Special Issue "Crystal Plasticity"

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).

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A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Wojciech Polkowski
E-Mail Website
Guest Editor
Łukasiewicz Research Network - Krakow Institute of Technology, Poland
Interests: severe plastic deformation; plasticity; materials strengthening; solid/liquid interfacial phenomena; high temperature materials; intermetallics
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Special Issue Information

Dear Colleagues,

The term of “Crystal Plasticity” builds a bridge between pure crystallography, materials science, and industrial processing of commonly applied materials pieces (sheets, plates, wires, etc.).

As materials scientists and technologists working in the field of (poly)crystals plasticity, we all tend to provide valuable quantitative and qualitative indicators that describe the process→(crystalline) structure→properties relationship. Generally, our efforts are focused on recognizing possible ways to improve materials’ behavior under predicted operational conditions and applied mechanical and/or thermal external loadings. However, we all know that this goal can be achieved only by having well-established knowledge on crystal structure evolution regarding mechanical and plastic deformation processing.

Nowadays, the  research on crystal plasticity-related phenomena is of high practical importance in the view of the following:

  • The on-going progress in conventional fabrication techniques (as a forging or a cold rolling processes);
  • The design of new processing methods (e.g., various complex severe plastic deformation techniques);
  • The development of novel materials (e.g., high-entropy alloys, intermetallics, bulk metallic glasses, ultra-finegrained alloys, nano-steel, etc.).

In this regard, this Special Issue is especially dedicated to theoretical and experimental research works providing new insights and practical findings in the field of crystal plasticity-related topics. Potential papers include but are not limited to the following subjects, covering processing of modern functional and structural materials:

  • Dislocation theory;
  • Crystal lattice phase transformations and atomic reordering;
  • Materials strengthening;
  • Crystallographic texture changes;
  • Materials processing;
  • Microstructure evolution.

Dr. Wojciech Polkowski
Guest Editor

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Keywords

  • Plasticity
  • Crystallographic texture
  • Severe plastic deformation
  • Cold/hot plastic deformation processing
  • Strengthening
  • Metals and alloys
  • Intermetallics

Published Papers (26 papers)

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Editorial

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Editorial
Crystal Plasticity
Crystals 2021, 11(1), 44; https://doi.org/10.3390/cryst11010044 - 06 Jan 2021
Viewed by 558
Abstract
The Special Issue on “Crystal Plasticity” is a collection of 25 original articles (including one review paper) dedicated to theoretical and experimental research works providing new insights and practical findings in the field of crystal plasticity-related topics [...] Full article
(This article belongs to the Special Issue Crystal Plasticity)

Research

Jump to: Editorial, Review

Article
Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review
Crystals 2021, 11(1), 42; https://doi.org/10.3390/cryst11010042 - 04 Jan 2021
Cited by 1 | Viewed by 769
Abstract
The bridge between classical continuum plasticity and crystal plasticity is becoming narrower with continuously improved computational power and with engineers’ desire to obtain more information and better accuracy from their simulations, incorporating at the same time more effects about the microstructure of the [...] Read more.
The bridge between classical continuum plasticity and crystal plasticity is becoming narrower with continuously improved computational power and with engineers’ desire to obtain more information and better accuracy from their simulations, incorporating at the same time more effects about the microstructure of the material. This paper presents a short overview of the main current techniques employed in crystal plasticity formulations for finite element analysis, as to serve as a point of departure for researchers willing to incorporate microstructure effects in elastoplastic simulations. We include both classical and novel crystal plasticity formulations, as well as the different approaches to model dislocations in crystals. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Heterogeneous Deformation Behavior of Cu-Ni-Si Alloy by Micro-Size Compression Testing
Crystals 2020, 10(12), 1162; https://doi.org/10.3390/cryst10121162 - 21 Dec 2020
Cited by 1 | Viewed by 751
Abstract
The aim of this study is to investigate a characteristic deformation behavior of a precipitation strengthening-type Cu-Ni-Si alloy (Cu-2.4Ni-0.51Si-9.3Zn-0.15Sn-0.13Mg) by microcompression specimens. Three micropillars with a square cross-section of 20 × 20 × 40 μm3 were fabricated by focused ion beam (FIB) [...] Read more.
The aim of this study is to investigate a characteristic deformation behavior of a precipitation strengthening-type Cu-Ni-Si alloy (Cu-2.4Ni-0.51Si-9.3Zn-0.15Sn-0.13Mg) by microcompression specimens. Three micropillars with a square cross-section of 20 × 20 × 40 μm3 were fabricated by focused ion beam (FIB) micromachining apparatus and tested by a machine specially designed for microsized specimens. The three pillars were deformed complicatedly and showed different yield strengths depending on the crystal orientation. The micromechanical tests revealed work hardening by the precipitation clearly. Electron backscattered diffraction analysis of a deformed specimen showed a gradual rotation of grain axis at the grain boundaries after the compression test. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Influence of Trapped Gas on Pore Healing under Hot Isostatic Pressing in Nickel-Base Superalloys
Crystals 2020, 10(12), 1147; https://doi.org/10.3390/cryst10121147 - 17 Dec 2020
Cited by 2 | Viewed by 552
Abstract
Under the typical hot isostatic pressing (HIP) processing conditions, plastic deformation by dislocation slip is considered the primary mechanism for pore shrinkage, according to experimental observations and deformation mechanism maps. In the present work, a crystal plasticity model has been used to investigate [...] Read more.
Under the typical hot isostatic pressing (HIP) processing conditions, plastic deformation by dislocation slip is considered the primary mechanism for pore shrinkage, according to experimental observations and deformation mechanism maps. In the present work, a crystal plasticity model has been used to investigate the influence of applied pressure and holding time on porosity reduction in a nickel-base single crystal superalloy. The influence of trapped gas on pore shrinkage is modeled by coupling mechanical deformation with pore–gas interaction. In qualitative agreement with experimental investigations, we observe that increasing the applied pressure or the holding time can effectively reduce porosity. Furthermore, the effect of pore shape on the shrinkage is observed to depend on a combination of elastic anisotropy and the complex distribution of stresses around the pore. Simulation results also reveal that, for pores of the same shape, smaller pores (radius < 0.1 μm) have a higher shrinkage rate in comparison to larger pores (radius ≥ 0.1 μm), which is attributed to the increasing pore surface energies with decreasing pore sizes. It is also found that, for smaller initial gas-filled pores (radius < 0.1 μm), HIP can result in very high gas pressures (on the order of GPa). Such high pressures either act as a driving force for argon to diffuse into the surrounding metal during HIP itself, or it can result in pore re-opening during subsequent annealing or mechanical loading. These results demonstrate that the micromechanical model can quantitatively evaluate the individual influences of HIP processing conditions and pore characteristics on pore annihilation, which can help optimize the HIP process parameters in the future. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Mathematical Modeling of Plastic Deformation of a Tube from Dispersion-Hardened Aluminum Alloy in an Inhomogeneous Temperature Field
Crystals 2020, 10(12), 1103; https://doi.org/10.3390/cryst10121103 - 02 Dec 2020
Cited by 2 | Viewed by 420
Abstract
The effect of temperature distribution on a stress–strain state tube made of disperse-hardened aluminum alloy subjected to internal pressure was investigated. The mathematical model is based on equations of physical plasticity theory and principles of mechanics of deformable solids. The results of this [...] Read more.
The effect of temperature distribution on a stress–strain state tube made of disperse-hardened aluminum alloy subjected to internal pressure was investigated. The mathematical model is based on equations of physical plasticity theory and principles of mechanics of deformable solids. The results of this investigation demonstrate that varying the outer wall temperature in the range of 200 K at a fixed temperature of the inner wall leads to a significant change in the plastic resistance limit (for the considered tube sizes, this change is approximately 15%). An increase of the tube wall temperature reduces the resistance to plastic deformation. For the same absolute temperature difference between the outer and inner walls, the plastic resistance limit is less for the higher temperature of the inner wall of the tube. A decrease of the distances between the hardening particles at the same volume fraction of second phase leads to a significant increase in the pressure required to achieve plastic deformation of the tube walls. An increase in tube wall temperature reduces the resistance to plastic deformation. For the same absolute temperature difference between the outer and inner walls, the plastic resistance limit is lower for the higher temperature of the inner tube wall. The decrease of the distance between the hardening particles at the same volume fraction of the second phase leads to a significant increase in the pressure required to achieve plastic deformation of the tube walls. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Regularized Yield Surfaces for Crystal Plasticity of Metals
Crystals 2020, 10(12), 1076; https://doi.org/10.3390/cryst10121076 - 25 Nov 2020
Cited by 2 | Viewed by 607
Abstract
The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of [...] Read more.
The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of regularized yield surfaces are calibrated to exactly interpolate certain points on the facets of the perfect Schmid yield surface, while the different stress predictions in the corners are taken as the error estimate. Calibrations are discussed for slip systems commonly activated for bcc and fcc metals. It is found that the quality of calibrations of the ideal rate-independent behavior requires very large yield-surface exponents. However, the rounding of the corners of the yield surface can be regarded as an improved approximation accounting for the instant, thermal strain-rate sensitivity, which is directly related to the yield-surface exponent. Distortion of the crystal yield surface during latent hardening is also discussed, including Bauschinger behavior or pseudo slip systems for twinning, for which the forward and backward of the slip system are distinguished. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Microstructural Influence on Stretch Flangeability of Ferrite–Martensite Dual-Phase Steels
Crystals 2020, 10(11), 1022; https://doi.org/10.3390/cryst10111022 - 09 Nov 2020
Cited by 1 | Viewed by 591
Abstract
This work investigated the microstructural effect on stretch flangeability of ferrite–martensite dual-phase (DP) steels. Three types of DP steels with various martensitic structures were prepared for the research: fibrous martensite in water-quenched (WQ) sample, chained martensite in air-quenched (AQ) sample, and coarse martensite [...] Read more.
This work investigated the microstructural effect on stretch flangeability of ferrite–martensite dual-phase (DP) steels. Three types of DP steels with various martensitic structures were prepared for the research: fibrous martensite in water-quenched (WQ) sample, chained martensite in air-quenched (AQ) sample, and coarse martensite in step-quenched (SQ) sample. The WQ specimen exhibited the highest mechanical strength and hole expansion ratio compared to the AQ and SQ samples despite their similar fraction of martensite. Such a result was explained in view of uniform distribution of fine martensite and high density of geometrically necessary dislocations in the WQ specimen. Meanwhile, most cracks initiated at either rolling or transverse direction during the stretch flangeability test regardless of the martensitic morphology. It was attributed to the highest average normal anisotropy in the direction of 45° to rolling direction. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Effect of 3D Representative Volume Element (RVE) Thickness on Stress and Strain Partitioning in Crystal Plasticity Simulations of Multi-Phase Materials
Crystals 2020, 10(10), 944; https://doi.org/10.3390/cryst10100944 - 17 Oct 2020
Cited by 7 | Viewed by 1004
Abstract
Crystal plasticity simulations help to understand the local deformation behavior of multi-phase materials based on the microstructural attributes. The results of such simulations are mainly dependent on the Representative Volume Element (RVE) size and composition. The effect of RVE thickness on the changing [...] Read more.
Crystal plasticity simulations help to understand the local deformation behavior of multi-phase materials based on the microstructural attributes. The results of such simulations are mainly dependent on the Representative Volume Element (RVE) size and composition. The effect of RVE thickness on the changing global and local stress and strain is analyzed in this work for a test case of dual-phase steels in order to identify the minimal RVE thickness for obtaining consistent results. 100×100×100 voxel representative volume elements are constructed by varying grain size and random orientation distribution in DREAM-3D. The constructed RVEs are sliced in depth up to 1, 5, 10, 15, 20, 25, 30, 40, and 50 layers to construct different geometries with increasing thickness. Crystal plasticity model parameters for ferrite and martensite are taken from already published data and assigned to respective phases. Although the global stress/strain behavior of different RVEs is similar (<5% divergence), the local stress/strain partitioning in RVEs with varying thickness and grain size shows a considerable variation when statistically compared. It is concluded that two-dimensional (2D) RVEs can be used for crystal plasticity simulations when global deformation behavior is of interest. Whereas, it is necessary to consider three-dimensional (3D) RVEs, which have a specific thickness and number of grains for determining stabilized and more accurate local deformation behavior. This estimation will help researchers in optimizing the computation time for accurate mesoscale simulations. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Bridging the Gap between Bulk Compression and Indentation Test on Room-Temperature Plasticity in Oxides: Case Study on SrTiO3
Crystals 2020, 10(10), 933; https://doi.org/10.3390/cryst10100933 - 14 Oct 2020
Cited by 5 | Viewed by 840
Abstract
Dislocation-based functionalities in inorganic ceramics and semiconductors are drawing increasing attention, contrasting the conventional belief that the majority of ceramic materials are brittle at room temperature. Understanding the dislocation behavior in ceramics and advanced semiconducting materials is therefore critical for the mechanical reliability [...] Read more.
Dislocation-based functionalities in inorganic ceramics and semiconductors are drawing increasing attention, contrasting the conventional belief that the majority of ceramic materials are brittle at room temperature. Understanding the dislocation behavior in ceramics and advanced semiconducting materials is therefore critical for the mechanical reliability of such materials and devices designed for harvesting the dislocation-based functionalities. Here we compare the mechanical testing between indentation at nano-/microscale and bulk uniaxial deformation at macroscale and highlight the dislocation plasticity in single crystal SrTiO3, a model perovskite. The similarities and differences as well as the advantages and limitations of both testing protocols are discussed based on the experimental outcome of the crystal plasticity, with a focus on the pre-existing defect population being probed with different volumes across the length scales (“size effect”). We expect this work to pave the road for studying dislocation-based plasticity in various advanced functional ceramics and semiconductors. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
The Effect of Equal-Channel Angular Pressing on Microstructure, Mechanical Properties, and Biodegradation Behavior of Magnesium Alloyed with Silver and Gadolinium
Crystals 2020, 10(10), 918; https://doi.org/10.3390/cryst10100918 - 10 Oct 2020
Cited by 2 | Viewed by 562
Abstract
The effect of equal channel angular pressing (ECAP) on the microstructure, texture, mechanical properties, and corrosion resistance of the alloys Mg-6.0%Ag and Mg-10.0%Gd was studied. It was shown that ECAP leads to grain refinement of the alloys down to the average grain size [...] Read more.
The effect of equal channel angular pressing (ECAP) on the microstructure, texture, mechanical properties, and corrosion resistance of the alloys Mg-6.0%Ag and Mg-10.0%Gd was studied. It was shown that ECAP leads to grain refinement of the alloys down to the average grain size of 2–3 μm and 1–2 μm, respectively. In addition, in both alloys the precipitation of fine particles of phases Mg54Ag17 and Mg5Gd with sizes of ~500–600 and ~400–500 nm and a volume fraction of ~9% and ~8.6%, respectively, was observed. In the case of the alloy Mg-6.0%Ag, despite a significant grain refinement, a drop in the strength characteristics and a nearly twofold increase in ductility (up to ~30%) was found. This behavior is associated with the formation of a sharp inclined basal texture. For alloy Mg-10.0%Gd, both ductility and strength were enhanced, which can be associated with the combined effect of significant grain refinement and an increased probability of prismatic and basal glide. ECAP was also shown to cause a substantial rise of the biodegradation rate of both alloys and an increase in pitting corrosion. The latter effect is attributed to an increase in the dislocation density induced by ECAP and the occurrence of micro-galvanic corrosion at the matrix/particle interfaces. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Fatigue Crack Initiation of Metals Fabricated by Additive Manufacturing—A Crystal Plasticity Energy-Based Approach to IN718 Life Prediction
Crystals 2020, 10(10), 905; https://doi.org/10.3390/cryst10100905 - 06 Oct 2020
Cited by 1 | Viewed by 574
Abstract
There has been a long-standing need in the marketplace for the economic production of small lots of components that have complex geometry. A potential solution is additive manufacturing (AM). AM is a manufacturing process that adds material from the bottom up. It has [...] Read more.
There has been a long-standing need in the marketplace for the economic production of small lots of components that have complex geometry. A potential solution is additive manufacturing (AM). AM is a manufacturing process that adds material from the bottom up. It has the distinct advantages of low preparation costs and a high geometric creation capability. However, the wide range of industrial processing conditions results in large variations in the fatigue lives of metal components fabricated using AM. One of the main reasons for this variation of fatigue lives is differences in microstructure. Our methodology incorporated a crystal plasticity finite element model (CPFEM) that was able to simulate a stress–strain response based on a set of randomly generated representative volume elements. The main advantage of this approach was that the model determined the elastic constants (C11, C12, and C44), the critical resolved shear stress (g0), and the strain hardening modulus (h0) as a function of microstructure. These coefficients were determined based on the stress–strain relationships derived from the tensile test results. By incorporating the effect of microstructure on the elastic constants (C), the shear stress amplitude (Δτ2) can be computed more accurately. In addition, by considering the effect of microstructure on the critical resolved shear stress (g0) and the strain hardening modulus (h0), the localized dislocation slip and plastic slip per cycle (Δγp2) can be precisely calculated by CPFEM. This study represents a major advance in fatigue research by modeling the crack initiation life of materials fabricated by AM with different microstructures. It is also a tool for designing laser AM processes that can fabricate components that meet the fatigue requirements of specific applications. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Accurate Estimation of Brittle Fracture Toughness Deterioration in Steel Structures Subjected to Large Complicated Prestrains
Crystals 2020, 10(10), 867; https://doi.org/10.3390/cryst10100867 - 25 Sep 2020
Cited by 2 | Viewed by 475
Abstract
Studies have suggested that brittle fractures occur in steel because microcracks in the brittle layer at grain boundaries propagate as a result of the increase in piled-up dislocations. Therefore, prestraining can approach the limits of a material, which could lead to a decrease [...] Read more.
Studies have suggested that brittle fractures occur in steel because microcracks in the brittle layer at grain boundaries propagate as a result of the increase in piled-up dislocations. Therefore, prestraining can approach the limits of a material, which could lead to a decrease in fracture toughness. However, strains are tensors comprising multiple components, so the effect of prestrain on fracture toughness is not simple. Additionally, the mechanism of change in critical stress due to prestrain has not been thoroughly investigated. For the lifetime evaluation of steel structures with a complicated load history, it is important to generalize the effect of complicated prestrain on the decrease in fracture toughness. In this paper, a single prestrain was applied in a direction different from the crack opening direction. A general three-point bending test was employed for fracture evaluation. Numerical analyses using the strain gradient plasticity (SGP) theory, which is a method based on the finite element method (FEM) are carried out; conventional macroscopic material damage rules are considered as well. Using these FEM analyses, the critical stress is calculated. Finally, the change in critical stress can be expressed by the yield point increase and dislocation density and formulated based on the identified micromechanisms. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Statistical Crystal Plasticity Model Advanced for Grain Boundary Sliding Description
Crystals 2020, 10(9), 822; https://doi.org/10.3390/cryst10090822 - 16 Sep 2020
Cited by 1 | Viewed by 704
Abstract
Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model [...] Read more.
Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which takes into account intragranular dislocation sliding, crystallite lattice rotation and grain boundary sliding. A key advantage of our model over the classical Taylor-type models is that it also includes a consideration of grain boundaries and possible changes in their mutual arrangement. The constitutive relations are defined in rate form and in current configuration, which makes it possible to use additive contributions of intragranular sliding and grain boundary sliding to the strain rate at the macrolevel. In describing grain boundary sliding, displacements along the grain boundaries are considered explicitly, and changes in the neighboring grains are taken into account. In addition, the transition from displacements to deformation (shear) characteristics is done for the macrolevel representative volume via averaging, and the grain boundary sliding submodel is attributed to a separate structural level. We have also analyzed the interaction between grain boundary sliding and intragranular inelastic deformation. The influx of intragranular dislocations into the boundary increases the number of defects in it and the boundary energy, and promotes grain boundary sliding. The constitutive equation for grain boundary sliding describes boundary smoothing caused by diffusion effects. The results of the numerical experiments are in good agreement with the known experimental data. The numerical simulation demonstrates that analysis of grain boundary sliding has a significant impact on the results, and the multilevel constitutive model proposed in this study can be used to describe different inelastic deformation regimes, including superplasticity and transitions between conventional plasticity and superplasticity. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Use of the Correlation between Grain Size and Crystallographic Orientation in Crystal Plasticity Simulations: Application to AISI 420 Stainless Steel
Crystals 2020, 10(9), 819; https://doi.org/10.3390/cryst10090819 - 16 Sep 2020
Cited by 2 | Viewed by 751
Abstract
Crystal plasticity models attempt to reproduce the complex deformation processes of polycrystalline metals based on a virtual representation of the real microstructure. When choosing this representation, a compromise must be made between level of detail at the local level and statistical significance of [...] Read more.
Crystal plasticity models attempt to reproduce the complex deformation processes of polycrystalline metals based on a virtual representation of the real microstructure. When choosing this representation, a compromise must be made between level of detail at the local level and statistical significance of the aggregate properties, also taking into account the computational cost of each solution. In this work, the correlation between crystallographic orientation and grain size is considered in the definition of virtual microstructures for the simulation of the mechanical behavior of AISI 420 stainless steel (consisting of a ferrite matrix with large carbide precipitates), in order to improve the accuracy of the solution without increasing model complexity or computation time. Both full-field (DAMASK) and mean-field models (Visco Plastic Self Consistent (VPSC)) are used together in combination with experimental results to study the validity of the assumptions done in each of the models. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
On the Applicability of Stereological Methods for the Modelling of a Local Plastic Deformation in Grained Structure: Mathematical Principles
Crystals 2020, 10(8), 697; https://doi.org/10.3390/cryst10080697 - 12 Aug 2020
Cited by 1 | Viewed by 582
Abstract
Analysis of systems and structures from their cross-sectional images finds applications in many branches. Therefore, the question of content, quantity, and accuracy of information obtained from various techniques based on cross-sectional views of structures is particularly important. Application of conventional techniques for two-dimensional [...] Read more.
Analysis of systems and structures from their cross-sectional images finds applications in many branches. Therefore, the question of content, quantity, and accuracy of information obtained from various techniques based on cross-sectional views of structures is particularly important. Application of conventional techniques for two-dimensional imaging on the analysis of structure from a cross-sectional image is limited. The reason for this limitation is the fact that these techniques use a fixed cross-sectional plane and therefore cannot check the 3D structural changes caused by deformation. Geometric orientation of a grained structure must be considered when data, scanned from a cross section, is processed in order to obtain information about local deformation in this structure. The so-called degree of structure orientation in 3D can be estimated experimentally from the cross-sectional image of the structure by the statistical (Saltykov) method of oriented testing lines. Subsequently if the correlation between orientation and deformation were to be known a detailed map of local deformation in the structure could be revealed. Unfortunately, exact theoretical works dealing with the assessment of local deformation by means of change of structure orientation in 3D are still missing. Our work seeks to partially remove this shortcoming. In our work we are interested in how the transformation of the image of a grained structure in a cross-sectional plane reflects structure deformation. An initial shape of grains is assumed which is transformed into a deformed shape by analytic calculation. We present brief mathematical derivations aimed at the problem of single grain-surface area deformation. The main goal of this work led to the design of a computationally low consuming procedure for quantification of local deformation in a grained structure based on the distortion of the image of this structure in a cross-sectional view. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Kinetics of Capability Aging in Ti-13Nb-13Zr Alloy
Crystals 2020, 10(8), 693; https://doi.org/10.3390/cryst10080693 - 11 Aug 2020
Cited by 2 | Viewed by 669
Abstract
Metals for biomedical implant applications require a simultaneous achievement of high strength and low Young’s modulus from the viewpoints of mechanical properties. The American Society for Testing and Materials (ASTM) standards suggest two types of processing methods to confer such a mechanical performance [...] Read more.
Metals for biomedical implant applications require a simultaneous achievement of high strength and low Young’s modulus from the viewpoints of mechanical properties. The American Society for Testing and Materials (ASTM) standards suggest two types of processing methods to confer such a mechanical performance to Ti-13Nb-13Zr alloy: solution treatment (ST) and capability aging (CA). This study elucidated the kinetics of CA process in Ti-13Nb-13Zr alloy. Microstructural evolution and mechanical change were investigated depending on the CA duration from 10 min to 6 h. The initial ST alloy possessed the full α′-martensitic structure, leading to a low strength, low Young’s modulus, and high ductility. Increasing CA duration increased mechanical strength and Young’s modulus in exchange for the reduction of ductility. Such a tendency is attributed to the decomposition of α′ martensite into (α+β) structure, particularly hard α precipitates. Mechanical compatibility (i.e., Young’s modulus compensated with a mechanical strength) of Ti-13Nb-13Zr alloy rarely increased by changing CA duration, suggestive of the intrinsic limit of static heat treatment. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Study on Texture and Grain Orientation Evolution in Cold-Rolled BCC Steel by Reaction Stress Model
Crystals 2020, 10(8), 680; https://doi.org/10.3390/cryst10080680 - 06 Aug 2020
Cited by 2 | Viewed by 539
Abstract
The evolution of texture and grain orientations in a cold-rolled steel of BCC structure was simulated by a reaction stress (RS) model. The results show that cold-rolled texture could be assessed based on a RS model because the stress and strain are considered [...] Read more.
The evolution of texture and grain orientations in a cold-rolled steel of BCC structure was simulated by a reaction stress (RS) model. The results show that cold-rolled texture could be assessed based on a RS model because the stress and strain are considered to remain consistent in the deformation process. The strain consistency is actualized by the cooperation of two plastic strains and an elastic strain. The accumulation range of each reaction stress and different activation abilities of {110}<111> and {112}<111> slip systems strongly affect the calculated deformation textures. The values of reaction stress are influenced by elastic anisotropy; however, the effects are greatly reduced because its corresponding reaction stress accumulation is limited. Typical α-fiber and γ-fiber textures are achieved when the reaction stress accumulation coefficients αijs are chosen suitably. Furthermore, the αij values that are selected based on statistically calculated textures can also be used to simulate the orientation change of multiple orientations. The existence of reaction stress is able to stabilize crystallographically symmetrical orientations under rolling deformation, in which the Schmid factors of several slip systems are identical. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Mechanisms of Grain Structure Evolution in a Quenched Medium Carbon Steel during Warm Deformation
Crystals 2020, 10(7), 554; https://doi.org/10.3390/cryst10070554 - 29 Jun 2020
Cited by 1 | Viewed by 540
Abstract
The as-quenched medium-carbon low-alloy Fe-0.36wt.%C-1wt.%Cr steel was subjected to warm deformation via uniaxial compression at temperatures of 400–700 °C and strain rates of 10−4–10−2 s−1. At low temperatures (400–550 °C), the microstructure evolution was mainly associated with dynamic [...] Read more.
The as-quenched medium-carbon low-alloy Fe-0.36wt.%C-1wt.%Cr steel was subjected to warm deformation via uniaxial compression at temperatures of 400–700 °C and strain rates of 10−4–10−2 s−1. At low temperatures (400–550 °C), the microstructure evolution was mainly associated with dynamic recovery with the value of activation energy of 140 ± 35 kJ/mol. At higher temperatures (600–700 °C), dynamic recrystallization was developed, and activation energy in this case was 243 ± 15 kJ/mol. The presence of nanoscale carbide particles in the structure at temperatures of 400–600 °C resulted in the appearance of threshold stresses. A two-component <001>//compression direction (CD) and <111>//CD deformation texture was formed during deformation. Deformation at the low temperatures resulted in the formation of elongated ferritic grains separated mainly by high-angle boundaries (HAB) with a strong <001>//CD texture. The grains with the <111>//CD orientation were wider in comparison with those with the <001>//CD orientation. The development of substructure in the form of low-angle boundaries (LAB) networks was also observed in the <111>//CD grains. The development of dynamic recrystallization restricted the texture formation. The processing map for warm deformation of the 0.36C-1Cr steel was constructed. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Microstructure, Texture, and Strength Development during High-Pressure Torsion of CrMnFeCoNi High-Entropy Alloy
Crystals 2020, 10(4), 336; https://doi.org/10.3390/cryst10040336 - 24 Apr 2020
Cited by 5 | Viewed by 1121
Abstract
The equiatomic face-centered cubic high-entropy alloy CrMnFeCoNi was severely deformed at room and liquid nitrogen temperature by high-pressure torsion up to shear strains of about 170. Its microstructure was analyzed by X-ray line profile analysis and transmission electron microscopy and its texture by [...] Read more.
The equiatomic face-centered cubic high-entropy alloy CrMnFeCoNi was severely deformed at room and liquid nitrogen temperature by high-pressure torsion up to shear strains of about 170. Its microstructure was analyzed by X-ray line profile analysis and transmission electron microscopy and its texture by X-ray microdiffraction. Microhardness measurements, after severe plastic deformation, were done at room temperature. It is shown that at a shear strain of about 20, a steady state grain size of 24 nm, and a dislocation density of the order of 1016 m−2 is reached. The dislocations are mainly screw-type with low dipole character. Mechanical twinning at room temperature is replaced by a martensitic phase transformation at 77 K. The texture developed at room temperature is typical for sheared face-centered cubic nanocrystalline metals, but it is extremely weak and becomes almost random after high-pressure torsion at 77 K. The strength of the nanocrystalline material produced by high-pressure torsion at 77 K is lower than that produced at room temperature. The results are discussed in terms of different mechanisms of deformation, including dislocation generation and propagation, twinning, grain boundary sliding, and phase transformation. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Effect of Strain on Transformation Diagrams of 100Cr6 Steel
Crystals 2020, 10(4), 326; https://doi.org/10.3390/cryst10040326 - 21 Apr 2020
Cited by 2 | Viewed by 875
Abstract
Based on dilatometric tests, the effect of various values of previous deformation on the kinetics of austenite transformations during the cooling of 100Cr6 steel has been studied. Dilatometric tests have been performed with the use of the optical dilatometric module of the plastometer [...] Read more.
Based on dilatometric tests, the effect of various values of previous deformation on the kinetics of austenite transformations during the cooling of 100Cr6 steel has been studied. Dilatometric tests have been performed with the use of the optical dilatometric module of the plastometer Gleeble 3800. The obtained results were compared to metallographic analyses and hardness measurements HV30. Uniaxial compression deformations were chosen as follows: 0, 0.35, and 1; note that these are true (logarithmic) deformations. The highly important finding was the absence of bainite. In addition, it has been verified that with the increasing amount of deformation, there is a further shift in the pearlitic region to higher cooling rates. The previous deformation also affected the temperature martensite start, which decreased due to deformation. The deformation value of 1 also shifted the critical cooling rate required for martensite formation from the 12 °C/s to 25 °C/s. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Mechanical and Thermal Properties of Low-Density Al20+xCr20-xMo20-yTi20V20+y Alloys
Crystals 2020, 10(4), 278; https://doi.org/10.3390/cryst10040278 - 07 Apr 2020
Cited by 10 | Viewed by 1659
Abstract
Refractory high-entropy alloys (RHEAs) Al20+xCr20-xMo20-yTi20V20+y ((x, y) = (0, 0), (0, 10), and (10, 15)) were computationally studied to obtain a low density and a better mechanical property. The density functional theory (DFT) method [...] Read more.
Refractory high-entropy alloys (RHEAs) Al20+xCr20-xMo20-yTi20V20+y ((x, y) = (0, 0), (0, 10), and (10, 15)) were computationally studied to obtain a low density and a better mechanical property. The density functional theory (DFT) method was employed to compute the structural and mechanical properties of the alloys, based on a large unit cell model of randomly distributed elements. Debye–Grüneisen theory was used to study the thermal properties of Al20+xCr20-xMo20-yTi20V20+y. The phase diagram calculation shows that all three RHEAs have a single body-centered cubic (BCC) structure at high temperatures ranging from 1000 K to 2000 K. The RHEA Al30Cr10Mo5Ti20V35 has shown a low density of 5.16 g/cm3 and a hardness of 5.56 GPa. The studied RHEAs could be potential candidates for high-temperature application materials where high hardness, ductility, and low density are required. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Late Age Dynamic Strength of High-Volume Fly Ash Concrete with Nano-Silica and Polypropylene Fibres
Crystals 2020, 10(4), 243; https://doi.org/10.3390/cryst10040243 - 26 Mar 2020
Cited by 10 | Viewed by 1164
Abstract
The dynamic behaviour of high-volume fly ash concrete with nano-silica (HVFANS) and polypropylene fibres at curing ages of 7 to 90 days was determined by using a split Hopkinson pressure bar (SHPB) machine. At each curing age, the concrete samples were laboratory tested [...] Read more.
The dynamic behaviour of high-volume fly ash concrete with nano-silica (HVFANS) and polypropylene fibres at curing ages of 7 to 90 days was determined by using a split Hopkinson pressure bar (SHPB) machine. At each curing age, the concrete samples were laboratory tested at different temperatures conditions under strain rates reached up to 101.42 s−1. At room temperature, the results indicated that the dynamic compressive strength of plain concrete (PC) was slightly higher than HVFANS concrete at early curing ages of 7 and 28 days, however, a considerable improvement in the strength of HVFANS concrete was noted at a curing age of 90 days and recorded greater values than PC owing to the increase of fly ash reactivity. At elevated temperatures, the HVFANS concrete revealed a superior behaviour than PC even at early ages in terms of dynamic compressive strength, critical strain, damage and toughness due to increase of nano-silica (NS) activity during the heating process. Furthermore, equations were suggested to estimate the dynamic increase factor (DIF) of both concretes under the investigated factors. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Modeling the Local Deformation and Transformation Behavior of Cast X8CrMnNi16-6-6 TRIP Steel and 10% Mg-PSZ Composite Using a Continuum Mechanics-Based Crystal Plasticity Model
Crystals 2020, 10(3), 221; https://doi.org/10.3390/cryst10030221 - 20 Mar 2020
Cited by 10 | Viewed by 1487
Abstract
A Transformation-Induced Plasticity (TRIP) steel matrix reinforced with magnesium-partially stabilized zirconia (Mg-PSZ) particles depicts a superior energy absorbing capacity during deformation. In this research, the TRIP/TWIP material model already developed in the framework of the Düsseldorf Advanced Material Simulation Kit (DAMASK) is tuned [...] Read more.
A Transformation-Induced Plasticity (TRIP) steel matrix reinforced with magnesium-partially stabilized zirconia (Mg-PSZ) particles depicts a superior energy absorbing capacity during deformation. In this research, the TRIP/TWIP material model already developed in the framework of the Düsseldorf Advanced Material Simulation Kit (DAMASK) is tuned for X8CrMnNi16-6-6 TRIP steel and 10% Mg-PSZ composite. A new method is explained to more accurately tune this material model by comparing the stress/strain, transformation, twinning, and dislocation glide obtained from simulations with respective experimental acoustic emission measurements. The optimized model with slight modification is assigned to the steel matrix in 10% Mg-PSZ composite material. In the simulation model, zirconia particles are assigned elastic properties with a perfect ceramic/matrix interface. Local deformation, transformation, and the twinning behavior of the steel matrix due to quasi-static tensile load were analyzed. The comparison of the simulation results with acoustic emission data shows good correlation and helps correlate acoustic events with physical attributes. The tuned material models are used to run full phase simulations using 2D Electron Backscatter Diffraction (EBSD) data from steel and 10% Mg-PSZ zirconia composites. Form these simulations, dislocation glide, martensitic transformation, stress evolution, and dislocation pinning in different stages of deformation are qualitatively discussed for the steel matrix and ceramic inclusions. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
How Nanoscale Dislocation Reactions Govern Low- Temperature and High-Stress Creep of Ni-Base Single Crystal Superalloys
Crystals 2020, 10(2), 134; https://doi.org/10.3390/cryst10020134 - 22 Feb 2020
Cited by 3 | Viewed by 993
Abstract
The present work investigates γ-channel dislocation reactions, which govern low-temperature (T = 750 °C) and high-stress (resolved shear stress: 300 MPa) creep of Ni-base single crystal superalloys (SX). It is well known that two dislocation families with different b-vectors are required to form [...] Read more.
The present work investigates γ-channel dislocation reactions, which govern low-temperature (T = 750 °C) and high-stress (resolved shear stress: 300 MPa) creep of Ni-base single crystal superalloys (SX). It is well known that two dislocation families with different b-vectors are required to form planar faults, which can shear the ordered γ’-phase. However, so far, no direct mechanical and microstructural evidence has been presented which clearly proves the importance of these reactions. In the mechanical part of the present work, we perform shear creep tests and we compare the deformation behavior of two macroscopic crystallographic shear systems [ 01 1 ¯ ] ( 111 ) and [ 11 2 ¯ ] ( 111 ) . These two shear systems share the same glide plane but differ in loading direction. The [ 11 2 ¯ ] ( 111 ) shear system, where the two dislocation families required to form a planar fault ribbon experience the same resolved shear stresses, deforms significantly faster than the [ 01 1 ¯ ] ( 111 ) shear system, where only one of the two required dislocation families is strongly promoted. Diffraction contrast transmission electron microscopy (TEM) analysis identifies the dislocation reactions, which rationalize this macroscopic behavior. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Article
Ca-induced Plasticity in Magnesium Alloy: EBSD Measurements and VPSC Calculations
Crystals 2020, 10(2), 67; https://doi.org/10.3390/cryst10020067 - 24 Jan 2020
Cited by 5 | Viewed by 1191
Abstract
In the present work, Ca-induced plasticity of AZ31 magnesium alloy was studied using electron backscattered diffraction (EBSD) measurements supported by viscoplastic self-consistent (VPSC) calculations. For this purpose, alloy samples were stretched to various strains (5%, 10%, and 15%) at room temperature and a [...] Read more.
In the present work, Ca-induced plasticity of AZ31 magnesium alloy was studied using electron backscattered diffraction (EBSD) measurements supported by viscoplastic self-consistent (VPSC) calculations. For this purpose, alloy samples were stretched to various strains (5%, 10%, and 15%) at room temperature and a strain rate of 10−3 s−1. The EBSD measurements showed a higher activity of non-basal slip system (prismatic slip) as compared to that of tension twins. The VPSC confirmed the EBSD results, where it was found that the critical resolved shear stress of the various slip systems and their corresponding activities changed during the stretching of the alloy samples. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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Review

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Review
Mechanisms-Based Transitional Viscoplasticity
Crystals 2020, 10(3), 212; https://doi.org/10.3390/cryst10030212 - 18 Mar 2020
Cited by 3 | Viewed by 1031
Abstract
When metal is subjected to extreme strain rates, the conversation of energy to plastic power, the subsequent heat production and the growth of damages may lag behind the rate of loading. The imbalance alters deformation pathways and activates micro-dynamic excitations. The excitations immobilize [...] Read more.
When metal is subjected to extreme strain rates, the conversation of energy to plastic power, the subsequent heat production and the growth of damages may lag behind the rate of loading. The imbalance alters deformation pathways and activates micro-dynamic excitations. The excitations immobilize dislocation, are responsible for the stress upturn and magnify plasticity-induced heating. The main conclusion of this study is that dynamic strengthening, plasticity-induced heating, grain size strengthening and the processes of microstructural relaxation are inseparable phenomena. Here, the phenomena are discussed in semi-independent sections, and then, are assembled into a unified constitutive model. The model is first tested under simple loading conditions and, later, is validated in a numerical analysis of the plate impact problem, where a copper flyer strikes a copper target with a velocity of 308 m/s. It should be stated that the simulations are performed with the use of the deformable discrete element method, which is designed for monitoring translations and rotations of deformable particles. Full article
(This article belongs to the Special Issue Crystal Plasticity)
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