Large Indentation Depths Research Articles

Lattice rotation caused by wedge indentation of a single crystal: Dislocation dynamics compared to crystal plasticity simulations

A number of recent experimental efforts such as electron back scattering technique and three-dimensional X-ray structural microscopy have revealed the intriguing formation of sectors of lattice rotation fields under indentation. In the case of wedge indentation, the in-plane rotation changes sign from one sector to another. Although the lattice rotation fields can be used to compute the geometrically necessary dislocation (GND) densities, it remains unclear how these sectors can be related to the hardness and therefore to the indentation size effects, i.e., the increase of indentation hardness with the decrease of indentation depth. Crystal plasticity simulations in this work reproduce the experimental findings at large indentation depth. On the contrary, discrete dislocation plasticity can only capture the sectors found experimentally when there is a high obstacle density and large obstacle strength. Obstacle density and strength, however, have little effect on the hardness. In other words, there is no one-to-one correspondence between the lattice rotation patterns and the indentation size effects. The presence of obstacles favors the dislocation arrangements that lead to the experimentally found rotation sectors. Using the similarity solutions of indentation fields and the solution of localized deformation fields near a stationary crack, a simple model is developed that explains the dislocation pattern evolution, its relationship to the lattice misorientations, and more importantly its dependence on obstacles.

Abrasive wear of nanoscale single crystal silicon

Nanoscale three-body and two-body abrasive wear on the monocrystalline silicon are investigated using a large-scale molecular dynamics approach. A nanoscale model of three-body abrasion is proposed to evaluate the movement pattern of a sphere particle. It is concluded that the rolling movement of a particle is observed without sliding in the present nanoscale computation process. It is found that there exists a large elastic recovery which prevents the sphere particle from sliding. A modified e/h criterion is proposed to predict the movement pattern of a particle. The result confirms the crucial effect of the elastic recovery on movement pattern. The plowing is also observed as a main wear pattern in three-body abrasion at the nanoscale, whereas the wear mechanism will transform from plowing into cutting at a large indentation depth for two-body abrasion. The cutting tendency is increased with increasing indentation depth. In both the three-body and two-body abrasion, friction force is directly proportional to normal force which governs the friction rule. A turning point is found lied on frictional line related to normal force, which indicates a transition of wear mechanism in two-body abrasion. It is also examined that three-body abrasion is able to cause more massive phase transformation than two-body abrasion although it is with shallower groove in three-body abrasion than in two-body abrasion.

Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young's Modulus Evaluation

The Oliver and Pharr method is the prevailing process for thin films Young's modulus evaluation. Introduced initially for homogeneous materials, this method does not account for the substrate and can consequently lead to significant error, especially at large indentation depths. We suggest here possible methods to improve the accuracy by making use of inverse analysis and finite element computations of the one layer elastic indentation problem.

Elastic-plastic behavior of cyclotrimethylene trinitramine single crystals under spherical indentation: Modeling and simulation

A nonlinear anisotropic elastic-plastic model is developed for single crystals of the energetic material cyclotrimethylene trinitramine (RDX). Numerical simulations of spherical indentation on oriented single crystals are performed; predictions are compared with experimental data and observations from the literature. Model predictions for elastic response and initial yield using elastic constants obtained from resonant ultrasound spectroscopy agree with experimental data; predicted forces using constants obtained from Brillouin scattering tend to exceed experimental data. Influences of elastic anisotropy and elastic nonlinearity are significant. Predicted slip system activity is in reasonable agreement with that deduced from experimental surface profiles when a uniform strength of G/20 is assigned to all six slip systems, with G an effective elastic shear modulus. Predicted indentation forces in the post-yield regime exceed those observed in experiments, suggesting that surface and possibly subsurface fractures may contribute to a loss of stiffness in experiments at larger indentation depths.

Depth-sensing analysis of cytoskeleton organization based on AFM data

Atomic force microscopy is a common technique used to determine the elastic properties of living cells. It furnishes the relative Young's modulus, which is typically determined for indentation depths within the range 300-500nm. Here, we present the results of depth-sensing analysis of the mechanical properties of living fibroblasts measured under physiological conditions. Distributions of the Young's moduli were obtained for all studied cells and for every cell. The results show that for small indentation depths, histograms of the relative values of the Young's modulus described the regions rich in the network of actin filaments. For large indentation depths, the overall stiffness of a whole cell was obtained, which was accompanied by a decrease of the modulus value. In conclusion, the results enable us to describe the non-homogeneity of the cell cytoskeleton, particularly, its contribution linked to actin filaments located beneath the cell membrane. Preliminary results showing a potential application to improve the detection of cancerous cells, have been presented for melanoma cell lines.

Analysis of spherical indentation of materials with plastically graded surface layer

In the present work, a comprehensive parametric study for establishing contact mechanics of instrumented normal spherical indentation on homogeneous materials and materials with plastically graded surface layer (PGSL) was undertaken by dimensional analysis and finite element modeling. The spherical indentation response for homogeneous materials can be described only by two dimensionless parameters: strain hardening exponent and a unified parameter that can describe effects of both the normalized yield strength and the normalized indentation depth. The influences of these two parameters were investigated for a wide range of engineering materials, and the results may be used as an estimate of loading response and pile-up/sink-in behavior when the material properties are known. In the materials with PGSL, a linear gradient in yield strength, and no variation in elastic modulus and strain hardening exponent were explored. The indentation response of the materials with PGSL can be described only by three dimensionless parameters: the normalized indentation depth, the dimensionless strength gradient parameter, and the normalized PGSL thickness. The effects of these three parameters were studied systematically. The normalized pile-up/sink-in parameter is found to be an increasing function of the strength gradient parameter. The normalized pile-up/sink-in parameter increases (decreases) with increasing PGSL thickness for a fixed positive (negative) gradient case at large indentation depth. The results also indicate that the materials with positive PGSL can bear more loads and have significantly more resistance to contact crack formation.

Atomistic simulations of the effect of a void on nanoindentation response of nickel

Three-dimensional molecular dynamics simulations have been performed to investigate the effect of a void on the nanoindentation of nickel thin film. The radius and depth of the void are varied to explore how they influence the nanoindentation. The simulation results reveal that the presence of a void softens the material and allows for a larger indentation depth at a given load compared to the no void case. The radius and depth of the void have a major effect on the indentation behaviors of the thin film. It is also observed that the void will collapse during the nanoindentation of crystal with void. And when the indentation depth is sufficiently large, the void will disappear. It is found that the indentation depth needed to make the void disappear depends on the void size and location.

Interaction of dislocations with incoherent interfaces in nanoscale FCC–BCC metallic bi-layers

Dislocation nucleation and propagation in a Cu–Nb bi-layer with an incoherent face-centered cubic (FCC)–body-centered cubic (BCC) interface are examined using atomistic simulations. The nanoindentation model is applied to generate dislocations at and near the surface in one of the layers and push them through the interface into the other layer. The reasons for high strength levels in multilayered metallic composites with incoherent interfaces are investigated. The interface acts as a very strong barrier to dislocation propagation. It is found that even under severe deformation at large indentation depths, no dislocations are transmitted across the interface from Cu into Nb. While dislocation transmission from Nb to Cu can be, in general, observed, it occurs under high loading forces. In both cases, the presence of the interface results in considerable strengthening of the bi-layer. Mechanisms of interactions between gliding dislocations and the incoherent interface have been studied in detail. In particular, interface shear at the interface under complex three-dimensional loading conditions is analyzed.

Microstructure, nickel suppression and mechanical characteristics of electropolished and photoelectrocatalytically oxidized biomedical nickel titanium shape memory alloy

A new surface modification protocol encompassing an electropolishing pretreatment (EP) and subsequent photoelectrocatalytic oxidation (PEO) has been developed to improve the surface properties of biomedical nickel titanium (NiTi) shape memory alloy (SMA). Electropolishing is a good way to improve the resistance to localized breakdown of NiTi SMA whereas PEO offers the synergistic effects of advanced oxidation and electrochemical oxidation. Our results indicate that PEO leads to the formation of a sturdy titania film on the EP NiTi substrate. There is an Ni-free zone near the top surface and a graded interface between the titania layer and NiTi substrate, which bodes well for both biocompatibility and mechanical stability. In addition, Ni ion release from the NiTi substrate is suppressed, as confirmed by the 10-week immersion test. The modulus and hardness of the modified NiTi surface increase with larger indentation depths, finally reaching plateau values of about 69 and 3.1 GPa, respectively, which are slightly higher than those of the NiTi substrate but much lower than those of a dense amorphous titania film. In comparison, after undergoing only EP, the mechanical properties of NiTi exhibit an inverse change with depth. The deformation mechanism is proposed and discussed. Our results indicate that surface modification by dual EP and PEO can notably suppress Ni ion release and improve the biocompatibility of NiTi SMA while the surface mechanical properties are not compromised, making the treated materials suitable for hard tissue replacements.

Size Dependent Hardness of Polyamide/Imide

Indentation experiments with indentation depths in the nano- and micrometer ranges in the literature have shown that that an indentation size effect similar to metals is present in polymers. In this paper we present indentation ex- periments of a polyamide/imide polymer of indentation depths in the range of 1 to 30 microns. An increase in hardness of about 70% was observed at small indentation depths compared to hardness at large indentation depths. The indentation re- sults are discussed with respect to an indentation hardness rule based on Frank elasticity suggested in a previous paper by the authors. It is found that the hardness model agrees well with the experiments.

Finite element analysis of cylindrical indentation for determining plastic properties of materials in small volumes

The cylindrical indentation is analysed, using the finite element method, for determining the plastic properties of elastic–plastic materials and the effect of strain hardening. The results are compared with those obtained from spherical indentation, the commonly used technique for measuring plastic properties of materials in small volumes. The analysis shows that the deformation under a cylindrical indenter quickly reaches a fully plastic state and that the size (diameter) of the plastic zone remains constant during further indentation. The indentation load is proportional to the indentation depth at large indentation depth, from which the indentation pressure Pm at the onset of yielding can be readily extrapolated. The analysis of cylindrical indentation suggests that it does not need parameters such as impression radius (a) and contact stiffness (S) for determining the plastic behaviour of materials. Thus, the cylindrical indentation can suppress the uncertainties in measuring material properties.

A New Model Developed to Evaluate the Contact Area Arising During Nano-indentation Tests With Pileup Behavior of Metal Materials

A new mechanical model is developed in this paper for metal materials to investigate the behavior arising during the loading/unloading process of an indentation test. Two governing differential equations are derived for the depth solution of the indenter tip and the depth solution formed at the separation point, expressed in a power form. All spring/block and damping coefficients shown in these governing differential equations associated with the elastic/plastic and viscous behaviors are determined by the real-coded genetic algorithm. With the aid of experimental results of the depth at the indenter tip shown at large and small indentation depths, aluminum and steel were used as two examples of soft materials in this paper. The pileup behavior is implicitly included in the evaluation of the contact projected area (A) in the present model. A significant difference in is caused if the pileup is not considered in the model. Under a constant maximum load, the contact area is slightly increased by decreasing the loading/unloading rate.

Mechanical Behavior of Ceramic/SAM Bilayer Coatings

ABSTRACTCeramic/self-assembled monolayer (SAM) bilayer films can provide adequate protection and/or act as a multipurpose coating for microelectronics and MEMS applications, due to synergistic effects of the hybrid film structure. The organic SAM acts as a “template” for the growth of the ceramic film while the hard ceramic can provide protection from environmental and mechanical impact. To process the bilayer films, a low-temperature solution deposition technique (biomimetic process) is employed using phosphonate-based SAM and zirconium oxide precursors. A particulate zirconium oxide film is formed by enhanced hydrolysis of zirconium sulfate solutions in the presence of HCl at about 80°C, and its particle size and thickness effects are discussed. In addition, microstructure and micromechanics involved in the synthesis of both zirconia films and SAM are systematically assessed. Especially, mechanical properties such as Young's modulus and hardness are analyzed using a nanoindenter, as well as with the aid of theoretical models. Further, the substrate effects resulting from a large indentation depth relative to the film thickness are eliminated to obtain the “film-only” properties. This study also highlights the role of compliant SAM layer in forming a strain-tolerant bilayer film.

Hertzian analysis of the self-consistency and reliability of the indentation hardness measurements on superhard nanocomposite coatings

The measurement of elastic properties of superhard nanocomposite coatings can be subject to a number of possible errors, such as indentation size effects (indenter tip blunting, non-representative small volume of the material to be tested upon nanoindentation and a too small stress under the indenter which does not reach the yield stress of that material if a too low load is used), the composite effect of the system of superhard coating on a softer substrate, high compressive or tensile stress in the coatings, drifts and/or stiffness of the indenter etc. We shall present a systematic study of these possible artefacts on superhard coatings using a large range of applied loads on a number of super- and ultrahard samples. The hardness values obtained from the indentation measurements are compared with the Vickers hardness calculated from the projected area of the plastic deformation. The data will be also compared with finite element method computer modeling in order to obtain a deeper insight into the complex problems. It will be shown that reliable results can be obtained if sufficiently thick coatings are used which allows one to obtain load independent values of hardness measured at sufficiently large indentation depths. Hertzian analysis of the non-linear elastic response upon unloading provides analytical solutions that can be used in order to check if the hardness values measured on the super- and ultrahard coatings are self-consistent. In particular, it is possible to estimate the maximum tensile stress that the coatings survive without failure. This stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of GPa. The results show a very good agreement with the theoretical predictions based on the Universal Binding Energy Relation.

Limits to the strength of super- and ultrahard nanocomposite coatings

Hertzian analysis of the nonlinear elastic response upon unloading provides analytical solutions that were used to verify if the hardness values measured on the super- and ultrahard coatings are self-consistent. The analytical solutions were also used to estimate the tensile strength of the coatings. The highest tensile stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of Gpa, thus giving an estimate of their tensile strength. The results show that the tensile strength of the superhard nanocomposites reaches an appreciable fraction of the ideal cohesive strength that is predicted on the basis of the universal binding energy relation. The data are compared with finite element computer modeling in order to obtain a deeper insight into the complex problems. Reliable values of the hardness can be obtained if coatings of a thickness greater than 8 μm are used and the load-independent values are measured at sufficiently large indentation depths of greater than 0.3 μm.

Viscoelasticity in Polymer Films on Rigid Substrates

AbstractThe viscoelasticity of two thermally crosslinked polymer coatings was examined in terms of relaxation of the applied stress after a sudden strain. Two different transient methods were utilized: flat‐ended cylindrical indentation testing of a polymer film on a rigid substrate and tensile testing of a corresponding free‐standing polymer film. The correlation between tensile and indentation tests was studied. The mechanical response of a viscoelastic layer deposited on a rigid substrate was investigated as a function of indentation depth. There was good agreement between the results of the tensile and indentation tests for thick film layers at moderate indentation depths. The findings indicate that the substrate influences the coating performance by reducing the viscous contribution to the stress response and amplifying the magnitude of the equilibrium modulus for large indentation depths. The indentation method utilized here was shown to be a potentially suitable tool for the determination of Poisson's ratio of polymer films. magnified image

Comment on: “Effects of the substrate on the determination of thin films mechanical properties by nanoindentation” by Saha and Nix [Acta Mater 2002;50:23

The calculation of Saha and Nix of the reduced elastic modulus of a thin film on a substrate is extended. The indenter shape is explicitly taken into account for an idealized pyramidal or conical indenter, yielding qualitatively better agreement with experimental values especially for large indentation depths.

Nonlinear Elastic Analysis of the Hardness Test on Rubber-Like Materials

Abstract Both the Ogden-Tschoegl nonlinear elastic constitutive law and a contact algorithm in the general-purpose finite-element program AFEM have been used to examine the use of IRHD values to relate the elastic properties of elastomers. We are aware that large deformations of rubber specimens and complicated interface conditions are involved in this so-called simple test. However, from the finite-element results, we find that the linearly elastic Hertz contact solution is a reasonably accurate model. This can be attributed to several points. First, the hardness test involves mainly compression and shear deformation and the linearly elastic behavior is more closely followed in rubbers for the above two types of deformation. Second, although nonlinear effects become significant in soft rubbers and higher indentation cases, the ASTM D 1415 standard defines larger indentation depth differences for smaller IRHD values. The definition itself compensates for the nonlinear effects. Third, although the interfacial stress field changed due to different frictional conditions, we calculated the IRHD values only from indentation depth difference and total load applied to the steel ball. Both the indentation depth difference and the total load are obtained from far-field conditions and do not change significantly. We should note that using linear elasticity to correlate the elastic moduli and IRHD values is simply a special case in rubber elasticity. We conveniently get rubber's elastic moduli from IRHD values based on linear elasticity, but the complete rubber-like material behavior has to be obtained from more general experiments and described by a nonlinear constitutive law such as the Ogden-Tschoegl model.