Special Issue "Crystal Plasticity at Micro- and Nano-scale Dimensions"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Inorganic Crystalline Materials".

Deadline for manuscript submissions: closed (15 November 2020).

Special Issue Editors

Prof. Dr. Ronald W. Armstrong
E-Mail Website
Guest Editor
Department of Mechanical Engineering, A. James Clark School of Engineering, University of Maryland, College Park, MD 20742, USA
Interests: dislocation mechanics; constitutive equations; Hall–Petch relations; Zerilli–Armstrong equations; microstructural stereology; high rate metal deformations; ductile-brittle transition behaviors; X-ray diffraction imaging
Special Issues and Collections in MDPI journals
Prof. Wayne L. Elban
E-Mail Website
Guest Editor
Department of Engineering, Loyola University Maryland, Baltimore, MD 21210, USA
Interests: mechanical properties; indentation hardness; microstructural characterization; historical ferrous metallurgy
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The advent of “nanotechnology” in the 1980s is often credited to the foresight expressed in one of Nobel Prize winner Richard Feynman’s lectures in late 1959, “There’s Plenty of Room at the Bottom”. The lecture featured the potential advantages in chemistry to be gained by the manipulation of atoms on an atomic scale, and that nano-scale mechanical devices would be designed and developed in future engineering applications. The lecture presaged the Nobel Prize winning developments of atomic force microscopy and scanning tunneling microscopy. An important industrial impetus was provided by the development of micro-electro-mechanical system (MEMS) devices, and also later by developments of both nano-scale testing systems, such as nano-indentation hardness testing, and micro-scale specimen fabrication methods, such as the focused ion beam (FIB) manufacturing of micro-pillars and the production of nano-particles and nano-wires.  Instead, less attention has been given to enabling the order-of-magnitude strength advantage provided in nano-scale crystal dimensions and within nano-polycrystalline microstructures, both of which are topics included in the present Crystals journal’s Special Issue. Such an achievement in the strength levels has coincided with other recent advancements in the crystal dislocation mechanics theories accounting for such crystal deformation properties. The advanced testing methods and related model simulations of the crystal properties provide an opportunity for quantitatively accounting for the character of the individual dislocations or their interactions within small groups. The aim of the present Special Issue is to provide a welcome venue for contributed works on this rapidly developing subject. 

Prof. Ronald W. Armstrong
Prof. Wayne Elban
Guest Editors

Manuscript Submission Information

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Keywords

  • micro-crystals
  • nano-crystals
  • strength
  • plasticity
  • dislocations
  • simulations

Published Papers (22 papers)

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Editorial

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Open AccessEditorial
Crystal Strengths at Micro- and Nano-Scale Dimensions
Crystals 2020, 10(2), 88; https://doi.org/10.3390/cryst10020088 - 05 Feb 2020
Viewed by 804
Abstract
Higher strength levels, achieved for dimensionally-smaller micro- and nano-scale materials or material components, such as MEMS devices, are an important enabler of a broad range of present-day engineering devices and structures. Beyond such applications, there is an important effort to understand the dislocation [...] Read more.
Higher strength levels, achieved for dimensionally-smaller micro- and nano-scale materials or material components, such as MEMS devices, are an important enabler of a broad range of present-day engineering devices and structures. Beyond such applications, there is an important effort to understand the dislocation mechanics basis for obtaining such improved strength properties. Four particular examples related to these issues are described in the present report: (1) a compilation of nano-indentation hardness measurements made on silicon crystals spanning nano- to micro-scale testing; (2) stress–strain measurements made on iron and steel materials at micro- to nano-crystal (grain size) dimensions; (3) assessment of small dislocation pile-ups relating to Griffith-type fracture stress vs. crack-size calculations for cleavage fracturing of α-iron; and (4) description of thermally-dependent strain rate sensitivities for grain size strengthening and weakening for macro- to micro- to nano-polycrystalline copper and nickel materials. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Research

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Open AccessArticle
Mechanical Behavior of Al–Al2Cu–Si and Al–Al2Cu Eutectic Alloys
Crystals 2021, 11(2), 194; https://doi.org/10.3390/cryst11020194 - 16 Feb 2021
Viewed by 352
Abstract
In this study, laser rapid solidification technique was used to refine the microstructure of ternary Al–Cu–Si and binary Al–Cu eutectic alloys to nanoscales. Micropillar compression testing was performed to measure the stress–strain response of the samples with characteristic microstructure in the melt pool [...] Read more.
In this study, laser rapid solidification technique was used to refine the microstructure of ternary Al–Cu–Si and binary Al–Cu eutectic alloys to nanoscales. Micropillar compression testing was performed to measure the stress–strain response of the samples with characteristic microstructure in the melt pool regions. The laser-remelted Al–Al2Cu–Si ternary alloy was observed to reach the compressive strength of 1.59 GPa before failure at a strain of 28.5%, which is significantly better than the as-cast alloy with a maximum strength of 0.48 GPa at a failure strain of 4.8%. The laser-remelted Al–Cu binary alloy was observed to reach the compressive strength of 2.07 GPa before failure at a strain of 26.5%, which is significantly better than the as-cast alloy with maximum strength of 0.74 GPa at a failure strain of 3.3%. The enhanced compressive strength and improved compressive plasticity were interpreted in terms of microstructural refinement and hierarchical eutectic morphology. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Transformation of SnS Nanocompisites to Sn and S Nanoparticles during Lithiation
Crystals 2021, 11(2), 145; https://doi.org/10.3390/cryst11020145 - 29 Jan 2021
Viewed by 624
Abstract
SnS nanomaterials have a high initial capacity of 1000 mAh g−1; however, this cannot be retained throughout electrochemical cycling. The present study provides insight into this capacity decay by examining the effect that Li intercalation has on SnS “nanoflowers” attached on [...] Read more.
SnS nanomaterials have a high initial capacity of 1000 mAh g−1; however, this cannot be retained throughout electrochemical cycling. The present study provides insight into this capacity decay by examining the effect that Li intercalation has on SnS “nanoflowers” attached on carbon substrates’ such as artificial graphite. Scanning and transmission electron microscopy reveal that lithiation of such materials disrupts their initial morphology and produces free-standing Sn and SnS nanoparticles that dissolve in the electrolyte and disperse uniformly over the entire electrode surface. As a result, the SnS is rendered inactive after initial cycling and contributes to the formation of the solid electrolyte interface layer, resulting in continuous capacity decay during long term cycling. This is the first study that illustrates the morphological effects that the conversion mechanism has on SnS anodes. In order to fully utilize SnS materials, it is necessary to isolate them from the electrolyte by fully encapsulating them in a matrix. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Prospects of Using Small Scale Testing to Examine Different Deformation Mechanisms in Nanoscale Single Crystals—A Case Study in Mg
Crystals 2021, 11(1), 61; https://doi.org/10.3390/cryst11010061 - 14 Jan 2021
Viewed by 500
Abstract
The advent of miniaturised testing techniques led to excessive studies on size effects in materials. Concomitantly, these techniques also offer the capability to thoroughly examine deformation mechanisms operative in small volumes, in particular when performed in-situ in electron microscopes. This opens the feasibility [...] Read more.
The advent of miniaturised testing techniques led to excessive studies on size effects in materials. Concomitantly, these techniques also offer the capability to thoroughly examine deformation mechanisms operative in small volumes, in particular when performed in-situ in electron microscopes. This opens the feasibility of a comprehensive assessment of plasticity by spatially arranging samples specifically with respect to the crystal unit cell of interest. In the present manuscript, we will showcase this less commonly utilised aspect of small-scale testing on the case of the hexagonal metal Mg, where, besides dislocation slip on different slip planes, twinning also exists as a possible deformation mechanism. While it is close to impossible to examine individual deformation mechanisms in macroscale tests, where local multiaxial stress states in polycrystalline structures will always favour multiple mechanisms of plasticity, we demonstrate that miniaturised uniaxial experiments conducted in-situ in the scanning electron microscope are ideally suited for a detailed assessment of specific processes. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Thermal Stability of Nanocrystalline Gradient Inconel 718 Alloy
Crystals 2021, 11(1), 53; https://doi.org/10.3390/cryst11010053 - 11 Jan 2021
Viewed by 487
Abstract
Gradient structures containing nanograins in the surface layer have been introduced into Inconel 718 (IN718) nickel-based alloy using the surface mechanical grinding treatment technique. The thermal stability of the gradient IN718 alloy was investigated. Annealing studies reveal that nanograins with a grain size [...] Read more.
Gradient structures containing nanograins in the surface layer have been introduced into Inconel 718 (IN718) nickel-based alloy using the surface mechanical grinding treatment technique. The thermal stability of the gradient IN718 alloy was investigated. Annealing studies reveal that nanograins with a grain size smaller than 40 nm exhibited significantly better thermal stability than those with larger grain size. Transmission electron microscopy analyses reveal that the enhanced thermal stability was attributed to the formation of grain boundaries with low energy configurations. This study provides new insight on strategies to improve the thermal stability of nanocrystalline metals. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Micromechanics of Void Nucleation and Early Growth at Incoherent Precipitates: Lattice-Trapped and Dislocation-Mediated Delamination Modes
Crystals 2021, 11(1), 45; https://doi.org/10.3390/cryst11010045 - 07 Jan 2021
Viewed by 345
Abstract
The initial stages of debonding at hard-particle interfaces during rupture is relevant to the fracture of most structural alloys, yet details of the mechanistic process for rupture at the atomic scale are poorly understood. In this study, we employ molecular dynamics simulation of [...] Read more.
The initial stages of debonding at hard-particle interfaces during rupture is relevant to the fracture of most structural alloys, yet details of the mechanistic process for rupture at the atomic scale are poorly understood. In this study, we employ molecular dynamics simulation of a spherical Al2Cu θ precipitate in an aluminum matrix to examine the earliest stages of void formation and nanocrack growth at the particle-matrix interface, at temperatures ranging from 200–400 K and stresses ranging from 5.7–7.2 GPa. The simulations revealed a three-stage process involving (1) stochastic instantaneous or delayed nucleation of excess free volume at the particle-matrix interface involving only tens of atoms, followed by (2) steady time-dependent crack growth in the absence of dislocation activity, followed by (3) dramatically accelerated crack growth facilitated by crack-tip dislocation emission. While not all three stages were present for all stresses and temperatures, the second stage, termed lattice-trapped delamination, was consistently the rate-limiting process. This lattice-trapped delamination process was determined to be a thermally activated brittle fracture mode with an unambiguous Arrhenius activation energy of 1.37 eV and an activation area of 1.17 Å2. The role of lattice-trapped delamination in the early stages of particle delamination is not only relevant at the high strain-rates and stresses associated with shock spallation, but Arrhenius extrapolation suggests that the mechanism also operates during quasi-static rupture at micrometer-scale particles. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessFeature PaperArticle
Interdependent Linear Complexion Structure and Dislocation Mechanics in Fe-Ni
Crystals 2020, 10(12), 1128; https://doi.org/10.3390/cryst10121128 - 11 Dec 2020
Viewed by 507
Abstract
Using large-scale atomistic simulations, dislocation mechanics in the presence of linear complexions are investigated in an Fe-Ni alloy, where the complexions appear as nanoparticle arrays along edge dislocation lines. When mechanical shear stress is applied to drive dislocation motion, a strong pinning effect [...] Read more.
Using large-scale atomistic simulations, dislocation mechanics in the presence of linear complexions are investigated in an Fe-Ni alloy, where the complexions appear as nanoparticle arrays along edge dislocation lines. When mechanical shear stress is applied to drive dislocation motion, a strong pinning effect is observed where the defects are restricted by their own linear complexion structures. This pinning effect becomes weaker after the first dislocation break-away event, leading to a stress-strain curve with a profound initial yield point, similar to the static strain aging behavior observed experimentally for Fe-Mn alloys with the same type of linear complexions. The existence of such a response can be explained by local diffusion-less and lattice distortive transformations corresponding to L10-to-B2 phase transitions within the linear complexion nanoparticles. As such, an interdependence between a linear complexion structure and dislocation mechanics is found. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Elastic Coefficients of β-HMX as Functions of Pressure and Temperature from Molecular Dynamics
Crystals 2020, 10(12), 1123; https://doi.org/10.3390/cryst10121123 - 10 Dec 2020
Cited by 1 | Viewed by 533
Abstract
The isothermal second-order elastic stiffness tensor and isotropic moduli of β-1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 104 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated β-HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Tensile Deformation of Ultrafine-Grained Fe-Mn-Al-Ni-C Alloy Studied by In Situ Synchrotron Radiation X-ray Diffraction
Crystals 2020, 10(12), 1115; https://doi.org/10.3390/cryst10121115 - 07 Dec 2020
Viewed by 620
Abstract
Intermetallic compounds are usually considered as deleterious phase in alloy designing and processing since their brittleness leads to poor ductility and premature failure during deformation of the alloys. However, several studies recently found that some alloys containing large amounts of NiAl-type intermetallic particles [...] Read more.
Intermetallic compounds are usually considered as deleterious phase in alloy designing and processing since their brittleness leads to poor ductility and premature failure during deformation of the alloys. However, several studies recently found that some alloys containing large amounts of NiAl-type intermetallic particles exhibited not only high strength but also good tensile ductility. To clarify the role of the intermetallic particles in the excellent tensile properties of such alloys, the tensile deformation behavior of an ultrafine-grained Fe-Mn-Al-Ni-C alloy containing austenite matrix and B2 intermetallic particles was investigated by using in situ synchrotron radiation X-ray diffraction in the present study. The elastic stress partitioning behavior of two constituent phases during tensile deformation were quantitively measured, and it was suggested that B2 particles played an important role in the high strength and large tensile ductility of the material. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Determination of Long-Range Internal Stresses in Cyclically Deformed Copper Single Crystals Using Convergent Beam Electron Diffraction
Crystals 2020, 10(12), 1071; https://doi.org/10.3390/cryst10121071 - 24 Nov 2020
Viewed by 381
Abstract
Understanding long range internal stresses (LRIS) may be crucial for elucidating the basis of the Bauschinger effect, plastic deformation in fatigued metals, and plastic deformation in general. Few studies have evaluated LRIS using convergent beam electron diffraction (CBED) in cyclically deformed single crystals [...] Read more.
Understanding long range internal stresses (LRIS) may be crucial for elucidating the basis of the Bauschinger effect, plastic deformation in fatigued metals, and plastic deformation in general. Few studies have evaluated LRIS using convergent beam electron diffraction (CBED) in cyclically deformed single crystals oriented in single slip and there are no such studies carried out on cyclically deformed single crystals in multiple slip. In our earlier and recent study, we assessed the LRIS in a cyclically deformed copper single crystal in multiple slip via measuring the maximum dislocation dipole heights. Nearly equal maximum dipole heights in the high dislocation density walls and low dislocation density channels suggested a uniform stress state across the labyrinth microstructure. Here, we evaluate the LRIS by determining the lattice parameter in the channels and walls of the labyrinth dislocation structure using CBED. Findings of this work show that lattice parameters obtained were almost equal near the walls and within the channels. Thus, a homogenous stress state within the heterogeneous dislocation microstructure is again suggested. Although the changes in the lattice parameter in the channels are minimal (less than 10−4 nm), CBED chi-squared analysis suggests that the difference between the lattice parameter values of the cyclically deformed and unstrained copper are slightly higher in the proximity of the walls in comparison with the channel interior. These values are less than 6.5% of the applied stress. It can be concluded that the dominant characteristics of the Bauschinger effect may need to include the Orowan-Sleeswyk mechanism type of explanation since both the maximum dipole height measurements and the lattice parameter assessment through CBED analysis suggest a homogenous stress state. This work complements our earlier work that determined LRIS based on dipole heights by assessing LRIS through a different methodology, carried out on a cyclically deformed copper single crystal oriented for multiple slip. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Investigating the Interaction between Persistent Slip Bands and Surface Hard Coatings via Crystal Plasticity Simulations
Crystals 2020, 10(11), 1012; https://doi.org/10.3390/cryst10111012 - 06 Nov 2020
Cited by 1 | Viewed by 648
Abstract
Fatigue cracks often initiate from the surface extrusion/intrusions formed due to the operation of persistent slip bands (PSBs). Suppression of these surface topographical features by hard surface coatings can significantly extend fatigue lives under lower stress amplitudes (i.e., high cycle fatigue), while cracks [...] Read more.
Fatigue cracks often initiate from the surface extrusion/intrusions formed due to the operation of persistent slip bands (PSBs). Suppression of these surface topographical features by hard surface coatings can significantly extend fatigue lives under lower stress amplitudes (i.e., high cycle fatigue), while cracks initiate early in the coating or in the coating–substrate interface under higher stress amplitudes (i.e., low cycle fatigue), deteriorating the fatigue performance. However, both beneficial and detrimental effects of the coatings appear to be affected by the coating–substrate material combination and coating thickness. A quantitative understanding of the role of these factors in the fatigue performance of materials is still lacking. In this study, crystal plasticity simulations were employed to elucidate the dependence of the coating’s effects on two factors—i.e., the coating thickness and loading amplitudes. The results revealed that the thicker coatings more effectively suppress the operation of the PSBs, but generate higher tensile and shear stresses, normal and parallel to the interfaces, respectively, promoting interfacial delamination. The tensile stresses parallel to the interface within the coating, which favors coating fracture, are not sensitive to the coating thickness. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Crystallographic Orientation Dependence of Mechanical Responses of FeCrAl Micropillars
Crystals 2020, 10(10), 943; https://doi.org/10.3390/cryst10100943 - 16 Oct 2020
Viewed by 541
Abstract
Iron-chromium-aluminum (FeCrAl) alloys are used in automobile exhaust gas purifying systems and nuclear reactors due to its superior high-temperature oxidation and excellent corrosion resistance. Single-phase FeCrAl alloys with a body centered cubic structure plastically deform through dislocation slips at room temperature. Here, we [...] Read more.
Iron-chromium-aluminum (FeCrAl) alloys are used in automobile exhaust gas purifying systems and nuclear reactors due to its superior high-temperature oxidation and excellent corrosion resistance. Single-phase FeCrAl alloys with a body centered cubic structure plastically deform through dislocation slips at room temperature. Here, we investigated the orientation dependence of mechanical responses of FeCrAl alloy through testing single-crystal and bi-crystal micropillars in a scanning electron microscopy at room temperature. Single-crystal micropillars were fabricated with specific orientations which favor the activity of single slip system or two slip systems or multiple slip systems. The strain hardening rate and flow strength increase with increasing the number of activated slip system in micropillars. Bi-crystal micropillars with respect to the continuity of slip systems across grain boundary were fabricated to study the effect of grain boundary on slip transmission. The high geometrical compatibility factor corresponds to a high flow strength and strain hardening rate. Experimental results provide insight into understanding mechanical response of FeCrAl alloy and developing the mechanisms-based constitutive laws for FeCrAl polycrystalline aggregates. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
On the Size Effect of Strain Rate Sensitivity and Activation Volume for Face-Centered Cubic Materials: A Scaling Law
Crystals 2020, 10(10), 898; https://doi.org/10.3390/cryst10100898 - 03 Oct 2020
Viewed by 483
Abstract
In a recent experimental study of indentation creep, the strain rate sensitivity (SRS) and activation volume v* have been noticed to be dependent on the indentation depth or loading force for face-centered cubic materials. Although several possible interpretations have been proposed, the fundamental mechanism is still not well addressed. In this work, a scaling law is proposed for the indentation depth or loading force-dependent SRS. Moreover, v* is indicated to scale with hardness H by the relation ln(v*/b3)/lnH=2 with the Burgers vector b. We show that this size effect of SRS and activation volume can mainly be ascribed to the evolution of geometrically necessary dislocations during the creep process. By comparing the theoretical results with different sets of reported experimental data, the proposed law is verified and a good agreement is achieved. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
The Effect of Strain Rate on the Deformation Processes of NC Gold with Small Grain Size
Crystals 2020, 10(10), 858; https://doi.org/10.3390/cryst10100858 - 24 Sep 2020
Cited by 1 | Viewed by 639
Abstract
The strength of nanocrystalline (NC) metal has been found to be sensitive to strain rate. Here, by molecular dynamics simulation, we explore the strain rate effects on apparent Young’s modulus, flow stress and grain growth of NC gold with small size. The simulation [...] Read more.
The strength of nanocrystalline (NC) metal has been found to be sensitive to strain rate. Here, by molecular dynamics simulation, we explore the strain rate effects on apparent Young’s modulus, flow stress and grain growth of NC gold with small size. The simulation results indicate that the apparent Young’s modulus of NC gold decreases with the decrease of strain rate, especially for strain rates above 1 ns−1. The rearrangement of atoms near grain boundaries is a response to the decrease of apparent Young’s modulus. Indeed, the flow stress is also sensitive to the strain rate and decreases following the strain rate’s decrease. This can be found from the change of strain rate sensitivity and activation volume with the strain rate. Temperature has little effect on the activation volume of NC gold with small grain size, but has an obvious effect on that of relatively large grain size (such as 18 nm) under low strain rate (0.01 ns−1). Finally, grain growth in the deformation process is found to be sensitive to strain rate and the critical size for grain growth increases following the decrease of strain rate. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Extraordinary Response of H-Charged and H-Free Coherent Grain Boundaries in Nickel to Multiaxial Loading
Crystals 2020, 10(7), 590; https://doi.org/10.3390/cryst10070590 - 08 Jul 2020
Cited by 2 | Viewed by 644
Abstract
The cohesive strength of Σ 3, Σ 5, and Σ 11 grain boundaries (GBs) in clean and hydrogen-segregated fcc nickel was systematically studied as a function of the superimposed transverse biaxial stresses using ab initio methods. The obtained results for H-free GBs revealed a quite different response of the coherent twinning boundary Σ 3 to the applied transverse stresses in comparison to the other GB types. While the cohesive strength of Σ 5 and Σ 11 GBs increased with increasing level of tensile transverse stresses, the strength of Σ 3 GB remained constant for any applied levels of transverse stresses. In the case of GBs with segregated hydrogen, the cohesive strength of Σ 3 was distinctly reduced for all levels of transverse stresses, while the strength reduction of Σ 5 and Σ 11 GBs was significant only for a nearly isotropic (hydrostatic) triaxial loading. This extraordinary response explains a high susceptibility of Σ 3 GBs to crack initiation, as recently reported in an experimental study. Moreover, a highly triaxial stress at the fronts of microcracks initiated at Σ 3 boundaries caused a strength reduction of adjacent high-energy grain boundaries which thus became preferential sites for further crack propagation. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Influence of the Rake Angle on Nanocutting of Fe Single Crystals: A Molecular-Dynamics Study
Crystals 2020, 10(6), 516; https://doi.org/10.3390/cryst10060516 - 17 Jun 2020
Cited by 2 | Viewed by 693
Abstract
Using molecular dynamics simulation, we study the cutting of an Fe single crystal using tools with various rake angles α . We focus on the (110)[001] cut system, since here, the crystal plasticity is governed by a simple mechanism for not too strongly negative rake angles. In this case, the evolution of the chip is driven by the generation of edge dislocations with the Burgers vector b = 1 2 [ 111 ] , such that a fixed shear angle of ϕ = 54.7 is established. It is independent of the rake angle of the tool. The chip form is rectangular, and the chip thickness agrees with the theoretical result calculated for this shear angle from the law of mass conservation. We find that the force angle χ between the direction of the force and the cutting direction is independent of the rake angle; however, it does not obey the predictions of macroscopic cutting theories, nor the correlations observed in experiments of (polycrystalline) cutting of mild steel. Only for (strongly) negative rake angles, the mechanism of plasticity changes, leading to a complex chip shape or even suppressing the formation of a chip. In these cases, the force angle strongly increases while the friction angle tends to zero. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Atomic Force Microscopy Study of Discrete Dislocation Pile-ups at Grain Boundaries in Bi-Crystalline Micro-Pillars
Crystals 2020, 10(5), 411; https://doi.org/10.3390/cryst10050411 - 20 May 2020
Cited by 1 | Viewed by 710
Abstract
Compression tests at low strains were performed to theoretically analyze the effects of anisotropic elasticity, misorientation, grain boundary (GB) stiffness, interfacial dislocations, free surfaces, and critical force on dislocation pile-ups in micro-sized Face-Centered Cubic (FCC) Nickel (Ni) and α -Brass bi-crystals. The spatial variations of slip heights due to localized slip bands terminating at GB were measured by Atomic Force Microscopy (AFM) to determine the Burgers vector distributions in the dislocation pile-ups. These distributions were then simulated by discrete pile-up micromechanical calculations in anisotropic bi-crystals consistent with the experimentally measured material parameters. The computations were based on the image decomposition method considering the effects of interphase GB and free surfaces in multilayered materials. For Ni and α -Brass, it was found that the best predicted step height spatial profiles were obtained considering anisotropic elasticity, free surface effects, a homogeneous external stress and a certain critical force in the material to equilibrate the dislocation pile-ups. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Plasticity through De-Twinning in Twinned BCC Nanowires
Crystals 2020, 10(5), 366; https://doi.org/10.3390/cryst10050366 - 01 May 2020
Cited by 1 | Viewed by 931
Abstract
The deformation behaviour of twinned FCC nanowires has been extensively investigated in recent years. However, the same is not true for their BCC counterparts. Very few studies exist concerning the deformation behaviour of twinned BCC nanowires. In view of this, molecular dynamics (MD) [...] Read more.
The deformation behaviour of twinned FCC nanowires has been extensively investigated in recent years. However, the same is not true for their BCC counterparts. Very few studies exist concerning the deformation behaviour of twinned BCC nanowires. In view of this, molecular dynamics (MD) simulations have been performed to understand the deformation mechanisms in twinned BCC Fe nanowires. The twin boundaries (TBs) were oriented parallel to the loading direction [110] and the number of TBs is varied from one to three. MD simulation results indicate that deformation under the compressive loading of twinned BCC Fe nanowires is dominated by a unique de-twinning mechanism involving the migration of a special twin–twin junction. This de-twinning mechanism results in the complete annihilation of pre-existing TBs along with reorientation of the nanowire. Further, it has been observed that the annihilation of pre-existing TBs has occurred through two different mechanisms, one without any resolved shear stress and other with finite and small resolved shear stress. The present study enhances our understanding of de-twinning in BCC nanowires. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Analysis of the Crack Initiation and Growth in Crystalline Materials Using Discrete Dislocations and the Modified Kitagawa–Takahashi Diagram
Crystals 2020, 10(5), 358; https://doi.org/10.3390/cryst10050358 - 01 May 2020
Viewed by 842
Abstract
Crack growth kinetics in crystalline materials is examined both from the point of continuum mechanics and discrete dislocation dynamics. Kinetics ranging from the Griffith crack to continuous elastic-plastic cracks are analyzed. Initiation and propagation of incipient cracks require very high stresses and appropriate [...] Read more.
Crack growth kinetics in crystalline materials is examined both from the point of continuum mechanics and discrete dislocation dynamics. Kinetics ranging from the Griffith crack to continuous elastic-plastic cracks are analyzed. Initiation and propagation of incipient cracks require very high stresses and appropriate stress gradients. These can be obtained either by pre-existing notches, as is done in a typical American Society of Testing and Materials (ASTM) fatigue and fracture tests, or by in situ generated stress concentrations via dislocation pile-ups. Crack growth kinetics are also examined using the modified Kitagawa–Takahashi diagram to show the role of internal stresses and their gradients needed to sustain continuous crack growth. Incipient crack initiation and growth are also examined using discrete dislocation modeling. The analysis is supported by the experimental data available in the literature. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessArticle
Hardness-Depth Relationship with Temperature Effect for Single Crystals—A Theoretical Analysis
Crystals 2020, 10(2), 112; https://doi.org/10.3390/cryst10020112 - 13 Feb 2020
Viewed by 694
Abstract
In this paper, a mechanistic model is developed to address the effect of temperature on the hardness-depth relationship of single crystals. Two fundamental hardening mechanisms are considered in the hardness model, including the temperature dependent lattice friction and network dislocation interaction. The rationality [...] Read more.
In this paper, a mechanistic model is developed to address the effect of temperature on the hardness-depth relationship of single crystals. Two fundamental hardening mechanisms are considered in the hardness model, including the temperature dependent lattice friction and network dislocation interaction. The rationality and accuracy of the developed model is verified by comparing with four different sets of experimental data, and a reasonable agreement is achieved. In addition, it is concluded that the moderated indentation size effect at elevated temperatures is ascribed to the accelerated expansion of the plasticity affected region that results in the decrease of the density of geometrically necessary dislocations. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessReview
Emission of Dislocations from Grain Boundaries and Its Role in Nanomaterials
Crystals 2021, 11(1), 41; https://doi.org/10.3390/cryst11010041 - 31 Dec 2020
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Abstract
The Frank-Read model, as a way of generating dislocations in metals and alloys, is widely accepted. In the early 1960s, Li proposed an alternate mechanism. Namely, grain boundary sources for dislocations, with the aim of providing a different model for the Hall-Petch relation [...] Read more.
The Frank-Read model, as a way of generating dislocations in metals and alloys, is widely accepted. In the early 1960s, Li proposed an alternate mechanism. Namely, grain boundary sources for dislocations, with the aim of providing a different model for the Hall-Petch relation without the need of dislocation pile-ups at grain boundaries, or Frank-Read sources inside the grain. This article provides a review of his model, and supporting evidence for grain boundaries or interfacial sources of dislocations, including direct observations using transmission electron microscopy. The Li model has acquired new interest with the recent development of nanomaterial and multilayers. It is now known that nanocrystalline metals/alloys show a behavior different from conventional polycrystalline materials. The role of grain boundary sources in nanomaterials is reviewed briefly. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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Open AccessReview
Review of γ’ Rafting Behavior in Nickel-Based Superalloys: Crystal Plasticity and Phase-Field Simulation
Crystals 2020, 10(12), 1095; https://doi.org/10.3390/cryst10121095 - 29 Nov 2020
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Abstract
Rafting is an important phenomenon of the microstructure evolution in nickel-based single crystal superalloys at elevated temperature. Understanding the rafting mechanism and its effect on the microstructure evolution is of great importance in determining the structural stability and applications of the single crystal [...] Read more.
Rafting is an important phenomenon of the microstructure evolution in nickel-based single crystal superalloys at elevated temperature. Understanding the rafting mechanism and its effect on the microstructure evolution is of great importance in determining the structural stability and applications of the single crystal superalloys. Phase-field method, which is an excellent tool to analyze the microstructure evolution at mesoscale, has been gradually used to investigate the rafting behavior. In this work, we review the crystal plasticity theory and phase-field method and discuss the application of the crystal plasticity theory and phase-field method in the analysis of the creep deformation and microstructure evolution of the single crystal superalloys. Full article
(This article belongs to the Special Issue Crystal Plasticity at Micro- and Nano-scale Dimensions)
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