Indentation size effects in face centered cubic single crystal thin films

Recent micro- and nano-indentation experiments have shown strong indentation size effects at the micron and sub-micron scales. Classical plasticity theories cannot explain the indentation size effect because their constitutive models possess no intrinsic material lengths. The Mechanism-based Strain-Gradient (MSG) plasticity theory and its simplified version, the Conventional theory of Mechanism-based Strain-Gradient plasticity (CMSG), have been established from the Taylor dislocation model and have successfully explained the indentation size effect. This paper provides a review of these theories and their applications to study the indentation of face- and body-centred-cubic metals and thin films on hard or soft substrates.

Synthesis of carbon nanofibers: effects of Ni crystal size during methane decomposition

A study of particle size effect and interface fracture in aluminum alloy composite via an extended conventional theory of mechanism-based strain-gradient plasticity

The pop-in effect in nanoindentation of metals represents a major collective dislocation phenomenon that displays sensitivity in the local surface microstructure and residual stresses. To understand the deformation mechanisms behind pop-ins in metals, large scale molecular dynamics simulations are performed to investigate the pop-in behavior and indentation size effect in undeformed and deformed Cu single crystals. Tensile loading, unloading, and reloading simulations are performed to create a series of samples subjected to a broad range of tensile strains with/without pre-existing dislocations. The subsequent nanoindentation simulations are conducted to investigate the coupled effects of prestrain and the presence of resulting dislocations and surface morphology, as well as indenter size effects on the mechanical response in indentation processes. Our work provides detailed insights into the deformation mechanisms and microstructure-property relationships of nanoindentation in the presence of residual stresses and strains.

Indentation size effect: an improved mechanistic model incorporating surface undulation and indenter tip irregularity

Indentation size effect in nanohardness

Interactive effect of indenter size and specimen thickness in Hertzian indentation test

Indenter size effect on the reversible incipient plasticity of Al (001) surface is studied by quasicontinuum simulations. Results show that the incipient plasticity under small indenter, the radius of which is less than ten nanometers, is dominated by a simple planar fault defect that can be fully removed after withdrawal of the indenter; otherwise, irreversible incipient plastic deformation driven by a complex dislocation activity is preferred, and the debris of deformation twins, dislocations, and stacking fault ribbons still remain beneath the surface when the indenter has been completely retracted. Based on stress distributions calculated at an atomic level, the reason why the dislocation burst instead of a simple fault ribbon is observed under a large indenter is the release of the intensely accumulated shear stress. Finally, the critical load analysis implies that there exists a reversible-irreversible transition of incipient plasticity induced by indenter size. Our findings provide a further insight into the incipient surface plasticity of face-centered-cubic metals in nano-sized contact issues.

Several attempts have been made over recent years to understand indentation size effect (ISE). The theoretical models, based essentially on strain gradient plasticity theories, such as the Nix–Gao model, predict that ISE is caused by an increase in the density of dislocations as the indentation size decreases. Molecular dynamics simulation results tend to confirm this fact, but the truth is that very few experimental studies exist on the direct observation of how dislocations are generated and accommodated in the vicinity of nanoindentations. In this study, using a Ni transmission electron microscopy thin foil as model material, we show that when the material is submitted to atomic force microscopy-based nanoindentation a high dislocation density zone is generated at the centre of the indented region, and that prismatic loop and helical dislocations are emitted sidewards from the central region of the nanoindentation along the ⟨1 1 0⟩ directions. Moreover, we show that the dislocation array formed during the nanoindentation process is far from the ideal model proposed by Nix and Gao, based on load axi-centred dislocation loops. With this study we aim at contributing to a better comprehension of ISE mechanisms in ductile metals.

The Knoop microhardness anisotropy profile was determined for the basal plane of a Czochralski grown alumina single crystal for indentation test loads from 100 through 1000 g. Microhardness maxima occur at low indentation test loads for the long axis of the Knoop indenter parallel to the 〈2[Onemacr][Onemacr]0〉. Minima exist for the long axis parallel to the 〈10[Onemacr]0〉. This low indentation test load profile is attributed to slip on the primary slip system, the (0001)〈[Onemacr][Onemacr]20〉, as previously noted by Brookes and co‐workers. The degree of the microhardness anisotropy decreases for higher indentation test loads. This results from the activation of multiple slip systems to accommodate the greater amounts of plastic flow required by the larger indentation sizes. The microhardness profile becomes more uniform with increasing indentation test load until the Knoop microhardness approaches a test‐load‐independent, orientation‐independent microhardness of 1167 ± 34 kg/mm2. The indentation size effect (ISE) was further investigated through lubricated indentation hardness measurements. Lubrication of the test specimen surface significantly reduces the ISE. Results indicate that friction between the test specimen surface and the indenter facets is a major portion of the ISE.

The aim of the submitted work is to study the relationship between the local deformation and the indentation size effect (ISE). A local value of reduction of the area (Z) was used as the measure of the deformation. Applied loads in the micro-hardness test ranged between 0.09807 to 0.9807 N. The micro-hardness was measured on the cross section in the longitudinal axis of the fractured sample after the uniaxial tension test. The material of the sample was 99.5% aluminium. The influence of both load and deformation on the ISE was evaluated by the analysis of variance (ANOVA). The influence of the load was also evaluated by Meyer’s index n, PSR method, and Hays–Kendall approach. The influence of both factors on the measured value of micro-hardness and therefore on the ISE is statistically significant. The ISE is normal in the areas with high deformation, on the contrary, in areas with low deformation, it has a “reverse” character. The difference between load independent “true hardness” and measured micro-hardness HV0.05 increases with increasing deformation.

This research investigates deformation behavior of polystyrene (PS) as a thermoplastic resist material for the thermal nanoimprint lithography (T-NIL) process. Molecular dynamics modeling was conducted on a PS substrate with dimensions 58 × 65 × 61 Å that was imprinted with a rigid, spherical indenter. The effect of indenter size, force, and imprinting duration were evaluated in terms of indentation depth, penetration depth, recovery depth, and recovery percentage of the polymer. The results show that the largest indenter, regardless of force, has the most significant impact on deformation behavior. The 40 Å indenter with a 1 µN of force caused the surface molecules to descend to the lowest point compared to the other indenters. An increase in indenter size resulted in higher penetration depth, recovery depth, and recovery percentage. Higher durations of imprint cycle (400 fs) resulted in plastic deformation of the PS material with minimal recovery (4 Å). The results of this research lay the foundation for explaining the effect of several T-NIL process parameters on virgin PS thermoplastic resist material.

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.

The increasing hardness with decreasing penetration depth, referred to as indentation size effect (ISE) was previously investigated experimentally and theoretically by many researchers, however the mechanisms responsible for ISE are still being discussed. Generally, ISE is related to the density of geometrically necessary dislocation stored within a small volume beneath the indenter tip. In this study ISE is investigated experimentally in a single crystal copper using spherical indenter tips of different radii. Some new aspects of ISE are shown: a qualitative change of shape of residual impression (pile-up/sink-in pattern) when tip radius or load is modified, an increase of maximum pop-in load with decrease of tip radius as well as the well-known increase of hardness when tip radius decreases are analyzed. As we observe a difference of the residual imprint morphology which depends on tip radius and load, we apply two methods of hardness estimation: true hardness and nominal hardness. The former is determined on the basis of direct measurement of the contact area while accounting for a specific pile-up pattern, while the latter is determined by measuring the contact area using residual penetration depth. We show that hardness–tip radius relationship has a linear form for the nominal hardness and bilinear form for the true hardness.

The height difference Δhb between the ideally sharp Berkovich indenter tip and a Δhb rounded tip was measured by direct observation using atomic force microscopy (AFM). The accuracy of the indirect area function method for measuring h was confirmed. The Δhb indentation size effects (ISE) in (100) single crystal copper, (100) single crystal tungsten, and fused quartz were characterized by applying the ISE model considering the rounded tip effect. The model fits the data these materials well, even though fused quartz does not deform by dislocations. However, a very small value of the ISE characteristic length h' was obtained for fused quartz. The present h' value for (100) copper is 32% larger than a previously-measured value for polycrystalline copper. This may indicate that grain boundaries suppress the dislocation activity envisioned in the ISE model.