Scaling approach to conical indentation in elastic-plastic solids with work hardening

We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Micro/Nanomechanical and Tribological Properties of thin Diamond-Like Carbon Coatings

The diamond-like carbon (DLC) films with different thicknesses on 9Crl8 bearing steels were prepared using vacuum magnetic-filtering arc plasma deposition. Vickers indentation. nanoin-dentation and nanoscratch tests were used to characterize the DLC films with a wide range of applied loads. Mechanical and tribological behaviors of these submicron films were investigated and interpreted. The hardnesses of 9Crl8 and DLC, determined by nanoindentation, are approximately 8GPa and 60GPa respectively; their elastic moduli are approximately 25OGPa and 600GPa respectively. The friction coefficients of 9Crl8, DLC. organic coating, determined by nanoscratch, are approximately 0. 35, 0. 20 and 0. 13 respectively. It is demonstrated that nanoindentation and nanoscratch tests can provide more information about the near-surface elastic-plastic deformation, friction and wear properties. The correlation of mechanical properties and scratch resistance of DLC films on 9Crl8 steels can provide an assessment for the load-carrying capacity and wear resistance

Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Microstructure and mechanical properties at TiCp/Ni-alloy interfaces in laser-synthesized coatings

Titanium carbide particle (TiCp) reinforced Ni alloy composite coatings were synthesized by laser cladding using a cw 3 kW CO2 laser. Two kinds of coatings were present in terms of TiCp origins, i.e. undissolved and in situ reacted TiCp, respectively. The former came from the TiCp pre-coated on the sample, whereas the latter from in situ reaction between titanium and graphite in the molten pool during laser irradiation. Conventional and high-resolution transmission electron microscope observations showed the epitaxial growth of TiC, the precipitation of CrB, and the chemical reaction between Ti and B elements around phase interfaces of undissolved TiCp. The hardness, H, and elastic modulus, E, were measured by nanoindentation of the matrix near the TiCp interface. For undissolved TiCp, the loading curve revealed pop-in phenomena caused by the plastic deformation of the crack formation or debounding of TiCp from the matrix. As for in situ generated TiCp, no pop-in mark appears. On the other hand, in situ reacted TiCp led to much higher hardness and modulus than that in the case of undissolved TiCp. The coating reinforced by in situ generated TiCp displayed the highest impact wear resistance at both low and high impact conditions, as compared with coatings with undissolved TiCp and without TiCp. The impact wear resistance of the coating reinforced by undissolved TiCp increases at a low impact work but decreases at a high impact work, as compared with the single Ni alloy coating. The degree of wear for the composite coating depends primarily on the debonding removal of TiCp.

Relationships Between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Conical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Properties of amorphous carbon-silicon alloys deposited by a high plasma density source

The addition of silicon to hydrogenated amorphous carbon can have the advantageous effect of lowering the compressive stress, improving the thermal stability of its hydrogen, and maintaining a low friction coefficient up to high humidity. Most experiments to date have been on hydrogenated amorphous carbon-silicon alloys (a-C1-xSix:H) deposited by rf plasma enhanced chemical vapor deposition. This method gives alloys with sizeable hydrogen content and only moderate hardness. Here we use a high plasma density source known as the electron cyclotron wave resonance source to prepare films with higher sp3 content and lower hydrogen content. The composition and bonding in the alloys is determined by x-ray photoelectron spectroscopy, Rutherford backscattering, elastic recoil detection analysis, visible and ultraviolet (UV) Raman spectroscopy, infrared spectroscopy, and x-ray reflectivity. We find that it is possible to produce relatively hard, low stress, low friction, almost humidity insensitive a-C1-xSix:H alloys with a good optical transparency and a band gap well over 2.5 eV. The friction behavior and friction mechanism of these alloys are studied and compared with that of a-C:H, ta-C:H, and ta-C. We show how UV Raman spectroscopy allows the direct detection of Si-C, Si-Hx, and C-Hx vibrations, not seen in visible Raman spectra. © 2001 American Institute of Physics.

Properties of a-C:H films deposited from a methane electron cyclotron wave resonant plasma

An electron cyclotron wave resonant methane plasma discharge was used for the high rate deposition of hydrogenated amorphous carbon (a-C:H). Deposition rates of up to ∼400 Å/min were obtained over substrates up to 2.5 in. in diameter with a film thickness uniformity of ∼±10%. The deposited films were characterised in terms of their mass density, sp3 and hydrogen contents, C-H bonding, intrinsic stress, scratch resistance and friction properties. The deposited films possessed an average sp3 content, mass density and refractive index of ∼58%, 1.76 g/cm3 and 2.035 respectively.Mechanical characterisation indicated that the films possessed very low steady-state coefficients of friction (ca. 0.06) and a moderate shear strength of ∼141 MPa. Nano-indentation measurements also indicated a hardness and elastic modulus of ∼16.1 and 160 GPa respectively. The critical loads required to induce coating failure were also observed to increase with ion energy as a consequence of the increase in degree of ion mixing at the interface. Furthermore, coating failure under scratch test conditions was observed to take place via fracture within the silicon substrate itself, rather than either in the coating or at the film/substrate interface. © 2003 Elsevier B.V. All rights reserved.

Elastic Behaviour and Microstructural Characteristics of Nd60Al10Fe20Co10 Bulk Metallic Glass Investigated by Ultrasonic Measurement under Pressure

An ultrasonic pulse-echo method was used to measure the transit time of longitudinal and transverse (10 MHz) elastic waves in a Nd60Al10Fe20Co10 bulk metallic glass (BMG). The measurements were carried out under hydrostatic pressure up to 0.5 GPa at room temperature. On the basis of experimental data for the sound velocities and density, the elastic moduli and Debye temperature of the BMG were derived as a function of pressure. Murnaghan's equation of state is obtained. The normal behaviour of the positive pressure dependence of the ultrasonic velocities was observed for this glass. Moreover, the compression curve, the elastic constants, and the Debye temperature of the BMG are calculated on the basis of the similarity between their physical properties in the glassy state and those in corresponding crystalline state. These results confirm qualitatively the theoretical predictions concerning the features of the microstructure and interatomic bonding in the Nd60Al10Fe20Co10 BMG.

Experimental Verification And Theoretical Analysis Of The Relationships Between Hardness, Elastic Modulus, And The Work Of Indentation

The relationship between hardness (H), reduced modulus (E-r), unloading work (W-u), and total work (W-t) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (W-e), H, W-t, and W-u are obtained using Johnson's expanding cavity model and Lame solution. Consequently, it is found that the W-e should be distinguished from W-u, rather than their equivalence as suggested in ISO14577, and (H/E-r)/(W-u/W-t) depends mainly on the conical angle, which are also verified with numerical simulations. (C) 2008 American Institute of Physics.

The Characterization Of Creep And Time-Dependent Properties Of Bulk Metallic Glasses Using Nanoindentation

Viscoelastic deformation and creep behavior of La- and Ce-based bulk metallic glasses (BMGs) with low glass transition temperature are investigated through nanoindentation at room temperature. Creep compliance and retardation spectra are derived to study the creep mechanism. The time-dependent displacement can be well described by a generalized Kelvin model. A modification is proposed to determine the elastic modulus from the generalized Kelvin model. The results are in excellent agreement with the elastic modulus determined by uniaxial compression tests. (c) 2007 Published by Elsevier B.V.

Scaling Functions In Conical Indentation Of Elastic-Plastic Solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

 Instrumented indentation tests have been widely adopted for elastic modulus determination. Recently, a number of indentation-based methods for plastic properties characterization have been proposed, and rigorous verification is absolutely necessary for their wide application. In view of the advantages of spherical indentation compared with conical indentation in determining plastic proper-ties, this study mainly concerns verification of spherical indentation methods. Five convenient and simple models were selected for this purpose, and numerical experiments for a wide range of materials are carried out to identify their accuracy and sensitivity characteristics. The verification results show that four of these five methods can give relatively accurate and stable results within a certain material domain, which is defined as their validity range and has been summarized for each method.

Effective elastic modulus of bone-like hierarchical materials

A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.

Structure and mechanical properties of ceramic coatings fabricated by plasma electrolytic oxidation on aluminized steel

Ceramic coatings were formed by plasma electrolytic oxidation (PEO) on aluminized steel. Characteristics of the average anodic voltages versus treatment time were observed during the PEO process. The micrographs, compositions and mechanical properties of ceramic coatings were investigated. The results show that the anodic voltage profile for processing of aluminized steel is similar to that for processing bulk Al alloy during early PEO stages and that the thickness of ceramic coating increases approximately linearly with the Al layer consumption. Once the Al layer is completely transformed, the FeAl intermetallic layer begins to participate in the PEO process. At this point, the anodic voltage of aluminized steel descends, and the thickness of ceramic coating grows more slowly. At the same time, some micro-cracks are observed at the Al2O3/FeAl interface. The final ceramic coating mainly consists of gamma-Al2O3, mullite, and alpha-Al2O3 phases. PEO ceramic coatings have excellent elastic recovery and high load supporting performance. Nanohardness of ceramic coating reaches about 19.6 GPa. (c) 2007 Elsevier B. V. All rights reserved.