(No.12132005, No.12135008)
NUCLEAR TECHNIQUES, Volume. 45, Issue 12, 120601(2022)
Research on multi-scale creep behaviors of UN-U 3Si 2 composite fuels
UN-U 3Si 2 composite fuels have a promising prospect in advanced future accident tolerant fuel elements. Its irradiation creep and thermal creep caused by in-reactor operation have an important influence on the irradiation-induced thermo-mechanical coupling behavior and safety of the fuel elements.
This study aims to develop a stochastic modeling method according to the metallographic structure of composite fuel and numerical simulation of the uniaxial tensile creep test of the UN-U 3Si 2 composite fuel (20% U 3Si 2).
Based on the data of creep experiments from literatures, the dominated creep mechanisms of UN and U 3Si 2 polycrystalline fuels were analyzed, and their creep rate models considering vacancy diffusion and dislocation motion mechanisms were obtained by curve fitting. Then, the correlation model between the macroscopic creep of composite fuel and the contribution of each component was established on the basis of the homogenization theory and the removal of irradiation swelling effect. Finally, based on the metallographic structure diagram of composite fuels in the literatures, stochastic modeling method was developed and applied to the numerical simulation of the uniaxial tensile creep test of the UN-U 3Si 2 composite fuel (20% U 3Si 2).
The model predictions of UN and U 3Si 2 creep rates are in good agreement with the experimental results, validating the effectiveness of the model. The contribution of the component fuels to the macroscopic equivalent creep of the composite fuel is obtained by analysis of the underlying creep mechanism. When the fission density reaches 4.32×1027 fissions·m-3, the maximum von Mises stress at the interface between particles and matrix is about 6 times of the homogeneous tensile stress applied externally.
The research results indicate that the difference in the irradiation swelling of UN and U 3Si 2 will result in the strong internal mechanical interaction in the composite fuel whilst the existence of weakened stress regions leads to the negligible effect of irradiation swelling on the macroscopic equivalent creep strain of the composite fuel.
(No.12132005, No.12135008)
自福岛发生核事故以来,开发具有更高安全性的燃料一直是核领域关注的焦点。耐事故燃料应能提升反应堆在严重事故工况下的安全性,同时也能保持甚至提升正常运行状态下的性能[
UN-U
3Si
2复合燃料芯块在服役过程中会产生复杂的辐照-热-力耦合行为,其宏观蠕变性能直接影响其安全性。燃料的蠕变会引起应力松弛效应,影响复合燃料芯块内部的力学场及芯块与包壳之间的力学相互作用[
已有的燃料蠕变性能研究主要针对UO
2燃料展开,关于UN、U
3Si
2高铀密度燃料蠕变的理论及实验研究较少,关于UN-U
3Si
2复合燃料的蠕变模型研究尚未见报道。Zeisser等[
利用文献中已有的蠕变实验数据,基于不同条件下的主控蠕变机制建立了UN和U 3Si 2的蠕变率模型,并基于均匀化理论获得UN-U 3Si 2复合燃料的宏观等效蠕变应变与各组分贡献的关联模型。建立了组分随机分布的有限元模型,计算模拟了UN-U 3Si 2复合燃料辐照条件下的拉伸蠕变实验,获得了各组分对宏观蠕变应变的定量贡献及主控的蠕变机制,并考察了燃料辐照肿胀对复合燃料多尺度蠕变行为的影响。
1 UN和
UN-U 3Si 2复合燃料由UN和U 3Si 2组成,本节给出其弹性性能和辐照肿胀模型。
1.1 弹性常数
UN的弹性模量(
EUN)和泊松比(
νUN)分别为[
式中: ρ是理论密度比,%,本文取100; T是温度,K。
U
3Si
2的弹性模量(
1.2 辐照肿胀模型
UN和U
3Si
2的辐照体积肿胀采用如下经验模型描述[
式中: Bu表示燃耗,单位为FIMA(Fissions Per Initial Heavy Metal Atoms)。
2 复合燃料的多尺度蠕变模型
2.1 多晶材料相的蠕变率模型
由于目前缺乏完善的UN和U 3Si 2蠕变率模型,本研究结合文献报道的实验结果,综合考虑辐照蠕变和热蠕变的贡献,并基于不同应力及辐照工况条件下的蠕变机制分析,建立两种组分材料的新蠕变率模型。
UN和U
3Si
2均为多晶材料,多晶材料的蠕变变形主要有以下几种典型机制[
对于UN材料,根据实验结果[
式中:
对于U
3Si
2材料,根据实验结果[
式中: A1=6.524 8×10-23, A2=4.792, Q A=172 647 J·mol-1, B1=3.361 6×10-29, B2=3.578 6×10-6, Q B=171 453 J·mol-1。
Figure 1.Comparison of the calculated and experimental values of the UN creep model (a) and the U 3Si 2 creep model (b) (color online)
2.2 复合燃料的宏观等效蠕变模型
在宏观外载作用下,UN-U
3Si
2复合燃料试样的宏观蠕变变形来自于UN和U
3Si
2的蠕变贡献。可以基于均匀化理论[
对于计算模拟中的每个增量步,以增量步起始时刻的构形作为参考构形,各应变增量满足:
式中:
由于蠕变应变为偏斜张量,而辐照肿胀应变为球形张量,则复合燃料的宏观体积变化主要来自各组分材料辐照肿胀的贡献。由于弹性应变的贡献可以忽略,可得复合燃料拉伸方向( x方向)的宏观等效蠕变应变增量满足:
式中:
3 复合燃料单轴拉伸蠕变实验模拟的有限元模型
基于§1中的UN和U 3Si 2燃料弹性模型和辐照肿胀模型,以及§2.1中建立的UN和U 3Si 2多晶燃料蠕变率模型,建立了旋转坐标系下的三维大变形增量本构关系,推导了应力更新算法和一致刚度模量,并编写了UMAT子程序,在ABAQUS有限元计算平台实现了UN-U 3Si 2复合燃料的单轴拉伸蠕变实验的有限元模拟。
目前,UN-U
3Si
2复合燃料芯块主要是U
3Si
2和UN粉末共同烧结制备而成[
Figure 2.Microstructure of UN-U 3Si 2 composite fuel pellets
根据复合燃料的微观结构特征和两相分布情况,暂不考虑孔隙的存在,本文针对立方体形代表性体元发展了如下的随机建模方法:
1)将整个立方体体元划分均匀的六面体网格;
2)在计算前,借助外部程序进行随机建模,获得两相材料的空间分布情况,并输出文本文档;
3)在计算开始时刻,通过UMAT读取上述文本文档和单元积分点坐标,根据积分点坐标判断材料属性,并记录材料状态变量;
4)在每一个增量步开始时,读取最初记录的材料状态变量,并调用对应的材料子程序。
Figure 3.Flowchart diagram of random distribution modeling
Figure 4.Schematic diagram of random distribution model
根据细观力学的思想,复合燃料在宏观上由代表性体元周期性排列得到。在宏观外载作用下,代表性体元的变形亦周期性分布[
其中:如
Figure 5.Schematic diagram of periodic boundary conditions and applied loads for cube-shaped voxels
4 结果与讨论
4.1 辐照肿胀对复合燃料多尺度蠕变行为的影响
本文模拟复合燃料辐照条件下的单轴拉伸蠕变实验,考虑了两种材料的辐照肿胀贡献,以更好地模拟复合燃料的辐照效应。虽然在计算宏观等效蠕变应变时,已经去除了辐照肿胀所引起的体积应变贡献,但是各组分材料的辐照肿胀会影响复合燃料细观的应力状态,进而影响多尺度的蠕变变形。为了研究辐照肿胀对复合燃料多尺度蠕变行为的影响,本文也对不考虑组分材料辐照肿胀的算例进行了计算模拟,获得了在均布拉力50 MPa、温度500 K、裂变率1020 fissions·m-3·s-1条件下的结果。
Figure 6.Comparison of macroscopic equivalent creep strain with and without irradiation swelling
Figure 7.Von Mises stress contourplots (section view) at the fission density of 4.32×1027 fissions·m-3 (a) With radiation swelling, (b) Without radiation swelling
Figure 8.Equivalent creep contour plots (section view) at the fission density of 4.32×1027 fissions·m-3 (a) With radiation swelling, (b) Without radiation swelling
结合以上结果可知,由于两相材料的辐照肿胀不同,两相材料之间需要变形协调,导致两相之间存在较为强烈的力学相互作用。但由于离开界面处的基体应力及颗粒相的应力被削弱了,所以两相材料的辐照肿胀对复合燃料宏观等效蠕变的影响可以忽略。
4.2 复合燃料宏观蠕变应变的细观主导机制分析
通过均匀化方法,可以得到弥散相和基体相对总蠕变应变的贡献,也可以得到不同机制蠕变的占比情况,分别如图
Figure 9.Contribution of dispersed phase and matrix to total creep strain
Figure 10.Proportions of different creep contribution
5 结语
本文基于已有文献中的蠕变实验结果,综合考虑了辐照蠕变及热蠕变的贡献,通过分析各种条件下的主导蠕变机制建立了UN和U 3Si 2多晶燃料的蠕变率模型,证明了模型的合理有效性;同时利用均匀化理论建立了UN-U 3Si 2复合燃料宏观等效蠕变和两相贡献的关联模型;并发展了随机建模方法,实现了UN-U 3Si 2复合燃料辐照条件下的单轴拉伸蠕变实验的有限元模拟,获得两相材料在复合燃料宏观蠕变中的定量贡献,并分析了主控的蠕变机制。同时,考察了组分材料的辐照肿胀对复合燃料多尺度蠕变行为的影响,得到的主要结论如下:
1)考虑和不考虑辐照肿胀的计算结果表明:由于组分材料的辐照肿胀行为的差异性,导致复合燃料的颗粒和基体相产生了强烈的力学相互作用,在裂变密度达到4.32×1027 fissions·m-3时的最大von Mises应力约为外部均布拉力的6倍;由于同时存在细观应力被削弱的区域,组分材料不同的辐照肿胀对宏观等效蠕变应变的影响很小,可以忽略。
2)在均布拉力50 MPa、温度500 K、裂变率1020fissions·m-3·s-1的条件下,基体相对总蠕变的贡献较大,在裂变密度达到4.32×1027 fissions·m-3时,拉伸方向的基体蠕变在总蠕变中的占比约79%;在此参数范围内,辐照扩散机制蠕变占主导,其占比随燃耗的增长逐渐减小;而辐照位错蠕变的占比随燃耗的增长逐渐增大,归功于组分辐照肿胀对细观应力场的影响;热扩散机制蠕变和热位错机制蠕变基本没有贡献。
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Qingfeng YANG, Zhexiao XIE, Ping CHEN, Jing ZHANG, Shixin GAO, Guochen DING, Yi ZHOU, Chunyu YIN, Shurong DING, Liang HE, Dan SUN. Research on multi-scale creep behaviors of UN-U 3Si 2 composite fuels[J]. NUCLEAR TECHNIQUES, 2022, 45(12): 120601
Category: Research Articles
Received: Apr. 12, 2022
Accepted: --
Published Online: Jan. 3, 2023
The Author Email: DING Shurong (dingshurong@fudan.edu.cn)