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Article(id=1249065620055204762, tenantId=1146029695717560320, journalId=1249024468962553931, issueId=1249065613306569569, articleNumber=null, orderNo=null, doi=10.11868/j.issn.1005-5053.2025.000146, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1754236800000, receivedDateStr=2025-08-04, revisedDate=null, revisedDateStr=null, acceptedDate=1756310400000, acceptedDateStr=2025-08-28, onlineDate=1775730050338, onlineDateStr=2026-04-09, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775730050338, onlineIssueDateStr=2026-04-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775730050338, creator=13041195026, updateTime=1775730050338, updator=13041195026, issue=Issue{id=1249065613306569569, tenantId=1146029695717560320, journalId=1249024468962553931, year='2025', volume='45', issue='5', pageStart='1', pageEnd='182', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1775730048728, creator=13041195026, updateTime=1775730148042, updator=13041195026, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1249066029947757306, tenantId=1146029695717560320, journalId=1249024468962553931, issueId=1249065613306569569, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1249066029951951611, tenantId=1146029695717560320, journalId=1249024468962553931, issueId=1249065613306569569, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=161, endPage=170, ext={EN=ArticleExt(id=1249065620919231396, articleId=1249065620055204762, tenantId=1146029695717560320, journalId=1249024468962553931, language=EN, title=Numerical simulation of temperature and deformation during sintering process of ceramic shell for titanium alloy investment casting, columnId=1249065616670396851, journalTitle=Journal of Aeronautical Materials, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Titanium alloy investment castings are widely used in the aerospace industry. During the manufacturing process, titanium is prone to reacting with the ceramic shell, which leads to defects such as shell cracking and casting deformation. Therefore, it is important to investigate the temperature distribution and deformation behavior during the sintering process of ceramic shell to improve the performance of the ceramic shell and enhancing the quality of casting. An advanced Monte Carlo method is employed to establish the radiative heat transfer model. Additionally, considering the impact of thermal damage, a coupled thermo-mechanical-damage constitutive model is established. A specialized simulation software is created through secondary development based on ABAQUS to investigate the sintering process of ceramic shell. Thermo-physical parameters of the ceramic shell are measured to provide data support for the simulations. The proposed models are experimentally validated using a flat-plate specimen, and experimental results agree well with the simulated outcomes. Using the developed software, a comprehensive study is conducted on the temperature distribution and deformation behavior of the ceramic shell in an annular-stepped specimen under various process schemes. The results indicate that a non-uniform temperature distribution during the sintering process is more likely to induce significant deformation and even cracking in the shells, particularly at structural protrusions. Moreover, as the sintering temperature rises, the decreased viscosity of the glassy phase in the ceramic shell will also intensify thermal stress accumulation and localized deformation. The simulation study on the temperature distribution and deformation behavior of the ceramic shell during the sintering process provides theoretical insights and technical support for optimizing the sintering process of the ceramic shell and improving the qualification rate of titanium alloy investment castings.

, correspAuthors=Qingyan XU, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright ©2025 Journal of Aeronautical Materials. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Xuewei YAN, Shuang MAO, Qihang YANG, Juhuai MA, Xiwang QIE, Meijuan ZHANG, Hai NAN, Qingyan XU), CN=ArticleExt(id=1249065625285500984, articleId=1249065620055204762, tenantId=1146029695717560320, journalId=1249024468962553931, language=CN, title=钛合金熔模铸造陶瓷型壳焙烧过程温度与变形数值模拟, columnId=1249065616850751931, journalTitle=航空材料学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

钛合金熔模铸件广泛应用于航空航天领域，在制备过程中，钛与陶瓷型壳易发生反应，从而导致型壳开裂、铸件变形等问题。因此，开展型壳焙烧过程温度分布和变形行为研究，对于提升型壳性能、改善铸件质量具有重要意义。本工作采用改进的蒙特卡洛方法构建辐射传热模型，考虑热损伤影响，建立“热-力-损伤”力学本构模型，基于ABAQUS二次开发专用模拟软件，开展型壳焙烧过程数值模拟研究。对陶瓷型壳的关键热物性参数进行实验测试，为数值模拟提供数据支撑。通过平板试件对建立的模型进行实验验证，模拟和实验结果吻合较好。采用开发的模拟软件，对环形阶梯件陶瓷型壳不同方案焙烧过程温度分布和变形行为进行模拟研究，结果表明：焙烧过程中温度的不均匀分布会导致型壳变形甚至开裂，尤其在结构突出部位更为显著。此外，随着焙烧温度升高，型壳内部玻璃相黏度降低，也会加剧热应力积累和型壳局部变形。通过对陶瓷型壳焙烧过程温度与变形的模拟研究，为型壳焙烧工艺优化以及钛合金熔模铸件合格率提升提供理论依据和技术支撑。

, correspAuthors=许庆彦, authorNote=null, correspAuthorsNote=
许庆彦（1971—），男，博士，教授，研究方向为航空发动机高温合金涡轮叶片定向凝固多尺度、全流程建模与仿真，联系地址：北京市海淀区清华大学李兆基科技大楼（100084），E-mail：
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figureFileBig=RCRTh4EmQPjrS14R95oZeg==, tableContent=null), ArticleFig(id=1249065631925084494, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.3, caption=Three-dimensional mesh models of sintering furnace and annular-stepped specimen ceramic shell　（a）sintering furnace model and position of ceramic shell；（b）ceramic shell model and locations of temperature monitoring points, figureFileSmall=rTH9o6/AYDOMjAqfyruFFg==, figureFileBig=IsacoQdu67MMpy5GTZrB9w==, tableContent=null), ArticleFig(id=1249065632034136404, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=图3, caption=焙烧炉及环形阶梯件陶瓷型壳三维网格模型　（a）焙烧炉模型及型壳位置；（b）型壳模型及温度监测点位置, figureFileSmall=rTH9o6/AYDOMjAqfyruFFg==, figureFileBig=IsacoQdu67MMpy5GTZrB9w==, tableContent=null), ArticleFig(id=1249065632151576924, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.4, caption=Simulation results of temperature field at different time during the sintering process of flat-plate specimen　 （a）t = 1309 s；（b）t = 12109 s；（c）t = 23564 s；（d）t =25300 s, figureFileSmall=0RXe1a6gpPbFgsIhRoiz4g==, figureFileBig=jnHkuiehBf/fn3cnARqXpg==, tableContent=null), ArticleFig(id=1249065632248045923, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=图4, caption=平板试件焙烧过程不同时刻温度场模拟（a）t = 1309 s；（b）t = 12109 s；（c）t = 23564 s；（d）t =25300 s, figureFileSmall=0RXe1a6gpPbFgsIhRoiz4g==, figureFileBig=jnHkuiehBf/fn3cnARqXpg==, tableContent=null), ArticleFig(id=1249065632331932008, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.5, caption=Comparison of simulation and experiment results at different temperature testing positions during the sintering process of flat-plate specimen　（a）point 1；（b）point 2；（c）point 3；（d）point 4, figureFileSmall=nSiZGZI5xITcoZbtVMwyDA==, figureFileBig=PIeMvVVx77hKhHPbA54sIg==, tableContent=null), ArticleFig(id=1249065632461955436, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=图5, caption=平板试件焙烧过程不同测温点模拟和实验结果对比　（a）测温点1；（b）测温点2；（c）测温点3；（d）测温点4, figureFileSmall=nSiZGZI5xITcoZbtVMwyDA==, figureFileBig=PIeMvVVx77hKhHPbA54sIg==, tableContent=null), ArticleFig(id=1249065632604561778, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.6, caption=Comparison of simulation（a） and experiment（b） results of deformation after sintering of flat-plate specimen, figureFileSmall=Wu7Pvo1+WVBV6LOPLv1Isw==, figureFileBig=bxnAcjoLKvB7885/M6fGjw==, tableContent=null), ArticleFig(id=1249065634206785910, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=图6, caption=平板试件焙烧后变形量模拟（a）和实验（b）结果对比, 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tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.8, caption=Variation of temperature over time at different monitoring points with sintering scheme 3, figureFileSmall=gCBpetLf/GPlR9mBnaRR/g==, figureFileBig=Tk33JjSuJDHVVtwy7bC9ng==, tableContent=null), ArticleFig(id=1249065634714296710, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=图8, caption=焙烧方案3不同监测点温度随时间变化, figureFileSmall=gCBpetLf/GPlR9mBnaRR/g==, figureFileBig=Tk33JjSuJDHVVtwy7bC9ng==, tableContent=null), ArticleFig(id=1249065634856903051, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Fig.9, caption=Simulation results of temperature field in the ceramic shell during the holding process in stage 3 with different sintering schemes 　（a）scheme 1；（b）scheme 2；（c）scheme 3；（1）overall distribution；（2）longitudinal section, 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tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=EN, label=Tab.1, caption=

Sintering process schemes of annular-stepped specimen ceramic shell

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Sintering process schemeStage 1Stage 2Stage 3
Heating time/hHolding temperature/ ℃Holding time/hHeating time/hHolding temperature/ ℃Holding time/hHeating time/hHolding temperature/ ℃Holding time/h
1150021700219502
21500217002110002
31500217002110502
), ArticleFig(id=1249065635838370224, tenantId=1146029695717560320, journalId=1249024468962553931, articleId=1249065620055204762, language=CN, label=表1, caption=

环形阶梯件陶瓷型壳焙烧方案

, figureFileSmall=null, figureFileBig=null, tableContent=
Sintering process schemeStage 1Stage 2Stage 3
Heating time/hHolding temperature/ ℃Holding time/hHeating time/hHolding temperature/ ℃Holding time/hHeating time/hHolding temperature/ ℃Holding time/h
1150021700219502
21500217002110002
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钛合金熔模铸造陶瓷型壳焙烧过程温度与变形数值模拟
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闫学伟 1 , 毛爽 1 , 杨其航 2 , 马聚怀 2 , 郄喜望 3 , 张美娟 3 , 南海 3 , 许庆彦 2, *
航空材料学报 | 研究论文 2025,45(5): 161-170
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航空材料学报 | 研究论文 2025, 45(5): 161-170
钛合金熔模铸造陶瓷型壳焙烧过程温度与变形数值模拟
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闫学伟1, 毛爽1, 杨其航2, 马聚怀2, 郄喜望3, 张美娟3, 南海3, 许庆彦2, *
作者信息
  • 1郑州航空工业管理学院 航空发动机学院，郑州 450046
  • 2清华大学 材料学院 先进成形制造教育部重点实验室，北京 100084
  • 3中国航发北京航空材料研究院，北京 100095

通讯作者:

许庆彦（1971—），男，博士，教授，研究方向为航空发动机高温合金涡轮叶片定向凝固多尺度、全流程建模与仿真，联系地址：北京市海淀区清华大学李兆基科技大楼（100084），E-mail：
Numerical simulation of temperature and deformation during sintering process of ceramic shell for titanium alloy investment casting
Xuewei YAN1, Shuang MAO1, Qihang YANG2, Juhuai MA2, Xiwang QIE3, Meijuan ZHANG3, Hai NAN3, Qingyan XU2, *
Affiliations
  • 1School of Aero Engine，Zhengzhou University of Aeronautics，Zhengzhou 450046，China
  • 2Key Laboratory for Advanced Materials Processing Technology（Ministry of Education），School of Materials Science and Engineering，Tsinghua University，Beijing 100084，China
  • 3AECC Beijing Institute of Aeronautical Materials，Beijing 100095，China
出版时间: 2025-10-01 doi: 10.11868/j.issn.1005-5053.2025.000146
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摘要
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钛合金熔模铸件广泛应用于航空航天领域，在制备过程中，钛与陶瓷型壳易发生反应，从而导致型壳开裂、铸件变形等问题。因此，开展型壳焙烧过程温度分布和变形行为研究，对于提升型壳性能、改善铸件质量具有重要意义。本工作采用改进的蒙特卡洛方法构建辐射传热模型，考虑热损伤影响，建立“热-力-损伤”力学本构模型，基于ABAQUS二次开发专用模拟软件，开展型壳焙烧过程数值模拟研究。对陶瓷型壳的关键热物性参数进行实验测试，为数值模拟提供数据支撑。通过平板试件对建立的模型进行实验验证，模拟和实验结果吻合较好。采用开发的模拟软件，对环形阶梯件陶瓷型壳不同方案焙烧过程温度分布和变形行为进行模拟研究，结果表明：焙烧过程中温度的不均匀分布会导致型壳变形甚至开裂，尤其在结构突出部位更为显著。此外，随着焙烧温度升高，型壳内部玻璃相黏度降低，也会加剧热应力积累和型壳局部变形。通过对陶瓷型壳焙烧过程温度与变形的模拟研究，为型壳焙烧工艺优化以及钛合金熔模铸件合格率提升提供理论依据和技术支撑。

熔模铸造  /  陶瓷型壳  /  焙烧过程  /  数值模拟

Titanium alloy investment castings are widely used in the aerospace industry. During the manufacturing process, titanium is prone to reacting with the ceramic shell, which leads to defects such as shell cracking and casting deformation. Therefore, it is important to investigate the temperature distribution and deformation behavior during the sintering process of ceramic shell to improve the performance of the ceramic shell and enhancing the quality of casting. An advanced Monte Carlo method is employed to establish the radiative heat transfer model. Additionally, considering the impact of thermal damage, a coupled thermo-mechanical-damage constitutive model is established. A specialized simulation software is created through secondary development based on ABAQUS to investigate the sintering process of ceramic shell. Thermo-physical parameters of the ceramic shell are measured to provide data support for the simulations. The proposed models are experimentally validated using a flat-plate specimen, and experimental results agree well with the simulated outcomes. Using the developed software, a comprehensive study is conducted on the temperature distribution and deformation behavior of the ceramic shell in an annular-stepped specimen under various process schemes. The results indicate that a non-uniform temperature distribution during the sintering process is more likely to induce significant deformation and even cracking in the shells, particularly at structural protrusions. Moreover, as the sintering temperature rises, the decreased viscosity of the glassy phase in the ceramic shell will also intensify thermal stress accumulation and localized deformation. The simulation study on the temperature distribution and deformation behavior of the ceramic shell during the sintering process provides theoretical insights and technical support for optimizing the sintering process of the ceramic shell and improving the qualification rate of titanium alloy investment castings.

investment casting  /  ceramic shell  /  sintering process  /  numerical simulation
闫学伟, 毛爽, 杨其航, 马聚怀, 郄喜望, 张美娟, 南海, 许庆彦. 钛合金熔模铸造陶瓷型壳焙烧过程温度与变形数值模拟. 航空材料学报, 2025 , 45 (5) : 161 -170 . DOI: 10.11868/j.issn.1005-5053.2025.000146
Xuewei YAN, Shuang MAO, Qihang YANG, Juhuai MA, Xiwang QIE, Meijuan ZHANG, Hai NAN, Qingyan XU. Numerical simulation of temperature and deformation during sintering process of ceramic shell for titanium alloy investment casting[J]. Journal of Aeronautical Materials, 2025 , 45 (5) : 161 -170 . DOI: 10.11868/j.issn.1005-5053.2025.000146
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熔模铸造作为一种精密成形技术，具有成形快捷、尺寸精度高、表面粗糙度低等优点，广泛应用于航空航天、工业制造、汽车、医疗等领域[1-3]。钛合金具有密度低、比强度高、耐高温及耐腐蚀性强等特点，常应用于制备航空航天关键结构件[4-5]。据统计，当前航空航天领域90%以上钛合金铸件均采用熔模铸造技术制备[6]。而在钛合金熔模铸造过程中，型壳质量直接影响铸件尺寸精度、表面质量、力学性能等。此外，钛合金在高温下化学活性极高，易与坩埚、型壳等发生反应，导致凝固缺陷频发[7-8]。因此，为制备高质量高性能的钛合金铸件，要求型壳具有良好的高温强度、热震稳定性、化学惰性等[9]。陶瓷型壳制备工序较为复杂，主要包含蜡模组装、涂覆浆料、撒砂干燥、脱蜡、焙烧等，尤其在焙烧过程，易发生物理和化学变化，如烧结收缩、相变、应力演化等行为，对型壳甚至铸件的最终性能产生较大影响[10]。因此，深入探究焙烧过程型壳的温度分布和力学演化行为对相变和宏观变形的影响规律，进而优化焙烧工艺参数，对于提升型壳和铸件质量具有重要意义。
近年来，国内外研究人员针对陶瓷型壳制备和焙烧开展广泛研究。范李鹏等[11]采用碳酸锆铵黏结剂和氧化钇制备钛合金熔模铸造型壳，对型壳面层和背层进行热重分析-差式扫描量热法（thermogravimetry-differential scanning calorimetry，TG-DSC）分析，研究表明，Y2O3陶瓷型壳室温强度、高温强度和残余强度能够满足钛合金熔模铸造对型壳的强度要求。Dubrovin等[12]通过添加TiO2和Al粉复合添加剂，在相对较低的焙烧温度下，获得高强度和热化学稳定性较好的α-Al2O3陶瓷型壳，以避免对超高温设备的依赖。Chen等[13]研究颗粒分布和烧结温度对Al2O3陶瓷性能的影响，研究发现，增加细粉末比例可降低浆料黏度，优化颗粒分布能够减少烧结收缩。Venkat等[14]研究不同Al2O3含量和硅溶胶黏结剂对浆料特性、生坯与焙烧后强度以及透气性的影响，成功制备出尺寸稳定性较好的单晶高压涡轮叶片熔模铸造莫来-Al2O3陶瓷型壳。Zhang等[15]研究烧结温度和硅树脂含量对陶瓷型壳性能的影响，结果表明，硅树脂含量为20%（质量分数，下同）、烧结温度为1300 ℃时，陶瓷型壳弯曲强度达到最大值，为提升陶瓷型壳的性能提供有效途径。近年来，3D打印技术也逐步用于制备复杂结构的陶瓷型壳。Xu等[16]采用光固化3D打印与凝胶注模技术制备Al2O3陶瓷型壳，并通过添加蓝晶石增强型壳性能，研究表明，蓝晶石分解产生的体积膨胀可有效抑制烧结收缩与孔隙率。Li等[17]采用3D立体光刻技术制备Al2O3陶瓷样品，研究烧结温度对微观组织和力学性能的影响，结果表明，随着烧结温度升高，陶瓷样品抗弯强度增加，孔隙率降低。综上所述，通过实验探究型壳的焙烧等制备工艺，对于提升型壳质量和性能起到重要的推动作用，但也存在耗时耗力、成本昂贵等局限，且往往受限于实验条件难以实现工艺参数的精准调控。借助数值模拟技术，对型壳焙烧过程的温度场、应力场及其烧结收缩行为进行模拟仿真，可显著降低研发成本与周期。王玉莲等[18]基于型壳在不同温度下物性变化，建立升温、保温和降温阶段的“热-力”耦合模型，研究熔模铸造型壳焙烧过程变形行为，并通过实验验证模型可靠性，模拟结果误差小于15%。崔新鹏等[19]对铝矾土-硅溶胶型壳抗弯弹性模量和平均线膨胀系数进行测量，并基于ProCAST软件对钛合金骨架进行应力模拟。金煜俊等[20]通过测量陶瓷型壳参数，建立传热模型，基于逆向凝固理论开发温度场模拟求解器，研究复杂薄壁骨架型壳的升温与降温规律，研究发现，复杂型壳尖角部位温度变化速率较大，易导致开裂。
总之，目前针对型壳焙烧的研究大多还依赖“试错”实验，模拟相关研究还较少，专用模拟软件几乎空白。针对这些问题，本工作采用改进的蒙特卡洛方法构建陶瓷型壳焙烧过程辐射传热模型[21]，考虑热损伤的影响，建立型壳焙烧过程力学本构模型[22-24]。基于ABAQUS二次开发专用模拟软件，探究型壳焙烧过程温度分布与力学演化行为。通过实验测定型壳关键热物性参数，为数值模拟提供必要的数据支撑。利用平板试件进行焙烧实验，设置多个测温点验证模型的准确性。采用开发的模拟软件，对环形阶梯件陶瓷型壳的焙烧过程进行数值模拟，探究不同焙烧方案型壳温度分布和应力变形行为，分析温度梯度及相变行为与型壳变形之间的关联，为型壳的制备提供理论参考。
1　实验方法
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1.1　模型验证及热物性参数测试实验
本工作采用的陶瓷型壳是由Al2O3、SiO2和Y2O3陶瓷浆料通过多次浸涂和撒砂制备而成，其中外层为Al2O3和SiO2，最内层为Y2O3，如图1（a）所示。采用平板试件进行模型验证，平板试件尺寸为180 mm×109 mm×25 mm。设置4个测温点追踪不同位置的温度变化情况，并将测试和模拟结果进行对比，测温点1、2和4位于平板试件角部，测温点3位于平板试件中心，如图1（b）所示。考虑到陶瓷试件在焙烧过程中发生复杂的物理和化学变化，因此采用三阶段焙烧工艺：第一阶段为升温1 h，500 ℃保温2 h；第二阶段为升温1 h，700 ℃保温2 h；第三阶段为升温1 h，1050 ℃保温4 h。
为获得模拟所需参数，对型壳部分热物性参数进行测试。分别采用耐驰LFA467导热仪、TA Q600同步热分析仪和IET-1600 VP高温动态弹性性能测试仪测试型壳热扩散系数α、比热容c和弹性模量E，试样尺寸分别为10 mm×10 mm×2 mm、2 mm×2 mm×2 mm和150 mm×37 mm×9.7 mm，测试温度范围均为25～1200 ℃。根据热扩散系数、比热容和密度乘积得到导热系数λ，测得的热物性参数如图2所示。
1.2　几何模型及模拟方案
采用UG软件分别建立焙烧炉、平板试件和环形阶梯件陶瓷型壳的几何模型。其中焙烧炉尺寸为3400 mm×2200 mm×2200 mm，在焙烧炉两侧装有加热单元。为了方便边界条件赋值，实际模拟过程中，将加热单元简化为炉壁两侧的加热面；焙烧炉的网格尺寸为50 mm，网格量为38128，如图3（a）所示。环形阶梯件陶瓷型壳由浇注系统和圆环阶梯组成，总高度为410 mm，平均厚度约10 mm，网格尺寸为5 mm，网格量为331865，放置于焙烧炉中心位置，型壳底部铺设有耐火砖，如图3（b）所示。数值模拟过程中，设置3个温度监测点（图3（b）），监测点1位于浇注系统底部，监测点2位于环形铸件型壳的中间部位，监测点3位于浇口杯处，观察焙烧过程中型壳不同部位温度变化情况。为考察焙烧温度的影响，设置3种不同焙烧方案，如表1所示，其中第三阶段焙烧保温温度分别为950、1000 ℃和1050 ℃，保温时间均为2 h。为实现陶瓷型壳焙烧过程数值模拟，对边界条件、温度载荷及受力情况等进行设置。基于建立的辐射传热模型，设置射线数和辐射率，其中射线条数为1000，加热面和型壳表面的辐射率为0.9，焙烧炉其他表面的辐射率为0.75，焙烧炉内表面设置为热绝缘，焙烧炉和型壳的初始温度和环境温度均设置为22 ℃。此外，通过传热分析获得不同焙烧阶段型壳的温度载荷信息，然后将节点温度作为边界条件加载到型壳进行变形分析。根据设定的焙烧方案，在瞬态求解器中设置焙烧开始和结束时间以及时间步长，获得焙烧过程中型壳的温度场分布情况，并对型壳不同部位监测点温度变化进行记录和分析。
2　结果与讨论
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2.1　平板试件焙烧过程数值模拟及实验验证
平板试件焙烧过程不同时刻温度场模拟结果如图4所示。从图中可以看出，平板试件在焙烧过程中升温呈明显的非均匀性，尤其是在初始升温阶段（图4（a）），平板试件边缘由于受加热体直接辐射温度迅速升高，而在平板试件内部和底部升温较慢。这种温度梯度主要是由热辐射传递的滞后性和陶瓷材料自身的热传导特性所导致。随着焙烧时间增加（图4（b）），热量逐步向内部传递，但试件边缘和其他部位仍存在较大温差。此外，当温度升高到500～650 ℃时，平板试件处于相变温度区间，内部晶型转变和玻璃相形成可能因温度不均而分布不一致，从而影响组织均匀性和力学性能。当进入高温焙烧升温阶段（图4（c））时，试件边缘和其他部位的温差更为显著，这种过大的温差，可能会引起热应力集中，进而增加变形或开裂的风险。当进入高温焙烧保温阶段（图4（d））时，平板试件的温度场并未立即达到预设值1050 ℃，不同部位仍存在温差。随着焙烧时间增加，持续的热量输入使试样温度逐渐趋于均匀。由于陶瓷材料的热传导性能较差，因此，适当延长保温时间，可以使热量充分扩散，进而减少应力集中，降低变形或开裂的风险。
平板试件焙烧过程4个测温点（图1（b））的模拟和实验结果如图5所示。可以看出，由于测温点1、2和4位于平板试件边缘，距离加热单元较近，升温速率较大；测温点3位于平板试件中心，热量传递滞后，升温速率较小，且最高温度值略低于边缘区域，这与陶瓷材料热传导性能较差的特性一致。由于测温点1距离炉门较近，炉门的密封性略差，存在一定对流散热，导致其温度值低于测温点2和4。总体来看，模拟和实验结果吻合较好，尤其是在高温焙烧阶段，模拟和实验结果差别很小，从而验证建立模型的可靠性。而在初始保温阶段，实验结果略高于模拟结果，可能是由于加热功率的波动或局部热辐射增强。在建模过程中，仅考虑辐射换热，忽略对流和热传导的影响，而实际上，焙烧炉内空气存在自然对流，尤其在炉门附近。同时，平板试件放置于炉内，底部和炉体之间热传导也未考虑，从而产生误差。在数值模拟过程中使用陶瓷材料的热物性参数（如比热、导热系数等）是通过小尺寸试样测试得到的，而实际试件往往存在浆料涂覆不均、孔隙率等问题，也在一定程度影响模拟结果的准确性。
平板试件焙烧后变形量的模拟和实验结果如图6所示。可以看出，在平板试件边缘，尤其角部区域变形较大，中心区域变形较小。这是由于焙烧过程中平板试件的边缘受热辐射更直接、温度梯度更大，导致热应力的非均匀分布。变形量与温度场分布（图4）密切相关，在高温区（边缘）因热膨胀受限产生压应力，而低温区（中心）受拉应力，从而导致平板试样产生翘曲变形。因此，在实际焙烧过程中，需要对边缘区域增加支撑结构使其受热均匀，减少开裂风险。由图6（a）可以看出，平板试样焙烧后经模拟预测最大变形量约为0.77 mm；由于变形量较小，且受测量方法限制，实验测量值约为0.65 mm，二者存在一定误差。产生误差的原因一方面是由于实验过程中平板试件与炉体接触存在微小摩擦阻力，而在模拟过程中假设其为自由变形，未考虑约束效应；另一方面，构建的本构模型采用连续损伤力学模型，未能真实反映陶瓷材料内部结构的离散特征。总体来说，通过实验初步验证该模型对平板试件焙烧过程中变形趋势的预测能力，为复杂结构陶瓷型壳的变形分析奠定基础。
2.2　环形阶梯件陶瓷型壳焙烧过程数值模拟
为探究环形阶梯件陶瓷型壳在不同焙烧阶段的温度变化，对表1中方案3（第三阶段保温温度为1050 ℃，保温时间为2 h）型壳焙烧过程的温度变化进行分析，如图7所示。可以看出，在焙烧过程中型壳不同部位的温度变化存在差异，这是由型壳自身结构以及与焙烧炉加热单元的相对位置不同导致的。在初始升温阶段（图7（a）），加热单元的热量通过辐射传递到型壳表面，使其温度迅速升高，型壳内部以及被遮挡部位（如型壳底部）升温相对较慢，这是由于热量需要经型壳表面通过热传导传递。当进入第一阶段保温时（图7（b）），型壳表面的温度逐步上升到所设定的温度，型壳内部温度略低，随着焙烧时间增加，型壳温度分布逐渐趋于一致，约为500 ℃。第二阶段和第一阶段焙烧过程的温度变化情况类似，进入升温阶段，型壳温度逐渐升至700 ℃（图7（c）），随着保温时间增加，型壳各部位温度趋于均匀分布（图7（d））。需要指出的是，第一阶段焙烧过程中，型壳内成分和组织变化较小；第二阶段焙烧过程中，型壳内部发生相变，并逐步形成低黏度液态玻璃相[18,20]。由图7（e）可以看出，焙烧温度从700 ℃上升到1050 ℃过程中，型壳表面升温明显先于内部，并且由于浇口杯和直浇道的位置较高，与加热单元距离较近，使浇口杯及直浇道上部的温度比型壳下部上升快。这种焙烧过程中产生的温度不均匀现象是导致热应力的原因之一，严重时可能导致型壳发生变形甚至开裂。第三阶段保温过程中，随着焙烧时间增加，型壳各部位温度逐步均匀（图7（f）），此时型壳内部将持续发生相变，直至最终形成稳定性较好的玻璃相，进而抑制晶粒长大，提升型壳致密度。
为更加直观地观察焙烧过程中型壳局部位置的温度场变化规律，对型壳不同部位进行温度监测，监测点位置如图3（b）所示，方案3中3个监测点温度随时间变化如图8所示。可以看出，3个监测点温度变化与设定的升温速率及保温时间基本保持一致。在初始升温阶段，温度曲线有所波动，这是由型壳受到加热单元的热辐射，不同部位升温速率存在差异导致的。当进入第一阶段保温过程时，可以发现，在开始一段时间内温度并未达到设定的500 ℃，这是由于热量传输需要一定时间；因此，在实际焙烧过程中，适当增加保温时间可以使型壳内溶剂得到充分挥发。而在第二和第三升温阶段，由于热量积累，升温速率较为稳定，与预设温度保持一致。研究表明，过高的升温速率会使型壳不同位置之间温差增大，型壳产生变形或开裂的可能性增大，升温速率过低，一方面会导致陶瓷内部形成粗大组织，降低型壳力学性能，另一方面会延长焙烧时间[25]。因此，型壳焙烧过程中，选择适中的升温速率尤为重要。第二阶段保温过程中，型壳内部开始发生晶型转变，在该阶段型壳内部生成低黏度的液态玻璃相，型壳的热稳定性和力学性能显著降低，此时型壳极易发生变形[18]。第三阶段焙烧过程中，随着温度升高，玻璃相黏度降低，极易进入晶界内，型壳强度降低，显微结构也发生变化。此时，型壳在自身重力和热载荷作用下发生变形。可以发现，监测点3位于浇口杯附近，由于结构突出，靠近焙烧炉加热单元，直接受到热辐射，升温速率最高。监测点2位于型壳主体部位，厚度较大，热阻较高，导致升温滞后。
3种焙烧方案下陶瓷型壳第三阶段保温过程温度场模拟结果如图9所示，保温温度分别为950、1000 ℃和1050 ℃。可以看出，在不同焙烧方案下，型壳的温度变化趋势大致相同，型壳表面温度高于内部，这是由于型壳表面从焙烧炉的加热单元获取热量后逐步传递到型壳内部，导致型壳不同部位存在一定温差。在方案1中（图9（a-1）和（a-2）），型壳温度分布范围约为939～950 ℃，温差相对较小，约为11 ℃，表明此时型壳的热量传递较为均衡，有利于减少热应力集中，降低型壳变形或开裂风险。方案2中（图9（b-1）和（b-2）），型壳温度分布范围约为970～1000 ℃，最大温差约30 ℃，局部区域存在微小波动，但整体均匀性较好。在方案3中（图9（c-1）和（c-2）），型壳温度分布范围约为1020～1050 ℃，温度梯度较大，这可能与高温热辐射效率的变化以及陶瓷内部相变加剧有关。型壳几何结构对温度分布也具有显著影响，在靠近加热单元的浇口杯和直浇道等位置由于直接受热，温度相对较高，型壳底部或被遮挡的区域因热传递滞后，温度上升较慢，这种差异在高温条件下（如方案3）更为明显，可能导致局部热应力集中，进而影响型壳力学性能和烧结质量。焙烧温度和保温时间对型壳相变行为有较大影响。焙烧温度过低可能使玻璃相形成不充分，导致型壳致密性下降。焙烧温度过高，可能因玻璃相流动性增强导致晶界迁移过快，形成粗大晶粒或孔隙，降低型壳力学性能。如果保温时间不足，相变反应可能进行不完全，导致莫来石或玻璃相分布不均，型壳强度和热稳定性下降。延长保温时间可使Al2O3和SiO2充分反应，形成均匀的莫来石网络结构，从而提高型壳高温稳定性。如果保温时间过长，会导致晶粒过度生长，从而降低型壳力学性能。
3种焙烧方案下陶瓷型壳应力分布与变形量模拟结果分别如图10和图11所示。可以看出，型壳应力分布与变形量存在一定对应关系，在应力集中区域型壳变形显著，尤其是结构突出、热辐射直接作用的部位。3种焙烧方案下，型壳变形趋势较为一致，浇口杯和直浇道等突出结构因直接受热且力学支撑较弱，变形量较大，底部区域由于热传递滞后以及结构稳定性较高，变形量较小。在方案1中，应力分布相对均匀，最大应力值较低，主要集中在型壳过渡区域，如浇口杯与直浇道连接处（图10（a-1）和（a-2））。型壳整体变形较小（图11（a-1）和（a-2）），这是由于较低温度梯度（约11 ℃）和缓慢的玻璃相形成过程，可减少热应力集中。在方案2中，型壳出现明显的应力集中，尤其在浇口杯和直浇道上部区域，应力值显著升高（图10（b-1）和（b-2）），这与该区域温度梯度增大和玻璃相黏度降低密切相关。型壳变形量有所增加，局部区域（如浇口杯附近）出现较大变形（图11（b-1）和（b-2）），这与温度梯度较大（约30 ℃）以及相变过程中热应力积累有关。在方案3中，热应力在结构突出部位积累加剧（图10（c-1）和（c-2））。型壳变形最为显著，最大变形位于浇口杯处，约为2.65 mm（图11（c-1）和（c-2）），这是由于高温导致玻璃相黏度急剧降低，晶界迁移加速，加之较大温度梯度，使型壳局部区域出现严重变形，甚至可能引起开裂风险。经过对比发现，随着焙烧温度升高，温度梯度增大，玻璃相黏度降低，导致热应力累积加剧，型壳整体变形量递增，局部区域（如浇口杯和直浇道连接处）甚至出现非连续变形，可能引发微裂纹或尺寸超差。这种非均匀变形现象与温度场模拟结果（图7和图9）吻合较好，进一步验证热应力是导致型壳变形的主要因素之一。变形分布也与材料相变密切相关，相变诱导体积效应（如莫来石形成过程的收缩）以及材料非均质性（内层Y2O3与外层Al2O3/SiO2的热膨胀系数差异）进一步加剧变形分布复杂性。
3　结论
收起
（1）采用改进的蒙特卡洛方法并考虑热损伤影响，建立陶瓷型壳焙烧过程温度场模型和力学本构模型；采用平板试件对模型进行实验验证，模拟和实验结果吻合较好。
（2）对陶瓷型壳不同温度下的比热容、导热系数、弹性模量等热物性参数进行实验测试，并通过计算得到导热系数，为数值模拟提供必要的数据支撑。
（3）对环形阶梯件陶瓷型壳焙烧过程进行数值模拟，探究3种焙烧方案下陶瓷型壳的温度场、应力分布和变形行为。结果表明，陶瓷型壳在焙烧过程中温度分布不均匀会导致型壳产生变形甚至开裂，尤其在结构突出部位更为显著。此外，随着焙烧温度的升高，型壳内部玻璃相黏度降低，也会加剧热应力的积累和局部变形。
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2025年第45卷第5期
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doi: 10.11868/j.issn.1005-5053.2025.000146
  • 接收时间：2025-08-04
  • 首发时间：2026-04-09
  • 出版时间：2025-10-01
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  • 收稿日期：2025-08-04
  • 录用日期：2025-08-28
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    1郑州航空工业管理学院 航空发动机学院，郑州 450046
    2清华大学 材料学院 先进成形制造教育部重点实验室，北京 100084
    3中国航发北京航空材料研究院，北京 100095

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许庆彦（1971—），男，博士，教授，研究方向为航空发动机高温合金涡轮叶片定向凝固多尺度、全流程建模与仿真，联系地址：北京市海淀区清华大学李兆基科技大楼（100084），E-mail：
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2种不同金属材料的力学参数
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Genus		 种数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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