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Showing papers on "Indentation published in 1994"


Journal ArticleDOI
TL;DR: In this article, the authors show how the indentation modulus can be calculated for arbitrary anisotropic solids and give results for solids with cubic crystal symmetry for a flat triangular punch on a half space.
Abstract: The unloading process in an indentation experiment is usually modeled by considering the contact of a rigid punch with an elastically isotropic half space. Here we extend the analysis to elastically anisotropic solids. We review some of the basic formulae for describing the indentation of elastically anisotropic solids with axisymmetric indenters. We show how the indentation modulus can be calculated for arbitrary anisotropic solids and give results for solids with cubic crystal symmetry. We have calculated the contact stiffness for a flat triangular punch on a half space for various anisotropic materials. The indentation modulus for a triangular indenter is typically 5–6% higher than that for an axisymmetric indenter and varies only slightly with the orientation of the indenter in the plane of the indentation. We have conducted microindentation experiments to measure the indentation moduli of differently oriented surfaces of both cubic and hexagonal single crystals. For copper and β-brass, the (111) indentation moduli are approximately 10 and 25% larger than the {100} modulus. The (110) moduli are typically slightly smaller than the (111) moduli. The indentation modulus of zinc varies by as much as a factor of two, depending on the sample orientation. The hardnesses of the single crystals do not vary much with the orientation of the plane of indentation. For /gb-brass, the hardness of a {110} surface is only about 13% lower than the hardness of a {100} or {111} surface; for copper, the {110} hardness is 6% higher than for the other orientations. For zinc the maximum change in hardness with orientation is 20%.

489 citations


Journal ArticleDOI
TL;DR: In this article, the theoretical foundation for the commonly used Vickers test was explored and the influence of large elastoplastic deformations was also assessed, based on the finite element method.

368 citations


Journal ArticleDOI
25 Feb 1994-Science
TL;DR: Distributed irreversible deformation in otherwise brittle ceramics has been observed in Hertzian contacts in silicon carbide and micaceous glass-ceramic, and an important manifestation is an effective "ductility" in the indentation stress-strain response.
Abstract: Distributed irreversible deformation in otherwise brittle ceramics (specifically, in silicon carbide and micaceous glass-ceramic) has been observed in Hertzian contacts. The deformation takes the form of an expanding microcrack damage zone below the contact circle, in place of the usual single propagating macrocrack (the Hertzian "cone fracture") outside. An important manifestation of this deformation is an effective "ductility" in the indentation stress-strain response. Control of the associated brittle-ductile transition is readily effected by appropriate design of weak interfaces, large and elongate grains, and high internal stresses in the ceramic microstructure.

312 citations


Journal ArticleDOI
TL;DR: An atomic force microscope (AFM) with a specially prepared diamond tip was used to measure indentation hardness with an indentation depth as low as 1 nm as discussed by the authors, which is much smaller than the depth of more than 20 nm that have been reported to date.
Abstract: An atomic force microscope (AFM), with a specially prepared diamond tip, has been modified to measure indentation hardness with an indentation depth as low as 1 nm. This indentation depth is much smaller than the depth of more than 20 nm that have been reported to date. The AFM indentation technique allows the hardness measurements of surface monolayers and ultrathin films in multilayered structures at very shallow depths and low loads. The nanoindentation hardness of single crystal silicon is measured using this technique. A subtraction technique is also described which allows the actual hardness measurements of rough surfaces such as magnetic thin film rigid disks.

239 citations


Journal ArticleDOI
TL;DR: In this paper, the Hertzian indentation response of a machinable mica-containing glass-ceramic is studied, and the deformation is attributed to shear-driven sliding at the weak interfaces between the mica flakes and glass matrix.
Abstract: The Hertzian indentation response of a machinable mica-containing glass-ceramic is studied. Relative to the highly brittle base glass from which it is formed, the glass-ceramic shows evidence of considerable “ductility” in its indentation stress-strain response. Section views through the indentation sites reveal a transition from classical cone fracture outside the contact area in the base glass to accumulated subsurface deformation-microfracture in the glass-ceramic. The deformation is attributed to shear-driven sliding at the weak interfaces between the mica flakes and glass matrix. Extensile microcracks initiate at the shear-fault interfaces and propagate into the matrix, ultimately coalescing with neighbors at adjacent mica flakes to effect easy material removal. The faults are subject to strong compressive stresses in the Hertzian field, suggesting that frictional tractions are an important element in the micromechanics. Bend-test measurements on indented specimens show that the glass-ceramic, although weaker than its base glass counterpart, has superior resistance to strength degradation at high contact loads. Implications of the results in relation to microstructural design of glass-ceramics for optimal toughness, strength, and wear and fatigue properties are discussed.

176 citations


Journal ArticleDOI
TL;DR: In this article, the role of substrate and interface adhesion on the force-displacement behavior of thin films indented with spherical tipped indenters is schematically summarized, and the authors also provide a more tractable solution to the contact problem.

168 citations


Journal ArticleDOI
TL;DR: In this article, experiments have been conducted to simulate the Cenozoic arc-continent collision in Taiwan with a foreland-dipping backstop, and the experimental modelling shows that the faults or shear zones are rotated around the indentation point of the backstop by transcurrent and bookshelf faulting.

127 citations


Journal ArticleDOI
TL;DR: In this article, the mechanical properties of compositionally modulated Au-Ni films were investigated by submicrometer depth-sensing indentation and by deflection of micrometer-scale cantilever beams.
Abstract: The mechanical properties of compositionally modulated Au-Ni films were investigated by submicrometer depth-sensing indentation and by deflection of micrometer-scale cantilever beams. Films prepared by sputter deposition with composition wavelengths between 0.9 and 4.0 nm were investigated. Strength was found to be high and invariant with composition wavelength. Experimental and data analysis methods were developed to provide more accurate and precise measurements of elastic stiffness. Large enhancements in stiffness (the “supermodulus effect”) were not observed. Rather, relatively small but significant minima were observed at a composition wavelength of about 1.6 nm by both techniques. These variations were found to be strongly correlated with variations in the average lattice parameter normal to the plane of the film. Both structural and mechanical property variations are consistent with a simple model in which the film consists of bulk-like Au and Ni layers with interfaces of constant thickness.

125 citations


Journal ArticleDOI
Abstract: As an alternative to traditional tensile testing of materials subjected to creep, indentation testing is examined. Axisymmetric punches of shapes defined by smooth homogeneous functions are analysed in general at power law behaviour both from a theoretical and a computational point of view. It is first shown that by correspondence to nonlinear elasticity and self-similarity the problem to determine time-dependent properties admits reduction to a stationary one. Specifically it is proved that the creep rate problem posed depends only on the resulting contact area but not on specific punch profiles. As a consequence the relation between indentation depth and contact area is history independent. So interpreted, the solution for a flat circular cylinder (Boussinesq) is not only of intrinsic interest but serves as a reference solution to generate results for various punch profiles. This is conveniently carried out by cumulative superposition and in particular ball indentation (Brinell) is analysed in depth. A carefully designed finite element procedure based on a mixed variational principle is used to provide a variety of explicit results of high accuracy pertaining to stress and deformation fields. Universal relations for hardness at creep are proposed for Boussinesq and Brinell indentation in analogy with the celebrated formula by Tabor for indentation of strain-hardening plastic materials. Quantitative comparison is made with a diversity of experimental data attained by earlier writers and the relative merits of indentation strategies are discussed.

120 citations


Journal ArticleDOI
TL;DR: In this article, an ultrasonic method has been applied for a comparative analysis of the damage detected after static indentation and after low-velocity impact on a composite with quasi-isotropic lay-up.

94 citations


Journal ArticleDOI
TL;DR: Differences between the finite deformation response and the linear response are shown to be significant when the compression rate is fast or when the indenter is impermeable, and they are compared with the response obtained using the linear infinitesimal response.
Abstract: The nonlinear indentation response of hydrated articular cartilage at physiologically relevant rates of mechanical loading is studied using a two-phase continuum model of the tissue based on the theory of mixtures under finite deformation. The matrix equations corresponding to the governing mixture equations for this nonlinear problem are derived using a total Lagrangian penalty finite element method, and solved using a predictor-corrector iteration within a modified Newton-Raphson scheme. The stress relaxation indentation problem is examined using either a porous (free draining) indenter or solid (impermeable) indenter under fast and slow compression rates. The creep indentation problem is studied using a porous indenter. We examine the finite deformation response and compare with the response obtained using the linear infinitesimal response. Differences between the finite deformation response and the linear response are shown to be significant when the compression rate is fast or when the indenter is impermeable. The finite deformation model has a larger ratio of peak-to-equilibrium reaction force, and higher relaxation rate than the linear model during the early relaxation period, but a similar relaxation time. The finite deformation model predicts a slower creep rate than the linear model, as well as a smaller equilibrium creep displacement. The pressure distribution below the indenter, particularly near the loaded surface is also larger with the finite deformation model.

Journal ArticleDOI
TL;DR: In this article, the authors used a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation, based on the observation that the crack lengths of the small indentations are changed under the influence of residual stress field created by the large indentations.
Abstract: A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.

Journal ArticleDOI
TL;DR: In this article, the development of Vickers indent-induced tracks with increasing indent load has been studied in two Y2O3-stabilizel ZrO2 ceramics.
Abstract: The development of Vickers indent-induced tracks with increasing indent load has been studied in two Y2O3-stabilizel ZrO2 ceramics. Such cracks form as radial or Palmqvist cracks at low loads, assume “kidney” shapes at intermediate loads, and finally form median (half-penny) cracks at high loads. The plastic zone directly beneath the indent is uncracked; a significant portion of the plasticity induced by indentation occurs by martensitic transformation.

Journal ArticleDOI
TL;DR: In this article, the fracture behavior of PZT specimens driven at their resonant frequency by the application of an ac voltage was investigated and compared with fracture behaviour of monotonically loaded PZTs.
Abstract: The fracture behavior of PZT specimens driven at their resonant frequency by the application of an ac voltage was investigated and compared with fracture behavior of monotonically loaded PZT. Microcracking was observed in the cyclically loaded specimens; above 150°C, the micro-cracks were dispersed in small clusters, while at T≤ 86°C, microcracks were generated in a densely populated region near the failure site (indentation). Macrocrack growth also demonstrated a temperature dependence, with crack growth occurring at T > 150°C but not at T≤ 86°C.

Journal ArticleDOI
TL;DR: In this article, a model was developed relating the indentation hardness of organic molecular solids to their cohesive energy density, the length of the Burgers vector, the weakest plane from the crystal structure and crystal structural parameters.
Abstract: A model has been developed relating the indentation hardness of organic molecular solids to their cohesive energy density, the length of the Burgers vector, the weakest plane from the crystal structure and crystal structural parameters. Whilst the described model is pragmatic, calculated indentation values for a variety of materials based on the weakest plane using specific Burgers vectors agree well with those from literature data.

Journal ArticleDOI
TL;DR: In this article, the authors used nanoindentation to study the mechanical properties of Ag/Ni multilayered thin films and found that both the hardness and the elastic modulus of the multi-layer thin films had values between those for homogeneous Ag and Ni thin films.
Abstract: Nanoindentation was used to study the mechanical properties of Ag/Ni multilayered thin films. Both the hardness and the elastic modulus of the multilayered thin films had values between those for homogeneous Ag and Ni thin films. The trend in the hardness with layer repeat length can be explained by the effects of both the stress and the microstructure. No evidence for interfacial effects on hardness was found. A decrease in modulus at the smallest repeat lengths was compared with literature data on the elastic constants of Ag/Ni multilayers.

Journal ArticleDOI
TL;DR: In this paper, the hardness, H, and rate sensitivity of the hardness are measured in molybdenum at room and low temperature (160 and 170 K) using as-received and annealed specimens.
Abstract: The hardness, H , and rate sensitivity of the hardness, m = ∂ ln H /∂ ln ∊ eff | x p , where ∊ eff is an effective strain rate and x p the plastic depth, are measured in molybdenum at room and low temperature (160 and 170 K) using as-received and annealed specimens. Based on these measurements it is found that H separates into two components: one depending on indentation rate and temperature, and the other depending on the starting state of the material. An activation volume is defined, v ∗ = 9 kT/mH , which falls within the range of values derived from other experimental techniques. The values of m obtained from indentation creep, indentation load relaxation, and indentation rate-change experiments agree closely with each other provided a consistent analysis is used. The results of these experiments suggest that the rate- and temperature-dependence of the hardness can be used to discriminate between strengthening mechanisms at low temperature.


Journal ArticleDOI
TL;DR: In this article, stable indentation cracks were grown in four-point bend tests to study the fracture toughness of two Y2O3-stabilized ZrO2 ceramics.
Abstract: Stable indentation cracks were grown in four-point bend tests to study the fracture toughness of two Y2O3-stabilized ZrO2 ceramics containing 3 and 4 mol% Y2O3. By combining microscopic in situ stable crack growth observations at discrete stresses with crack profile measurements, the dependence of toughness on crack extension was determined from crack extension plots, which graphically separate the crack driving residual stress intensity and applied stress intensity factors. Both materials exhibit steeply rising R-curves, with a plateau toughness of 4.5 and 3.1 Mpa·m1/2 for the 3- and 4-mol% materials, respectively. The magnitude of the plateau toughness reflects the fraction of tetragonal grains contributing to transformation toughening.

Journal ArticleDOI
TL;DR: In this article, an attempt is made to explain the anisotropy of indentation-induced deformation and fracture of sapphire for different crystallographic planes indented by a variously oriented triangular diamond indenter.
Abstract: An attempt is made to explain the anisotropy of indentation-induced deformation and fracture of sapphire for different crystallographic planes indented by a variously oriented triangular diamond indenter. The anisotropic surface deformation and fracture of the indented crystal are discussed using a new effective resolved shear stress (ERSS) model. The patterns of the surface traces of twins and cracks are predicted on the basis of the ERSS-calculations performed for all the slip and twinning systems which are potentially activated during room temperature indentation. The theoretical prediction of the ERSS model agrees very well with the observed hardness anisotropy. The present work is the first application of the continuous indentation test to the anisotropic surface deformation of single crystals.

Journal ArticleDOI
Maarten Buijs1
TL;DR: The relation between the mechanical properties of brittle surfaces and an expression for removal rate obtained from the modeling of solid-particle erosion has been investigated with the aid of indentation-fracture theory as discussed by the authors.
Abstract: The relation between the mechanical properties of brittle surfaces and an expression for removal rate obtained from the modeling of solid-particle erosion has been investigated with the aid of indentation-fracture theory. Different types of glass have been used in this investigation to avoid the complications that microstructure introduces to the description of the mechanical properties of ceramics in general. It appears that the dependence of the removal rate on the material parameters of elasticity, hardness, and fracture toughness can be well described by indentation-fracture theory. Although different types of glass allow a much more accurate validation of theory than other ceramics, they still do not discriminate between the various expressions for crack length and cracking depth that coexist in indentation-fracture theory.

Journal ArticleDOI
TL;DR: In this article, a particular formulation of the three-dimensional finite element method is established for the elastic analysis of the triangular pyramidal indentation, and numerical analyses are carried out under several conditions to investigate the influences of the elastic properties of the material and the apical angle α of the triangle pyramid indenter on the loadisplacement (P-h) relationship.
Abstract: A particular formulation of the three-dimensional finite-element method is established for the elastic analysis of the triangular pyramidal indentation. Numerical analyses are carried out under several conditions to investigate the influences of the elastic properties of the material and the apical angle α of the triangular pyramidal indenter on the loadisplacement (P-h) relationship. The analytical results are expressed by P [dbnd] CE∗ (tan α)h 2, where E∗ is the plane strain modulus of the material and C is a geometrical factor equal to 1·02. The value of C is a factor of 1·60 larger than the theoretical value for a conical indenter, 2/π. The analytical results are evaluated by nano-indentation measurements on five glasses; one is as fused and the others are mechanically surface polished. The experimental geometrical factor obtained on the former glass agrees well with the calculated value, while those on the latter glasses are slightly higher. The experimental P-h curves of the mechanically su...

Journal ArticleDOI
TL;DR: In this article, the authors describe a quantitative model designed to explore the increase in systems hardness attributable to stresses created on the coating by the upthrust of substrate. But the authors do not consider how the upwelling of displaced substrate material creates an upward pressure on coating inducing elastic flexure which, in turn, resists the substrate deformation.
Abstract: In order to design the hard coating best suited to engineer the surface of a given substrate for a particular application, it is important that we have a clear picture of the mechanisms by which thin hard coated systems work. In this paper we describe a quantitative model designed to explore the increase in systems' hardness attributable to stresses created on the coating by the upthrust of substrate. material flowing plastically in response to indentation. Thus the model considers how the upwelling of displaced substrate material creates an upward pressure on the coating inducing elastic flexure which, in turn, resists the substrate deformation. The influence of this flexure has been investigated using a combination of existing analytical solutions (e.g. plate theory) to determine the overall effect on the indentation response of coated systems. The resulting model is critically compared with previous work. Experimental verification is provided by diverse experimental data from indentation tests on thin (1–24 μm) coatings of TiN and Cr on various metal substrates, sugar on chocolate substrates and other results drawn from the literature. The model helps to identify Eh 3 / d 3 H 0 as a dimensionless parameter which provides a means of condensing all available data onto a single “master” curve. Further developments are discussed.

Journal ArticleDOI
TL;DR: In this article, different diamond indenters, which are attached to single leaf springs of various stiffnesses, are used to study the effects of tip radius and apex angle on the measured hardness values.
Abstract: The Point Contact Microscope (PCM), developed in NTT's Kaneko Research Laboratory, is used to conduct hardness tests on polycarbonate and gold at indentation depths in the range of about 5-100 nm. Different diamond indenters, which are attached to single leaf springs of various stiffnesses, are used to study the effects of tip radius and apex angle on the measured hardness values. The indentation depth versus force and hardness versus force relations for various tip conditions are examined. It is found that the hardness value obtained increases for small values of indentation load and approaches a tip-independent value for larger loads. The hardness is sensitive to the indentation force and tip radius in the limit of small indentation depths

Journal ArticleDOI
TL;DR: In this paper, the fracture toughness of coarse-grained A12O3 was studied in the short-crack regime utilizing the stable propagation of indentation cracks in bending.
Abstract: The fracture toughness of coarse-grained A12O3, known for pronounced “Iong”-crack R-curve behavior, was studied in the “short”-crack regime utilizing the stable propagation of indentation cracks in bending. A combination of in situ microscopic crack growth observations and mechanical testing enabled measurement of crack extension curves. They reflect the contributions of residual indentation stress intensity and applied bending stress intensity on the total crack driving stress intensity and allow determination of the residual stress factor χ and the toughness KR. The results indicate that χ depends on indentation load and AR is surprisingly constant rather than increasing. To resolve the latter contradiction with long-crack R-curve behavior, combined short/long-crack fracture tests were performed with the same specimens. Starting with stable indentation crack growth and continuing with stable long-crack extension, the previous toughness results were confirmed, i.e., constant toughness from indentation cracks and increasing toughness from long cracks. The influence of crack-opening behavior on bridging-controlled R-curve toughening can qualitatively explain the observed discrepancies.

Journal ArticleDOI
TL;DR: In this article, the authors describe the experimental procedure for obtaining stress-strain curves from hardness tests and the indentation test conditions under which the conversion of the hardness-average strain data to flow stressstrain data is simple and straightforward in the sense that the constraint factor which is the correlating parameter for the above conversion is not only independent of strain but also easily computable on the basis of known mechanical properties of the test material.
Abstract: Hardness is a measure of the resistance of a material to indentation and a wide variety of indentation tests have been devised to measure the hardness of materials. In the case of hardness tests which utilize spherical balls as the indentor, it is also possible to derive flow stress-strain relationships from hardness tests carried out either over a range of loads (static test) or over a range of impact velocities (dynamic test). This paper first describes the experimental procedure for obtaining stress-strain curves from hardness tests. In addition, the paper also analyzes in detail, the indentation test conditions under which the conversion of the hardness-average strain data to flow stress-strain data is simple and straightforward in the sense that the constraint factor which is the correlating parameter for the above conversion is not only independent of strain but also easily computable on the basis of known mechanical property data of the test material.

Journal ArticleDOI
TL;DR: In this paper, the fracture toughness of a commercial, hot-pressed, in situ-toughened silicon nitride with an elongated grain structure is determined by four different testing methods.
Abstract: The fracture toughness of a commercial, hot-pressed, in situ-toughened silicon nitride with an elongated grain structure is determined by four different testing methods. The fracture toughness is found to be 5.76 +/- 0.27, 8.48 +/- 0.50, 10.16 +/- 0.66, and 10.68 +/- 0.39 MPa x m(exp 1/2), respectively, by indentation crack size measurement, indentation strength, single-edge-precracked-beam, and chevron-notched-beam methods. The discrepancy in fracture toughness between the testing methods is related to R-curve behavior, as measured using the indentation strength technique. These results indicate that there is no unique fracture toughness value and that a fracture toughness testing method with appropriate qualifiers is needed for rising R-curve materials. Therefore, care should be taken in interpreting and utilizing fracture toughness values evaluated from different testing methods if a material exhibits a rising R-curve. Complete characterization of the R-curve may be a prerequisite.

Journal ArticleDOI
TL;DR: In this article, it is shown that Auerbach's law in the strictest sense only applies to well-abraded specimens and a novel application of Weibull statistics is presented which allows the distribution of fracture loads to be predicted for any specimen surface condition for a given indentor size.
Abstract: The indentation strength of brittle solids is traditionally characterized by Auerbach's law, which predicts a linear relationship between the load required to initiate a Hertzian cone crack and the radius of a spherical indentor. This paper reviews both the energy balance and flaw statistical explanations of Auerbach's law. It is shown that Auerbach's law in the strictest sense only applies to well-abraded specimens. A novel application of Weibull statistics is presented which allows the distribution of fracture loads to be predicted for any specimen surface condition for a given indentor size. The indentation strength of a brittle solid, for both spherical and cylindrical indentors, is shown to be influenced by both its surface flaw statistics and the degree of interfacial friction. It is observed that the indentation strength of soda-lime glass is increased by a factor of about three times that expected for frictionless contact, and that for a fully bonded indentor, conical fractures cannot occur.

Journal ArticleDOI
TL;DR: In this paper, the fracture properties of a series of polycrystailine aluminas were examined using indentation strength and double cantilever beam techniques, and a model was developed for the general response, combining increasing toughening by ligamentary bridging at small crack lengths and increasing residual-stress relief by lateral cracking at large indentation loads.
Abstract: The fracture properties of a series of three polycrystailine aluminas are examined using indentationstrength and double cantilever beam techniques The indentation-strength response is shown to be sigmoidal with concave-down behavior at small indentation loads and concave-up behavior at large indentation loads A model is developed for the general response, combining increasing toughening by ligamentary bridging at small crack lengths and increasing residual-stress relief by lateral cracking at large indentation loads The model is fit to the strength data and used to deconvolute the underlying toughness variation and predict the intrinsic strength of the materials Direct measurements of toughness using the “long-crack” double cantilever beam geometry are shown to overestimate the toughness variations effective during “short-crack” strength tests

Journal ArticleDOI
TL;DR: In this article, the impression creep behavior of lead was investigated using a 100 μm diameter punch at ambient and elevated temperatures (433 K-563 K) under punching stresses of 6-70 MPa.
Abstract: The impression creep behavior of lead was investigated using a 100 μm diameter punch at ambient and elevated temperatures (433 K-563 K) under punching stresses of 6–70 MPa. The results were compared with the data obtained from conventional creep tests reported in the literature. Unlike the indentation creep test, the impression creep test showed a steady-state velocity after a short transient period when the flat-end cylindrical punch was pushed against the lead surface by a constant load. Both the temperature and stress dependences were comparable to those of the constant stress tensile creep tests under similar conditions. A master curve for lead was established by collecting data from the impression creep tests and the constant stress tensile creep tests. The indentation creep measurements for lead were included also. However, the indentation data depend on the load applied.