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学者姓名:陈子勇
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Abstract :
In this work, the modification mechanism of Sr on Si phase was studied, and the effect of Sr element on the microstructure and mechanical properties of Al-12Si-4Cu-2Ni-Mg alloy was analyzed. The microstructure and twins of the alloy were characterized and analyzed using scanning electron microscopy, electron spectroscopy, and transmission electron microscopy. The results show that the twin plane re-entrant edge (TPRE) mechanism and impurity induced twinning (IIT) mechanism cannot fully explain the modification mechanism of Si phase in Al-12Si-4Cu-2Ni-Mg alloy. Various nano-precipitates appeared on the Si phase of the as-cast alloy, including a large amount of Al rich nano-precipitates, Sr rich nano precipitates near twins, and a small amount of AlCu nano- precipitates. These nano-precipitates and Sr atoms together lead to changes in the size and morphology of the Si phase. With an increase in the Si phase modification degree, the ultimate tensile strength (UTS) and elongation (El) of the alloy at room temperature improved. Excessive Sr leads to the formation of coarse Al2Si2Sr, which is not conducive to improving the modification degree and room temperature mechanical properties of the alloy. Sr had no effect on the morphology, type, and quantity of Ni-rich intermetallic compounds in the T6-treated Al12Si-4Cu-2Ni-Mg alloys. The UTS and El of T6 alloys at high temperature are closely related to the degree of modification of Si phase in the alloy. The three-dimensional overlapping structure of the second phase in the T6- state Al-12Si-4Cu-2Ni-Mg-0.01 Sr alloy is stable, and its UTS and El reach a peak at high temperature.
Keyword :
Mechanical properties Mechanical properties Modification mechanism Modification mechanism Al-Si-Cu-Ni-Mg alloy Al-Si-Cu-Ni-Mg alloy Twins Twins Nano-precipitates Nano-precipitates
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GB/T 7714 | Yang, Zian , Xiang, Zhilei , Li, Jihao et al. The influence of Sr on the modification mechanism and mechanical properties of Al-12Si-4Cu-2Ni-Mg alloy [J]. | MATERIALS TODAY COMMUNICATIONS , 2025 , 43 . |
MLA | Yang, Zian et al. "The influence of Sr on the modification mechanism and mechanical properties of Al-12Si-4Cu-2Ni-Mg alloy" . | MATERIALS TODAY COMMUNICATIONS 43 (2025) . |
APA | Yang, Zian , Xiang, Zhilei , Li, Jihao , Huang, Jingcun , Li, Leizhe , Li, Meng et al. The influence of Sr on the modification mechanism and mechanical properties of Al-12Si-4Cu-2Ni-Mg alloy . | MATERIALS TODAY COMMUNICATIONS , 2025 , 43 . |
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Abstract :
In the present work, the hot deformation behavior and microstructural evolution of a TiB2/Al-Zn-Mg-Cu-Zr composite were studied. Hot compression tests were conducted within a temperature range of 370 degrees C to 490 degrees C and a strain rate of 0.001 s(-1) to 10 s(-1). We established the Arrhenius constitutive equation with Zener-Hollomon parameters and processing maps and discussed the microstructural evolution during hot deformation. The results indicated that the safe processing parameter region falls within 370 degrees C-490 degrees C and 0.001 s(-1)-0.025 s(-1). The influence of the strain rate on the safe processing range is more dominant than that of deformation temperature, which is primarily attributed to TiB2. Dynamic softening is primarily governed by dynamic recovery (DRV). Small particles (eta, Al3Zr) can pin dislocations, promoting the rearrangement and annihilation of dislocations and facilitating DRV. Higher temperatures and lower strain rates facilitated dynamic recrystallization (DRX). Continuous dynamic recrystallization (CDRX) occurs near high-angle grain boundaries induced by strain-induced boundary migration (SIBM). TiB2 and large second-phase particles generate high-density geometrically necessary dislocations (GNBs) during hot deformation, which serve as nucleation sites for discontinuous dynamic recrystallization (DDRX). This enhances dynamic softening and improves formability.
Keyword :
composites composites microstructure microstructure constitutive equation constitutive equation hot deformation hot deformation
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GB/T 7714 | Huang, Jingcun , Xiang, Zhilei , Li, Meng et al. Hot Deformation Behavior and Microstructural Evolution of a TiB2/Al-Zn-Mg-Cu-Zr Composite [J]. | MATERIALS , 2024 , 17 (7) . |
MLA | Huang, Jingcun et al. "Hot Deformation Behavior and Microstructural Evolution of a TiB2/Al-Zn-Mg-Cu-Zr Composite" . | MATERIALS 17 . 7 (2024) . |
APA | Huang, Jingcun , Xiang, Zhilei , Li, Meng , Li, Leizhe , Chen, Ziyong . Hot Deformation Behavior and Microstructural Evolution of a TiB2/Al-Zn-Mg-Cu-Zr Composite . | MATERIALS , 2024 , 17 (7) . |
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Abstract :
We investigated the microstructure evolution of a 6 wt% TiB2-reinforced Al-Zn-Mg-Cu-Zr composite subjected to hot compression at temperatures within the range 370 degrees C-490 degrees C, at strain rates between 0.001 s-1 and 10 s-1. The microstructure evolution was characterized by electron backscatter diffraction and transmission electron microscopy. Dynamic recovery and dynamic recrystallization mechanisms were analyzed, with a focus on nucleation at original grain boundaries and TiB2 particles. The results show that recovery is the main dynamic softening mechanism due to the high dislocation mobility in the Al matrix. However, low temperature and high strain rate results in a large number of small recrystallized grains, whereas high temperature and low strain rate results in a few large recrystallized grains. Dynamic recrystallization is mainly attributed to particle-stimulated nucleation occurring near TiB2 particles/clusters, especially TiB2 particles/clusters at grain boundaries. Relations between the observed dynamic recrystallization and the Zener-Hollomon parameter are discussed.
Keyword :
Dynamic recrystallization Dynamic recrystallization Zener-Hollomon parameter Zener-Hollomon parameter Hot deformation Hot deformation Particle-stimulated nucleation Particle-stimulated nucleation
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GB/T 7714 | Huang, Jingcun , Chen, Ziyong , Jensen, Dorte Juul et al. Effect of TiB2 particles on dynamic recrystallization in TiB2-reinforced Al-Zn-Mg-Cu-Zr during hot compression [J]. | MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING , 2024 , 910 . |
MLA | Huang, Jingcun et al. "Effect of TiB2 particles on dynamic recrystallization in TiB2-reinforced Al-Zn-Mg-Cu-Zr during hot compression" . | MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 910 (2024) . |
APA | Huang, Jingcun , Chen, Ziyong , Jensen, Dorte Juul , Yu, Tianbo . Effect of TiB2 particles on dynamic recrystallization in TiB2-reinforced Al-Zn-Mg-Cu-Zr during hot compression . | MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING , 2024 , 910 . |
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Abstract :
In this study, in order to obtain excellent mechanical properties in TiB2/Al-Cu-Mn-Cd composite, an optimized heat treatment, i.e., short-time solution treatment at 535 degrees C for 1 h following long-time solution at 523 degrees C for 11 h, and aging treatment, i.e., aged at 170 degrees C for 12 h, is proposed. In addition, this study investigated the connection between microstructure evolution and mechanical properties during heat treatment. The results show that with adoption of the optimized solution treatment, the area fraction of second and eutectic Al2Cu phases decreased from 5.08% in the as-cast state to less than 0.36% owing to improvement of dissolution efficiency in the high-temperature short-time solution. Comparing mechanical properties of the composite in the as-cast state and in the peak-aged state, average ultimate tensile strength and yield strength increased from 211.9 MPa to 523.0 MPa and from 115.8 MPa to 451.8 MPa, respectively. However, average elongation slightly decreased from 8.78% to 8.24%. Strength contribution of the peak-aged TiB2/Al-Cu-Mn-Cd composite was mainly ascribed to Cd-rich, theta '' and theta ' precipitates. In the peak-aged state, number density and average diameter of the plate-like theta '' and theta ' precipitates reached 4.266 x 10(21) m(3) and 64.30 nm, respectively, and severe lattice distortions occurred around the Cd-rich precipitates, providing the strongest precipitation strengthening. These findings indicate that the two-stage solution treatment successfully solved the problem of the eutectic phase at the triangular grain boundary being difficult to dissolve in a TiB2/Al-Cu-Mn-Cd composite, and excellent mechanical properties were acquired with the optimized aging treatment.
Keyword :
TiB2/Al-Cu-Mn-Cd composite TiB2/Al-Cu-Mn-Cd composite microstructure evolution microstructure evolution mechanical properties mechanical properties two-stage solution treatment two-stage solution treatment
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GB/T 7714 | Li, Jihao , Xiang, Zhilei , Shen, Gaoliang et al. Microstructure Evolution and Mechanical Properties of TiB2/Al-Cu-Mn-Cd Composite with the Adoption of Two-Stage Solution and Aging Treatment [J]. | CRYSTALS , 2024 , 14 (10) . |
MLA | Li, Jihao et al. "Microstructure Evolution and Mechanical Properties of TiB2/Al-Cu-Mn-Cd Composite with the Adoption of Two-Stage Solution and Aging Treatment" . | CRYSTALS 14 . 10 (2024) . |
APA | Li, Jihao , Xiang, Zhilei , Shen, Gaoliang , Huang, Jingcun , Sun, Wenchao , Yang, Zian et al. Microstructure Evolution and Mechanical Properties of TiB2/Al-Cu-Mn-Cd Composite with the Adoption of Two-Stage Solution and Aging Treatment . | CRYSTALS , 2024 , 14 (10) . |
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Abstract :
Alloy composition and heat treatment processes have limited possibility to enhance ultra-high strength of aluminum alloys, which restricts their widespread application in lightweight equipment. Consequently, high-density dislocations and grain refinement are suggested to strengthen ultra-high strength aluminum alloys. Herein, a novel nanostructured Al-Zn-Mg-Cu-Zr-Sc (AZMCZS) alloy with homogeneous microstructure is prepared through the synergistic processing of hot extrusion and high-pressure torsion. Additionally, the microstructures and strengthening mechanisms of the nanostructured Al alloy are analyzed. It is observed that the ultimate tensile strength of the nanostructured Al alloy reaches nearly 1 GPa, and the elongation of the alloy is 1.9%. The nanostructured Al alloy mainly consists of nanoscale grains (approximate to 117.7 nm), high-density dislocations (2.4 x 1015 m-2), nano-sized precipitates (the size of 20-51 nm), and solute atom clusters (approximate to 3 nm). The multiple strengthening mechanisms of the nanostructured Al alloy are revealed in terms of grain refinement, dislocations, precipitates, and solute atom clusters. Grain refinement and dislocation strengthening show superior outcomes and are considered to be the predominant strengthening mechanisms. These findings demonstrate that this nanostructural architecture offers a new way to design super-strength metals and alloys by effectively controlling the processing regime of severe plastic deformation. A nanostructured Al-Zn-Mg-Cu-Zr-Sc alloy is designed and successfully prepared through synergy processing of hot extrusion and high-pressure torsion (HPT). The average grain size of the nanostructured alloy prepared by HPT is about 117.7 nm. The nanostructured alloy exhibits a ultra-high tensile strength of 970 MPa, and approaching 1 GPa level strength.image (c) 2024 WILEY-VCH GmbH
Keyword :
high-pressure torsion high-pressure torsion Al-Zn-Mg-Cu-Zr-Sc alloy Al-Zn-Mg-Cu-Zr-Sc alloy hot extrusion hot extrusion nanostructure nanostructure strength strength
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GB/T 7714 | Shen, Gaoliang , Li, Mingxi , Liu, Jiashuo et al. Approaching 1 GPa Ultra-High Tensile Strength in a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy Prepared by Severe Plastic Deformation [J]. | ADVANCED ENGINEERING MATERIALS , 2024 , 26 (12) . |
MLA | Shen, Gaoliang et al. "Approaching 1 GPa Ultra-High Tensile Strength in a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy Prepared by Severe Plastic Deformation" . | ADVANCED ENGINEERING MATERIALS 26 . 12 (2024) . |
APA | Shen, Gaoliang , Li, Mingxi , Liu, Jiashuo , Zheng, Ruixiao , Xiang, Zhilei , Ma, Xiaozhao et al. Approaching 1 GPa Ultra-High Tensile Strength in a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy Prepared by Severe Plastic Deformation . | ADVANCED ENGINEERING MATERIALS , 2024 , 26 (12) . |
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Abstract :
Al-Zn-Mg-Cu aluminum alloys have the advantages of high specific strength, easy processing, and high toughness, showing great potential application in the aerospace field. However, ultra-high strength aluminum alloys usually contain coarse microstructures, micro-segregation, and casting defects that seriously deteriorate mechanical properties. Here, we report a high-strength aluminum alloy (Al-10.5Zn-2.0Mg-1.2Cu-0.12Zr-0.1Er) prepared by rapid solidification and hot extrusion to explore the microstructure modification of the alloy based on this strategy. The results show that: rapid-solidification technology can significantly refine alloy grains, alloy ribbons were composed of alpha (Al) equiaxed fine grains, and the average grain size was less than 6 mu m. After extrusion, the alloy had partially recrystallized, existing coarse second-phase (T-phase) and needle-shaped precipitates were MgZn2 (eta-phase), and the tensile strength and elongation of the extruded bar were 466.4 MPa and 12.9%, respectively. After T6 heat treatment, the tensile strength of the alloy reached 635.8 MPa, while elongation decreased to 10.5%. According to microstructure analysis and considering the contributions of grain boundary, dislocation, and precipitation-strengthening to the improvement of the mechanical properties, it was found that precipitation-strengthening is the main strengthening mechanism. Our research shows that rapid-solidification and hot-extrusion technology have great potential for improving the microstructures and mechanical properties of aluminum alloys.
Keyword :
extrusion extrusion rapid solidification rapid solidification microstructure microstructure Al-Zn-Mg-Cu alloy Al-Zn-Mg-Cu alloy mechanical property mechanical property
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GB/T 7714 | Shen, Gaoliang , Xiang, Zhilei , Ma, Xiaozhao et al. Investigation of Microstructures and Mechanical Properties of Ultra-High Strength Al-Zn-Mg-Cu Alloy Prepared by Rapid Solidification and Hot Extrusion [J]. | METALS , 2023 , 13 (2) . |
MLA | Shen, Gaoliang et al. "Investigation of Microstructures and Mechanical Properties of Ultra-High Strength Al-Zn-Mg-Cu Alloy Prepared by Rapid Solidification and Hot Extrusion" . | METALS 13 . 2 (2023) . |
APA | Shen, Gaoliang , Xiang, Zhilei , Ma, Xiaozhao , Huang, Jingcun , Zhao, Yueqing , Li, Jihao et al. Investigation of Microstructures and Mechanical Properties of Ultra-High Strength Al-Zn-Mg-Cu Alloy Prepared by Rapid Solidification and Hot Extrusion . | METALS , 2023 , 13 (2) . |
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Abstract :
Near-alpha titanium alloys are widely used in aeroengine blades due to their excellent specific strength and mechanical properties. The mechanical properties of near-a titanium alloys are closely related to the evolution of the microstructure and precipitates. In this paper, the microstructure and mechanical properties of a new type of multi-component near-a titanium alloy sheet after rolling, 700 ? aging, and 800 ? aging were studied. The results show that the strength of the alloy after aging at 700 ? increases from 1156 MPa to 1304 MPa, respectively, but decreases to 1246 MPa with the aging temperature increasing. The ductility of the alloy aged at 700 ? is lower than that of the rolled state, but the ductility increases slightly with the aging temperature increasing. The effect of aging heat treatment on the microstructure and precipitation behavior of alloy plates has been studied and compared with alloys before aging. After heat treatment, the content of primary a decreases from 25% to 5%, respectively. Two kinds of silicide precipitate at different positions, with the large-size spherical silicide being (Ti, Zr, Nb)(5)Si-3, and the small-size fusiform silicide being (Ti, Zr, Nb)(6)Si-3, respectively. Ti3Al was precipitated in the primary a phase, during the aging process. The silicides exhibit the strengthening effect on the alloy, but the effect weakens when the silicides grow up. The loss in ductility is mainly attributed to the precipitation of the a(2) phase after aging treatment. However, ductility is improved after applying higher aging temperatures as the size of the a(2) phase becomes smaller, and the distribution of them tends to become dispersed.
Keyword :
& alpha;(2) phase & alpha;(2) phase silicides silicides high-temperature titanium alloy high-temperature titanium alloy microstructure microstructure heat treatment heat treatment near-& alpha near-& alpha
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GB/T 7714 | Han, Jingyu , Xiang, Zhilei , Ma, Xiaozhao et al. Evolution on the Microstructure and Mechanical Properties of a New Multicomponent Near-Alpha Titanium Alloy after Rolling and Heat Treatments [J]. | METALS , 2023 , 13 (7) . |
MLA | Han, Jingyu et al. "Evolution on the Microstructure and Mechanical Properties of a New Multicomponent Near-Alpha Titanium Alloy after Rolling and Heat Treatments" . | METALS 13 . 7 (2023) . |
APA | Han, Jingyu , Xiang, Zhilei , Ma, Xiaozhao , Zhou, Zongyi , Huang, Jingcun , Li, Jihao et al. Evolution on the Microstructure and Mechanical Properties of a New Multicomponent Near-Alpha Titanium Alloy after Rolling and Heat Treatments . | METALS , 2023 , 13 (7) . |
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Abstract :
Nanocrystalline (NC) structure can lead to the considerable strengthening of metals and alloys. Obtaining appropriate comprehensive mechanical properties is always the goal of metallic materials. Here, a nanostructured Al-Zn-Mg-Cu-Zr-Sc alloy was successfully processed by high-pressure torsion (HPT) followed by natural aging. The microstructures and mechanical properties of the naturally aged HPT alloy were analyzed. The results show that the naturally aged HPT alloy primarily consists of nanoscale grains (similar to 98.8 nm), nano-sized precipitates (20-28 nm in size), and dislocations (1.16 x 10(15) m(-2)), and exhibits a high tensile strength of 851 & PLUSMN; 6 MPa and appropriate elongation of 6.8 & PLUSMN; 0.2%. In addition, the multiple strengthening modes that were activated and contributed to the yield strength of the alloy were evaluated according to grain refinement strengthening, precipitation strengthening, and dislocation strengthening, and it is shown that grain refinement strengthening and precipitation strengthening are the main strengthening mechanisms. The results of this study provide an effective pathway for achieving the optimal strength-ductility match of materials and guiding the subsequent annealing treatment.
Keyword :
high-pressure torsion high-pressure torsion Al-Zn-Mg-Cu-Zr-Sc alloy Al-Zn-Mg-Cu-Zr-Sc alloy mechanical properties mechanical properties microstructure microstructure natural aging natural aging
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GB/T 7714 | Shen, Gaoliang , Xiang, Zhilei , Ma, Xiaozhao et al. Microstructures and Mechanical Properties of a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy under Natural Aging [J]. | MATERIALS , 2023 , 16 (12) . |
MLA | Shen, Gaoliang et al. "Microstructures and Mechanical Properties of a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy under Natural Aging" . | MATERIALS 16 . 12 (2023) . |
APA | Shen, Gaoliang , Xiang, Zhilei , Ma, Xiaozhao , Huang, Jingcun , Li, Jihao , Wang, Bing et al. Microstructures and Mechanical Properties of a Nanostructured Al-Zn-Mg-Cu-Zr-Sc Alloy under Natural Aging . | MATERIALS , 2023 , 16 (12) . |
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Evolution laws of microstructures, mechanical properties, and fractographs after different solution temperatures were investigated through various analysis methods. With the increasing solution temperatures, contents of the primary alpha phase decreased, and contents of transformed beta structures increased. Lamellar alpha grains dominated the characteristics of transformed beta structures, and widths of secondary alpha lamellas increased monotonously. For as-forged alloy, large silicides with equiaxed and rod-like morphologies, and nano-scale silicides were found. Silicides with large sizes might be (Ti, Zr, Nb)(5)Si-3 and (Ti, Zr, Nb)(6)Si-3. Rod-like silicides with small sizes precipitated in retained beta phase, exhibiting near 45 degrees angles with alpha/beta boundaries. Retained beta phases in as-heat treated alloys were incontinuous. 980STA exhibited an excellent combination of room temperature (RT) and 650 degrees C mechanical properties. Characteristics of fracture surfaces largely depended on the evolutions of microstructures. Meanwhile, silicides promoted the formation of mico-voids.
Keyword :
solution temperatures solution temperatures microstructures microstructures mechanical properties mechanical properties fractographs fractographs silicides silicides
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GB/T 7714 | Ma, Xiaozhao , Xiang, Zhilei , Li, Tao et al. Evolution laws of microstructures and mechanical properties during heat treatments for near-alpha high-temperature titanium alloys [J]. | INTERNATIONAL JOURNAL OF MINERALS METALLURGY AND MATERIALS , 2022 , 29 (8) : 1596-1607 . |
MLA | Ma, Xiaozhao et al. "Evolution laws of microstructures and mechanical properties during heat treatments for near-alpha high-temperature titanium alloys" . | INTERNATIONAL JOURNAL OF MINERALS METALLURGY AND MATERIALS 29 . 8 (2022) : 1596-1607 . |
APA | Ma, Xiaozhao , Xiang, Zhilei , Li, Tao , Chen, Yilan , Liu, Yingying , Chen, Ziyong et al. Evolution laws of microstructures and mechanical properties during heat treatments for near-alpha high-temperature titanium alloys . | INTERNATIONAL JOURNAL OF MINERALS METALLURGY AND MATERIALS , 2022 , 29 (8) , 1596-1607 . |
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Abstract :
Ti-6.5Al-2.5Sn-9Zr-0.5Mo-0.25Si-1Nb-1W-0.1Er-xB (x = 0, 0.1, 0.2, 0.4, 0.6 and 0.8 wt%) with different boron contents are fabricated for investigation. Influences of boron element and its amounts on phase constitutions, microstructures, textures and compression mechanical properties are carefully studied. With the increasing boron additions, contents of TiB phase increase, and the maximum intensities of textures decrease. Microstructures are significantly and continuously refined after adding boron element and with the increasing boron additions, and turning point of refinement rates for different microstructural parameters is found at 0.2 wt% boron content. Strengths increase monotonously, while elongations increase firstly and decrease afterwards. The maximum value of elongation is acquired at boron content of 0.2 wt%. On the premise of ensuring plasticity, 0.2 wt% boron content is the most appropriate amount for microstructural refinement and mechanical properties enhancement for current near alpha titanium alloys. Meanwhile, aspect ratios of TiB whiskers increase with the increasing boron contents. Lots of near equiaxed alpha grains or alpha grains with irregular morphologies are discovered around TiB phase. Distorted and twisted alpha grain boundaries are also obviously detected in boron containing alloys. Moreover, premature fracture of alloys containing TiB whiskers is largely influenced by the fracture of these brittle reinforcements. (C) 2021 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
Keyword :
Fracture behaviors Fracture behaviors Near alpha titanium alloy Near alpha titanium alloy Boron element Boron element Textures Textures Microstructures Microstructures Mechanical properties Mechanical properties
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GB/T 7714 | Ma, Xiaozhao , Xiang, Zhilei , Tan, Chao et al. Influences of boron contents on microstructures and mechanical properties of as-casted near alpha titanium alloy [J]. | JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY , 2021 , 77 : 1-18 . |
MLA | Ma, Xiaozhao et al. "Influences of boron contents on microstructures and mechanical properties of as-casted near alpha titanium alloy" . | JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY 77 (2021) : 1-18 . |
APA | Ma, Xiaozhao , Xiang, Zhilei , Tan, Chao , Wang, Zhitian , Liu, Yingying , Chen, Ziyong et al. Influences of boron contents on microstructures and mechanical properties of as-casted near alpha titanium alloy . | JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY , 2021 , 77 , 1-18 . |
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