Size-Dependent Structural Phase Transition Behaviors of CaF<sub>2</sub> Nanocrystals

GONG Lei; WANG Jingshu; ZHANG Junkai; CHEN Guangbo; ZHANG Han; WU Xiaoxin; HU Tingjing; CUI Hang

doi:10.11858/gywlxb.20210842

Volume 36 Issue 2

Apr 2022

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Abstract

References

Chinese Journal of High Pressure Physics > 2022 > 36(2): 021102.

YIN Xiaowen, TIAN Ze, HAN Yang, LI Zhiqiang. Numerical Simulation on Fluid Causing Fatigue of Industrial Pipeline System[J]. Chinese Journal of High Pressure Physics, 2018, 32(6): 064102. doi: 10.11858/gywlxb.20180559

Citation:

GONG Lei, WANG Jingshu, ZHANG Junkai, CHEN Guangbo, ZHANG Han, WU Xiaoxin, HU Tingjing, CUI Hang. Size-Dependent Structural Phase Transition Behaviors of CaF₂ Nanocrystals[J]. Chinese Journal of High Pressure Physics, 2022, 36(2): 021102. doi: 10.11858/gywlxb.20210842

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Size-Dependent Structural Phase Transition Behaviors of CaF₂ Nanocrystals

doi: 10.11858/gywlxb.20210842

1.
Key Laboratory of Functional Materials Physics and Chemistry of the Ministry of Education, National Demonstration Center for Experimental Physics Education, Jilin Normal University, Siping 136000, Jilin, China
2.
State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, Jilin, China

Funds: National Natural Science Foundation of China (11904128); Thirteenth Five-Year Program for Science and Technology of Education Department of Jilin Province (JJKH20200410KJ); Academic Graduate Students Scientific Research Innovation Fund of Jilin Normal University (202005)

More Information

Author Bio:
GONG Lei (1998－), female, bachelor, major in high pressure structural phase transition of nanomaterials. E-mail: gl15734441063@126.com
Corresponding author: WANG Jingshu (1982－), female, doctor, associate professor, major in high pressure behavior of nanomaterials. E-mail: wjs@jlnu.edu.cn
Received Date: 12 Jul 2021
Rev Recd Date: 05 Aug 2021
Accepted Date: 12 Jul 2021

Abstract

Abstract

CaF₂ nanocrystals with a size of 11 nm have been investigated using X-ray diffraction technique under high pressure. A phase transition from the fluorite structure to the α-PbCl₂-type structure has been observed at 12 GPa, which is much higher than the value observed in the bulk CaF₂ and slightly lower than the one in smaller-sized CaF₂ nanocrystals. The compressibility of the CaF₂ nanocrystals is discussed, an obviously higher incompressibility than the bulk CaF₂ is observed. The α-PbCl₂-type metastable phase is retained when the pressure is released to ambient conditions. The unique high-pressure behaviors of the 11 nm-sized CaF₂ nanocrystals are attributed to defects and grain size effect. The grain size effect is considered to be the main factor influencing the high-pressure behaviors of the CaF₂ nanocrystals. When the size of the CaF₂ nanocrystals is as small as 11 nm, the higher surface energy leads to the enhancement of the structural stability and the increase of the bulk modulus.
- high pressure,
- CaF₂ nanocrystals,
- phase transition,
- X-ray diffraction,
- size effect

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管道运输是近现代主要运输方式之一。在石油工业促进下管道运输逐步发展成大范围、大跨度、大容量、多介质运输网络系统。然而，复杂管网系统可能面临诸如维护成本高、检测周期长、工艺更新快、极端环境影响加大的问题，致使管路系统发生失效破坏，造成严重的经济损失和环境污染。其中由疲劳引起的失效破坏因预测难度大、事故影响范围广等特点成为研究热点。

在工程结构中疲劳是主要的失效机理之一^[1]。在材料科学中疲劳是循环力作用下材料产生的失效。其机理可以描述为：当载荷超过某极限时会在应力集中处产生微裂纹，造成材料的几何不连续^[2]，并逐步发展至不稳定状态而导致突然失效^[3]。在ASTM标准中使用疲劳寿命(N_f)表征材料在自然失效前所能承担的应力循环次数^[4]。对于一些材料，此参数即为低应力幅状态下判断材料是否失效的理论值^[5]。这里，裂纹成为研究重点，前人对裂纹缺陷与疲劳失效之间的关系做了大量研究^[6-9]。其中Hussain^[10]在1997年对已提出的一些短裂纹疲劳分析模型和观点进行了对比和评判。在石油和天然气管道运输中，运输介质的特殊性和管道铺设的地理特殊性使工况变得异常复杂，相关研究包含：水土侵蚀后悬空管的疲劳失效及影响因素^[11]，悬跨管路中波浪、海流和不同裂纹凹痕对寿命的影响^[12]，从模态、位移、转角响应和动应力幅值方面对冰振下天然气管线进行分析^[13]等。同时还研究了管系中非常温运输介质的动态变化对裂纹萌生的影响，并对裂纹的萌生方向进行了理论预测，依照Fatemi-Socie准则和Miner准则进行了解析计算^[14]。

到目前为止，管道疲劳计算主要运用针对不同裂纹形式所建立的模型进行数值计算，同时就不同法兰管件在不同载荷和裂纹形式下进行力学模拟和分析，所涉及的疲劳计算软件有MSC.Fatigue、nCode DesignLife、CAE SAR Ⅱ、ANSYS。为模拟实际工况，软件间的耦合同样是研究热点，例如：利用Fluent和Abaqus耦合分析超音速进气道流振动^[15]，通过ANSYS和Franc 3D联合分析含裂纹的核级管道^[16]，使用ANSYS Workbench和CFX估算飞机液压管道的动态特性^[17]。

当前研究主要根据实际管道中发生破坏的管道部件进行失效验证和失效机理模拟，对于疲劳的预测主要集中在理论推导和拟合，而对整体管道的疲劳模拟和预测比较缺乏。主要原因是模型生成软件、力学计算软件和疲劳分析软件三者之间的信息传递存在不兼容现象。ANSYS Workbench平台很好地解决了此问题，它包含自底向上的几何模型创建模块、静态和动态的力学分析模块、通用的流体计算软件和nCode DesignLife疲劳分析软件，能在一个工程中通过简单操作将不同的计算模块联系起来进行耦合计算，解决了因复杂模型造成的大量数据在不同软件之间传递的困难。

本研究针对管道系统的疲劳分析，利用ANSYS Workbench的各种模块，并结合单向流固耦合方法，研究复杂管道内流体及其激振力对整个管道系统疲劳的影响。

1. 数值模拟

1.1 模块选择与模型建立

本研究的计算模块包含：有限元基本模块、Fluent计算模块和nCode DesignLife疲劳模块。其中流体和固体部分采用单向流固耦合方法，并将计算数据与疲劳软件共享，得到理想的疲劳分析结果。

直管尺寸参考ASME B36.19M或ASME B36.10M标准，弯头(Elbows A & B)、支座三通(Supported Tee)、四通(Four-Way)、异径三通(Reducer Tee)、法兰(Flange)、法兰垫片(Spacer)参考ASME B16.1标准，选用250磅级，其中法兰片中螺栓参考ASME B18.2.1重型六角头螺栓，螺母参考ASME B18.2.2重型六角螺母。具体尺寸为：法兰直径444.5 mm，法兰厚度47.752 mm，凸台面直径357.124 mm；毂直径320.548 mm，毂面贯穿长度60.452 mm；螺栓件数量为16组，螺栓直径25.4 mm；弯头及三通中基础面到中心的距离266.7 mm，基础面尺寸254.0 mm，基础面厚度31.75 mm，肋板厚度22.352 mm，螺栓孔排列半径和孔直径200.152 mm；直管中弯头中心到基本面的距离292.1 mm，长弯头中心到基本面的距离419.1 mm。

1.2 装配与网格划分

ANSYS Workbench中通过Geometry模块完成模型装配，得到如图 1所示的管道系统。定义四通(Four-way)、三通出口(Tee-Out)及B类弯头(Elbow B)所在平面为x-z平面。

图 1 管道系统几何模型

Figure 1. Geometrical model of pipeline system

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整体网格节点数为4 814 382，单元数为16 531 216，单元类型为四面体(Tet 4)和三棱柱(Wed 6)。为判定网格质量，统计了网格正交品质和倾斜度，结果如图 2和图 3所示。

图 2 网格正交品质统计

Figure 2. Statistics for orthogonal quality of meshing

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图 3 网格倾斜度统计

Figure 3. Statistics for inclination of meshing

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1.3 参数确定

参数主要为求解方程中的常量，与模型、工况和求解方法密切相关。对于结构计算部分，根据GB 50316-2008工业金属管道设计规范和ASME B16.5标准(工业管道压力分级：10~42 MPa为高压，大于42 MPa为超高压)，结合本研究中流体为液态水，选择较低的压力12 MPa作为工况压力。剩余参数单独讨论。

(1) 流体计算参数

将管道主体模型抑制后，Fluent软件内物理模型选择Realizable k-ε湍流模型，材料属性中选择water-liquid(h20〈1〉)作为流体材料，计算域中的实体均选择fluid。求解方法选用SIMPLEC方法。速度入口边界条件需要确定雷诺数Re、湍流强度I和湍流尺度λ，由下式确定

R e = \frac{ρ v_{0} D}{η}, I \approx 0.16 {({R e}_{DH})}^{1 - / 8}, λ = 0.07 L

$Re = \frac{{\rho {v_0}D}}{\eta }, \;\;\;\;\;\;\;\;I \approx 0.16{\left( {{{Re}_{{\text{DH}}}}} \right)^{1-/8}}, \;\;\;\;\;\;\;\lambda = 0.07L$

(1)

式中：ρ为密度，v₀为入口速度，D为几何限度(直径)，η为流体黏度，L为特征长度(本研究中为管道直径)，Re_DH表示基于水力直径的雷诺数。

(2) 疲劳计算参数

分析疲劳时，首先需要导入载荷曲线，即力-时间或振幅-时间曲线，通常由实验获得。本研究着眼于不同子系统与整体系统之间疲劳的相互影响，而通过实验获得与本系统匹配良好的载荷曲线较为困难，为此人工导入常见的白噪声载荷曲线(见图 4，其中纵轴振幅表示加载应力与最大应力的比值)，在所设计的工况下获得接近实际的疲劳分析结果。

图 4 白噪声载荷时程曲线

Figure 4. Load-time curve of white noise

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模拟使用的算法必须与材料模型中提供的S-N曲线(一定循环特征下标准试件的疲劳强度与疲劳寿命的关系曲线，也称应力-寿命曲线)类型一致，且因系统的复杂性，应力组合方法选择带符号的von-Mises等效应力(Signed von Mises)，平均应力修正使用FKM，即使用4个系数定义平均应力的敏感程度。小循环修正选择BS7608，即最大应力循环高于S-N曲线的NC1(10⁶)时，S-N斜率关系式变为b₂=-b₁/(2b₁-1)，否则b₂=0，且损伤为零。图 5给出了本研究所使用材料灰铸铁(Grey Cast Iron BS1452 Grade250)和结构钢(Structural Steel BS4360 Grade 40B)的标准S-N曲线，图中UTS表示抗拉极限强度，S₀为疲劳极限强度，b₁、b₂为斜率, σ为应力，n为循环次数。

图 5 标准S-N曲线

Figure 5. Standard S-N curve

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2. 结果与讨论

计算结果包含流体、结构和疲劳3部分。流体结果主要包含管路系统各部分流速云图。结构计算结果主要包含流体映射力、应力和应变最值及云图。疲劳结果包含管系寿命云图、关键部件和子系统的应力-循环次数曲线。

2.1 流场结果分析

已知工业管道系统的正常流速为1.5~3.0 m/s。首先通过流体计算结果选择分析工况。不同入口速度v₀下管道子系统流速云图如图 6所示，其中v为流速。

图 6 不同入口速度下管路子系统流速

Figure 6. Flow rate of pipeline subsystem for different inlet velocities

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可以看出：入口速度为1 m/s时子系统内流速仅0.36 m/s，远低于要求的正常流速；当入口速度为10 m/s时，子系统流速达到上限要求。因此，以下主要讨论入口速度为3、5、7和10 m/s时的疲劳。

2.2 结构计算结果分析

静力学计算包含映射力导入、管道内部压力设置、边界条件设置。本研究主要针对管道系统在随机激振力作用下的疲劳响应，为避免连接工艺造成的疲劳失效，管路连接部分设置为固支连接。映射力、结构应力最大值σ_max和应变最大值ε_max的计算结果见表 1和表 2，部分部件的应力云图见图 7和图 8。

表 1 管道系统内流体对结构的映射力

Table 1. Mapping force of fluid in pipeline system to structure

Component	v₀/(m·s^-1)	Mapping force/N
Component	v₀/(m·s^-1)	x	y	z
Elbow A	3	1.86	124.00	-147.94
	5	282.56	39.96	-332.05
	7	561.72	142.27	-707.51
	10	5 677.60	-2 269.10	-797.02
Elbow B	3	-0.32	-44.00	2.26
	5	865.42	-1 068.40	0.24
	7	1 745.20	-2 095.90	-9.68
	10	18 628.00	-18 369.00	580.01
Tee-support	3	136.32	-0.23	-3.15
	5	682.44	0.04	-3.56
	7	1 093.30	-1.14	-0.15
	10	2 715.60	-6.83	-32.04
Tee-out	3	472.57	-0.01	343.97
	5	1 707.60	-0.65	1 092.30
	7	3 031.30	-0.24	2 002.40
	10	13 840.00	-20.37	9 474.50
Four-way	3	-8.02	0.25	-186.31
	5	-7.74	1.70	-615.87
	7	-19.67	3.66	-1 173.30
	10	126.58	13.93	-2 455.70

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| 显示表格

表 2 计算结果

Table 2. Calculated results

v₀/(m·s^-1)	σ_max/MPa	ε_max/10^-3	Position with maximum stress
3	285.34	2.28	Tee-out
5	285.37	2.28	Tee-out
7	285.30	2.28	Tee-out
10	287.11	2.29	Tee-out

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| 显示表格

图 7 四通的应力云图

Figure 7. Stress nephogram of four-way

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图 8 三通出口的应力云图

Figure 8. Stress nephogram of tee-out

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由表 1数据可知：不同入口速度条件下异径三通出口x-z平面上的映射力远大于其他部件，说明在系统中此部分的疲劳寿命可能较其他部件低；通过法兰部件改变流体流动方向时，法兰部件所在平面两个方向上的映射力远大于另一方向，说明法兰部件较其他管道部件更容易发生疲劳失效或寿命降低。

从图 7和图 8显示的入口流速为5 m/s时四通和三通出口的静态应力计算结果可以看出，应力最大值发生在法兰管件内部的界面变化处，其余部分均未达到屈服应力。这说明所选择的应力疲劳分析方法是可行的，并且管系连接件可能是发生疲劳的重点部位。

从表 1和表 2数据不难看出，应力最大值(σ_max)和应变最大值(ε_max)受管系初始流体速度的影响较小，因此管路系统整体疲劳寿命结果的影响因素可能是疲劳分析时向管道内施加的随机激振力。

2.3 疲劳计算结果分析

疲劳计算结果包含整体系统和重点部件的疲劳寿命云图，以及各子系统和各部件的应力-疲劳寿命(σ-lg n)曲线，用以和标准S-N曲线(见图 5)对比。

2.3.1 疲劳云图分析

图 9为管道整体系统的疲劳云图，图 10、图 11和图 12分别为四通、出流三通和支座三通的疲劳云图。

图 9 管道系统整体疲劳寿命云图

Figure 9. Fatigue life nephogram of pipeline system

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图 10 四通的疲劳寿命云图

Figure 10. Fatigue life nephogram of four-way

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图 11 出流三通的疲劳寿命云图

Figure 11. Fatigue life nephogram of tee-out

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图 12 支座三通的疲劳寿命云图

Figure 12. Fatigue life nephogram of tee-support

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可以看出：在整体管道系统中未发生疲劳失效破坏，说明管路在本研究所设条件下可以正常运行；但是在出流三通、四通、支座三通位置出现了疲劳寿命极低值，与结构计算中预测的可能出现寿命低值的位置和最终模拟位置相同；最小寿命为1 948，大于抗拉极限强度(UTS)寿命1 000，再次验证了之前选用应力疲劳模型的正确性。

2.3.2 应力-寿命曲线分析

通过在nCode DesignLife软件中提取一定数量模型结点，将这些结点包含的应力和寿命数据记录下来，获得对应部分的S-N曲线，其中包含A类弯头、B类弯头、支座三通、出流三通和四通，如图 13~图 17所示，并与标准S-N曲线(见图 5)进行对比。图 13~图 17所示曲线的变化规律可大致归纳为：不同部件和子系统在相同循环区间内呈现的变化趋势相同，不同入口流速条件下曲线间未发生明显偏移，当循环次数的对数值在3~7范围内时曲线整体呈现非线性变化趋势。

图 13 A类弯头的应力-疲劳寿命曲线

Figure 13. Stress-life curve of A class elbows

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图 14 B类弯头的应力-疲劳寿命曲线

Figure 14. Stress-life curve of B class elbows

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图 15 支座三通的应力-疲劳寿命曲线

Figure 15. Stress-life curve of tee-support

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图 16 出流三通的应力-疲劳寿命曲线

Figure 16. Stress-life curve of tee-out

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图 17 四通的应力-疲劳寿命曲线

Figure 17. Stress-life curve of four-way

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标准S-N曲线(见图 5)中，灰铸铁和结构钢材料曲线在10³~10⁷的循环区间内呈线性变化。而模拟结果中S-N曲线呈现下凹的非线性变化，说明疲劳寿命对应力的敏感度较标准值从常量变为变量，即在寿命区间前段应力变化引起的疲劳变化较小，而在寿命区间后半段应力变化引起的疲劳变化较大。同时也发现抗拉极限强度和疲劳极限强度所对应的寿命得到较大的增强，但在极值之间的寿命却并非等值增加。

从图 18中不难发现，在入口流速为5 m/s的条件下，5种法兰管件在不同取值区间上都满足整体S-N曲线变化趋势，且与单个部件的S-N曲线变化趋势基本相同。说明在管道系统中各部件与整体拥有基本相同的特征曲线，验证了系统对部件的影响同样能反作用于整体。

图 18 不同法兰管件的应力-疲劳寿命曲线

Figure 18. Stress-life curve of various flanges

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3. 结论

(1) 管道系统中只要保证各个子系统内流速处于合理区间内，入口流速对整体系统的影响很小，因此工业实际中需要对各部分进行流速监控，保证其处在合理可控范围之内。

(2) 管道系统内的连接部是发生疲劳失效的重点区域，其中连接不同子系统的三通和四通类法兰管件是影响整体疲劳寿命的关键，并且其疲劳失效多发生于相贯线处的管道内部，需要重点关注。

(3) 管路系统有助于增加内部各个法兰管件在极限状态下的疲劳寿命，降低疲劳敏感度。因此各个法兰管件在短期内可以承受更大的应力变化，在寿命的中后期能更快地趋于稳定，即疲劳极限强度得以提高，但在正常工作条件下对疲劳寿命的增强没有极限状态明显。

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