Nanoindentation Size Effect Research Articles

Novel nanoindentation strain rate sweep method for continuously investigating the strain rate sensitivity of materials at the nanoscale

We introduce a new nanoindentation method to continuously measure the hardness while sweeping through orders of magnitudes of strain rates within a single experiment. While nanoindentation already allows the determination of the strain rate sensitivity of materials by means of strain rate jump tests, these are typically limited to few discrete strain rates. With the new method, the strain rate sensitivity can be measured continuously as a function of the strain rate. Applications to fused silica, Zn-22 %Al superplastic alloy, single crystalline aluminum, various nanocrystalline metals and a palladium-based metallic glass are shown. Besides some discrepancy with the reference measurements, the new method seems only affected by the presence of a strong nanoindentation size effect. Provided this indentation size effect is not excessively large and can be corrected for accurately, the method proves robust, with no suggestion that the direction of the strain rate sweep affects the evaluation of the strain rate sensitivity.

Nanoindentation size effects of mechanical and creep performance in Ni-based superalloy

Nanoindentation technique was adopted to study indentation size effects of physical-mechanical and creep performance with various depths (200–2000 nm) in GH901 utilising sharp and spherical tip. Residual impressions of both indenters with pile-up patterns are discussed. Nanohardness, reduced modulus and elastic recovery rates curves versus maximum displacement of two tips are obtained and nanohardness size effects are discussed with different models for Berkovich tip. The data obtained with spherical indentation are analysed separately by establishing stress–strain diagram. The creep results using Berkovich tip indicate that creep strain rate declines while creep stress exponent first decreases and then increases with the increasing depth; the creep stress exponent (n) values, 2.39–7.35, imply the dominant creep deformation mechanism is dislocation control.

Micro mechanical property investigations of Ni-based high-temperature alloy GH4169 based on nanoindentation and CPFE simulation

In this research, the microscopic deformation behavior of GH4169 superalloy is investigated by a series of nanoindentation experiments and simulations based on crystal plasticity finite element (CPFE) model, including hardness, creep displacement and stress distribution around indentation. In this regard, the crystal plasticity constitutive model based on dislocation slip for face-centered cubic (FCC) crystal of concern is summarized and numerically implemented at first. Moreover, nanoindentation experiments are performed on specimens with various peak loads and load times to investigate the mechanical response and deformation mechanism at the micro-scale. Nanoindentation test results show that load rate, peak load, and nanoindentation size effect (ISE) all affect the microscopic deformation behavior of GH4169. The value of creep stress exponent, m, calculated from the creep experimental data is greater than 3, indicating that dislocation slip is dominant creep mechanism at room temperature.The nanoindentation simulation data based on the crystal elastic–plastic parameters determined by the trial-and-error method are in good agreement with the experimental data, demonstrating that the CPFE simulation results are credible. Therefore, this study can be used as a reference to investigate other alloy materials.

Nanoindentation Size Effects in Lithiated and Sodiated Battery Electrode Materials

Abstract Deformation and stress in battery electrode materials are strongly coupled with diffusion processes, and this coupling plays a crucial role in the chemical and structural stability of these materials. In this work, we performed a comparative study of the mechanical characteristics of two model materials (lithiated and sodiated germanium (Ge)) by nanoindentation. A particular focus of the study was on the indentation size effects and harnessing them to understand the chemo-mechanical interplay in these materials. While the quasi-static measurement results showed no significant size dependence, size effects inherent in the nanoindentation creep response were observed and utilized to investigate the deformation mechanism of each material. Supplemented by computational chemo-mechanical modeling, we found that lithiated Ge creeps through a stress-gradient-induced diffusion (SGID) mechanism but a model combining the SGID and conventional shear transformation deformation (STD) mechanisms was needed to capture the creep behavior of sodiated Ge. Broadly, this work reveals the importance of stress-diffusion coupling in governing the deformation of active electrode materials and provides a quantitative framework for characterizing and understanding such coupling.

Nanoindentation Creep Behavior of Single‐Crystal Bi2Se3 Topological Insulator

A single‐crystal Bi2Se3 topological insulator is fabricated using the Bridgman–Stockbarger method. The crystal structure and atomic lattice parameters are identified by X‐ray diffraction analysis. The nanoindentation size effect on creep displacement, activation volume, and strain rate sensitivity (SRS) with different maximum holding loads between 1000 and 5000 μN is investigated using depth‐sensing nanoindentation. Furthermore, the effect of the loading rate on the steady‐state creep displacement and SRS is analyzed and discussed. Results show Bi2Se3's low resistance to plastic deformation and a significant increase of creep displacement with increasing holding load and holding rate. Additionally, creep strain rate, activation volume, and SRS are also calculated from the secondary stage creep, and results are compared with those of other flexible electronic materials.

A dislocation-based yield strength model for nano-indentation size effect

This paper presents a dislocation-based yield strength model for the nano-indentation size effect. The model is based on functional expressions involving the densities of statistically stored dislocations and geometrically necessary dislocations. A single-phase austenitic stainless steel (316L) and a ferrite-austenite dual-phase steel (2205) are used here as the case-study materials to validate the proposed model. Experimental testing and finite element modelling of nano-indentation of the two materials are presented. Experimental tests are performed in the indentation load range from 1000[Formula: see text] to 10000[Formula: see text]. For 2205 steel, finite element modelling is performed using a dual-phase microstructure-based model. It is shown that, with consideration of statistically stored dislocations and geometrically necessary dislocations, finite element modelling results can reproduce measured load–displacement curves and hence, the size effect, within an error range of about 5%.

Modelling of nanoindentation behaviour in MgO doped alumina

Here we report the modelling of the nanoindentation behaviour of 1–5 wt% MgO doped alumina ceramics. It is well-known that the nanoindetation technique is highly efficient in digging out the mechanical properties of various materials including ceramics especially, at small length scale. The samples prepared by the pressureless sintering technique are characterized by the x-ray diffraction, field emission scanning electron microscopy and the nanoindentation techniques. The experimental results obtained from the nanoindentation experiments exhibit a unique nanoindentation size effect as well as the occurrences of localized plasticity events. This unique observation is what drives the inspiration for modelling such behaviours. The modelling of this nanoindentation size effect identifies that it could be linked to the load dependent spatial variations in both the dislocation loop interaction zone size and the deformation resistance. The localized plasticity events are found to happen due to the simultaneous contributions from dislocation nucleation, localized shear deformation bands formation and microcracking formations. The critical loads at which localized plasticity events are initiated increase with the amount of MgO. It happens due to the simultaneous enhancements in the relative density, spinel phase, relative amount of fine grains, and decrease in average size of the fine grains. The implications of these observations for microstructural design of structural ceramics like alumina with enhanced contact deformation resistance at the nanoscale are also discussed.

Microstructure Observation and Nanoindentation Size Effect Characterization for Micron-/Nano-Grain TBCs

Microstructure observation and mechanical properties characterization for micron-/nano-grain thermal barrier coatings were investigated in this article. Scanning electron microscope images demonstrated that both micron-grain coating and nano-grain coating had micrometer-sized columnar grain structures; while the nano-grain coating had the initial nanostructures of the agglomerated powders reserved by the unmelted particles. The mechanical properties (hardness and modulus) of micron-/nano-grain coatings were characterized by using nanoindentation tests. The measurements indicated that the nano-grain coating possessed larger hardness and modulus than the micron-grain coating; which was related to the microstructure of coatings. Nanoindentation tests showed that the measured hardness increased strongly with the indent depth decreasing; which was frequently referred to as the size effect. The nanoindentation size effect of hardness for micron-/nano-grain coatings was effectively described by using the trans-scale mechanics theory. The modeling predictions were consistent with experimental measurements; keeping a reasonable selection of the material parameters.

Nanoindentation size effect on stochastic behavior of incipient plasticity in a LiTaO3 single crystal

We investigated the characteristic of first pop-in event under spherical nanoindentation in the typical orientation (0 1 1¯ 2), i.e., Y-42° plane of a LiTaO3 single crystal. Three spherical tips with different radii were adopted to probe yield stress and its stochastic behavior as the incipient plasticity occurred. The values of yield stress were 10.75 ± 0.78, 6.3 ± 0.44 and 5.36 ± 0.4 GPa, which were equivalent to E/14, E/30 and E/36 under spherical tips with radii of 0.76, 2.95 and 9.8 μm, respectively. The occurrence of incipient plasticity exhibited a uniform and scattering distribution in a wide range under all the tips. The activation volumes of plastic unit were computed based on the statistical distribution of yield stress, which were 6, 12 and 12 Å3 for 0.76, 2.95 and 9.8 μm tips. A strong indentation size effect was revealed on the threshold stress for evoking incipient plasticity and the critical volume for plastic unit activation. Furthermore, incipient plasticity of LiTaO3 single crystal was confirmed to be loading history-independent. The obtained yield stress and its statistic distribution were similar within the range of loading rate from 0.125 to 2 mN/s.

Phase-field modeling of multivariant martensitic microstructures and size effects in nano-indentation

A finite-strain phase-field model is developed for the analysis of multivariant martensitic transformation during nano-indentation. Variational formulation of the complete evolution problem is developed within the incremental energy minimization framework. Computer implementation is performed based on the finite-element method which allows a natural treatment of the finite-strain formulation and of the contact interactions. A detailed computational study of nano-indentation reveals several interesting effects including the pop-in effect associated with nucleation of martensite and the energy-lowering breakdown of the symmetry of microstructure. The effect of the indenter radius is also examined revealing significant size effects governed by the interfacial energy.

Revealing Nanoindentation Size-Dependent Creep Behavior in a La-Based Metallic Glassy Film.

We systematically studied nanoindentation size effect on creep deformation in a La-based metallic glassy film, including holding depth effect and indenter size effect. Creep displacement was mainly dependent on both holding strain and deformation volume beneath indenter. Under elastic holding, creep strain was merely holding strain–dependent. While for plastic holding, creep strain was greatly enhanced by adopting smaller indenter and/or decreasing holding depth at the same holding strain. A strong nanoindentation size effect on creep resistance was validated. Strain rate sensitivities (SRS) were calculated, which were obviously higher at elastic regions than at plastic holdings. The relationship between SRS value and creep mechanism in metallic glass was discussed.

Nanoindentation Investigation on the Size-Dependent Creep Behavior in a Zr-Cu-Ag-Al Bulk Metallic Glass

Nanoindentation technology has been widely adopted to study creep behavior in small regions. However, nanoindentation creep behavior of metallic glass is still not well understood. In the present work, we investigated nanoindentation size effects on creep deformation in a Zr-based bulk metallic glass at room temperature. The total creep strain and strain rate of steady-state creep were gradually decreased with increasing holding depth under a Berkovich indenter, indicating a length-scale-dependent creep resistance. For a spherical indenter, creep deformations were insignificant in elastic regions and then greatly enhanced by increasing holding strain in plastic regions. Strain rate sensitivities (SRS) decreased with increasing holding depth and holding strain at first, and then stabilized as holding depth was beyond about 500 nm for both indenters. SRS values were 0.4–0.5 in elastic regions, in which atomic diffusion and free volume migration could be the creep mechanism. On the other hand, evolution of the shear transformation zone was suggested as a creep mechanism in plastic regions, and the corresponding SRS values were in the range of 0.05 to 0.3.

Model of nanoindentation size effect incorporating the role of elastic deformation

Based on the classical Nix-Gao model of indentation size effect (ISE), a new model incorporating the role of elastic deformation is proposed for modeling ISE at indentation depths below 100 nm. We show that, while elastic deformation is generally not associated with the generation of geometrically necessary dislocations (GNDs), neglecting it can lead to severe overestimation of both the nanoindentation hardness and GND density at small indentation depths, particularly below 100 nm, and the reverse ISE is also described. In this sense, elastic deformation can play an essential role in estimating nanoindentation hardness at small indentation depths. It is shown that our model predictions are in good agreement with experimental results on nanoindentation of single Cu and MgO crystals. A similar model applied to ISE in ion-irradiated metallic materials, where the irradiation hardening effect and ISE are successfully separated, enables analysis of irradiation hardening in ion-irradiated metallic materials without the interference of ISE.

Indentation size effects in spherical nanoindentation analyzed by experiment and non-local crystal plasticity

Nanoindentation has become a rather mature tool to characterize and measure mechanical properties of materials on micro- and nanometer length scales. However, the different types of indentation size effects (ISE) hamper the assessment of true, i.e., scale independent, material properties by nanoindentation. In the present study, the mechanisms of the ISE in spherical indentation have been investigated and quantified. Furthermore, it has been shown that the determination of non-local crystal plasticity parameters from nanoindentation results is possible. The thus-parameterized non-local crystal plasticity describes the higher-order size effect occurring in spherical indentation correctly and offers the possibility to understand the mutual contributions of geometrically necessary dislocations (GND) and statistically stored dislocations (SSD) to the material response. Nanoindentation experiments have been performed into a single grain of an ARMCO iron specimen, where the load displacement curves have been recorded, and the post-indentation surface topologies have been characterized. Furthermore, transmission electron microscopy has been performed to analyse the plastically deformed volume beneath the indentation. By comparing experimental and numerical nanoindentation results with respect to the plastic zone and dislocation structures, we validate the non-local crystal plasticity model of indentation and increase our understanding of the underlying mechanisms of the ISE in spherical indentation.

Nanoindentation Size Effect of Tungsten Single Crystal

The load-displacement curves, elastic modulus, indent morphology, nanohardness and elastic recovery of high purity tungsten single crystal were investigated by nanoindentation and scanning probe microscopy. Results show that W (111) crystal plane undergoes elastic deformation and plastic deformation during the loading-unloading process, and the load-displacement curve does not show discontinuity, which demonstrates that cracks and brittle fracture are not formed in the indents. Moreover, the pile-up behavior around indents reveals that tungsten single crystal has a low work hardening tend. The nanohardness and elastic modulus of tungsten single crystal were measured by continuous stiffness measurement (CSM), and a size effect on the nanohardness and elastic modulus of tungsten single crystal was observed, which decrease with the increase of indentation depth. The Nix-Gao model was employed to analyze the nanoindentation mechanical characteristics of tungsten single crystals, and the characteristic length ( h * ), the intrinsic hardness in the limit of infinite depth ( H 0 ) and size effect index ( m ) were calculated to be 1490 nm, 6.79 GPa and 0.18, respectively, which indicates that tungsten single crystal has a significant size effect when the indentation depth is below 1490 nm, and the size effect becomes more insignificant when indentation depth is above 1490 nm. When the impression is deeper than 2450 nm, the nanoindentation size effect on the hardness will disappear.

Review of Nanoindentation Size Effect: Experiments and Atomistic Simulation

Nanoindentation is a well-stablished experiment to study the mechanical properties of materials at the small length scales of micro and nano. Unlike the conventional indentation experiments, the nanoindentation response of the material depends on the corresponding length scales, such as indentation depth, which is commonly termed the size effect. In the current work, first, the conventional experimental observations and theoretical models of the size effect during nanoindentation are reviewed in the case of crystalline metals, which are the focus of the current work. Next, the recent advancements in the visualization of the dislocation structure during the nanoindentation experiment is discussed, and the observed underlying mechanisms of the size effect are addressed. Finally, the recent computer simulations using molecular dynamics are reviewed as a powerful tool to investigate the nanoindentation experiment and its governing mechanisms of the size effect.

Nanoindentation simulation on single crystal copper by quasi-continuum method

Considering that nanoindentation size effect under very small nano scale could not be effectively investigated by traditional experimental methods, this paper proposed to use quasi-continuum (QC) method to establish a multi-scale simulation model for nanoindentation process on single crystal copper at very small depth, below 20Å. And different-size small indenters were adopted in this paper with their radiuses ranging from 2nm to 10nm. The simulation results showed that the contact stiffness did not show indentation size effect, but the values fluctuated on a horizontal line; that the nano-hardness showed obvious indentation size effect.

Erratum to: Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Erratum to: Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

In the present research, hierarchical structure observation and mechanical property characterization for a type of biomaterial are carried out. The investigated biomaterial is Hyriopsis cumingii, a typical limnetic shell, which consists of two different structural layers, a prismatic “pillar” structure and a nacreous “brick and mortar” structure. The prismatic layer looks like a “pillar forest” with variation-section pillars sized on the order of several tens of microns. The nacreous material looks like a “brick wall” with bricks sized on the order of several microns. Both pillars and bricks are composed of nanoparticles. The mechanical properties of the hierarchical biomaterial are measured by using the nanoindentation test. Hardness and modulus are measured for both the nacre layer and the prismatic layer, respectively. The nanoindentation size effects for the hierarchical structural materials are investigated experimentally. The results show that the prismatic nanostructured material has a higher stiffness and hardness than the nacre nanostructured material. In addition, the nanoindentation size effects for the hierarchical structural materials are described theoretically, by using the trans-scale mechanics theory considering both strain gradient effect and the surface/interface effect. The modeling results are consistent with experimental ones.

Thermal stability, dynamic mechanical analysis and nanoindentation behavior of FeSiB(Cu) amorphous alloys

The aim of the present study is to investigate the crystallization behavior, microstructural evolution and mechanical behavior of the Fe-based amorphous alloy with three various compositions (at%): Fe80.75Si8B11.25 (Cu-free and Silicon-rich alloys), Fe85.2Si0.9B12.62Cu1.28 and Fe78.6Si1.8B17.75Cu1.85 (Cu-containing and Si-poor alloys). The presence of Cu decreased the activation energy of the first crystallization peak and glass transition temperature. Furthermore, anomalous behavior was observed in Avrami exponent at the final stage of the crystallization of the Cu-containing alloys. Absence of Cu resulted in a coarse dendritic structure while finer and equiaxed grains were achieved by Cu addition. Nanoindentation size effect (the decrease of hardness with the increase of indentation depth) was observed in amorphous ribbons (regardless of composition) from 10 to 70mN load and further increase of load did not change the hardness and Young׳s modulus noticeably. Isothermal annealing effectively increased the hardness (H) and Young׳s modulus (Er) of the alloys. In addition, it was found that the plastic work of nanoindentation decreased after annealing in Cu-free alloy whereas it increased in Cu-containing one which could be due to the refined microstructure. Besides, shear bands around the indents in amorphous ribbons were disappeared after 1h annealing which could be due to the change in plastic deformation mechanism from shear banding to strain-hardening.