Indentation Load-depth Curves Research Articles

Investigation of the Anisotropic Mechanical Behaviors of Copper Single Crystals Through Nanoindentation Modeling

A crystal plasticity finite element method constitutive model was developed to investigate the anisotropic mechanical behaviors of (001), (011), and (111) initially orientated copper (Cu) single crystals during nanoindentation deformation. The numerical load-indentation depth curve and hardness-indentation depth curve were compared with experimental observations to validate the established three-dimensional (3D) CPFEM model. The difference of indentation loads between (111) crystal and (001) crystal is ~10.68 pct, and the difference of indentation modulus between (111) surface and (001) surface is ~10.80 pct. The numerical results show the noticeable indentation size effect for three crystals, and slightly different hardness values on different crystallographic planes. The equivalent plastic strain and lattice rotation angles were also analyzed on three through-thickness cross sections to study the plastic deformation-induced texture anisotropy.

Evaluation of mechanical properties using spherical ball indentation and coupled finite element–element-free galerkin approach

ABSTRACTIn the present work, the mechanical properties of pressure tube material (Zr-Nb2.5) are evaluated using the coupled finite element–element-free Galerkin approach. Penalty approach is used to impose contact constraints and non-penetration condition at the interface. An efficient node-to-segment algorithm is employed to model the contact behavior. An updated Lagrangian approach is used to model the large deformation. Loading and unloading response of the indentation process is analyzed using von-Mises and Gurson-Tvergaard-Needleman (GTN) plasticity models. In multiple indentations, the indentation depth is progressively increased up to a maximum specified limit with partial unloading. Load-indentation depth curves are used to extract the flow properties of the material.

Quantifying Grain Level Stress-Strain Behavior for AM40 via Instrumented Microindentation

ABSTRACTMicroindentation is performed on hot isostatic pressed (HIP) Mg-Al (AM40) alloy samples produced by high-pressure die cast (HPDC) process for the purpose of quantifying the mechanical properties of the α-Mg grains. The process of obtaining elastic modulus and hardness from indentation load-depth curves is well established in the literature. A new inverse method is developed to extract plastic properties in this study. The method utilizes empirical yield strength-hardness relationship reported in the literature together with finite element modeling of the individual indentation. Due to the shallow depth of the indentation, indentation size effect (ISE) is taken into account when determining plastic properties. The stress versus strain behavior is determined for a series of indents. The resulting average values and standard deviations are obtained for future use as input distributions for microstructure-based property prediction of AM40.

Contact size-independent method for estimation of creep properties with spherical indentation

Steady-state creep constitutes a major portion in the creep (strain vs. time) curve and is usually analyzed in characterizing creep behavior. In this numerical study, adopting a power-law creep material model, we propose a contact size-independent method for deriving creep properties from short-time spherical indentation test. Using finite element (FE) method with a wide range of creep properties, we investigate the characteristics of steady-state creep, while a fixed observation point beneath the indenter is employed to measure the material response to the indentation. We then establish functions that map indentation load–depth data to stress–strain rate data which provides creep properties without measuring the contact area. The proposed method provides the creep coefficients and the creep exponents with great accuracy from the indentation load–depth curves.

Spherical indentation method to evaluate material properties of high-strength materials

The spherical indentation method of Lee et al. (2005, 2010) [8,10] is extended for property evaluation of high-strength materials. By considering the finite deformation of elastic indenter due to high-strength of the indented material, regression functions are generated to map the indentation load–depth curve into the stress–strain curve. A property evaluation program is then written to produce material properties by using the indentation load–depth data from the loading/unloading process. Finally, the nano-indention tests with a spherical indenter are carried on Germanium Ge (100) and Silicon Si (100) to verify the proposed method using the experimental load–depth curves.

Prediction of viscoplastic properties of polymeric materials using sharp indentation

The present study proposes a new indentation method to predict the viscoplastic properties of polymeric materials utilizing three different indentation experiments. Numerical experiments with finite element method (FEM) are first carried out to simulate response of materials with various elastic and viscoplastic properties. The strain rate is featured by a loading rate of indentation, and the hardening rate can be captured through variations of the indenter shape. Next, a parametric FEM study is conducted to build the relationship between indentation load-depth curves and material parameters. Dimensionless analysis is employed to represent the relationship with simple formulae, through which, a reverse algorithm is proposed to extract the viscoplastic properties. Finally, both numerical and experimental investigations are performed to verify the proposed method.

Estimation of principal directions of Bi-axial residual stress using instrumented Knoop indentation testing

We propose a novel method for estimating stress directionality p and principal direction θp using four Knoop indentations. Indentation load-depth curves with a Knoop indenter are shifted with respect to indenter orientation to stress direction. Based on this phenomenon, we derived p and θp theoretically in terms of the indentation load differences between a stressed and an unstressed sample. Plastic zone beneath the Knoop indenter was theoretically estimated based on expanding cavity model for confirming separate plastic zones of four Knoop indentations. The proposed models and algorithms were verified by indentation experiments under various applied stress states that are generated using a stress-generating jig with two independent orthogonal loading axes. Estimated principal directions showed good agreement with applied principal directions. For small target area when considering in-field application, we proposed an estimation method of one load difference with other three load differences, and it was verified as feasible method with experimental results.

Characterization of materials' elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter

Abstract

Numerical comparison between Berkovich and conical nano-indentations: Mechanical behaviour and micro-texture evolution

A crystal plasticity finite element method (CPFEM) model has been developed to investigate the influence of indenter geometry on the mechanical behaviour and micro-texture evolution during nano-indentation of single crystal aluminium. The developed model has been validated by comparison with experimental observations. The numerical results show that indenter geometry influences the load–indentation depth curve, hardness and elastic modulus significantly. The surface profile, equivalent plastic strain distribution and micro-texture evolution during nano-indentation have been analysed in detail.

Evaluation of the material’s damage in gas turbine rotors by instrumented spherical indentation

Experimental indentations are carried out on items of two different materials, taken in several location of various components from high pressure gas turbine rotor which have seen an extensive service. The components object of investigation consisted in 1st and 2nd high pressure turbine wheels made in nickel-base superalloy (Inconel 718), the spacer ring (Inconel 718) and the compressor shaft made in CrMoV low alloy steel (ASTM A471 type10). Aim of the work is to set up the capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage, resulting from temperature field and stresses acting on components during service. To perform this task load-indentation depth curves will be acquired in various zones of the above mentioned components. The analysis of the results has allowed to identify an energy parameter which shows a linear evolution with the mean temperature acting on the components.

Temperature dependent deformation mechanisms in pure amorphous silicon

High temperature nanoindentation has been performed on pure ion-implanted amorphous silicon (unrelaxed a-Si) and structurally relaxed a-Si to investigate the temperature dependence of mechanical deformation, including pressure-induced phase transformations. Along with the indentation load-depth curves, ex situ measurements such as Raman micro-spectroscopy and cross-sectional transmission electron microscopy analysis on the residual indents reveal the mode of deformation under the indenter. While unrelaxed a-Si deforms entirely via plastic flow up to 200 °C, a clear transition in the mode of deformation is observed in relaxed a-Si with increasing temperature. Up to 100 °C, pressure-induced phase transformation and the observation of either crystalline (r8/bc8) end phases or pressure-induced a-Si occurs in relaxed a-Si. However, with further increase of temperature, plastic flow rather than phase transformation is the dominant mode of deformation. It is believed that the elevated temperature and pressure together induce bond softening and “defect” formation in structurally relaxed a-Si, leading to the inhibition of phase transformation due to pressure-releasing plastic flow under the indenter.

High-pressure (GPa) impedance measurements based on an indentation-induced local stress field

Electrical measurements of conducting and dielectric materials under high pressures (in the order of GPa) reveal important information regarding orbital overlaps, electronic states, changes in transition temperatures, and activation volumes (Delta V). In this study, we demonstrate a new method for high-pressure impedance measurements, up to 4 GPa, utilizing an indentation-induced local stress field. The current system does not require any pressure mediums or pressure calibrations. The Delta V for O2- ion conduction in 10 mol\% Y2O3-doped zirconia at 500 degrees C was estimated to be 3.0 cm(3) mol(-1). Delta V increased with increasing temperatures from 500 to 600 degrees C. The technique also allows the concurrent determination of the effective elastic modulus by fitting the experimental data obtained from the indentation load-depth profile curve with the Hertzian elastic model. The experimental values were consistent with the theoretical values. (C) 2013 Elsevier B.V. All rights reserved.

Correction of indentation load–depth curve based on elastic deformation of sharp indenter

Indenters in numerical analyses are usually assumed rigid. For rigid indenters, the ratios of Kick’s law coefficient to elastic modulus (C/E) are equal for materials with equal values of yield strain (εo) and strain hardening coefficient (n). However, this is not the case for elastic indenters as indenter deformation leads to a shift of the load–depth (P–h) curve.In this study, we employ conical indenters with half-included angle θ=70.3°, tip radius R=0.025mm to derive a corrected P–h curve; maximum indentation depth is set to hmax=0.05mm. Applying finite element analysis (FEA), we show that materials with equal εo and n give equal C/E-values for rigid indenters but different C/E-values for elastic indenters. To account for the elastic deformation of the indenter, we establish a method by introducing a correction factor κ so that equal C/E-values are obtained. It is found that for a given θ, κ does not change when varying indenter size, indentation depth and indenter tip-radius. For a different indenter angle θ, a different value of κ is obtained, yet by following the same correction procedure.We further demonstrate that corresponding κ values for triangular pyramidal indenters are different from those of conical ones, due to the difference in actual projected contact areas. Consequently, the proposed method is applicable to any indenter shape.

Characterization of the viscoelastic-plastic properties of UPVC by instrumented sharp indentation

The yielding behavior of glassy polymers may be sensitive to the hydrostatic pressure and also be influenced by the strain rate. Thus, the yield strength is a function of hydrostatic pressure and strain rate instead of a constant. In this paper, using dimensional analysis and finite element simulations, we established a method to estimate the yield strength of glassy polymers by instrumented indentation. Together with the method for determining shear creep compliance proposed in our previous work, the viscoelastic-plastic properties of glassy polymers can be extracted from a single indentation load-depth curve. Applications were illustrated on unplasticized polyvinyl chloride (UPVC). The shear creep compliance and yield strength of UPVC were successfully determined by a single indentation test. Using these parameters, the true stress–strain curves of UPVC under different strain rates were approximately predicted according to a linear viscoelastic-perfectly plastic constitutive description.

Nanoindentation analysis of the pop-in events on SiGe single layer

The growth of metastable silicon germanium (Si0.8Ge0.2) thin film on Si(100) by ultrahigh-vacuum chemical vapor deposition has been subjected to residual indentation studies. A nanoindentation system has been applied to analyze SiGe film after different annealing treatments. A number of phenomena have been found for the heteroepitaxial growth of SiGe film at the critical thickness of 350nm, including single discontinuity (the so-called “pop-in” event) as well as the elastic/plastic contact translation. Atomic force microscopy is employed to investigate the surface impression. Pop-in events in the load-indentation depth curves of 400 and 500°C and no nano-cracks in the vicinity regions are found. The values of H ranging from 13.13±0.9, 21.66±1.3, 18.52±1.1, 14.47±0.7GPa and the values of E ranging from 221.8±5.3, 230.7±6.4, 223.5±4.6, 156.7±3.8GPa, are obtained. The elastic/plastic contact translation of the SiGe film occurs at different annealing conditions, with hf/hmax values in the range of 0.501, 0.392, 0.424, and 0.535 for samples are treated at RT, 400, 500, and 600°C, respectively. The mechanism responsible for the pop-in event in such crystal structure is due to the interaction of the indenter tip with the pre-existing threading dislocations, since the release of the indentation load is bound to be reflected in the directly compressed volume.

Mechanical response of novel SiOC glasses to high temperature exposition

Abstract The presented work describes mechanical properties of materials prepared by the pyrolysis of polysiloxane resins. The polymeric precursors have different chemical composition. Materials under investigation are predetermined for high temperature resistant applications usually in composite form, i.e. accompanied by some reinforcement. Instrumented hardness tests were employed for material characterisation. The Vickers hardness, Martens hardness and indentation elastic modulus were the key parameters, determined either from the standard optical technique or load–indentation depth curves. The influence of mechanical properties on the monomers ratio was established. The exposition to the temperature between 1200 °C and 1500 °C in air was applied to observe damage caused by these severe conditions.

An alternative to the determination of the effective zero point in instrumented indentation: Use of the slope of the indentation curve at indentation load values

In instrumented indentation testing, especially in the nano and micro scales, low scale artefacts such as sensor sensitivity, surface roughness, imperfect indenter tip geometry and material heterogeneity can create significant deviations of the measured indentation load-depth curve from the ideal curve corresponding to the bulk material.This study assesses the influence of an offset of the measured penetration depth on the identified bulk mechanical parameter values when using a reverse analysis model based on spherical indentation. It is shown through numerical examples that significant errors arise if the identification procedure is based on the load values recorded at penetration depth values. In over to overcome this effect, an alternative exploitation of the reverse analysis model is proposed, which is based on the use of the slope of the indentation curve at indentation load values. In addition, it is proposed to neglect the data at low load values in order to avoid the effect of low scale artefacts on the shape of the indentation curve at low load values.The proposed approach is applied to the numerical examples, and then an experimental case of a blunted indenter tip is presented. In all cases, the proposed approach provides accurate identification results which are not affected by low scale artefacts. The proposed approach can be significantly useful when analysing indentation curves obtained in the nano and micro scales, as well as indentation curves obtained in industrial conditions.

Numerical simulation and experimental validation of the microindentation test applied to bulk elastoplastic materials

The main objective of this work is to compare numerically simulated load–indentation depth curves together with deformation and stress fields underneath a sharp indenter for a set of mystical materials. Firstly, a numerical simulation and experimental validation of the microindentation test applied to three different bulk elastoplastic materials (copper, stainless steel and pure aluminium) using two indenters (Berkovich and spherical) are presented. The simulation of these microindentation tests is carried out using the finite element large strain elastoplastic and contact models. The corresponding results are particularly aimed at addressing the following aspects: the influence of the indenter geometry on both the load–indentation depth curve and range of plastic strains involved in the test, the comparison of the 3D results for the sharp indenter with those of the 2D approximation, the capabilities of the modelling through experimental validation of the numerical predictions and, in addition, an assessment of the indentation size effect. Secondly, the numerical results of Berkovich indentation applied to a set of mystical materials are exhaustively discussed. Although it is effectively shown that these mystical materials exhibit indistinguishable load–penetration depth curves during the loading phase, an important aspect that has not been previously addressed is that some clear differences in their responses are obtained for the unloading stage. Finally, the deformation and stress contours at the maximum indentation force and after unloading are particularly analysed.

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.

A study on robust indentation techniques to evaluate elastic–plastic properties of metals

Spherical indentation is studied based on numerical analysis and experiment, to develop robust testing techniques to evaluate isotropic elastic–plastic material properties of metals. The representative stress and plastic strain concept is critically investigated via finite element analysis, and some conditions for the representative values are suggested. The representative values should also be a function of material properties, not only indenter angle for sharp indenter and indentation depth for spherical indenter. The pros and cons of shallow and deep spherical indentation techniques are also discussed. For an indentation depth of 20% of an indenter diameter, the relationships between normalized indentation parameters and load–depth data are characterized, and then numerical algorithm to estimate material elastic–plastic curve is presented. From the indentation load–depth curve, the new approach provides stress–strain curve and the values of elastic modulus, yield strength, and strain-hardening exponent with an average error of less than 5%. The method is confirmed to be valid for various elastic properties of indenter. Experimental validation of the approach then is performed by using developed micro-indentation system. For the material severely disobeying power law hardening, a modified method to reduce errors of predicted material properties is contrived. It is found that our method is robust enough to get ideal power law properties, and applicable to input of more complex physics.