Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

Mechanical properties of ZnS nanobelts

Mechanical properties of ZnS nanobelts were measured at room temperature by direct nanoindentation experiments. It was found that the ZnS nanobelts achieve 79% increase in hardness but 52% decrease in elastic modulus compared to bulk ZnS. The nanobelts were found to exhibit creep under indentation. Indentation cracking was preferred along the belt growth direction. Indentation deformation behavior and fracture mechanisms of the ZnS nanobelts are discussed in conjunction with their crystalline structure, size effect, and surface-to-volume ratio.     

Measurement of elastic properties of calcium silicate hydrate with atomic force microscopy

Atomic force microscopy (AFM) based indentation is compared to conventional nanoindentation for measuring mechanical properties of cement pastes. In evaluating AFM as a mechanical characterization tool, various analytical and numerical modeling approaches are compared. The disparities between the numerical self-consistent approach and analytical solutions are determined and reported. The measured elastic Young’s modulus determined from AFM indentation tests are compared to elastic Young’s modulus determined from nanoindentation tests of cement paste. These results indicate that the calcium silicate hydrate (C-S-H) phase of hydrated Portland cement has different properties on the different length scales probed by AFM versus nanoindenters. Packing density of C-S-H particles is proposed as an explanation for the disparity in the measured results.     

Aspect ratio dependence of the elastic properties of ZnO nanobelts

The Young's modulus of ZnO nanobelts was measured with an atomic force microscope by means of the modulated nanoindentation method. The elastic modulus was found to depend strongly on the width-to-thickness ratio of the nanobelt, decreasing from about 100 to 10 GPa, as the width-to-thickness ratio increases from 1.2 to 10.3. This surprising behavior is explained by a growth-direction-dependent aspect ratio and the presence of stacking faults in nanobelts growing along particular directions.     

Determination of Young’s modulus in polyester-Al2O3 and epoxy-Al2O3 nanocomposites using the Digital Image Correlation method

Young’s modulus of nano-composite systems composed of unsaturated polyester and epoxy resins with alumina nanoparticles of different sizes has been experimentally estimated. The nanoparticles used were spherical alpha-Al₂O₃ having 30-40 and 200 nm in diameter. Young’s modulus was estimated using an inverse problem that is solved by means of the classical Levenberg-Marquardt technique. A cantilever beam under bending was used in the experiments and the experimental procedure was performed using the Digital Image Correlation method, which is a well-established optical-numerical method for estimating full-field displacement. Experimental results indicate that Young’s modulus increases with increasing nanoparticle volume fraction. Finally, the estimated Young’s moduli were compared with classical theoretical models, showing that the experimental results are in agreement with literature data.     

Weibull modulus of nano-hardness and elastic modulus of hydroxyapatite coating

Here we report the microstructural dependence of nano-hardness (H) and elastic modulus (E) of microplasma sprayed (MIPS) 230 μm thick highly porous, heterogeneous hydroxyapatite (HAP) coating on SS316L. The nano-hardness and Young’s modulus data were measured on polished plan section (PS) of the coating by the nanoindentation technique with a Berkovich indenter. The characteristic values of nano-hardness and Young’s modulus were calculated through the application of Weibull statistics. Both nano-hardness and the Young’s modulus data showed an apparent indentation size effect. In addition, there was an increasing trend of Weibull moduli values for both the nano-hardness and the Young’s modulus data of the MIPS-HAP coating as the indentation load was enhanced from 10 to 1,000 mN. An attempt was made in the present work, to provide a qualitative model that can explain such behavior.     

Indentation mechanics and fracture behavior of metal/ceramic nanolaminate composites

Composite laminates on the nanoscale have unique properties, such as high strength, high wear resistance, and biocompatibility. In this paper we report on the nanoindentation behavior of a model metal–ceramic nanolaminate consisting of alternating layers of aluminum and silicon carbide (Al/SiC) processed by PVD on a Si substrate. Composites with different layer thicknesses were fabricated and the effect of layer thickness on Young’s modulus and hardness was quantified. The effect of indentation depth on modulus and hardness was studied. The damage that took place during nanoindentation was examined by cross-sectioning the samples by focused ion beam (FIB) technique and imaging the surface using scanning electron microscopy (SEM). Finite element modeling (FEM) of nanoindentation of nanolaminates was conducted. The damage patterns observed in experiments were qualitatively supported by the numerical simulations.     

Young’s moduli of functionalized single-wall carbon nanotubes under tensile loading

This paper quantitatively investigates the effect of chemical functionalization on the axial Young’s moduli of single-walled carbon nanotubes (SWCNTs) based on molecular mechanics (MM) simulation, in which the COMPASS force field is used to model the interatomic interactions in a nonfunctionalized nanotube or a functionalized nanotube grafted with vinyl groups. We obtain the axial Young’s moduli of both functionalized and nonfunctionalized SWCNTs. The influences of the number and distribution density of the sp³-hybridized carbon atoms and the radius and chirality of the SWCNTs on Young’s moduli are studied. The results indicate that Young’s moduli depend strongly on the chirality of the SWCNTs and the distribution density of the sp³-hybridized carbon atoms. A 37.50% content of sp³-hybridized carbon atoms may degrade Young’s modulus by up to 33.36%. In addition, MM simulations show that the functionalization of SWCNTs results in a decrease of Young’s moduli of the corresponding SWCNT/polyethylene composites.     

Microindentation study of Ti–6Al–4V alloy

In order to study the micromechanical behavior of Ti–6Al–4V alloy, microindentation experiments were performed with five different maximum loads of 100, 150, 200, 250 and 300 mN, and with three loading speeds of 6.4560, 7.7473 and 9.6841 mN/s respectively. The experimental results revealed that loading speed has little influence on microhardness and Young’s modulus. Microindentation hardness experiments showed strong indentation size effects, i.e. increase of indentation hardness with the decrease of indentation load or depth. Then microindentation constitutive equation that described the stress as a function of the strain was proposed through dimensional analysis. And the finite element simulation results showed that the predicted computational indentation data from developed constitutive equation can track the microindentation experimental data of Ti–6Al–4V alloy.     

Fabrication of ZnS/ZnO hierarchical nanostructures by two-step vapor phase method

A simple two-step vapor phase method is presented to fabricate ZnS/ZnO hierarchical nanostructures in bulk quantities. That is ZnS nanobelts were first synthesized and then used as substrate for growth of ZnO nanorod arrays. Investigation results demonstrate that the polar surfaces of ZnS nanobelts could induce a preferred asymmetric growth of ZnO nanorods on the side surfaces. But it is believed that if the local concentration of ZnO was high enough, ZnO nanorods could also grow symmetrically on the top/bottom surface of the ZnS nanobelts. The optical property of the products was also recorded by means of photoluminescence (PL) spectroscopy.     

On elastic nanoindentation of coated half-spaces by point indenters of non-ideal shapes

The elastic contact of non-ideal conical and Berkovich indenters with bi-layer half-spaces is investigated. Blunted tips are simulated as smooth surfaces. The boundary element method is employed to carry out the numerical simulations of nanoindentation. An analytical analysis of the influence of the coating thickness and the tip bluntness magnitude on the nanoindentation loading curve is realized. The dimensionless compression force is introduced in order to describe the nanoindentation at different approaches between the indenter and the coated half-space. A practical technique for determining the Young's modulus of coatings is proposed. The technique is based on the modelling of indentation of the blunted indenter tip into the coating/substrate composite. This technique is applied to the nanoindentation study of nanocrystalline Cr?coatings on silicon and glass substrates being tested by a diamond Berkovich indenter with a blunted tip.     

Preparation of high purity ZnO nanobelts by thermal evaporation of ZnS

High purity one-dimensional ZnO nanobelts were synthesized by thermally evaporating commercial ZnS powders in a hydrogen-oxygen mixture gas at 1050 degrees C. It was found that these ZnO nanobelts had a single crystal hexagonal wurtzite structure growing along the [0001] direction. They had a rectangle-shaped cross-section with typical widths of 20 to 100 nanometers and lengths of up to hundreds of micrometers with lattice constants of a = 0.325 nm and c = 0.520 nm. The self-catalytic hydrogen-oxygen assisted growth of ZnO nanobelt is discussed. The photoluminescence (PL) characterization of the ZnO nanobelts shows strong near-band UV emission (about 383 nm) and one broad peak at 501 nm, which indicates that the ZnO nanobelts have good potential application in optoelectronic devices.     

Measurement of Young’s relaxation modulus using nanoindentation

In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these methods for measuring relaxation functions.     

Different mechanical properties of the pristine and hydrogen passivated ZnO nanowires

We comparatively calculate the Young’s moduli of the pristine and the hydrogen passivated ZnO nanowires using the first-principles approaches. It is found that the pristine nanowire has the higher Young’s modulus, but the corresponding hydrogen passivated nanowire has the lower Young’s modulus than that of bulk ZnO. The physical origin of the opposite tendency can be attributed to both the different surface relaxations of the two kinds of ZnO nanowires and the core nonlinear effect.     

Two-step method to evaluate equibiaxial residual stress of metal surface based on micro-indentation tests

The present study proposed a method to evaluate the equibiaxial compressive residual stress of a metal surface by means of a depth-sensing indentation method using a spherical indenter. Inverse analysis using the elastic–plastic finite-element model for an indentation test was established to evaluate residual stress from the indentation load–depth curve. The proposed inverse analysis utilizes two indentation test results for a reference specimen whose residual stress is already known and for a target specimen whose residual stress is unknown, in order to exclude the effect of other unknown mechanical properties, such as Young’s modulus and yield stress. Residual stress estimated by using the indentation method is almost identical to that measured by X-ray diffraction for indentation loads of 0.49–0.98 N. Therefore, it can be concluded that the proposed method can effectively evaluate residual stress on metal surface.     

Some issues on nanoindentation method to measure the elastic modulus of particles in composites

The application of the indentation method to measure the elastic modulus of particles embedded in a composite is theoretically investigated in this paper by finite element simulation. The Oliver–Pharr method, which is widely used in commercial nanoindentation instruments, is used to probe the elastic modulus of the particle from the simulated indentation curve. The predicted elastic modulus is then compared with the inputted value. Two cases are studied, that of a stiff particle embedded in a soft matrix and a soft particle embedded in a stiff matrix. In both of these cases, there exists a particle-dominated depth. If the indentation depth lies within this particle-dominated depth, the Oliver–Pharr method is able to be applied to measure the particle’s elastic modulus with sufficient accuracy if the real contact area is used. This could lead to an experimentally-convenient method of determining the primary properties of individual particle, providing they can be well dispersed in the polymeric matrix.     

Scaling functions in conical indentation of elastic-plastic solids

Summary 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 ν are known.     

First-principles studies of the electronic and mechanical properties of ZnO nanobelts with different dominant surfaces

The electronic and elastic properties of [0001] ZnO nanobelts with different lateral dimensions have been studied by employing first-principles approaches. We find that the surface effects are dominant for the energetic stability of the nanobelt, while the quantum confinement effect plays an important role in the band gaps of the nanobelts. More importantly, we show that the different dominant surfaces of nanobelts have important influences on the band gaps, but minimal effects on the size dependence of the Young's modulus. The Young's modulus is larger than the bulk value and decreases with the increase of the square root of the cross-sectional area of the nanobelts. Finally, we find that the continuum-based model proposed for the Young's modulus of nanostructures is applicable for ZnO nanowires of 10-200?nm diameter, but not for ultrathin nanowires and nanobelts.     

Density functional theory investigation of the mechanical properties of single-walled carbon nanotubes

We detail the results of our first-principles study based on density functional theory on the elastic properties of (6, 6) single-walled carbon nanotubes (SWCNTs) in both periodic and non-periodic systems. The Young’s modulus and the shear modulus of nanotubes were evaluated through applying axial and torsion strains on periodic, H-, and C-capped nanotubes. Based on our first-principles calculations, the Young’s modulus of the periodic nanotube tens to increase as the nanotube’s length increases, and finally approaches a constant value at long tube lengths. It was found that the Young’s modulus characteristic of H- and C-capped nanotubes exhibit contradictory behaviors during compression with the periodic nanotube. Our calculations also predict that the Young’s and Shear moduli of C-capped nanotubes are larger than those of other types of nanotubes.     

Identification of stiffness tensor components of wood cell walls by means of nanoindentation

A new procedure to characterize the full set of elastic constants of wood cell walls was developed. For the first time, not only the longitudinal modulus, but also the transverse- and the shear modulus were determined in one experimental setup at micron scale. For this purpose, nanoindentation experiments were performed at variable angles between the indentation direction and the direction of cellulose microfibrils in wood cell walls. Using an approach based on anisotropic indentation theory a relationship between the indentation moduli obtained experimentally and the elastic material constants of the cell wall was derived. Using an error minimization procedure, the values of the elastic material constants were finally calculated. As typically observed for natural materials, our experimental results are characterized by high variability. Particularly the elastic modulus in longitudinal cell direction is highly sensitive to small changes in the local orientation of cellulose microfibrils. Nonetheless, reasonable estimates of 26.3 GPa for the longitudinal elastic modulus of the secondary wood cell wall S2, 4.5 GPa for the transverse modulus, and – for the first time – a value of 4.8 GPa for the shear modulus of wood cell wall material were obtained.