Special Issue "Crystal Indentation Hardness"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystal Engineering".

Deadline for manuscript submissions: closed (30 September 2017)

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Guest Editor
Prof. Dr. Ronald W. Armstrong

Department of Mechanical Engineering, A. James Clark School of Engineering, University of Maryland, College Park, MD 20742, USA
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Interests: crystal dislocations; x-ray diffraction imaging; polycrystalline microstructures; mechanical properties; constitutive equations
Guest Editor
Dr. Stephen M. Walley

Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
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Interests: high rate deformation; history of mechanical testing of materials; energetic crystals and polymers
Guest Editor
Prof. Dr. Wayne L. Elban

Department of Engineering, Loyola University Maryland, Baltimore, MD 21210, USA
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Interests: mechanical properties; indentation hardness; microstructural characterization; historical ferrous metallurgy

Special Issue Information

Dear Colleagues,

Determinations of the indentation hardness properties of crystals have expanded to cover the full characterizations of their important elastic, plastic and cracking behaviors, particularly as accomplished with the increased measuring capabilities of nanoindentation hardness testing. No crystal structure of any bonding type is either too soft or too hard to prevent measurement with a suitable probing indenter. The current Special Issue is devoted to surveying the topic with emphasis given in a collection of reports to: (1) the diversity of crystals being tested; (2) the variety of measuring techniques; and (3) the wealth of information being obtained.

Prof. Dr. Ron Armstrong
Prof. Dr. Stephen Walley
Prof. Dr. Wayne L. Elban
Guest Editors

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Keywords

  • indentation hardness

  • nanoindentation testing

  • elastic loading

  • plastic deformation

  • indentation fracture mechanics

Published Papers (21 papers)

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Editorial

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Open AccessEditorial Crystal Indentation Hardness
Crystals 2017, 7(1), 21; https://doi.org/10.3390/cryst7010021
Received: 5 January 2017 / Accepted: 6 January 2017 / Published: 12 January 2017
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Abstract
There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring
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There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring capabilities achieved in a continuously recorded test procedure. The new results have been smoothly merged with other advances in conventional hardness testing and with parallel developments in improved model descriptions of both elastic contact mechanics and dislocation mechanisms operative in the understanding of crystal plasticity and fracturing behaviors. No crystal is either too soft or too hard to prevent the determination of its elastic, plastic and cracking properties under a suitable probing indenter. A sampling of the wealth of measurements and reported analyses associated with the topic on a wide variety of materials are presented in the current Special Issue. Full article
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Research

Jump to: Editorial, Review

Open AccessArticle A New Method for Evaluating the Indentation Toughness of Hardmetals
Crystals 2018, 8(5), 197; https://doi.org/10.3390/cryst8050197
Received: 2 March 2018 / Revised: 29 March 2018 / Accepted: 25 April 2018 / Published: 3 May 2018
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Abstract
This paper proposes a new method of evaluating the indentation toughness of hardmetals using the length of Palmqvist cracks (C) and Vickers indentation diagonal size (di). Indentation load “P” is divided into two parts: Pi
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This paper proposes a new method of evaluating the indentation toughness of hardmetals using the length of Palmqvist cracks (C) and Vickers indentation diagonal size (di). Indentation load “P” is divided into two parts: Pi for plastic indentation size and Pc for Palmqvist cracks. Pi depends upon the square of the indentation size (di2) and Pc depends upon (C3/2). The new method produces a very good linear relationship between the calculated indentation toughness values and the standard conventional linear elastic fracture mechanics toughness values with the same cemented carbide materials for a large number of standard Kennametal grades for both straight WC-Co carbide grades and grades containing cubic carbides. The new method also works on WC-Co hardmetal data selected from recently published literature. The technique compares the indentation toughness values of WC-Co materials before and after vacuum annealing at high temperature. The indentation toughness values of annealed carbide samples were lower than for un-annealed WC-Co hardmetals. Full article
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Open AccessCommunication A Study of Extended Defects in Surface Damaged Crystals
Crystals 2018, 8(2), 67; https://doi.org/10.3390/cryst8020067
Received: 7 November 2017 / Revised: 9 January 2018 / Accepted: 24 January 2018 / Published: 30 January 2018
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Abstract
We have analyzed by transmission electron microscopy silicon and GaAs crystals polished with sandpapers of different grain size. The surface damage induced a crystal permanent convex curvature with a radius of the order of a few meters. The curvature is due to a
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We have analyzed by transmission electron microscopy silicon and GaAs crystals polished with sandpapers of different grain size. The surface damage induced a crystal permanent convex curvature with a radius of the order of a few meters. The curvature is due to a compressive strain generated in the damaged zone of the sample. Contrary to what was reported in the literature, the only defects detected by transmission electron microscopy were dislocations penetrating a few microns from the surface. Assuming the surface damage as a kind of continuous indentation, a simple model able to explain the observed compressive strain is given. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Nanoindentation-Induced Pile-Up in the Residual Impression of Crystalline Cu with Different Grain Size
Crystals 2018, 8(1), 9; https://doi.org/10.3390/cryst8010009
Received: 25 October 2017 / Revised: 9 December 2017 / Accepted: 19 December 2017 / Published: 26 December 2017
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Abstract
Nanoindentation morphologies of crystalline copper have been probed at the grain scale. Experimental tests have been conducted on nanocrystalline (NC), ultrafine-grained (UFG), and coarse-grained (CG) copper samples with a new Berkvoich indenter at the strain rate of 0.04/s without holding time at an
[...] Read more.
Nanoindentation morphologies of crystalline copper have been probed at the grain scale. Experimental tests have been conducted on nanocrystalline (NC), ultrafine-grained (UFG), and coarse-grained (CG) copper samples with a new Berkvoich indenter at the strain rate of 0.04/s without holding time at an indentation depth of 2000 nm at room temperature. As the grain size increases, the height of the pile-up around the residual indentation increases and then exhibits a slightly decrease in the CG Cu. The maximum of the pile-up in the CG Cu obviously deviates from the center of the indenter sides. Our analysis has revealed that the dislocation motion and GB activities in the NC Cu, some cross- and multiple-slip dislocations inside the larger grain in the UFG Cu, and forest dislocations from the intragranular Frank-Read sources in the CG Cu would directly induce this distinct pile-up effect. Full article
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Open AccessArticle Local Stress States and Microstructural Damage Response Associated with Deformation Twins in Hexagonal Close Packed Metals
Crystals 2018, 8(1), 1; https://doi.org/10.3390/cryst8010001
Received: 17 November 2017 / Revised: 13 December 2017 / Accepted: 18 December 2017 / Published: 21 December 2017
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Abstract
The current work implements a correlative microscopy method utilizing electron back scatter diffraction, focused ion beam and digital image correlation to accurately determine spatially resolved stress profiles in the vicinity of grain/twin boundaries and tensile deformation twin tips in commercially pure titanium. Measured
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The current work implements a correlative microscopy method utilizing electron back scatter diffraction, focused ion beam and digital image correlation to accurately determine spatially resolved stress profiles in the vicinity of grain/twin boundaries and tensile deformation twin tips in commercially pure titanium. Measured local stress gradients were in good agreement with local misorientation values. The role of dislocation-boundary interactions on the buildup of local stress gradients is elucidated. Stress gradients across the twin-parent interface were compressive in nature with a maximum stress magnitude at the twin boundary. Stress profiles near certain grain boundaries initially display a local stress minimum, followed by a typically observed “one over square root of distance” variation, as was first postulated by Eshelby, Frank and Nabarro. The observed trends allude to local stress relaxation mechanisms very close to the grain boundaries. Stress states in front of twin tips showed tensile stress gradients, whereas the stress state inside the twin underwent a sign reversal. The findings highlight the important role of deformation twins and their corresponding interaction with grain boundaries on damage nucleation in metals. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle The Effect of the Vertex Angles of Wedged Indenters on Deformation during Nanoindentation
Crystals 2017, 7(12), 380; https://doi.org/10.3390/cryst7120380
Received: 30 September 2017 / Revised: 11 December 2017 / Accepted: 12 December 2017 / Published: 14 December 2017
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Abstract
In order to study the effect of the angle of wedged indenters during nanoindentation, indenters with half vertex angles of 60°, 70° and 80° are used for the simulations of nanoindentation on FCC aluminum (Al) bulk material by the multiscale quasicontinuum method (QC).
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In order to study the effect of the angle of wedged indenters during nanoindentation, indenters with half vertex angles of 60°, 70° and 80° are used for the simulations of nanoindentation on FCC aluminum (Al) bulk material by the multiscale quasicontinuum method (QC). The load-displacement responses, the strain energy-displacement responses, and hardness of Al bulk material are obtained. Besides, atomic configurations for each loading situation are presented. We analyze the drop points in the load-displacement responses, which correspond to the changes of microstructure in the bulk material. From the atom images, the generation of partial dislocations as well as the nucleation and the emission of perfect dislocations have been observed with wedged indenters of half vertex angles of 60° and 70°, but not 80°. The stacking faults move beneath the indenter along the direction [ 1 1 ¯ 0 ] . The microstructures of residual displacements are also discussed. In addition, hardness of the Al bulk material is different in simulations with wedged indenters of half vertex angles of 60° and 70°, and critical hardness in the simulation with the 70° indenter is bigger than that with the 60° indenter. The size effect of hardness in plastic wedged nanoindentation is observed. There are fewer abrupt drops in the strain energy-displacement response than in the load-displacement response, and the abrupt drops in strain energy-displacement response reflect the nucleation of perfect dislocations or extended dislocations rather than partial dislocations. The wedged indenter with half vertex angle of 70° is recommended for investigating dislocations during nanoindentation. Full article
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Open AccessArticle Vickers Hardness of Diamond and cBN Single Crystals: AFM Approach
Crystals 2017, 7(12), 369; https://doi.org/10.3390/cryst7120369
Received: 23 October 2017 / Revised: 4 December 2017 / Accepted: 5 December 2017 / Published: 12 December 2017
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Abstract
Atomic force microscopy in different operation modes (topography, derivative topography, and phase contrast) was used to obtain 3D images of Vickers indents on the surface of diamond and cBN single crystals with high spatial resolution. Confocal Raman spectroscopy and Kelvin probe force microscopy
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Atomic force microscopy in different operation modes (topography, derivative topography, and phase contrast) was used to obtain 3D images of Vickers indents on the surface of diamond and cBN single crystals with high spatial resolution. Confocal Raman spectroscopy and Kelvin probe force microscopy were used to study the structure of the material in the indents. It was found that Vickers indents in diamond has no sharp and clear borders. However, the phase contrast operation mode of the AFM reveals a new viscoelastic phase in the indent in diamond. Raman spectroscopy and Kelvin probe force microscopy revealed that the new phase in the indent is disordered graphite, which was formed due to the pressure-induced phase transformation in the diamond during the hardness test. The projected contact area of the graphite layer in the indent allows us to measure the Vickers hardness of type-Ib synthetic diamond. In contrast to diamond, very high plasticity was observed for 0.5 N load indents on the (001) cBN single crystal face. Radial and ring cracks were absent, the shape of the indents was close to a square, and there were linear details in the indent, which looked like slip lines. The Vickers hardness of the (111) synthetic diamond and (111) and (001) cBN single crystals were determined using the AFM images and with account for the elastic deformation of the diamond Vickers indenter during the tests. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Quantitative Imaging of the Stress/Strain Fields and Generation of Macroscopic Cracks from Indents in Silicon
Crystals 2017, 7(11), 347; https://doi.org/10.3390/cryst7110347
Received: 10 October 2017 / Revised: 7 November 2017 / Accepted: 8 November 2017 / Published: 14 November 2017
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Abstract
The crack geometry and associated strain field around Berkovich and Vickers indents on silicon have been studied by X-ray diffraction imaging and micro-Raman spectroscopy scanning. The techniques are complementary; the Raman data come from within a few micrometres of the indentation, whereas the
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The crack geometry and associated strain field around Berkovich and Vickers indents on silicon have been studied by X-ray diffraction imaging and micro-Raman spectroscopy scanning. The techniques are complementary; the Raman data come from within a few micrometres of the indentation, whereas the X-ray image probes the strain field at a distance of typically tens of micrometres. For example, Raman data provide an explanation for the central contrast feature in the X-ray images of an indent. Strain relaxation from breakout and high temperature annealing are examined and it is demonstrated that millimetre length cracks, similar to those produced by mechanical damage from misaligned handling tools, can be generated in a controlled fashion by indentation within 75 micrometres of the bevel edge of 200 mm diameter wafers. Full article
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Open AccessArticle Microindentation Hardness of Protein Crystals under Controlled Relative Humidity
Crystals 2017, 7(11), 339; https://doi.org/10.3390/cryst7110339
Received: 9 October 2017 / Revised: 30 October 2017 / Accepted: 31 October 2017 / Published: 4 November 2017
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Abstract
Vickers microindentation hardness of protein crystals was investigated on the (110) habit plane of tetragonal hen egg-white lysozyme crystals containing intracrystalline water at controlled relative humidity. The time evolution of the hardness of the crystals exposed to air with different humidities exhibits three
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Vickers microindentation hardness of protein crystals was investigated on the (110) habit plane of tetragonal hen egg-white lysozyme crystals containing intracrystalline water at controlled relative humidity. The time evolution of the hardness of the crystals exposed to air with different humidities exhibits three stages such as the incubation, transition, and saturation stages. The hardness in the incubation stage keeps a constant value of 16 MPa, which is independent of the humidity. The incubation hardness can correspond to the intrinsic one in the wet condition. The increase of the hardness in the transition and saturation stages is well fitted with the single exponential curve, and is correlated with the reduction of water content in the crystal by the evaporation. The saturated maximum hardness also strongly depends on the water content equilibrated with the humidity. The slip traces corresponding to the (11 ̅0)[110] slip system around the indentation marks are observed in not only incubation but also saturation stages. It is suggested that the plastic deformation in protein crystals by the indentation can be attributed to dislocation multiplication and motion inducing the slip. The indentation hardness in protein crystals is discussed in light of dislocation mechanism with Peierls stress and intracrystalline water. Full article
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Open AccessArticle Nanoindentation of HMX and Idoxuridine to Determine Mechanical Similarity
Crystals 2017, 7(11), 335; https://doi.org/10.3390/cryst7110335
Received: 28 September 2017 / Revised: 27 October 2017 / Accepted: 28 October 2017 / Published: 1 November 2017
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Abstract
Assessing the mechanical behavior (elastic properties, plastic properties, and fracture phenomena) of molecular crystals is often complicated by the difficulty in preparing samples. Pharmaceuticals and energetic materials in particular are often used in composite structures or tablets, where the individual grains can strongly
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Assessing the mechanical behavior (elastic properties, plastic properties, and fracture phenomena) of molecular crystals is often complicated by the difficulty in preparing samples. Pharmaceuticals and energetic materials in particular are often used in composite structures or tablets, where the individual grains can strongly impact the solid behavior. Nanoindentation is a convenient method to experimentally assess these properties, and it is used here to demonstrate the similarity in the mechanical properties of two distinct systems: individual crystals of the explosive cyclotetramethylene tetranitramine (HMX) and the pharmaceutical idoxuridine were tested in their as-precipitated state, and the effective average modulus and hardness (which can be orientation dependent) were determined. Both exhibit a hardness of 1.0 GPa, with an effective reduced modulus of 25 and 23 GPa for the HMX and idoxuridine, respectively. They also exhibit similar yield point behavior. This indicates idoxuridine may be a suitable mechanical surrogate (or “mock”) for HMX. While the methodology to assess elastic and plastic properties was relatively insensitive to specific crystal orientation (i.e., a uniform distribution in properties was observed for all random crystals tested), the indentation-induced fracture properties appear to be much more sensitive to tip-crystal orientation, and an unloading slope analysis is used to demonstrate the need for further refinement in relating toughness to orientation in these materials with relatively complex slip systems and crystal structures. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Comparative Study of Phase Transformation in Single-Crystal Germanium during Single and Cyclic Nanoindentation
Crystals 2017, 7(11), 333; https://doi.org/10.3390/cryst7110333
Received: 30 September 2017 / Revised: 29 October 2017 / Accepted: 30 October 2017 / Published: 1 November 2017
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Abstract
Single-crystal germanium is a semiconductor material which shows complicated phase transformation under high pressure. In this study, new insight into the phase transformation of diamond-cubic germanium (dc-Ge) was attempted by controlled cyclic nanoindentation combined with Raman spectroscopic analysis. Phase transformation from dc-Ge to
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Single-crystal germanium is a semiconductor material which shows complicated phase transformation under high pressure. In this study, new insight into the phase transformation of diamond-cubic germanium (dc-Ge) was attempted by controlled cyclic nanoindentation combined with Raman spectroscopic analysis. Phase transformation from dc-Ge to rhombohedral phase (r8-Ge) was experimentally confirmed for both single and cyclic nanoindentation under high loading/unloading rates. However, compared to single indentation, double cyclic indentation with a low holding load between the cycles caused more frequent phase transformation events. Double cyclic indentation caused more stress in Ge than single indentation and increased the possibility of phase transformation. With increase in the holding load, the number of phase transformation events decreased and finally became less than that under single indentation. This phenomenon was possibly caused by defect nucleation and shear accumulation during the holding process, which were promoted by a high holding load. The defect nucleation suppressed the phase transformation from dc-Ge to r8-Ge, and shear accumulation led to another phase transformation pathway, respectively. A high holding load promoted these two phenomena, and thus decreased the possibility of phase transformation from dc-Ge to r8-Ge. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Atomistic Studies of Nanoindentation—A Review of Recent Advances
Crystals 2017, 7(10), 293; https://doi.org/10.3390/cryst7100293
Received: 12 September 2017 / Revised: 25 September 2017 / Accepted: 26 September 2017 / Published: 29 September 2017
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Abstract
This review covers areas where our understanding of the mechanisms underlying nanoindentation has been increased by atomistic studies of the nanoindentation process. While such studies have been performed now for more than 20 years, recent investigations have demonstrated that the peculiar features of
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This review covers areas where our understanding of the mechanisms underlying nanoindentation has been increased by atomistic studies of the nanoindentation process. While such studies have been performed now for more than 20 years, recent investigations have demonstrated that the peculiar features of nanoplasticity generated during indentation can be analyzed in considerable detail by this technique. Topics covered include: nucleation of dislocations in ideal crystals, effect of surface orientation, effect of crystallography (fcc, bcc, hcp), effect of surface and bulk damage on plasticity, nanocrystalline samples, and multiple (sequential) indentation. In addition we discuss related features, such as the influence of tip geometry on the indentation and the role of adhesive forces, and how pre-existing plasticity affects nanoindentation. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Mechanical Anisotropy in Austenitic NiMnGa Alloy: Nanoindentation Studies
Crystals 2017, 7(8), 254; https://doi.org/10.3390/cryst7080254
Received: 23 June 2017 / Revised: 14 August 2017 / Accepted: 15 August 2017 / Published: 17 August 2017
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Abstract
Abstract: Mechanical anisotropy in an austenitic ferromagnetic shape memory alloy (SMA), Ni50Mn26.25Ga23.75, is investigated along (010), (120), (121), (231) and (232) using nanoindentation. While (010) exhibits the highest reduced modulus, Er, and hardness, H
[...] Read more.
Abstract: Mechanical anisotropy in an austenitic ferromagnetic shape memory alloy (SMA), Ni50Mn26.25Ga23.75, is investigated along (010), (120), (121), (231) and (232) using nanoindentation. While (010) exhibits the highest reduced modulus, Er, and hardness, H, (232) shows the lowest amongst the grain orientations examined in this study. The significant elastic anisotropy measured is attributed to differences in planar packing density and number of in-plane Ni–Mn and Ni–Ga bonds, whereas the plastic anisotropy is due to the differences in the onset of slip, which is rationalized by recourse to Schmid factor calculations. This would help determine the grain orientations in austenitic NiMnGa which exhibit better mechanical properties for SMA applications such as improving vibration damping characteristics of the alloy. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Atomistic Insights into the Effects of Residual Stress during Nanoindentation
Crystals 2017, 7(8), 240; https://doi.org/10.3390/cryst7080240
Received: 21 June 2017 / Revised: 26 July 2017 / Accepted: 30 July 2017 / Published: 1 August 2017
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Abstract
The influence of in-plane residual stress on Hertzian nanoindentation for single-crystal copper thin film is investigated using molecular dynamics simulations (MD). It is found that: (i) the yield strength of incipient plasticity increases with compressive residual stress, but decreases with tensile residual stress;
[...] Read more.
The influence of in-plane residual stress on Hertzian nanoindentation for single-crystal copper thin film is investigated using molecular dynamics simulations (MD). It is found that: (i) the yield strength of incipient plasticity increases with compressive residual stress, but decreases with tensile residual stress; (ii) the hardness decreases with tensile residual stress, and increases with compressive residual stress, but abruptly drops down at a higher compressive residual stress level, because of the deterioration of the surface; (iii) the indentation modulus reduces linearly with decreasing compressive residual stress (and with increasing tensile residual stress). It can be concluded from the MD simulations that the residual stress not only strongly influences the dislocation evolution of the plastic deformation process, but also significantly affects the size of the plastic zone. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Theoretical Study on Electronic, Optical Properties and Hardness of Technetium Phosphides under High Pressure
Crystals 2017, 7(6), 176; https://doi.org/10.3390/cryst7060176
Received: 4 April 2017 / Revised: 18 May 2017 / Accepted: 15 June 2017 / Published: 18 June 2017
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Abstract
In this paper, the structural properties of technetium phosphides Tc3P and TcP4 are investigated by first principles at zero pressure and compared with the experimental values. In addition, the electronic properties of these two crystals in the pressure range of
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In this paper, the structural properties of technetium phosphides Tc3P and TcP4 are investigated by first principles at zero pressure and compared with the experimental values. In addition, the electronic properties of these two crystals in the pressure range of 0–40 GPa are investigated. Further, we discuss the change in the optical properties of technetium phosphides at high pressures. At the end of our study, we focus on the research of the hardness of TcP4 at different pressures by employing a semiempirical method, and the effect of pressure on the hardness is studied. Results show that the hardness of TcP4 increases with the increasing pressure, and the influence mechanism of pressure effect on the hardness of TcP4 is also discussed. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessArticle Application of the Improved Inclusion Core Model of the Indentation Process for the Determination of Mechanical Properties of Materials
Crystals 2017, 7(3), 87; https://doi.org/10.3390/cryst7030087
Received: 9 February 2017 / Revised: 7 March 2017 / Accepted: 14 March 2017 / Published: 16 March 2017
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Abstract
The improved Johnson inclusion core model of indentation by conical and pyramidal indenters in which indenter is elastically deformed and a specimen is elastoplastically deformed under von Mises yield condition, was used for determination of mechanical properties of materials with different types of
[...] Read more.
The improved Johnson inclusion core model of indentation by conical and pyramidal indenters in which indenter is elastically deformed and a specimen is elastoplastically deformed under von Mises yield condition, was used for determination of mechanical properties of materials with different types of interatomic bond and different crystalline structures. This model enables us to determine approximately the Tabor parameter С = НМ/YS (where НМ is the Meyer hardness and YS is the yield stress of the specimen), size of the elastoplastic zone in the specimen, effective apex angle of the indenter under load, and effective angle of the indent after unloading. It was shown that the Tabor parameter and the size of elastoplastic deformation zone increase monotonically with the increase of the plasticity characteristic indentation test results significantly more informative. Full article
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Review

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Open AccessReview A Novel Approach to Modelling Nanoindentation Instabilities
Crystals 2018, 8(5), 200; https://doi.org/10.3390/cryst8050200
Received: 17 January 2018 / Revised: 25 April 2018 / Accepted: 27 April 2018 / Published: 3 May 2018
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Abstract
We review the recently developed models for load fluctuations in the displacement controlled mode and displacement jumps in the load controlled mode of indentation. To do this, we devise a method for calculating plastic contribution to load drops and displacement jumps by setting-up
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We review the recently developed models for load fluctuations in the displacement controlled mode and displacement jumps in the load controlled mode of indentation. To do this, we devise a method for calculating plastic contribution to load drops and displacement jumps by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities by including relevant dislocation mechanisms. These equations are then coupled to the equation defining constant displacement rate or load rate. The model for the displacement controlled mode using a spherical indenter predicts all the generic features of nanoindentation such as the elastic branch followed by several force drops of decreasing magnitudes and residual indentation depth after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted numbers for all the quantities match experiments on single crystals of Au using a spherical indenter. We extend the approach to model the load controlled nanoindentation experiments that employ a Berkovich indenter. We first identify the dislocation mechanisms contributing to different regions of the F z curve as a first step for obtaining a good fit to a given experimental F z curve. This is done by studying the influence of the parameters associated with various dislocation mechanisms on the model F z curves. The study also demonstrates that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes and residual plasticity after unloading for a range of model parameter values. Furthermore, an optimized set of parameter values can be easily determined that give a good fit to the experimental load–displacement curves for Al single crystals of ( 110 ) and ( 133 ) orientations. Our model also predicts the indentation size effect in a region where the displacement jumps disappear. The good agreement of the results of the models with experiments supports our view that the present approach can be used as an alternate method to simulations. The approach also provides insights into several open questions. Full article
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Open AccessReview Thickness-Dependent Strain Rate Sensitivity of Nanolayers via the Nanoindentation Technique
Crystals 2018, 8(3), 128; https://doi.org/10.3390/cryst8030128
Received: 14 January 2018 / Revised: 19 February 2018 / Accepted: 21 February 2018 / Published: 9 March 2018
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Abstract
The strain rate sensitivity (SRS) and dislocation activation volume are two inter-related material properties for understanding thermally-activated plastic deformation, such as creep. For face-centered-cubic metals, SRS normally increases with decreasing grain size, whereas the opposite holds for body-center-cubic metals. However, these findings are
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The strain rate sensitivity (SRS) and dislocation activation volume are two inter-related material properties for understanding thermally-activated plastic deformation, such as creep. For face-centered-cubic metals, SRS normally increases with decreasing grain size, whereas the opposite holds for body-center-cubic metals. However, these findings are applicable to metals with average grain sizes greater than tens of nanometers. Recent studies on mechanical behaviors presented distinct deformation mechanisms in multilayers with individual layer thickness of 20 nanometers or less. It is necessary to estimate the SRS and plastic deformation mechanisms in this regime. Here, we review a new nanoindentation test method that renders reliable hardness measurement insensitive to thermal drift, and its application on SRS of Cu/amorphous-CuNb nanolayers. The new technique is applied to Cu films and returns expected SRS values when compared to conventional tensile test results. The SRS of Cu/amorphous-CuNb nanolayers demonstrates two distinct deformation mechanisms depending on layer thickness: dislocation pileup-dominated and interface-mediated deformation mechanisms. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessReview Indentation Plasticity and Fracture Studies of Organic Crystals
Crystals 2017, 7(11), 324; https://doi.org/10.3390/cryst7110324
Received: 23 September 2017 / Revised: 18 October 2017 / Accepted: 23 October 2017 / Published: 27 October 2017
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Abstract
This review article summarizes the recent advances in measuring and understanding the indentation-induced plastic deformation and fracture behavior of single crystals of a wide variety of organic molecules and pharmaceutical compounds. The importance of hardness measurement for molecular crystals at the nanoscale, methods
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This review article summarizes the recent advances in measuring and understanding the indentation-induced plastic deformation and fracture behavior of single crystals of a wide variety of organic molecules and pharmaceutical compounds. The importance of hardness measurement for molecular crystals at the nanoscale, methods and models used so far to analyze and estimate the hardness of the crystals, factors affecting the indentation hardness of organic crystals, correlation of the mechanical properties to their underlying crystal packing, and fracture toughness studies of molecular crystals are reviewed. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessReview Review of Nanoindentation Size Effect: Experiments and Atomistic Simulation
Crystals 2017, 7(10), 321; https://doi.org/10.3390/cryst7100321
Received: 26 September 2017 / Revised: 17 October 2017 / Accepted: 20 October 2017 / Published: 23 October 2017
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Abstract
Nanoindentation is a well-stablished experiment to study the mechanical properties of materials at the small length scales of micro and nano. Unlike the conventional indentation experiments, the nanoindentation response of the material depends on the corresponding length scales, such as indentation depth, which
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Nanoindentation is a well-stablished experiment to study the mechanical properties of materials at the small length scales of micro and nano. Unlike the conventional indentation experiments, the nanoindentation response of the material depends on the corresponding length scales, such as indentation depth, which is commonly termed the size effect. In the current work, first, the conventional experimental observations and theoretical models of the size effect during nanoindentation are reviewed in the case of crystalline metals, which are the focus of the current work. Next, the recent advancements in the visualization of the dislocation structure during the nanoindentation experiment is discussed, and the observed underlying mechanisms of the size effect are addressed. Finally, the recent computer simulations using molecular dynamics are reviewed as a powerful tool to investigate the nanoindentation experiment and its governing mechanisms of the size effect. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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Open AccessReview Progress in Indentation Study of Materials via Both Experimental and Numerical Methods
Crystals 2017, 7(10), 258; https://doi.org/10.3390/cryst7100258
Received: 19 June 2017 / Revised: 8 August 2017 / Accepted: 9 August 2017 / Published: 13 October 2017
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Abstract
Indentation as a method to characterize materials has a history of more than 117 years. However, to date, it is still the most popular way to measure the mechanical properties of various materials at microscale and nanoscale. This review summarizes the background and
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Indentation as a method to characterize materials has a history of more than 117 years. However, to date, it is still the most popular way to measure the mechanical properties of various materials at microscale and nanoscale. This review summarizes the background and the basic principle of processing by indentation. It is demonstrated that indentation is an effective and efficient method to identify mechanical properties, such as hardness, Young’s modulus, etc., of materials at smaller scale, when the traditional tensile tests could not be applied. The review also describes indentation process via both experimental tests and numerical modelling in recent studies. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness) Printed Edition available
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