Showing papers on "Indentation published in 2008"

Biomechanics of Articular Cartilage and Determination of Material Properties

Abstract: Descriptions of the mechanical behaviors of articular cartilage and their correlations with collagen, proteoglycan, water, and ions are summarized, with particular emphasis on understanding the osmotic effect inside the tissue. First, a descriptive explanation is presented of the biphasic theory required to understand how interstitial water contributes toward the viscoelastic behavior of any hydrated soft tissue. Then, the famous osmotic effect in charged, hydrated soft tissue is interpreted in light of the triphasic mixture theory framework. In the introduction of mechanical testing methods, our emphasis is on the popular indentation technique, which can determine the material properties of cartilage in situ or in vivo. The widely accepted indentation analysis solutions in cartilage biomechanics history are summarized and evaluated. At the end of this paper, a new generalized correspondence principle between charged, hydrated soft tissue and linear, isotropic, elastic material (i.e., elasticity theory) is introduced. This principle makes the employment of triphasic theory as straightforward as using an elasticity theory to solve any equilibrium problem where the elasticity theory can be used to model the material. By using this generalized correspondence principle, the fixed charge density of bovine cartilage has been simply and conveniently calculated from the indentation testing data. The results of proteoglycan content from this mechanical test are remarkably consistent with those from standard biochemical assay. This new correspondence principle significantly improves the power of indentation tests in the determination of mechanoelectrochemical properties of articular cartilage.

Probing elasticity and adhesion of live cells by atomic force microscopy indentation.

Abstract: Atomic force microscopy (AFM) indentation has become an important technique for quantifying the mechanical properties of live cells at nanoscale. However, determination of cell elasticity modulus from the force–displacement curves measured in the AFM indentations is not a trivial task. The present work shows that these force–displacement curves are affected by indenter-cell adhesion force, while the use of an appropriate indentation model may provide information on the cell elasticity and the work of adhesion of the cell membrane to the surface of the AFM probes. A recently proposed indentation model (Sirghi, Rossi in Appl Phys Lett 89:243118, 2006), which accounts for the effect of the adhesion force in nanoscale indentation, is applied to the AFM indentation experiments performed on live cells with pyramidal indenters. The model considers that the indentation force equilibrates the elastic force of the cell cytoskeleton and the adhesion force of the cell membrane. It is assumed that the indenter-cell contact area and the adhesion force decrease continuously during the unloading part of the indentation (peeling model). Force–displacement curves measured in indentation experiments performed with silicon nitride AFM probes with pyramidal tips on live cells (mouse fibroblast Balb/c3T3 clone A31-1-1) in physiological medium at 37°C agree well with the theoretical prediction and are used to determine the cell elasticity modulus and indenter-cell work of adhesion.

Microstructure and properties of carbon nanotube/zirconia composite

Abstract: Sintering and hot pressing have been used for preparation of monolithic ZrO2 and zirconia–carbon nanotube (CNT) composite. The effect of the processing route and the CNT's addition on the microstructure, fracture/mechanical and electrical properties of the zirconia has been investigated at room temperature. The microstructure of the sintered and hot-pressed monolithic ZrO2 consists of a submicron-sized grains. The matrix of the ZrO2–CNT composite consists of a grains with even smaller size (approximately 140 nm) with relatively well dispersed carbon nanotubes. The hardness and the indentation toughness of the sintered monolithic zirconia are 1297 kg/mm2 and 8.01 MPa m0.5 and of the hot-pressed monolithic zirconia 1397 kg/mm2 and 6.24 MPa m0.5, respectively. The addition of the CNT's decreased the hardness and indentation toughness to 830 kg/mm2 and 5.6 MPa m0.5 however the electrical resistivity decreased significantly in comparison to the monolithic zirconia to the value of 0.1 Ω cm.

Intrinsic Length Scales in Tool-Rock Interaction

Abstract: Indentation and cutting experiments in rocks reveal that the action of a tool can induce either ductile and/or brittle failure, with the ductile mode associated with damage of the rock and/or plastic flow, and the brittle mode with the propagation of cracks. In normal indentation, the development of a damaged zone precedes the initiation of tensile cracks; in cutting, the failure mechanism switches from a ductile to a brittle mode as the depth of cut is increased beyond a threshold value. In this paper, we first argue that these observations can be accounted for by introducing an intrinsic length scale lm ∼ ( KIc ∕ σc )2 in the rock description (with KIc denoting the toughness and σc the compressive strength). Next, we report the results of numerical simulation of indentation and cutting tests with the discrete element method. After showing that the internal length scale lm can be modified by the ratio of the shear to normal bond strength, we illustrate by numerical simulations that the selection of the f...

Preparation and properties of metallic, superhard rhenium diboride crystals.

Abstract: Single crystals of ReB2 have been prepared from an aluminum flux under inert gas flow. The crystals are typically 1−3 mm in diameter and 500 μm thick, growing along the [002] direction with a distinct hexagonal morphology. Vickers microhardness and nanoindentation testing indicate that the (002) plane possesses the highest hardness with measured values of 40.5 and 36.4 GPa, respectively. The elastic anisotropy was examined and the indentation moduli of the basal plane and an (hk0) plane of unknown indices are 675 and 510 GPa, respectively. Four-probe electrical resistivity measurements demonstrate that ReB2 is the hardest material known to exhibit metallic behavior. Thermogravimetric analysis indicates that the crystals are stable in air up to 1000 °C due to the formation of a protective boron oxide coating.

Poroelastic nanoindentation responses of hydrated bone

Abstract: Indentation techniques are used for the measurement of mechanical properties of a wide range of materials. Typical elastic analysis for spherical indentation is applicable in the absence of time-dependent deformation, but is inappropriate for materials with time-dependent creep responses active in the experimental time frame. In the current work, a poroelastic analysis—a mechanical theory incorporating fluid motion through a porous elastic network—is used to examine spherical indentation creep responses of hydrated biological materials. Existing analytical and finite element solutions for the poroelastic Hertzian indentation problem are reviewed, and a poroelastic parameter identification scheme is developed. Experimental data from nanoindentation of hydrated bone immersed in water and polar solvents (ethanol, methanol, acetone) are examined within the poroelastic framework. Immersion of bone in polar solvents with decreasing polarity results in increased stiffness, decreased Poisson’s ratio, and decreased hydraulic permeability. Nanoindentation poroelastic analysis results are compared with existing literature for bone poroelasticity at larger length scales, and the effective pore size probed in indentation creep experiments was estimated to be 1.6 nm, consistent with the scale of fundamental collagen–apatite interactions. Results for water permeability in bone were compared with studies of water diffusion through fully dense bone.

The mechanical properties of a surface-modified layer on polydimethylsiloxane

Abstract: Surface-modification of the elastomer poly(dimethylsiloxane) by exposure to oxygen plasma for four minutes creates a thin, stiff film. In this study, the thickness and mechanical properties of this surface-modified layer were determined. Using the phase image capabilities of a tapping-mode atomic-force microscope, the surface-modified region was distinguished from the bulk PDMS; specifically, it suggested a graded surface layer to a depth of about 200 nm. Load-displacement data for elastic indentation using a compliant AFM cantilever was analyzed as a plate bending on an elastic foundation to determine the elastic modulus of the surface (37 MPa). An applied uniaxial strain generated a series of parallel nano-cracks with spacing on the order of a few microns. Numerical analyses of this cracking phenomenon showed that the depth of these cracks was in the range of 300-600 nm and that the surface layer was extremely brittle, with its toughness in the range of 0.1-0.3 J/m(2).

Size effect in the initiation of plasticity for ceramics in nanoindentation

Abstract: The indentation size effect has been observed for many years and is usually associated with increasing hardness as the depth of indentation is reduced for pyramidal indenters. The indentation size effect for spherical indenters has recently been associated with an increase in the yield stress of metals proportional to the inverse cube root of indenter radius [Spary, I.J., Bushby, A.J., Jennett, N.M., 2006. On the indentation size effect in spherical indentation. Philos. Mag. 86 (33), 5581–5593]. Here we investigate ceramic materials where the yield point is high enough to be easily distinguished in nanoindentation tests. A robust method for determining the yield point from a nanoindentation test with spherical indenters is presented. The results for a range of ceramics confirm that the increase in yield pressure is directly proportional to the inverse cube root of indenter radius. Furthermore, the yield pressure is also shown to be proportional to the inverse square root of the contact radius. Revisiting data in the literature shows that this inverse square root relationship is also true for pyramidal indenters. This implies that the indentation size effect is driven by the contact area rather than by the depth of indentation or by the indenter radius.

Mechanics of indentation of plastically graded materials—I: Analysis

Abstract: 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.

Hardness-packing density scaling relations for cohesive-frictional porous materials

Abstract: Recent progress in instrumented nanoindentation makes it possible today to test in situ phase properties and structures of porous materials that cannot be recapitulated ex situ in bulk form. But it requires a rigorous indentation analysis to translate indentation data into meaningful mechanical properties. This paper reports the development and implementation of a multi-scale indentation analysis based on limit analysis, for the assessment of strength properties of cohesive-frictional porous materials from hardness measurements. Based on the separation-of-scale condition, we implement an elliptical strength criterion which results from the nonlinear homogenization of the strength properties of the constituents (cohesion and friction), the porosity and the microstructure, into a computational yield design approach to indentation analysis. We identify the resulting upper bound problem as a second-order conical optimization problem, for which advanced optimization algorithms became recently available. The upper bound yield design solutions are benchmarked against solutions from comprehensive elastoplastic contact mechanics finite element solutions and lower bound solutions. Furthermore, from a detailed parameter study based on intensive computational simulations, we identify characteristic hardness–packing density scaling relations for cohesive-frictional porous materials. These scaling relations which are developed for two pore-morphologies, a matrix–pore morphology and a polycrystal (perfect disordered) morphology, are most suitable for the reverse analysis of the strength parameters of cohesive-frictional solids from indentation hardness measurements.

Higher accuracy analysis of instrumented indentation data obtained with pointed indenters

Abstract: We review current practice for describing force–displacement curves from pointed indenters, highlighting the consequences of the simplifications normally adopted. We derive two corrections, the 'variable epsilon factor' and the 'radial displacement correction.' These are especially important for highly elastic materials such as fused silica where the combined corrections can amount to 13% in the contact area, significantly increasing the accuracy of hardness and modulus results. In contrast, the so-called beta factor has minor importance. We compare our analytical results with finite element (FE) calculations and experimental results. Indenter area functions, obtained using the corrections, agree well with independent direct measurements by a traceably calibrated metrological atomic force microscope (AFM). Further formulae are derived to calculate the complete force–displacement curve of conical indenters and the indentation elastic and total energy. These formulae immediately identify a physical material limit above which a cone cannot generate plastic deformation; for a Berkovich indenter this is a hardness-to-modulus ratio of 0.18.