Low Indentation Depths Research Articles

Indentation size effects of mechanical behavior and shear transformation zone in thin film metallic glasses

Indentation size effect of mechanical behavior and shear transformation zone (STZ) in magnetron-sputtered La-Co-Al, Zr-Cu-Ni-Al, Ni-Nb and W-Ru-B thin film metallic glasses (TFMGs) has been systematically investigated with a geometrically self-similar Berkovich indenter. Unlike the crystalline metals and bulk-sized MG, the hardness in TFMGs is smaller in the lower indentation depth, which accords with the lower creep resistance and STZ activation energy. By analogy with the geometrically necessary dislocations in the crystalline materials, here we propose that the “strain-gradient-induced” STZs in MGs underneath a geometrically self-similar tip have the weakening effect instead of strengthening effect. The intrinsic profuse fertile sites in TFMGs limit the strengthening effect from scarcity of STZ nucleation sites and highlight the softening effect from “strain-gradient-induced” STZs, eventually conducing to the reverse ISE in TFMGs.

Mechanical modeling and characterization of meniscus tissue using flat punch indentation and inverse finite element method.

In this paper, to characterize the mechanical properties of meniscus by considering its local microstructure, a novel nonlinear poroviscoelastic Finite Element (FE) model has been developed. To obtain the mechanical response of meniscus, indentation experiments were performed on bovine meniscus samples. The ramp-relaxation test scenario with different depths and preloads was designed to capture the mechanical characteristics of the tissue in different regions of the medial and lateral menisci. Thereafter, a FE simulation was performed considering experimental conditions. Constitutive parameters were optimized by solving a FE-based inverse problem using the heuristic Simulated Annealing (SA) optimization algorithm. These parameters were ranged according to previously reported data to improve the optimization procedure. Based on the results, the mechanical properties of meniscus were highly influenced by both superficial and main layers. At low indentation depths, a high percentage relaxation (p < 0.01) with a high relaxation rate (p < 0.05) was obtained, due to the poroelastic and viscoelastic nature of the superficial layer. Increasing both penetration depth and preload level involved the main layer response and caused alterations in hyperelastic and viscoelastic parameters of the tissue, such that for both layers, the shear modulus was increased (p < 0.01) while the rate and percentage of relaxation were decreased (p < 0.01). Results reflect that, shear modulus of the main layer in anterior region is higher than central and posterior sites in medial meniscus. In contrast, in lateral meniscus, posterior side is stiffer than central and anterior sides.

Influence of solid solution strengthening on the local mechanical properties of single crystal and ultrafine-grained binary Cu–AlXsolid solutions

Abstract

Orientation-dependent mechanical behavior and phase transformation of mono-crystalline silicon

We perform a large-scale molecular dynamics simulation of nanoindentation on the (100), (110), and (111) oriented silicon surface to investigate the orientation-dependent mechanical behavior and phase transformation of monocrystalline silicon. The results show both the remarkable anisotropic mechanical behavior and structure phase transformation of monocrystalline silicon. The mechanical behavior of the (110) and (111) oriented surfaces are similar (has a high indentation modulus, low critical indentation depth for the onset of plastic deformation) but quite different from the (100) oriented surface. The mechanical behavior is carefully linked to the phase transformation. The formation of crystalline bct5 phase and β-Si phase is the fundamental phase transformation mechanism for (100) oriented surface. But, a large number of amorphous silicon can be found beneath the indenter for (110) and (111) oriented surface beside the bct5 phase and β-Si phase. The β-Si phase region is relatively small for (110) and (111) oriented surface, even cannot be detected for (111) oriented surface. This result highlights the dominating role of the amorphous transformation in the mechanical behavior of monocrystalline silicon. Additionally, our results indicate that the high pressure phases form a symmetrical, anisotropic pattern on the indented surface for all three oriented surface which is linked to the active {111}〈110〉 slip systems.

Role of grain boundary on the sources of size effects

The present paper investigates the effects of grain boundary (GB) on the sources of size effects. Up to now, several studies have been conducted to address the role of GBs in size effects from the atomistic point of view. However, a study which addresses the effects of GB on different governing mechanisms of size effects as the sample length scale varies has not been presented yet. Here, samples with different length scales are studied to capture the role of GB in size effects as the grain size changes. The response of single and bi-crystal Ni thin films with two different sizes are studied during nanoindentation experiment using large scale atomistic simulation. Various symmetric and asymmetric tilt GBs are incorporated to study the effects of GB geometry on the response of samples during nanoindentation. The sources of size effects are analyzed in each sample using the atomistic information obtained from the simulations. The results show that the size effects mechanism influenced by GBs changes from dislocation nucleation and source exhaustion to the forest hardening mechanism as the grain size increases. In the case of small bi-crystal samples, dislocation nucleation and source exhaustion govern the size effects. The GB contributes to the dislocation nucleation beneath the indenter which reduces the strength of sample by providing required dislocations to sustain the imposed plastic deformation. Also, the GB itself is the source of defects which can affect the sample strength depending on the indentation depth at which the dislocation is nucleated from the grain boundary. Increasing the indentation depth, some of the dislocations are blocked by the GB. However, there is no noticeable additional hardness due to the dislocations blockage by GB. Furthermore, the results show that the coherent twin boundaries shows the best performance during the nanoindentation. In the case of large bi-crystal samples, the GB does not influence the size effects at lower indentation depths where the source exhaustion is the controlling mechanism of size effects. However, at higher indentation depths, the dislocation interaction with GB contributes to the forest hardening mechanism and induces some hardening. It is observed that the dislocations are firstly absorbed by the GB. Increasing the indentation depth, some dislocations start dissociating into the next grain. However, it is observed that more dislocations are nucleated in the upper grain. The results show that the main role of GB at larger length scale is to change the pattern of dislocation structure in a way that the dislocations are piled up near the GB which increases the hardness.

3D Analysis and Nano-Indentation Mechanical Characterization of a Commercial Zr44-Ti11-Cu10-Ni10-Be25 Metal Glassy Alloy

Stiffness and elastic mechanical properties of the Zr44-Ti11-Cu10-Ni10-Be25 metal glass Alloy have been investigated by nanoindentation and Atomic Force Microscopy.Continuous stiffness measurements were carried out on the as received samples. Max indentation depth of 2000 Nm has been chosen. A 3D analysis of the indent traces has been performed using a Atomic Force Microscope: pile-up at the indentation edge was observed. These metallic glasses, therefore, although showing brittle like linear elastic behaviour up to failure are still capable of undergoing plastic shear flow at the nanoscale level that may potentially lead to high material ultimate properties. Elastic modulus of 116,2 ± 0,9 GPa has been found to be independent on indentation depth while a high hardness of 8,0 ± 0,8 GPa has been measured at low indentation depths (100 nm) that progressively reduces to a constant value of 7,0 ± 0,1 GPa at increasing depths (up to 2000 nm).

Finite element study for conical indentation of elastoplastic micropolar material

Numerous experiments have repetitively shown that the material behavior presents effective size dependent mechanical properties at scales of microns or submicrons. In this paper, the size dependent behavior of micropolar theory under conical indentation is studied for different indentation depths and micropolar material parameters. To illustrate the effectiveness of the micropolar theory in predicting the indentation size effect (ISE), an axisymmetric finite element model has been developed for elastoplastic contact analysis of the micropolar materials based on the parametric virtual principle. It is shown that the micropolar parameters contribute to describe the characteristic of ISE at different scales, where the material length scale regulates the rate of hardness change at large indentation depth and the value of micropolar shear module restrains the upper limit of hardness at low indentation depth. The simulation results showed that the indentation loads increase as the result of increased material length scale at any indentation depth, however, the rate of increase is higher for lower indentation depth, relative to conventional continuum. The numerical results are presented for perfectly sharp and rounded tip conical indentations of magnesium oxide and compared with the experimental data for hardness coming from the open literature. It is shown that the satisfactory agreement between the experimental data and the numerical results is obtained, and the better correlation is achieved for the rounded tip indentation compared to the sharp indentation.

Nanoindentation and AFM Studies on Tungsten Carbide Crystals in WC-Co Hardmetal

The room temperature elastic and plastic properties of the WC grains of WC-9%Co hardmetal were investigated by nanoindentation and atomic force microscope (AFM). Two easily distinguishable crystallographic planes (using EBSD analyses) were investigated, namely the basal and prismatic planes, on which nanoindentation tests were performed with different applied loads from 1 mN to 50 mN to determine the hardness and reduced-modulus, respectively. The results deriving from nanoindentation show significantly higher indentation hardness on basal planes (HIT=28.9±0.1 GPa) than on prismatic ones (HIT=21.9±0.1 GPa) over 10 mN load. For loads below that the results were inconsistent. The corresponding indents were checked by AFM and correct values of hardness were found. The discrepancies indicate the inaccuracy of the built-in evaluation procedure (Oliver-Pharr method) in this low load, or more precisely in the low indentation depth range. It is pointed out that below 50 nm contact depth the applied built-in contact area-contact depth function is not appropriate and a new correct contact area-contact depth function is proposed, thus the resulting recalculated hardness values are in good agreement with the AFM measurements.

Characterization of Anisotropy in Hardness and Indentation Modulus by Nanoindentation

This paper provides a useful guide how to characterize material anisotropy by nanoindentation. Hardness and indentation modulus of austenitic stainless steel (grade A304) were characterized by instrumented indentation at the grain scale (at low indentation load and depth of penetration). We applied the grid indentation method on an area containing several grains with different crystallographic orientation which was simultaneously characterized by electron back-scatter diffraction. Hardness and indentation modulus dependencies on crystallographic orientation were then evaluated and compared with single crystal Young’s modulus and finite element simulations.

Effect of Crystallographic Orientation on Hardness and Indentation Modulus in Austenitic Stainless Steel

The most commonly used method for the analysis of instrumented indentation test (Oliver-Pharr) is based on isotropic elastic solution of contact problem which is not necessarily valid when indenting at the scale of one (anisotropic) grain. In this paper, we performed the grid indentation method at the sub-micron scale (at low indentation load and depth of penetration) on an area containing several grains with different crystallographic orientation which was simultaneously characterized by electron back-scattered diffraction. Measured dependencies of hardness and indentation modulus on crystallographic orientation were compared with analytical solution and finite element simulations.

A study on nanoindentation and tribological behaviour of multifunctional ZnO/PMMA nanocomposite

This work aims to compare the scratch hardness with the indentation hardness of ZnO nanoparticle reinforced polymethylmethacrylate (ZnO/PMMA) composites obtained from nanoindentation measurements. 50μm thick films ZnO/PMMA nanocomposites were produced by the in-situ spin coating method. Scratch hardness was measured from the scratch width origin at low load during the course of the scratch measurements. A good correlation was found between the scratch hardness and the indentation hardness at low indentation depth, where a linear relationship between hardness and the reinforcement content of ZnO nanoparticles was observed. The composite was structurally established by transmission electron microscopy and furrier transform infrared spectroscopy.

Exfoliated Graphite Reinforced PMMA Composite: A Study on Nanoindentation and Scratch Behavior

The present work aims to compare the scratch hardness (Hs) with the indentation hardness (HIT) obtained from nanoindentation measurements of exfoliated graphite/poly (methyl methacrylate) (EG/PMMA) composites. EG/PMMA composites with thickness 50 μm each were produced by in situ melt mixing method. Scratch hardness was measured from the scratch width formed at low applied load during the course of the scratch measurements. The measured scratch hardness values were compared with the indentation hardness. There is a good correlation between the scratch hardness and the indentation hardness at low indentation depths, with a linear relationship between hardness and the reinforcement content of exfoliated graphite.

Elevated temperature nanoindentation behaviour of polyamide 6

AbstractIt has been found, in this study, that there is no close correlation between the tensile and nanoindentation moduli of polyamide 6 (PA6) at high temperatures. It is demonstrated that heat modifies the surface of PA6 specimens, but its effect on the nanomechanical properties is minor. The main spurious factor which affects the nanoindentation results is adhesion, especially at low indentation depths. The overestimation in the measured indentation moduli can be corrected by performing indentations with loads high enough so that the modulus is independent of the applied load. It is concluded that the lack of strict correlations between the tensile and indentation moduli (after corrections of adhesion) is caused by the shift in the glass transition temperature of PA6 owing to the hydrostatic stress imposed by the indenter. Further proof is given with two examples on hydrostatic pressure‐dependent polymers: polytetrafluoroethylene and polycarbonate. Copyright © 2011 Society of Chemical Industry

Modification of composite hardness models to incorporate indentation size effects in thin films

The indentation hardness of copper films of thickness 25 to 1400 nm on oxidized silicon substrates is determined by nanoindentation. The load-displacement curves are analysed using the Oliver and Pharr method. An indentation size effect is observed at low relative indentation depths for the copper films. Composite hardness models are applied to the data without an indentation size effect and the Korsunksy and Puchi–Cabrera models are found to give very good fits to this data. The Nix and Gao mechanism based strain gradient plasticity (MSG) model is used to account for the indentation size effect. An attempt is made to modify the existing composite hardness models using the MSG model to incorporate indentation size effect. By modification of both the Korsunsky and Puchi-Cabrera models a good fit to the entire range of data is obtained.

Comparison between nanoindentation and scratch test hardness (scratch hardness) values of copper thin films on oxidised silicon substrates

In this paper we measured for the first time the scratch hardness of copper thin films and compared this with hardness measured from nanoindentation. Copper films with thicknesses in the range 100 nm to 500 nm were deposited by rf magnetron sputtering on silicon substrates. Scratch hardness was determined by CSM™ scratch tester using scratch widths at low loads. The measured hardness values were compared with conventional nanoindentation hardness measurement by CSM™ nanohardness tester. At these low indentation depths there is a good correlation between the scratch hardness and the nanoindentation hardness, with an increase in hardness as the film thickness decreases.

Determination of plastic properties of polycrystalline metallic materials by nanoindentation: experiments and finite element simulations

Nanoindentation experiments at low indentation depths are strongly influenced by micromechanical effects, such as the indentation size effect, pile-up or sink-in behaviour and crystal orientation of the investigated material. For an evaluation of load–displacement data and a reconstruction of stress–strain curves from nanoindentations, these micromechanical effects need to be considered. The influence of size effects on experiments were estimated by comparing the results of finite element simulation and experiments, using uniaxial stress–strain data of the indented material as input for the simulations. The experiments were performed on conventional and ultrafine-grained copper and brass, and the influence of the indentation size effect and pile-up formation is discussed in terms of microstructure. Applying a pile-up correction on Berkovich and cube-corner indentation data, a piecewise reconstruction of stress–strain curves from load–displacement data is possible with Tabor's concept of representative strain. A good approximation of the slope of the stress–strain curve from the indentation experiments is found for all materials down to an indentation depth of 800 nm.

Incipient yielding behavior during indentation for gold thin films before and after annealing

We studied the deformation mechanisms and mechanics during indentation of polycrystalline gold thin films at depths below 100 nm. The measured material hardness decreased from 2.1 ± 0.1 to 1.7 ± 0.1 GPa after annealing for 4 h at 177 °C. Upon closer inspection, the hardness trends in the gold thin films were discovered to vary according to the indentation depth. At nanometer depths, the material hardness was quantified using multiple parameters, some of which were independent of the area calibration for the tip. The annealed specimen was very “hard” at low indentation depths, relatively soft at moderate indentation depths, and finally harder until the grain-size limit was reached. The as-deposited specimen demonstrated a relatively continuous harness trend as function of indentation depth, exhibiting monotonic convergence to Hall–Petch limited behavior. Discrete displacement jump events (excursions or “pop-ins”) were frequently observed for the annealed specimen but not for the as-deposited specimen. Variation in hardness, excursion activity, and displacement during the hold at maximum load was observed according to the applied loading, which was parametrically varied at constant strain rates. Hardness results are explained in terms of the population and evolution of defects present within the specimens. The population of point defects is also influential, and critical thermal fluctuations, as well as the thermally activated process of diffusion, are believed to influence hardness at the specimen’s free surface and further into its volume. After converging to a monotonic trend (proper tip engagement), the modulus of the gold was measured to be 106.0 ± 12.9 and 101.3 ± 6.0 GPa for the respective Au/Cr/Si specimens. These values exceeded predictions from the aggregate polycrystalline material theory, a representation used to estimate results for anisotropic single crystals. Exaggerated modulus measurements are explained as the result of the contribution of modulus mismatch with the substrate, pileup at the indentor tip, residual stress in the films, and crystallographic anisotropy of the gold.

Material structure, stiffness, and adhesion: why attachment pads of the grasshopper (Tettigonia viridissima) adhere more strongly than those of the locust (Locusta migratoria) (Insecta: Orthoptera)

The morphology, ultrastructure, effective elastic modulus, and adhesive properties of two different smooth-type attachment pads were studied in two orthopteran species. Tettigonia viridissima (Ensifera) and Locusta migratoria (Caelifera) have a similar structural organization of their attachment pads. They both possess a flexible exocuticle, where the cuticular fibrils are fused into relatively large rods oriented at an angle to the surface. The compliant material of the pad contributes to the contact formation with the substrate. However, the pad material structure was found to be different in these two species. L. migratoria pads bear a thick sub-superficial layer, as well as a higher density of rods. The indentation experiments showed a higher effective elastic modulus and a lower work of adhesion for L. migratoria pads. When the indentations were made at different depths, a higher effective elastic modulus was revealed at lower indentation depths in both species. This effect is explained by the higher stiffness of the superficial pad layer. The obtained results demonstrate a clear correlation between density of the fibres, thickness of the superficial layer, compliance of the pad, and its adhesive properties. Such material structures and properties may be dependent on the preferred environment of each species.

Determination of HgCdTe elasto-plastic properties using nanoindentation

Depth sensing indentation has been used to investigate the elasto-plastic behavior of Hg0.7Cd0.3Te prepared by molecular beam epitaxy, liquid phase epitaxy, as well as of bulk Hg0.7Cd0.3Te prepared by the modified Bridgman method. It was found that Hg0.7Cd0.3Te was characterized by a modulus of elasticity of E avg ∼ 50 GPa and hardness of H avg ∼ 0.66 GPa, independent of growth technology. The measured hardness was observed to increase with decreasing size of indentation owing to the nucleation of dislocations within the plastic zone. The elasto-plastic response of the samples to nanoindentation was observed to be purely elastic at low indentation depths and developed into ∼10% elastic and ∼90% plastic response, with an increase in penetration contact depth to above 100 nm exhibiting significant amounts of creep. The transition from purely elastic to elasto-plastic behavior has been observed to be marked by discontinuities, or “pop-in” events in the indenter load-penetration curves, with the indentation zone maximum sheer stress varying with HgCdTe growth method in the range 1.1–1.8 GPa. This onset and subsequent flow of plasticity is postulated to be associated with the spontaneous nucleation and propagation of dislocations.

Influence of indentation depth on the determination of the apparent Young's modulus of bi-layer material: Experiments and numerical simulation

Depth sensing indentation experiments have been conducted on stainless steel thin films deposited by reactive magnetron sputtering on AU4G aluminium-alloy substrates to highlight that elastic response of bi-layer materials can be specific of the coating alone only for very low indentation depths. It is shown experimentally that Bückle's rule is at least one order of magnitude too high when applied by default to determine coating-specific elastic response. These results have been confirmed by boundary element numerical simulation underlining that elastic response of a thin film deposited on substrate deviates from the coating’s response above relative indentation depth around 1–2%.