Indenter Orientation Research Articles

Atomistic understanding of the variable nano-hardness of C-plane sapphire considering the crystal anisotropy

Nanoindentation test method is widely used to measure the material hardness, which is a standard test and the effect of measurement error is limited. However, the measured results of the nano-hardness for the same plane of single crystal materials, such as sapphire, were very different. The possible reason for the difference of nano-hardness is induced by the anisotropy of single crystal materials. In this study, nanoindentation tests were carried out to obtain the nano-hardness of C-plane sapphire. The tests with two different indenter orientations were designed as follow. On C-plane, one edge of the Berkovich indenter was indented parallel to the direction [101‾0], as well as one edge indented perpendicular to the direction [101‾0] for comparison. The average hardness was 25.58 GPa and 29.64 GPa respectively. Molecular dynamics simulation was employed to reveal the generation mechanism of anisotropy in nanoindentation process. The results showed that the distribution of subsurface dislocations and the activation of slip systems were affected by indenter orientations, which resulted in the difference in nano-hardness. When one edge of the Berkovich indenter was indented perpendicular to the direction [101‾0], C-plane sapphire had a stronger ability to resist deformation, showing a higher hardness on the macroscopic level.

Characterizing elastic constants of anisotropic materials by spherical indentation method

By the theoretical analysis and the finite element (FE) method, a new model for measuring the elastic constants of transversely isotropic materials has been proposed from spherical indentation. A theoretical analysis of the spherical indentationmodulus for the materials is presented. Extensive spherical indentation tests were implemented by three dimensional (3D) FE simulations. By fitting the simulation results, the analytical relationship correlating the elastic parameters with the indentation moduli at three different indentation orientation angles (0°, 45°, and 90°) was set up. The effectiveness of the proposed method was examined by a series of numerical indentation experiments. It is found that the calculated values by the proposed method are well consistent with the input elastic parameters. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, this method was applied to carbon fiber materials. The results calculated by the method proposed in this paper were compared with results obtained by the theoretical model and experimental measurement to verify the effectiveness of this method. Thus the proposed method is practiced and could be used to identify the elastic properties of transversely isotropic materials.

Material removal behavior analysis of ZnSe crystal during side-forward nanoscratching

Zinc selenide (ZnSe) crystal is difficult to cut due to its high brittleness. A better understanding of the material removal mechanism of ZnSe crystal is indispensable to help achieve a high-quality machined surface. In this paper, a theoretical model is first developed for analyzing the material removal behavior of brittle crystals during side-forward nanoscratching using the Berkovich indenter. The model correlates scratching parameters with scratch behavior parameters, morphology parameters, material removal modes, and material mechanical properties. To validate the model, the nanoindentation and side-forward nanoscratch tests of ZnSe crystal are carried out, and the effects of load and strain rate on the mechanical properties and scratch behavior of ZnSe crystal are investigated. The results show that the hardness decreases first and then stabilizes as the indentation load increases; the elastic modulus generally increases with the indentation load while it increases sharply at a very small strain rate. The results also show that with an increasing scratching normal load, the elastic recovery decreases first and then stabilizes while the friction coefficient increases slightly first and then stabilizes; with the increase of strain rate, the elastic recovery, scratching load, and friction coefficient decrease quickly at first and then increase by a similar power function. The model is proven to be applicable to determining the scratching load, friction coefficient, scratching depth, and elastic recovery with pile-up parameters, groove parameters, indenter orientation angle, and mechanical properties of ZnSe crystal, which has an average relative error of less than 14%. Furthermore, the effects of scratching direction on the scratching load and friction coefficient are discussed using the model. The results show that for side-forward scratching, the maximum normal load always occurs which is independent of the indenter orientation angle, while a relatively small friction coefficient exists. This research provides insights into the material removal behavior and mechanism in ultra-precision machining of ZnSe crystal.

Material removal mechanism and penetration depth modeling of CF/PEEK composites under nano-scratching

In order to investigate the material removal mechanism of carbon fiber-reinforced thermoplastics (CFRTP), nanoscratching experiments of carbon fiber-reinforced polyetheretherketone (CF/PEEK), as a typical kind of thermoplastic composite, were performed along various feed directions of the indenter and fiber orientations. Material removal mechanism was researched based on surface and subsurface morphological features. Experimental results indicated that chips were easily attached to the sample surface and difficult to remove, while chips containing much resin tended to accumulate and were tough to break. In addition, under the radial load, it was often observed that the interface remained still well, even though the breaking occurred inside the fibers during the scratching process. And under the axial load, there was crack deflection near the resin which inhibited the cracks expansion between the fibers. Furthermore, a penetration depth modeling to the normal load for CF/PEEK nanoscratching was developed, taking into account the impacts of elastic recovery, anisotropy, heterogeneity and stress distribution of material. Experimental validations showed that the prediction results evaluated by theoretical model was close to the actual results.

Biaxial residual stress measurement by indentation energy difference method: Theoretical and experimental study

In this paper, an energy difference method is proposed to estimate biaxial stress components based on indentation technique. The indentation energy is chosen as an analytical parameter, which can be calculated directly from the load-depth curve. The presence of residual stress in a material causes the change of indentation energy. The mapping relationship between uniaxial stress and indentation energy difference was established by finite element analysis. Meanwhile, the Knoop tip was applied since the indentation response varies according to the indenter orientation. Using this feature, a biaxial stress state can be transformed into two equivalent uniaxial stress states by indentation energy conversion. Finally, the biaxial residual stress components can be solved by the energy difference functions of two orthogonal indentations. A portable indentation instrument was developed to implement this approach, which is suitable for in-site measurement. The obtained results show good agreements with the artificial stresses applied by cross-shape sample experiment.

A new methodology for measuring residual stress using a modified Berkovich nano-indenter

In this paper, a new methodology, based on nanoindentation, is proposed to estimate the magnitude and orientation of the principal residual stress components, in a non-equi-biaxial residual stress field at the nanoscale. The proposed method exploits the force-penetration response provided by a modified Berkovich tip that, compared to the most traditional one, is characterized by a preferential elongated size. This feature allows in estimating non-equibiaxial residual stress field since the force-penetration response changes according to the indenter orientation. No observation of the residual imprint is required. Principal stress components and orientations are estimated thanks to theoretical and finite element analysis, establishing a linear relation between stress components and load variations respect to the stress-free sample. Finite element analysis is used to calibrate the model coefficients and to verify the accuracy of this approach for isotropic metals. Obtained results revealed that the method is well suitable in estimating both tensile and compressive residual stresses with an average error lower than 6% for the first case and lower than 10% for the second one.

Simulating Knoop hardness anisotropy of aluminum and β-HMX with a crystal plasticity finite element model

We report a crystal plasticity finite element model for simulating the variation of the Knoop hardness number with indenter orientation, i.e., the hardness anisotropy. We propose a modification to the Voce hardening law to include the effects of slip on multiple systems on the hardening rate. The model is validated using single crystal aluminum in a two-step procedure: (a) calibration of the material model with single crystal tension experiments, and (b) prediction of the hardness anisotropy of the {001}, {011} and {021} planes. The predicted hardness anisotropy follows experimental trends very well for the {001} and {021} planes, while for the {011} plane there is a deviation of the predictions from experiments at higher angles of the indenter. The model is then used to simulate the hardness anisotropy of the (010), (011) and (110) planes of β-HMX measured by Gallagher et al. (2015). Due to the lack of single crystal data, we were unable to calibrate the model prior to simulating the hardness anisotropy. Hence, we assumed unknown variables to make predictions for comparison to experiments, including the set of active slip systems and the hardening and twinning behavior. From simulations of the indentation of the (010) plane with the set of slip systems from Barton et al (2009) we found that the hardness anisotropy is inversely proportional to the activity of the slip system (101)[01¯0], and to a lesser extent the twin system. Suppressing the (101)[01¯0] slip system improved the predictions, suggesting that the viable set of slip systems for β-HMX need not include it. The predicted twinning activity did not match well with the observations from Gallagher et al. (2015). Suppressing the twinning resulted in a better prediction of the hardness anisotropy. Due to the simplicity of the twinning part of the model we do not make definite conclusions related to twinning. We report predictions for the hardness anisotropy of the (011) and (110) planes of β-HMX using parameters that maximized agreement between simulations and experimental indentation of (010) plane. These predictions are in reasonable agreement with experiments. In addition, we report the predictions of the hardness anisotropy using the sets of slip systems proposed by Pal and Picu (2018) and Zhou et al. (2012), which both gave inferior agreement with experiments.

Anisotropy in the hardness of single crystal tungsten before and after neutron irradiation

In this work, the hardness of single crystal tungsten (W) after low, medium and high temperature neutron irradiation, reaching up to 1200°C, is studied. Micro-hardness tests with Vickers pyramid indenter are performed on reference and neutron irradiated samples by varying the orientation of the indenter on the single crystal tungsten contact surface. Due to the availability of multiple slip systems, the anisotropy of the hardness is characterized to allow the construction of uncertainty bands as well as dependence of the absolute value of the hardness on the orientation of the indenter wedges and principal crystallographic axes of the crystal. The applied neutron fluence and flux is representative for the ITER reactor, where tungsten is selected as armour material for plasma facing components. The neutron irradiation is performed in the BR2 reactor with mixed neutron spectrum up to 1 dpa (end of life fluence for ITER) but with appropriate measures to reduce the thermal neutron flux, such that the spurious transmutation into rhenium is reduced. The hardness study is accompanied with a detailed microscale examination to deduce the true indenter surface area. As a result, the true values of the hardness accounting for the pile-up effects are obtained as a function rotation angle of the indenter. The variation of the hardness as a function of indenter orientation before and after irradiation is discussed based on the indenter-slip system geometry. A simple but efficient methodology is proposed to deduce the true hardness and its angle-dependent variation for single crystal tungsten.

ESTIMATION OF ANISOTROPIC ELASTIC PROPERTIES OF CARBON FIBERS USING NANOINDENTATION

Understanding the mechanical behavior of carbon fiber reinforced polymers requires knowledge on the deformation behavior of carbon fibers, they are highly anisotropic and heterogeneous. Nanoindentation is an efficient method for determining the mechanical properties in small volumes of materials. For isotropic materials, a single nanoindentation test can evaluate an elastic properties of the material. But for anisotropic material, the difficulty increases since measured indentation modulus depends on five elastic parameters (El,Et,Glt, νlt,and νtt) of the material. Nanoindentation experiments are performed on carbon fibers orientated between 0° to 90° at ten different orientations to the fiber axis. From theoretical models given by Vlassak et al. and Delafargue and Ulm, the elastic constants are predicted numerically by comparing the results of indentation modulus versus orientation angle with the experiments.

Local analysis on dislocation structure and hardening during grain boundary pop-ins in tungsten

In the present work, dislocation structures at the grain boundary (GB) pop-in events were studied around and below the Berkovich indentations using electron channeling contrast imaging (ECCI) in polycrystalline tungsten. The GB pop-in events were identified as displacement bursts in the load–displacement curve, and the indentation experiments were stopped just after the occurrence of the displacement burst. A significant hardness increase was observed before the GB pop-in event. The careful ECCI analysis on the sequential polished cross sections clearly shows the dislocation pile-up in the vicinity of the GB along with transmitted dislocations in the adjacent grain. The transmitted dislocations were also found to be influenced by the indenter orientation with respect to the GB.

Nanoindentation of Aluminum Single Crystals: Experimental Study on Influencing Factors.

Results from nanoindentation of aluminum single crystals deliver valuable information as model systems for understanding technical aluminum alloys. The effect of the crystal orientation and the azimuthal indenter orientation on indentation hardness and modulus was studied by Vickers indentation (max. load 10 mN) on single crystal surfaces with (100), (110), and (111) orientations. The average indentation hardness varied, depending on the crystallographic orientation, by 1.8%. The anisotropy of the elastic modulus (1.1% of the average modulus) is lowered (indentation averaging effect). This is predicted by explicit approximation of the contact problem (conical indenter, orthotropic material). It was found that indentation hardness and modulus vary periodically with the azimuthal indenter orientation on (100)- and (110)-oriented surfaces (relative amplitude of 1.8% for indentation hardness and 2.6% of the modulus). This is attributed to the combined effect of the indenter geometry and crystal symmetry. For the first time, this effect was quantified for aluminum single crystals.

Deformation mechanisms under nanoscratching of Si: effect of scratching speed, load and indenter orientation

The deformation peculiarities under the nanoscratching of Si(100) as a function of three factors—(i) orientation of the Berckovich indenter (face-on and edge-on), (ii) load and (iii) scratching speed - were investigated in this work. The load and scratching speed have a mutual influence and their certain combination plays a determining role in the development of one or another mechanism of deformation under the nanoscratching of Si. Along with the phase transformation, three peculiar mechanisms of deformation were found to be involved in the scratching process: brittle fracture (BF), plastic flow (PF) and ductile cutting (DC). The evolution and the relative contribution of these deformation mechanisms in the interval of loads 2–20mN and scratching speeds 20–300 μm/s were studied. It was shown that scratch hardness depends strongly on the scratching speed and load, but this dependence has distinctive features for scratches formed though PF and DC mechanisms.

Morphometric classification of swell-dominated embayed beaches

Globally, embayed beaches are common to hilly and mountainous coastlines. They are typically characterised by two headlands that are a primary control on incident wave exposure and beach morphodynamics. Embayed beaches exist under a range of headland morphologies and degree of embaymentisation. Here, we present a generalised embayment morphometric parameter (γe) which classifies the geomorphological setting of embayed beaches based on the embayment indentation and area. We apply this to 168 swell-dominated embayed beaches from 6 regions using open-access imagery. The embayment morphometric parameter (γe) was subjected to k-means cluster analysis to identify 4 classes of embayed beaches with increasing γe indicating greater headland influence and impact on incident wave exposure. The Classes range from 1 to 4 with increasing degree of embayment. The most common is Class 2 (43%, n = 73) which represents embayed beaches that have moderate embayment indentation and headland influence. There are clear trends in embayment geometry regardless of location, wave climate or tidal regimes. Within the embayments, there were 6 possible headland orientations (types H1–H6). The most common (58%, n = 97) is when both headlands are orientated outwards from the beach (H6) and may result in greater morphological beach response from less headland shadowing, compared with headlands orientated inwards onto the beach (H1). In summary, we have developed a simple classification scheme for embayed beaches based on degree of indentation and headland orientation that can be applied to any embayed beach globally.

Indentation and hydride orientation in Zr-2.5%Nb pressure tube material

In this study, indentations were made on Zr-2.5%Nb pressure tube material to induce multi-axial stress field. An I-shaped punch mark was indented on the Pressure tube material with predefined punch load. Later material was charged with 50 wppm of hydrogen. The samples near the punch mark were metallographically examined for hydrides orientation. It was observed that hydrides exhibited preferentially circumferential orientation far away from the indent to mixed orientation containing both circumferential and radial hydrides near the indent. This is probably as a result of stress field generated by indentation. Extent of radial hydride formation was observed to be varying with indentation load.

Molecular dynamics simulation of friction and heat properties of Nano-texture GOLD film in space environment

In this paper, a molecular dynamics model is proposed to describe the collision friction of a hinge mechanism in the space environment. The EAM potential is used to describe the interaction between atoms. Based on the model, the collision friction process and thermal properties between the indenter and smooth gold film surface at different indenter amplitudes, frequencies and crystal orientations are studied. The temperature distribution and collision friction mechanism of the gold film are analyzed. The simulation results show that increasing the vibration frequency of the indenter in a certain frequency range can reduce the friction force. The amplitude of the indenter and crystal orientations at different frequencies shows different effects on the average friction force and the surface temperature of the substrate. In addition, textures are also made on the gold film and the effects of texture width and texture depth on the friction and thermal properties are investigated. The results show that the textured surface can significantly reduce the friction force. The average friction force and the surface temperature of the substrate decrease with the increase of texture depth, and increase with the increase of texture width. The average friction force and the surface temperature of the substrate are more sensitive to the texture depth.

MRI based 3D finite element modelling to investigate deep tissue injury

Pressure ulcers occur due to sustained mechanical loading. Deep tissue injury is a severe type of pressure ulcer, which is believed to originate in subcutaneous tissues adjacent to bony prominences. In previous experimental-numerical studies the relationship between internal tissue state and damage development was investigated using a 2D analysis. However, recent studies suggest that a local analysis is not sufficient. In the present study we developed a method to create animal-specific 3D finite element models of an indentation test on the tibialis anterior muscle of rats based on MRI data. A detailed description on how the animal specific models are created is given. Furthermore, two indenter geometries are compared and the influence of errors in determining the indenter orientation on the resulting internal strain distribution in a defined volume of tissue was investigated. We conclude that with a spherically-shaped indenter errors in estimating the indenter orientation do not unduly influence the results of the simulation.

Molecular Dynamics Simulation on B3-GaN Thin Films under Nanoindentation.

The B3-GaN thin film was investigated by performing large-scale molecular dynamics (MD) simulation of nanoindentation. Its plastic behavior and the corresponding mechanism were studied. Based on the analysis on indentation curve, dislocation density, and orientation dependence, it was found that the indentation depths of inceptive plasticity on (001), (110), and (111) planes were consistent with the Schmid law. The microstructure evolutions during the nanoindentation under different conditions were focused, and two formation mechanisms of prismatic loop were proposed. The “lasso”-like mechanism was similar to that in the previous research, where a shear loop can translate into a prismatic loop by cross-slip; and the extended “lasso”-like mechanism was not found to be reported. Our simulation showed that the two screw components of a shear loop will glide on another loop until they encounter each other and eventually produce a prismatic dislocation loop.

Deformation and fracture in (0001) and (10-10) GaN single crystals

ABSTRACTIndentation techniques were utilised to induce deformation on polar (0001) c-plane and non-polar m-plane GaN single crystal. Cracking was more sensitively dependent on the orientation of the indenter tip, compared to hardness. The indentation-induced plastic deformation and fracture sequences were studied by cathodoluminescence imaging and optical microscopy, respectively. Polar GaN was harder than non-polar, while pop-in discontinuities occurred at lower loads in polar than non-polar GaN. Dislocation arrangements were more isotropic at the polar than the non-polar orientation. Polar GaN was more susceptible to cracking compared to non-polar. Indentation at the high load regime fostered radial and lateral crack formation at both indenter orientations in polar GaN. Post-indentation lateral crack propagation was observed in situ in polar GaN.This is part of a thematic issue on Nanoscale Materials Characterisation and Modeling by Advances Microscopy Methods - EUROMAT.

Finite element modeling of nanoindentation response of elastic fiber-matrix composites

Abstract

Effect of Indentation Orientation on the Onset of Plastic Deformation for a MAX Phase Ti<sub>2</sub>AlC

Effect of Indentation Orientation on the Onset of Plastic Deformation for a MAX Phase Ti<sub>2</sub>AlC