Analysis of indentation loading curves obtained using conical indenters

Using dimensional analysis and finite-element calculations we determine the functional form of indentation loading curves for a rigid conical indenter indenting into elastic-perfectly plastic solids. The new results are compared with the existing theories of indentation using conical indenters, including the slip-line theory for rigid-plastic solids, Sneddon's result for elastic solids, and Johnson's model for elastic-perfectly plastic solids. In the limit of small ratio of yield strength (Y) to Young's modulus (E), both the new results and Johnson's model approach that predicted by slip-line theory for rigid-plastic solids. In the limit of large Y/E, the new results agree with that for elastic solids. For a wide range of Y/E, some difference is found between Johnson's model-and the present result. This study also demonstrates the possibilities and limitations of using indentation loading curves to extract fundamental mechanical properties of solids.

Nonuniformity Effect of Surface-Nanocrystalline Materials in Nanoindentation Test

In the present research, microstructures of the surface-nanocrystalline Al alloy material are observed and measured based on the transmission electron microscopy (TEM) technique, and the corresponding mechanical behaviors are investigated experimentally and theoretically. In the experimental research, the nanoindentation test method is used, and the load and microhardness curves are measured, which strongly depend on the grain size and grain size nonuniformity. Two kinds of the nanoindentation test methods are adopted: the randomly selected loading point method and the continuous stiffness method. In the theoretical modeling, based on the microstructure characteristics of the surface-nanocrystalline Al alloy material, a dislocation pile-up model considering the grain size effect and based on the Mott theory is presented and used. The hardness-indent depth curves are predicted and modeled.

Substrate Effects on the Micro/Nanomechanical Properties of TiN Coatings

Nanoindentation and nanoscratch tests were performed for titanium nitride (TiN) coatings on different tool steel substrates to investigate the indentation/scratch induced deformation behavior of the coatings and the adhesion of the coating–substrate interfaces and their tribological property. In this work, TiN coatings with a thickness of about 500 nm were grown on GT35, 9Cr18 and 40CrNiMo steels using vacuum magnetic-filtering arc plasma deposition. In the nanoindentation tests, the hardness and modulus curves for TiN/GT35 reduced the slowest around the film thickness 500 nm with the increase of indentation depth, followed by TiN/9Cr18 and TiN/40CrNiMo. Improving adhesion properties of coating and substrate can decrease the differences of internal stress field. The scratch tests showed that the scratch response was controlled by plastic deformation in the substrate. The substrate plays an important role in determining the mechanical properties and wear resistance of such coatings. TiN/GT35 exhibited the best load-carrying capacity and scratch/wear resistance. As a consequence, GT35 is the best substrate for TiN coatings of the substrate materials tested.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Scaling, Dimensional Analysis, and Indentation Measurements

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Asymptotic analysis based on K-S constitutive law for a rubber wedge compressed by a line load at its tip

In the present paper, a rubber wedge compressed by a line load at its tip is asymptotically analyzed using a special constitutive law proposed by Knowles and Sternberg (K-S elastic law) [J. Elasticity 3 (1973) 67]. The method of dividing sectors proposed by Gao [Theoret. Appl. Fract, Mech. 14 (1990) 219] is used. Domain near the wedge tip can be divided into one expanding sector and two narrowing sectors. Asymptotic equations of the strain-stress field near the wedge tip are derived and solved numerically. The deformation pattern near a wedge tip is completely revealed. A special case. i.e. a half space compressed by a line load is solved while the wedge angle is pi.

The Response Of Porous Al2O3 Probed To Nanoindentation

The response of porous Al2O3 to nanoindentation was investigated at microscopic scales (nm-mu m) and under ultra-low loads from 5 to 90 mN with special attention paid to the dependence of the load-depth behaviour to sample porosity. It was found that the load-depth curves manifest local responses typical of the various porous structures investigated. This is particularly clear for the residual deformation after load removal. Similarly, the limited mean pressure of the sample containing small grains and interconnected pores is consistent with its porous structure. By comparison, the samples with larger grain size and various porous structures exhibit higher pressures and smaller residual deformations that can be attributed to the mechanical response of the solid phase. (C) 2007 Elsevier B.V. All rights reserved.

The Newest Developments Of Load-Unload Response Ratio (Lurr)

The Load Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It is inspiring that its predictions using LURR have been improving. Since 2004 we have made a major breakthrough in intermediate-term earthquake forecasting of the strong earthquakes on the Chinese mainland using LURR and successfully predicted the Pakistan earthquake with magnitude M 7.6 on October 8, 2005. The causes for improving the prediction in terms of LURR have been discussed in the present paper.

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.

Effect Of Load Triaxiality On Polymorphic Transitions In Zinc Oxide

Molecular dynamics (MD) simulations and first-principles calculations are carried out to analyze the stability of both newly discovered and previously known phases of ZnO under loading of various triaxialities. The analysis focuses on a graphite-like phase (FIX) and a body-centered-tetragonal phase (BCT-4) that were observed recently in [0 1 (1) over bar 0]- and [0 0 0 1]-oriented nanowires respectively under uniaxial tensile loading as well as the natural state of wurtzite (WZ) and the rocksalt (RS) phase which exists under hydrostatic pressure loading. Equilibrium critical stresses for the transformations are obtained. The WZ -> HX transformation is found to be energetically favorable above a critical tensile stress of 10 GPa in [0 1 (1) over tilde 0] nanowires. The BCT-4 phase can be stabilized at tensile stresses above 7 GPa in [0 0 0 1] nanowires. The RS phase is stable at hydrostatic pressures above 8.2 GPa. The identification and characterization of these phase transformations reveal a more extensive polymorphism of ZnO than previously known. A crystalline structure-load triaxiality map is developed to summarize the new understanding. (c) 2007 Elsevier Ltd. All rights reserved.

Plastic deformation in Ce-based bulk metallic glasses during depth-sensing indentation

The deformation behavior and the effect of the loading rate on the plastic deformation features in (numbers indicate at.%) Ce60Al15Cu10Ni15, Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu20Nb2, and Ce70Al10Cu20 bulk metallic glasses (BMGs) were investigated through nanoindentation. The load-displacement (P-h) curves of Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu2, and Ce70Al10Cu20 BMGs exhibited a continuous plastic deformation at all studied loading rate. Whereas, the P-h curves of Ce60Al15Cu10Ni15 BMG showed a quite unique feature, i.e. homogeneous plastic deformation at low loading rates, and a distinct serrated flow at high strain rates. Moreover, a creep deformation during the load holding segment was observed for the four Ce-based BMGs at room temperature. The mechanism for the appearance of the "anomalous" plastic deformation behavior in the Ce-based BMGs was discussed. (c) 2006 Elsevier B.V. All rights reserved.

Lattice type of fracture model for concrete

Concrete is usually described as a three-phase material, where matrix, aggregate and interface zones are distinguished. The beam lattice model has been applied widely by many investigators to simulate fracture processes in concrete. Due to the extremely large computational effort, however, the beam lattice model faces practical difficulties. In our investigation, a new lattice called generalized beam (GB) lattice is developed to reduce computational effort. Numerical experiments conducted on a panel subjected to uniaxial tension show that the GB lattice model can reproduce the load-displacement curves and crack patterns in agreement to what are observed in tests. Moreover, the effects of the particle overlay on the fracture process are discussed in detail. (C) 2007 Elsevier Ltd. All rights reserved.

Fatigue-crack closure measurements on 2024-t3 sheet specimens

A computer-controlled procedure has been developed for automatic measurement of the crack opening stress S-op during fatigue tests. A crack opening displacement gauge (GOD meter) is used to obtain digital data on the load versus COD curves. Three methods for deriving S-op from the data sets are compared: (1) a slope method, (2) a tangent lines intersecting method, and (3) a tangent point method. The effect of the position of the COD meter with respect to the crack tip on S-op is studied in tests of 2024-T3 specimens. Results of crack growth and S-op are presented for CA loading with an overload, and with an overload followed by an underload.

A new expression of hardening coefficients for fcc-crystal and calibration of the material constants

In order to describe the effect of latent hardening on the macro-plastic behavior of foc-crystal, a new expression for hardening coefficient is proposed in which there are 12 material constants, each having clear physical meaning. And a method of material constant calibration is suggested and used to determine the material constants of copper and aluminum crystal. The simulated load-elongation curves along various crystallographic orientations are comparable with the experimental ones.

Plastic stress-strain fields and blunting effects during large deformations

Plastic stress-strain fields of two types of steel specimens loaded to large deformations are studied. Computational results demonstrate that, owing to the fact that the hardening exponent of the material varies as strain enlarges and the blunting of the crack tip, the well known HRR stress field in the plane strain model can only hold for the stage of a small plastic strain. Plastic dilatancy is shown to have substantial effects on strain distributions and blunting. To justify the constitutive equations used for analysis and to check the precision of computations, the load-deflection of a three-point bend beam and the load-elongation of an axisymmetric bar notched by a V-shaped cut were tested and recorded. The computed curves are in good accordance with experimental data.