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Article(id=1244340206174847976, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, articleNumber=null, orderNo=null, doi=10.11776/j.issn.1000-4939.2025.06.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1678032000000, receivedDateStr=2023-03-06, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774603423874, onlineDateStr=2026-03-27, pubDate=1765728000000, pubDateStr=2025-12-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774603423874, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774603423874, creator=13701087609, updateTime=1774603423874, updator=13701087609, issue=Issue{id=1244340201636610993, tenantId=1146029695717560320, journalId=1244295746212642849, year='2025', volume='42', issue='6', pageStart='1207', pageEnd='1446', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774603422792, creator=13701087609, updateTime=1774603751062, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244341578555306992, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244341578555306993, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1285, endPage=1291, ext={EN=ArticleExt(id=1244340208288777214, articleId=1244340206174847976, tenantId=1146029695717560320, journalId=1244295746212642849, language=EN, title=Study on dynamic cracking behavior of high burnup fuel particles with fission gas release, columnId=1244340205327593820, journalTitle=Chinese Journal of Applied Mechanics, columnName=Solid Mechanics, runingTitle=null, highlight=null, articleAbstract=

A large number of fission pores are generated in ceramic fuel under high burnup conditions, and the fission gas released into the crack cavity has a great influence on the crack propagation behavior. In this study, a dynamic crack propagation model under variable internal pressure is developed to address the dynamic cracking technique of the coupling effect between the internal pressure and crack propagation. The internal pressure in crack cavity varies with crack propagation, while the cracking behavior is simulta-neously affected by the pressure. The presented model is successfully applied to simulate the cracking behavior of ceramic fuel particles of high burnup structure, and the mechanical effect of fission gas release on crack propagation is studied. Based on the cohesive element, the crack initiation and propagation process are simulated, and the mechanical research method of gas release on crack propagation is established here. Furthermore, the effects of gas pressure on the crack initiation and propagation process in fuel particles are analyzed. The results show that the release of gas into the crack cavity can inhibit crack propagation based on gas pressure and crack geometry characteristics. For different initial gas pressures, the larger the initial gas pressure is, the longer the crack propagation length will be. The developed dynamic cracking simulation technique provides an analytical method and numerical foundation for accurately analyzing the failure of dispersion fuel meat. It also provides a method to study the coupling of load and crack propagation.

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陶瓷燃料在高燃耗条件下产生大量裂变气孔，气孔中的裂变气体释放至裂纹空腔对裂纹扩展行为具有较大的影响。开发了一种变内压作用下的裂纹动态扩展模型，实现了裂纹空腔内压与裂纹扩展过程相互耦合作用的动态开裂技术。内压大小随裂纹扩展而变化，同时开裂行为受内压大小的影响。并将此模型成功应用于高燃耗结构陶瓷燃料颗粒内的开裂行为模拟，研究了裂变气体释放对裂纹扩展的力学作用。基于全局内聚力单元模拟了裂纹产生和扩展过程，建立了气体释放对裂纹扩展力学作用的研究方法，分析了气体压力对燃料颗粒内部裂纹产生和扩展过程的影响。结果表明，气体总量不变情况下气体释放至裂纹空腔会基于气体压力和裂纹几何特征对裂纹扩展产生抑制的效果。对于不同气体初始压力的情况，气体初始压力越大，止裂时裂纹扩展长度越长。该动态裂纹模拟技术为精确研究弥散型燃料芯体失效提供了分析方法及数值参考，也为载荷与裂纹扩展相耦合的情况提供一种研究方法。

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李群，教授。E-mail:
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label=图6, caption=不同气体初始压力时气体压力随裂纹扩展长度变化曲线, figureFileSmall=pw4EDORVAFe46RBxNXgwgQ==, figureFileBig=0UhNhqPf4Q7xJLRjEBCBsw==, tableContent=null), ArticleFig(id=1244340226831794791, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340206174847976, language=EN, label=Tab.1, caption=

The crack length of different models with various initial fission gas pressure

, figureFileSmall=null, figureFileBig=null, tableContent=
起裂情况气孔初始压力/MPa
120150180210240
裂纹止裂长度/μm01.23.88.8≥9.0
), ArticleFig(id=1244340226945041005, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340206174847976, language=CN, label=表1, caption=

不同气体初始压力模型起裂情况

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起裂情况气孔初始压力/MPa
120150180210240
裂纹止裂长度/μm01.23.88.8≥9.0
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考虑裂变气体释放的高燃耗燃料颗粒动态开裂行为研究
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晁昊宇 1 , 董颖璇 1 , 曹肸丞 1 , 吕俊男 2 , 李群 1
应用力学学报 | 固体力学 2025,42(6): 1285-1291
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应用力学学报 | 固体力学 2025, 42(6): 1285-1291
考虑裂变气体释放的高燃耗燃料颗粒动态开裂行为研究
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晁昊宇1, 董颖璇1, 曹肸丞1, 吕俊男2, 李群1
作者信息
  • 1.西安交通大学航天航空学院机械结构强度与振动国家重点实验室，710049　西安
  • 2.中国核动力研究设计院反应堆燃料及材料重点实验室，610213　成都

通讯作者:

李群，教授。E-mail:
Study on dynamic cracking behavior of high burnup fuel particles with fission gas release
Haoyu CHAO1, Yingxuan DONG1, Xicheng CAO1, Junnan LÜ2, Qun LI1
Affiliations
  • 1.State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, 710049 Xi'an, China
  • 2.National Key Laboratory of Nuclear Reactor Technology, Nuclear Power Institute of China, 610213 Chengdu, China
出版时间: 2025-12-15 doi: 10.11776/j.issn.1000-4939.2025.06.008
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摘要
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陶瓷燃料在高燃耗条件下产生大量裂变气孔，气孔中的裂变气体释放至裂纹空腔对裂纹扩展行为具有较大的影响。开发了一种变内压作用下的裂纹动态扩展模型，实现了裂纹空腔内压与裂纹扩展过程相互耦合作用的动态开裂技术。内压大小随裂纹扩展而变化，同时开裂行为受内压大小的影响。并将此模型成功应用于高燃耗结构陶瓷燃料颗粒内的开裂行为模拟，研究了裂变气体释放对裂纹扩展的力学作用。基于全局内聚力单元模拟了裂纹产生和扩展过程，建立了气体释放对裂纹扩展力学作用的研究方法，分析了气体压力对燃料颗粒内部裂纹产生和扩展过程的影响。结果表明，气体总量不变情况下气体释放至裂纹空腔会基于气体压力和裂纹几何特征对裂纹扩展产生抑制的效果。对于不同气体初始压力的情况，气体初始压力越大，止裂时裂纹扩展长度越长。该动态裂纹模拟技术为精确研究弥散型燃料芯体失效提供了分析方法及数值参考，也为载荷与裂纹扩展相耦合的情况提供一种研究方法。

陶瓷燃料颗粒  /  内聚力单元法  /  动态开裂  /  裂变气体

A large number of fission pores are generated in ceramic fuel under high burnup conditions, and the fission gas released into the crack cavity has a great influence on the crack propagation behavior. In this study, a dynamic crack propagation model under variable internal pressure is developed to address the dynamic cracking technique of the coupling effect between the internal pressure and crack propagation. The internal pressure in crack cavity varies with crack propagation, while the cracking behavior is simulta-neously affected by the pressure. The presented model is successfully applied to simulate the cracking behavior of ceramic fuel particles of high burnup structure, and the mechanical effect of fission gas release on crack propagation is studied. Based on the cohesive element, the crack initiation and propagation process are simulated, and the mechanical research method of gas release on crack propagation is established here. Furthermore, the effects of gas pressure on the crack initiation and propagation process in fuel particles are analyzed. The results show that the release of gas into the crack cavity can inhibit crack propagation based on gas pressure and crack geometry characteristics. For different initial gas pressures, the larger the initial gas pressure is, the longer the crack propagation length will be. The developed dynamic cracking simulation technique provides an analytical method and numerical foundation for accurately analyzing the failure of dispersion fuel meat. It also provides a method to study the coupling of load and crack propagation.

ceramic fuel particle  /  cohesive element  /  dynamic cracking  /  fission gas
晁昊宇, 董颖璇, 曹肸丞, 吕俊男, 李群. 考虑裂变气体释放的高燃耗燃料颗粒动态开裂行为研究. 应用力学学报, 2025 , 42 (6) : 1285 -1291 . DOI: 10.11776/j.issn.1000-4939.2025.06.008
Haoyu CHAO, Yingxuan DONG, Xicheng CAO, Junnan LÜ, Qun LI. Study on dynamic cracking behavior of high burnup fuel particles with fission gas release[J]. Chinese Journal of Applied Mechanics, 2025 , 42 (6) : 1285 -1291 . DOI: 10.11776/j.issn.1000-4939.2025.06.008
正文
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在高燃耗辐照条件下，陶瓷燃料颗粒内产生大量裂变气体，不断聚集形成气泡，导致燃料颗粒辐照肿胀并出现大量微裂纹，最终影响基体的力学性能及整个燃料元件的结构完整性[1-3]。高燃耗结构（high burnup structure，HBS）陶瓷燃料颗粒的开裂是弥散型燃料元件失效的根源[4-5]。燃料微裂纹空腔中存在裂变气体导致内压的产生，内压大小随裂纹扩展而变化，同时开裂行为受内压大小的影响。故高燃耗陶瓷燃料开裂是内压作用和裂纹扩展过程相互耦合的行为，其动态开裂模拟是分析陶瓷燃料颗粒开裂失效的关键技术。因此，考虑裂变气体内压作用下的裂纹动态扩展模拟研究对深入分析弥散燃料元件失效机理具有重要意义。
高燃耗陶瓷燃料颗粒为多孔几何结构[6]，气孔中存在由裂变气体导致的内压[7-8]。失效过程中燃料颗粒在裂变气孔内压的作用下应力失配，产生大量非自相似分布的微裂纹，裂变气体释放至裂纹面中[9-11]。现有研究大多仅考虑了裂变气体，聚集于气孔中时燃料颗粒内的应力分布[3，12-13]，未考虑裂变气体释放至裂纹空腔对燃料颗粒开裂的作用及其对燃料颗粒内应力场的影响。裂变气体释放至裂纹空腔后，主要在裂纹内产生作用，影响裂尖场并驱动裂纹的开裂扩展。在裂纹扩展过程中，随着裂纹面几何尺寸的改变，裂变气体内压也随之变化。故不考虑裂变气体内压变化的燃料颗粒开裂分析是不准确的。本质上，裂变气体内压作用下的陶瓷燃料颗粒裂纹扩展是一个变内压作用下的裂纹动态扩展问题，气体内压是影响裂纹起裂/止裂的主导因素。因此在裂纹扩展过程中，需要准确捕捉裂纹面，并实时更新载荷。
采取全局内聚力单元法结合自定义子程序可以实现气体内压与裂纹扩展过程耦合作用的燃料颗粒开裂行为模拟研究。全局内聚力单元法可以模拟出非自相似裂纹的分叉和聚合，这种方法不需要包含预制裂纹，也不需重新划分网格，便于获取裂纹位置和裂纹尺寸[14]。全局内聚力单元法适用于流体压力等复杂载荷情况的裂纹扩展分析[15-16]，可用于颗粒内裂纹的动态扩展。有限元框架中调用自定义载荷子程序可以实现裂纹面上载荷大小和位置的变化，读取结果文件子程序可以实时提取有限元计算过程中的数值结果。将根据裂纹尺寸和位置情况求得的当前载荷情况投入运算，即可实现裂变气体作用下裂纹动态扩展。
本研究基于全局内聚力单元法建立了变内压作用下的裂纹动态扩展模型，并将其应用于裂变气体作用下的陶瓷燃料颗粒动态开裂模拟研究。分析了裂变气体内压和裂纹空腔尺寸等关键参数对燃料颗粒内部裂纹扩展的影响机理。通过开发变压力驱动的动态裂纹起裂/止裂模拟技术，可探索裂变气体释放行为对弥散燃料芯体失效的力学作用，对高燃耗陶瓷燃料颗粒在极端工况下的失效分析和结构优化具有重要意义。
1　变内压作用下的裂纹动态扩展模型
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1.1　燃料颗粒结构模型
本节开发了具有变内压作用的裂纹动态扩展模型。裂纹面通过内聚力单元设定进行扩展，裂纹空腔中的内压随裂纹扩展尺寸变化而改变。内压大小和裂纹扩展过程相互耦合，即裂纹面所受内压大小随裂纹扩展而变化，同时开裂行为受内压大小的影响而起裂或者止裂。本节开展了陶瓷燃料颗粒动态开裂行为研究，对提出方法的可行性进行验证。
燃料颗粒是核燃料元件的核心部分，在辐照条件下燃料颗粒内部会产生裂变气体，聚集在颗粒内部的大量气孔中对燃料相造成压力，同时颗粒外的基体部分会对燃料颗粒的膨胀起到约束作用。在高温和高燃耗条件下，气孔内部裂变气体的压力会达到上百兆帕，使气孔附近产生微裂纹。由于燃料颗粒内气孔数量繁多，分布不均，相距较近的气孔间相互作用会导致气孔间出现应力集中，燃料颗粒整体结构复杂，难以直接进行研究，有必要提取单一气孔及附近燃料相结构进行简化。
如图1所示，从高燃耗陶瓷燃料颗粒中抽象出局部单气孔开裂模型。由于气孔间距较近时，气孔会发生合并形成大气孔，因此独立的气孔周围会存在一定厚度的燃料相，气孔中存在裂变气体诱导的内压Pg，同时燃料相球壳会由于受到外部燃料相约束作用产生反力。以此法建立的气孔—燃料相球壳模型可以代表燃料颗粒内任意尺寸和位置的气孔及其周围燃料相结构。在气体内压作用下，气孔周围产生微裂纹，裂纹空腔中同样存在裂变气体诱导的压力。裂纹在气体内压作用下开始扩展，而裂纹面所受气体压力随裂纹几何尺寸改变而发生变化，成为控制裂尖起裂/止裂的驱动力。
1.2　气体释放模型
气体的初始压力Pg采用超高压下实际气体的状态方程来计算[17-18]
其中：ng为裂变气体总量，单位为mol；Vg为气体总体积，即气孔体积，单位为m3；T为温度，单位为K；R为气体普适常数，R=（8.31141±0.00026）J•mol-1•K-1；a和b为实际气体状态方程参数，a=5.57×10-5m3，b=2.39×10-5m3；Df为燃料相密度，Df=10.96×106/（1+ρg）g/m3，ρg表示燃料颗粒气孔的孔隙度；β为裂变气体（Xe+Kr）的裂变产额值，取值为0.26；Mf为燃料相的摩尔质量，二氧化铀，270.027 7 g/mol；BU为燃耗，单位FIMA。
裂纹扩展后气体压力发生变化，假设裂纹空腔几何尺寸为Vc，则裂纹扩展后的气体压力Pga为
其中：nga为气体总量；Vga为气体总体积，即气孔与裂纹空腔体积之和，分别由式（4）、式（5）计算确定；Δng为裂纹扩展过程中气体变化量，是温度和燃耗等因素的函数，目前尚无显式表达式。在本工作中，由于温度和燃耗不变，忽略增量Δng，认为气体总量不变。
令裂纹空腔中的初始压力为Pg，Vc代表裂纹空腔体积。裂纹扩展过程中的气体压力随之改变，表示为Pga。Pga应是Vc的函数Pga（Vc），在具体问题中进行相应表达。Vc在二维情况下退化为几何面积S，可由多边形面积公式计算得到。
其中：n为多边形顶点个数；（xi，yi）为多边形顶点坐标，xn+1=x1，yn+1=y1。
1.3　内聚力单元
裂纹扩展面上设为内聚力单元，其本构关系满足以下关系
其中，裂纹面上的应力σ为张开位移δ的函数。而开裂过程形成新裂纹面过程中释放的能量定义为其断裂能G，表征为
当cohesive单元两侧牵引力增加时，牵引力随着开裂界面上的位移增加而增加，当牵引力达到设定的断裂强度时，此时单元开始损伤，牵引力达到最大值后开始下降，该阶段为材料的损伤扩展阶段，直到牵引力下降至0，此时单元完全失效断裂能达到其最大的临界断裂能GIC（即曲线下包含的面积）。根据研究对象的不同，cohesive单元有多种本构形式，燃料颗粒属于陶瓷材料，使用最简单的双线性本构即可对其开裂行为进行描述（图2）。
cohesive单元属性中，损伤起始应力σmax为材料的开裂强度σb，由材料的断裂韧性KIC可计算出损伤失效位移为
其中，损伤起始位移δIn取0.05δcn。
cohesive刚度根据下式计算得到
由于使用cohesive单元模拟裂纹扩展，因此在误差允许的情况下，裂纹空腔体积Vc可用简化式（11）代替，即
其中：n为与气孔相连的失效单元数；ui1、ui2、ui3、ui4为cohesive单元4个结点的位移；li为cohesive单元长度。当cohesive单元长度均相同时，可进一步简化为
其中：l为cohesive单元长度；d为cohesive单元平均宽度。
至此，可根据式（7）~式（10）定义的cohesive单元模拟裂纹动态扩展过程。而裂纹中的压力变化根据式（3）~式（8）计算得到。
2　陶瓷燃料颗粒动态开裂行为及结果
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2.1　基本模型与参数
本研究聚焦于变内压作用下的裂纹动态扩展，故针对单个气孔起裂做如下假设:①气孔为均匀的圆形，选取周围矩形区域燃料相，给动态裂纹的起裂/止裂预留充足几何空间；②由于选取的燃料相边界与气孔距离大于气孔半径，可忽略燃料颗粒内其他气孔的干涉影响；③裂纹沿平行于裂尖前缘方向起裂扩展，即I型起裂/止裂过程；④周围环境压力作用等效为远场应力。有限元模型和网格划分结果如图3所示。选取矩形燃料相，燃料相中心初始有一气孔，将燃料相上下切割，允许裂纹从气孔沿水平方向产生。
燃料相尺寸为10 μm×5 μm，气孔为半径1 μm圆型气孔。燃料相有限元网格采用CPS4R，沿图3（b）中的水平轴线处插入cohesive单元COH2D4，划分好的网格单元总数超过5 000，cohesive单元数为90。网格尺寸为0.2 μm，由于使用内聚力单元模拟裂纹，裂纹尺寸为各开裂单元长度之和，存在一定网格依存性，即裂纹长度存在0.2 μm以内的误差，在可接受范围内。
载荷与边界条件如图3（a）所示，气孔对周围燃料相产生压力，同时随着裂纹扩展，裂纹面上也会产生对裂纹面的压力。为防止模型上下两部分分离，产生刚体位移，限制模型左右两端y方向位移，因此若裂纹扩展至模型边缘，即裂纹长度达到9.0 μm即视为未止裂。
二氧化铀（UO2）是轻水堆、重水堆及实验堆中常用的一种陶瓷核燃料，具有热中子俘获截面低、熔点高、熔点内具有各向同性、辐照稳定性好等优点，因此采用UO2作为燃料相模拟变内压作用下的动态开裂行为。UO2燃料颗粒的弹性模量Ef是温度和燃耗的函数[18-19]，根据试验数据可拟合如下式。
其中，T表示温度，单位为℃。弹性模量的单位为MPa。UO2泊松比为0.316。UO2材料的开裂强度由下式计算得到[13]。
断裂韧性KIC取1.30 MPa•m0.5[20]，结合式（13）和式（14）计算得到的高燃耗燃料弹性模量Ef和开裂强度σb，代入式（9）计算可得损伤失效位移δcn＝0.15 μm。
最终，根据计算，cohesive单元断裂强度近似取100 MPa，断裂能取0.000 5 MPa。内聚力参数会影响裂纹起裂时的压力与裂纹扩展长度，上述材料参数均由查阅相关文献获取并确定，因此不对其具体的影响机制进行研究。
2.2　数值结果与讨论
采用图2中的全局内聚力单元模型对图3中的UO2陶瓷燃料中单个裂变气孔周围微裂纹动态开裂进行模拟分析。通过对比考虑裂纹空腔中裂变气体内压变化前后的裂纹扩展结果，讨论了陶瓷燃料中裂变气体释放对开裂行为的影响。裂变气体内压随裂纹扩展而发生变化。此外，进一步分析了微裂纹几何特征对动态裂纹扩展的影响。
2.2.1　裂变气体内压对开裂行为的影响
考虑气体初始压力为150 MPa的模型。恒定裂变气体内压与考虑内压变化的微裂纹扩展模拟结果应力云图对比如图4所示。
当裂纹空腔中的裂变气体内压恒定不变时，模拟得到的裂纹扩展结果如图4（a）所示。陶瓷燃料为脆性材料，裂纹在较大的内压驱动下在燃料相中迅速失稳扩展。另一方面，考虑裂变气体内压变化时，裂纹面所受气体压力值为裂纹几何尺寸的函数，随着裂纹的扩展而相应减小，如图5所示。在变裂变气体内压作用下，裂纹扩展结果如图4（b）所示。裂尖仅在裂纹扩展长度l＝1.2 μm后就止裂了，图4（b）中的裂纹扩展结果和物理场数值更符合工程实际情况。
考虑气体变化影响时，燃料颗粒中的应力场和裂纹长度发生了明显的变化，变压力作用下的裂尖应力场明显降低，裂纹扩展长度减少，此时气体内压与裂纹扩展的耦合作用抑制了裂纹扩展，起到了止裂的作用。显然考虑气体释放至裂纹空腔对裂纹扩展具有不可忽视的影响，要更详细分析这种影响，需要调整相关参数得到更加准确详细的结论。
对弥散燃料辐照后高温失效的微观分析可知[6]，包壳初始起泡时，燃料颗粒内部就已经出现了裂纹，这些裂纹有的贯穿了燃料颗粒，有的仅进入燃料颗粒表层；而在起泡后期，裂纹已穿出燃料颗粒进入到基体中。故颗粒中的微裂纹是燃料颗粒开裂的根源，而微裂纹是由于裂变气体内压增大而使燃料颗粒内部张力超过其承受极限造成的。本研究开发的变内压-裂纹扩展耦合作用下的开裂模型在实现陶瓷燃料颗粒中微裂纹扩展过程上则更为准确，因为内聚力单元中的开裂判据是根据断裂韧性建立的。采用此模型计算得到的含裂纹燃料颗粒物理场更接近真实值，这个方法也可以很容易地扩展应用到具有变压力裂纹扩展的类似系统中。
2.2.2　裂变气体初始压力对开裂行为的影响
裂变气体的初始压力对裂纹扩展具有一定影响。本节对不同气体初始压力模型进行研究。气体初始压力分别取120、150、180、210、240 MPa，分别计算了不同裂变气体初始压力作用下的裂纹动态扩展结果，裂纹空腔中气体压力随裂纹长度变化如图6所示。图中黑点标出的数值为止裂时的裂纹长度及对应的气体压力，曲线上无点表示裂纹未产生或未止裂。根据计算，恒定压力模型和变压力模型下计算得到的裂纹扩展长度结果如表1所示。
由计算结果可知，随气体初始压力增大，裂纹最终扩展长度增加，裂纹扩展长度受到气体压力变化影响而减小，即气体释放对裂纹扩展起到抑制作用。止裂时的气体压力随初始气体压力的增大而减小。已知裂变气体初始压力值与燃耗相关，可进一步研究燃耗与弥散燃料芯体失效的关系。
高燃耗燃料颗粒在堆内运行环境下的开裂行为是多因素耦合作用的结果。现有的燃料颗粒高燃耗结构开裂分析大都从强度模型出发[21-22]，对陶瓷燃料颗粒的强度和开裂影响因素进行分析研究仅能对威胁燃料失效的因素进行定性分析，以强度分析得到的结论仅在燃料颗粒开裂前有效。而陶瓷燃料颗粒的开裂在高燃耗下是必然的[6]，事故工况下，陶瓷燃料颗粒中的微裂纹联通形成贯穿裂纹[3]，芯体内部燃料颗粒破裂的比例很高。燃料颗粒的开裂是弥散燃料芯体开裂以及宏观燃料元件起泡失效的前提。有研究通过构建考虑裂纹空腔气体压力作用下的金属基体解析模型对芯体开裂行为进行分析[3]，但值得注意的是，金属基体中的裂纹尖端对周围夹杂颗粒非常敏感，故陶瓷燃料颗粒的开裂行为研究是弥散燃料芯体开裂模型的基础。本研究提出的方法弥补了弥散燃料芯体开裂行为数值模拟研究中开裂模型缺乏的不足，揭示了裂变气体释放的重要影响，给出了影响燃料颗粒动态开裂行为的影响因素，为后续进行整个高燃耗颗粒开裂分析奠定了基础。
本模型计算结果分析表明，高燃耗陶瓷燃料颗粒中的开裂行为主要与裂变气体的释放量相关。而裂纹扩展过程中，裂纹空腔中的气体内压与开裂行为相互耦合，驱动了裂尖的动态起裂/止裂行为。裂变气体释放量是弥散燃料元件失效评估的重要参数，不考虑裂纹空腔中的裂变气体诱导内压变化是无法准确分析计算芯体失效行为的。此外，在实际弥散燃料芯体中，很难直接通过实验测量得到裂变气体释放量。因此，根据本研究建立的模型，可通过分析裂纹特征对裂变气体释放量进行间接估算，进而评估弥散燃料元件失效行为和宏观包壳起泡行为。
3　结论
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本研究开发了变内压-裂纹扩展耦合作用下的开裂模型，并将其应用于燃料颗粒开裂的动态模拟。采用全局内聚力单元对高燃耗燃料颗粒内考虑气体释放至裂纹空腔的单气孔模型裂纹扩展进行数值模拟研究，分析了裂变气体压力对裂纹动态过程（起裂/止裂）的影响，主要结论如下。
1）通过用户自定义子程序可建立气体复杂载荷位置和数值大小变化条件下的燃料开裂行为模型，有效地模拟高燃耗陶瓷燃料颗粒内气体载荷主导的燃料颗粒开裂过程。
2）对单气孔产生的微裂纹扩展过程进行了研究，发现气体内压变化将抑制燃料颗粒中的裂纹扩展。对比未考虑裂变气体在裂纹空腔中变化的裂纹扩展结果，考虑裂纹空腔中的裂变气体释放对燃料相的开裂行为分析更加准确。
3）分析了气体初始压力对裂纹动态扩展的影响。结果表明，气体总量不变情况下，气体释放至裂纹空腔会基于气体压力和裂纹几何特征对裂纹扩展产生抑制的效果。裂纹最终扩展长度受裂变气体初始压力的影响，气体初始压力越大，止裂时裂纹扩展长度越长。
基金
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  • 国家自然科学基金资助项目(12172270)
  • 反应堆燃料及材料重点实验资助项目(K902023-04-FW-HT-20220003)
文献
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2025年第42卷第6期
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doi: 10.11776/j.issn.1000-4939.2025.06.008
  • 接收时间：2023-03-06
  • 首发时间：2026-03-27
  • 出版时间：2025-12-15
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  • 收稿日期：2023-03-06
基金
国家自然科学基金资助项目(12172270)
反应堆燃料及材料重点实验资助项目(K902023-04-FW-HT-20220003)
作者信息
    1.西安交通大学航天航空学院机械结构强度与振动国家重点实验室，710049　西安
    2.中国核动力研究设计院反应堆燃料及材料重点实验室，610213　成都

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2种不同金属材料的力学参数
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Number of
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Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
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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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