Indentation Pile-up Research Articles

Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip

Abstract

Indentation response of single-crystal copper using rate-independent crystal plasticity

We studied single-crystal copper of three different crystallographic orientations [(100), (011) and (111)] for nanoindentation response via a numerical simulation model using spherical indenters of radius (R) 3.4 μm and 10 μm. The model uses rate-independent crystal plasticity with a finite strain implemented as a user routine in the commercial finite element software ABAQUS. The model takes into account active crystallographic slip, orientation effects during nanoindentation computation, and the effect of friction between the indenter and copper substrate. We compared the load–displacement curve and indentation pile-up patterns obtained from the simulations with experimental measurements available in the literature. The indentation load and mean effective pressure beneath the indenter p m were found to be highest for (111) orientation and lowest for (100). The simulation and experimental data agree well.

Molecular dynamic simulations of nanoindentation in aluminum thin film on silicon substrate

In the present work, the nanoindentation of aluminum thin film on silicon substrate is investigated by three-dimensional molecular dynamic (MD) simulation. The film/substrate system is modeled by taking Lennard–Jones (LJ) potential to describe the interaction at the film–substrate interface. Different loading rate from 50 to 250 m/s is carried out in the simulation. The results showed that the hardness of the film increased with the loading rate. In order to study the effect of substrate on the mechanical properties of thin film, nanoindentation process on monolithic Al material is also simulated. The simulation results revealed that indentation pile-up in the aluminum film is significantly enhanced by the substrate. The substrate also affects the loading force during the nanoindentation. At the beginning of the indentation, the loading force is not affected by the substrate. Then, it is getting smaller caused by the interface. As the film is penetrated, the loading force increased rapidly caused by the hard substrate. These results were coincident with the previous reported experiments.

A critical assessment of indentation-based ductile damage quantification

This paper scrutinizes the reliability of indentation-based damage quantification, frequently used by many industrial and academic researchers. In this methodology, damage evolution parameters for continuum damage models are experimentally measured by probing the deformation-induced degradation of either hardness or indentation modulus. In this critical assessment the damage evolution in different sheet metals was investigated using this indentation approach, whereby the obtained results were verified by other experimental techniques (scanning electron microscopy, X-ray microtomography and highly sensitive density measurements), and by finite element simulations. This extensive experimental–numerical assessment reveals that the damage-induced degradation of both hardness and modulus is at least partially, but most likely completely, masked by other deformation-induced microstructural mechanisms (e.g. grain shape change, strain hardening, texture development, residual stresses and indentation pile-up). It is therefore concluded that hardness-based or modulus-based damage quantification methods are intrinsically flawed and should not be used for the determination of a damage parameter.

Orientation effects in nanoindentation of single crystal copper

Numerical simulations and experimental results of nanoindentation on single crystal copper in three crystallographic orientations [(1 0 0), (0 1 1) and (1 1 1)] using a spherical indenter (3.4 μm radius) were reported. The simulations were conducted using a commercial finite element code (ABAQUS) with a user-defined subroutine (VUMAT) that incorporates large deformation crystal plasticity constitutive model. This model can take full account of the crystallographic slip as well as the orientation effects during nanoindentation. Distributions of the out-of-plane displacements and shear stresses as well as shear strains were obtained for indentation depths of up to 310 nm. The experimental studies were conducted using an MTS Nano Indenter (XP) system from which the load–displacement relationships were obtained while the surface topography as well as the surface profile along a line scan of indents were obtained using a Digital Instruments (Dimension 3100) atomic force microscope (AFM). The top views of the indent pile-up patterns under the spherical indenter show two-fold, three-fold, and four-fold symmetries for the (0 1 1), (1 1 1), and (1 0 0) orientations, respectively. Attempt was made to relate the anisotropic nature of the surface topographies around the indents in different crystallographic orientations of the single crystal copper specimens with the active slip systems and local texture variations. A reasonably good agreement had been obtained on several aspects of nanoindentation between the experimental and numerical results reported in this investigation as well as similar results reported in the literature. Thus, material properties of single crystal copper can be determined based on an appropriate numerical modeling of the nanoindentation on three crystallographic orientations.

Initial stages of contact-induced plasticity in sapphire. I. Surface traces of slip and twinning

The present study focuses on the effects of surface orientation on the peculiarities of the earliest stages of nanoindentation-induced plasticity in sapphire (Al2O3) single crystal surfaces. The previous theoretical analyses do not account for all the experimentally observed trends. Additional considerations are required to bridge the gap between experimental results and theoretical predictions. Of key importance are accounting for the sense of twinning shear, the multiplicity of slip and twinning systems involved and an appropriate criterion for the transition from elastic to elastic-plastic regime. The present study supplements a continuum-based stress analysis with the above considerations and compares the resulting theoretical predictions with the experimental results for basal [C, (0001)], rhombohedral [R,(1102)] and prism [A,(1210) and M,(1010)] surfaces. Surface patterns of slip and twining are scrutinized in Part I. Previously unexplained features justified by the results obtained by the present authors include the distribution of the linear surface features ascribed to twinning and the symmetry of indentation pile-up. Part II focuses on the mechanisms of the transition between the elastic and elastic–plastic regimes.

Mechanics of indentation of plastically graded materials—I: Analysis

The introduction of controlled gradients in plastic properties is known to influence the resistance to damage and cracking at contact surfaces in many tribological applications. In order to assess potentially beneficial effects of plastic property gradients in tribological applications, it is essential first to develop a comprehensive and quantitative understanding of the effects of yield strength and strain hardening exponent on contact deformation under the most fundamental contact condition: normal indentation. To date, however, systematic and quantitative studies of plasticity gradient effects on indentation response have not been completed. A comprehensive parametric study of the mechanics of normal indentation of plastically graded materials was therefore undertaken in this work by recourse to finite element method (FEM) computations. On the basis of a large number of computational simulations, a general methodology for assessing instrumented indentation response of plastically graded materials is formulated so that quantitative interpretations of depth-sensing indentation experiments could be performed. The specific case of linear variation in yield strength with depth below the indented surface is explored in detail. Universal dimensionless functions are extracted from FEM simulations so as to predict the indentation load versus depth of penetration curves for a wide variety of plastically graded engineering metals and alloys for interpretation of, and comparisons with, experimental results. Furthermore, the effect of plasticity gradient on the residual indentation pile-up profile is systematically studied. The computations reveal that pile-up of the graded alloy around the indenter, for indentation with increasing yield strength beneath the surface, is noticeably higher than that for the two homogeneous reference materials that constitute the bounding conditions for the graded material. Pile-up is also found to be an increasing function of yield strength gradient and a decreasing function of frictional coefficient. The stress and plastic strain distributions under the indenter tip with and without plasticity gradient are also examined to rationalize the predicted trends. In Part II of this paper, we compare the predictions of depth-sensing indentation and pile-up response with experiments on a specially made, graded model Ni–W alloy with controlled gradients in nanocrystalline grain size.

Numerical analysis of the contact stresses developed during the indentation of coated systems with substrates with orthotropic properties

Many works in the literature have analyzed the contact stresses developed during the indentation of coated systems. In general, the damage observed in systems with soft substrates is characterized by circular cone cracks that propagate at the edge of the indentations. In systems with soft substrates, recent works have also shown that the amount of substrate indentation pile-up presents direct relationship with a peak in radial stresses at film surface and, consequently, with the amount of indentation circular cracks. In this work, a series of finite element analyses was conducted to simulate the indentation of systems with an elastic film and an elastic-plastic substrate. Two values of film thickness were selected and, in each simulation, substrates were divided into two layers with different plastic properties. The layer on the bottom was considered isotropic and the layer attached to the film presented plastic properties along the loading direction ( z) that were different from the plastic properties along the radial and tangential directions. Different ratios between axial and radial/tangential properties were considered. Results indicated that the amount of substrate pile-up and, consequently, the peak in radial stresses at film surface, could be significantly reduced in coated systems with substrates with orthotropic plastic properties.

Numerical and experimental analyses on the contact stresses developed during single and successive indentations of coated systems

The mechanical behavior of materials is commonly characterized through the indentation test, during which complex stress and strain fields are developed. In this work, the single and successive spherical indentation of coated systems was studied through experimental and finite element method (FEM) analyses, with emphasis on the causes of the contact stresses at the indentation edge. Considering a system with an AA 6061 substrate and a chromium nitride (CrN) film, a series of single indentations was initially simulated varying the normal load and the diameter of the sphere. These FEM analyses provided values such as the height of indentation pileup and the distribution of radial stresses along the film surface. In both cases, FEM values could be associated with experimental results, by direct measurement of pileup heights and by the amount of circular cracks that propagated during single indentations, respectively. The results indicated that pileup height plays an important role on the stresses responsible for the propagation of indentation circular cracks. However, a direct correlation between the amount of substrate plastic deformation and pileup height was not possible. The numerical and experimental analyses of successive indentations provided further insights on the propagation of circular cracks and its relation with the stress fields and the height of pileups.

A method for making substrate-independent hardness measurements of soft metallic films on hard substrates by nanoindentation

A new method for making substrate-independent hardness measurements by nanoindentation techniques that applies to soft metallic films on very hard substrates is presented. The primary issue to be addressed is substrate-induced enhancement of indentation pileup and the ways it influences the indentation contact area. On the basis of experimental observations of soft aluminum films deposited on silicon, glass, and sapphire substrates, an empirical relationship was derived that relates the amount of pileup to the contact depth. From this relationship and the associated experimental observations, a method was developed that allows the intrinsic hardness of the film to be estimated, even when the indenter penetrates through the film into the substrate. The method should prove useful for very thin films (<100 nm) in which it is not possible to make measurements at penetration depths small enough to avoid subtrate effects.

Some recent innovations in small specimen testing

New innovative small specimen test techniques are described. Finite element simulations show that combinations of cone indentation pile-up geometry and load–penetration depth relations can be used to determine both the yield stress and strain-hardening behavior of a material. Techniques for pre-cracking and testing sub-miniaturized fracture toughness bend bars, with dimensions of 1.65×1.65×9 mm 3, or less, are described. The corresponding toughness–temperature curves have a very steep transition slope, primarily due to rapid loss of constraint, which has advantages in some experiments to characterize the effects of specified irradiation variables. As one example of using composite specimens, an approach to evaluating helium effects is proposed, involving diffusion bonding small wires of a 54Fe-based ferritic–martensitic alloy to a surrounding fracture specimen composed of an elemental Fe-based alloy. Finally, we briefly outline some potential approaches to multipurpose specimens and test automation.

Substrate effects on nanoindentation mechanical property measurement of soft films on hard substrates

Substrate effects on the measurement of thin film mechanical properties by nanoindentation methods have been studied experimentally using a model soft film on hard substrate system: aluminum on glass. The hardness and elastic modulus of aluminum films with thicknesses of 240, 650, and 1700 nm sputter-deposited on glass were systematically characterized as a function of indenter penetration depth using standard nanoindentation methods. Scanning electron and atomic force microscopy of the hardness impressions revealed that indentation pileup in the aluminum is significantly enhanced by the substrate. The substrate also affects the form of the unloading curve in a manner that has important implications for nanoindentation data analysis procedures. Because of these effects, nanoindentation measurement techniques overestimate the film hardness and elastic modulus by as much as 100% and 50%, respectively, depending on the indentation depth. The largest errors occur at depths approximately equal to the film thickness.

Nanoindentation Hardness of Soft Films on Hard Substrates: Effects of the Substrate

ABSTRACTThe ability to accurately measure the mechanical properties of thin metallic films is important in the semiconductor industry as it relates to device reliability issues. One popular technique for measuring thin film mechanical properties is nanoindentation. This technique has the advantage of being able to measure properties such as hardness and elastic modulus without removing a film from its substrate. However, according to a widely-held rule of thumb, intrinsic film properties can be measured in a manner which is not influenced by the substrate only if the indentation depth is kept to less than 10% of the film thickness, which is often not practical. In this work, a method for making substrate independent hardness measurements of soft metallic films on hard substrates is proposed. The primary issue to be addressed is the substrate-induced enhancement of indentation pile-up and the ways in which this pile-up influences the contact area determined from analyses of nanoindentation load-displacement data. Based on experimental observations of soft aluminum films on silicon, glass, and sapphire substrates, a simple empirical relationship is derived which relates the amount of pile-up to the contact depth. From this relationship, a simple method is developed which allows the intrinsic hardness of the film to be measured by nanoindentation methods even when the indenter penetrates through the film into the substrate.