High-strain-rate superplasticity in an AZ91 magnesium alloy processed byingot metallurgy rout

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附着强度 英语

附着强度 英语

附着强度英语Adhesive StrengthThe concept of adhesive strength is a fundamental aspect of material science and engineering, with far-reaching implications in various industries. Adhesives are materials that facilitate the bonding of two or more surfaces, creating a strong and durable connection. The strength of this bond, known as adhesive strength, is a critical factor in determining the overall performance and reliability of the joined components.Adhesive strength is influenced by a multitude of factors, including the chemical composition of the adhesive, the surface properties of the materials being bonded, the environmental conditions, and the applied stresses. Understanding and optimizing these factors is crucial for ensuring the integrity and longevity of adhesive-based assemblies.One of the primary determinants of adhesive strength is the chemical composition of the adhesive itself. Adhesives can be classified into various categories, such as epoxies, acrylics, silicones, and polyurethanes, each with its own unique properties andperformance characteristics. The choice of adhesive depends on the specific application, the materials being bonded, and the desired level of strength and durability.Epoxy adhesives, for instance, are known for their exceptional strength and resistance to environmental factors, making them a popular choice for applications in the aerospace, automotive, and construction industries. These adhesives form a strong covalent bond with the substrate, resulting in a high-strength connection that can withstand significant stresses and loads.Acrylic adhesives, on the other hand, offer a more versatile and flexible bonding solution. They are commonly used in the electronics and consumer goods industries, where the ability to bond a wide range of materials, including plastics and metals, is essential. Acrylic adhesives typically exhibit good impact resistance and can accommodate slight movements or deformations in the bonded components.Silicone adhesives, in contrast, are prized for their excellent resistance to high temperatures, weathering, and chemical exposure. They are often employed in applications where these environmental factors are a concern, such as in the automotive, aerospace, and construction industries. Silicone adhesives can form strong bonds with a variety of substrates, including glass, metal, and plastic.Polyurethane adhesives, meanwhile, are known for their superior flexibility and impact resistance. They are commonly used in the construction and transportation industries, where the ability to accommodate movement and vibration is crucial. Polyurethane adhesives can form strong bonds with a wide range of materials, including wood, concrete, and various plastics.The surface properties of the materials being bonded also play a significant role in determining the adhesive strength. The surface roughness, wettability, and chemical composition of the substrates can influence the adhesive's ability to form a strong and durable bond. Surface preparation techniques, such as cleaning, etching, or priming, can be employed to enhance the adhesion properties of the materials, thereby improving the overall adhesive strength.Environmental factors, such as temperature, humidity, and exposure to chemicals or UV radiation, can also have a significant impact on the adhesive strength. Adhesives may experience degradation or weakening over time due to these environmental stresses, leading to a reduction in the overall bond strength. Understanding and mitigating these environmental factors is essential for ensuring the long-term performance and reliability of adhesive-based assemblies.The applied stresses on the bonded assembly are another criticalfactor in determining the adhesive strength. Adhesives can experience various types of stresses, including tensile, shear, peel, and cleavage stresses, each of which can have a different effect on the bond strength. Designing the bonded assembly to minimize the impact of these stresses, through the use of appropriate joint geometries and load-bearing configurations, can help maximize the adhesive strength and ensure the overall integrity of the assembly.In addition to these fundamental factors, advances in adhesive technology have led to the development of specialized adhesives that can further enhance the adhesive strength. For example, structural adhesives, which are designed to withstand high loads and stresses, are commonly used in the aerospace and automotive industries. These adhesives can provide superior strength and durability, often outperforming traditional mechanical fasteners in certain applications.Another example of advanced adhesive technology is the use of nanoparticle-reinforced adhesives. These adhesives incorporate nanoscale reinforcements, such as carbon nanotubes or graphene, which can significantly improve the adhesive strength, toughness, and thermal stability of the bond. The incorporation of these nanomaterials can lead to enhanced interfacial interactions between the adhesive and the substrate, resulting in a stronger and more resilient bond.In conclusion, adhesive strength is a critical factor in the design and performance of a wide range of products and structures. Understanding the factors that influence adhesive strength, such as the chemical composition of the adhesive, the surface properties of the materials being bonded, environmental conditions, and applied stresses, is essential for ensuring the reliability and durability of adhesive-based assemblies. Advances in adhesive technology, including the development of specialized structural adhesives and nanoparticle-reinforced adhesives, have further expanded the capabilities and applications of adhesive bonding in various industries.。

超声微锻造辅助定向能量沉积316L_不锈钢微观组织与力学性能研究

超声微锻造辅助定向能量沉积316L_不锈钢微观组织与力学性能研究

第15卷第7期孟宝,等:镁锂合金微型热管电场辅助超塑挤压成形19and Superplastic Forming of Negative Angle Box-ShapedParts[D]. Harbin: Harbin Institute of Technology, 2017:3-14.[5] 李淼泉, 吴诗. LY12CZ铝合金在强电场中的超塑性变形[J]. 塑性工程学报, 1996, 3(3): 41-46.LI Miao-quan, WU Shi. Superlastic Deformation of LY12CZ Aluminum Alloy under an Electric Field[J].Journal of Plasticity Engineering, 1996, 3(3): 41-46. [6] 蔡春波, 高少伟, 高桂丽, 等. 脉冲电流对Al-Cu-Mn-Zr合金时效处理组织及性能的影响[J]. 金属热处理,2023, 48(4): 104-110.CAI Chun-bo, GAO Shao-wei, GAO Gui-li, et al. Effectof Pulse Current on Microstructure and Properties of Al-Cu-Mn-Zr Alloy after Aging Treatment[J]. Heat Treatment of Metals, 2023, 48(4): 104-110.[7] WANG Yao-li, WANG Guang-xin, ZHANG Ke-ke. Elec-tro-Superplastic Solid State Welding of 40Cr/QCr0.5[J].Materials, 2018, 11(7): 1153.[8] WANG Guo-feng, LI Xiao, LIU Si-yu, et al. ImprovedSuperplasticity and Microstructural Evolution of Ti2AlNbAlloy Sheet during Electrically Assisted Superplastic GasBulging[J]. The International Journal of Advanced Manufacturing Technology, 2018, 99(1): 773-787.[9] YOSHIDA H, SASAKI Y. Low Temperature and HighStrain Rate Superplastic Flow in Structural Ceramics In-duced by Strong Electric-Field[J]. Scripta Materialia, 2018, 146: 173-177.[10] 林赟, 唐国翌, 孙强, 等. Inconel690合金的电致塑性拉拔研究[J]. 热加工工艺, 2010, 39(24): 80-82.LIN Yun, TANG Guo-yi, SUN Qiang, et al. Investigationof Electro-Plastic Drawing on Inconel690 Alloy[J]. HotWorking Technology, 2010, 39(24): 80-82.[11] 刘建龙, 王效岗, 王皓悦. 微挤压模具设计[J]. 模具技术, 2016(5): 26-29.LIU Jian-long, WANG Xiao-gang, WANG Hao-yue. TheDesign of Micro Extrusion Die[J]. Die and Mould Tech-nology, 2016(5): 26-29.[12] 李细锋, 曹旭东, 王斌, 等. 钛合金电辅助塑性成形技术研究进展[J]. 航空制造技术, 2021, 64(17): 22-30.LI Xi-feng, CAO Xu-dong, WANG Bin, et al. ResearchProgress on Electrically-Assisted Plastic Forming Techn-ology of Titanium Alloy[J]. Aeronautical ManufacturingTechnology, 2021, 64(17): 22-30.[13] 蔡贇, 孙朝阳, 万李, 等. AZ80镁合金动态再结晶软化行为研究[J]. 金属学报, 2016, 52(9): 1123-1132.CAI Yun, SUN Zhao-yang, WAN Li, et al. Study on Dy-namic Recrystallization Softening Behavior of AZ80 Magnesium Alloy[J]. Acta Metallurgica Sinica, 2016, 52(9): 1123-1132.[14] ZHANG Cun-sheng, WANG Cui-xue, ZHANG Qing-you,et al. Influence of Extrusion Parameters on Microstruc-ture, Texture, and Second-Phase Particles in an Al-Mg-SiAlloy[J]. Journal of Materials Processing Technology, 2019, 270: 323-334. [15] XU Jie, ZHU Xiao-cheng, SHAN De-bin, et al. Effect ofGrain Size and Specimen Dimensions on Micro-Formingof High Purity Aluminum[J]. Materials Science and En-gineering: A, 2015, 646: 207-217.[16] CHEN Liang, ZHAO Guo-qun, YU Jun-quan, et al.Analysis and Porthole Die Design for a Multi-Hole Ex-trusion Process of a Hollow, Thin-Walled Aluminum Pro-file[J]. The International Journal of Advanced Manufac-turing Technology, 2014, 74(1): 383-392.[17] DEMIRCI H İ, EVLEN H. Effect of Extrusion Ratio onthe Wear Behaviour of Al-Si and Al-Mg Alloys[J]. Jour-nal of Alloys and Compounds, 2012, 510(1): 26-32. [18] GUAN Yan-jin, ZHANG Cun-sheng, ZHAO Guo-qun, etal. Design of a Multihole Porthole Die for AluminumTube Extrusion[J]. Materials and Manufacturing Proc-esses, 2012, 27(2): 147-153.[19] YU Zi-jian, XU Chao, MENG Jian, et al. Effects of Ex-trusion Ratio and Temperature on the Mechanical Proper-ties and Microstructure of As-Extruded Mg-Gd- Y-(Nd/Zn)-Zr Alloys[J]. Materials Science and Engineer-ing: A, 2019, 762: 138080.[20] 尹传龙, 齐凯华, 翟军, 等. 难以挤压成型的铝型材断面形状的局部优化[J]. 铝加工, 2022(5): 25-28.YIN Chuan-long, QI Kai-hua, ZHAI Jun, et al. AluminumProfile does not Apply to Local Optimization of Extru-sion[J]. Aluminium Fabrication, 2022(5): 25-28.[21] 王少华, 刘惠, 陈宗强, 等. 大型带筋薄壁圆管铝型材挤压成形数值模拟[J]. 锻压技术, 2022, 47(4): 181-189.WANG Shao-hua, LIU Hui, CHEN Zong-qiang, et al.Numerical Simulation on Extrusion Forming for LargeRibbed Thin-Walled Circular Tube Aluminum Profile[J].Forging & Stamping Technology, 2022, 47(4): 181-189. [22] PARK S Y, KIM W J. Difference in the Hot CompressiveBehavior and Processing Maps between the As-Cast andHomogenized Al-Zn-Mg-Cu (7075) Alloys[J]. Journal ofMaterials Science & Technology, 2016, 32(7): 660-670. [23] LIN Y C, XIA Yu-chi, CHEN Xiao-min, et al. Constitu-tive Descriptions for Hot Compressed 2124-T851 Aluminum Alloy over a Wide Range of Temperature andStrain Rate[J]. Computational Materials Science, 2010,50(1): 227-233.[24] LIU Yong-da, XU Jie, ZHANG Zheng-wu, et al. Mi-cro-Extrusion Process and Microstructure Evolution ofMiniature Heat Pipe in 6063 Aluminum Alloy[J]. The In-ternational Journal of Advanced Manufacturing Technol-ogy, 2022, 120(9/10): 6463-6480.[25] SELLARS C M, MCTEGART W J. On the Mechanism ofHot Deformation[J]. Acta Metallurgica, 1966, 14(9): 1136-1138.[26] DONATI L, TOMESANI L. The Effect of Die Design onthe Production and Seam Weld Quality of Extruded Alu-minum Profiles[J]. Journal of Materials Processing Technology, 2005, 164/165: 1025-1031.责任编辑:蒋红晨精 密 成 形 工 程第15卷 第7期20 JOURNAL OF NETSHAPE FORMING ENGINEERING2023年7月收稿日期:2023–05–29 Received :2023-05-29基金项目:山东省重点研发项目(2021CXGC010206)Fund :Key R&D Project of Shandong Province(2021CXGC010206) 作者简介:王硕(1997—),男,硕士生,主要研究方向为超声微锻造辅助增材制造。

变形对LF2铝合金高温流变应力的影响

变形对LF2铝合金高温流变应力的影响

作用增强, 使金属原子热震动的振幅增大, 即原子
间的动能增大, 原子间的临界切应力减弱, 滑移阻
力减小, 新的滑移不断产生, 同时增加了非晶扩散
机理及晶间粘性流动, 使变形阻力降低; ②动态回 复及动态再结晶引起的软化程度也随温度的升高
而增大, 从而减轻或消除由于塑性变形所产生的
加工硬化, 使塑性变形阻力降低, 从而导致合金的 应 力 水 平 降 低[3-5]。
2.2 应变速率对流变应力的影响 由图 2 可看出, 在同一变形温度下, 材料的流
变应力随应变速率的提高而增大。这是因为, 随应
变速率的提高, 单位时间内的应变增加, 位错产 生、运动的数目增大, 位错运动的速度也增大, 加 工硬化的作用更加明显, 从而导致合金变形的临 界 切 应 力 增 大 , 即 流 变 应 力 增 大 , 说 明 LF2 铝 合 金是正应变速率敏感性材料。
Key wor ds: flow stress; strain rate; deformation temperature
在 一 定 的 变 形 温 度 、变 形 程 度 和 变 形 速 度 条 件下的屈服极限, 称为金属的塑性变形阻力或真 应力。金属塑性变形阻力的大小取决于金属的化 学 成 分 、金 属 的 组 织 、变 形 温 度 、 变 形 速 度 、变 形 程度以及与这些有关的各个过程, 如加工硬化、 再 结 晶 、动 态 回 复 等 。 而 变 形 温 度 、变 形 速 度 、变 形程度这三个因素构成金属塑性变形时的热力学 条件 。 [1-2] 以往的研究大多是关于高温等温压缩试 验, 得出材料的真应力- 真应变的关系[3-6], 本文主要 针对前两个条件对 LF2 铝合金进行高温等温拉伸 试验研究, 确定材料的应力应变, 分析应变速率与 变形温度对材料热变形流变应力的影响规律。

激发光强度 英文

激发光强度 英文

激发光强度英文The excitation of light intensity can be achieved through various methods, such as using a high-powered laser or a strong light source. This can cause the atoms of a material to become excited and emit light at a higher intensity. Another way to increase light intensity is by using optical amplifiers, which can boost the strength of the light signal.In addition, the use of reflective materials or surfaces can help to enhance the intensity of light by reflecting and concentrating the light in a specific direction. This can be particularly useful in applications where a high level of light intensity is required, such as in scientific research or industrial processes.Furthermore, the design of optical systems can also play a crucial role in maximizing light intensity. By carefully engineering the components of an optical system, such as lenses, mirrors, and filters, it is possible to optimize the transmission and concentration of light, leading to a higher intensity of light output.Moreover, advancements in technology have led to the development of specialized light sources, such as LEDs and lasers, which are capable of emitting light at extremely high intensities. These light sources can be used in a wide range of applications, including medical imaging, telecommunications, and industrial manufacturing.In conclusion, there are various methods andtechnologies available to increase the intensity of light. By utilizing high-powered light sources, optical amplifiers, reflective materials, and advanced optical system designs,it is possible to achieve a higher level of light intensity for a wide range of applications.激发光强度可以通过多种方法实现,例如使用高功率激光或强光源。

多向锻造法细化镁合金晶粒的研究现状

多向锻造法细化镁合金晶粒的研究现状

多向锻造法细化镁合金晶粒的研究现状张坚;曹富荣【摘要】多向锻造技术能显著细化晶粒,大幅改善材料的力学性能,是一种极具潜力的大塑性变形工艺。

综述了多向锻造技术细化镁合金晶粒的研究现状,介绍了多向锻造技术的工艺流程以及晶粒细化机制,展望了多向锻造技术未来的研究方向。

%Multiple forging is a potential severe plastic deformation technique for grain refinement and improvement of mechanical properties. The research progress of grain refinement of magnesium alloys by multiple forging was reviewed, and the technological process of multiple forging and grain refinement mechanism was described. The development prospects of this technique was also discussed.【期刊名称】《精密成形工程》【年(卷),期】2016(008)005【总页数】4页(P154-157)【关键词】多向锻造;大塑性变形;镁合金【作者】张坚;曹富荣【作者单位】东北大学材料科学与工程学院,沈阳 110819;东北大学材料科学与工程学院,沈阳 110819【正文语种】中文【中图分类】TG319镁合金是目前工程应用中最轻的结构材料,和铝合金、钛合金并称为三大轻金属结构材料。

镁合金具有比强度高、比刚度高、阻尼减震性好、尺寸稳定性好、机加工方便、易于回收等优点,被誉为“21世纪绿色工程金属结构材料”[1]。

镁及镁合金是密排六方结构,如图1所示[2],可开动的滑移系少,塑性成形能力差,但是通过晶粒细化可以有效地改善镁合金的力学性能。

高滑移率 磨耗测试 英语

高滑移率 磨耗测试 英语

高滑移率磨耗测试英语High Slip Ratio Abrasion Testing.High Slip Ratio Abrasion (HSRA) testing is a specialized abrasion testing method used to evaluate the wear resistance of materials under conditions that simulate real-world applications where high slip ratios are present. HSRA testing involves subjecting a test specimen to controlled sliding contact against an abrasive surface while maintaining a high slip ratio between the two surfaces. This simulates conditions where there is a significant difference in velocity between the contacting surfaces, such as in tires, brakes, and other automotive components.Principle of HSRA Testing.HSRA testing is based on the principle that wear occurs due to a combination of adhesion, plowing, and cutting mechanisms. When two surfaces slide against each other, theasperities (microscopic peaks and valleys) on the surfaces interact, leading to the formation of adhesive junctions. These junctions can break apart, resulting in material removal from one or both surfaces. In addition, the asperities can plow into the softer surface, creating grooves or furrows. If the slip ratio is high, the plowing action becomes more pronounced, leading to increased wear.HSRA Test Setup and Procedure.HSRA testing is typically performed using a specialized tribometer, which allows for precise control of the test conditions. The test setup consists of a rotating disk, which serves as the abrasive surface, and a stationary pin or block, which represents the test specimen. The specimen is pressed against the rotating disk with a predetermined normal load, and a tangential force is applied to maintain a desired slip ratio. The slip ratio is defined as theratio of the tangential velocity of the disk to the linear velocity of the specimen.The test is conducted over a specified duration oruntil a predetermined wear depth is reached. During the test, various parameters are monitored, including the coefficient of friction, wear volume, and wear rate. The wear rate is typically expressed in terms of mm³/Nm, which represents the volume of material removed per unit of sliding distance and normal load.Factors Affecting HSRA Wear.The HSRA wear performance of a material is influenced by several factors, including:Material properties: The hardness, toughness, and microstructure of the material play a significant role in its resistance to wear.Surface roughness: Rougher surfaces tend to exhibit higher wear rates due to increased adhesion and plowing.Normal load: Higher normal loads lead to increased contact pressures, resulting in higher wear rates.Slip ratio: As mentioned earlier, higher slip ratios promote plowing and cutting mechanisms, leading to increased wear.Abrasive characteristics: The hardness, shape, and size of the abrasive particles can affect the wear rate.Applications of HSRA Testing.HSRA testing has numerous applications in various industries, including:Automotive: Evaluating the wear resistance of tires, brake pads, and other components subjected to high slip ratios.Mining and construction: Assessing the wear performance of materials used in excavators, bulldozers, and other heavy equipment.Aerospace: Investigating the wear behavior of materials used in aircraft tires and landing gear.Medical: Evaluating the wear resistance of implantsand surgical tools that experience sliding contact.Advantages of HSRA Testing.Simulates real-world conditions where high slip ratios are present.Provides quantitative data on wear volume and wear rate.Helps identify materials with superior wear resistance.Facilitates the development of wear-resistant coatings and surface treatments.Limitations of HSRA Testing.May not fully replicate all aspects of wearexperienced in real-world applications.Can be time-consuming and expensive, especially for long-duration tests.Requires specialized equipment and expertise toconduct the tests effectively.Conclusion.HSRA testing is a valuable tool for evaluating the wear resistance of materials under conditions of high slip ratios. It provides insights into the mechanisms of wearand helps identify materials and surface treatments thatcan minimize wear and extend the service life of components. However, it is important to note the limitations of HSRA testing and consider it as part of a comprehensivematerials characterization program.。

大学英语4级翻译练习(真题集合)

大学英语4级翻译练习(真题集合)
The Chinese knot was originally invented by the craftsmen. After hundreds of years’ continuous improvement, it has become a kind of elegant and colorful art and craft. In ancient times, it was used to record events, but now it is used mainly for decorative purposes. Knot, pronounced “jie” in Chinese, means love, marriage and reunion. The Chinese knot is used as gifts to exchange or as decorations to pray for good luck and ward off evil spirits. This form of handicraft has been passed down from generation to generation, and has become increasingly popular in China and around the world.
The Yellow River is over 5,400 km long and is the second longest river in China. Seen from the map, the Yellow River lies in the shape of a huge “几”. The upper reaches of the Yellow River are the main producing area of wool, leather and other livestock products. The middle and lower reaches are one of the origins of China’s agriculture. The Yellow River is considered as the Mother River of the Chinese people. The drainage area of the Yellow River is honored as the cradle of the Chinese people and also one of the origins of world civilization. It is said that Huangdi, legendary ruler and ancestor of the Chinese nation, was born here. It is said man was made by Nv Wa (a legendary goddess) with the mud in the Yellow River.

Quasi-static and high strain rate response of aluminum matrix syntactic

Quasi-static and high strain rate response of aluminum matrix syntactic

Quasi-static and high strain rate response of aluminum matrix syntactic foams undercompressionKyle Myers a ,Bálint Katona b ,Pedro Cortes a ,c ,Imre Norbert Orbulov b ,d ,⇑aMaterials Science and Engineering,Youngstown State University,Youngstown,OH 44555,USAb Department of Materials Science and Engineering,Faculty of Mechanical Engineering,Budapest University of Technology and Economics,Bertalan Lajos utca 7,Budapest 1111,Hungary cCivil/Environmental and Chemical Engineering,Youngstown State University,Youngstown,OH 44555,USA d MTA–BME Research Group for Composite Science and Technology,M }uegyetem rakpart 3,Budapest 1111,Hungary a r t i c l e i n f o Article history:Received 28June 2015Received in revised form 19September 2015Accepted 24September 2015Available online 1October 2015Keywords:A.Foams B.FractureB.Mechanical properties D.Mechanical testinga b s t r a c tAluminum alloy matrix syntactic foams were produced by inert gas pressure infiltration.Four differentalloys and ceramic hollow spheres were applied as matrix and filler material,respectively.The effects of the chemical composition of the matrix and the different heat-treatments are reported at different strain-rates and in compressive loadings.The higher strain rates were performed in a Split-Hopkinson pressure bar system.The results show that,the characteristic properties of the materials strongly depends on the chemical composition of the matrix and its heat-treatment condition.The compressive strength of the investigated foams showed a limited sensitivity to the strain rate,its effect was more pro-nounced in the case of the structural stiffness and fracture strain.The failure modes of the foams have explicit differences showing barreling and shearing in the case of quasi-static and high strain rate com-pression respectively.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionMetal matrix syntactic foams (MMSFs)are particle reinforced composites,filled by hollow spheres.This type of material is inter-esting since when compared to other metal foams it combines lower maximum porosity and higher density with greatly increased quasi-static compressive strength.Moreover,it main-tains the advantages and useful properties of metal foams such as low density,thermal and environmental resistance.In most cases the matrix material is aluminum alloy,but steel [1–5],mag-nesium [6]and titanium [7–9]matrices have also been investi-gated.As reinforcement,commercially available ceramic [10–15]or metallic [10]hollow spheres are the most common systems on MMSFs.Additional serious efforts have been made to reduce the cost of MMSFs by using low cost perlite [16–18]or pumice [19].MMSFs can be applied in numerous fields;for instance,due to their damping capacity and low density features,they can be used as automotive brake rotors,and steer rods,or as covers/hulls/pack-aging (sandwich cores)structures.Their high-energy absorption capability and high compressive strength can also be beneficial in crash energy absorption zones (aerospace and ground trans-portation)and protective panels’applications (vehicles,buildings).MMSFs also have shown electromagnetic (EM)damping properties that can be applied in the EM and microwave shielding field.The main loading mode of metallic foams is compression,and the compressive behavior of MMSFs has been widely studied [20–27].Due to its importance,their testing methodology and characteristic properties under quasi-static conditions have been summarized in standard procedures [28].However,the effects of higher strain rates have not completely investigated.This would be important in the perspective of collision dampers or protective applications.For example,Balch et al.fabricated aluminum matrix/hollow ceramic microsphere syntactic foams (SFs)by liquid metal infiltration of commercially pure and 7075aluminum.The SFs showed quasi-static compressive strengths of 100MPa and 230MPa,respectively.The dynamic compression tests proved $10–30%increase in peak strength compared to the quasi-static results,and the strain rate sensitivities of these foams were similar to those of aluminum matrix composite materials [29].Luong et al.determined the strain rate dependence of compressive response for A4032aluminum alloy/hollow fly ash cenosphere composites./10.1016/positesa.2015.09.0181359-835X/Ó2015Elsevier Ltd.All rights reserved.⇑Corresponding author at:Department of Materials Science and Engineering,Faculty of Mechanical Engineering,Budapest University of Technology and Economics,Bertalan Lajos utca 7,Budapest 1111,Hungary.Tel.:+3614632386;fax:+3614631366.E-mail addresses:orbulov@eik.bme.hu ,orbulov@ (I.N.Orbulov).They reported that the composite showed a higher strength and a energy absorption capability at higher strain rates[30].Similar tests were performed on AZ91D magnesium alloy compositesfilled with5wt%hollowfly ash pared to the matrix alloy,the energy absorption was higher in their counterpart com-posites at comparable strain rates[31].Luong et al.also studied the quasi-static and dynamic properties of aluminum alloy matrix SiC hollow particle reinforced(A356/SiC)SFs.The composites were manufactured using SiC hollow spheres with identical outer diam-eter($1mm),but with different wall thicknesses(67.8±13.6and 79.3±20.5l m).The different types of SFs had a specific quasi-static compressive strength of89.1and87.4MPa/g cmÀ3,and a specific high strain rate(2100sÀ1)compressive strength of81.2 and76.1MPa/(g cmÀ3),respectively.It was determined that the samples did not show strain rate sensitivity[23,32].Gupta et al. produced Mg based SFs with extremely low density(0.97g cmÀ3),filled with SiC hollow spheres.The peak strength and the elastic energy absorbed up to the peak strength showed an increasing trend by increasing the strain rates(from1330to2300sÀ1).The values at high strain rate were up to1.5times higher than the cor-responding quasi-static values.The failure at high strain rates was observed to be crushing of the particles,plastic deformation of the matrix,and propagation of cracks along the precipitates on the grain boundaries[33].Santa-Maria et al.determined the quasi-static and dynamic mechanical properties of A380–Al2O3MMSFs with six different microsphere sizes and different size ranges. The tests were conducted at strain rates between880and 1720sÀ1and revealed that the properties of MMSFs containing hollow spheres with an average diameter of0.425–0.85and 0.85–1mm were not strain rate-dependent and,therefore,their performance would have been similar to that determined from quasi-static tests[24].Zou et al.investigated the dynamic mechan-ical behavior of aluminum matrix SFs using a Split-Hopkinson pressure bar system.The MMSFs were fabricated by pressure infil-tration technique and had a porosity ratio of45%.The energy absorption capability of the SFs exceeded70%under dynamic load-ing than that shown under quasi-static loading rates.During the deformation process,the syntactic foam exhibited a remarked energy absorption capability due to the reduction of original pores in SFs caused by cenospheres rupture.Hence,aluminum matrix SFs are suitable for applications in the aerospace and automobilefield due to their high strength–density ratio and excellent energy absorption capabilities[34].Dou et al.investigated the high strain rate compression behavior of cenosphere–pure aluminum SFs,and compare their performance to that displayed under quasi-static loading rate conditions.It was found that the foams exhibited dis-tinct strain rate sensitivity and that the peak strengths increased from$45–75to$65–120MPa.Also,they observed an increase in the energy absorption capacity by$50–70%[35].Goel et al. studied the compression behavior of aluminum cenosphere SFs at strain rates ranging from quasi-static conditions to1400sÀ1. The compressive strength and energy absorption of the investi-gated foams attained a maximum at strain rates of approximately 750sÀ1,and then decreased as the strain rate increased.It was also found that the foam with coarser cenospheres appeared to be more strain rate sensitive.An empirical relation was also developed to predict the dynamic compressive strength of the aluminum ceno-sphere based SFs[36–38].Fiedler et al.addressed the dynamic analysis of low cost expanded perlite/aluminum(EP/A356)SFs under dynamic compressive loading conditions.Stresses were found to slightly increase at higher strain rates,indicating positive strain-rate sensitivity.The perlite particles had positive effect on the compression resistance at high loading velocities.A possible explanation was connected to the pressure built-up of the entrapped air within the particles,and the stabilization of adjacent metal struts[39].Mondal et al.assessed the deformation response and energy absorption characteristics of closed cell aluminum-fly ash particle composite foams under compressive loading condi-tions at different strain rates(from10À2to101sÀ1).The influence of strain rate on the deformation responses was found to be very marginal;the strain rate sensitivity was measured to be very low (0.02–0.04)when the foam relative density was greater than0.1, while it was found to be negative when the foam relative density was less than0.1[40,41].Lehmhus,Peroni et al.studied the mechanical behavior of syntactic foams made of glass micro-spheres mixed in an iron matrix.Different types of foams were investigated varying the strength of the glass and its weight per-centage content.The experimental characterization was performed by means of compression tests at three different strain-rate levels. The results showed that the strain-rate behavior of the foams was mainly governed by the matrix.It was justified(based on the experimental results),that after the plateau in the densification region,the curves seem to remain parallel to each other [5,42,43].Rabiei et al.produced steel–steel and aluminum–steel composite metal foams(CMFs)with different sphere sizes by stan-dard powder metallurgy and gravity fed casting techniques.When comparing the specific energy absorption of the CMFs at50%strain of the same loading rates,the smaller 2.2mm sphere CMF absorbed about30%more energy than the larger5.2mm sphere CMF at high loading rates.As the loading rate increased,a consis-tent improvement of the yield strength of the material was also observed[44–46].All these previous works,reveal useful information about the dynamic compressive properties of specific grade foams.However, the effect of the chemical composition of the metallic matrix and of heat-treatment were not reported.Therefore the aim of the present paper is to extend the available data regarding the quasi-static and dynamic compressive properties of MMSFs based on different matrices and different heat-treatment conditions.2.Materials and experimental methods2.1.Investigated materials and productionThe investigated MMSFs were produced by the combination of commercially available aluminum alloys(Al99.5,AlSi12,AlMgSi1 and AlCu5)and Globocer grade ceramic hollow spheres provided by Hollomet GmbH[10].The nearest ASM equivalent,the nominal chemical compositions,the ultimate tensile strength(UTS)values (in solution treated state,for comparison)and the melting point (T melting)of the applied aluminum alloy matrix materials are listed in Table1.The composition was measured by an EDAX Genesis energy dispersive X-ray spectroscope(EDS)and only the signifi-cant elements are tabulated.The reinforcement,consisting of cera-mic hollow spheres were made of the combination of Al2O3(33wt %),amorphous SiO2(48wt%)and mullite(3Al2O3Á2SiO2,19wt%)as measured by XRD and EDS.The true(particle)density of the hol-low spheres was0.816g cmÀ3,and their average diameter and wall thickness was£1444±79.9l m and58.0±3.21l m respectively. Here,the volume fraction of the hollow spheres on each manufac-tured MMSF was maintained at64vol%;typical for randomly close packed structure[47,48].The investigated MMSFs were produced by liquid state,inert gas assisted pressure infiltration technique.In this process the molten matrix alloy was squeezed in between the ceramic hollow spheres.Here,a carbon steel mold was coated with a thin carbon layer,andfilled up to half height with hollow spheres.The carbon layer ensured the easy removal of the manufactured MMSF block after the infiltration process.An(Al2O3)insulator layer was placed on top of the spheres;the role of this layer was to separate the matrix materials from the spheres during thefirst part of theK.Myers et al./Composites:Part A79(2015)82–9183infiltrating procedure.Finally,an aluminum block(which acted as the matrix material)was placed into the container.Subsequently, the mold was placed into the pressure infiltration chamber,and Argon(Ar)gas was used to provide the required threshold pressure for infiltrating.During thefirst part of the infiltration procedure, heating and a rough vacuum were applied,and once the melted matrix metal formed a liquid cork above the reinforcement,the pressure was increased to a set value.The generated pressure dif-ference above and under the liquid metal cork induced the metal to infiltrate into the reinforcement across the insulator layer.The casting temperature and pressure of the MMSF blocks was set to T melting+50°C and400kPa respectively,while the infiltration time (during which the infiltration pressure was maintained)was set to 10s.During the manufacturing process,the infiltration parameters were continuously monitored by a computer controlled data acqui-sition system.After the injection of the molten matrix,the mold was cooled,and the MMSF block removed for machining.For fur-ther details about the production phase,please refer to[49,50].After the production,the density and the porosity of the pro-duced blocks were investigated.The theoretical density(q T)was calculated from the density of the constituents(q S and q M for the hollow spheres and for the matrix,respectively)and from the vol-ume fraction(V S)of the hollow spheres(Eq.(1)).q T¼V S q Sþð1ÀV SÞq Mð1ÞOn the other hand,the real densities(q R)of each block were measured by the Archimedes’method,and the porosity in the sam-ples,introduced by the hollow spheres(P S)was calculated by Eq.(2).P S¼V SrR3ð2Þwhere r and R are the inner and outer radii of the hollow spheres, respectively.Additional porosity may also exist in the matrix of the blocks,due to the possibility of insufficient infiltration pressure. This,unintended porosity(P U)was determined by Eq.(3).P U¼ð1ÀV SÞq TÀq Rq Tð3ÞDue to the nature of liquid pressure infiltration(64vol%,homo-geneous distribution of hollow spheres,isotropic properties)the density can be considered homogeneous and valid for all speci-mens.All these calculated and measured values are listed in Table2.Here,the negative values shown in the unintended poros-ity indicate that a part of the hollow spheres was infiltrated and consequently,the total porosity(P T)decreased.All of the specimens were homogenized(‘-O’tag at the end of the specimens’designation)at520°C for30min.The specimens were cooled in water,and the compression tests were performed immediately after the homogenization process,to avoid any cold aging effect(especially in the case of the AlCu5matrix).The AlMgSi1and AlCu5specimens were also tested in an aged condi-tion(‘-T6’tag in the designation),involving a14h long aging pro-cess at170°C(followed by water cooling)just after the homogenization stage.Again,the T6treated specimens were inves-tigated immediately after the aging process.2.2.ExperimentalCylindrical specimens with dimensions of£12.7mm for the quasi-static and the high strain rate compression tests were machined from the produced MMSF blocks.The aspect ratio of the specimens was H/D=1in all cases,and the specimens were heat-treated,following the aforementioned homogenization or T6treated process.The quasi-static compression tests were performed on a MTS 810type universal testing machine in a four column tool at room temperature.The surfaces of the tool were grinded and polished. The specimens and the tool were lubricated with anti-seize mate-rial.The average strain rate was0.01sÀ1,which ensured quasi-static compression.Six specimens were compressed from each specimen group,up to50%engineering strain to get representative results and to verify repeatability(overall,36specimens were tested).The tests were performed and evaluated according to the ruling standard of compression tests on cellular materials[28].The high strain rate compression testing was conducted using a split-Hopkinson pressure bar(SHPB).Both the incident and trans-mission bars were made of a C-350maraging steel with a Young’s modulus of195GPa.The length and diameter of the bars were 1.8m and£19.05mm respectively.Strain gauges were placed at an equal distance away from the sample on both the incident and transmission bar to collect the pulse signals.The generated pulse signals were initially acquired through a signal conditioning amplifier and collected by a PicoScope oscilloscope.A76.2mm long striker bar was projected at the incident bar using a pressure chamberfilled to either138or552kPa.These incident striking pressures resulted in averaged strains rate of933sÀ1and 2629sÀ1respectively.The stresses,strains,and strain rates wereTable1Properties of the matrix materials.Matrix ASM equivalent Main component(wt%)UTS(MPa)T melting(°C)Al Si Fe Mg Cu OtherAl99.5Al105099.50.10.1––0.375660 AlSi12A413.08612.80.10.1– 1.0115575 AlMgSi1Al6082a97 1.10.5 1.1–0.3125650 AlCu5Al201195––– 4.50.5190630a Closest equivalent,significant difference in Mn content that should be0.4...1wt%.Table2Density and porosity values of the produced MMSF blocks.Matrix q M(g cmÀ3)q S(g cmÀ3)q T(g cmÀ3)q R(g cmÀ3)P S(%)P U(%)P T(%)Al99.5 2.710.816 1.50 1.8349.78À7.9241.86 AlSi12 2.65 1.48 1.78À7.3042.48 AlMgSi1 2.70 1.49 1.80À7.4942.29 AlCu5 2.81 1.53 1.84À7.2942.49 84K.Myers et al./Composites:Part A79(2015)82–91all calculated by a proprietary REL’s SurePulseimum stress value was taken from the highest value of the stress–strain curve for each sample,sion modulus was determined by the slope of points recorded.Seven specimens were specimen group to attain representative repeatability (overall,42specimens were tested).To investigate the failure mechanisms,tested specimens were examined.The compressed cut into two halves along their axis,mounted grinded on an automatic grinding and SiC papers and diamond suspension,respectively 3.Results and discussion 3.1.Mechanical propertiesDuring the compressive tests,the loading force and the defor-mation were registered from which the engineering stress–engi-neering strain curves for the quasi-static and for the high strain rate loading were calculated and plotted.Fig.1shows the typical engineering stress–engineering strain curves for quasi-static and high strain rate cases (Al99.5-O;note the similar stress,but differ-ent strain scales on the corresponding axes).In the case of com-pressive loading of cellular materials,the characteristic properties are particularly defined in well-known standards [28].The initial slope of the registered curves corresponds to the struc-tural stiffness (S (MPa)).The two main strength properties are the yield strength at 0.2%plastic strain (r Y (MPa))and the compressive strength (r C (MPa)).In the case of Globocer reinforced MMSFs at quasi-static conditions,these strength values are relatively close to each other,while in the case of higher strain rates,the difference is larger.The fracture strain (e C (%))is defined as the abscissa of the alloying the matrix material.This phenomenon was consistent on the three investigated strain rates.The figure also shows the effect of Mg–Si ($2wt%)and Cu ($4.5wt%)alloying which resulted in a more pronounced compressive strength increment than pure Si alloying.A relatively small amount of Mg–Si or Cu alloying was sufficient to reach the same increment as it was ensured by the $13wt%Si.In the quasi-static conditions,the T6treatment of the material was also effective and resulted in a $40%and $20%increment in the case of Mg–Si and Cu alloying,respectively.At higher strain rates,the increment became smaller ($10%)in the case of Mg–Si,and larger (up to $40%)in the case of Cu pared to the Al99.5-O MMSFs,the compressive strength was significantly increased by the strain rate;the average increment was $20%and $45%in the case of 933s À1and 2629s À1strain rates,respectively.The sensitivity to the strain rate can be quanti-by the strain rate sensitivity parameter (R )that is defined (4)[24,29,54].r d Àr q r Ã1ln _e d _e qwhere r is the stress at a given strain,r *is the quasi-static stress,when the strain is 0.2%(r Y ),and _eis the strain rate.The subscripts and ‘q’stands for the dynamic and quasi-static loading,respec-tively.MMSFs can exhibit abrupt variations in stress during com-pression that are not seen in alloys or composites with monotonicFig.1.Typical engineering stress–engineering strain curves of Al99.5-O MMSF for (a)quasi-static and (b)high strain rate loading.pressive strength of the investigated MMSFs.K.negligible.Meanwhile,in the case of T6treatment,the difference between the higher strain rates became significant,and higher stiffness values were measured at the 2629s À1strain rate.The fracture strains were also measured and are shown in Fig.fracture strains were significantly ($50%)lower in the case higher strain rates,and no significant difference between the strain rates were observed.This can be explained based AlSi12-O 101.388.4101.70.0139AlMgSi1-O 110.678.465.80.0535Fig.3.Strain rate sensitivity of the investigated MMSFs.Fig.4.Yield strength of the investigated MMSFs.Fig.5.Structural stiffness of the investigated MMSFs.Fig.6.Fracture strains of the investigated MMSFs.Fig.7.Fracture energies of the investigated MMSFs.8.Absorbed energy values of the investigated MMSFs,measured up to thetests.different fracture mechanisms which correspond todifferent loading conditions.In the quasi-static loading case,occurrence of fracture depended only on the relative strengthconstituents[29].In contrast,in the case of dynamic loading,short time impulse of the striking energy did not allowstructural rearrangement in the composite,resulting in a differentFig.9.The absorbed energies of the investigated MMSFs measured up to(a)2.45%and(b)8.12%end strains.times higher than that displayed at the quasi-static Similar results were observed in the case of8.12%based Fig.9b),where the smallest increment was about mechanismsfailure mechanisms,the different MMSFs,had very fracture scheme,only the loading rate had significant effect fracture mechanism.In Fig.10the failure steps of an specimen is presented at different strain values.Fig.10a cross section of the specimen after2%plastic deformation,where there were no broken hollow spheres(the specimen absolutely intact),proving that the initial plastic deformation originated from the plastic deformation of the matrixDue to the64vol%of the reinforcement,small displacements between the hollow spheres were possible by the deformation the matrix(the maximal volume fraction of reinforcementbe74vol%in the case of spheres with identical outerFig.10b represents the specimen after30%plastic deformation. well-defined band with broken spheres can be observeddle of the specimen.The spheres were broken in thisfew of them were completely collapsed.Some barrelingfriction between the specimen and the tool’s platesCross-sections of a quasi-statically loaded(0.01sÀ1)Al99.5-O specimen at different strains:(a)2%,(b)30%and(c)60%.(For interpretation of the references legend,the reader is referred to the web version of this article.)Al99.5-O specimen loaded at933sÀ1,(a)cross section of the full specimen,(b)and(c)magnified parts of the crossof the references to color in thisfigure legend,the reader is referred to the web version of this article.)observable.After further compression,the whole specimen deformed (Fig.10c),and the deformation and the failure were dif-fuse.Due to the gradual nature of the failure,large amounts of mechanical energy were absorbed during the whole process (Fig.8).In Fig.11the homogenized,Al99.5-O based MMSF is presented after testing at 933s À1loading rate.Some significant differences can be observed in Fig.11after 2.45%plastic deformation (see Table 4)compared to the specimens tested in thequasi-staticAl99.5-O specimen loaded at 2629s À1,(a)cross section of the full specimen,(b)and (c)magnified parts of the cross of the references to color in this figure legend,the reader is referred to the web version of this article.)Table 5Literature data for the compressive strength and energy absorption capability of similar foams.MatrixFillerCompressive strength (MPa)Energy absorption (J cm À3)Ref.Q–SDynamic (s À1)Q–S Dynamic Cp-Al SL7565vol%(<75l m)109140@230055@60%–[29]Al7075-O 199231@2300––Al7075-T6229248@230036@25%–Al4032Fly-ash 5vol%(44–106l m)254219@754––[30]256@1293–280@1629–288@2136–A356SiC HS 60vol%(1mm)163124@940––[23],[32]119@970–125@1160–123@1165–121@1220–119@1310–130@1425–125@1520–A380Al 2O 340–50vol%(0–0.5mm)165160@100048@40%–[24]Al 2O 340–50vol%(1–2mm)120140@100039@47%–Al6061Cenospheres 45vol%(200l m)4548@265018@47%28@43@2650s À1[34]55@335033@43@3350s À1Cp-AlCenospheres 70vol%(90l m)75108@140027@40%–[35]114@3000–119@500040@40%@5000s À1Cenospheres 65vol%(150l m)4565@220017@40%–69@4400–69@500029@40%@5000s À1Al2014Cenospheres 34vol%(90l m)184190@156@30%56@30%@1s À1[36],[37]195@1050@30%@10s À1197@420–223@75070@30%@50s À1210@90064@30%@900s À1204@140060@30%@1400s À1Cenospheres 35vol%(200l m)161167@151@30%51@30%@1s À1187@1050@30%@10s À1206@75063@30%@750s À1197@140058@30%@1400s À1A356Globomet 316–65vol%(2.2mm)8288@178041@50%43@50%@1780s À1[44],[45],[46]87@146543@50%@1465s À1Globomet 316–65vol%(4mm)75105@143137@50%38@50%@1431s À1Globomet 316–65vol%(5.2mm)8390@19225@10%10@10%@1922s À185@7677@10%@767s À1condition.First,while$2%deformation caused no cracks in the quasi-static condition,all of the hollow spheres exhibited ruptures in their walls at933sÀ1loading rate.The arrows in Fig.11point out some of the most obvious cracks that had occurred in the cera-mic microspheres.Moreover these ruptures were parallel to the loading direction.This phenomenon refers to some additional radial forces caused by some kind of constrain in the deformation (due to the friction between the loading bars and the specimens). Considering this,and the sudden,but relatively low energy loading rate(compared to the higher loading rate),the hollow spheres remained spherical.In the magnified images(Fig.11b and c)some cracks were observed in the matrix between the hollow spheres (designated by ellipses in Fig.11b and c).These cracks appear to be initiated from the brittle cracks of the hollow spheres(see right side ellipse in Fig.11c),presumably due to the enlarged gas pres-sure inside the hollow spheres as suggested by Rabiei et al.,for the case of steel hollow sphere consisting CMFs[45].The cracks stopped in the matrix material or reached a neighboring hollow sphere and decayed in the interface between the sphere and the matrix material.In Fig.12the Al99.5-O matrix syntactic foam is shown after the highest strain rate compression(at2629sÀ1)up to8.12%deforma-tion.Due to the higher impact energy of the compression test,the deformation was significantly larger.The hollow spheres were completely broken and eitherflattened or slipped along some main large,almost linear cracks.In some cases,the specimens were sep-arated into two or three parts along these cracks(Fig.12a).Most of the hollow spheres were broken into numerous particles that had been removed from their original cavities during the grinding and polishing sequence,leaving dark pores in Fig.12a.Two specific examples for the broken hollow spheres are shown in Fig.12b and c.The cracks between the neighboring hollow spheres were significantly larger and wider due to the larger pressure caused by the sudden and relatively large deformation.Due to the large number of matrix materials and hollow sphere grades reported in the literature,it is not an obvious task to com-pare these results against other works.However,some efforts have been made on thisfield,and a literature data has been listed in Table5,to situate the investigated materials amongst the MMSFs from other research groups.This comparison has been performed from the compressive strength point of view.4.ConclusionsFrom the detailed and discussed investigations the following conclusions can be drawn.The engineering stress–engineering strain curves for quasi-static and high strain rate conditions are significantly different in the case of the investigated MMSFs,however the curves can be effectively analyzed by the application of the same (and standardized)characteristic properties.The chemical composition of the matrix material,the applied heat treatment and the loading rate have different,but signifi-cant effects on the characteristic compressive properties of the MMSFs.Considering the combined effect of these parame-ters,the compressive properties of the MMSFs can therefore be tailored for individual requirements of given applications. The failure modes in quasi-static and dynamic conditions were also different.In the case of quasi-static loading,a slow and dif-fuse compression of the specimen was observed.The hollow spheres were broken andflattened,the matrix material deformed plastically and the specimen remained intact.In the case of higher loading rates(933sÀ1)the nature of the failure changed due to the restricting effects of the material during the sudden loading.Here,the hollow spheres ruptured linearly.In the case of the highest loading rates(2629sÀ1)the hollow spheres were cracked into many pieces,and the specimens bro-ken into two or three large pieces.In the case of higher loading rates,cracks were initiated from the brittle ruptures of the hollow spheres,due to the high gas pressure in the spheres caused by the large plastic deformation.The cracks propagated into the matrix material,or reached the neighboring hollow spheres and decayed in the interface layer.In the case of a higher loading rate(2629sÀ1),larger and wider cracks were observed compared to the lower,but still dynamic loading rate of933sÀ1.AcknowledgementThis paper was supported by the János Bolyai Research Scholar-ship of the Hungarian Academy of Sciences.References[1]Castro G,Nutt SR.Synthesis of syntactic steel foam using gravity-fedinfiltration.Mater Sci Eng A2012;553:89–95.[2]Castro G,Nutt SR.Synthesis of syntactic steel foam using mechanical pressureinfiltration.Mater Sci Eng A2012;535:274–80.[3]Weise J,Lehmhus D,Baumeister J,Kun R,Bayoumi M,Busse M.Production andproperties of316L stainless steel cellular materials and syntactic foams.Steel Res Int2014;85(3):486–97.[4]Luong DD,Shunmugasamy VC,Gupta N,Lehmhus D,Weise J,Baumeister J.Quasi-static and high strain rates compressive response of iron and Invar matrix syntactic foams.Mater Des2015;66:516–31.[5]Peroni L,Scapin M,Avalle M,Weise J,Lehmhus D.Dynamic mechanicalbehavior of syntactic iron foams with glass microspheres.Mater Sci Eng A 2012;552:364–75.[6]Xia X,Feng J,Ding J,Song K,Chen X,Zhao W,et al.Fabrication andcharacterization of closed-cell magnesium-based composite foams.Mater Des 2015;74:36–43.[7]Mondal DP,Datta Majumder J,Jha N,Badkul A,Das S,Patel A,et al.Titanium-cenosphere syntactic foam made through powder metallurgy route.Mater Des 2012;34:82–9.[8]Xue X-B,Wang L-Q,Wang M-M,LüW-J,Zhang D.Manufacturing,compressivebehaviour and elastic modulus of Ti matrix syntactic foam fabricated by powder metallurgy.Trans Nonferrous Metals Soc China2012;22:188–92. 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[17]Taherishargh M,Belova IV,Murch GE,Fiedler T.On the mechanical propertiesof heat-treated expanded perlite–aluminium syntactic foam.Mater Des 2014;63:375–83.[18]Taherishargh M,Sulong MA,Belova IV,Murch GE,Fiedler T.On the particle sizeeffect in expanded perlite aluminium syntactic foam.Mater Des 2015;66:294–303.[19]Taherishargh M,Belova IV,Murch GE,Fiedler T.Pumice/aluminium syntacticfoam.Mater Sci Eng A2015;635:102–8.[20]Tao XF,Zhao pressive behavior of Al matrix syntactic foams toughenedwith Al particles.Scripta Mater2009;61(5):461–4.[21]Orbulov IN,Ginsztler pressive behaviour of metal matrix syntacticfoams.Acta Polytech Hungarica2012;9(2):43–56.[22]Rohatgi PK,Kim JK,Gupta N,Alaraj S,Daoud pressive characteristics ofA356/fly ash cenosphere composites synthesized by pressure infiltration posites Part A2006;37(3):430–7.[23]Luong DD,Strbik III OM,Hammond VH,Gupta N,Cho K.Development of highperformance lightweight aluminum alloy/SiC hollow sphere syntactic foams and compressive characterization at quasi-static and high strain rates.J Alloys Comp2013;550:412–22.[24]Santa Maria JA,Schultz BF,Ferguson JB,Guptan N,Rohatgi PK.Effect of hollowsphere size and size distribution on the quasi-static and high strain rate90K.Myers et al./Composites:Part A79(2015)82–91。

大塑性变形制备块体超细晶材料的概述

大塑性变形制备块体超细晶材料的概述

大塑性变形技术(SPD)制备块体超细晶/纳米晶材料的概述摘要:从制备块体超细晶/纳米晶角度引出了大塑性变形技术,重点概述了等径角挤压、高压扭转、累积叠轧焊等技术;同时分析了SPD材料的强度与超塑性等性能特征,并对其未来发展做出了展望。

关键词:超细晶;大塑性变形;等径角挤压;高压扭转;超塑性1 前言根据晶粒尺度的不同,通常将材料分为:粗晶材料(晶粒大于1μm);超细晶材料(晶粒大小在0.1μm到1μm之间);纳米晶材料(晶粒小于100nm)[1]。

晶粒大小是影响多晶金属材料性能的重要因素,由亚微米级晶粒组成的超细晶/纳米晶金属材料由于具有很小的晶粒尺寸和独特的缺陷结构,在室温下不仅具有高的强度、硬度和耐磨性,而且还具有良好的塑性和韧性,在一定的温度范围内还具备超塑性,在磁性材料、催化剂、半导体等方面具有广阔的应用前景。

因此,制备大尺寸、无污染、无微孔隙且晶粒尺寸细小均匀的块体超细晶/纳米晶材料一直是人们研究的热点。

机械化合金加压成块法、电沉积法、非晶晶化法和剧烈塑性变形(Severe Plastic Deformation, SPD)等都可以制备块体超细晶/纳米晶材料,其中SPD被认为是最有希望实现工业化生产的有效途径之一[2]。

SPD具有强烈的晶粒细化能力,可以直接将材料的内部组织细化到亚微米乃至纳米级,其主要的变形方式是剪切变形。

组织细化的主要目的在于[3]:1)充分挖掘材料的潜能,获得满足军事和日益发展的航空航天等领域对高强高韧材料的需求;2)在较高温度下提高材料的超塑性能力,以提高零件的生产效率和开拓难变形材料如镁合金等的加工制备新途径。

Valiev教授认为,采用SPD方法制备超细晶/纳米结构金属应该满足多项条件[4]:1)大塑性变形量;2)相对低的变形温度;3)变形材料内部承受高压。

在这些原则的指导下,大塑性变形工艺得到了迅猛发展,出现了一系列的制备工艺:等通道转角挤压(ECAE)、高压扭转(HPT)、往复挤压(CEC)、累积轧制(ARB)、大挤压比挤压(HRE)、超音喷丸(USSP)等。

高铁技术的英语作文初一

高铁技术的英语作文初一

Highspeed rail,commonly known as bullet trains,has revolutionized the way we travel.It is a testament to the advancements in modern transportation technology.Heres an essay on highspeed rail technology suitable for a junior high school student:The Marvel of Modern Transportation:HighSpeed RailIn the realm of transportation,the advent of highspeed rail has been nothing short of a marvel.It has transformed the way we travel,making long distances seem shorter and more accessible than ever before.The concept of highspeed rail is not new,but its recent advancements have made it a preferred mode of travel for many.Introduction to HighSpeed RailHighspeed rail is a type of rail transport that operates significantly faster than traditional rail traffic.It is characterized by its highspeed train sets and dedicated tracks,which allow for speeds exceeding200kilometers per hour.The technology behind highspeed rail is a combination of aerodynamics,advanced materials,and sophisticated control systems.History and DevelopmentThe idea of highspeed rail was first realized in Japan with the Shinkansen,which began operations in1964.Since then,countries like France,Germany,and China have developed their own highspeed rail networks.The development of highspeed rail has been driven by the need for efficient,environmentally friendly,and comfortable transportation options.Technological InnovationsThe technology behind highspeed rail is continually evolving.Key innovations include:1.Aerodynamics:Highspeed trains are designed with aerodynamic shapes to reduce air resistance,allowing them to travel at high speeds with minimal energy loss.2.Maglev Technology:Some highspeed trains use magnetic levitation,which reduces friction by levitating the train above the tracks,further increasing speed and efficiency.3.Regenerative Braking:This system captures the energy generated during braking andreuses it to power the train,making highspeed rail more energyefficient.4.Advanced Materials:The use of lightweight materials in the construction of highspeed trains reduces the overall weight,allowing for higher speeds and lower energy consumption.5.Control Systems:Sophisticated control systems ensure the safety and precision of highspeed rail operations,including automatic train control and realtime monitoring of train performance.Benefits of HighSpeed RailThe benefits of highspeed rail are numerous and include:1.Time Efficiency:Highspeed rail significantly reduces travel time between cities, making it a viable alternative to air travel for shorter distances.2.Environmental Impact:Compared to other forms of transportation,highspeed rail produces less carbon dioxide and other pollutants,contributing to a cleaner environment.3.Economic Growth:The development of highspeed rail networks stimulates economic growth by improving connectivity between regions,encouraging tourism,and facilitating business activities.4.Safety:Highspeed rail is considered one of the safest modes of transportation,with a low rate of accidents and fatalities.Challenges and the FutureDespite its many advantages,highspeed rail faces challenges such as high initial infrastructure costs,land acquisition issues,and competition from other modes of transportation.However,with ongoing technological advancements and increasing environmental concerns,the future of highspeed rail looks promising.In conclusion,highspeed rail is a remarkable achievement in the field of transportation technology.It offers a fast,efficient,and environmentally friendly way to travel,and as technology continues to advance,we can expect even greater improvements in speed, comfort,and safety.This essay provides a comprehensive overview of highspeed rail technology,its history, technological innovations,benefits,and future prospects,making it suitable for a junior high school students understanding and writing ability.。

大塑性变形制备块体超细晶材料的概述

大塑性变形制备块体超细晶材料的概述

大塑性变形技术(SPD)制备块体超细晶/纳米晶材料的概述摘要:从制备块体超细晶/纳米晶角度引出了大塑性变形技术,重点概述了等径角挤压、高压扭转、累积叠轧焊等技术;同时分析了SPD材料的强度与超塑性等性能特征,并对其未来发展做出了展望。

关键词:超细晶;大塑性变形;等径角挤压;高压扭转;超塑性1 前言根据晶粒尺度的不同,通常将材料分为:粗晶材料(晶粒大于1μm);超细晶材料(晶粒大小在0.1μm到1μm之间);纳米晶材料(晶粒小于100nm)[1]。

晶粒大小是影响多晶金属材料性能的重要因素,由亚微米级晶粒组成的超细晶/纳米晶金属材料由于具有很小的晶粒尺寸和独特的缺陷结构,在室温下不仅具有高的强度、硬度和耐磨性,而且还具有良好的塑性和韧性,在一定的温度范围内还具备超塑性,在磁性材料、催化剂、半导体等方面具有广阔的应用前景。

因此,制备大尺寸、无污染、无微孔隙且晶粒尺寸细小均匀的块体超细晶/纳米晶材料一直是人们研究的热点。

机械化合金加压成块法、电沉积法、非晶晶化法和剧烈塑性变形(Severe Plastic Deformation, SPD)等都可以制备块体超细晶/纳米晶材料,其中SPD被认为是最有希望实现工业化生产的有效途径之一[2]。

SPD具有强烈的晶粒细化能力,可以直接将材料的内部组织细化到亚微米乃至纳米级,其主要的变形方式是剪切变形。

组织细化的主要目的在于[3]:1)充分挖掘材料的潜能,获得满足军事和日益发展的航空航天等领域对高强高韧材料的需求;2)在较高温度下提高材料的超塑性能力,以提高零件的生产效率和开拓难变形材料如镁合金等的加工制备新途径。

Valiev教授认为,采用SPD方法制备超细晶/纳米结构金属应该满足多项条件[4]:1)大塑性变形量;2)相对低的变形温度;3)变形材料内部承受高压。

在这些原则的指导下,大塑性变形工艺得到了迅猛发展,出现了一系列的制备工艺:等通道转角挤压(ECAE)、高压扭转(HPT)、往复挤压(CEC)、累积轧制(ARB)、大挤压比挤压(HRE)、超音喷丸(USSP)等。

力学名词英文翻译

力学名词英文翻译

力学通类名词力学 mechanics牛顿力学 Newtonian mechanics经典力学 classical mechanics静力学 statics运动学 kinematics动力学 dynamics动理学 kinetics宏观力学 macroscopic mechanics,macromechanics 细观力学 mesomechanics微观力学 microscopic mechanics,micromechanics 一般力学 general mechanics固体力学 solid mechanics流体力学 fluid mechanics理论力学 theoretical mechanics应用力学 applied mechanics工程力学 engineering mechanics实验力学 experimental mechanics计算力学 computational mechanics理性力学 rational mechanics物理力学 physical mechanics地球动力学 geodynamics力 force作用点 point of action作用线 line of action力系 system of forces力系的简化 reduction of force system 等效力系 equivalent force system刚体 rigid body力的可传性 transmissibility of force平行四边形定则 parallelogram rule 力三角形 force triangle力多边形 force polygon零力系 null-force system平衡 equilibrium力的平衡 equilibrium of forces平衡条件 equilibrium condition平衡位置 equilibrium position平衡态 equilibrium state分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier 拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿--雅可比方程 Hamilton-Jacobi equation 作用--角度变量 action-angle variables阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method 并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of-phase component超调量 overshoot参量[激励]振动 parametric vibration 模糊振动 fuzzy vibration临界转速 critical speed of rotation 阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu-bov-Mitropol'skii method 马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法 harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态 natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB method, Wentzel-Kramers-Brillouin method缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱 cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration 隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振 surge摆振 shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation 驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque 陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance 姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法 Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support-foundation system 静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession 半频进动 half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl连续过程 continuous process碰撞截面 collision cross section通用气体常数 conventional gas constant 燃烧不稳定性 combustion instability稀释度 dilution完全离解 complete dissociation火焰传播 flame propagation组份 constituent碰撞反应速率 collision reaction rate 燃烧理论 combustion theory浓度梯度 concentration gradient阴极腐蚀 cathodic corrosion火焰速度 flame speed火焰驻定 flame stabilization火焰结构 flame structure着火 ignition湍流火焰 turbulent flame层流火焰 laminar flame燃烧带 burning zone渗流 flow in porous media, seepage 达西定律 Darcy law赫尔-肖流 Hele-Shaw flow毛[细]管流 capillary flow过滤 filtration爪进 fingering不互溶驱替 immiscible displacement 不互溶流体 immiscible fluid互溶驱替 miscible displacement互溶流体 miscible fluid迁移率 mobility流度比 mobility ratio渗透率 permeability孔隙度 porosity多孔介质 porous medium比面 specific surface迂曲度 tortuosity空隙 void空隙分数 void fraction注水 water flooding可湿性 wettability地球物理流体动力学 geophysical fluid dynamics 物理海洋学 physical oceanography大气环流 atmospheric circulation海洋环流 ocean circulation海洋流 ocean current旋转流 rotating flow平流 advection埃克曼流 Ekman flow埃克曼边界层 Ekman boundary layer大气边界层 atmospheric boundary layer大气-海洋相互作用 atmosphere-ocean interaction 埃克曼数 Ekman number罗斯贝数 Rossby unmber罗斯贝波 Rossby wave斜压性 baroclinicity正压性 barotropy内磨擦 internal friction海洋波 ocean wave盐度 salinity环境流体力学 environmental fluid mechanics 斯托克斯流 Stokes flow羽流 plume理查森数 Richardson number污染源 pollutant source污染物扩散 pollutant diffusion噪声 noise噪声级 noise level噪声污染 noise pollution排放物 effulent工业流体力学 industrical fluid mechanics流控技术 fluidics轴向流 axial flow并向流 co-current flow对向流 counter current flow横向流 cross flow螺旋流 spiral flow旋拧流 swirling flow滞后流 after flow混合层 mixing layer抖振 buffeting风压 wind pressure附壁效应 wall attachment effect, Coanda effect 简约频率 reduced frequency爆炸力学 mechanics of explosion终点弹道学 terminal ballistics动态超高压技术 dynamic ultrahigh pressure technique 流体弹塑性体 hydro-elastoplastic medium热塑不稳定性 thermoplastic instability空中爆炸 explosion in air地下爆炸 underground explosion水下爆炸 underwater explosion电爆炸 discharge-induced explosion激光爆炸 laser-induced explosion核爆炸 nuclear explosion点爆炸 point-source explosion殉爆 sympathatic detonation强爆炸 intense explosion粒子束爆炸 explosion by beam radiation聚爆 implosion起爆 initiation of explosion 爆破 blasting霍普金森杆 Hopkinson bar电炮 electric gun电磁炮 electromagnetic gun爆炸洞 explosion chamber轻气炮 light gas gun马赫反射 Mach reflection基浪 base surge成坑 cratering能量沉积 energy deposition爆心 explosion center爆炸当量 explosion equivalent 火球 fire ball爆高 height of burst蘑菇云 mushroom侵彻 penetration规则反射 regular reflection崩落 spallation应变率史 strain rate history流变学 rheology聚合物减阻 drag reduction by polymers挤出[物]胀大 extrusion swell, die swell 无管虹吸 tubeless siphon剪胀效应 dilatancy effect孔压[误差]效应 hole-pressure[error]effect 剪切致稠 shear thickening剪切致稀 shear thinning触变性 thixotropy反触变性 anti-thixotropy超塑性 superplasticity粘弹塑性材料 viscoelasto-plastic material 滞弹性材料 anelastic material本构关系 constitutive relation麦克斯韦模型 Maxwell model沃伊特-开尔文模型 Voigt-Kelvin model宾厄姆模型 Bingham model奥伊洛特模型 Oldroyd model幂律模型 power law model应力松驰 stress relaxation应变史 strain history应力史 stress history记忆函数 memory function衰退记忆 fading memory应力增长 stress growing粘度函数 voscosity function相对粘度 relative viscosity复态粘度 complex viscosity拉伸粘度 elongational viscosity拉伸流动 elongational flow第一法向应力差 first normal-stress difference 第二法向应力差 second normal-stress difference 德博拉数 Deborah number魏森贝格数 Weissenberg number动态模量 dynamic modulus振荡剪切流 oscillatory shear flow宇宙气体动力学 cosmic gas dynamics等离[子]体动力学 plasma dynamics电离气体 ionized gas行星边界层 planetary boundary layer阿尔文波 Alfven wave泊肃叶-哈特曼流] Poiseuille-Hartman flow 哈特曼数 Hartman number生物流变学 biorheology生物流体 biofluid生物屈服点 bioyield point生物屈服应力 bioyield stress电气体力学 electro-gas dynamics铁流体力学 ferro-hydrodynamics血液流变学 hemorheology, blood rheology 血液动力学 hemodynamics磁流体力学 magneto fluid mechanics磁流体动力学 magnetohydrodynamics, MHD 磁流体动力波 magnetohydrodynamic wave磁流体流 magnetohydrodynamic flow磁流体动力稳定性 magnetohydrodynamic stability 生物力学 biomechanics生物流体力学 biological fluid mechanics生物固体力学 biological solid mechanics宾厄姆塑性流 Bingham plastic flow开尔文体 Kelvin body沃伊特体 Voigt body可贴变形 applicable deformation可贴曲面 applicable surface边界润滑 boundary lubrication液膜润滑 fluid film lubrication向心收缩功 concentric work离心收缩功 eccentric work关节反作用力 joint reaction force微循环力学 microcyclic mechanics微纤维 microfibril渗透性 permeability生理横截面积 physiological cross-sectional area 农业生物力学 agrobiomechanics纤维度 fibrousness硬皮度 rustiness胶粘度 gumminess粘稠度 stickiness嫩度 tenderness渗透流 osmotic flow易位流 translocation flow蒸腾流 transpirational flow过滤阻力 filtration resistance压扁 wafering风雪流 snow-driving wind停滞堆积 accretion遇阻堆积 encroachment沙漠地面 desert floor流沙固定 fixation of shifting sand流动阈值 fluid threshold固体力学弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk楔 wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff-Muskhelishvili method 基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforced Plate中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳 Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳 Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity 颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱 Wrinkle塑性全量理论 Total theory of plasticity 滑动 Sliding微滑 Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的 Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振 Flutter弹性波 Elastic wave简单波 Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave 竖直剪切波 Vertical shear wave 体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波 Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔 Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透 Perforation层裂 Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem 静力安定定理 Static shake-down theorem率相关理论 rate dependent theorem载荷因子 load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷 step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension 加速度波 acceleration wave本构方程 constitutive equation 完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态 hydrostatic state of stress 对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment累积塑性应变 accumulated plastic strain永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material 刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material材料稳定性 stability of material应变偏张量 deviatoric tensor of strain应力偏张量 deviatori tensor of stress应变球张量 spherical tensor of strain应力球张量 spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material 极限分析 limit analysis极限设计 limit design极限面 limit surface上限定理 upper bound theorem上屈服点 upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面 initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface 截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服 Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissible Field流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory of Plasticity 米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间 Haigh-Westergaard stress space 洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程 Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶 Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy 机动分析 kinematic analysis结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法 moment distribution method 力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法 matri displacement method 单元刚度矩阵 element stiffness matrix 单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method 屈曲模态 buckling mode复合材料力学 mechanics of composites复合材料 composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料 foamed composite颗粒复合材料 particulate composite层板 Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片 Ply多胞固体 cellular solid膨胀 Expansion压实 Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变 ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor 强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus 横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracture mechanics, LEFM 弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM 断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹 Crack裂缝 Flaw缺陷 Defect割缝 Slit微裂纹 Microcrack折裂 Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角 crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle, CTOA裂尖张开位移 crack tip opening displacement, CTOD 裂尖奇异场 crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth裂纹[扩展]减速 crack retardation止裂 crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factor HRR场 Hutchinson-Rice-Rosengren Field 守恒积分 conservation integral有效应力张量 effective stress tensor 应变能密度 strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区 heat affected zone, HAZ延脆转变温度 brittle-ductile transition temperature剪切带 shear band剪切唇 shear lip无损检测 non-destructive inspection双边缺口试件 double edge notched specimen, DEN specimen单边缺口试件 single edge notched specimen, SEN specimen三点弯曲试件 three point bending specimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen 中心裂纹板试件 center cracked panel specimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen。

超塑性合金

超塑性合金

超塑性合金超塑性是指材料在一定的内部(组织)条件(如晶粒形状及尺寸,相变等)和外部(环境)条件下(如温度、应变速率等),呈现出异常低的流变抗力、异常高的流变性能(例如大的延伸率)的现象。

超塑性现象最早的报道是在1920年,ROSENHAIN等发现Zn-4Cu-7Al合金在低速弯曲时,可以弯曲近180&ordm;。

最初发现的超塑性合金是锌与22%铝的合金。

1928年英国物理学家森金斯下了一个定义:凡金属在适当的温度下变得像软糖一样柔软,而且其应变速度为每秒10毫米时产生300%以上的延伸率,均属超塑性现象。

1945年苏联包奇瓦尔等针对这一现象提出了“超塑性”这一术语,并在许许多多有色金属共晶体及共析体合金中,发现了不少的延展性特别显著的特异现象。

超塑性合金是指那些具有超塑性的金属材料。

超塑性是一种奇特的现象。

具有超塑性的合金能像饴糖一样伸长10倍、20倍甚至上百倍,既不出现缩颈,也不会断裂。

在通常情况下,金属的延伸率不超过90%,而超塑性材料的最大延伸率可高达1000%~2000%,个别的达到6000%。

金属只有在特定条件下才显示出超塑性。

在一定的变形温度范围内进行低速加工时可能出现超塑性。

1920年,德国人罗森汉在锌-铝-铜三元共晶合金的研究中,发现这种合金经冷轧后具有暂时的高塑性。

最初发展的超塑性合金是一种简单的合金,如锡铅、铋锡等。

一根铋锡棒可以拉伸到原长的19.5倍,然而这些材料的强度太低,不能制造机器零件,所以并没有引起人们的重视。

60年代以后,研究者发现许多有实用价值的锌、铝、铜合金中也具有超塑性,于是前苏联、美国和西欧一些国家对超塑性理论和加工发生了兴趣。

特别在航空航天上,面对极难变形的钛合金和高温合金,普通的锻造和轧制等工艺很难成形,而利用超塑性加工却获得了成功。

到了70年代,各种材料的超塑性成型已发展成流行的新工艺,全世界都在追寻金属的超塑性,并已发现170多种合金材料具有超塑性。

热压缩7075铝合金流变应力特征

热压缩7075铝合金流变应力特征

高温变形的物理本质和规律, 建立有关流变应力 模型, 为制定和优化加工工艺参数提供依据。
本 文 在 Gleeble-1500 热 模 拟 机 上 对 7075 圆 柱试样进行高温等温压缩实验, 研究了该合金高 温塑性变形过程中的流变应力特征, 分析其高温 流变应力和在热变形条件下该合金的流变应力与 变形温度、应变速率间的关系, 为实际生产的热加 工工艺提供理论依据。
7075 合 金 高 温 变 形 时 的 流 变 应 力 行 为 与 位 错和原子的作用行为有关。稳态变形过程中, 流变 应力基本保持不变(图 1)。此时, 合金变形的实质 为位错的增殖和位错间由于相互作用而引起的相 互销毁和重组之间达到动态平衡, 合金变形组织 中的亚晶平均大小、亚晶间平均取向差以及平衡 位错密度保持基本不变, 表现出强烈的动态回复 和动态再结晶行为。由此可见, 7075 铝合金高温 变形时的组织特征亦可用稳态流变应力或 Zener-Hollomon 参数进行表征, 即变形组织和 Z 参数间存在某种对应关系, 这种关系可为合金变 形组织的预测、控制和优化提供依据。
之间的摩擦力, 在试样两端和压头上涂上石墨润 滑剂。试样取下立即水淬, 以保持材料在高温下的 组织状态。
3 讨论
3.1 应变速率对流变应力的影响
2 实验结果及分析
从图 1 可看出, 随应变速率的升高, 合金的稳 态流变应力增大, 但并不是成比例增大。通常采用
图 1 为 实 验 所 获 得 的 7075 铝 合 金 应 力- 应 不同的数学模型— ——本构方程( 或称流动方程) 来
超过 0.99。由此可以认为, 7075 铝合金在高温压 缩变形时的流变应力- 应变速率关系满足指数关 系的形式, 说明该合金高温塑性变形过程也是一 种高温蠕变的热激活过程。

英语作文-如何进行高强度间歇训练

英语作文-如何进行高强度间歇训练

英语作文-如何进行高强度间歇训练High-Intensity Interval Training (HIIT) has gained immense popularity in recent years due to its effectiveness in improving cardiovascular health, boosting metabolism, and enhancing overall fitness levels. HIIT involves alternating between short bursts of intense exercise and brief periods of rest or lower-intensity exercise. This type of training can be customized to suit individual fitness levels and goals, making it accessible to people of all fitness backgrounds. In this article, we will explore how to effectively implement high-intensity interval training into your workout routine.First and foremost, it's important to understand the principles behind HIIT. The key is to push your body to its limits during the high-intensity intervals, followed by periods of recovery to allow your heart rate to decrease. This cycle of exertion and recovery challenges your cardiovascular system and encourages your body to adapt and become more efficient at utilizing oxygen. As a result, you burn more calories both during and after your workout, leading to increased fat loss and improved endurance.To get started with HIIT, choose exercises that engage multiple muscle groups and elevate your heart rate quickly. Examples include sprinting, cycling, jumping jacks, burpees, and high knees. Aim to perform each exercise at maximum intensity for 20 to 60 seconds, followed by a recovery period of 10 to 30 seconds. Repeat this cycle for 15 to 30 minutes, depending on your fitness level and goals.When designing your HIIT workout, focus on variety and progression. Incorporate a mix of cardio, strength, and plyometric exercises to keep your body challenged and prevent plateaus. As you become fitter, gradually increase the duration of your high-intensity intervals or decrease the length of your recovery periods to intensify the workout. Additionally, consider adding resistance or increasing the difficulty of the exercises to further enhance muscle strength and endurance.Proper form is crucial during HIIT to prevent injury and maximize results. Pay attention to your posture, alignment, and breathing technique throughout each exercise. Ifyou're new to HIIT or unsure about proper form, consider working with a certified personal trainer who can provide guidance and instruction.Consistency is key when it comes to HIIT. Aim to incorporate HIIT workouts into your routine 2 to 4 times per week, allowing for adequate rest and recovery between sessions. Listen to your body and adjust the intensity and duration of your workouts as needed to avoid overtraining and burnout.In addition to the physical benefits, HIIT can also have a positive impact on your mental health. The intense bursts of exercise release endorphins, which are neurotransmitters that promote feelings of happiness and reduce stress. Incorporating HIIT into your routine can help improve your mood, boost your energy levels, and enhance your overall sense of well-being.In conclusion, high-intensity interval training is a highly effective and efficient way to improve cardiovascular health, increase metabolism, and enhance overall fitness levels. By understanding the principles of HIIT and following a well-designed workout plan, you can achieve your fitness goals and experience the numerous benefits that HIIT has to offer. So lace up your sneakers, push yourself to the limit, and unleash your full potential with HIIT!。

应变速率 英语

应变速率 英语

应变速率英语The concept of strain rate, central to materials science and engineering, refers to the rate of change of strain with respect to time. It is a crucial parameter that governs the mechanical behavior of materials under dynamic loading conditions. Understanding strain rate in the context of materials' response to external forces is essential for predicting and optimizing material performance in various applications.In the English language, the term "strain rate" is often used interchangeably with "rate of strain" or "strain rate of change." These terms describe the same phenomenon: how quickly a material deforms when subjected to external forces. The importance of strain rate lies in its ability to influence material properties such as strength, ductility, and toughness. For instance, metals and polymers often exhibit higher strength and lower ductility at higher strain rates, due to the faster accumulation of microstructural changes within the material.The study of strain rate effects is particularly relevant in dynamic loading scenarios such as impacttesting, ballistic impact, and explosive shock waves. In these situations, the duration of loading is short, and the strain rates can be extremely high. Materials musttherefore possess sufficient resistance to failure under these extreme conditions to ensure safe and reliable performance.In addition to its application in materials testing, strain rate analysis is also employed in other fields such as geophysics and civil engineering. For instance, thestudy of earthquake-resistant structures often involves understanding how materials behave at high strain rates. Similarly, in geophysics, strain rate analysis is used to investigate the deformation and flow of rocks and soils within the Earth's crust.Moreover, strain rate has implications for materials processing techniques such as metalworking, plastic molding, and glassblowing. By controlling the rate of deformation during these processes, manufacturers can achieve desired material properties and dimensional accuracy.In summary, strain rate is a fundamental concept in materials science and engineering that has wide-rangingapplications across multiple fields. Its significance liesin its ability to govern material behavior under dynamic loading conditions, influencing properties such as strength, ductility, and toughness. By understanding and manipulating strain rate, we can optimize material performance in a diverse range of applications, from automotive safety systems to earthquake-resistant infrastructure.**应变速率与材料行为:英语语境下的科学现象探索** 在材料科学和工程领域,应变速率是一个核心概念,它指的是应变随时间变化的速率。

近年内最具代表性之学理创新与应用技术突破(至多五项)

近年内最具代表性之学理创新与应用技术突破(至多五项)

一、近年內最具代表性之學理創新與應用技術突破(至多五項)。

(1) 在鋁鋰合金及鋁鋰基金屬複材方面,在國際、國內發表卅餘篇論文,並曾在國內外作過二十餘次之演講與報告;亦曾先後協同台中航發中心、金屬中心、中鋼公司、以及工研院工材所熟悉此種材料的特性。

(2) 在震波與高速負載下的金屬與金屬複材形變破壞,亦完成十餘種材料的測試與分析,建立一套動態形變破壞之微觀分析基礎。

(3) 在超塑性材料研究方面,從事將較便宜且易取得的厚板,加工製成昂貴不易買到的超塑性薄板,目前7475鋁材之最高形變量已達1500%。

曾與航發中心協力評估鋁鋰應用在飛機組件上,並已獲得國內專利。

也曾利用中鋼生產之鋁材,以熱機處理自製成長優異之超塑性薄板,單軸形變量亦達1000%以上。

而在Ti3Al基介金屬化合物超塑性,是與美國Rockwell公司合作,從事超塑機構之探討,在2 mm 板材上,已獲致1900%以上之高形變量。

(4) 在開發低溫超塑鋁合金的過程中,也進行SEM與TEM微組織觀察,對晶粒滑移與晶粒旋轉、晶粒中差排之性質、和其晶粒與相鄰晶粒之方向關係等,與機性數據與活化能印證,對超塑機構進一步認識。

(5) 最近致力於金屬複材在室溫或中高溫高速負載下的應力與應變特性,並研發細晶粒鋁基複材之低溫或高速超塑性,是相當令人興奮之題目,現在8090鋁材在350o C之低溫形變量達710%,5083鋁材在230o C之低溫形變量達511%,AZ91鎂合金在250o C之低溫形變量達1200 %,AZ31鎂合金在300o C之低溫及1x10-2 s-1之高速形變量達1000 %,6061鋁材在610o C之高溫形變量達500%,1050純鋁材在640o C之高溫形變量達210%,在6061/15%SiC(p)、2024/15%SiC(p)、及pure-Al/15%SiC(p)複材於10-1 - 10o s-1已有250%以上之高速變形量。

在過去兩年,被邀請於國際會議超塑性組發表數次,並核准專利七項,其中鋁基方面之專利技術皆已轉為中鋼或金屬中心,鎂基方面因方通過,仍在協議中。

超高韧性水泥基复合材料的波传播试验研究

超高韧性水泥基复合材料的波传播试验研究

DOI: 10.3785/j.issn.1008-973X.2020.05.002超高韧性水泥基复合材料的波传播试验研究李庆华,舒程岚青(浙江大学 建筑工程学院,浙江 杭州 310058)摘 要:为了研究超高韧性水泥基复合材料(UHTCC )中应力波的传播特性,采用Hopkinson 杆加载UHTCC 试件,测得UHTCC 在0.2、0.3、0.4、0.5 MPa 冲击气压下的应力波信号. 通过对比入射杆波形,验证相同加载条件下加载波形的一致性. 分别采用两点法和峰值法计算每种冲击气压下UHTCC 中应力波的波速,结果显示,两点法适用性较广,计算结果较稳定,利用峰值法测波速则需要入射杆和试件波阻抗相近. 计算结果显示,UHTCC 中应力波波速、衰减系数随冲击气压均无明显变化,平均波速为3.060 km/s ,平均衰减系数为2.777 m −1. 可以利用朱-王-唐本构模型参数表达材料中应力波的波速和衰减,也可以利用实测的波速和衰减系数将UHTCC 的朱-王-唐冲击本构模型表示为只含单个准静态参数的方程,从而提供通过试验直接确定UHTCC 动态本构的方法.关键词: 应力波;波速;超高韧性水泥基复合材料(UHTCC );衰减;朱-王-唐本构模型中图分类号: TU 528 文献标志码: A 文章编号: 1008−973X (2020)05−0851−07Experimental study on stress wave propagation in ultra hightoughness cementitious compositesLI Qing-hua, SHU Cheng-lan-qing(College of Civil Engineering and Architecture , Zhejiang University , Hangzhou 310058, China )Abstract: The ultra high toughness cementitious composite (UHTCC) specimens were loaded with Hopkinson bar,and the stress wave signals in UHTCC under impact pressure of 0.2, 0.3, 0.4, 0.5 MPa were measured, in order to study the propagation characteristics of stress waves in UHTCC. The consistency of the loading waveforms under the same loading conditions was verified by comparing the incident bar waveforms. The stress wave speeds in UHTCC under different impact pressures were calculated by two methods, i.e. two point method and peak value method. Results show that the two point method is more applicable and the calculation results are relatively stable.However, the peak value method requires similar wave impedance of the incident bar and the specimen. Calculation results show that the stress wave speed and attenuation coefficient in UHTCC do not change significantly with the impact pressure, and the average wave speed is 3.060 km/s, as well as the average attenuation coefficient is 2.775 m −1.The wave speed and attenuation of stress waves in material can be expressed by parameters of Zhu-Wang-Tang constitutive model. Correspondingly, the measured wave speed and attenuation coefficient can represent the Zhu-Wang-Tang impact constitutive model of UHTCC as an equation with a single quasi-static parameter. An experimental method to determine the dynamic constitutive of UHTCC directly is provided.Key words: stress wave; wave speed; ultra high toughness cementitious composite (UHTCC); attenuation;Zhu-Wang-Tang constitutive model在冲击、爆炸等高速荷载作用下,材料受荷局部的应力、应变、质点速度等在短时间内发生剧烈变化,这种剧烈扰动向外扩散,就会形成应力波[1]. 应力波的传播导致材料中的应力、应变处收稿日期:2019−04−22. 网址:/eng/article/2020/1008-973X/202005002.shtml 基金项目:国家自然科学基金资助项目(51622811,51678522).第 54 卷第 5 期 2020 年 5 月浙 江 大 学 学 报(工学版)Journal of Zhejiang University (Engineering Science)Vol.54 No.5May 2020于动态变化中,应力波反射叠加之后还可能使材料发生背面断裂[2],与静态荷载下材料的破坏方式和破坏过程完全不同. 研究材料在高速荷载下的性能和破坏模式,首先须解决应力波在材料中如何传播的问题.关于波传播的试验研究主要有2个方向:1)通过测量的波传播信号分析计算材料中的应力波传播参数,如波速、衰减系数、峰值等;2)通过波传播试验反推材料的动态本构.在波传播参数方面,Bacon[3]定义复数形式的传播系数来描述黏弹性材料中应力波的衰减和弥散,并给出该传播系数的测定方法,但该方法计算过程较复杂. Siviour[4]利用Hopkinson压杆加载有机玻璃,计算波速和弹性模量,但实验采用间接测量方式,不能考虑试件中应力波的衰减. Ju等[5]采用活性粉末混凝土(reactive powder con-crete,RPC)和聚乙烯纤维模拟天然砂岩,通过分离式Hopkinson压杆(split Hopkinson pressure bar,SHPB)研究不同孔隙体积分数对反射波峰值和耗能的影响,提出冲击荷载下孔隙的2种响应模式,但这种试验方法无法测得材料中的应力波信号.胡时胜等[6]利用Hopkinson杆层裂试验装置,通过直接在试件表面黏贴应变片测得C30混凝土中应力波的波速和衰减系数. 赖建中等[7]采用与胡时胜等[6]相似的试验方法,测得RPC中的应力波传播信号,讨论冲击气压与衰减的关系. 综合以上研究可以发现,Hopkinson杆是波传播试验中常用的加载装置,因为这种加载装置通过波形加载,避免直接撞击和爆炸的加载方式带来的不确定性[8].此外,通过在试件表面黏贴应变片,可以获得材料中的应力波传播信号,进而分析材料中应力波的波速、衰减、峰值等.在材料动态本构方面,学者们基于试验和模拟结果提出多种混凝土的本构模型[9-11]. 其中,国内学者提出的朱-王-唐(Z-W-T)本构模型[9]由于能够较好地描述材料在动、静态荷载下的非线性黏弹性行为,应用较广泛[12-13]. 目前获取材料的Z-W-T本构的主要方式是将实测应力应变曲线按Z-W-T本构方程直接拟合,通过这种方式可以直接得到材料的完整Z-W-T本构方程,且拟合效果通常较好,说明Z-W-T本构适用于描述混凝土[14]、超高性能水泥基材料(ultra-high performance ce-[15]混凝土(polypropylene fiber reinforced concrete,PFRC)[16]等水泥基材料,但这种方式得到的本构方程的适用范围有待考究.超高韧性水泥基复合材料(ultra high tough-ness cementitious composite,UHTCC)[17-18],也称工程水泥基复合材料(engineered cementitious com-posite,ECC)[19]、应变硬化水泥基材料(strain hardening cement-based composite,SHCC)[20]、高性能纤维增强水泥基材料(ultra high performance fiber reinforced cementitious composite,UHPFRCC)[21]等,通过掺入少量短纤维改善材料的微观结构[22],使其具有独特的应变硬化和韧性特征[23-25]. 在掺入适量比例的纳米S i O2和钢纤维后,UHTCC在保持原有裂缝控制能力的基础上,抗压强度提升到50 MPa以上[26],能够承受更高强度的荷载,适用于防护工程. 落锤冲击试验[27]和SHPB试验[28]都表明UHTCC具有较好的冲击韧性,冲击耗能较混凝土、钢纤维混凝土优势明显,因此,UHTCC具有可观的防护工程应用前景. 不过,作为防护工程的材料,UHTCC不仅须具备较高的抗压强度,其在冲击、爆炸、撞击等动态荷载下的响应更须明确,即须明确应力波在UHTCC材料中的传播特性.本研究通过试验研究UHTCC的应力波传播特性. 采用Hopkinson杆加载,通过在试件表面黏贴多组应变片,获取试件上不同位置的应力波信号. 由实测信号推算UHTCC中应力波的传播参数,并对比2种波速计算方法的适用性. 探讨通过试验测试UHTCC材料的朱-王-唐冲击本构参数的方法.1 试验概况1.1 试件制备本试验试件为细长圆柱体,试件长为1 000 mm、直径为76 mm. 采用精密机械加工的不锈钢模具浇筑而成. UHTCC的原材料包括:52.5水泥、粉煤灰、精细砂、纳米二氧化硅、钢纤维、聚乙烯醇(polyvinyl alcohol,PVA)纤维、高效减水剂、水. 试验材料配比如表1所示. 表中,ρB为质量浓度.按表1的比例称量各种原材料,将所有干料加入搅拌机,干拌1 min;加入水和减水剂,搅拌852浙江大学学报(工学版)第 54 卷入PVA 纤维和钢纤维,搅拌至纤维完全分散. 将搅拌好的UHTCC 浆体分3次装入模具,每次加入均振动1 min. 在浇筑完成后用塑料膜封口,在室温中放置24 h 后拆模,置于标准养护室内养护28 d.在养护结束后,将试件上、下两端面打磨平整. 测量并记录每根试件的长度和重量,试件密度取平均值为1 793.8 kg/m 3. 另外,测量本试验材料56 d 龄期的立方体抗压强度,为50.22 MPa.1.2 试验装置本试验采用直径为80 mm 的Hopkinson 杆作为加载装置,试验装置如图1所示. 撞击杆为变截面短杆,以产生短历时的三角形波. 入射杆和试件表面均布置应变片. 入射杆在固定位置处布置1组2个应变片,用于记录入射杆波形信号. 试件上应变片的位置与撞击端的距离L 分别为150、225、300、375、450 mm. 试验采用冲击气压控制加载,选取0.2、0.3、0.4、0.5 MPa 这4种冲击气压.2 试验结果2.1 加载波形一致性验证为了验证本试验装置加载波形的一致性,在相同冲击气压下,对比多次试验中入射杆上的入射波信号和反射波信号,如图2所示,图中, t 为时间,U 为电压. 图2列出在0.2 MPa 冲击气压下,7次波传播试验的入射波和反射波信号,每次试验均为初次冲击,图例中数字为试验编号. 由图2(a )可以看出,7次试验的入射波波形起伏基本一致,致,可以认为本试验装置在子弹撞击入射杆时产生的入射波形一致性较高. 由图2(b )可以看出,入射杆上的反射波波形基本一致,峰值略有差异,最大峰值差约为0.06 V ,占最大峰值的13%,反射波的一致性略差于入射波. 这与入射杆和试件接触面的微小差异有关,因为每次试验都须更换试件,试件表面的平整度、试件与入射杆的对中、试件与入射杆接触面真空脂的厚薄均会影响接触面的情况,从而导致入射杆上反射波峰值的差异. 反射波峰值差异扣除入射波峰值差异后余下部分才是入射杆和试件接触面情况引起的差异,因此,接触面引起的峰值差异约占最大峰值的6.5%,误差范围较小. 综上所述,本试验装置产生的加载波形一致性较好.2.2 UHTCC 中的实测波形图在0.2、0.3、0.4、0.5 MPa 冲击气压下,实测的典型波形曲线如图3所示. 各组气压下的实测波形均为近似三角形,且试件上不同位置的波形均保持完整,维持三角波形状. 随着冲击气压的增表 1 UHTCC 材料配合比Tab.1 Mix proportions of UHTCC材料ρB /(kg·m −3)材料ρB /(kg·m −3)胶凝材料 1 265.0微型钢纤维78.0水448.0PVA 28.7砂370.3减水剂7.3纳米SiO 240.0−−图 1 UHTCC 应力波传播试验装置Fig.1 Experimental device of stress wave propagation in UHTCC图 2 入射杆实测波形对比Fig.2 Comparison of measured waveforms on incident bar第 5 期李庆华, 等:超高韧性水泥基复合材料的波传播试验研究[J]. 浙江大学学报:工学版,2020, 54(5): 851–857.8533 UHTCC中的应力波波速和峰值衰减3.1 试件上两点测波速第1种测波速的方法是在试件上取2点进行测量,为了简化表达,称之为两点法. 两点法测波速的表达式为式中:C为材料中的应力波波速,∆L为2个测量点之间的距离,∆t为2个测量点之间应力波传播用时.式(1)中∆t的取值对波速计算影响最大. 由于波峰相对于波的起始点更易精准判断,为了准确测量∆t,取波峰到达2个应变片的时间差作为∆t.波速较快,若测量点间距过近,则∆t过小,微小的测量误差就可能引起较大的波速测量误差,因此,在测量波速时尽量选取相距较远的2个应变片作为测量点,具体波速计算数据如表2所示.表中,I为冲击气压,C0为平均波速. 除了编号为表 2 两点法得到的波速计算表Tab.2 Wave velocity calculation table calculated by two point methodI/MPa∆L/mm∆t/μs C/(km·s−1)C0/(km·s−1)0.1830097.8 3.0673.0740.20300102.4 2.9300.2530093.0 3.2260.30300102.6 2.9243.0370.3030094.8 3.1650.30300102.4 2.9300.30300105.6 2.8410.3330090.2 3.3260.40300102.2 2.9353.0760.4030086.6 3.4640.40300104.4 2.8740.4030099.0 3.0300.4530096.4 3.1123.0620.5030097.2 3.0860.5022566.2 3.3990.50300105.2 2.8520.50300104.8 2.863图 3 不同冲击气压下的典型波形图Fig.3 Waveforms under different impact pressures854浙江大学学报(工学版)第 54 卷其他试件均采用1号和5号应变片作为测量点.按冲击气压分类,列出每一个档次的冲击气压下波速的平均值,可见波速随冲击气压的波动较小,考虑到试验中不可避免的测量误差,可以认为在本次试验中波速不变,平均波速为3.060 km/s.3.2 入射杆波形测波速由计算出的波速和测得的单个波的历时可以计算出加载应力波的波长约为480 mm ,试件直径为76 mm ,则试件直径与波长比值约为0.16,当试件直径远小于波长时,满足一维应力波假定[29].根据一维应力波理论可知,试验材料的波速还可以由入射杆上的应变信号计算. 应力波在不同波阻抗的介质中传播时,会在介质界面发生反射和透射. 反射波峰值可以由入射波峰值及2种介质的波阻抗表示:式中:σR 为反射波应力;σI 为入射波应力;A 1ρ1C 1为介质1的波阻抗,A 1、ρ1、C 1分别为入射杆横截面积、密度和波速;A 2ρ2C 2为介质2的波阻抗,A 2、ρ2、C 2分别为试件的横截面积、密度和波速.根据式(2)可以将C2表示为在本试验中,A 1、ρ1、C 1、 A 2、ρ2均为已知量;σR 、σI 是待测值,可以取入射杆上入射波和反射波的应力峰值.入射杆材料屈服强度高,在本试验气压下入射杆仍处于弹性状态,所以入射杆应力峰值等于相应的应变峰值乘以入射杆材料的弹性模量. 有则式中:εI 为入射波应变峰值,εR 为反射波应变峰值,E 1为入射杆弹性模量.由此,C 2可以由入射杆上的应变表示:试件中的波速可以通过在入射杆上黏贴一个应变片,取应变信号的最大值和最小值计算得出.入射杆应变片测得的典型波形如图4所示.击入射杆产生的入射波形,第2个波为入射波在入射杆与试件界面部分反射形成的拉伸波,第3个波为反射的拉伸波传播到入射杆靠近撞击杆的自由端时发生二次反射形成的压缩波. 在计算试件中波速时,只须取第1、2个波的峰值,保留正负号. 该方法通过测峰值得到波速,简称峰值法. 峰值法以一维应力波传播理论为基础,试验可行性高,只须在入射杆上布置一个应变片,排除了不同应变片间的测量差异. 经过实际验算,采用该方法计算得到的结果离散性较大,甚至有个别波形的拉伸波峰值绝对值大于压缩波峰值,从而计算出负波速,显然不合理,部分计算结果如表3所示. 表中,U I 为入射波峰电压,U R 为反射波峰电压,C 2为计算波速. 产生如此大误差的原因,可能是UHTCC 的波阻抗相较于入射杆材料的波阻抗较小,根据反射应力(式(2))可知,当介质2的波阻抗远小于介质1的波阻抗时,反射波的绝对值与入射波绝对值相近,差值相较于峰值比例较小,易受测量误差影响. 利用式(6)计算波速主要由实测的2个峰值之间的差值决定,因此在利用入射杆波形计算时会产生巨大误差.对比分析两点法和峰值法可以看出,两点法表 3 峰值法得到的波速计算结果Tab.3 Wave velocity calculation results obtained by peakvalue methodI /MPa U I /V U R /V C 2/(km·s −1)0.180.637 60−0.574 7 1.263 80.180.127 30−0.121 80.538 00.250.216 10−0.191 8 1.449 50.30 2.538 40−2.292 2 1.240 90.453.296 96−2.782 02.063 1图 4 入射杆上一点处的典型波形Fig.4 Typical waveform at a point on incident bar第 5 期李庆华, 等:超高韧性水泥基复合材料的波传播试验研究[J]. 浙江大学学报:工学版,2020, 54(5): 851–857.855测波速适用性更广,测得结果直接可靠;峰值法测波速试验方法简便,但仅限于被测材料波阻抗与入射杆材料波阻抗在相近量级的情况,适用范围较小.3.3 UHTCC中的应力波峰值衰减波形图显示,在0.3、0.4、0.5 MPa冲击气压下,各截面峰值随着波的传播呈现较明显的下降趋势,符合黏弹性材料的衰减特性. 在0.2 MPa下的多次试验显示,波峰呈现出上下波动,没有统一的衰减趋势,可能是由于0.2 MPa冲击气压下冲击强度弱,材料尚未进入黏弹性状态,衰减趋势不明显. 根据黏弹性材料的应力波峰值呈指数衰减[6],对0.3、0.4、0.5 MPa冲击气压下的峰值进行指数拟合,各组气压下的衰减系数平均值呈现出较小的波动,0.3、0.4、0.5 MPa对应的平均衰减系数分别为2.93、2.74、2.66 m−1. 衰减系数取平均值,为2.777 m−1.4 UHTCC的朱-王-唐冲击本构参数朱-王-唐本构模型由1个弹簧(非线性)和2个Maxwell体(一个低频,一个高频)并联组成,如图5所示. 朱-王-唐本构方程如下:˙ε式中:σ为应力;ε为应变;为应变率;t为时间;等式右边前3项表征材料的非线性弹性响应,对应图5中的非线性弹簧,E0、α、β为材料的弹性参数;等式右边第1个积分项对应图5中的低频Maxwell体,用于描述低应变率下材料的黏弹性响应,E1、θ1为低频Maxwell体的弹性常数和松弛时间;等式右边第2个积分项对应高频M a x-well体,描述材料在高应变率下的黏弹性响应,E2、θ2为高频Maxwell体的相应参数.根据文献[9]对朱-王-唐本构的总结,α、β远小于E0,因此只有当ε > 0.01时,才须考虑非线性.在本试验中未出现大于0.01的应变,因此在应用朱-王-唐本构模型时可以不考虑非线性. 此外,在冲击荷载作用下,低频Maxwell体在加载结束前都不能恢复松弛,此时的低频Maxwell体将简化为一个线性弹簧,弹性常数为E1. 朱-王-唐冲击本构方程可以简写为式中:E a为2个弹簧的弹性常数之和,E a=E0+E1.结合应力波传播理论,将冲击荷载下的朱-王-唐本构代入波传播的控制方程组,求解这组偏微分控制方程组,可以得到特征波速:应力波峰值随传播距离呈指数衰减:式中:σ为一点的应力波峰值,σ*为初始应力,x为σ所在的点与初始应力点之间的距离,αa为衰减系数.通过求解可以得到衰减系数公式:由式(9)、(11),可以用C v、αa表示高频Max-well体的参数E2、θ2:将计算得到的C v、αa、ρ2代入式(12)、(13),得出UHTCC材料中E2、θ2关于E a的表达式:UHTCC的朱-王-唐冲击本构可以表示为式中:E a可以通过准静态试验测出. UHTCC的冲击朱-王-唐本构转化为只含准静态材料参数的方程. 通过波传播试验和准静态试验共同测定材料图 5 朱-王-唐本构物理模型856浙江大学学报(工学版)第 54 卷的物理意义,得到的本构方程能够真实反映材料的非线性和黏弹性特性.5 结 论(1)通过对比几次同等加载条件下入射杆上的入射波形和反射波形,验证本试验装置加载波形的一致性.(2)在波速测试方法中,两点测量法结果较为稳定准确,入射杆波形法只适用于试件波阻抗与入射杆波阻抗量级相似的情况.(3)UHTCC 中的应力波波速、峰值衰减系数随冲击气压均没有明显变化,平均波速为3.060 km/s ,平均峰值衰减系数为2.777 m −1.(4)按照朱-王-唐本构模型的定义可以将高频参数E 2、θ2用具有实际意义的材料参数表达.在通过波传播试验确定波速和衰减后,朱-王-唐冲击本构可以表示为只含单个准静态参数的方程.(5)接下来可以通过相应的准静态试验测出剩余的准静态参数,从而确定UHTCC 的朱-王-唐本构方程,并进一步通过试验检验朱-王-唐本构对UHTCC 的适用性.参考文献(References):王礼立. 应力波基础[M]. 北京: 国防工业出版社, 1985.[1]王礼立, 胡时胜, 杨黎明, 等. 材料动力学[M]. 合肥: 中国科技大学出版社, 2017.[2]BACON C. An experimental method for considering dispersionand attenuation in a viscoelastic Hopkinson bar [J]. Experimental Mechanics , 1998, 38(4): 242–249.[3]SIVIOUR C R. A measurement of wave propagation in the splitHopkinson pressure bar [J]. Measurement Science and Technology , 2009, 20(6): 1–5.[4]JU Y, YANG Y M, MAO Y Z, et al. 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Materials Transactions,V ol.43,No.1(2002)pp.78to80c 2002The Japan Institute of MetalsRAPID PUBLICATIONHigh-Strain-Rate Superplasticity in an AZ91Magnesium Alloy Processed by Ingot Metallurgy RouteHiroyuki Watanabe1,Toshiji Mukai1,Koichi Ishikawa1and Kenji Higashi21Osaka Municipal Technical Research Institute,Osaka536-8553,Japan2Department of Metallurgy and Materials Science,Osaka Prefecture University,Sakai599-8531,Japan High-strain-rate superplastic magnesium alloy,AZ91,was processed through the ingot metallurgy route.The relationship between working temperature and resulting grain size indicated that the grain size tends to decrease with decreasing working temperature in AZ91. Based on this preliminary result,the ingot was hot extruded at a relatively low temperature of523K with a reduction ratio of44.A very fine grain size of1.7µm was attained only by hot extrusion.Thefine-grained structure was stable blow573K.Owing to thefine grain size, high-strain-rate superplasticity was observed at temperatures of∼548K.(Received September21,2001;Accepted November14,2001)Keywords:magnesium alloy,grain refinement,hot extrusion,high-strain-rate superplasticity1.IntroductionRecent research activities of magnesium become higher in order to reduce the weight of components such as motor vehi-cles especially from the ecological point of view.This is not only a result of magnesium’s relatively low density,which can directly and substantially reduce weight,but is also a re-sult of its good damping characteristics,dimensional stability, machinability,and low casting cost.These attributes enable magnesium to economically replace many zinc and aluminum die castings,as well as cast iron and steel components.An AZ91alloy is the most widely used cast magnesium alloy. This is because this alloy shows a good combination of high strength at room temperature,good castability and excellent corrosion resistance.Die casting has been a principal technique for the fabri-cation of magnesium components because of its high pro-ductivity,suitable strength,quality and dimensional control. The fabrication is also performed by semi-solid process-ing of thixotropic molding.However,fabrication by plas-tic forming also has considerable potential because the al-loys have higher ductility and strength than the castings,1) and because plastic forming enables high productivity.It is expected that processes utilizing plastic forming will be developed.In wrought magnesium alloys,grain refine-ment is essential for attaining superior mechanical prop-erties such as higher strength2)and higher ductility3–6)at room temperature,and high-strain-rate superplasticity at el-evated temperatures.7)Especially,high-strain-rate superplas-ticity,defined as superplasticity occurring at strain rates at or above10−2s−1,8)is of great interest because it is ex-pected to result in economically-viable,near-net-shape form-ing techniques under the commercial hot working rates. High-strain-rate superplasticity has also been demonstrated in magnesium-based materials,especially in powder metallurgy (PM)processed materials.7)To date,however,superplastic forming of magnesium-based materials has not been adopted industrially.One of the reason is that the simple and inexpen-sive process for attaining veryfine grained materials has not been established in magnesium-based materials.Although se-vere plastic deformation,such as equal-channel-angular ex-trusion(ECAE),and PM route using rapidly solidified pow-der(RSP)are the promising route for attainingfine-grained magnesium-based materials,it is expected from the industrial point of view that the high-strain-rate superplastic materials produced by conventional working technique,such as extru-sion and rolling are to be developed.It has been pointed out that hot deformation accompanied by DRX is a promising route for refining the microstruc-ture of magnesium alloys.9)To date,grain refinement dur-ing hot deformation has also been demonstrated in ingot met-allurgy(IM)and PM AZ91alloy.10–17)The relationship be-tween working temperature and resulting grain size is shown in Fig.1for AZ91prepared by IM(extrusion,ECAE and rolling)and PM(extrusion of RSP and machined chip)routes. The grain size tends to decrease with decreasing working temperature.This suggests the strategies for grain refine-ment in magnesium:decrease the temperature in the process. The present paper was motivated by this preliminary result. The purpose of the present investigation is two-fold.First, to refine the microstructure of IM AZ91alloy by hot extru-sion at a relatively low temperature.Second,to examine the high-strain-rate superplastic behavior of the extruded mate-rial.2.ExperimentalThe material used in the present study was a commercial magnesium alloy,AZ91.The alloy was initially produced by ingot casting.The material was solution treated at686K for 48h,followed by hot extrusion at523K with a reduction ratio of44.Microstructures were observed by a color laser3D pro-file microscope using a light screen mode and a transmission electron microscope.Tensile specimens,machined directly from the extruded bars,had tensile axes parallel to the extruded direction.The specimens had a gauge length of5mm and a gauge diame-ter of2.5mm.To investigate the high-strain-rate superplasticHigh-Strain-Rate Superplasticity in an AZ91Magnesium Alloy Processed by Ingot Metallurgy Route79Fig.1The relationship between working temperature and the resulting grain size in AZ91magnesium alloy.behavior of the extruded material,constant strain rate tensile tests were carried out at1×10−2s−1at temperatures ranging from523to623K in air.In addition,a strain rate change test was carried out at548K to obtain the strain rate sensitivity exponent,m,over the wide range of strain rates.3.Results and Discussion3.1Microstructures of extruded materialThe microstructure of as-extruded AZ91was composed of equiaxed matrix grains and uniformly dispersedfine particles. The particles were observed to reside in the grain boundaries. The particle seems to be Mg17Al12.18)The particle diameter was estimated to be about0.3µm from the transmission elec-tron micrographs.The matrix grain size,d(d=1.74L;L is the linear intercept size),of the as-extruded material was mea-sured to be1.7µm.It is noted thatfine-grained AZ91was at-tained only by hot extrusion.The grain refinement is probably attributed to the dynamic recrystallization during hot extru-sion.10)The grain size of the present material is also included in Fig.1.It is evident that the small grain size of the present material is also owing to the low extrusion temperature.The typical microstructure of extruded material is shown in Fig.2after the specimen was annealed at548K for1.8ks. The grains were stillfine at this temperature.The grain sizes at given temperatures are shown in Fig.3.The grain size was remained almost unchanged at temperatures below573K,but rapidly increased at higher temperatures.It is suggested that the Mg17Al12precipitates can not contribute to pin thegrain Fig.2Typical microstructure of extruded AZ91followed by static anneal-ing at548K for1.8ks.Fig.3The variation in grain size as a function of annealing temperature in AZ91processed by various routes.boundaries no longer at high temperatures.In Fig.3,the grain sizes of AZ91alloy processed by various routes are also in-cluded.It is obvious that PM alloy processed from RSP shows the high grain size stability even at673K.This is probably associated with the existence of stable oxide particles,which are introduced during atomization process.3.2Superplastic propertiesThe variation in(a)flow stress and(b)elongation-to-failure as a function of temperature is shown in Fig.4.Theflow stress was determined at afixed strain of0.1.Theflow stress decreased monotonically with temperature below573K,but increased rapidly above this temperature and again decreased with temperature.The increase inflow stress above575K is probably associated with the rapid grain growth as has been shown in Fig.3,since theflow stress offine-grained material often depends on the grain size.The maximum elongation of 354%was obtained at a temperature of548K.The elongation value decreased at temperatures above598K in connect with the increase inflow stress and grain growth.Iwasaki et al.12) have already examined the superplastic behavior of IM AZ91 alloy at a temperature of573K.The data of IM AZ91by Iwasaki et al.12)is included in Fig.4.Their extruded material has similar grain size to the present result,although there is no description on the precipitates.It is evident that the present material exhibited lowerflow stress and larger elongation at a80H.Watanabe,T.Mukai,K.Ishikawa and K.HigashiFig.4The variation in (a)flow stress and (b)elongation-to-failure as a function of temperature at a strain rate of 1×10−2s −1of as-extruded AZ91.The data for documented IM AZ91alloy 12)is also included in thefigure.Fig.5The variation in flow stress as a function of strain rate of as-extruded AZ91at a temperature of 548K obtained by strain rate change test.temperature of 573K in spite of the similar initial grain size.The lower extrusion temperature of the present material may resulted in different distribution and size of precipitates,and thus difference in grain size stability at elevated temperature.To characterize the effect of strain rate on plastic flow be-havior,strain rate change test was carried out at 548K.The variation in flow stress as a function of strain rate is plotted in Fig.5.The flow stress for the present alloy increased with strain rate.The m -value,which was estimated from the slope of the line,exhibited 0.5in the strain rate range investigated.This high m -value of 0.5suggests the occurrence of super-plasticity.19)It was found that the high-strain-rate superplas-ticity was attained in the IM AZ91alloy processed by hot extrusion of ingot.4.SummaryHot extrusion was conducted at a relatively low tempera-ture of 523K to refine the microstructure of an ingot metal-lurgy magnesium alloy,AZ91.The resulting matrix grain size was 1.7µm.Tensile tests revealed that high-strain-rate super-plasticity was attained at ∼548K.The m -value was 0.5,and the large elongations of over 300%was obtained at a high strain rate of 1×10−2s −1.However,deformation above 598K vanished superplasticity because of the rapid grain growth.AcknowledgementsThis work was supported by “the Priority Group of Platform Science and Technology for Advanced Magnesium Alloys,Ministry of Culture,Science and Education”(11225209),and by the Light Metal Education Foundation Inc.REFERENCES1)T.Mukai,H.Watanabe and K.Higashi:Mater.Sci.Forum 350–351(2000)159–170.2)K.Kubota,M.Mabuchi and 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