Indenter Radius Research Articles

The role of indenter radius on spherical indentation of high purity magnesium loaded nearly parallel to the c-axis

The current work proposes two main contributions based on a study of the effect of indenter radius on spherical indentation of magnesium where loading is nearly parallel to the c-axis. First, it is illustrated that high purity magnesium shown a strong indentation size effect for spherical indentation. The CRSS for basal slip and extension twinning are estimated by extrapolation of the RSS data for an infinitely large indenter radius. Second, it is shown that the number of twins which de-twin during unloading depends on the indenter size, indentation depth, and the magnitude of the plastic strain and stress under the indenter.

Implications of Multi-asperity Contact for Shear Stress Distribution in the Viable Epidermis – An Image-based Finite Element Study

Understanding load transfer mechanisms from the surface of the skin to its deeper layers is crucial in gaining a fundamental insight into damage phenomena related to skin tears, blisters and superficial/deep tissue ulcers. It is unknown how shear stresses in the viable epidermis are conditioned by the skin surface topography and internal microstructure and to which extent their propagation is conditioned by the size of a contacting asperities.In this computational study, these questions were addressed by conducting a series of contact finite element analyses simulating normal indentation of an anatomically-based two-dimensional multi-layer model of the skin by rigid indenters of various sizes and sliding of these indenters over the skin surface. Indentation depths, local (i.e. microscopic) coefficients of friction and Young's modulus of the stratum corneum were also varied. For comparison purpose and for isolating effects arising purely from the skin microstructure, a geometrically-idealised equivalent multi-layer model of the skin was also considered.The multi-asperity contact induced by the skin topographic features in combination with a non-idealised geometry of the skin layers lead to levels of shear stresses much higher than those produced in the geometrically-idealised case. These effects are also modulated by other system parameters (e.g. local coefficient of friction, indenter radius).These findings have major implications for the design and analyses of finite element studies aiming at modelling the tribology of skin, particularly if the focus is on how surface shear stress leads to damage initiation which is a process known to occur across several length scales.

Cylindrical lateral depth-sensing indentation of anisotropic elastic tissues: Effects of adhesion and incompressibility

ABSTRACTA two-dimensional frictionless adhesive contact problem for a parabolic indenter pressed against an orthotropic elastic layer resting on a smooth rigid substrate is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. In the case of a relatively small contact zone with respect to the layer thickness, the fourth-order asymptotic solution (up to terms of order ) is obtained, and the pull-off force is expanded in terms of the non-dimensional measure of the work of adhesion. In particular, a pinch/compression method for soft tissue is considered, and the testing methodology is suggested based on a least-squares best fit of the first-order asymptotic model to the depth-sensing indentation data for recovering two of the three independent elastic moduli which characterize an incompressible transversely isotropic material. The case of a weakly compressible material, which is important for biological tissues, is also discussed. The developed asymptotic model can be effectively used for small values of a certain dimensionless parameter, which is proportional to the work of adhesion and the indenter radius squared, on the one side, and inversely proportional to the effective elastic modulus and the elastic layer thickness cubed, on the other.

Unified curve of the edge chipping resistance in connection with the rounding radius indenter

The results of a combined computational and experimental research into the fracture resistance of ceramic materials by specimen edge chipping are provided. The chipping was performed with conic diamond indenters that had spherical tip radii of 100, 200 and 400μm. The computational analysis was conducted on the basis of finite element modeling by means of ANSYS software. The parameters of the basic distances in an analysis of the stress, strain, and displacement fields in the chipping zone for the tests (upper and lower limit) have been established for the above-mentioned indenters in order to ensure the correct comparative assessment of the materials under research. Unified curves of edge chipping resistance of the ceramic materials have been obtained for the indenters with various spherical tip radii.

On the determination of elastic moduli of cells by AFM based indentation

The atomic force microscopy (AFM) has been widely used to measure the mechanical properties of biological cells through indentations. In most of existing studies, the cell is supposed to be linear elastic within the small strain regime when analyzing the AFM indentation data. However, in experimental situations, the roles of large deformation and surface tension of cells should be taken into consideration. Here, we use the neo-Hookean model to describe the hyperelastic behavior of cells and investigate the influence of surface tension through finite element simulations. At large deformation, a correction factor, depending on the geometric ratio of indenter radius to cell radius, is introduced to modify the force-indent depth relation of classical Hertzian model. Moreover, when the indent depth is comparable with an intrinsic length defined as the ratio of surface tension to elastic modulus, the surface tension evidently affects the indentation response, indicating an overestimation of elastic modulus by the Hertzian model. The dimensionless-analysis-based theoretical predictions, which include both large deformation and surface tension, are in good agreement with our finite element simulation data. This study provides a novel method to more accurately measure the mechanical properties of biological cells and soft materials in AFM indentation experiments.

Radius and angle determination of diamond Berkovich indenter

Abstract In this work, a new measurement method based on atomic force microscope (AFM) and confocal laser scanning microscope (CLSM) is proposed to determine the radius and angle parameters of diamond Berkovich indenter. In order to accurately describe the real tip shape, a comprehensive geometrical model that takes the effects of indenter edge radius and tip radius into account is established. Resultantly, a sophisticated area function is formulated to fit the AFM acquired topographies. Comparison reveals that the fitted data of indenter radius have a satisfactory consistency with the experimental results. For the determination of angle parameters, the CLSM relevant 3D topography acquisition, angle calculation and error correction methods are constructed. Experimental observations validate that the CLSM method is capable of accurately determining the angle parameters of diamond Berkovich indenter.

Atomistic simulation on nanomechanical response of indented graphene/nickel system

Molecular dynamics (MD) simulations were carried out to study the nanoindentation mechanical properties of graphene/nickel system. The effects of indenter radius, loading speed, and number of graphene layers were investigated. The results show that the indentation response of graphene/nickel system includes elastic regime, plastic regime and graphene ruptures regime. The contact stiffness, elastic capacity and the load bearing capacity are visibly improved by graphene coverage. The indenter radius significantly influences the ultimate indentation depth and corresponding forces. The increasing number of graphene layers significantly enhances the elastic capacity and the ultimate forces of graphene/nickel system.

Precise measurements of capsule mechanical properties using indentation

Application of elastic theory to experimental data of capsule and particle compression under-predicts the value of material properties such as the Young's modulus by up to 100% when the effect of the rigid substrate is neglected, as is commonly done in the literature. Results of numerical simulations, spanning the range from thin-shelled capsules to solid particles, are presented in terms of correction factors that account for the substrate. In addition, the scaling relationship between indentation force and displacement is characterised for arbitrary shell thicknesses and indenter radii.

Scratch resistance of superhard carbon coatings – A new approach to failure and adhesion evaluation

Scratch testing was methodically studied by examining the adhesion of tetrahedral amorphous carbon coatings (ta-C). Usually, critical loads LC are used as a parameter to characterize the adhesion strength of coatings in scratch testing. However, the comparability of the critical loads for different materials and coating thicknesses is limited. The critical loads result from different coating failure mechanisms that require a careful investigation with respect to plastic substrate deformation and coating thickness.In this work, the different failure modes of ta-C coatings occurred in strong dependence on the geometrical proportions (indenter radius and coating thickness) for a wide range of hardness and Young's modulus: Adhesive failure in the center of the groove was located at cohesive bending cracks for coating thickness of 1 to 3μm. For increasing coating thickness failure by spallations was found instead of bending cracks. At the edge of the groove outside the scratch-induced substrate plasticity, wing-shaped delaminations were observed for all test and coating configurations.A new method was introduced that quantifies the adhesive failure by means of segmentation of an optical image. The relative area of delamination was found to correlate with calculated shear stresses at the interface plane outside the heavily deformed scratch track. Furthermore, it was possible to distinguish the effect of two different plasma pretreatments on adhesion regardless of the coating thickness. Thus, this new method expanded the information gained from the standard scratch test and allows a better interpretation of coating adhesion than the LC-evaluation.

Finite element simulation of Reference Point Indentation on bone

Reference Point Indentation (RPI) is a novel technique aimed to assess bone quality. Measurements are recorded by the BioDent instrument that applies multiple indents to the same location of cortical bone. Ten RPI parameters are obtained from the resulting force–displacement curves. Using the commercial finite element analysis software Abaqus, we assess the significance of the RPI parameters. We create an axisymmetric model and employ an isotropic viscoelastic-plastic constitutive relation with damage to simulate indentations on a human cortical bone. Fracture of bone tissue is not simulated for simplicity. The RPI outputs are computed for different simulated test cases and then compared with experimental results, measured using the BioDent, found in literature. The number of cycles, maximum indentation load, indenter tip radius, and the mechanical properties of bone: Young׳s modulus, compressive yield stress, and viscosity and damage constants, are varied. The trends in the RPI parameters are then investigated.We find that the RPI parameters are sensitive to the mechanical properties of bone. An increase in Young׳s modulus of bone causes the force-displacement loading and unloading slopes to increase and the total indentation distance (TID) to decrease. The compressive yield stress is inversely proportional to a creep indentation distance (CID1) and the TID. The viscosity constant is proportional to the CID1 and an average of the energy dissipated (AvED). The maximum indentation load is proportional to the TID, CID1, loading and unloading slopes, and AvED. The damage parameter is proportional to the TID, but it is inversely proportional to both the loading and unloading slopes and the AvED. The value of an indenter tip radius is proportional to the CID1 and inversely proportional to the TID. The number of load cycles is inversely proportional to an average of a creep indentation depth (AvCID) and the AvED. The indentation distance increase (IDI) is strongly inversely proportional to the compressive yield stress, and strongly proportional to the viscosity constant and maximum applied load, but has weak relation with the damage parameter, indenter tip radius, and elastic modulus. This computational study advances our understanding of the RPI outputs and provides a starting point for more comprehensive computational studies of the RPI technique.

High-precision radius measurement of ball indenter

Abstract To solve the problem of calibrating the radius of a ball indenter in a hardness tester, a laser confocal radius measurement and calibration method for the ball indenter is proposed without separating the ball from the body of the indenter. The laser confocal radius measurement and calibration method uses the maximum of the confocal axial intensity curve to precisely identify the cat’s eye and confocal position of the test ball indenter. The distance between these two positions is then measured to achieve high-precision radius measurement. The theoretical analyses and experimental results indicate that the radius measurement uncertainty of the ball indenter with a diameter of 1.5875 mm is within 0.12 μm.

Effect of Actual Indenter Shape on the Results of Spherical Nanoindentation

Actual shape of the diamond spherical indenter of nominal radius 20 μm was investigated in this study. 3D reconstruction was performed by atomic force microscope and by the method of stereopair using SEM images of the tip taken under several different angles. The results were compared with the shape obtained indirectly by the calibration performed on specimens with known Young’s modulus. It was found that lower effective values of tip radius for the small penetration depths are caused by the irregular geometry of contact between indenter and specimen surface. With increasing penetration depth the radius increased to the theoretical values and it decreased again for high penetration depths. The stress-strain curves were determined using corrected effective indenter radius.

Spherical indentation of porous ceramics: Cracking and toughness

A combined experimental-numerical approach is used to characterise the fracture of a porous bulk ceramic material (La0.6Sr0.4Co0.2Fe0.8O3) with porosities of 5–45%, undergoing spherical indentation. The Gurson model was used in FEM to describe the porosity densification. Indentation-induced radial cracks were observed, when the applied contact pressure exceeded threshold values, with no Hertzian ring-cone cracks found. FEM analysis indicated that the cracks propagated mainly during unloading, driven by the tensile hoop stress generated near the contact circle. The stress intensity at the crack tip was estimated using an approximate analysis of the FEM stress field to derive toughness values that were consistent with values determined by conventional methods, provided that the crack length is sufficiently large compared with the contact radius and can be measured accurately. The absence of ring-cone cracks during loading is due to the material’s high modulus-to-hardness ratio and the small indenter radius as predicted by established theory.

Brittle-Ductile Transition Index for Small-Contact Damages to Geo-Materials

Based on loading and failure analyses, a brittle-ductile transition index IT is derived for ball indentation, ball impingement, and liquid drop impact: IT=KIcn/σC2 n/3. Materials with low index numbers respond brittle (elastic), whereas materials with high index numbers respond ductile (plastic). For n=2, the index has a linear relationship to a critical indenter (particle, drop) radius, which determines whether materials respond elastically or plastically. The index is inversely related to the ratio between critical plastic load and critical elastic load. The numbers for n depend on the loading situation: ball indentation, n=6/3; ball impingement, n=5/3; liquid drop impact, n=2/3. Experimental results are analyzed to verify the index. Additional transition situations are analyzed and linked to the transition index.

Universal scaling laws for homogeneous dislocation nucleation during nano-indentation

We perform atomistic simulations to study the mechanism of homogeneous dislocation nucleation in two dimensional (2D) hexagonal crystals during nanoindentation with a circular indenter of radius R. We study both a realistic embedded atom method (EAM) potential for Al in addition to simple pair-wise potentials: Lennard-Jones, Morse, and Hookean springs. The nucleation process is governed by the vanishing of the energy associated with a single energy eigenmode. The critical eigenmode, or dislocation embryo, is found to be localized along a line (or plane in 3D) of atoms with a lateral extent, ξ, at some depth, Y⁎, below the surface. For all interatomic potentials, the scaled critical load, Fc/R, and scaled critical contact length, Cc/R, decrease to R-independent values in the limit of large R. However, ξ/R and Y⁎/R display non-trivial scaling with R despite the R independence of Fc/R and Cc/R. We show that although both the interaction potential and the orientation of the lattice affect the prefactors in the scaling relations, all the scaling laws are robust. Furthermore, we show that a stability criterion proposed by Van Vliet et al. based on the minimum eigenvalue, Λ, of the local acoustic tensor predicts the location, orientation, and polarization of the dislocation embryo with a high degree of accuracy for all potentials and crystallographic orientations. However, we also show that, for all crystallographic orientations and interaction potentials, Λ erroneously indicates instability before the true instability occurs.

A new tribological experimental setup to study confined and sheared monolayers.

We have developed an original experimental setup, coupling tribology, and velocimetry experiments together with a direct visualization of the contact. The significant interest of the setup is to measure simultaneously the apparent friction coefficient and the velocity of confined layers down to molecular scale. The major challenge of this experimental coupling is to catch information on a nanometer-thick sheared zone confined between a rigid spherical indenter of millimetric radius sliding on a flat surface at constant speed. In order to demonstrate the accuracy of this setup to investigate nanometer-scale sliding layers, we studied a model lipid monolayer deposited on glass slides. It shows that our experimental setup will, therefore, help to highlight the hydrodynamic of such sheared confined layers in lubrication, biolubrication, or friction on solid polymer.

Dislocation Formation via an r-Plane Slip Initiated by Plastic Deformation during Nano-Indentation of a High Quality Bulk GaN Surface

ABSTRACTBulk GaN substrates are of significant interest because they offer both high quality and low dislocation densities. Our group has previously reported the formation and movement of dislocations in high quality bulk GaN in response to nano-indentation. We have also proposed a mechanism involving an r-plane (-1012) slip initiated by plastic deformation during a pop-in event, a theory that was supported by molecular dynamics simulations. Herein, we present experimental evidence for this r-plane (-1012) slip mechanism in an indented GaN surface using nano-indentation with an indenter having a smaller radius (∼100 nm) and imparting a lower pop-in load (∼400 μN) compared to the values applied in our previous studies. In addition, this study included TEM observations immediately after the plastic deformation, such that cross-sectional TEM images of the indented surface of the c-plane bulk GaN were acquired just after the pop-in event. The pyramidal dislocation line of an r-plane slip was clearly observed and was inclined by 43° relative to the c-plane surface. Neither a basal c-plane slip nor a prism m-plane slip occurred as a result of dislocation multiplication as secondary or tertiary slip systems, even though these slips had been identified when employing a larger radius indenter and a higher pop-in load. From these experimental results, we were able to confirm that plastic deformation in bulk GaN is initiated via an r-plane slip.

Atomistic simulations of the nanoindentation-induced incipient plasticity in Ni3Al crystal

In this work, the indentation-induced incipient plasticity of Ni3Al crystal is investigated by performing molecular dynamics (MD) simulations. Simulation results reveal that the incipient plasticity of Ni3Al is originated from the homogeneous nucleation of the 1/6〈112〉-type Shockley partial dislocation. The critical load, critical contact pressure, dislocation nucleation site and active slip system are significantly affected by crystallographic orientation, model size, indenter radius and temperature. The choice of interatomic potential has significant implications for the indentation behavior of Ni3Al. Some benchmarks for evaluating the credibility of interatomic potentials are presented. The pop-in phenomena are correlated with dislocation generation, multiplication and reactions. The formation mechanisms of complex stacking faults (CSFs), antiphase boundaries (APBs) and superlattice intrinsic stacking faults (SISFs) are clarified. The highest indentation modulus is obtained in (111) indentation followed by the (110) and (100) cases. The indentation modulus and the depth of nucleation sites increase with increasing indenter radius but the maximum shear stress decreases. The maximum shear stress and indentation modulus decrease linearly with increasing temperature, reflecting the stress-assisted and thermally activated nature of dislocation nucleation.

Hertzian load–displacement relation holds for spherical indentation on soft elastic solids undergoing large deformations

In this paper we investigate the validity of the Hertz theory at very large deformations by performing rigid spherical indentation on soft, linearly elastic silicone substrates using nanoindentation tests and finite element method. We show that the theory significantly underestimates and overestimates the contact radius and maximum contact pressure, respectively, as the ratio of indenter displacement δ to the indenter radius R exceeds 0.1. However, the loading load–displacement relation still holds (<3% discrepancy) for δ/R as large as 0.66 with a maximum principal strain of 46.6%. This agreement arises from a near cancellation of two non-Hertzian effects: the spherical (as opposed to paraboloidal) shape of the indenter, and the large deformation behavior of the linear elastic system. Our simulation results show that the Hertzian load–displacement relation does not hold for thin films where the ratio of thickness H to R is smaller than 20. We also consider rigid indentation on an elastic sphere with a radius of kR, and reveal that the elastic sphere is large enough to be treated as a half-space for k>10. Our results may provide practical guidelines to proper sample preparation and better interpretation of indentation data of elastic soft elastomers and gels.

Berkovich nanoindentation on single SiGe epitaxial films

In this work, a Berkovich nanoindentation was employed to measure the elastic–plastic transition of the SiGe film. Pop-in events are observed from the penetration depths of 17.1 to 18.2nm, 15.2 to 15.65nm, and 15.5 to 17nm; while the conditions at RT are annealed at 800 and 900°C, respectively. However, pop-in events are not clear at the condition of 1000°C because of the highest thermal activation. To explain the experiments, final depth after complete unloading (hf), maximum indentation depth (hmax) and recovery ratio (hf/hmax) data are given in the range of 0.215, 0.257, and 0.447 when the conditions are at 800, 900, and 1000°C, respectively. We can refereed that the conclusion of a smaller indenter radius might result in elbows. Thermal activation is used to assist in the formation of islands on the surface and leads to the increased Rms. Transmission electron microscopy results revealed a serial nucleation seed that induced dislocation propagation after 900°C-annealing, and creating a number of random dislocations after 1000°C-annealing. The importance of the relative elastic–plastic transition of 503nm SiGe films and pop-in (the load penetration curves exhibits one or more discontinuities on loading which is called as pop-in event) and elbow (a longer portion of the unloading curve) events on the response of the thermal treatment is highlighted.