Indenter Radius Research Articles

Nanoscratch testing of atomic layer deposition and magnetron sputtered TiO2 and Al2O3 coatings on polymeric substrates

Titania and alumina thin films are commercially important materials, finding a wide variety of applications. These materials are commonly deposited onto glass substrates by reactive magnetron sputtering techniques, or more recently by atomic layer deposition (ALD). Such films have been well-characterized in terms of their structures and properties, including their nanomechnical and nanotribological properties. There is increasing demand, though, to deposit thin (<100 nm) functional films onto polymeric substrates, which can provide cost and weight savings and opens up the potential of deposition in large throughput roll-to-roll coating systems. However, polymeric substrates impose severe limitations due to both their thermal and mechanical properties. In the former case, production is restricted to low temperature processes and in the latter case, the substrate offers negligible load support for the thin ceramic coating. While nanoindentation and nanotribological testing of thin ceramic coatings on rigid substrates have become established techniques, the same cannot be said of testing similar “hard” coatings on “soft” flexible polymeric substrates. It is recognized that the coating/substrate system is very different in nature and the mechanisms of failure may also be very different. Sub-100 nm titania and alumina coatings have, therefore, been deposited onto a range of polymeric substrate materials by low temperature ALD and, for comparison purposes, magnetron sputtering techniques, including mid-frequency pulsed dc and high power impulse magnetron sputtering. Nanoscratch testing has been carried out on these coatings usingspherical indenters. Indenter radius and loading rate were varied and their influence on the elastoplastic properties of the film and the substrate are considered and comparisons are made withthesame coating materials deposited onto “rigid” substrates.

Simulation of Spherical Nanoindentation of Nanocomposites Using FEM

The study of polymer/clay nanocomposites has attracted major research and commercial interests due to their superior mechanical and thermal properties to those of the neat polymers. The present work is to modelling the spherical nanoindentation of exfoliated polymer /clay nanocomposite that has nonlinear elastic behavior using numerical simulation. A two dimensional simulation is done and the effect of friction coefficient and indenter radius on load-displacement curve is investigated. It is observed that the simulation results of nanoindentation do not depend on the friction coefficient of indenter and specimen significantly.

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.

Multiscale Analysis on Two Dimensional Nanoscale Sliding Contacts of Textured Surfaces

Nanoscale sliding contacts are the major factors that influence the friction and result in wear in micro/nanoelectromechanical systems. Many experimental studies indicated that some surface textures could help improve the contact characteristics and reduce friction forces. However, the experimental results may be biased, due to the contamination of the sample surface or substantial defects in the materials. Numerical methods, such as continuum mechanics, meet great challenges when they are applied at length of nanoscale, and the time cost of molecular dynamics (MD) simulation can be extremely high. Therefore, multiscale method, which can capture atomistic behaviors in the region underlying micro/nano physical processes by MD simulations and models other regions by continuum mechanics, offers a great promise. Coupling MD simulation and finite element method, the multiscale method is used to investigate two dimensional nanoscale sliding contacts between a rigid cylindrical tip and an elastic substrate with textured surface, in which adhesive effects are considered. Two series of nanoscale surface textures with different asperity shapes, different asperity heights, and different spacings between asperities are designed. For different heights of asperities or different spacings between asperities, average potential energy, normal forces, mean normal forces, friction forces, and mean friction forces are compared to observe how these parameters influence friction characteristics; then, the optimal asperity height or spacing is discovered. Through the average potential energy, normal forces, mean normal forces, friction forces, and mean friction forces comparisons between smooth surface and textured surfaces, a better shape is advised to indicate that asperity shape plays an important role in friction force reduction. The influences of the indentation depth and radius of the rigid cylindrical tip are analyzed to find out the sensitivity of surface textures to these two parameters. Effects of sliding speed on the characteristics of nanoscale sliding contacts are also discussed. The results show that, with proper asperity height and proper spacing between asperities, surface textures can reduce friction forces effectively. Coefficients of friction (COFs) of all the cases are calculated and compared. Some negative COFs caused by significant adhesive effects are discovered, which are different from traditional macroscopic phenomena.

A contribution to understanding of low-load spherical indentation—Comparison of tests on polymers and fused silica

Abstract

Strain rate effects in the indentation behavior of foam-based sandwich structures

Indentation tests have been undertaken at quasi-static and impact rates of strain on sandwich structures based on six different types of polymer foam core and two types of composite skin. Initially, the influence of strain rate on the compression properties of the sandwich structures has been investigated, where it has been shown that the plastic collapse strength of the foam cores is rate sensitive, increasing by approximately 100% over the range of strain rates considered. The indentation behavior of the sandwich structures was characterized using a Meyer indentation law of the form P = Cαn, where P is the applied force, α is the resulting indentation, and C, the contact stiffness and n, the indentation exponent, are constants for a given system. It has been shown that the value of the exponent, n, does not vary significantly with the properties of the core or the skin, typically being close to unity for all tests. The contact stiffness C varied greatly and was found to depend on the plastic collapse strength of the foam and the properties of the skin. It has been shown that a plot of C vs. plastic collapse strength containing all of the quasi-static and dynamic data appears to yield a unique relationship for the systems considered here. Tests have also shown that C varies with indentor radius, with the greatest sensitivity to indentor radius being observed in the higher modulus foams. These results highlight the importance of using the appropriate dynamic contact properties when modeling the impact response of foam-based sandwich structures.

A hybrid model for multiscale simulations of nanoindentation

A numerical model for multiscale simulations of nanoindentation has been established by coupling molecular dynamics (MD) simulations with finite element analysis. The multiscale simulations are performed for two-dimensional nanoindentation of a cylindrical indenter against a copper (1 1 1) substrate. Results show that the load–depth curves obtained from both multiscale and full MD simulations match each other reasonably well and no visible discontinuity of deformation is observed in the handshake region. In the beginning, the normal load increases gradually, corresponding to elastic substrate deformation, followed by sudden drops in load–depth curves, which are related to the nucleation and movement of dislocations. The simulations also reveal that indenter radius and indentation velocity significantly affect the nanoindentation process. By the use of multiscale method, the system size to be explored can be greatly expanded without increasing computational cost.

Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa.

A Discrete Dislocation Plasticity Analysis of a Single-Crystal Half-Space Indented by a Rigid Cylinder

Elastic-plastic indentation of a single-crystal half-space by a rigid cylinder was analyzed by discrete dislocation plasticity. Short-range dislocation interactions were modeled by a set of constitutive rules of dislocation emission, glide, pinning (by obstacles), and annihilation. The occurrence of the first dislocation dipole, multiplication of dislocations, and evolution of subsurface stress field were examined in terms of contact load, dislocation source density, slip-plane distance and orientation angle, and indenter radius. In the presence of defects (dislocation sources), the critical load for dislocation initiation is less than that of a defect-free medium and depends on dislocation source density, slip-plane distance, and indenter radius. The critical indenter radius resulting in deformation under the theoretical material strength is determined from numerical results, and the role of dislocation obstacles is interpreted in terms of their spatial density. Simulations provide insight into yielding and plastic deformation of indented single-crystal materials, and establish a basis for developing coarse-grained plasticity models of localized contact deformation in polycrystalline solids.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elastoplastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two-dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 μm and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E = 13.56 GPa and Poisson’s ratio of 0.3. Plasticity was incorporated using both Drucker–Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force–indentation curve for both von Mises and Drucker–Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5 mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 μm with a von Mises model, and from 0.09 to 0.02 μm with Drucker–Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

Simulation of Deep Spherical Indentation Using Eulerian Finite Element Methods

Simulation of deep indentation, and the associated pile-up effects, requires a robust and accurate finite element model capable of naturally handling the large deformations present. This work successfully demonstrates that the Eulerian formulation is capable of accurately reproducing the forces and general material response of deep indentation. It was found that, in the absence of friction, sink-in dominates at indentation depths less than 1.1% of the indenter radius, there is a transition from sink-in to pile-up from 1.1% to 2.3% of the indenter radius, and pile-up is fully developed at indentation depths larger than 13.2% of the indenter radius for the 4340 steel workpiece and the 0.508 mm radius indenter presented in this work. Friction tended to marginally increase the sink-in and transition depths as well as reduce the material height at the onset of fully developed pile-up due to a reduction in the tensile radial strain directly under the indenter.

Deformation behavior and mechanical properties of polycrystalline and single crystal alumina during nanoindentation

► The nanoscale pop-in phenomena of alumina crystals were discussed. ► Hardness exhibits strong ISE at small indentation depth range of ∼100 nm. ► The maximum resolved shear stress occurs at a different position for each crystal. ► The dislocation loop radii were estimated successfully for pop-in events. ► The indenter tip radii play an important role during nanoindentation tests. The nanoscale pop-in phenomena in polycrystalline α-Al 2 O 3 and single crystal α-Al 2 O 3 (0 0 0 1) were comparatively investigated by nanoindentation with Berkovich indenters. It was found that different radii and loading rates have significant effects on the pop-ins formation, stress distributions and dislocation nucleations. Using the Hertzian contact theory and energetic model approach, the pop-in observations and resolved shear stress analysis are consistent with the explanation that the first pop-in corresponds to the nucleation of homogeneous dislocations when the theoretical shear strength is exceeded.

Effects of elastic indenter deformation on spherical instrumented indentation tests: the reduced elastic modulus

Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/Ei (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, Er/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/δmax (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load–displacement (P − δ) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/Ei , from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, Ac , and lower than 5% in the ratio H/Er . However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/Ei , the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio δe/δmax , where δe is the point corresponding to zero load of a straight line with slope S from the point (Pmax, δmax ), varied less than 5% with the ratio E/Ei . Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddon's equation, did not reveal the necessity of correction with the ratio E/Ei . The most affected parameter in the indentation curve, as a consequence of the indentation deformation, was the ratio between the residual indentation depth after complete unloading and the maximum indenter displacement, δr/δmax (up to 26%), but this variation did not significantly decrease the capability to estimate hardness and elastic modulus based on the ratio of the residual indentation depth to maximum indentation depth, hr/hmax . In general, the results confirm the convenience of the use of the reduced modulus in the spherical instrumented indentation tests.

Study of effect of indenter shape in nanometric scratching process using molecular dynamics

In this paper three-dimensional molecular dynamics (MD) simulations are performed to investigate the effect of indenter shape on the nanometric scratching process of copper. In the simulations two types of indenters (sharp and blunt) are used to study the effect of indenter shape on the workpiece deformation and friction. The results show that indenter shape significantly affects the nanoscratch deformation. The blunt indenter causes larger deformation region and much more dislocations at both the indentation and scratch stages. During the scratching stage the blunt indenter results in larger chip volume in front of the indenter. The results also show that there is a size effect on how the indenter shape influences the nanometric scratching process. For small indenters (radius of 1.9 nm) the blunt indenter may result in bigger friction coefficient than the sharp indenter, while for bigger indenters (radii of 3 nm and 4.5 nm) it is reversed. The simulation results indicate that generally the sharp surface asperities in MEMS cause more friction. However, when the asperities are rather small, the blunt asperities may result in more friction. Furthermore, both the friction coefficient and scratch hardness decrease with the increase of the radius of the blunt indenter.

Study on the Relationship between the Restitution Coefficient and the Adhesion Strength of the Coating

By using shore hardness test method, the effects of adhesion strength, coating thickness, basic material, and hammer on the restitution coefficient are studied experimentally and theoretically. The results show that the restitution coefficient increases with the curvature radius of the hammer indenter. In the same condition, the larger the restitution coefficient, the stronger the adhesion strength, while the smaller the restitution coefficient, and the weaker the adhesion strength.

Inception of plasticity in the presence of vacancies in FCC single crystals: indenter size effect

ABSTRACTAtomistic simulations of nanoindentation tests were used to study the indenter radius size effect in the presence of vacancies in a (111) single crystal of nickel. For radii from 2 nm to 8 nm, the maximum shear stresses under the indenter at the onset of plastic deformation in crystals with vacancies were compared to those which cause yield in perfect crystals by placing a single vacancy in a position near the maximum shear stress underneath the indenter tip. The effect of the presence of vacancies is lowered by decreasing the indenter radius. Results obtained for several random distributions of vacancies, in the range 3.3e-4 to 0.0033, show that placing a single vacancy near a specific location produces similar results as using larger numbers of vacancies while simplifying the complexity of the simulation. Finally, visualizations of atomic configurations of a single crystal with vacancy concentration of 3.3e-4 for radii of 4 nm and 6nm show that the heterogeneous nucleation is a size dependent phenomenon.

Atomistic studies of nanohardness size effects

Atomistic simulations of nanoindentations with spherical and Berkovich indenters were carried out to study the effects of size on nanohardness. For spherical indenters with the radii ranging from 10 A to 50 A, it was found that nanohardness was inversely proportional to the indenter radius. For Berkovich indenters, it was found that nanohardness roughly followed a trend that was inversely proportional to the indentation depth. It was concluded that the indentation size effect at the atomistic scale might follow a trend similar to that observed at the micron and sub-micron scales.

Dynamical multiscale simulation of nanoindentation

A dynamical multiscale method has been carried out for studying the nanoindentation process. By imposing the temperature control in the atomic region and performing the low-pass filter method nearby the handshaking regime, the total coupled model exhibits the dynamical behavior in terms of the nodal and atomic displacement distribution. Furthermore, we investigate the effect of indenter temperature and radius in the two-dimensional multiscale nanoindentation model and the simulation results are qualitatively in agreement with the experiments.

Mechanics of Indentation into Micro- and Nanoscale Forests of Tubes, Rods, or Pillars

The force-depth behavior of indentation into fibrillar-structured surfaces such as those consisting of forests of micro- or nanoscale tubes or rods is a depth-dependent behavior governed by compression, bending, and buckling of the nanotubes. Using a micromechanical model of the indentation process, the effective elastic properties of the constituent tubes or rods as well as the effective properties of the forest can be deduced from load-depth curves of indentation into forests. These studies provide fundamental understanding of the mechanics of indentation of nanotube forests, showing the potential to use indentation to deduce individual nanotube or nanorod properties as well as the effective indentation properties of such nanostructured surface coatings. In particular, the indentation behavior can be engineered by tailoring various forest features, where the force-depth behavior scales linearly with tube areal density (m, number per unit area), tube moment of inertia (I), tube modulus (E), and indenter radius (R) and scales inversely with the square of tube length (L2), which provides guidelines for designing forests whether to meet indentation stiffness or for energy storage applications in microdevice designs.

Nonlinear elastic load–displacement relation for spherical indentation on rubberlike materials

Because of the lack of universal contact models for nonlinear strain problems, indentation analysis on rubberlike materials is confined to small deformation in which Hertz's solution is applied. Recognizing that deep indentation may provide more material information, in this paper we propose a nonlinear elastic model for large spherical indentation of rubberlike materials based on the higher-order approximation of spherical function and Sneddon's solution. The effect of limiting network stretch is studied on the initial elastic modulus for lightly cross-linked rubbers. With the comparisons of the finite-element simulation and the experimental result, the proposed model is verified to predict the large indentation of rubberlike materials over the indentation depth of 0.8 times the indenter radius.