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Effect of nitrogen content on the microstructure and mechanical properties of titanium-bearing nonquenched and tempered steel after hot forging
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作者 YU Dajiang GAO Jiaqiang ZHAO Sixin 《Baosteel Technical Research》 CAS 2023年第2期1-6,共6页
The microstructure and mechanical properties of titanium(Ti)-bearing medium-carbon nonquenched and tempered steel with different nitrogen content before and after hot forging were investigated through smelting,forging... The microstructure and mechanical properties of titanium(Ti)-bearing medium-carbon nonquenched and tempered steel with different nitrogen content before and after hot forging were investigated through smelting,forging,and laboratory tests.The results show that the grain size of nonquenched and tempered steel was gradually refined,and the ferrite content gradually increased with an increase in nitrogen content.The grain size of the material with low nitrogen content increased abnormally,and its impact properties significantly decreased after hot forging.The grain size of nonquenched and tempered steel with higher nitrogen content was slightly larger than that before forging,and the tensile and yield strength increased,but the impact toughness was not significantly reduced.The Ti-bearing nonquenched and tempered steel showed better strength and toughness after hot forging with the addition of 0.010%0.015%nitrogen. 展开更多
关键词 nonquenched and tempered steel nitrogen content TITANIUM FORGING mechanical properties MICROSTRUCTURE
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Tempered分数阶微分方程Nagumo型唯一解
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作者 黄洪鸿 《理论数学》 2023年第11期3254-3261,共8页
本文重点讨论Tempered分数阶微分方程柯西问题Nagumo迭代近似值的唯一性和收敛性。首先把柯西问题转化成等价Volterra积分方程,证出解的唯一性。然后,运用迭代方法,我们将Nagumo型唯一性和迭代近似值序列扩展到Tempered分数阶微分方程。
关键词 tempered分数阶算子 Nagumo型唯一性 迭代法
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A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation
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作者 Wenhui Guan Xuenian Cao 《Communications on Applied Mathematics and Computation》 2021年第1期41-59,共19页
By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov te... By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative,the fractional central difference operator to discritize the space Riesz fractional partial derivative,and the classical central difference formula to discretize the advection term,a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion equation.The stability and the convergence analysis of the numerical method are given.Numerical experiments show that the numerical method is effective. 展开更多
关键词 Caputo tempered fractional advection-diffusion equation Fractional-compact Grünwald–Letnikov tempered Fractional central difference operator Stability Convergence
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Research into Grinding Hardening of Microalloyed Non-quenched and Tempered Steel 被引量:2
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作者 HAN Zheng-tong ZHANG Ning-ju +1 位作者 GAO Ding YANG Gang 《Journal of China University of Mining and Technology》 EI 2007年第2期238-241,共4页
Grinding hardening is a new technology of hardening steel piece surfaces with grinding heat generated in the grinding process instead of with a high or medium frequency induction heating method,which can effectively i... Grinding hardening is a new technology of hardening steel piece surfaces with grinding heat generated in the grinding process instead of with a high or medium frequency induction heating method,which can effectively integrate grinding and surface hardening. Experimental studies were carried out on grinding hardening of non-quenched and tempered steel. Through grinding experiments with variable depths of cut and feeding rate,the variation in the depth of the hardening layer was studied and the microstructure of the hardening zone of the test pieces was subsequently ana-lyzed. In the end,the hardening effect of non-quenched and tempered steel was compared with that of 40Cr steel,which revealed the superiority of non-quenched and tempered steel in grinding hardening technology. 展开更多
关键词 non-quenched and tempered steel 40Cr steel GRINDING surface hardening
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TEMPERED BAINITE EMBRITTLEMENT IN SOME STRUCTURAL STEELS 被引量:1
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作者 HU Guangli LIU Zhengtang WANG Ping HUA Wenjun KANG Mokuang Northwestern Polytechnical University,Xi’an,China HU Guangli,Associate Professor,Department of Materials Science and Engineering,Northwestern Polytechnical University,Xi’an,China 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 1989年第5期337-342,共6页
The variations of microstructures and mechanical properties of steels 15CrMnMoV, 18Mn2CrMoB,18Cr2Ni4W,30CrMnSi,30CrMnSiNi2 and 40CrMnSiMoV,which were tempered at different temperatures after austempering and continuou... The variations of microstructures and mechanical properties of steels 15CrMnMoV, 18Mn2CrMoB,18Cr2Ni4W,30CrMnSi,30CrMnSiNi2 and 40CrMnSiMoV,which were tempered at different temperatures after austempering and continuous cooling at given rates, have been investigated.Based on the experimental results,the behaviour and mechanism of tempered bainite embrittlement(TBE)have been discussed.Finally,the theoretical and prac- tical basis for selecting the optimum tempering temperature of steels with bainite structure af- ter heat treatment are proposed. 展开更多
关键词 AUSTEMPERING tempered bainite embrittlememt mechanical stability
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Tempered分数阶微分方程解的全局存在性和稳定性
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作者 张玉瑶 钟文勇 《吉首大学学报(自然科学版)》 CAS 2020年第2期5-8,22,共5页
首先建立了关于tempered分数阶导数的比较原理和不等式,然后利用凸Lyapunov函数建立了含Caputo型tempered分数阶导数的微分方程初值问题解的全局存在性和稳定性的判断准则.
关键词 Caputo型分数阶微分方程 tempered分数阶微分方程 全局存在性 稳定性 凸Lyapunov函数
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Effect of cooling rate on microstructure and mechanical properties of CB2 tempered martensitic steel
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作者 Yu-lin Ma Yue Liu +2 位作者 Li-ping Zhang Xu Jiang Chun-ming Liu 《China Foundry》 SCIE 2020年第2期158-166,共9页
The cooling rate of casting has a significant effect on microstructure and mechanical properties of castings.The 9Cr-1.5Mo-1Co cast steel,referred to as CB2,is one of the most promising alloys for various cast compone... The cooling rate of casting has a significant effect on microstructure and mechanical properties of castings.The 9Cr-1.5Mo-1Co cast steel,referred to as CB2,is one of the most promising alloys for various cast components to be used under ultrasupercritical conditions.In this study,HRTEM,SEM,and XRD methods were used for qualitative and quantitative analyses of contents,phases,and sizes of the inclusions and precipitates,as well as microstructure observation of the tempered martensitic steel at different cooling rates.Traditional tensile tests were conducted to characterize the material mechanical properties.Results show that the size of the boron nitride and precipitate,the width of the martensite lath and the content of theδ-ferrite are reduced as the cooling rate increases from 5-8℃·min^-1(CB2-S steel)to 50-60℃·min^-1(CB2-F steel).The precipitates are mainly composed of M23C6 and a small amount of M3C.The average diameters of the M23C6 precipitates in CB2-F and CB2-S are 202 nm and 209 nm,respectively.The inclusions are mainly composed of BN,Al2O3 and MnO2,and the inclusion ratios are 0.1969%for the CB2-F and 0.06556%for CB2-S steel.The average martensite lath widths of CB2-F and CB2-S steels are 289 nm and 301 nm,respectively.Furthermore,the M3C having a diameter of about 150 nm and a thickness of 20 nm is observed in theδ-ferrite of the tempered CB2-S steel.The presence of theδ-ferrite reduces the precipitation strengthening and dislocation density in CB2-S steel.In addition,the lower cooling rate stabilizes theδ-ferrite structure at room temperature. 展开更多
关键词 tempered martensitic STEEL CASTING microstructure M23C6 mechanical properties INCLUSIONS Δ-FERRITE
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Effect of Rare Earths on Tempered Martensite Embrittlement of Steel
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作者 高国忠 贺维勇 +1 位作者 高炬 陈继志 《Journal of Rare Earths》 SCIE EI CAS CSCD 1998年第1期42-46,共5页
The mechanical properties of SiMnCr and SiMnMo steels tempered in lowtemperature range were studied. The results show that there is no notable effect of RE on material strength during lowtemperature tempering. There a... The mechanical properties of SiMnCr and SiMnMo steels tempered in lowtemperature range were studied. The results show that there is no notable effect of RE on material strength during lowtemperature tempering. There are toughness troughs of tempered martensite embrittlement(TME) at 350 ℃ and 400 ℃ for steel SiMnCr and SiMnMo respectively. RE raises the toughness of TME troughs to some extent by refining grains and restraining embrittlment of austenite grain boundary, although it does not change TME temperature. 展开更多
关键词 Rare earths STEEL tempered martensite embrittlement
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Rotating arc horizontal narrow gap welding of high strength quenched and tempered steel
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作者 郭宁 杨春利 +3 位作者 韩焱飞 贾传宝 杜永鹏 张琳琳 《China Welding》 EI CAS 2010年第4期31-35,共5页
Rotating arc borizontal narrow gap welding of quenched & tempered (Q&T) steel was innovatively performed for solving the bottleneck that the molten pool sagged due to the gravity. The shapely multilayer single pas... Rotating arc borizontal narrow gap welding of quenched & tempered (Q&T) steel was innovatively performed for solving the bottleneck that the molten pool sagged due to the gravity. The shapely multilayer single pass horizontal joint could be obtairzed by using the rotating are welding process. The cold crack was not observed in the joint without controlling the heat input and selecting the consumables intentionally. Microstructure of the joint could be divided into three zones: base metal zone (BMZ) , heat-affected zone ( HAZ) and weld zone (WZ). Because of the characteristic of the rotating arc horizontal welding process, the defects in the joints were slag inclztsion formed at the interlayer of lower side wall. Tbe tensile strength and hardness of HAZ and WZ were larger than those of BMZ. The impact toughness in WZ, HAZ and BM at 0 % is equal to 11.5, 212 and 236 J, respectively. 展开更多
关键词 horizontal welding rotating arc quenched and tempered steel narrow gap welding
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Development of non-quenched and tempered bolt steel
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作者 BAI Xifeng~(1)),ZHAO Xuebo~(1)),REN Yuhui~(1)),WANG Bingxi~(2)) and GUO Dayong~(2)) 1) Wire rod plant,Anshan Iron & Steel Co.,Ltd. 2) Technology Center,Anshan Iron & Steel Co.,Ltd.,Anshan 114021,China 《Baosteel Technical Research》 CAS 2010年第S1期62-,共1页
The 8.8 grade non-quenched and tempered bolt steel was studied according to the process conditions of wire rod plant and customer requirments.Three types of experimental steel grades were selected.10MnSiTi Nb and 20Mn... The 8.8 grade non-quenched and tempered bolt steel was studied according to the process conditions of wire rod plant and customer requirments.Three types of experimental steel grades were selected.10MnSiTi Nb and 20Mn2VTi(N) were chosen as the formal steel after several experimemts. 展开更多
关键词 non-quenched and tempered steel BOLT mechanical property
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A Finite-Difference Approximation for the Oneand Two-Dimensional Tempered Fractional Laplacian
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作者 Yaoqiang Yan Weihua Deng Daxin Nie 《Communications on Applied Mathematics and Computation》 2020年第1期129-145,共17页
This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.T... This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s). 展开更多
关键词 tempered fractional Laplacian Finite-diff erence scheme Linear and quadratic interpolations Bilinear and biquadratic interpolations Convergence rates
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Laser Beam Welding of 600 MPa Quenched and Tempered High-Strength Steel
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作者 Pritchard Elmon Marozva Bruno Roberts Mose +1 位作者 Abdel-Monem El-Batahgy Thomas Ochuku Mbuya 《World Journal of Engineering and Technology》 2022年第2期241-253,共13页
Conventional fusion arc welding of high-strength quenched and tempered steel can be improved through the use of non-conventional laser beam welding. This article presents the investigations of autogenous bead on plate... Conventional fusion arc welding of high-strength quenched and tempered steel can be improved through the use of non-conventional laser beam welding. This article presents the investigations of autogenous bead on plate and butt CO<sub>2</sub> Laser Welding (LW) of 7 mm thick high-strength quenched and tempered low alloy SM570 (JIS) steel plates. The influence of laser welding parameters, mainly welding speed, defocusing distance and shielding gas flow rate on the weld profile, i.e., weld zone penetration depth and width, microstructure and mechanical properties of welded joints was determined. All welded joints showed smooth and uniform weld beads free from superficial porosity and undercuts. The selected best welding conditions were a laser power of 5.0 kW, welding speed of 500 mm/min, argon gas shielding flow rate of 30 L/min and a defocusing distance of -0.5 mm. It was observed that these conditions gave complete penetration and minimized the width of the weld bead. The microstructure of the welded joints was evaluated by light optical microscopy. The weld metal (WM) and heat-affected zone (HAZ) near weld metal achieved maximum hardness (355 HV). The tensile fractured samples showed the ductile mode of failure and ultimate tensile strength of 580 MPa. 展开更多
关键词 Laser Welding High-Strength Steel Quenched and tempered Bead on Plate Joint Butt Joint Heat-Affected Zone (HAZ) CO2 Autogenous Laser Welding Mechanical Properties
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Corrosion behavior of tempered dual-phase steel embedded in concrete 被引量:2
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作者 Oguzhan Kelestemur Mustafa Aksoy Servet Ylldlz 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2009年第1期43-50,共8页
Dual-phase (DP) steels with different martensite contents were obtained by appropriate heat treatment of an SAE1010 structural carbon steel, which was cheap and widely used in the construction industry. The corrosio... Dual-phase (DP) steels with different martensite contents were obtained by appropriate heat treatment of an SAE1010 structural carbon steel, which was cheap and widely used in the construction industry. The corrosion behavior of DP steels in concrete was investigated under various tempering conditions. Intercritical annealing heat treatment was applied to the reinforcing steel to obtain DP steels with different contents of martensite. These DP steels were tempered at 200, 300, and 400℃ for 45 min and then cooled to room temperature. Corrosion experiments were conducted in two stages. In the first stage, the corrosion potential of DP steels embedded in concrete was measured every day for a period of 30 d based on the ASTM C 876 standard. In the second stage, the anodic and cathodic polarization values of these steels were obtained and subsequently the corrosion currents were determined with the aid of cathodic polarization curves. It was observed that the amount of second phase had a definite effect on the corrosion behavior of the DP steel embedded in concrete. As a result of this study, it is found that the corrosion rate of the DP steel increases with an increase in the amount of martensite. 展开更多
关键词 dual-phase steel CORROSION tempering treatment MARTENSITE CONCRETE
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Prediction of Mechanical Properties of 50CrVA Tempered Steel Strip for Horn Diaphragm Based on BPANN
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作者 江树勇 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2009年第5期791-795,共5页
50CrVA cold-rolled spring steel strip was used to fabricate the diaphragm of the automotive horn. The material parameters which were taken into account in the design of the dia-phragm involve elongation, elastic limit... 50CrVA cold-rolled spring steel strip was used to fabricate the diaphragm of the automotive horn. The material parameters which were taken into account in the design of the dia-phragm involve elongation, elastic limit, Young's modulus, yield strength and tensile strength. The tempering process was carried out in order to enable the diaphragm to possess the excellent mechanical properties, such as high elastic limit, high fatigue strength and perfect stress relaxation resistance. As a nonlinear information processing system, the backpropagation artificial neural network (BPANN) was applied to predict and simulate the relationship between the mechanical properties of the diaphragm and the tempering process parameters. Experimental results show that a BPANN with 3-8-5 architec-ture is capable of predicting the relationship between the mechanical properties of the diaphragm and the tempering temperature successfully and lays the profound foundations for optimizing the design of the diaphragm. BPANN simulation results show that the tempering temperature ranging from 380 to 420 ℃ contributes to enhancing the comprehensive mechanical properties of the diaphragm including high Young's modulus, high elastic limit and high fatigue strength. 展开更多
关键词 artificial neural networks mechanical properties TEMPERING DIAPHRAGM 50CrVA
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On microstructure and performance of tempered high-boron high-speed steel roll
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作者 Fu Hanguang Du Zhongze +6 位作者 Li Ping Jiang Yehua Zhou Rong Cen Qihong Hou Jianqiang Lei Yongping Guo Hongxing 《China Foundry》 SCIE CAS 2012年第3期252-257,共6页
Influences of the tempering temperature on the microstructure, mechanical property and wear resistance of High-Boron High Speed Steel (HBHSS) roll materials were investigated by means of optical microscopy, scanning... Influences of the tempering temperature on the microstructure, mechanical property and wear resistance of High-Boron High Speed Steel (HBHSS) roll materials were investigated by means of optical microscopy, scanning electron microscopy (SEM), X-ray diffraction, hardness measurement, impact tester, tensile tester and pin abrasion tester. The results show that the as-cast structure of HBHSS consists of a great amount of martensite and M2(B,C) and a few retained austenites and M23(B,C)6. After solution treated at 1,050℃ and followed by oil cooling, the amount of M23(B,C)6 carbo-borides in quenched HBHSS increases obviously and the macrohardness of the quenched HBHSS is 66 HRC, which is very close to the 65.8 HRC of as-cast HBHSS. On the whole, the hardness of HBHSS alloy shows a trend of slight decrease with increasing tempering temperature when tempered below 500 ℃. While when above 500 ℃, the hardness increases slightly as the tempering temperature increases and reaches a peak at 525 ℃ and then decreases obviously. The impact toughness of HBHSS has a tendency to increase as the tempering temperature increases. Tempering can improve the tensile strength and elongation of HBHSS, but a higher tempering temperature causes a slight decrease in both tensile strength and elongation. Excellent wear resistance can be obtained by tempering at 500 to 550 ℃. 展开更多
关键词 high boron high speed steel tempering temperature carbo-boride metallic matrix mechanical properly wear resistance
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Effect of induction heating and tempering on properties and microstructures of quenched and tempered pipes
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作者 SUN Wen WU Cunyou +2 位作者 LIU Yaoheng MA Yannan ZHANG Zhonghua 《Baosteel Technical Research》 CAS 2020年第2期8-14,共7页
In this study,a C-Mn quenched steel tube was quickly tempered by induction heating,and the influence of the tempering temperature on its performance was studied and compared with that by traditional tempering. The res... In this study,a C-Mn quenched steel tube was quickly tempered by induction heating,and the influence of the tempering temperature on its performance was studied and compared with that by traditional tempering. The results show that the yield strength of both is quite strong with regular changes in the tempering temperature,but that the tensile strength of the tube tempered by induction heating is higher than that tempered by traditional tempering by about 25 MPa,and the elongation after induction tempering is significantly higher than that after traditional tempering. The differences in the microstructures of tubes after induction and traditional tempering were compared by metallographic microscope,scanning electron microscopy,and transmission electron microscopy.Theoretical analysis was also performed. Compared with traditional tempering,a fine dispersion of precipitated carbides occurs after induction tempering,which is the main reason for the performance differences. 展开更多
关键词 induction heating TEMPERING quenched steel tube property and microstructure
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Review on regulation of MnS in non-qquenched and tempered steel 被引量:1
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作者 Guo-xing Qiu Qing Du +3 位作者 Feng Lu De-jun Miao Yong-kun Yang Xiao-ming Li 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2024年第4期779-789,共11页
An overview of the current research status and control methods of MnS in non-quenched and tempered steel was provided.As a low-melting plastic inclusion,the morphology and distribution of MnS were influenced by variou... An overview of the current research status and control methods of MnS in non-quenched and tempered steel was provided.As a low-melting plastic inclusion,the morphology and distribution of MnS were influenced by various production processes.Therefore,control of MnS is a systematic problem that must be integrated into the entire production process.Based on the production process,the factors affecting the morphology and distribution of MnS in steel were introduced.The effects of oxygen activity,manganese,sulfur,and some alloys on MnS inclusion precipitation were summarized,mainly including MnS modification treatment and oxygen-sulfide composite precipitation control.It is believed that MnS precipitates during the solidification process of steel,and controlling the solidification cooling rate could effectively regulate the size and morphology of MnS,avoiding the precipitation of II-MnS.Additionally,by changing the deformation rate,deformation amount,deformation temperature during the hot deformation process,and heating time and temperature during heat treatment,the distribution and morphology of MnS could be improved.Through the fine control of the above process parameters,the number of II-MnS in steel could be effectively reduced,and their morphology could be improved,thereby enhancing the performance of non-quenched and tempered steel and promoting its wider application.Furthermore,applying laboratory research results to industrial production is an important direction for future research efforts in this field. 展开更多
关键词 MNS Non-quenched and tempered steel Control technology Process parameter MORPHOLOGY DISTRIBUTION
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Carbide-free tempered martensite in Fe-C steels
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作者 Zhiping Xiong Dezhen Yang +1 位作者 Hao Zhang Xingwang Cheng 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2024年第12期22-25,共4页
1.Introduction Quenched Fe-C martensite is very strong but brittle due to su-persaturated carbon atoms located at octahedron sites[1].In order to improve the ductility,tempering is necessary.With increasing tempering ... 1.Introduction Quenched Fe-C martensite is very strong but brittle due to su-persaturated carbon atoms located at octahedron sites[1].In order to improve the ductility,tempering is necessary.With increasing tempering temperature,the saturated carbon can be sequentially arranged as clusters,segregation into defects like dislocations and interfaces,transition carbides,and cementite[2].As a result,the strength is reduced and the ductility is improved predominantly due to the decreased amount of solid solution carbon[3]. 展开更多
关键词 MARTENSITE DUCTILITY TEMPERING
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Morphological transformation of elongated MnS inclusions in non-quenched and tempered steel during isothermal heating 被引量:1
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作者 Jun-yu Liu Cheng-song Liu +4 位作者 Rui-juan Bai Wei Wang Qing-bo Wang Hua Zhang Hong-wei Ni 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2023年第3期525-536,共12页
Elongated MnS inclusions in rolled non-quenched and tempered steel tend to cause the mechanical anisotropy of steel,deteriorate the mechanical properties and degrade the quality and service life of the steel products.... Elongated MnS inclusions in rolled non-quenched and tempered steel tend to cause the mechanical anisotropy of steel,deteriorate the mechanical properties and degrade the quality and service life of the steel products.To reveal the mechanisms of morphological transformation of strip-shaped MnS inclusions during isothermal heating,the effects of heat treatment time and temperature on the morphology,number density and size distribution of elongated MnS inclusions were systematically studied and discussed.A diffusion couple experiment was also conducted to clarify the diffusion mode of MnS inclusions.The experimental results showed that with the increase in isothermal heating time(from 0 to 10 h at 1473 K)and temperature(from 1173 to 1573 K for 3.0 h),the number density and average aspect ratio of MnS inclusions generally showed an increase and decrease trend,respectively,while the area fraction remained stable and only slightly fluctuated around 0.4%.In the diffusion couple,after the isothermal heating at 1473 K for 3.0 h,the elements Mn and S in the steel near the steel-MnS interface were very stable without any concentration gradient.The morphology change sequence of the elongated MnS inclusions in the rolled non-quenched and tempered steel during the isothermal heating was strip→cylinderization→spindle→spheroidization.Relationship between the diameter of MnS inclusion and the spacing between two MnS inclusions after splitting,and the fitting goodness of different n values under different experimental time and temperature confirmed that the driving force for the transformation of MnS inclusions during the isothermal heating was surface diffusion,instead of volume diffusion. 展开更多
关键词 Non-quenched and tempered steel MnS inclusion Isothermal heating Surface diffusion Morphological transformation
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Novel technique to investigate the convergence analysis of the tempered fractional natural transform method applied to diffusion equations
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作者 Nazek A.Obeidat Daniel E.Bentil 《Journal of Ocean Engineering and Science》 SCIE 2023年第6期636-646,共11页
In this research work,we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms(TFNT)and give error estimates.This efficient method is applied to mod... In this research work,we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms(TFNT)and give error estimates.This efficient method is applied to models,such as the time-space tempered fractional convection-diffusion equation(FCDE)and tempered fractional Black-Scholes equation(FBSE).We obtain exact solutions for these models using our methodology,which is very important for knowing the wave behavior in ocean engineering models and for the studies related to marine science and engineering.Finding exact solutions to tempered fractional differential equations(TFDEs)is far from trivial.Therefore,the proposed method is an excellent addition to the myriad of techniques for solving TFDE problems. 展开更多
关键词 tempered fractional calculus Diffusion equation Caputo derivative Riemann-Liouville derivative Integral transforms
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