Crystals

Editorial

Jump to: Research, Review

3 pages, 177 KiB

Open AccessEditorial

Crystal Plasticity (Volume II)

by Wojciech Polkowski

Crystals 2022, 12(10), 1344; https://doi.org/10.3390/cryst12101344 - 23 Sep 2022

Viewed by 1063

Abstract

When we announced the first volume of a Special Issue dedicated to “Crystal Plasticity”, we could not expect that a great collection of 25 excellent articles would be published [...] Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

Research

Jump to: Editorial, Review

8 pages, 2323 KiB

Open AccessCommunication

Synthesis and Characterization of Mechanically Alloyed Nanostructured (Ti,Cr)C Carbide for Cutting Tools Application

by Mohsen Mhadhbi and Wojciech Polkowski

Crystals 2022, 12(9), 1280; https://doi.org/10.3390/cryst12091280 - 9 Sep 2022

Cited by 3 | Viewed by 1591

Abstract

(Ti,Cr)C is a novel additive for high-performance cermets. In this work, a (Ti_0.8Cr_0.2)C nanostructured solid solution was synthesized via Mechanical Alloying (MA) from the mixture of of Ti, Cr, and C powders. The MA process was carried out at [...] Read more.

(Ti,Cr)C is a novel additive for high-performance cermets. In this work, a (Ti_0.8Cr_0.2)C nanostructured solid solution was synthesized via Mechanical Alloying (MA) from the mixture of of Ti, Cr, and C powders. The MA process was carried out at room temperature under argon atmosphere with a duration limited to 20 h. Phase changes and microstructure evolution of the powders during the MA process were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) techniques. The results of XRD analysis demonstrated the synthesis of (Ti,Cr)C solid solution with a crystallite size of about 10 nm that were micro-strained to about 1.34%. The crystallite size displays a decreasing trend with increasing milling time. The results of direct observations of structural features by TEM method in 20 h MAed samples shows a good agreement with the results from the XRD analyses. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

17 pages, 6690 KiB

Open AccessArticle

X-ray Line Profile Analysis of Austenitic Phase Transition and Morphology of Nickel-Free Fe-18Cr-18Mn Steel Powder Synthesized by Mechanical Alloying

by Eliza Romanczuk-Ruszuk, Krzysztof Nowik and Bogna Sztorch

Crystals 2022, 12(9), 1233; https://doi.org/10.3390/cryst12091233 - 1 Sep 2022

Cited by 1 | Viewed by 1757

Abstract

In this study, microstructural evolution and phase transition of nickel-free Fe-18Cr-18Mn (wt. %) austenitic steel powders, induced by mechanical alloying, were investigated. X-ray diffraction, scanning electron microscopy, and microhardness testing techniques were used to observe the changes in the phase composition and particle [...] Read more.

In this study, microstructural evolution and phase transition of nickel-free Fe-18Cr-18Mn (wt. %) austenitic steel powders, induced by mechanical alloying, were investigated. X-ray diffraction, scanning electron microscopy, and microhardness testing techniques were used to observe the changes in the phase composition and particle size as functions of milling time. The first 30 h of mechanical alloying was performed in an argon atmosphere followed by nitrogen for up to 150 h. X-ray diffraction results revealed that the Fe-fcc phase started to form after 30 h of milling, and its fraction continued to increase with alloying time. However, even after 150 h of milling, weak Fe-bcc phase reflections were still detectable (~3.5 wt. %). Basic microstructure features of the multi-phase alloy were determined by X-ray profile analyses, using the whole powder pattern modeling approach to model anisotropic broadening of line profiles. It was demonstrated that the WPPM algorithm can be regarded as a powerful tool for characterizing microstructures even in more complicated multi-phase cases with overlapping reflections. Prolonging alloying time up to 150 h caused the evolution of the microstructure towards the nanocrystalline state with a mean domain size of 6 nm, accompanied by high densities of dislocations exceeding 10¹⁶/m². Deformation-induced hardening was manifested macroscopically by a corresponding increase in microhardness to 1068 HV_0.2. Additionally, diffraction data were processed by the modified Williamson–Hall method, which revealed similar trends of domain size evolutions, but yielded sizes twice as high compared to the WPPM method. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

14 pages, 6199 KiB

Open AccessArticle

Mechanical Properties of Low Carbon Alloy Steel with Consideration of Prior Fatigue and Plastic Damages

by Qing Liu, Zhanzhan Tang, Xuan Yang, Zhixiang He, Hanyang Xue and Hanqing Zhuge

Crystals 2022, 12(7), 967; https://doi.org/10.3390/cryst12070967 - 11 Jul 2022

Cited by 3 | Viewed by 2293

Abstract

Mechanical properties, including the fatigue behavior of metals, are usually determined from damage-free specimens, but it is not well known how these properties change with respect to prior damages; hence, the present work aims to understand the remaining mechanical properties of low carbon [...] Read more.

Mechanical properties, including the fatigue behavior of metals, are usually determined from damage-free specimens, but it is not well known how these properties change with respect to prior damages; hence, the present work aims to understand the remaining mechanical properties of low carbon alloy steel Q345q with pre-damages. Low-cycle fatigue tests on the damage free specimens, tensile tests on the low-cycle fatigue damaged specimens, and fatigue tests on the plastic deformed specimens were carried out, respectively. The low-cycle fatigue life prediction formula was proposed. The influences of different kinds of pre-damages on the residual mechanical properties were analyzed. Results show that the stable hysteretic loops in the low-cycle fatigue tests are well-stacked. The material illustrates Masing behavior, and it has a good energy dissipation capacity. The ductility of the low-cycle fatigue-damaged materials decreases significantly in comparison with the undamaged ones. The low-cycle fatigue lives of Q345q steel are almost unaffected, so long as the pre-applied tensile strain is lower than 10%. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

32 pages, 1590 KiB

Open AccessArticle

Numerical Modeling and Simulations of Twinning-Induced Plasticity Using Crystal Plasticity Finite Element Method

by Rashid Khan, Tasneem Pervez, Adel Alfozan, Sayyad Zahid Qamar and Sumiya Mohsin

Crystals 2022, 12(7), 930; https://doi.org/10.3390/cryst12070930 - 30 Jun 2022

Cited by 4 | Viewed by 2182

Abstract

In the current work, a fully implicit numerical integration scheme is developed for modeling twinning-induced plasticity using a crystal plasticity framework. Firstly, the constitutive formulation of a twin-based micromechanical model is presented to estimate the deformation behavior of steels with low stacking fault [...] Read more.

In the current work, a fully implicit numerical integration scheme is developed for modeling twinning-induced plasticity using a crystal plasticity framework. Firstly, the constitutive formulation of a twin-based micromechanical model is presented to estimate the deformation behavior of steels with low stacking fault energy. Secondly, a numerical integration scheme is developed for discretizing constitutive equations through a fully implicit time integration scheme using the backward Euler method. A time sub-stepping algorithm and the two-norm convergence criterion are used to regulate time step size and stopping criterion. Afterward, a numerical scheme is implemented in finite element software ABAQUS as a user-defined material subroutine. Finally, finite element simulations are executed for observing the validity, performance, and limitations of the numerical scheme. It is observed that the simulation results are in good agreement with the experimental observations with a maximum error of 16% in the case of equivalent stress and strain. It is also found that the developed model is able to estimate well the deformation behavior, magnitude of slip and twin shear strains, and twin volume fraction of three different TWIP steels where the material point is subjected to tension and compression. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

17 pages, 5036 KiB

Open AccessArticle

Characterization of Microstructure and High Temperature Compressive Strength of Austenitic Stainless Steel (21-4N) through Powder Metallurgy Route

by Arun Prasad Murali, Dharmalingam Ganesan, Sachin Salunkhe, Emad Abouel Nasr, João Paulo Davim and Hussein Mohamed Abdelmoneam Hussein

Crystals 2022, 12(7), 923; https://doi.org/10.3390/cryst12070923 - 29 Jun 2022

Cited by 3 | Viewed by 2081

Abstract

Exposure of the engine valve to high temperatures led to the degradation of the valve material due to microstructural instability and deteriorating mechanical properties. Performance enhancement and alteration in microstructures can be attained through the powder metallurgy route which is a viable method [...] Read more.

Exposure of the engine valve to high temperatures led to the degradation of the valve material due to microstructural instability and deteriorating mechanical properties. Performance enhancement and alteration in microstructures can be attained through the powder metallurgy route which is a viable method to produce near net shape components. In this current study, the development of austenitic stainless steel (21-4N) through the powder metallurgy route as an alternate material for engine valves was investigated. Mechanical alloying was carried out for the pre-alloyed mixtures and consolidated using vacuum hot pressing. Sintering parameters were fixed at 1200 °C, 50 MPa and at a vacuum level of 10-3 Torr. A scanning electron microscope was used to analyze the morphology of the milled powders. Densities for the hot pressed powders were compared with theoretical densities and found to be around 98–99%. Observations regarding grain size, the presence of austenitic grain, heterogeneous distribution of metal carbides and analysis of chemical composition along the metal matrix were determined using both optical and electron microscopes. X-ray diffraction was carried out for both the consolidated and powder samples. The hot pressed samples exhibited a hardness value of 410 ± 10 Hv. An isothermal compression test for the sintered samples was carried out at a temperature of 650 °C and strain rate of 0.001 s⁻¹. It is showed that the compressive strength of 1380 MPa. An analysis between the room temperature yield strength obtained from hardness measurement and the strengthening mechanism based on the microstructure was conducted. Grain size, dislocation and solid solution are the major strengthening mechanisms which strengthen the material. Overall, the development of valve steel material through the powder metallurgy route exhibited improved metallurgical and mechanical properties in comparison to the corresponding cast product. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

24 pages, 8096 KiB

Open AccessArticle

Understanding the Plastic Deformation of Gradient Interstitial Free (IF) Steel under Uniaxial Loading Using a Dislocation-Based Multiscale Approach

by Hao Lyu and Annie Ruimi

Crystals 2022, 12(7), 889; https://doi.org/10.3390/cryst12070889 - 23 Jun 2022

Cited by 4 | Viewed by 2385

Abstract

Gradient interstitial free (IF) steels have been shown to exhibit a superior combination of strength and ductility due to their multiscale microstructures. The novelty of the work resides in the implementation of a modified slip transmission and a back-stress quantity induced by a [...] Read more.

Gradient interstitial free (IF) steels have been shown to exhibit a superior combination of strength and ductility due to their multiscale microstructures. The novelty of the work resides in the implementation of a modified slip transmission and a back-stress quantity induced by a long-range dislocation interaction in the dislocation-based multiscale model. This is an improvement over the model we previously proposed. Simulations are performed on IF specimens with gradient structures and with homogeneous structures. The macroscopic behavior of the samples under tension and compression is studied. The evolution of the microstructure such as dislocations, geometrically necessary dislocations (GNDs), and the effects of grain orientation is analyzed. Results show that with our enhanced model, the simulations can successfully reproduce the stress-strain curves obtained experimentally on gradient nano IF steel specimens under tension. The simulations also capture the tension-compression asymmetry (TCA) in specimens with homogeneous and gradient microstructures. The initial texture is found to have a significant effect on the TCA of specimens with gradient microstructures. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

8 pages, 4929 KiB

Open AccessCommunication

Microstructure and Superelastic Properties of FeNiCoAlTi Single Crystals with the <100> Orientation under Tension

by Li-Wei Tseng, Chih-Hsuan Chen, Yu-Chih Tzeng, Po-Yu Lee, Nian-Hu Lu and Yury Chumlyakov

Crystals 2022, 12(4), 548; https://doi.org/10.3390/cryst12040548 - 14 Apr 2022

Cited by 5 | Viewed by 1669

Abstract

The microstructure and superelastic response of an Fe₄₁Ni₂₈Co₁₇Al_11.5Ti_2.5 (at.%) single crystal along the <100> orientation was investigated under tension at room temperature after aging at 600 °C for 24 h. From the superelastic results, [...] Read more.

The microstructure and superelastic response of an Fe₄₁Ni₂₈Co₁₇Al_11.5Ti_2.5 (at.%) single crystal along the <100> orientation was investigated under tension at room temperature after aging at 600 °C for 24 h. From the superelastic results, the samples aged at 600 °C for 24 h exhibited 4.5% recoverable strain at room temperature. The digital image correlation (DIC) method was used to observe the strain distribution during the 6.5% applied strain loading. The DIC results showed that the strain was uniformly distributed during the loading and unloading cycles. Only one martensite variant was observed from the DIC results. This was related to the aging heat treatment times. The martensite morphology became a single variant with a longer aging time. The thermo-magnetization results indicated that the phase transformation and temperature hysteresis was around 36 °C. Increasing the magnetic field from 0.05 to 7 Tesla, the transformation temperatures increased. The maximum magnetization was 160 emu/g under the magnetic field of 7 Tesla. From the transmission electron microscopy results, the L1₂ precipitates were around 10 nm in size, and they were high in Ni content and low in Fe content. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

14 pages, 1574 KiB

Open AccessArticle

Unveiling the Mechanisms of High-Temperature 1/2[111] Screw Dislocation Glide in Iron–Carbon Alloys

by Ivaylo Hristov Katzarov and Ljudmil Borisov Drenchev

Crystals 2022, 12(4), 518; https://doi.org/10.3390/cryst12040518 - 8 Apr 2022

Cited by 3 | Viewed by 1891

Abstract

We have developed a self-consistent model for predicting the velocity of 1/2[111] screw dislocation in binary iron–carbon alloys gliding by a high-temperature Peierls mechanism. The methodology of modelling includes: (i) Kinetic Monte-Carlo (kMC) simulation of carbon segregation in the dislocation core and determination [...] Read more.

We have developed a self-consistent model for predicting the velocity of 1/2[111] screw dislocation in binary iron–carbon alloys gliding by a high-temperature Peierls mechanism. The methodology of modelling includes: (i) Kinetic Monte-Carlo (kMC) simulation of carbon segregation in the dislocation core and determination the total carbon occupancy of the core binding sites; (ii) Determination of kink-pair formation enthalpy of a screw dislocation in iron—carbon alloy; (iii) KMC simulation of carbon drag and determination of maximal dislocation velocity at which the atmosphere of carbon atoms can follow a moving screw dislocation; (iv) Self consistent calculation of the average velocity of screw dislocation in binary iron–carbon alloys gliding by a high-temperature kink-pair mechanism under a constant strain rate. We conduct a quantitative analysis of the conditions of stress and temperature at which screw dislocation glide in iron–carbon alloy is accomplished by a high-temperature kink-pair mechanism. We estimate the dislocation velocity at which the screw dislocation breaks away from the carbon cloud and thermally-activated smooth dislocation propagation is interrupted by sporadic bursts of dislocation activity. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

15 pages, 8281 KiB

Open AccessArticle

The Cooling Rate and Residual Stresses in an AISI 310 Laser Weld: A Meso-Scale Approach

by Edison A. Bonifaz and Andrés S. Mena

Crystals 2022, 12(4), 502; https://doi.org/10.3390/cryst12040502 - 6 Apr 2022

Cited by 3 | Viewed by 2340

Abstract

A three-dimensional coupled temperature-displacement finite element model was developed to generate values of temperature distribution, cooling rate, and residual stresses at the meso-scale level in a thick sheet AISI 310 laser welding test sample. High cooling rates (cooling time from liquid-to-solid temperatures) ranging [...] Read more.

A three-dimensional coupled temperature-displacement finite element model was developed to generate values of temperature distribution, cooling rate, and residual stresses at the meso-scale level in a thick sheet AISI 310 laser welding test sample. High cooling rates (cooling time from liquid-to-solid temperatures) ranging from 960 °C/s to 2400 °C/s were observed when the calculations were made at the meso-scale level. These high cooling rates that arise during the formation of the weld pool originate the highest observed residual stresses that evolve throughout the weld during the entire heating and cooling cycles. An ABAQUS CAE meso model with dimensions of 10 × 5 × 1 mm (element size 100 µ) constructed from a global macro model of 40 × 10 × 75 mm (element size 1 mm) via the submodeling technique is presented in the present paper. In both analyses, macro and meso, the C3D8T thermally coupled brick, trilinear displacement and temperature elements were used. To mesh the entire plate with elements of regular size 100 × 100 × 100 µ, a total of 30 million elements are necessary. With the present approach, 1 macro mesh of 30 thousand elements (1 × 1 × 1 mm) and a meso mesh of 50 thousand elements (100 × 100 × 100 µ) were enough to simulate the weld problem at the meso-scale level. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

16 pages, 2831 KiB

Open AccessArticle

An Integrative Simulation for Mixing Different Polycarbonate Grades with the Same Color: Experimental Analysis and Evaluations

by Jamal Alsadi, Rabah Ismail and Issam Trrad

Crystals 2022, 12(3), 423; https://doi.org/10.3390/cryst12030423 - 18 Mar 2022

Cited by 4 | Viewed by 2375

Abstract

The processing parameters’ impact such as temperature (Temp.), feed rate (F.R.), and speed (S.) at three distinct grades of the same color was explored in this study. To investigate the effect of the characteristics on color formulations, they were each adjusted to five [...] Read more.

The processing parameters’ impact such as temperature (Temp.), feed rate (F.R.), and speed (S.) at three distinct grades of the same color was explored in this study. To investigate the effect of the characteristics on color formulations, they were each adjusted to five different levels. For these grades, which were all associated with the same color, an intermeshing twin-screw extruder (TSE) was used. The compounded materials were molded into flat coupons then evaluated with a spectrophotometer for their CIE (L*, a*, b*, and dE*) values. A spectrophotometer was used to determine the color of a compounded plastic batch, which measured three numbers indicating the tristimulus values (CIE L*a*b*). The lightness axis, which ranged from 0 (black) to 100 (white), is known as the L*-axis (white). Redness-greenness and yellowness-blueness were represented by the other two coordinates, a* and b*, respectively. The color difference deviation (Delta E*) from a target was dimensionless, when dE* approached zero. However, the most excellent favorable color difference value occurred and different processing impact factors on polycarbonate grade were investigated. Using the response service design (RSD) software of Stat-Ease Design-Expert^® (Minneapolis, MN, USA), historical data were gathered and evaluated. To reduce the value of dE*, the impacts of these processing factors were investigated with the three processing parameters. The whole tristimulus color value could be simulated. Parameters were adjusted on 45 different treatments, using a five-level controlled response method to investigate their impact on color and detect non-optimal responses. The ANOVA for each grade was used to build the predicted regression models. The significant processing parameters were subjected to experimental running to simulate the regression models and achieve the best color, reducing waste. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

19 pages, 7853 KiB

Open AccessArticle

Micromechanical Effect of Martensite Attributes on Forming Limits of Dual-Phase Steels Investigated by Crystal Plasticity-Based Numerical Simulations

by Tarek Hussein, Muhammad Umar, Faisal Qayyum, Sergey Guk and Ulrich Prahl

Crystals 2022, 12(2), 155; https://doi.org/10.3390/cryst12020155 - 21 Jan 2022

Cited by 11 | Viewed by 4517

Abstract

This study analyses the effect of martensite grain size and its volume fraction in dual-phase (DP) steel on (1) the formability limit, (2) average global behavior under different loading conditions, and (3) damage initiation. The virtual RVEs (Representative Volume Elements) were constructed using [...] Read more.

This study analyses the effect of martensite grain size and its volume fraction in dual-phase (DP) steel on (1) the formability limit, (2) average global behavior under different loading conditions, and (3) damage initiation. The virtual RVEs (Representative Volume Elements) were constructed using DREAM.3D software with a variation of microstructural attributes. The numerical simulations were carried out using DAMASK, which evaluates the polycrystalline material point behavior and solves versatile constitutive equations using a spectral solver. The simulations were post-processed to obtain global and local stress, strain, and damage evolution in constructed RVEs. The global results were processed to obtain FLDs according to Keeler-Brazier (K-B) and Marciniak and Kuczynski (M-K) criteria. In this work, the capability of microstructure-based numerical simulations to analyze the FLDs has been established successfully. From Forming Limit Diagrams (FLDs), it was observed that formability changes by changing the strain hardening coefficients (n-values), the martensite fraction, and martensite grain sizes of DP steels. The improved formability was observed with lower martensite fraction, i.e., 17%, decreased martensite grain size, i.e., 2.6 µm, and higher strain hardening coefficient. The M-K approach shows the better capability to predict the formability by various loading conditions and clarifies the necking marginal zone of FLD. The damage propagation is also strongly affected by the loading conditions. The current study would be a good guide for designers during the manufacturing and selecting of appropriate DP steels based on the service loading conditions. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Graphical abstract

14 pages, 6346 KiB

Open AccessEditor’s ChoiceArticle

Numerical Investigation into the Influence of Grain Orientation Distribution on the Local and Global Elastic-Plastic Behaviour of Polycrystalline Nickel-Based Superalloy INC-738 LC

by Benedikt Engel, Mark Huth and Christopher Hyde

Crystals 2022, 12(1), 100; https://doi.org/10.3390/cryst12010100 - 13 Jan 2022

Cited by 6 | Viewed by 2700

Abstract

Polycrystalline nickel-based superalloys tend to have large grains within component areas where high loads are dominant during operation. Due to these large grains, caused by the manufacturing and cooling process, the orientation of each grain becomes highly important, since it influences the elastic [...] Read more.

Polycrystalline nickel-based superalloys tend to have large grains within component areas where high loads are dominant during operation. Due to these large grains, caused by the manufacturing and cooling process, the orientation of each grain becomes highly important, since it influences the elastic and plastic behaviour of the material. With the usage of the open source codes NEPER and FEPX, polycrystalline models of Inconel 738 LC were generated and their elastic and crystal plasticity behaviour simulated in dependence of different orientation distributions under uniaxial loading. Orientation distributions close to the [100] direction showed the lowest Young’s moduli as well as the highest elastic strains before yielding, as expected. Orientations close to the [

\bar{5}

89] direction, showed the lowest elastic strains and therefore first plastic deformation under strain loading due to the highest shear stress in the slip systems caused by the interaction of Young’s modulus and the Schmid factor. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

13 pages, 4064 KiB

Open AccessArticle

Numerical Investigation of Plastic Strain Homogeneity during Equal-Channel Angular Pressing of a Cu-Zr Alloy

by Jittraporn Wongsa-Ngam, Nitikorn Noraphaiphipaksa, Chaosuan Kanchanomai and Terence G. Langdon

Crystals 2021, 11(12), 1505; https://doi.org/10.3390/cryst11121505 - 3 Dec 2021

Cited by 2 | Viewed by 2382

Abstract

A three-dimensional finite element method (3D FEM) simulation was carried out using ABAQUS/Explicit software to simulate multi-pass processing by equal-channel angular pressing (ECAP) of a circular cross-sectional workpiece of a Cu-Zr alloy. The effective plastic strain distribution, the strain homogeneity and the occurrence [...] Read more.

A three-dimensional finite element method (3D FEM) simulation was carried out using ABAQUS/Explicit software to simulate multi-pass processing by equal-channel angular pressing (ECAP) of a circular cross-sectional workpiece of a Cu-Zr alloy. The effective plastic strain distribution, the strain homogeneity and the occurrence of a steady-state zone in the workpiece were investigated during ECAP processing for up to eight passes. The simulation results show that a strain inhomogeneity was developed in ECAP after one pass due to the formation of a corner gap in the outer corner of the die. The calculations show that the average effective plastic strain and the degree of homogeneity both increase with the number of ECAP passes. Based on the coefficient of variance, a steady-state zone was identified in the middle section of the ECAP workpiece, and this was numerically evaluated as extending over a length of approximately 40 mm along the longitudinal axis for the Cu-Zr alloy. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

15 pages, 7671 KiB

Open AccessArticle

Strain Rate and Temperature Effects on Tensile Properties of Polycrystalline Cu₆Sn₅ by Molecular Dynamic Simulation

by Wei Huang, Kailin Pan, Jian Zhang and Yubing Gong

Crystals 2021, 11(11), 1415; https://doi.org/10.3390/cryst11111415 - 19 Nov 2021

Cited by 4 | Viewed by 2668

Abstract

Intermetallic compounds (IMCs) are essential in the soldering of electronic products and are composed mainly of Cu₆Sn₅ and Cu₃Sn. They must maintain reliable mechanical and electrical connections. As they are usually only a few microns thick, and it [...] Read more.

Intermetallic compounds (IMCs) are essential in the soldering of electronic products and are composed mainly of Cu₆Sn₅ and Cu₃Sn. They must maintain reliable mechanical and electrical connections. As they are usually only a few microns thick, and it is difficult to study their mechanical properties by traditional methods. In this study, a 100 Å × 100 Å × 100 Å polycrystal with 10 grains was created by Atomsk through Voronoi tessellation based on a Cu₆Sn₅ unit cell. The effects of the temperature and strain rate on the tensile properties of the polycrystalline Cu₆Sn₅ were analyzed based on MEAM potential function using a molecular dynamics (MD) method. The results show that Young’s modulus and ultimate tensile strength (UTS) of the polycrystalline Cu₆Sn₅ decrease approximately linearly with an increase in temperature. At high strain rates (0.001–100 ps⁻¹), Young’s modulus and UTS of the Cu₆Sn₅ are logarithmic with respect to the strain rate, and both increase with an increase in strain rate. In addition, at low strain rates (0.00001–0.0005 ps⁻¹), the UTS has a quadratic increase as the strain rate increases. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

19 pages, 1077 KiB

Open AccessEditor’s ChoiceArticle

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

by Peter Trusov, Alexey Shveykin and Nikita Kondratev

Crystals 2021, 11(11), 1392; https://doi.org/10.3390/cryst11111392 - 15 Nov 2021

Cited by 11 | Viewed by 2684

Abstract

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms [...] Read more.

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

19 pages, 4026 KiB

Open AccessEditor’s ChoiceArticle

Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium

by Omid Sedaghat and Hamidreza Abdolvand

Crystals 2021, 11(11), 1382; https://doi.org/10.3390/cryst11111382 - 12 Nov 2021

Cited by 7 | Viewed by 2998

Abstract

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of [...] Read more.

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Graphical abstract

21 pages, 5894 KiB

Open AccessArticle

Rolling Texture of Cu–30%Zn Alloy Using Taylor Model Based on Twinning and Coplanar Slip

by Shih-Chieh Hsiao, Sin-Ying Lin, Huang-Jun Chen, Ping-Yin Hsieh and Jui-Chao Kuo

Crystals 2021, 11(11), 1351; https://doi.org/10.3390/cryst11111351 - 7 Nov 2021

Cited by 1 | Viewed by 1877

Abstract

A modified Taylor model, hereafter referred to as the MTCS (Mechanical-Twinning-with-Coplanar-Slip)-model, is proposed in the present work to predict weak texture components in the shear bands of brass-type fcc metals with a twin–matrix lamellar (TML) structure. The MTCS-model considers two boundary conditions (i.e., [...] Read more.

A modified Taylor model, hereafter referred to as the MTCS (Mechanical-Twinning-with-Coplanar-Slip)-model, is proposed in the present work to predict weak texture components in the shear bands of brass-type fcc metals with a twin–matrix lamellar (TML) structure. The MTCS-model considers two boundary conditions (i.e., twinning does not occur in previously twinned areas and coplanar slip occurs in the TML region) to simulate the rolling texture of Cu–30%Zn. In the first approximation, texture simulation using the MTCS-model revealed brass-type textures, including Y{1 1 1} <1 1 2> and Z{1 1 1} <1 1 0> components, which correspond to the observed experimental textures. Single orientations of C

(1 1 2) [\bar{1} \bar{1} 1]

and S’

(1 2 3) [\bar{4} \bar{1} 2]

were applied to the MTCS-model to understand the evolution of Y and Z components. For the Y orientation, the C orientation rotates toward T(5 5 2)[1 1 5] by twinning after 30% reduction and then toward Y(1 1 1)[1 1 2] by coplanar slip after over 30% reduction. For the Z orientation, the S’ orientation rotates toward T’

(3 2 1) [2 \bar{1} \bar{4}]

by twinning after 30% reduction and then toward Z

(1 1 1) [1 0 \bar{1}]

by coplanar slip after over 30% reduction. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Graphical abstract

15 pages, 3260 KiB

Open AccessArticle

Shape Memory Properties and Microstructure of New Iron-Based FeNiCoAlTiNb Shape Memory Alloys

by Li-Wei Tseng, Chih-Hsuan Chen, Wei-Cheng Chen, Yu Cheng and Nian-Hu Lu

Crystals 2021, 11(10), 1253; https://doi.org/10.3390/cryst11101253 - 15 Oct 2021

Cited by 8 | Viewed by 2389

Abstract

The shape memory properties and microstructure of Fe₄₁Ni₂₈Co₁₇Al_11.5(Ti+Nb)_2.5 (at.%) cold-rolled alloys were studied at the first time using the values reported in constant stress thermal cycling experiments in a three-point bending test. Thermo-magnetization curves [...] Read more.

The shape memory properties and microstructure of Fe₄₁Ni₂₈Co₁₇Al_11.5(Ti+Nb)_2.5 (at.%) cold-rolled alloys were studied at the first time using the values reported in constant stress thermal cycling experiments in a three-point bending test. Thermo-magnetization curves of 97% cold-rolled and solution-treated sample aged at 600 °C for 24, 48 and 72 h showed evidence of the martensitic transformation, and the transformation temperatures increased their values from 24 to 72 h. The alloy cold-rolled to 97% and then solution-treated at 1277 °C for 1 h showed that most grains were aligned near <100> in the rolling direction in the recrystallization texture. The intensity of texture was 13.54, and an average grain size was around 400 μm. The sample aged at 600 °C for 48 h showed fully recoverable strain up to 1.6% at 200 MPa stress level in the three-point bending test. However, the experimental recoverable strain values were lower than the theoretical values, possibly due to the small volume fraction of low angle grain boundary, the formation of brittle grain boundary precipitates, and a grain boundary constraint lower than the expected intensity of texture in the samples. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

9 pages, 3071 KiB

Open AccessArticle

Microstructural Evolution and Tensile Testing of a Bi–Sn (57/43) Alloy Processed by Tube High-Pressure Shearing

by Chuan-Ting Wang, Zheng Li, Yong He, Jing-Tao Wang and Terence G. Langdon

Crystals 2021, 11(10), 1229; https://doi.org/10.3390/cryst11101229 - 12 Oct 2021

Cited by 8 | Viewed by 2080

Abstract

Tube high-pressure shearing (t-HPS) processing was performed on a eutectic Bi–Sn (57/43) alloy for 0.25, 1, 5 and 20 turns. The selected samples were stored at room temperature for up to 56 days to examine the strain weakening and self-annealing behavior of the [...] Read more.

Tube high-pressure shearing (t-HPS) processing was performed on a eutectic Bi–Sn (57/43) alloy for 0.25, 1, 5 and 20 turns. The selected samples were stored at room temperature for up to 56 days to examine the strain weakening and self-annealing behavior of the alloy. The results showed that t-HPS processing gradually refined the microstructure and led to decreasing of microhardness, but microhardness increased slowly during the subsequent storage at room temperature. Shear localization of the eutectic structure during t-HPS processing was observed as large amounts of narrow dense lamellar zones were visible in the deformed microstructures. The Bi–Sn (57/43) alloy processed by t-HPS exhibited significantly enhanced superplastic properties with elongations up to >1800% in a sample after t-HPS processing for 20 turns. This high elongation is attributed to the breaking of the lamellar structure and the very small grain size. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

11 pages, 3930 KiB

Open AccessArticle

Study on Phase Transformation Orientation Relationship of HCP-FCC during Rolling of High Purity Titanium

by Fengmei Bai, Qingliang Zhu, Jiaming Shen, Zhihan Lu, Liqiang Zhang, Naqash Ali, Hongwei Zhou and Xianghua Liu

Crystals 2021, 11(10), 1164; https://doi.org/10.3390/cryst11101164 - 24 Sep 2021

Cited by 10 | Viewed by 5810

Abstract

High purity titanium (Ti) thin strip was prepared by rolling with large deformation and was characterized by the means of Transmission Electron Microscopy (TEM), selected area diffraction (SAED) pattern, high-resolution (HRTEM) analysis, as well as Transmission Kikuchi Diffraction (TKD). It is found that [...] Read more.

High purity titanium (Ti) thin strip was prepared by rolling with large deformation and was characterized by the means of Transmission Electron Microscopy (TEM), selected area diffraction (SAED) pattern, high-resolution (HRTEM) analysis, as well as Transmission Kikuchi Diffraction (TKD). It is found that there are face-centered cubic (FCC) Ti laths formed within the matrix of hexagonal close packing (HCP) Ti. This shows that the HCP-FCC phase transition occurred during the rolling, and a specific orientation relationship (OR) between HCP phase and FCC phase obeys ⟨0001⟩_α// ⟨001⟩_FCC and {100}_α//{110}_FCC. The ORs of HCP-FCC phase transition are deeply studied by TKD pole figure and phase transformation matrix. It is found that the derived results via pole figure and transformation matrix are equivalent, and are consistent with TEM-SAED analysis results, which proves that these two methods can effectively characterize the ORs of HCP-FCC phase transition and predict possible FCC phase variants. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

8 pages, 729 KiB

Open AccessArticle

Effects of the Rare Earth Y on the Structural and Tensile Properties of Mg-based Alloy: A First-Principles Study

by Yan Gao, Chuang Wu, Wenjiang Feng, Yan He, Haisheng He, Jingyu Yang and Xiuyan Chen

Crystals 2021, 11(8), 1003; https://doi.org/10.3390/cryst11081003 - 22 Aug 2021

Cited by 25 | Viewed by 2303

Abstract

In order to investigate the effect of the rare earth element Y on the strengthening potency of magnesium alloys and its strengthening mechanism under tension. In this paper, the solid solution structures with Y atom content of 1.8 at.% and 3.7 at.% were [...] Read more.

In order to investigate the effect of the rare earth element Y on the strengthening potency of magnesium alloys and its strengthening mechanism under tension. In this paper, the solid solution structures with Y atom content of 1.8 at.% and 3.7 at.% were built, respectively, and their cohesive energies and stress-strain curve were calculated in the strain range of 0–20%. The calculation results of the cohesive energies showed that the structure of element Y is more stable with the increase of strains. The calculation results of stress and strain showed that Y element can improve the yield strength and tensile strength of the Mg-based alloy, and the strengthening effect is better when the Y content is 3.7 at.%. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

10 pages, 3191 KiB

Open AccessEditor’s ChoiceCommunication

Investigation on the Effects of Grain Boundary on Deformation Behavior of Bicrystalline Pillar by Crystal Plasticity Finite Element Method

by Hui Zhou, Pei Wang and Shanping Lu

Crystals 2021, 11(8), 923; https://doi.org/10.3390/cryst11080923 - 9 Aug 2021

Cited by 5 | Viewed by 2556

Abstract

A dislocation density–grain boundary interaction scheme coupled with the dislocation density-based crystalline plasticity finite element method has been established and used to investigate the deformation behavior of bicrystalline pillars with the same grain boundary misorientation angle but different crystal orientations. It is found [...] Read more.

A dislocation density–grain boundary interaction scheme coupled with the dislocation density-based crystalline plasticity finite element method has been established and used to investigate the deformation behavior of bicrystalline pillars with the same grain boundary misorientation angle but different crystal orientations. It is found that the angle between the activated slip systems, which is determined by the crystal orientations, rather than the grain boundary misorientation angle, influences the interactions between the plastic slip and the grain boundary, which further influence the heterogeneous deformation of bicrystalline specimens. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

14 pages, 3840 KiB

Open AccessArticle

A Constitutive Relation Based on the Johnson–Cook Model for Ti-22Al-23Nb-2(Mo, Zr) Alloy at Elevated Temperature

by Yanju Wang, Duo Zhou, Yi Zhou, Aixue Sha, Huaxing Cheng and Yabin Yan

Crystals 2021, 11(7), 754; https://doi.org/10.3390/cryst11070754 - 28 Jun 2021

Cited by 5 | Viewed by 2388

Abstract

Although several schemes have been proposed to modify the classical Johnson–Cook (J-C) model, the effect of temperature on the flow stress of materials at different temperatures has not been clarified. In the current study, to investigate the deformation behavior of Ti-22Al-23Nb-2(Mo, Zr) alloy [...] Read more.

Although several schemes have been proposed to modify the classical Johnson–Cook (J-C) model, the effect of temperature on the flow stress of materials at different temperatures has not been clarified. In the current study, to investigate the deformation behavior of Ti-22Al-23Nb-2(Mo, Zr) alloy at different temperatures, uniaxial tension experiments were performed at both room (RT, 28 °C) and elevated temperatures, and a modified J-C model was developed to describe the temperature-dependent plastic flow. In tensile experiments, Ti₂AlNb-based alloy showed a continuous work hardening until reaching the ultimate strength at RT, while an apparent drop appeared in the flow stress after the peak stress at elevated temperature. Moreover, the experimental peak stress significantly depends on the testing temperature. To correctly describe the different variations of flow stresses at different temperatures, a parameter, S, which represents the softening behavior of flow stress, is integrated into the classical J-C model. In addition, the applicability and validity of the proposed J-C model were verified by calibration with experimental curves of different temperatures. On the other hand, the fractography of post-test specimens was examined to interrupt the increased fracture brittleness of Ti₂AlNb-based alloy at elevated temperatures. The proposed constitutive relation based on the J-C model is applicable to predict the deformation behavior of other Ti₂AlNb-based alloys at different temperatures. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

10 pages, 5552 KiB

Open AccessArticle

Twinning Behavior in Cold-Rolling Ultra-Thin Grain-Oriented Silicon Steel

by Bo Zhang, Li Meng, Guang Ma, Ning Zhang, Guobao Li, Kun Liu and Sheng Zhong

Crystals 2021, 11(2), 187; https://doi.org/10.3390/cryst11020187 - 14 Feb 2021

Cited by 3 | Viewed by 2262

Abstract

Twinning behaviors in grains during cold rolling have been systematically studied in preparing ultra-thin grain-oriented silicon steel (UTGO) using a commercial glassless grain-oriented silicon steel as raw material. It is found that the twinning system with the maximum Schmid factor and shear mechanical [...] Read more.

Twinning behaviors in grains during cold rolling have been systematically studied in preparing ultra-thin grain-oriented silicon steel (UTGO) using a commercial glassless grain-oriented silicon steel as raw material. It is found that the twinning system with the maximum Schmid factor and shear mechanical work would be activated. The area fraction of twins increased with the cold rolling reduction. The orientations of twins mainly appeared to be α-fiber (<110>//RD), most of which were {001}<110> orientation. Analysis via combining deformation orientation simulation and twinning orientation calculation suggested that {001}<110> oriented twinning occurred at 40–50% rolling reduction. The simulation also confirmed more {100} <011> oriented twins would be produced in the cold rolling process and their orientation also showed less deviation from ideal {001}<110> orientation when a raw material with a higher content of exact Goss oriented grains was used. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

13 pages, 5190 KiB

Open AccessArticle

Microstructural Changes in Ni-Al-Cr-Based Heat-Resistant Alloy with Re Addition

by Nina A. Koneva, Elena L. Nikonenko, Alisa V. Nikonenko and Natalya A. Popova

Crystals 2021, 11(2), 89; https://doi.org/10.3390/cryst11020089 - 21 Jan 2021

Cited by 2 | Viewed by 1748

Abstract

This paper presents scanning and transmission electron microscope investigations of the structure, phase composition, and morphology of a heat-resistant alloy modified by thermal treatment and additionally alloyed by rhenium. The rhenium alloy was obtained by using the directional crystallization technique. The structural investigations [...] Read more.

This paper presents scanning and transmission electron microscope investigations of the structure, phase composition, and morphology of a heat-resistant alloy modified by thermal treatment and additionally alloyed by rhenium. The rhenium alloy was obtained by using the directional crystallization technique. The structural investigations were carried out for two states of the alloy, i.e., (1) original (after the directional crystallization); (2) after the directional crystallization with 1150 °C annealing for 1 h and 1100 °C annealing for 480 h. It is shown that fcc-based γ- and γ′-phases are primary in all states of the alloy. The γ′-phase has an L1₂ structure, while γ-phase is a disordered phase. It was found that after directed crystallization, the volume fraction of the γ′ phase is ~85%, the fraction of the γ-phase is less than 10%. Annealing leads to an increase in the γ′- phase up to 90%, the proportion of the γ-phase practically does not change. Rhenium is a phase-formation element. The investigations show that high-temperature annealing modifies the structural and phase conditions of the heat-resistant alloy. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Graphical abstract

Review

Jump to: Editorial, Research

17 pages, 2694 KiB

Open AccessReview

Thermodynamic Modeling and Mechanical Properties of Mg-Zn-{Y, Ce} Alloys: Review

by Mohammad Aljarrah, Jasim Alnahas and Mohammed Alhartomi

Crystals 2021, 11(12), 1592; https://doi.org/10.3390/cryst11121592 - 20 Dec 2021

Cited by 11 | Viewed by 5562

Abstract

Magnesium alloys are a strong candidate for various applications in automobile and aerospace industries due to their low density and specific strength. Micro-alloying magnesium with zinc, yttrium, and cerium enhances mechanical properties of magnesium through grain refinement and precipitation hardening. In this work, [...] Read more.

Magnesium alloys are a strong candidate for various applications in automobile and aerospace industries due to their low density and specific strength. Micro-alloying magnesium with zinc, yttrium, and cerium enhances mechanical properties of magnesium through grain refinement and precipitation hardening. In this work, a critical review of magnesium-based binary systems including Mg-Zn, Mg-Y, Mg-Ce, Zn-Y, and Zn-Ce is presented. Based on the CALPHAD approach and first-principles calculations, thermodynamic modeling of Mg-Zn-Y and Mg-Zn-Ce ternary phase diagrams have been summarized. The influence of micro-alloying (yttrium and cerium) on the mechanical properties of magnesium is discussed. A comparison between mechanical properties of magnesium commercial alloys and magnesium–zinc–{yttrium and cerium} have been summarized in tables. Full article

(This article belongs to the Special Issue Crystal Plasticity (Volume II))

► Show Figures

Figure 1

Journal Menu

Journal Browser

Crystal Plasticity (Volume II)

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Related Special Issues

Published Papers (27 papers)

Editorial

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI