Evolution of grain structure in AA2195 Al-Li alloy plate during recrystallization

《2219铝合金各向异性塑性本构模型研究》篇一一、引言随着现代工业的快速发展，铝合金因其轻质、高强、耐腐蚀等特性在航空、汽车、船舶等领域得到了广泛应用。

其中，2219铝合金因其优异的综合性能，在航空航天领域的应用尤为突出。

然而，铝合金在塑性变形过程中表现出显著的各向异性特性，这对其力学性能和加工工艺提出了更高的要求。

因此，对2219铝合金各向异性塑性本构模型的研究具有重要的理论意义和实际应用价值。

二、文献综述近年来，关于铝合金塑性变形行为的研究已成为材料科学领域的热点。

其中，各向异性塑性本构模型的研究对于理解铝合金的力学行为、预测其塑性变形过程、优化加工工艺等方面具有重要意义。

目前，关于2219铝合金的各向异性塑性本构模型研究已经取得了一定的进展，但仍然存在一些亟待解决的问题，如模型参数的准确获取、模型精度和适用性的提高等。

三、2219铝合金各向异性塑性本构模型（一）模型选择与构建针对2219铝合金的各向异性塑性本构模型，本文选择了一种典型的各向异性塑性本构模型——Hill模型进行深入研究。

Hill模型能够较好地描述金属材料的各向异性特性，且在铝合金领域得到了广泛应用。

在Hill模型的基础上，结合2219铝合金的力学性能和塑性变形行为，构建了适用于该合金的各向异性塑性本构模型。

（二）模型参数的确定模型参数的准确获取是建立各向异性塑性本构模型的关键步骤。

本文通过对2219铝合金进行单轴拉伸试验、多轴弯曲试验等，获得了大量的实验数据。

利用这些实验数据，结合数值模拟方法，确定了Hill模型中的各项参数。

四、模型验证与应用（一）模型验证为了验证所建立的2219铝合金各向异性塑性本构模型的准确性，本文将模型预测结果与实验结果进行了对比。

通过对比发现，模型预测结果与实验结果具有较好的一致性，表明所建立的模型能够较好地描述2219铝合金的各向异性塑性变形行为。

（二）模型应用各向异性塑性本构模型的建立不仅有助于理解铝合金的力学行为，还可以为其在实际应用中的优化提供理论依据。

Microstructural Evolution in Directionally Solidified Ni-Base Superalloy IN792+HfS.M.Seo1)†,I.S.Kim1),J.H.Lee2),C.Y.Jo1),H.Miyahara3)and K.Ogi4)1)High Temperature Materials Research Group,KIMS,Changwon,641-010,Korea2)Dept.of Metall.&Mater.Eng.,Changwon Univ.,Changwon,641-773,Korea3)Dept.of Mater.Sci.&Eng.,Kyushu Univ.,Fukuoka,819-0395,Japan4)Oita National College of Technology,Oita,870-0152,Japan[Manuscript received September3,2007]Microstructural evolution during directional solidification(DS)of Ni-base superalloy IN792+Hf has been in-vestigated with an emphasis on theγ precipitates and M C-type carbides.The quantitative image analyses revealed that the increase in the solidification rate up to100µm/s at constant thermal gradient of178K/cm resulted in afine and uniform distribution ofγ precipitates.The relationship between the as-castγ size and cooling rate was also determined for DS IN792+Hf.In the mean time,the M C carbide size was found to be dependent both on the solidification rate and the S/L interface morphology while the area fraction of M C carbide was significantly influenced by the S/L interface morphology.KEY WORDS:IN792;M C corbide;Gamma prime;Solidification rate1.IntroductionNi-base superalloys are extensively used for tur-bine blades and vanes in aero-and industrial gas tur-bine engines.The mechanical properties of these al-loys depend on grain structure,dendrite arm spacing,γ precipitates,γ/γ eutectic and various types of sec-ondary phase such as carbide and boride[1].IN792+Hf is a Ni-base superalloy that contains about12wt pct Cr with a high Ti/Al ratio in its al-loy chemistry.A high Ti/Al compositional ratio in this alloy,however,promotes the formation of low strength eta(Ni3Ti)phase in preference to the de-sirableγ (Ni3Al)phase due to the strong segrega-tion propensity of Ti during solidification.Recently, Seo et al.[2]have shown that microsegregation also re-sulted in the formation of Cr-rich boride phases in the vicinity of eta phase in the as-cast directional solid-ification(DS)IN792+Hf.In addition,the formation of these phases was found to be deactivated with de-creasing the solidification rate because the solid-state diffusion at lower solidification rates decreased the mi-crosegregation.Even though the effect of solidifica-tion rate on the eta and boride formation in IN792+Hf has been well established,limited information is still available regarding the effect of solidification rate on the microstructural features such as M C carbide and γ precipitates that formed during the solidification and the subsequent cooling.In the present study,a series of directional solidi-fication experiments were carried out over a range of solidification rates and the influence of solidification rate on the microstructural evolution,especially onγ precipitates and M C carbides,was investigated.2.ExperimentalThe material used in the present study is the Ni-base superalloy IN792+Hf whose chemical comp-†Senior researcher,to whom correspondence should be ad-dressed,E-mail:castme@kims.re.kr.osition is listed in Table1.Specimens of5.0mm in diameter and80mm in length were directionally solid-ified under Ar atmosphere with various solidification rates(R),R=0.5–100µm/s and constant thermal gra-dient(G)at the S/L interface,178K/cm.The S/L interface was preserved by quenching the specimens after a desired volume fraction of original liquid was solidified.The DS specimens for microstructural observation were prepared by the standard metallographic proce-dures and examined by using an optical microscope and a scanning electron microscope(SEM).Comput-erized image analysis was also performed to quantita-tively analyze the size distribution ofγ precipitates and M C carbides.3.Results and Discussion3.1As-cast microstructureDS experiments were carried out with the solidifi-cation rates of R=0.5–100µm/s under constant ther-mal gradient G=178K/cm.For these DS conditions, the S/L interface morphology of the alloy developed from planar(R=0.5µm/s),to cellular(R=1.0µm/s), and to coarse andfine dendritic(R≥5.0µm/s)with gradually increasing R.Figure1(a)shows the typical as-cast microstructure of DS IN792+Hf solidified at R=50µm/s.The as-cast microstructure was charac-terized by the dendrite core and interdendritic region, which was composed of rosette shapedγ/γ eutectic, M C carbide,eta and Cr-rich boride phases(Fig.1(b)). Thefineγ particles also precipitated in the entireγmatrix during subsequent cooling after solidification.Most of the M C carbides existed near interden-dritic area.Since the major M C forming elements Ti, Ta and Hf exhibited a partitioning tendency to liquid, these elements would be rejected into interdendritic liquid during solidification[2].Therefore,as the solid-ification proceeds,M C carbide forming elements are enriched in interdendritic liquid,which results in the facilitation of nucleation and growth of M C carbide in interdendritic area.Table 1Chemical composition of Ni-base superalloy IN792+Hf (wt pct)Al Co Cr Hf Mo Ta Ti W C B Zr Ni 3.478.712.10.891.84.23.984.30.0720.0160.03Bal.Fig.1Typical as-cast microstructure of DS IN792+Hf solidified at R =50m/s:(a)optical micrograph and (b)de-tailed SEM micrograph near interdendriticregionFig.2Solidification paths of IN792+Hf predicted byThermo-Calc equilibrium and Scheil modelThe eta and boride phases always appeared in front of the coarse γ/γ eutectic as shown in Fig.1(b).Considering that the solidification of γ/γ eutectic proceeds toward the coarse γ [3],eta and boride phases expected to be developed from the residual liquid just after the completion of γ/γ eutectic reac-tion.3.2Solidification pathIn order to examine the solidification sequence of IN792+Hf during solidification,thermodynamic cal-culations were performed using Thermo-Calc soft-ware with Ni-Data developed by Thermo Tech Ltd.(UK).Figure 2presents the solidification paths of IN792+Hf alloy calculated by Thermo-Calc equilib-rium and Scheil model.In the equilibrium model,solidification products were γphase,M C and small amount of M 3B 2.However,the Scheil calculation accounting for the non-equilibrium solidification fea-tures predicted the solidification of γ/γ eutectic and eta phase in addition to primary γ,M C and M 3B 2.The predicted solidification path by Scheil model is asfollows:liquid (L)→primary γ(1608K)→M C car-bide (1596K)→γ/γ eutectic (1467K)→M 3B 2boride (1448K)→eta phase (1261K).Both equilibrium and Scheil model predicted that M C carbide formed at 1596K,which is about 12K lower than the crystallization temperature of primary γphase.This result is comparable to the microstruc-tural observation of Sun et al.[4]who reported that M C carbide forms just below the liquidus tempera-ture of IN792+Hf.In addition,the solidification se-quence of eta and boride phases predicted by Scheil calculation corresponds to the microstructural obser-vation result.However,the Scheil model predicted a very low crystallization temperature of eta phase (1261K)compared with the reported value of about 1402K [2].This discrepancy might be caused by the Hf solubility in eta phase.The Thermo-Calc Scheil model predicted little solubility of Hf in eta phase while the experimental result reported by Seo et al.[2]clearly showed that more than 12wt pct of Hf is dis-solved in eta phase.Therefore,considering that Hf is one of the major elements comprising the eta phase,the Scheil calculation with little Hf solubility in eta phase might delay the eta phase formation to lower temperature.3.3γ precipitatesThe γ precipitates are the primary strengthen-ing phase for Ni-base superalloys.A fine and uni-formly distributed γ size results in desirable mechan-ical properties.The relationship between the mor-phology/size of γ precipitates and the solidification rate is presented in Fig.3,where the microstructure was observed at the similar position of the DS sam-ple,such as the solidification fraction (f s )is about 0.15.The γ precipitates were very large,and showed an irregular and split shape when the solidification rate is very low (Fig.3(a)and (b)).However,the γ particles became obviously fine and their morphology developed from irregular to cuboidal with increasing the solidification rate.From the SEM micrographs shown in Fig.3,the size distribution of γ precipitates and their averageFig.3Effect of solidification rate on the morphology and size ofγ particles in the dendrite core region:(a)R=0.5µm/s,(b)1.0µm/s,(c)5.0µm/s,(d)10µm/s,(e)25µm/s and(f)50µm/sFig.4Size distribution of particles in the dendrite core(a)–(f)and their average size as a function of cooling rate (G·R)Fig.5M C carbide morphology developed from various solidification rates:(a)R=1.0µm/s,(b)5.0µm/s,(c)10µm/s,(d)25µm/s,(e)50µm/s and(f)100µm/sFig.6Effect of the solidification rate (and the S/L in-terface morphology)on the average size and area fraction of M C carbidesize were determined and were summarized in Fig.4.In the case of lower solidification rates,the γ particle size distributed over a wide range (from about 0.5µm to over 1.5µm for R =0.5µm/s)while it showed uni-form size distribution as the solidification rate gradu-ally increased.Figure 4(g)shows the effect of cooling rate (G ·R )on the average γ sizes in comparison with the reported values [5,6].The average γ particle size decreased with increasing the cooling rate in the double logarithmic plot.The linear regression on the basis of the data was derived as follows:d γ =0.33(G ·R )−0.334(1)where d γ is the average size of the γ precipitates.Although the as-cast γ size linear-logarithmically de-creased with increasing the cooling rate in the present study,significant differences still remained compared with the previous studies (Fig.4(g)).This result in-dicates that the as-cast γ size might be an alloy de-pendent,i.e .chemical composition,total amount of γ forming elements and segregation behavior of al-loying elements may influence on the as-cast γ size in Ni-base superalloys.In addition,the volume fraction of γ precipitates appears obviously low at R =0.5,1.0and 5.0µm/s,where the interface morphologies are planar,cellu-lar and coarse dendritic,respectively (Fig.3(a)–(c)).This result is expected to be related with the interface morphology.Macro-segregation occurs in the planar and cellular interface formed at relatively low solidi-fication rates of 0.5and 1.0µm/s.This appears to occur some in the coarse dendritic interface morphol-ogy at 5.0µm/s in the presence of convection which forms inevitably in the Bridgman type directional solidification [9].The γ forming elements (Al,Ti,Ta,Hf)must be lack at the low solidification fraction of DS samples (f s =0.15)due to macro-segregation.Macro-segregation due to the interface morphologies,such as the planar,cellular,and coarse dendritic in-terfaces,is expected to change the volume fraction of γ in the γmatrix.3.4MC carbideM C-type carbide that formed during directional solidification of Ni-base superalloy strengthens longi-tudinal grain boundaries at elevated temperatures.Italso has a significant effect on the solidification behav-ior of Ni-base superalloys [7,8].Figure 5shows the mor-phology evolution of M C carbide during directional solidification of IN792+Hf under various solidification rates.In the lower solidification rates of R =1.0and 5.0µm/s,the morphology of MC carbide exhibited a faceted blocky shape (Fig.5(a)–(b)).As the solidifi-cation rate increased,small script type M C carbides started to form together with large blocky shaped M C carbides (Fig.5(c)),and finally most of the M C car-bide morphologies changed to dendritic script type when the solidification rate is higher than 25µm/s (Fig.5(d)–(f)).Figure 6shows the variation of average M C car-bide size and area fraction as a function of solidifica-tion rate.The average M C carbide size was found to be dependent on the S/L interface morphology as well as the solidification rate.As the S/L inter-face morphology changes from cellular to dendritic (R =1.0µm/s to 5.0µm/s),the average M C carbide size slightly increased.However,in dendritic solid-ification conditions (R ≥5.0µm/s),the M C carbide size rapidly decreased with increasing the solidifica-tion rate at slower rates of R =5.0–25µm/s,and this tendency became sluggish at relatively high solidifica-tion rate range (R ≥25µm/s).The steep decrease in M C carbide size in the solidification range of R =5.0–25µm/s,appears to be due to the evolution of script type M C carbide and the coarse inter-dendritic spac-ing may provide the larger growth of M C carbide.The area fraction of M C carbide appears to be rather dependent on the S/L interface morphology than the solidification rate.The area fraction of M C carbide increased when the S/L interface changes from cellular to dendritic morphology.However,the increase in the solidification rate did not have a significant effect on the fraction of M C carbide,about 0.76%,where the S/L interface was dendritic morphology.The area fraction of M C carbide at 1.0µm/s,showing the cellular interface,is expected to be low due to the macro-segregation of carbide form-ing elements (Ti,Ta and Hf)at the low solidification fraction of f s =0.15.The lower area fraction of γ ,which contains Ti,Ta and Al shown in Fig.3(a),may also reveal the reducing of these elements due to the micro-and macro-segregation.4.Conclusions(1)The solidification path of IN792+Hf alloy pre-dicted by Thermo-Calc Scheil model is as follows:L →primary γ→M C →γ/γ eutectic →M 3B 2→eta phase.(2)The increase in the solidification rate up to 100µm/s at a constant thermal gradient of 178K/cm resulted in a fine and uniform distribution of γ pre-cipitates within supersaturated γmatrix.The as-cast γ size appeared to be alloy dependent and a following relationship between the γ size and cooling rate was established for DS IN792+Hf:d γ =0.33(G ·R )−0.334(3)The M C carbide size was found to be depen-dent on the S/L interface morphology as well as thesolidification rate while the area faction of M C car-bide was strongly related to the S/L interface mor-phology during directional solidification.The average M C size decreased with increasing the solidification rate,but its area fraction was nearly constant where the S/L interface exhibits dendritic morphology. AcknowledgementThis work was supported by the National Research Laboratory Project of Korean Ministry of Science and Technology.The authors also acknowledge thefinancial support of Japan Society for the Promotion of Science (JSPS)through the RONPAKU fellowship.REFERENCES[1]C.T.Sims,N.S.Stoloffand W.C.Hagel:Superalloys II,Wiley,New York,NY,1986,97.[2]S.M.Seo,I.S.Kim,J.H.Lee,C.Y.Jo,H.Miyahara andK.Ogi:Metall.Mater.Trans.A,2007,38A,883. [3]Y.Zhu,S.Zhang,L.Xu,J.Bi,Z.Q.Hu and C.X.Shi:Su-peralloys1988,eds.D.N.Duhl,TMS,Warrendale,PA, 1988,703.[4]W.R.Sun,J.H.Lee,S.M.Seo,S.J.Choe and Z.Q.Hu:Mater.Sci.Eng.A,1999,271,143.[5]K.O.Yu,J.J.Nichols and M.Robinson:J.Metals,1992,21.[6]X.Guo,H.Fu and J.Sun:Metall.Mater.Trans.A,1997,28A,997.[7]S.Tin and T.M.Pollock:Meter.Sci.Eng.A,2003,A348,111.[8]S.Tin,T.M.Pollock and W.Murphy:Metall.Mater.Trans.A,2001,32A,1743.[9]J.H.Lee,S.Liu and R.Trivedi:Metall.Mater.Trans.A,2005,36A,3111.。

《2219铝合金各向异性塑性本构模型研究》篇一一、引言在材料科学和工程领域，金属合金的塑性行为研究一直是重要课题。

2219铝合金作为一种常用的高强度、高塑性的工程材料，其力学性能和塑性行为的研究对于优化其应用性能具有重要意义。

各向异性塑性本构模型是描述材料在多方向应力作用下的塑性变形行为的重要工具。

本文旨在研究2219铝合金的各向异性塑性本构模型，探讨其在不同条件下的变形行为，以期为工程应用提供理论依据。

二、材料与方法1. 材料选择与准备本研究选择2219铝合金作为研究对象。

选用具有代表性的样品，并按照相关标准进行切割和加工，以确保样品的一致性和准确性。

2. 实验方法（1）进行拉伸实验，获得材料在不同方向上的应力-应变数据。

（2）通过金相显微镜和电子背散射衍射（EBSD）技术，观察和分析材料的微观结构。

（3）建立各向异性塑性本构模型，并利用实验数据进行模型参数的拟合和验证。

三、实验结果与分析1. 应力-应变曲线分析通过拉伸实验获得2219铝合金的应力-应变曲线。

在多个方向上进行的实验表明，该合金具有明显的各向异性特征。

在特定方向上，材料表现出较高的强度和塑性。

2. 微观结构分析利用金相显微镜和EBSD技术，观察到2219铝合金的微观结构具有明显的晶粒取向和相分布特征。

这些特征对材料的塑性变形行为具有重要影响。

3. 各向异性塑性本构模型的建立与验证基于实验数据和理论分析，建立2219铝合金的各向异性塑性本构模型。

该模型能够较好地描述材料在不同方向上的塑性变形行为。

通过与实验数据的对比，验证了模型的准确性和可靠性。

四、讨论1. 各向异性来源分析2219铝合金的各向异性主要来源于其微观结构的晶粒取向和相分布特征。

这些特征导致材料在不同方向上的力学性能存在差异，从而表现出各向异性的塑性变形行为。

2. 模型应用与优化建立的各向异性塑性本构模型可以应用于工程实际中，用于预测和评估2219铝合金在多方向应力作用下的塑性变形行为。

第50卷第4期中南大学学报(自然科学版) V ol.50No.4 2019年4月Journal of Central South University (Science and Technology)Apr. 2019 DOI: 10.11817/j.issn.1672−7207.2019.04.007退火温度对纯钛TA1织构及各向异性的影响张贵华，江海涛，吴波，杨永刚，田世伟，郭文启(北京科技大学 工程技术研究院，北京，100083)摘要：通过X线衍射(XRD)和电子背散射衍射(EBSD)等分析技术，研究退火温度对冷轧态TA1钛板显微组织及织构的影响规律。

研究结果表明：TA1钛板冷轧退火后，微观组织发生再结晶并形成典型的双峰分裂基面织构特征。

在退火温度不大于700 ℃时，组织变化主要以回复与再结晶的形核生长为主，生成>011(和)3<0231 )22111(类型再结晶织构组分，此时轧制织构组分逐渐消失；当退火温度达到800 ℃时，晶粒变化以合并1><00长大为主，再结晶织构组分>1)2(的强度也继续增强。

同时，织构组分对板材的各<0011213(和>1<001132向异性有着直接影响，由于棱锥型织构>11)2<00112(再结晶织构组分特征的作用，可开动3(和>1<0011)32的滑移系统分别为易激活的柱面<a>滑移和较难开动的基面<a>滑移或棱锥面<c+a>滑移，从而导致板面内TD方向的拉伸强度比RD方向的拉伸强度大，而45°方向强度最低，从而产生较大的板面各向异性。

关键词：TA1钛板；织构；退火；再结晶；各向异性；电子背散射衍射(EBSD)中图分类号：TG146.23 文献标志码：A 文章编号：1672−7207(2019)04−0806−08 Effect of annealing temperature on texture and anisotropy ofmechanical properties of pure titanium(TA1) sheetZHANG Guihua, JIANG Haitao, WU Bo, YANG Yonggang, TIAN Shiwei, GUO Wenqi (Institute of Engineering Technology, University of Science and Technology Beijing, Beijing 100083, China)Abstract: The effect of evolution of microstructure and texture of commercially pure titanium (TA1) annealed at different temperatures was investigated by X-ray diffraction (XRD), and electron backscattered diffraction (EBSD). The results show that recovery and recrystallization of the cold rolled TA1 titanium sheet occur during the annealing process, and typical TD-split basal texture was formed. When the annealing temperature is below 700 ℃, the microstructure is characterized by recovery and recrystallization, and recrystallization texture components are presented. The as-rolled texture component is gradually weakened and disappears with the increase of the heat treatment temperature. When the annealing temperature reaches 800 ℃, the grain growth is dominated by merged-growth and the intensity of11)2(recrystallized texture component continue to increase. In addition, anisotropy11<00<03(and>1>011)32of mechanical properties of TA1 sheet is related to the texture components. Due to pyramid textures>011(3<0312 and>11(recrystallization textures, the cylinder <a> slip is respectively easier to be activated and the base <00)2211<a> slip or pyramidal plane <c+a> slip becomes more difficult to be activated respectively, which leads to greater tensilestrength in the TD direction than the RD direction of the sheet. As a result, the anisotropy of mechanical properties of TA1 sheet is caused.Key words: TA1 titanium sheet; texture; annealing; recrystallization; anisotropy; electron backscattered diffraction (EBSD)收稿日期：2018−05−15；修回日期：2018−08−27基金项目(Foundation item)：国家重点研发计划项目(2016YFB0101605) (Project(2016YFB0101605) supported by the National Key Research and Development Program of China)通信作者：江海涛，博士，教授，从事金属材料方面研究；E-mail：****************.cn第4期张贵华，等：退火温度对纯钛TA1织构及各向异性的影响807工业纯钛在航空航天、舰船、核能等高科技领域均有广泛的用途[1−4]，在实际的应用中，除了固有的腐蚀性能外，其机械性能也是设计的重要标准。

Trans.Nonferrous Met.Soc.China29(2019)1816−1823Microstructure evolution of Al−Cu−Mg alloy duringrapid cold punching and recrystallization annealingZe-yi HU1,Cai-he FAN1,Dong-sheng ZHENG1,Wen-liang LIU1,Xi-hong CHEN21.College of Metallurgy and Material Engineering,Hunan University of Technology,Zhuzhou412007,China;2.CRRC Zhuzhou Electric Locomotive Co.,Ltd.,Zhuzhou412007,ChinaReceived31October2018;accepted30June2019Abstract:The microstructure evolution of spray formed and rapidly solidified Al−Cu−Mg alloy with fine grains during rapid cold punching and recrystallization annealing was investigated by transmission electron microscopy(TEM).The results show that the precipitates of fine-grained Al−Cu−Mg alloy during rapid cold punching and recrystallization annealing mainly consist of S phase and a small amount of coarse Al6Mn phase.With the increase of deformation passes,the density of precipitates increases,the size of precipitates decreases significantly,and the deformation and transition bands disappear gradually.In addition,the grains are refined and tend to be uniform.Defects introduced by rapid cold punching contribute to the precipitation and recrystallization,and promote nucleation and growth of S phase and recrystallization.Deformation and transition bands in the coarse grains transform into deformation-induced grain boundary during the deformation and recrystallization,which refine grains,obtain uniform nanocrystalline structure and promote homogeneous distribution of S phase.Key words:Al−Cu−Mg alloy;microstructure evolution;precipitate;recrystallization;deformation band;rapid cold punching1IntroductionAl−Cu−Mg alloy has been widely applied to aerospace and military industries because of its advantage such as high strength,good formability and heat resistance[1,2].Precipitation strengthening and grain refinement are the main strengthening and toughening methods.Under the conventional T6-like heat treatment,the main strengthening phase in Al−Cu−Mg alloy is S phase with low Cu/Mg ratios (Al2CuMg)andθ'phase(Al2Cu)with high Cu/Mg ratios[3−6].Deformation not only makes the material obtain good work hardening properties,but also introduces a large number of dislocations during the deformation.Aging process after deformation can release deformation stress,promote the dispersive nucleation and growth of precipitates,and even change the characteristics and precipitation sequence of precipitates[7−10].STYLES et al[11]investigated the relationship between the decomposition sequence of supersaturated solid solution and the phase in Al−Cu−Mg alloy,and pointed out that the formation time of S phase at higher temperature is much shorter than that at lower temperature.LI et al[12]investigated the effect of pre-deformation on the microstructure of high-purity Al−Cu−Mg alloy and found that the density of S'phase(Al2CuMg)increases while its size decreases with the increase of pre-deformation degree.YIN et al[13]studied the growth behavior of S precipitation phase particles within the grains of high strength Al−Cu−Mg alloy.It was reported that the structural units in the GPB region formed around S phase at higher aging temperature(above180°C)and hindered the growth of S phase along the width direction,resulting in the growth of S phase into columnar crystal.YANG et al[14] studied the effect of applied stress on the precipitation process ofθ'and S phases in Al−Cu−Mg alloy and found that applied stress prevented the precipitation ofθ'phase by changing theθ'/S ratio during the competitive precipitation,thereby the precipitation of S phase was promoted.It can be seen that the microstructure evolution and phase structure characteristics of Al−Cu−Mg alloy have been studied under the conventional deformation and aging temperatures.In the present work,the aluminum alloy cartridgeFoundation item:Project(2019JJ60050)supported by the Natural Science Foundation of Hunan Province,China Corresponding author:Cai-he FAN;Tel:+86-731-22183432;E-mail:369581813@DOI:10.1016/S1003-6326(19)65089-2Ze-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−18231817 was prepared by rapid cold punching andrecrystallization annealing,based on the spray formedAl−Cu−Mg alloy with fine grains.The precipitationphase,grain morphology and the evolution ofdeformation band during rapid cold punching andrecrystallization annealing were studied.The interactionbetween precipitation phase and recrystallization,theformation mechanism of deformation band and its effecton grain refinement were discussed.2ExperimentalFine-grained Al−Cu−Mg alloy cylindrical billet wasprepared by spray forming on a self-developed sprayforming device SD380.The chemical composition of thealloy is shown in Table1.The cylindrical billet wasextruded into round bar with a diameter of30mm by a1250T extruding machine at723K and the extrusionratio was15:1.Cylinder samples with20mm in lengthwere cut from the bar by wire-cutting machine and thenplaced in a self-designed stamping die.After four passesof rapid cold punching and recrystallization annealing,the aluminum alloy cartridges were prepared.Theschematic diagram of rapid cold punching is shownin Fig.1.The process of rapid cold punching andrecrystallization annealing is shown in Fig. 2.Inthe case of recrystallization annealing,the correspondingTable1Chemical composition of Al−Cu−Mg alloy(wt.%)Cu Mg Mn Si Fe Al4.51 1.460.56<0.05<0.05Bal.Fig.1Schematic diagrams of rapid cold punching:a—Sample; b—Drawing die;c—Punch Fig.2Process diagram of recrystallization annealing at763K for30min and rapid cold punching at298Kheating rate was623K/min.After holding for30min, the samples were cooled to room temperature and the next cold punching was performed.The process parameters of rapid cold punching are shown in Table2.The specimens were selected on the wall of cartridges for transmission electron microscopy(TEM) analysis.The preparation process of TEM specimens was as follows.The specimens were mechanically ground to 100μm before punching,and then finely ground to 70μm.After that,the specimens were twin jet electropolished in a mixed solution of25%nitric acid and75%methanol at253K using the voltage of20V. All specimens were washed in plasma cleaner Fishione, and their fine structures were observed in a Titan G2 60−300transmission electron microscope.The electron microscopic parameters observed by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM)were as follows.Acceleration voltage was200keV,half-convergence angle of electron beam was10mrad,inner half-angle of high-angle annular probe was36mrad,and beam spot diameter was 0.20nm.Table2Process parameters of rapid cold punchingPunch Diameter/mm Velocity/(mm·s−1)One-pass1030Two-pass1425Three-pass2020Four-pass27153Results3.1Precipitation phase characteristicsThe TEM images of the precipitation phases after recrystallization annealing of Al−Cu−Mg alloy specimens with different passes are shown in Fig.3.EDS spectra of precipitation phase in Fig.3(a)are shown in Fig.4.The main precipitation phase of the alloy is S1818Ze-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−1823Fig.3TEM images of precipitation phases in Al−Cu−Mg alloy specimens under different conditions:(a)As-extruded;(b)One-pass;(c)Two-pass;(d)Three-pass;(e,f)Four-passFig.4EDS spectra of precipitation phases in Al−Cu−Mg alloy specimens:(a)Position1in Fig.3(a);(b)Position2in Fig.3(a)Ze-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−18231819phase(Al2CuMg).Due to the addition of Mn,a small amount of coarse Al6Mn phase can be observed.With the increase of deformation passes,the degree of deformation increases,the density of precipitation phase increases,the size decreases,and the precipitation phase tends to disperse.As a result of high deformation temperature of hot extruded alloy,the coarse Al6Mn phase and S phase can be observed in the alloy (Fig.3(a)).After rapid cold punching of one pass and recrystallization annealing,the size of precipitation phase significantly decreases,especially the Al6Mn phase is refined obviously and its shape is elongated(Fig.3(b)). After rapid cold punching of two or three passes and recrystallization annealing,the sizes of Al6Mn and S phases decrease further,the amount of both phases increases,and the distribution of them in matrix tends to be more uniform.The elongated Al6Mn phase decreases continuously,and the spherical Al6Mn phase increases (Figs.3(c)and(d)).Compared with the cold-punched specimens in the first three passes,the precipitation phases in the specimens through rapid cold punching of four passes and recrystallization annealing need to be observed clearly at a larger multiple.A larger multiple was used to observe the region near the grain boundary (the square area in Fig.3(e)).It is found that the nano-sized precipitation phases are uniformly distributed in the matrix,and the size and morphology of the precipitation phases are basically the same(Fig.3(f)).3.2Grain morphologyFigure5shows TEM micrographs of Al−Cu−Mg alloy specimens after rapid cold punching of different passes and recrystallization annealing.With the increase of deformation passes,both the deformation and recrystallization degrees of the specimens increase,the grain size becomes finer and finer,and the grain structure becomes more uniform.Incomplete recrystallization occurs in as-extruded alloy specimens annealed at763K for30min.Substructure with high dislocation density still exists near the recrystallization zone.The recrystallized grains are mainly in micron size,and a small number of recrystallized grains are found in the vicinity of coarse recrystallized grains(Fig.5(a)).After rapid cold punching of one pass or two passes,the grain size of the specimens is obviously refined,the recrystallization degree increases and the dislocation density decreases,but it is still incomplete recrystallization.The recrystallized grains are mainly nanocrystalline,and some recrystallized grains grow to coarse grains(Figs.5(b)and(c)).After rapid cold punching of three passes and recrystallization annealing, the specimens are fully recrystallized,and the microstructure becomes uniform.There are no coarse recrystallized grains,the recrystallized grains are all nanocrystalline,the average grain size is less than 100nm,and the dislocation density is further reduced (Fig.5(d)).When the specimens are subjected torapid Fig.5TEM images of Al−Cu−Mg alloy specimens under different conditions:(a)As-extruded;(b)One-pass;(c)Two-pass;(d)Three-pass;(e)Four-passZe-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−1823 1820cold punching of four passes and recrystallization annealing,the fully recrystallized structure is more uniform and the recrystallized grains are mainly pared with the specimens through rapid cold punching of three passes,the grain size is further refined and the average grain size is less than50nm. Due to the increase of deformation degree and strain rate, the high dislocation density produced by cold punching still exists in the local region(Fig.5(e)).3.3Deformation band and transition bandTEM images of deformation and transition bands in Al−Cu−Mg alloy specimens cold-punched with different passes are presented in Fig.6.Deformation band with about100nm in width can be observed in coarse grains after single-pass rapid cold punching(Fig.6(a)).When the rectangular region in Fig.6(a)is further enlarged,the boundary of the deformation band with about10nm in thickness can be clearly observed,which is the transition band(Fig.6(b)).The transition band is obviously narrowed after rapid cold punching deformation of two passes(Fig.6(c)),and can hardly be observed in the case of rapid cold punching deformation of three passes (Fig.6(d)).4Analysis and discussion4.1Interaction between precipitation phases andrecrystallizationThe dissolving sequence of Al−Cu−Mg alloy from high to low is generally GP region,S'(Al2CuMg), S(Al2CuMg).In this the work,GP zones,S'and S phases are found in Al−Cu−Mg alloy specimens after rapid cold punching of different passes and recrystallization annealing(Fig.7).The GP region consists of Cu and Mg atom pairs enriched on{110}crystal plane[1](Fig.7(a)). These atom pairs strengthen the alloy by pinning dislocations.The S'phase,which is semi-coherent with the matrix,is mainly formed(Fig.7(b)).The non-coherent equilibrium phase of granular S phase is formed undergoing four passes(Fig.7(c)).Previous studies have shown that the precipitation sequence of precipitates in Al−Cu−Mg alloy is related to heating temperature,deformation amount and grain size after deformation[15,16].If the heating temperature can eliminate the high stress caused by strong deformation, the sequence is first transition phase,and then stable phase.If the heating temperature cannot eliminatethe Fig.6TEM images of deformation and transition bands in Al−Cu−Mg alloy specimens under different conditions:(a,b)One-pass;(c)Two-pass;(d)Three-passZe-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−18231821 Fig.7Phase morphologies of Al−Cu−Mg alloy specimens:(a)GP zones;(b)S'phase;(c)S phasehigh stress,the grain size is ultra-fine.The transition phase is inhibited,and the stable phase is generated directly when reprecipitated.Based on the spray forming and rapid solidification technique,fine-grained Al−Cu−Mg alloy billet is prepared in this work.The Al−Cu−Mg alloy cartridge is prepared by multi-pass rapid cold punching,high temperature recrystallization annealing,rapid heating and slow cooling.With the increase of deformation passes,the density of precipitation phases increases,and their size decreases significantly(Fig.3).A large number of S'phases can be observed in the specimen,which indicates that the main dissolving process during the forming of cartridge is first transition phase,and then the stable phase(Fig.7). Meanwhile,the grain structure of the specimen tends to be homogeneous and the grains are refined to nanocrystalline(Fig.5).Further analysis shows that the main reason for the above phenomena is the interaction between precipitates and recrystallization under the condition of rapid cold punching and high temperature recrystallization annealing[5,6].Rapid cold punching significantly increases the dislocation density and becomes the most effective absorption source of vacancy, thus increasing the number of vacancies diffused to dislocation.S'phase nucleates preferentially at dislocation.The high density dislocation introduced by rapid cold punching provides the effective nucleation sites for S'phase,thereby the nucleation number of S' phase increases with the increase of rapid cold punching passes.It was reported that dissolving and recrystallization compete and interact with each other during the recrystallization annealing of supersaturated solid solution after deformation,and that the recrystallization process depends on the instantaneous equilibrium of the dissolving and recrystallization[17].In this work,the defect introduced by rapid cold punching promotes dissolving and recrystallization nucleation,and the dissolving phase particles in turn pin the grain boundaries,thereby affecting the recrystallization nucleation and growth,so as to delay the recrystallization.Further study shows that the rapid cold punching and recrystallization annealing process can obviously promote the recrystallization of spray-formed Al−Cu−Mg alloy and refine the microstructure of the specimens.The main reasons are as follows.Firstly, rapid heating in this experiment makes the dissolving particles too late to produce,reduces effectively the recrystallization temperature,and promotes the occurrence of recrystallization,leading to the precipitates formed during the subsequent recrystallization annealing to affect the recrystallization to proceed in the recrystallized grains.Obviously,the recrystallization annealing temperature is the critical factor affecting precipitation and recrystallized grains[18].Secondly, there is a simple geometric relationship between the recrystallized grain size D N and precipitation phase volume fraction f and particle radius r[18,19]:D N≈2rf−1/3(1)As can be seen in Eq.(1),the larger the volume fraction of precipitation phase is,the smaller the radius of particles is,the finer the recrystallized grains are, which is consistent with the present result.Thirdly,the larger the deformation amount is,the larger the dislocation density is,thus increasing the deformation storage energy and the driving force of recrystallization. Meanwhile,the larger the deformation amount is,the greater the maximum orientation difference of the precipitation phase edge is.The larger orientation gradient is conducive to recrystallization nucleation,thus promoting the microstructure homogeneity and grain refinement of the alloy.Finally,certain amount of Mn is added to the alloy,resulting in intragranular segregation due to the grain boundary adsorption phenomenon of Mn. Elongated Al6Mn phase is easily formed during the rapid cold punching and recrystallization annealing(Fig.3(b)). The coarse Al6Mn phase can further improve the deformation storage energy and increase the orientation difference at the edge of precipitates,thereby promoting the occurrence recrystallization.Ze-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−1823 18224.2Formation mechanism of deformation band andits effect on grain refinementDuring large deformation of high stacking fault energy aluminum alloy polycrystal,due to different crystallographic orientations of adjacent grains at grain boundaries,the deformation of each grain must be coordinated with the adjacent grains to maintain the continuity of polycrystal deformation.In this experiment, the specimens are divided into different orientation zones in coarse grains,i.e.deformation bands,because of the inhomogeneous stress of grains propagating to adjacent grains or the instability of grains during plastic deformation.Figure8(a)shows the HRTEM image of the deformation and transition bands after rapid cold punching of one pass,and Fig.8(b)shows schematic diagram of deformation and transition bands.As can be seen,region B is the original orientation region of the grain,and region C is the deformation band with different orientations from the original grain.Region A is the transition band with drastic change of orientation from region B to region C,and the orientation change across the transition band A has great gradient orientation. Studies indicate[1,20]that transition band A can be either a wide orientation region or a narrow orientation region,and can be transformed into the large angle grain boundary,i.e.deformation-induced grain boundary, under high strain rate deformation condition.The mechanism of transformation from transition band to deformation-induced grain boundary can effectively refine coarse grains and play an important role in obtaining uniform fine grain structure.Studies[20,21]demonstrate that the occurrence of deformation band in high stacking fault energy polycrystal depends on the microstructure and deformation condition,and that the grain orientation determines the rotation of grains during deformation. The rotation of each part of coarse deformed grains varies greatly under the action of adjacent fine grains, resulting in deformation band or transition band.Lower deformation temperature will increase the inhomogeneity of deformation,so it helps to cause deformation band.In this experiment,the grain morphologies of Al−Cu−Mg alloy specimens under different states are observed (Fig.5).It is found that the coarse grains exist in extruded and one pass or two passes cold-punched specimens to a certain extent.Therefore,the deformation and transition bands can be observed in the coarse grains (Figs.6(a)and(b)).However,in the specimens after cold punching of three or four passes,the grain morphology tends to be consistent,the grain size is remarkably uniform and the deformation band is difficult to be observed in the specimens(Fig.6(d)).It can be seen that the combination of rapid cold punching deformation and recrystallization annealing process,and the formation of deformation and transition bands in the coarse grains under the process plays a decisive role in the grain refinement of the alloy,and there is a high correlation amongthem.Fig.8HRTEM image(a)and schematic diagram(b)of deformation and transition bands in Al−Cu−Mg alloy specimens undergoing one-pass deformation5Conclusions(1)The precipitates of Al−Cu−Mg alloy during rapid cold punching and recrystallization annealing mainly consist of S phase and a small amount of coarse Al6Mn phase.With the increase of deformation passes, the density of precipitates increases and the size decreases significantly.(2)Rapid cold punching promotes the dissolving and recrystallization nucleation of the specimens by introducing defect,and contributes to the nucleation and growth of S'phase and recrystallization,and thus obtaining the nanocrystalline structure and dispersed S phase.(3)Rapid cold punching favors the formation of deformation and transition bands in the coarse grains, and these bands transform into deformation-induced grain boundary during the deformation and recrystallization,thus effectively refining grains and obtaining uniform fine grains.Ze-yi HU,et al/Trans.Nonferrous Met.Soc.China29(2019)1816−18231823References[1]WANG Zhu-tang,TIAN er manual for Al alloys andprocessing version[M].3rd ed.Changsha:Central South University Press,2007.(in Chinese)[2]WILLIAMS J C,STARKE J E.Progress in structural materials foraerospace systems[J].Acta Materialia,2003,51(19):5775−5799. [3]WU Cui-lan,ZHOU Bin,NIU Feng-jiao,DUAN Shi-yun,GONGXiang-peng,CHEN Jiang-hua.Deformation-inducedΩphase precipitation strengthening of AlCuMg alloy with high Cu/Mg atomic ratio[J].Journal of Hunan University,2018,45(6):1−10.(in Chinese)[4]GAZIZOV M,KAIBYSHEV R.Effect of pre-straining on the agingbehavior and mechanical properties of an Al−Cu−Mg−Ag alloy[J].Materials Science and Engineering A,2015,625(14):119−130. [5]ZHAO Y L,YANG Z Q,ZHANG Z.Double-peak age strengtheningof cold-worked2024aluminum alloy[J].Acta Materialia,2013, 61(5):1624−1638.[6]ZUIKO I S,GAZIZOV M R,KAIBYSHEV R O.Effect ofthermomechanical treatment on the microstructure,phase composition,and mechanical properties of Al−Cu−Mn−Mg−Zr alloy [J].Physics of Metals and Metallography,2016,117(9):906−919. [7]XU Fu-shun,ZHANG Jin,DENG Yun-lai,ZHANG Xin-ming.Effectof snake rolling on strength,toughness and microstructure of Al−Cu−Mg alloy plate[J].The Chinese Journal of Nonferrous Metals,2017,27(10):2005−2011.(in Chinese)[8]MIRZAEI M,ROSHAN M R,JENABALI JAHROMI S A.Microstructure and mechanical properties relation in cold rolled Al2024alloy determined by X-ray line profile analysis[J].Materials Science and Engineering A,2015,620:44−49.[9]AN Li-hui,CAI Yang,LIU Wei,YUAN Shi-jian,ZHU Shi-qiang,MENG Fan-cheng.Effect of pre-deformation on microstructure and mechanical properties of2219aluminum alloy sheet by thermomechanical treatment[J].Transactions of Nonferrous Metals Society of China,2012,22(2):370−375.[10]LI Zhou-bing,SHEN Jian,LEI Wen-ping,YAN Liang-ming,LIJun-peng,MAO Bai-ping.Effects of prestretching on precipitated phase and mechanical properties of Al−Cu−Mg−Ag alloy[J].The Chinese Journal of Nonferrous Metals,2010,20(8):1508−1512.(in Chinese)[11]STYLES M J,MARCEAU R K W,BASTOW T J,BRAND H E A,GIBSON M A,HUTCHINSON C R.The competition between metastable and equilibrium S(Al2CuMg)phase during the decomposition of Al−Cu−Mg alloys[J].Acta Materialia,2015,98(1): 64−80.[12]LI Hui-zhong,LIU Ruo-mei,LIANG Xiao-peng,DENG Min,LIAOHui-juan,HUANG Lan.Effect of pre-deformation on micro-structures and mechanical properties of high purity Al−Cu−Mg alloy [J].Transactions of Nonferrous Metals Society of China,2016,26(6): 1482−1490.[13]YIN Mei-jie,CHEN Jiang-hua,LIU Chun-hui.Effect of interruptedageing on mechanical property and microstructure of AA2024alloy [J].The Chinese Journal of Nonferrous Metals,2015,25(12): 3271−3281.(in Chinese)[14]YANG Pei-yong,ZHENG Zi-qia,XU Fu-shun,LI Shi-chen,LI Jian,ZHOU Ming.Effect of external stress on kinetics of precipitation and morphologies of precipitates in Al−Cu−Mg alloy with high Cu/Mg ratio[J].Rare Metals,2006,30(3):324−328.[15]ZHAO Yun-long,YANG Zhi-qing,ZHANG Zhen,SU Guo-yue,MAXiu-liang.Double-peak age strengthening of cold-worked2024 aluminum alloy[J].Acta Materialia,2013,61(6):1624−1638. [16]MOGHANAKI S K,KAZEMINEZHAD M.Effects ofnon-isothermal annealing on microstructure and mechanical properties of severely deformed2024aluminum alloy[J].Transactions of Nonferrous Metals Society of China,2017,27(1): 1−9.[17]ZHOU Ze-peng,ZHANG Jing,DENG Yun-lai,ZHANG Xin-ming.Creep forming heat treatment technology of Al−Cu−Mg alloy[J].The Chinese Journal of Nonferrous Metals,2017,27(8):1607−1614.[18]PONGE D,GOTTSTEIN G.Necklace formation during dynamicrecrystallization:Mechanisms and impact on flow behavior[J].Acta Materialia,1998,46(1):69−80.[19]HUMPHREYS F J.A unified theory of recovery,recrystallizationand grain growth,based on the stability and growth of cellular microstructures—I[J].Acta Materialia,1997,45(10):4231−4240. [20]ZIEGENBEIN A,HAHNER P,NEUHAUSER H.Correlation oftemporal instabilities and spatial localization during Portiven-Le Chatelier deformation of Cu−10at.%Al and Cu−15at.%Al[J].Computational Materials Science,2000,19(3):27−34.[21]JIANG Hui-feng,ZHANG Qing-chuan,JIANG Zhen-yu,ZHAOSi-min,CHEN Zhong-jia,WU Xiao-ping.Investigation on the Portevin-Le Chatelier deformation bands in Al−Cu alloys[J].Journal of Experimental Mechanics,2004,19(4):430−436.Al−Cu−Mg合金在快速冷冲及再结晶退火过程中的显微组织演变胡泽艺1，范才河1，郑东升1，刘文良1，陈喜红21.湖南工业大学冶金与材料工程学院，株洲412007；2.中国中车株洲电力机车有限公司，株洲412007摘要：采用透射电镜技术(TEM)系统研究喷射成形快速凝固细晶Al−Cu−Mg合金在快速冷冲及再结晶退火工艺过程中的显微组织演变。

Phase stability and structural features of matrix-embedded hardening precipitates in Al–Mg–Si alloys in the earlystages of evolutionM.A.van Huisa,b,*,J.H.Chena,b,M.H.F.Sluiterb,c,H.W.Zandbergenaa National Center for HREM,Kavli Institute of Nanoscience,Delft University of Technology,Lorentzweg 1,NL-2628CJ Delft,The NetherlandsbNetherlands Institute for Metals Research,Delft University of Technology,Mekelweg 2,NL-2628CD Delft,The NetherlandscVirtual Materials Laboratory,Department of Materials Science,Delft University of Technology,Mekelweg 2,NL-2628CD Delft,The NetherlandsReceived 6July 2006;received in revised form 25September 2006;accepted 16November 2006Available online 30January 2007AbstractThe strength of Al–Mg–Si aluminium alloys depends critically on nanometre-size Mg x Si y Al z -type precipitates that have a face-cen-tered cubic-based structure.In this work,a large number of early structures are investigated by means of first-principles calculations.Both platelet-type and needle-type precipitates are considered.Calculations show that for alloys with an Mg:Si ratio smaller than one,needle-type precipitates with Si pillars extending in the needle direction are energetically favoured.The formation of Si pillars and the low density cylinder is described.For alloys with an Mg:Si ratio larger than one,platelet-type precipitates consisting of stacked layers of Mg,Si and Al atoms are energetically ing both the information on the formation enthalpies and the calculated lattice mismatch with the Al matrix,it is discussed which structures are likely to be formed.The earliest,most favourable structures with high Al content are the needle-type initial-b 00Mg 2Si 3Al 6structure and the platelet-type structures {MgSi}2Al 10,{MgAl}1Al 10,Mg 3Si 2Al 5and Mg 2Si 1Al 3.Ó2007Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.Keywords:Aluminium alloys;Nanostructure;Ordering;Precipitation1.IntroductionAluminium is increasingly used in the car industry because of its combination of strength and low weight.The low weight improves the car fuel efficiency,and it is also used to adjust the weight balance of the car.After the thermal treatments applied in the aluminium produc-tion factory,further processing takes place at the car facto-ries.First,the aluminium sheets are shaped into car parts by stamping.At this stage the aluminium should be easilydeformable.After it has been painted,it undergoes the final heat treatment,which is the bake hardening process at a temperature of $180°C.Here,a high density of Mg x Si y Al z precipitates are formed that are responsible for the large increase in strength.After this last thermal treatment the material should be hard and stifffor passenger protection.In order to ensure that the material is easily deformable during stamping,hardly deformable after paint bake hard-ening and that the material properties do not degenerate during storage,the composition of the alloy and the sequence of thermal treatments need to be fine-tuned very carefully,and detailed knowledge of the evolution of pre-cipitation during all industrial processing steps is of great importance.There are two main reasons why knowledge of the early precipitation stages is important:First,in the bake1359-6454/$30.00Ó2007Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.actamat.2006.11.019*Corresponding author.Address:National Center for HREM,Kavli Institute of Nanoscience,Delft University of Technology,Lorentzweg 1,NL-2628CJ Delft,The Netherlands.Tel.:+31152782272;fax:+31152783251.E-mail address:m.a.vanhuis@tnw.tudelft.nl (M.A.van Huis).Acta Materialia 55(2007)2183–2199hardening process that is currently applied by the alumin-ium industry,the annealing temperatures are too low and the annealing times too short to reach the b00Mg5Si6phase with maximum hardness.Therefore,in the cars currently being fabricated with these6xxx Al alloys,the hardness actually depends on precipitates in an earlier stage,which makes the study of these early stages so important.Second, knowledge of the early precipitation stages is required to develop pre-ageing treatments in order to prevent natural ageing.There is a storage time of typically a few months between the production of Al sheets and further processing at car factories.This natural ageing at room temperature leads to lower hardness after the quick-bake hardening. The hypothesis is that small clusters or precipitates are formed at room temperature and that these clusters should dissolve or transform before the large monoclinic harden-ing precipitates can be formed.It is necessary to know the structure of these unwanted small clusters in order to develop better pre-ageing treatments.The smallness of the clusters at the early stages makes investigation by means of electron microscopy very demanding.Atom probefield ion microscopy(APFIM) has been applied to the early precipitates stages in AA6xxx alloys[1]and provides information on the size and compo-sition of the precipitates,but the spatial resolution is very limited and,therefore,no detailed structural information is obtained from these experiments.There is great potential for improving the properties through computer simulations to optimize the microstructure byfine-tuning the thermal treatments and compositions.In a previous work[2],the authors performedfirst-prin-ciples calculations on the phase stability of the late phases (b00to b)and discussed their mutual structural relation-ships.In this work,the early stages that still have a face-centered cubic(fcc)-based structure were investigated by means offirst-principles calculations.Ravi and Wolverton [3]and Chakrabarti and Laughlin[4]reviewed the litera-ture on AA6xxx alloys.The contents of Si and Mg are in the range0.5–1.0wt.%,usually with an Mg:Si ratio smaller than one.A large number of structures were identified or proposed,based on experimental and theoretical results [5–15].The generic precipitation sequence for the AlMgSi alloys is as follows[2]:SSSS →clusters→initial-β”→pre-β” β’(Mg9Si5)→β(stable).β”(Mg5Si6)U2,U1ð1Þwhere SSSS is the supersaturated solid solution.The vari-ous phases are listed in Table1.The phase transformation from pre-b00to b00(or directly to U2)marks the transition from fcc-based structures to non-fcc-based structures. Early phases means all the fcc-based phases(SSSS up to pre-b00),while the other phases(up to b)are the late phases. In this work,the general term‘‘GP zone’’will not be used, as this word is not specific:it has been used for all early structures and for b00.The Mg x Si y Al z precipitate structures that were reported in the literature will now be briefly dis-cussed,starting with the smallest clusters.Much is still unclear about the structure of the earliest clusters(size<5nm),and reports in the literature are partly inconsistent.In alloys with ratio Mg:Si=2,plate-let-like structures were observed by means of high resolu-tion transmission electron microscopy(HRTEM)after artificial natural ageing at a temperature of343K.In order to explain their observations,Matsuda et al.[8]suggest that the platelets are{001}fcc composite{MgSi}slices which consist of alternatingÆ100æcolumns of Mg and Si atoms.Additional Al layers can be inserted in-between the{MgSi}layers.The phases{MgSi}1Al2and {MgSi}1Al6of this type were calculated by Ravi and Wol-verton[3].This work considers many more possibilities,for different stoichiometries,arrangements and spacings of AlTable1Overview of the complex precipitation sequence in MgSiAl6xxx alloysStage Solute concentration(at.%)Shape Description,featuresSSSS0–5%a Point defects Supersaturated solid solution:substitutional Mg and Si atoms,largeconcentration of vacanciesAtomic clusters1–15%a Dimers,trimers,clusters Early clustering of solute atoms,large degeneracy in formation enthalpy of structures,entropy effects very strongClusters(1–5nm)10–25%3d,2d Spherical,APFIM[1]and platelets,HRTEM[8]Initial-b0015–45%Needle Monoclinic cell,single Si pillars[15]Pre-b0035–60%Needle Monoclinic cell[9],double Si pillars,low density cylinder appearsb0050–90%Needle monoclinic cell[5]double Si pillars,LDC underwent0.5b shiftLate phases:B0,b0,U1,U260–100%Rod/lath Collection of hexagonal,trigonal and orthorhombic phases[2]b95–100%Cube Stable Mg2Si bulk phase with anti-fluorite structure[16],excess Si forms thediamond structureFor each stage,a tentative Al concentration is given based on results found in the literature(EDS measurements,experimental and theoretical structural refinements).a No real distinction can be made between the precipitate and the matrix.The particles are too immature and contain too much Al to determine where the interface is.2184M.A.van Huis et al./Acta Materialia55(2007)2183–2199layers,as displayed in Fig.1.The thermodynamically metastable Mg 1Al 3phase (L12-type)is also included,this phase can be considered as a {MgAl}platelet with a spac-ing consisting of a single Al layer:Mg 1Al 3={MgAl}1Al 2.Murayama et al.[1]have applied three-dimensional atom probe field ion microscopy (3D-APFIM)to alloys with Mg:Si ratios of 2and 1,after artificial natural ageing at 343K.They did not find any platelets.Instead,they found spherical clusters $2nm in size,with a high atomic Al con-centration of 80%.It is not clear whether the Mg and Si atoms are arranged in any particular way.Recently,a very early monoclinic stage has been iden-tified experimentally with a composition close to Mg 2Si 3Al 6[15].This phase will be called initial-b 00,as it can be considered an early precursor of the pre-b 00phases.The Al concentration is relatively high at $60%.It is observed experimentally that the cell dimensions are com-mensurate with the Al lattice and that the atomic posi-tions are very close to that of the Al matrix.Hence,this early structure is very coherent with the embedding Al matrix.This structure and a few variations of this struc-ture are shown in Figs.2(a)–(d)and 3.The precipitates are needle-shaped,and their most important feature are the Si pillars that extend along the b -axis.It was deter-mined experimentally that the Si pillars form a stable skel-eton,while the composition of the atoms in-between the columns is variable.This is a new and conceptually useful model,because it allows for fluctuations in stoichiometry within the precipitate,and therefore it can accommodate much configurational entropy,which is very advantageous at this stage of the precipitation sequence.These early pre-cipitates are possibly needle-shaped,because growth by extension of the stable Si columns (along the b -axis)is energetically favoured.Growth in the lateral directions is not favourable,as this requires nucleation of new Si columns.The b 00phase is important because it gives the best hard-ness [9,11].It has a monoclinic structure with composition Mg 5Si 6that was found by means of quantitative electron diffraction [5].The cell dimensions and atomiccoordinatesFig.1.Platelet-type,fcc-based precipitates.The Mg 1Si 1structure (IV,Table 3)is one of the energetically most favourable fcc composite phases when the cell dimensions are confined to Al matrix values.Al layers can be inserted as (001)planes,separating {MgSi}composite planes.Here,the Matsuda platelets (II)are formed that were reported experimentally [13].{MgAl}platelets are also considered.Alternatively,Al layers can be inserted as (010)planes,thereby forming platelets with Mg/Si <1(I)or Mg/Si >1(III).M.A.van Huis et al./Acta Materialia 55(2007)2183–21992185of the Mg 5Si 6structure are shown schematically in Fig.2i,where two conventional monoclinic unit cells are displayed.The cluster of five magnesium atoms in the Mg 5Si 6struc-ture is often called the ‘‘eye’’,as they resemble eyes in the HREM images [5].In this work,the ‘‘eye’’will be called the ‘‘low density cylinder’’(LDC)as this column,with a basis of five atoms,extends along the b -axis and has a low atomic concentration.The pre-b 00structures were stud-ied by Marioara et al.[9,11]and are a variation of the b 00Mg 5Si 6structure shown in Fig.2i.In the Marioara model [9],the Mg atoms in the LDC are partly replaced by Al atoms so that the composition becomes (Mg +Al)5Si 6.Furthermore,the Mg/Al atom in the center of the LDC (Mg atom #1in Fig.2i)is shifted by 0.5b ,which brings this atom into an fcc-type configuration.Consequently,the whole precipitate structure becomes an fcc-based structure.Pre-b 00structures are displayed in Fig.2f and h.The struc-tures are relatively commensurate with the Al lattice that can be easily recognized in Fig.2a–c.The late phases (b 0,B 0,U1,U2)consist of trigonal,hexagonal and orthorhom-bic structures and were investigated in a previous work [2].Finally,the stable b phase is the cubic anti-fluorite Mg 2Si phase that is present in over-aged specimens.In order to investigate the earliest stages of precipita-tion,when precipitates are still too small to be character-ized by means of electron microscopy,electronic density functional total energy calculations were performed on selected precipitate structures.This has provided insight in the energetics of the precipitation process.We did not use the embedded atom method or relatedsemi-empiricalFig.2.Evolution of the needle-type precipitates.All structures are periodic in all dimensions,and the needle stretches along the b -axis,because this direction has the smallest lattice mismatch with the Al matrix.First,solute atoms agglomerate into parallelogram-type structures ((a)–(c)).Two such clusters together form the initial-b 00structure [15]with single Si 2columns,on positions 6and 8((d)and (e)).As more Al atoms are replaced by solute atoms,double Si 2columns (positions 6and 8and 9and 10)are formed ((f)–(j)),and the LDC is also formed (positions 2–5become Mg atoms).In the more evolved stages,slices of Mg hexagons are formed (j)that are the main structural unit of the late phases [2].2186M.A.van Huis et al./Acta Materialia 55(2007)2183–2199schemes,because they are generally not as accurate and reliable as density functional theory.In particular,the pre-ferred tetrahedral orientation of the Si atoms (with four nearest neighbours making an angle of 109°)is best approached with DFT codes.2.Methodology and computational detailsThe formation enthalpies of the phases mentioned in Tables 1–3and displayed in Figs.2–4were calculated using the first-principles VASP code [17–19],with the efficient ultrasoft (US)pseudopotentials [20]and employing both the local density approximation (LDA)and the generalized gradient approximation (GGA).Energy and k -point con-vergence was ascertained for all systems in order to limit the uncertainty to 1meV atom À1or 0.1kJ mole À1.All cal-culations were performed with an energy cut-offof 200eV.For all structures,the density of the Monkhorst–Pack k -point grid was increased until the above-mentioned accu-racy was reached.For all grids thus obtained,the lineark -point spacing was <0.017A˚À1.For the b 00Mg 5Si 6struc-ture,for example,a k -point grid of 4·16·10(pertaining to the reciprocals of the a -,b -and c -axes,respectively)was required.The calculated enthalpies of the structures cannot be directly compared with the experimental data as they depend on the choice of pseudopotentials.Formation enthalpies,formulated as differences of enthalpies,how-ever,are in principle independent of the potentials and can be compared with experimental calorimetric data,where available.The formation enthalpy with respect tothe solid solution (SS)is defined asD H form SS ðMg x Si y Al a z Þ¼H ðMg x Si y Al a z ÞÀxH ðMgsubÞÀyH ðSi sub ÞÀzH ðAl fcc Þð2ÞFig.3.Structural refinement of the initial-b 00Mg 2Si 3Al 6structure:(a)experimental coordinates;the arrows indicate which atoms can be swapped [15];(b)refined atomic positions (VASP-GGA)with the cell dimensions confined to be commensurate with the Al matrix,using a primitive C-centered cell;(c)as (b),but now using a conventional monoclinic cell,i.e.,without symmetry operations caused by the C-centering;(d)refined structure (VASP-GGA)after full relaxation,both cell dimensions and atomic positions.Structures (b)and (c)both transform into the C-centered (d)structure when the cell dimensions are relaxed.Structural details are listed in Tables 6and 7.Table 2Most favourable interatomic distances calculated using VASP-GGA,derived from the thermodynamically most stable binary phases;the L10structure for Mg 1Si 1is displayed in Fig.4(a)All structures fcc-type structures d (A ˚)Structured (A ˚)Structure Al–Al2.86fcc Al 2.86fcc Al Mg–Mg3.19hcp Mg 3.20fcc Mg a Si–Si 2.36diamond Si 2.75fcc Si aMg–Si 2.75Mg 2Si (b ) 2.89Mg 1Si 1(L10)Mg–Al 3.01Mg 1Al 1(L10) 3.01Mg 1Al 1(L10)Si–Al2.76Si 1Al 1(L10)a2.76Si 1Al 1(L10)aaNot observed experimentally.Table 3Calculated structure for the Mg 1Si 1phase,Al matrix coherent (atomic positions relaxed)and fully relaxed (both cell and ions relaxed),calculated with VASP-GGA –the structure is displayed in Fig.4(a)Property Al matrix constrained Full relaxation Space group P 2/m P 2/m a (A ˚) 4.05 4.29b (A ˚) 4.05 3.91c (A ˚) 4.05 4.29b90.0°93.6°(x ,y ,z )Mg 1(0.744,0.000,0.256)(0.735,0.000,0.265)(x ,y ,z )Si 1(0.231,0.500,0.231)(0.287,0.500,0.287)M.A.van Huis et al./Acta Materialia 55(2007)2183–21992187where the E Mg,sub and E Si,sub are the enthalpies of Mg and Si atoms on substitutional sites in the Al matrix.When the formation enthalpy is negative,there is an energy gain with respect to the solid solution.The values ofH (Mg sub )and H (Si sub )and other details can be found in Ref.[2].An important aspect that should be considered is the interaction with the aluminium matrix.Because of interface strains caused by the interaction with the surrounding Al lattice,the unit cell of the precipitate material may have a different shape and volume from that without the influ-ence of the Al lattice (at standard pressure,and considering the precipitate material as bulk).Therefore,the precipitate structures were calculated in two modes:relaxing only the atomic positions while constraining the cell dimensions to be commensurate with the Al matrix; relaxing both the atomic positions and the lattice parameters (a ,b ,c ,a ,b ,c )in order to find the lowest-enthalpy structure.The precipitate will be called commensurate with the Al lat-tice when the corner points of the unit cell of the precipitate structure coincide with lattice points of the Al fcc matrix.This is analogous to the definition used by Sutton and Ball-uffi[21]for a commensurate interface.The first mode has the advantage that it is closer to the structural properties of the precipitates as embedded in Al,the latter mode has the advantage that phases also can be studied that are less commensurate or incommensurate with the Al matrix.Finally,in order to compare structures with different Al content,the formation enthalpy can also be expressed in kilojoules per mole of solute atoms,instead of kilojoules per mole.This transformation is achieved as follows:D H SS [kJ mole solute À1]=D H SS [kJ mole À1]/(x Si +x Mg ),where x Si and x Mg are the atomic fractions of Si and Mg in the precipitate Mg x Si y Al z (x =x Mg ,y =x Si ).The use of this transformation is that the three-dimensional common tangent hull is projected on a two-dimensional plane,as explained in Ref.[2].Fig.4.Correspondence between the Mg 1Si 1Matsuda phase displayed in (a)and (b)and the pre-b 00Mg 5Si 6phase (d).The pre-b 00structure contains two slices of the Matsuda phase separated by a planar defect.Si 2pillars stretching along the b -axis are formed across this planar defect.The 0.5b shift,which is the phase transformation from pre-b 00to b 00,is shown in (d)and (e).2188M.A.van Huis et al./Acta Materialia 55(2007)2183–21993.ResultsA very large number of early structures were calculated, and the phases displayed in Figs.1–4are only a small selec-tion.There is an infinite number of possibilities for arrang-ing the three different atoms in an fcc-type arrangement,so no attempt is made to list or calculate them all.It is also not very useful to try andfind the one‘‘most favourable’’early structure,as the entropy effects are very strong in the early stages,and there will be a large variation in stoi-chiometry and arrangements,i.e.,there is not a single ‘‘most favourable’’structure.In general,however,there will be an alternation of Mg and Si atoms,as they compen-sate for their different size relative to Al atoms.While it is relatively easy to determine which phases are stable at ther-mal equilibrium,the determination of the‘‘most metasta-ble’’phases is complicated as the relative stability of metastable phases changes during the evolution of precipi-tation.The Al content in the precipitate is indicative of the progress of the precipitation.So when comparing the sta-bility of early stages,it is useful to compare structures with similar Al content.From the very large collection of calcu-lated data,we present here the structures that are energet-ically favourable(given a certain fraction of Al),and we discuss common trends and typical features(such as the Si2pillars in the needle structures).First,the main struc-tural features of the phases will be discussed,followed by a discussion of the thermodynamic stability of the phases. Finally,the lattice mismatch with the Al lattice is discussed for the phases with the most favourable formation enthalpy.3.1.Structural features and relationsThe thermal treatment of the industrial process starts with quenching to room temperature after hot rolling, giving a supersaturated solid solution with substitutional Mg and Si atoms,and a certain concentration of vacancies ($0.01–0.10at.%).In this work,the influence of vacancies on the precipitation process is not considered,as those ques-tions are better addressed by other methods(such as molec-ular dynamics and the kinetic Monte-Carlo method).The substitutional atoms will start to form small clusters,such as dimers and trimers.This is often advantageous,because the formation energy of the strainfield of such a cluster is,in general,smaller than the sum of the energy of the strain fields of the isolated point defects.The strainfields are caused by the different size of the Mg and Si atoms in com-parison with Al.When Mg and Si are combined,they com-pensate for their large and small atomic size,causing less strain in the surrounding Al lattice.A second aspect is the chemical bonding.Considering the binary phase diagrams Mg–Si,Mg–Al and Si–Al,the Si–Al bonding is the weakest bond,actually there is no stable composite AlSi bulk phase at thermal equilibrium.Mg–Al and Mg–Si both have stable bulk phases,of which the Mg–Si bond(Mg2Si structure)is the strongest.The atomic size effect translates into ideal interatomic distances,shown in Table2.So,the ideal Si–Si interatomic distance,for example,is relatively small (2.36A˚in the diamond structure),while the ideal Mg–Al and Mg–Si interatomic distances are larger than the inter-atomic distance in the Al matrix:d Al–Al=2.86A˚.The structures whose formation enthalpies and relaxed lattice parameters were calculated in this work will now be described:first,the platelet-type structures(Fig.1)that have the most favourable formation enthalpy for Mg:Si ratios larger than one,followed by the needle-type struc-tures(Fig.2)that have the most favourable formation enthalpy for Mg:Si ratios smaller than one.The quantum mechanical refinement of the Mg2Si3Al6initial-b00struc-ture,which is the earliest precipitate structure that has been fully described experimentally(Fig.3),will also be shown. Finally,the correspondence between the platelet-type phases and the needle-type phases(Fig.4),will be shown, notably the relationship between Mg1Si1and Mg5Si6.3.1.1.Platelet-type phasesThe simplest fcc-based structures that the solute atoms can form are the Mg1Si1-type L10structures,displayed in Fig.1.They consist of stacking(010)fcc planes consisting of Mg,Si and Al atoms.Please note that the Mg1Si1struc-ture in Fig.1.IV is orthorhombic and that the structure is not precisely L10-type,because the atomic positions,in particular those of the Si atoms,deviate from the perfect fcc lattice.Structural details are given in Table3and dis-played in Figs.1.IV and4(a).When the cell shape is allowed to relax,the cell adopts a diamond shape,as shown in Fig.4(a).The Mg1Si1phase has never been observed experimentally by any technique.This is probably caused by the large lattice mismatch of this structure,as will be discussed in Section3.2.2.To reduce the strain partially, Al atoms can be added in several ways.Al layers can be inserted in-between the Mg(010)and Si(010)layers,as shown in Fig.1(platelet type I for Mg/Si<1and platelet type III for Mg/Si>1).Alternatively,(001)layers of Al can be inserted parallel to the monoclinic axis,so that Al slices are inserted in-between{MgSi}composite(001) planes(platelet type II in Fig.1).From an{100}view, the{MgSi}composite planes consist of alternating rows of Mg and Si atoms,which result in alternating bright and dark spots in high-resolution transmission electron microscopy(HREM)images[8].The current calculations show that,in the case of a precipitate with Mg:Si=1,the (100)stacking parallel to the monoclinic axis is favoured over(010)stacking(similar to platelet types I or III in Fig.1,but then with one Mg ending layer and one Si end-ing layer at the top/bottom).From the discussion of the formation enthalpies dis-cussed in Section 3.2.1,it will become clear that the needle-type structures are energetically more favourable in the case of Mg:Si<1.This is probably due to the fact that,in platelet type I,there are Si//Al interfaces which are energetically less favourable from the point of view of chemical bonding(see the discussion above).The MatsudaM.A.van Huis et al./Acta Materialia55(2007)2183–21992189structures seem relatively favourable,however,for the case of structures with Mg:Si>1(platelet type III)where there are no Si–Al bonds at all.It will also be shown below that the Mg2Si1Al3phase displayed in Fig.1.III(a)has a favour-able formation enthalpy,especially when considering that the Al content is50at.%so that it can be formed at early precipitation stages.This phase consists of three-layer Mg/Si/Mg platelets,separated by three Al layers.Struc-tural details are given in Table4.Other separations were also calculated,such as separation by one Al layer (Mg2Si1Al1)or separation byfive Al layers(Mg2Si1Al5), but these turned out slightly less favourable when the struc-tures were constrained to Al lattice dimensions.Appar-ently,the three Al layers separating the Mg2Si platelets are just sufficient to accommodate the strain induced by the platelet.Furthermore,the{MgAl}1Al10structure,a {MgAl}monolayer platelet separated byfive Al layers (similar to Fig.1.II(d)),is energetically very favourable.3.1.2.Needle-type precipitatesThe phases displayed in Fig.1all have a platelet-like morphology.However,the earliest experimentally detected precipitates in AA6xxx alloys with Mg:Si<1have a spher-ical or needle-like morphology with a monoclinic unit cell [15].As will become clear from the calculation of the for-mation enthalpies,these needle-type structures are energet-ically favoured for compositions with Mg:Si<1.Several of these phases are shown in Fig.2.All these structures are commensurate or nearly commensurate with the Al fcc lat-tice,which is easily recognized in Fig.2(a)–(c).The Mg2Si3Al6structure by Chen et al.,displayed in Fig.2(d),is the earliest structure that is experimentally well described[15].Details of this structure,such as experimen-tal and relaxed coordinates,are given in Fig.4and in Tables6and7.The most important feature of this struc-ture is the Si pillar(consisting of atoms#6and#8in Fig.2(d)),which extends along the paring this structure with the more evolved pre-b00structures,such as Mg2Si6Al3(Fig.2(f))and Mg4Si7(Fig.2(h)),the main dif-ference is that the latter structures have four Si pillars in the monoclinic cell,while the initial-b00structure has only two such pillars.Starting from the Mg2Si3Al6structure by Chen et al., Mg and Si atoms were substituted by Al atoms in order tofind the earliest structure which has a stable Si pillar. This structure,which we call the cluster structure,is dis-played in Fig.2(c).It consists of a parallelogram Mg2Si2 with an additional Si atom at the corner of the parallelo-gram,whereby a Si pillar is formed.When one more atom is replaced by Al,the structures displayed in Fig.2(a)or(b) are obtained.While these phases are identical in composi-tion,the structure in Fig.2(a)(parallelogram structure)is the energetically most favourable of the two.In the struc-ture in Fig.2(b),the Si pillar is disrupted by the Al for Si substitution and,consequently,the Si–Si interatomic dis-tance is larger than the interatomic distances in the fcc Al lattice.It is the small Si–Si interatomic distance that makes the Si pillars in the later structures so favourable.As d Si–Si decreases,it becomes closer to the ideal Si–Si interatomic distance of2.35A˚in diamond Si,as shown in Table2. As the precipitation progresses,the Si–Si distance in the pillar is decreasing,as shown in Table5.d Si–Si in the pillars decreases from2.68A˚in the cluster structure to2.50A˚for the most evolved pre-b00structures.The cluster structure shown in Fig.2(c)is the earliest structure where a Si pillar (with d Si–Si<d Al matrix)is found by means of calculations. The initial-b00structure(Fig.3(d))consists of two such ‘‘clusters’’in the monoclinic cell,which are positioned with respect to each other by a translation of(1/2,1/2,0)using monoclinic lattice vectors.However,the two clusters do not have the same shape.Apparently,the strain caused by the presence of the clusters is too large to accommodate two Si pillars in the monoclinic cell when it is constrained by the Al lattice.There are two main differences between the initial-b00 structures and the pre-b00structures.In the pre-b00struc-tures,there are four Si pillars per monoclinic cell instead of two,and the low density cylinder(LDC)consisting of a ring of Mg atoms is present(see also Table1),whereas it is absent in the initial-b00structures.Considering the ini-tial-b00structure in Fig.2(d),the position of the Mg atom at position7is incompatible with the pre-b00structures which have a Si atom at that position.Therefore,we propose the transition structure shown in Fig.4(e),where this Mg atom has shifted to position2or4,thereby partly building the LDC(consisting of atoms1–5in Fig.2(g)and(i))that is so typical of the pre-b00structures.The Mg4Si7structure shown in Fig.2(g)is the energetically most favourable nee-dle-type precipitate when the cell dimensions are fully relaxed,as will be discussed below.However,when the cell dimensions are confined to be commensurate with the Al matrix,the Mg4Si8Al10structure (Fig.2(j))is the energetically most favourable structure for Mg/Si<1.The double Si pillars are enclosed by hexagons consisting of Mg atoms,and the other half of the mono-clinic cell consists of Al atoms.Considering the periodicity in three dimensions,this structure consists of slices of‘‘Mg hexagons’’oriented in{301}Al planes,separated by slices of Al with approximately equal paringTable4Calculated structure for the Mg2Si1Al3phase,coherent with the Al matrix(only atomic positions relaxed)and fully relaxed(both cell and ionsrelaxed),calculated with VASP-GGA–the structure is shown schemat-ically in Fig.1.III(a)Property Al matrix constrained Full relaxationSpace group P2/m P2/ma(A˚) 4.05 4.18b(A˚)12.1512.23c(A˚) 4.05 4.18b90.0°90.3°(x,y,z)Mg1(0.747,0.337,0.253)(0.746,0.336,0.254)(x,y,z)Si1(0.231,0.500,0.231)(0.223,0.500,0.223)(x,y,z)Al1(0.250,0.000,0.750)(0.250,0.000,0.750)(x,y,z)Al2(0.249,0.160,0.249)(0.250,0.159,0.250)2190M.A.van Huis et al./Acta Materialia55(2007)2183–2199。

2195-T6铝锂合金搅拌摩擦焊接头微观组织结构与力学性能戴翔;石磊;武传松;蒋元宁;高嵩;傅莉
【期刊名称】《焊接学报》
【年(卷),期】2022(43)6
【摘要】采用搅拌摩擦焊对2 mm厚的2 195-T6铝锂合金进行焊接,利用OM,SEM,EBSD等分析技术探讨焊接速度对接头组织结构与力学性能的影响.结果表明,搅拌头转速为800 r/min、焊接速度在120~210 mm/min范围内,焊核区晶粒均较为细小,平均晶粒尺寸约为1μm.随着焊接速度的提高,大角度晶界含量增大,焊核区的{110}<110>织构和{011}<100>戈斯织构消失.接头硬度的最低值均出现在后退侧热影响区,且在焊接速度为180 mm/min时,接头的抗拉强度与断后伸长率达到最大值,最大抗拉强度为467 MPa,约为母材的86.3%,此时断后伸长率为5.0%,断裂模式为韧性断裂,但断口呈现一定的脆性断裂特征.
【总页数】11页(P25-34)
【作者】戴翔;石磊;武传松;蒋元宁;高嵩;傅莉
【作者单位】山东大学;齐鲁工业大学;西北工业大学
【正文语种】中文
【中图分类】TG442
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1.柱形光头搅拌针搅拌摩擦焊接铝锂合金接头组织及力学性能
2.铝锂合金搅拌摩擦焊搭接接头组织及力学性能
3.一种铝锂合金搅拌摩擦焊接头力学性能及微观组织
研究4.工艺参数对铝锂合金搅拌摩擦焊搭接接头力学性能的影响5.焊前和焊后热处理对2195铝锂合金双面搅拌摩擦焊接头组织与性能的影响
因版权原因，仅展示原文概要，查看原文内容请购买。

时效过程中亚晶界析出演变对7050铝合金性能的影响顾伟;李静媛;王一德【摘要】采用光学显微镜、电子背散射衍射和透射电镜,研究亚晶界析出演变对7050 铝合金时效过程电导率和冲击韧性的影响.结果表明:亚晶界上析出相转变后,在二级时效过程中完成长大过程,并使电导率升高,冲击韧性降低.时效过程中亚晶界取向差增大,有利于η′相在亚晶界形核.一级时效升温至二级时效使亚晶界η′相转变为η相,且电导率升高13.04%,冲击韧性降低53.91%.二级时效过程中,亚晶界η相持续转变长大、无析出自由区宽化以及晶内析出量增加,导致电导率升高,冲击韧性降低.统计 Graff 试剂侵蚀金相中的晶界长度演变确定亚晶界η相的转变长大完成过程为(121℃, 360 min)+(177℃, 60 min).%The effects of precipitation evolution at sub-grain boundaries on electrical conductivity and impact toughness of 7050 aluminum alloy during aging were investigated by optical microscopy, electron back scatter diffraction and transmission electron microscopy. The results show that the electrical conductivity increases and the impact energy drops due to the transformation and growth of precipitation.η′ phase prefers to precipitate at sub-grain boundaries as the misorientation increases. At the heating stage between two-step aging, the electrical conductivity rises by 13.04% and impact toughness decreases by 53.91% as transformation fromη′ toη. The microstructure evolutions includingη phase precipitating at sub-grain boundaries, precipitate spacing increasing and precipitation-free-zone widening improve the electrical conductivity but deteriorate the impact toughness. The length of grain boundaries etched by Graff solution andviewed in the optical microscopy was counted to ensure the transformation and growth ofηphase completed at (121℃, 360min)+(177℃, 60 min).【期刊名称】《中国有色金属学报》【年(卷),期】2015(025)008【总页数】8页(P2049-2056)【关键词】7050铝合金;亚晶界析出;时效;电导率;冲击韧性【作者】顾伟;李静媛;王一德【作者单位】北京科技大学材料科学与工程学院,北京 100083;北京科技大学材料科学与工程学院,北京 100083;北京科技大学材料科学与工程学院,北京 100083【正文语种】中文【中图分类】TG146.217050 高强度铝合金由于比强度高，常用于飞机的结构材料[1-2]。

《2219铝合金各向异性塑性本构模型研究》篇一一、引言随着现代工业的快速发展，铝合金因其轻质、高强、耐腐蚀等特性在航空、汽车、船舶等领域得到了广泛应用。

其中，2219铝合金以其优异的综合性能成为一种重要的结构材料。

然而，由于其材料内部晶粒取向的多样性，2219铝合金在塑性变形过程中表现出明显的各向异性。

因此，研究其各向异性塑性本构模型，对于提高材料的成形性能、优化设计以及指导实际生产具有重要意义。

二、文献综述在过去的研究中，许多学者对铝合金的塑性本构模型进行了深入研究。

其中，各向异性塑性本构模型因能更好地描述材料在不同方向上的力学行为而备受关注。

对于2219铝合金，其各向异性主要表现在屈服行为、流动应力和塑性变形机制等方面。

目前，虽然已有一些关于2219铝合金的塑性本构模型研究，但这些模型往往只能描述某一方面的力学行为，无法全面反映其各向异性特性。

因此，进一步研究2219铝合金的各向异性塑性本构模型具有迫切的现实需求。

三、材料与方法本研究采用实验与数值模拟相结合的方法，对2219铝合金的各向异性塑性本构模型进行研究。

首先，通过单轴拉伸实验，获取材料在不同方向上的应力-应变数据。

其次，利用数值模拟软件，建立不同晶粒取向下的有限元模型，对材料的塑性变形过程进行模拟。

最后，结合实验数据与模拟结果，建立反映2219铝合金各向异性特性的塑性本构模型。

四、实验结果与分析（一）单轴拉伸实验结果通过单轴拉伸实验，我们获得了2219铝合金在不同方向上的应力-应变曲线。

从曲线中可以看出，材料在不同方向上的屈服强度、流动应力和塑性变形行为存在明显差异，这表明了其各向异性特性。

（二）数值模拟结果利用数值模拟软件，我们建立了不同晶粒取向下的有限元模型，对材料的塑性变形过程进行了模拟。

模拟结果表明，不同晶粒取向下的材料在塑性变形过程中表现出明显的差异，这进一步验证了材料的各向异性特性。

（三）塑性本构模型建立与分析结合实验数据与模拟结果，我们建立了反映2219铝合金各向异性特性的塑性本构模型。