphology, and indentation size effects from nanoindentation experiments of 110-oriented single crystal copper. Through the combination of crystal plastic finite element simulation and nanoscratching experiments, the plastic flow of the material is thoroughly analyzed. The results demonstrate that the anisotropic scratching behavior is influenced by different orientations of individual grains, taking into account both statistical storage dislocations and geometrically necessary dislocations. The insights gleaned from this study offer a valuable contribution to our understanding of the plastic mechanisms of metals at a small scale, enhancing the design and performance of advanced materials for a wide range of applications.