Article(id=1246028558670349286, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1705334400000, receivedDateStr=2024-01-16, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775005958477, onlineDateStr=2026-04-01, pubDate=1719244800000, pubDateStr=2024-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775005958477, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775005958477, creator=13701087609, updateTime=1775005958477, updator=13701087609, issue=Issue{id=1246028557319783390, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='3', pageStart='289', pageEnd='426', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775005958156, creator=13701087609, updateTime=1775006058227, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246028977123471371, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246028977123471372, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=326, endPage=340, ext={EN=ArticleExt(id=1246028558947173354, articleId=1246028558670349286, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Peridynamic Modeling of Corrosion Fatigue in Metallic Materials, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Fatigue failure is the most common form of failure in engineering. Under the interaction betweenthe corrosive environment and fatigue load, the fatigue life of a structure is significantly reduced. It often consumes a lot of time and economic costs to evaluate the fatigue properties of materials or structures through corrosion fatigue experiments. Therefore, it is crucial to establish a reliable numerical prediction model for scientific research and engineering design. In this study, we develop a peridynamic corrosion fatigue model, which combines the peridynamic fatigue crack model and the peridynamic stress-corrosion model, according to the superposition model of corrosion fatigue. In this model, corrosion fatigue damage is a linear superposition of corrosion damage and fatigue damage, and the coupling between stress and corrosion is considered. Consequently, the effect of structural deformation on the corrosion rate, the heterogeneity of the products, and the geometry of the corrosion front can be considered simultaneously in the model. The new model is then applied to simulate the corrosion fatigue failure process (including crack initiation and crack growth phases) of stainless steel compact tensile specimens. The simulation results show that the model can accurately describe the complete corrosion fatigue failure process of the compact tensile specimen, with the corrosion fatigue crack initiating randomly but consistently around the expected high-stress region. The decrease in fatigue life due to the interaction between the corrosion environment and fatigue load is captured, and prolonged corrosion time exacerbates the reduction in fatigue life when a lower load is applied. The influence of loading frequency on corrosion fatigue behavior is investigated by calculating the crack initiation life and comparing crack length curves. The model can also capture the significant influence of loading frequency on the fatigue life in corrosion fatigue processes. Reducing the loading frequency extends the corrosion time between each cyclic load, intensifying corrosion damage and ultimately reducing the crack initiation life while accelerating crack growth. The numerical results demonstrate that the introduced mechano-chemical damage model can capture the loading frequency sensitivity.

, correspAuthors=Ziguang Chen, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, 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=Yusong Pan, Xulong Peng, Ziguang Chen), CN=ArticleExt(id=1246028568300470651, articleId=1246028558670349286, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=金属材料腐蚀疲劳的近场动力学模拟, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

疲劳破坏是工程中最常见的一种结构失效形式. 当工程结构在腐蚀环境中服役时,腐蚀环境和交变载荷的共同影响会显著降低结构的疲劳性能. 本文将近场动力学疲劳损伤与腐蚀损伤统一,考虑腐蚀疲劳演化中结构损伤为腐蚀损伤和疲劳损伤的线性叠加;结合近场动力学疲劳模型与应力腐蚀模型,建立近场动力学腐蚀疲劳模型. 该模型同时考虑了结构变形对腐蚀速率的影响和腐蚀前沿产物与几何形貌的非均质性. 应用该模型模拟研究了不锈钢紧凑拉伸试件中的腐蚀疲劳裂纹萌生、裂纹扩展阶段. 数值结果表明本文发展的近场动力学腐蚀疲劳模型可以描述腐蚀疲劳的损伤演化过程,引入的力学损伤与腐蚀损伤相互作用耦合模型以及应力腐蚀关系揭示了阳极溶解对试件疲劳寿命的影响以及疲劳寿命的加载频率敏感性.

, correspAuthors=陈子光, authorNote=null, correspAuthorsNote=
** E-mail:.
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金属材料腐蚀疲劳的近场动力学模拟
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潘雨崧 1 , 彭旭龙 2 , 陈子光 1, 3, **
固体力学学报 | 研究论文 2024,45(3): 326-340
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固体力学学报 | 研究论文 2024, 45(3): 326-340
金属材料腐蚀疲劳的近场动力学模拟
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潘雨崧1, 彭旭龙2, 陈子光1, 3, **
作者信息
  • 1华中科技大学航空航天学院工程力学系,武汉,430074
  • 2长沙理工大学土木工程学院,长沙,410114
  • 3工程结构分析与安全评定湖北省重点实验室,武汉,430074

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Peridynamic Modeling of Corrosion Fatigue in Metallic Materials
Yusong Pan1, Xulong Peng2, Ziguang Chen1, 3, **
Affiliations
  • 1Department of Engineering Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan, 430074
  • 2School of Civil Engineering, Changsha University of Science & Technology, Changsha, 410114
  • 3Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, 1037 Luoyu Road, Wuhan, 430074
出版时间: 2024-06-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.003
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疲劳破坏是工程中最常见的一种结构失效形式. 当工程结构在腐蚀环境中服役时,腐蚀环境和交变载荷的共同影响会显著降低结构的疲劳性能. 本文将近场动力学疲劳损伤与腐蚀损伤统一,考虑腐蚀疲劳演化中结构损伤为腐蚀损伤和疲劳损伤的线性叠加;结合近场动力学疲劳模型与应力腐蚀模型,建立近场动力学腐蚀疲劳模型. 该模型同时考虑了结构变形对腐蚀速率的影响和腐蚀前沿产物与几何形貌的非均质性. 应用该模型模拟研究了不锈钢紧凑拉伸试件中的腐蚀疲劳裂纹萌生、裂纹扩展阶段. 数值结果表明本文发展的近场动力学腐蚀疲劳模型可以描述腐蚀疲劳的损伤演化过程,引入的力学损伤与腐蚀损伤相互作用耦合模型以及应力腐蚀关系揭示了阳极溶解对试件疲劳寿命的影响以及疲劳寿命的加载频率敏感性.

近场动力学  /  腐蚀疲劳  /  力学损伤  /  腐蚀损伤  /  应力腐蚀

Fatigue failure is the most common form of failure in engineering. Under the interaction betweenthe corrosive environment and fatigue load, the fatigue life of a structure is significantly reduced. It often consumes a lot of time and economic costs to evaluate the fatigue properties of materials or structures through corrosion fatigue experiments. Therefore, it is crucial to establish a reliable numerical prediction model for scientific research and engineering design. In this study, we develop a peridynamic corrosion fatigue model, which combines the peridynamic fatigue crack model and the peridynamic stress-corrosion model, according to the superposition model of corrosion fatigue. In this model, corrosion fatigue damage is a linear superposition of corrosion damage and fatigue damage, and the coupling between stress and corrosion is considered. Consequently, the effect of structural deformation on the corrosion rate, the heterogeneity of the products, and the geometry of the corrosion front can be considered simultaneously in the model. The new model is then applied to simulate the corrosion fatigue failure process (including crack initiation and crack growth phases) of stainless steel compact tensile specimens. The simulation results show that the model can accurately describe the complete corrosion fatigue failure process of the compact tensile specimen, with the corrosion fatigue crack initiating randomly but consistently around the expected high-stress region. The decrease in fatigue life due to the interaction between the corrosion environment and fatigue load is captured, and prolonged corrosion time exacerbates the reduction in fatigue life when a lower load is applied. The influence of loading frequency on corrosion fatigue behavior is investigated by calculating the crack initiation life and comparing crack length curves. The model can also capture the significant influence of loading frequency on the fatigue life in corrosion fatigue processes. Reducing the loading frequency extends the corrosion time between each cyclic load, intensifying corrosion damage and ultimately reducing the crack initiation life while accelerating crack growth. The numerical results demonstrate that the introduced mechano-chemical damage model can capture the loading frequency sensitivity.

peridynamics  /  corrosion fatigue  /  mechanical damage  /  corrosion damage  /  stress corrosion
潘雨崧, 彭旭龙, 陈子光. 金属材料腐蚀疲劳的近场动力学模拟. 固体力学学报, 2024 , 45 (3) : 326 -340 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.003
Yusong Pan, Xulong Peng, Ziguang Chen. Peridynamic Modeling of Corrosion Fatigue in Metallic Materials[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (3) : 326 -340 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.003
疲劳断裂是工程问题中最常见、最基本的失效形式之一. 结构在腐蚀环境中发生的疲劳断裂现象称为腐蚀疲劳. 在腐蚀环境与交变应力的共同作用下,结构材料的断裂韧性可能大幅降低,加速疲劳裂纹的萌生与扩展,使得结构的疲劳强度显著降低,最终造成工程结构的过早失效[1]. 实际工程中,大量结构在腐蚀环境中(如酸、盐溶液、高温液体金属、生物环境、活性气体)服役[2]. 因此,腐蚀疲劳是工程中承受交变载荷的构件需要考虑的主要破坏因素之一,具有极大的威胁与广泛性,对腐蚀疲劳进行系统地研究具有重要的理论意义与工程价值[3-5].
腐蚀疲劳是典型的多物理场耦合过程,在过去的几十年里研究人员发展和完善了多种用于模拟复杂多物理场现象的数值模拟技术. 其中有限元法是最早用于模拟力学损伤与化学损伤相互作用的方法之一[6-8]. 此类方法以经典的连续理论(连续介质力学和扩散理论)为基础,在位移或物质浓度不连续的裂纹表面或腐蚀前缘等处会表现出数值奇异性. 近场动力学(Peridynamics,PD)理论是最近二十年来兴起的非局部理论. 该理论的非局部性和空间积分形式,使得损伤能以任意方式和方向进行演变,因此近场动力学天然地适合解决损伤和断裂等不连续问题[9-19].
近场动力学理论和相应的方法已成功应用于诸多领域[20-22]. 在腐蚀损伤方面,近场动力学腐蚀损伤模型由Chen和Bobaru[20]首次提出,该模型将金属离子在电解液中的扩散、腐蚀前沿溶解引起的相变和腐蚀层中的机械损伤有机地耦合在一起,提供了完整的腐蚀损伤描述方法和计算模拟框架[20]. 在非局部腐蚀模型(近场动力学模型)中,腐蚀过程中固液界面的演化是计算结果的一部分,而不是给定问题的一部分,而传统腐蚀模型需要预设界面移动速度. 此后,Siavash等[23]进一步提出了近场动力学应力腐蚀模型,模拟了铜片中因为应力分布不均造成的非均匀阳极溶解腐蚀. 在疲劳损伤方面,Silling和Askari[24]提出了近场动力学疲劳裂纹扩展模型,Zhang等[25]采用该模型,预测了改进紧凑拉伸试件的疲劳裂纹路径和疲劳寿命,验证了近场动力学疲劳裂纹扩展模型的准确性.
目前,近场动力学理论已广泛应用于研究各种材料与加载条件下的疲劳损伤与断裂[26-29],其中仅有少数研究中考虑了服役环境对疲劳行为的影响. 近来,Wang等[30]模拟了三维情况下镍基合金试件中的腐蚀疲劳过程,给出了详细的损伤演化过程. 该工作没有考虑腐蚀造成的界面演化和腐蚀过程中的应力(弹性变形)对腐蚀速率的影响,仅对裂纹萌生阶段进行了预测. 本文将应力与腐蚀速率之间的关系引入近场动力学的腐蚀疲劳模型,并且将界面化学反应的随机性引入该模型,考虑由材料结构非均质引起的应力集中所造成的局部腐蚀加速;采用该新模型,数值模拟研究紧凑拉伸试件腐蚀疲劳过程的损伤演化规律,分析不同载荷水平和加载频率对腐蚀疲劳的影响.
近场动力学是采用非局部相互作用思想对经典连续介质力学理论的一种重新表述,它通过求解空间积分方程描述物质的力学行为[31]. 键基近场动力学(Bond-based peridynamics,BB-PD)是一种常用的PD模型,其特点是假设物质点之间的相互作用力大小相同,方向相反,且均沿着两点连线方向. 该模型因为易于实现,因而受到广泛使用并已成功解决各种脆性断裂问题[32-36].
图1所示,在近场动力学理论中物体Ω中任意物质点x,在时刻t与其周围一定范围内的其他物质点存在直接相互作用,该作用范围记作Hx,称为物质点x的“近场域”. 在t时刻物质点x的近场动力学运动方程为[31]
式中ρbu分别是质量密度,体力密度与物质点的位移场. 积分域Hx是近场域,定义为:. 在二维问题中,近场域通常为圆心在x,半径为δ的圆形区域(三维问题中则是球体),δ也称作近场域尺寸. f是物质点x之间的近场力,描述两物质点之间的相互作用.
由于疲劳破坏经常是脆性断裂,断口没有明显的塑性变形,因此本文假设材料为线性微弹性材料,采用适用于微弹性材料的近场力函数[31]. 对于微弹性材料,近场力可由线性微弹性材料的微势能函数ω推导得到:
式中分别是两物质点的相对位置与相对位移. 对于线性微弹性材料,微势能函数ω为:
式中cξ)是键的微弹性模量,描述了键的弹性刚度,是连接物质点x之间的机械键的伸长率,称作键应变. 对于圆形近场域,近场力f表达式为:
本文研究的是平面问题,为保证满足快速收敛的需求,本文采用二维圆锥形微模量函数[37]
式中E是材料的杨氏模量.
BB-PD模型通过键的断裂表示材料的损伤,当键的伸长率超过临界值s0时,此机械键发生永久性不可逆的破坏. 近场键临界伸长率s0可以根据材料的断裂能确定,对于平面问题,s0与断裂能G0的关系为[37]
BB-PD模型中通过损伤因子d描述材料的损伤演化. 对PD模型采用均匀网格离散化后,物质点(或称节点)x处的损伤因子[38]为:
式中n为此物质点最初相连的机械键总数,nbroken为其中已断裂的机械键数量.
在键基近场动力学的基础上,Silling[24]根据Paris Law经验模型建立了适用于分析均匀材料疲劳损伤与断裂的近场动力学疲劳裂纹模型. 该模型在模拟疲劳裂纹扩展时,既不需要预先定义裂纹,也不需要额外的准则来预测裂纹扩展的方向,因此可以模拟疲劳破坏的全部三阶段:裂纹萌生阶段、裂纹扩展阶段和最终失效阶段. 为了体现材料中疲劳损伤的萌生与累积,该模型引入一个新的疲劳损伤变量λ,称作键的“剩余寿命”,每个键的剩余寿命相互独立并且随着循环加载次数N的增加而减少. λN)初始值为1,当某个键的剩余寿命λN)≤0时,此键因疲劳发生断裂. 文献[24]中Silling建立了λ与循环加载次数之间的关系:
式中为键的循环应变范围,smaxsmin分别是一次循环加载中最大与最小键应变. Am是近场动力学疲劳参数,在疲劳裂纹萌生阶段与扩展阶段分别为A1m1A2m2,由疲劳实验数据校准得到,校准方法可参考文献[25].
假设材料为线弹性,循环键应变可由最大键应变smax与载荷比R=smin/smax表示:
因此,在疲劳模拟中只需计算最大载荷情况.
在近场动力学模型中,腐蚀被视为溶解-扩散过程,物质点x的浓度为Cxt),与其近场域Hx内其他物质点通过扩散键传递浓度信息. 无源、无汇的PD传质方程是[21,39,40]
式中,Cxt)是点x在时间t的浓度,扩散键的微扩散率. 根据键两端物质点的属性(固相还是液相),微扩散率取值不同. 而物质点的固液相属性可以由该点的机械损伤因子表示,损伤因子为1则表示为液相(与周围物质点没有任何机械相互作用),而损伤因子小于1则表示该点为固相点. 这样,我们可以建立微扩散率与损伤因子dxt)间的关系函数[41,42]
式中:kdiss为微溶解系数,kLD)是液体中的微扩散系数. 如图2所示,如果扩散键两端的点都是液体点,kLD)根据电解液的扩散率D计算[40,43]
常温下金属在固体内部的扩散系数与液体中的相比相差若干数量级,因此在模型中,当扩散键两端都是固体节点时(损伤因子均小于1),扩散率被忽略不计(公式(11)). 若其中一个为固体,另一个是液体,则这种键是一个携带阳极溶解微通量的界面键,对应的k=kdiss被称为微溶解系数[41,42].
公式(10)模拟的是界面处阳极溶解的传质和离子在电解液中的扩散,为了描述了腐蚀过程中因界面溶解而导致的损伤演化,近场动力学腐蚀模型中引入了与浓度相关的腐蚀损伤模型(Corrosion-Dependent Damage model,CDD模型)[20]
式中dc表示物质点固相浓度降低造成的机械损伤,Csolid为金属固体未腐蚀时的固体浓度(单位体积中金属摩尔数),Csat为电解液中金属离子的饱和浓度. CDD模型表明,随着物质点中金属失电子转变成离子向外扩散,该材料点相连的部分机械键将断裂. 当物质点金属摩尔浓度降到液体中金属的饱和浓度Csat时,材料完全溶解,固体点转换为液体点,链接该物质点的所有机械键断裂,即d=1. 未发生任何腐蚀的金属物质点(浓度为Csolid),当不考虑机械加载导致的损伤时,其损伤为零.
在近场动力学腐蚀模拟中,金属/电解液界面δ距离内的固体区域为便是溶解区(如图2),其浓度值介于CsatCsolid之间,腐蚀导致的损伤通过公式(13)确定. 在数值计算中,本文通过随机断键的方式来实现公式(13)中的CDD模型,随机断键的几率由腐蚀导致的金属表面物质损失量决定. 具体的实现算法在参考文献[20]中. 通过随机断键,可在材料表面腐蚀区域引入一定的非均质损伤分布.
因为在CDD模型的数值实现中引入了随机性,随着腐蚀过程的进行,将会出现一种特殊情况:物质点所有机械键都已断开,但是其金属摩尔浓度仍然高于液体饱和浓度. 实际上,这部分材料松散地附着在材料基体上,很容易被液体冲走. 为了描述这种耦合的损伤/腐蚀依赖关系,所有损伤因子为d=1的固体节点都被转换为液体节点(即使它们的浓度可能大于Csat). 此模型亦被称为损伤依赖腐蚀模型(Damage-Dependent Corrosion model,DDC). 通过CDD和DDC模型,可有效地描述材料浓度和腐蚀损伤演化.
几乎所有的实验研究表明,拉伸弹性应力会增加阳极的溶解速率,而压应力则减慢腐蚀反应或者不促进腐蚀,这种现象通常使用力学化学理论来解释[44]. 根据文献[23],在近场动力学应力腐蚀模型中,弹性变形区域中kdiss与机械键的键应变之间的关系为[23]
式中,smaxsmin分别是连接到点xS的机械键的最大和最小键应变. 对于小变形问题,a是一个常数,对于平面应变等于1,对于平面应力条件则等于1/2[23].
对实际工程结构的完整性进行评估或对其腐蚀疲劳寿命进行预测时,需要理解裂纹萌生阶段点蚀的演化规律和裂纹扩展阶段的腐蚀演化与裂纹扩展间的相互作用. 目前Wei和Landers[45]提出的线性叠加模型及各种修正模型为腐蚀疲劳的主要分析方法. 该模型认为腐蚀疲劳的裂纹扩展速率可以看作是应力腐蚀和单纯疲劳损伤两个过程的裂纹扩展速率叠加的结果,即:
式中为腐蚀疲劳裂纹扩展速率;为应力腐蚀裂纹扩展速率;为惰性介质中的疲劳裂纹扩展速率.
在此理论的基础上,本文将近场动力学疲劳裂纹模型与应力腐蚀模型结合,腐蚀疲劳损伤视作疲劳损伤与应力腐蚀损伤的叠加,建立近场动力学腐蚀疲劳模型,如图3所示,该模型的计算流程如下:
(1)模型的初始化:进行节点生成、分配初始浓度与损伤和边界条件施加等操作;
(2)准静态求解:在当前载荷和损伤下求得准静态解,得到位移、键应变和键应变范围;
(3)更新机械损伤:若键应变大于临界键应变s0,直接破坏此机械键,反之则根据疲劳裂纹模型计算经过循环加载步长ΔN次后机械键的剩余寿命,破坏所有满足λ<0的机械键;
(4)更新腐蚀损伤:首先更新损伤因子d,并通过d更新微扩散系数,之后根据加载频率f得到循环加载步长ΔN所花费的时间间隔Δt,随后求解应力腐蚀模型中的PD扩散方程更新时间Δt内物质点的浓度C,通过浓度变化获得相应的腐蚀损伤,最后再次更新损伤因子d
(5)准静态求解:在当前载荷和损伤下求得准静态解,更新键应变,若键应变满足s>s0,破坏此键;
(6)重复第(2)~(5)步骤进行下一个循环加载ΔN的计算.
通过该方法可以在小变形假设下自然地将疲劳损伤和腐蚀损伤耦合. 在PD疲劳裂纹模型中,物质点承载位移(u)和疲劳载荷导致的损伤(df)信息;在应力腐蚀模型中,物质点携带浓度(C)和腐蚀导致损伤(dc)信息. 图4总结了腐蚀演化、损伤和疲劳之间的相互作用.
图4中的顶部开始,沿顺时针方向有:腐蚀溶解在腐蚀前沿附近引起腐蚀损伤,造成机械键破坏dc(参考公式(13));当损伤因子更新后,在当前疲劳载荷下,根据公式(1)求解并更新位移ud)(和键应变);根据公式(14)中的应力/腐蚀关系,可以更新腐蚀速率ks)(微溶解系数). 沿逆时针方向:腐蚀过程的演变导致固液边界移动,这进一步改变了疲劳载荷下的位移分布uC). 位移改变后会影响机械损伤的产生df(机械键的疲劳断裂和达到临界键应变后的直接断裂). 根据公式(11)中损伤依赖的腐蚀关系,更新微溶解系数kd),累积的机械损伤进一步推进腐蚀过程.
研究循环载荷与腐蚀环境的协同作用下,金属中的疲劳裂纹如何萌生和扩展是腐蚀疲劳研究的主要内容之一,通过该研究可为腐蚀环境下结构的耐久性、可靠性和损伤容限设计提供理论基础. 上节建立了近场动力学腐蚀疲劳模型,本节应用该模型模拟304L不锈钢紧凑拉伸试件的腐蚀疲劳过程,研究腐蚀环境中金属阳极溶解与疲劳行为的相互影响.
用于模拟的紧凑拉伸试件如图5所示(平面应变),疲劳载荷F=6 kN,载荷比R=0.1,加载频率f=1 Hz. 腐蚀环境中,循环载荷的频率会显著影响腐蚀疲劳过程,在后文中将讨论PD腐蚀疲劳模型中分析加载频率影响的能力. 为了模拟对比惰性环境和腐蚀环境下疲劳裂纹的萌生,本节不在试件中设置预裂纹(仅设置缺口). 假设材料为304L不锈钢,其杨氏模量E=190 GPa. 试件的PD疲劳参数通过文献实验[46,47]的数据校准后分别为:A1=1820.53、m1=2.08、A2=4.5914×1014m2=4.036.
根据文献[20]可知,不锈钢中固体浓度Csolid和饱和浓度Csat的典型值分别是143 M和5.1 M. 为模拟反应控制的腐蚀状态,假设腐蚀速率相对较小,根据文献[48],认为腐蚀前沿的溶解率Ddiss为0.01 μm2/s,对应的. 不锈钢中的应力依赖系数γ根据文献[48]中有关应力腐蚀开裂的研究取γ=100. 本文的目的是建立近场动力学腐蚀疲劳模拟框架,并以此定性地研究材料腐蚀疲劳行为. 针对实际服役工况中腐蚀疲劳行为的定量预测,还需要对溶解率、应力腐蚀依赖系数、断裂能等进行具体标定校准.
为模拟试件完全处于溶液中的腐蚀疲劳过程,将试件除了销钉孔以外的边界层和缺口内部设置为液体节点(销钉孔处需要插入销钉,本文暂时不做考虑,因此在销钉孔处施加零通量无腐蚀发生的条件),即金属离子浓度为0(反应控制腐蚀过程的浓度边界条件). 假设试件被新鲜的溶液反复持续冲刷,因此模拟过程中保持液体节点的金属离子浓度始终为0,试件的其余部分的初始浓度则设为Csolid(如图5所示). 采用Δx=0.15 mm和δx=4将试件离散为64722个计算节点.
我们首先模拟紧凑拉伸试件在惰性环境下的疲劳过程,为后续的腐蚀疲劳模拟结果提供对比参考. 试件的损伤与位移演化如图6所示. 在疲劳加载的初期,疲劳损伤正处于萌生阶段,此时位移分布均匀且呈现反对称现象. 随着疲劳过程的进行,由于应力集中现象,疲劳损伤逐渐在缺口尖端处萌生并发生累积(图6(e)),竖直方向位移也持续增大并出现不连续性(见图6(a)-(c)),最终疲劳裂纹在尖端处萌生并持续扩展(见图6(f)).
现保持疲劳载荷不变,在疲劳过程中引入腐蚀因素,试件在腐蚀疲劳过程的金属离子浓度,损伤演化和位移演化分别如图7上、中、下所示. 随着腐蚀疲劳的进行,由于浓度梯度引起的向外扩散,试件周围与中部缺口处的浓度逐渐降低(如图7(a)-(c)所示),腐蚀损伤逐渐在试件外边缘产生并累积(如图7(d)-(f)). PD模型中腐蚀损伤通过破坏机械键实现,因此缺口尖端的应力集中现象加剧,局部的应力水平提高,最终造成疲劳裂纹萌生和扩展所需的循环数显著减少.
腐蚀疲劳裂纹的萌生寿命是评价腐蚀疲劳的一个重要指标,同时也是评价模型可行性的一个重要标准. 图8中比较了腐蚀环境与惰性环境下的疲劳裂纹萌生寿命,其中腐蚀环境中的萌生寿命为了排除随机过程带来的偶然性影响,每种荷载都计算六次. 从结果可以看出腐蚀环境的计算结果呈现一定随机性,但两种环境中裂纹萌生寿命皆随荷载增大而减小,并且腐蚀环境下的裂纹萌生寿命显著降低. 此外根据图8(b)的寿命降低率(腐蚀环境下疲劳寿命的减少量与机械疲劳寿命的比值)可知,当疲劳载荷较大时,腐蚀环境中的萌生寿命与惰性环境接近,并且随着载荷减小,腐蚀环境导致的裂纹萌生寿命降低现象更加明显. 这是因为施加低荷载时会导致相对较长的萌生寿命,试件被腐蚀时间更长,金属表面附近腐蚀损伤更严重. 图9展示了荷载为6 kN的试件裂纹萌生时缺口处的损伤分布情况,可以看出裂纹萌生的位置呈现随机性,但总是位于试件的高应力区域. 尽管本文发展的PD腐蚀疲劳模型的计算结果存在一定偶然性,但实际的疲劳寿命也存在随机性,因此模拟结果可以接受的.
在腐蚀疲劳过程中,腐蚀环境与机械效应(疲劳载荷)之间存在着主导互换. 提取缺口尖端处的疲劳机械损伤和腐蚀损伤并绘制于图10中,在腐蚀疲劳初期,腐蚀损伤随时间均匀地增加,此时腐蚀损伤占主导(图10(d)-(e)). 随后,疲劳裂纹在缺口尖端萌生,裂纹进入扩展阶段(图10(b)). 此阶段腐蚀损伤累积的速率没有发生变化,裂纹的加速扩展说明在腐蚀损伤持续累积的情况下,相对于疲劳裂纹扩展引起的机械键断裂,腐蚀引起的机械键断裂在这一阶段是较小的,疲劳损伤成为了主要的损伤来源(图10(h)-(i)). 这表明疲劳引起的机械损伤大于腐蚀引起的损伤,从而实现了两者对结构失效的支配作用的互换.
为了更好地说明此现象,对试件施加6 kN疲劳载荷,并在腐蚀疲劳裂纹扩展至大约10 mm时视为试件失效,分别统计此过程中由腐蚀和疲劳造成的断键数量并展示在图中. 结果表明,整个腐蚀疲劳过程中,腐蚀引起的断键数量均匀增加,但在裂纹进入扩展阶段后,疲劳载荷引起的断键数迅速增加. 图11显示了疲劳损伤萌生之后的循环加载数和断键数,由结果可知,在腐蚀疲劳后期,疲劳所导致的断键数超过腐蚀损伤,疲劳损伤累积速度也超越腐蚀损伤,证明了两者对结构失效的支配作用的互换. 同时也可以看出腐蚀疲劳过程中,裂纹扩展阶段所占的比例远小于萌生阶段,裂纹萌生寿命占整个腐蚀疲劳的主要部分.
与惰性环境中的疲劳不同,由于腐蚀疲劳需要考虑腐蚀环境的作用,因此需要考虑频率因素的影响. 通常来说,f越大,疲劳载荷的作用越大,疲劳开裂过程越接近惰性环境中的疲劳. 反之,若f趋近于0,则腐蚀疲劳过程接近于应力腐蚀开裂,疲劳载荷的作用也减小,因此研究腐蚀疲劳的频率因素是非常必要的.
为验证加载频率对腐蚀疲劳的影响,现保持其他模型参数不变,分别采用f=0.1、1和5 Hz进行模拟,图12图13分别展示了裂纹转换为扩展阶段时试件的损伤分布和裂纹萌生寿命-加载频率关系,可以看出腐蚀疲劳明显受到加载频率因素的影响. 在图12中,试件的受损伤状态随着频率降低而加剧. 相较于f=1 Hz的情况,加载频率f=0.1 Hz的试件边缘受腐蚀更加严重,尤其是在应力集中较为明显的缺口处(图12中红色矩形内). 在图13观察裂纹萌生寿命随着频率的降低而降低. 此外,加载频率越高,试件的裂纹萌生寿命与惰性环境中的越接近,但不论频率多少,腐蚀环境下试件的疲劳性能相较于惰性环境皆有所降低. 导致这种结果的原因是降低加载频率会改变每个加载周期内腐蚀环境对材料的作用时间. 加载频率越低则代表每个循环载荷周期内材料受到的腐蚀时间越长,受到的腐蚀损伤越严重,因而降低了萌生寿命.
为了研究加载频率对裂纹扩展的影响,在试件缺口尖端设置长度为0.9 mm的预裂纹后进行模拟,获得的裂纹萌生寿命曲线和裂纹长度曲线如图14(a)所示. 在裂纹扩展阶段,降低加载频率会使得裂纹扩展加快,低频率加载时有更严重的腐蚀损伤,试件的完整性更差,裂纹尖端的应力强度因子增加,促进了疲劳裂纹扩展,最终使得低频率加载试件的裂纹扩展寿命低于高频率加载的试件. 实验[49]中研究了腐蚀疲劳的加载频率敏感性,实验结果图14(b)展示了海水环境中,施加不同加载频率时紧凑拉伸试件的裂纹长度与循环加载次数的关系. 通过比较看出PD模拟结果中裂纹增长速度与实验结果有相同的趋势,可认为PD模型能够捕获腐蚀疲劳中的加载频率敏感性.
值得注意的是,本文提出的近场动力学腐蚀疲劳模型,是结合已有的近场动力学疲劳模型[24]和应力腐蚀模型[23]得到的,其中,疲劳模型基于Paris Law经验模型,将经典的Paris Law疲劳模型转化成近场动力学键的剩余寿命模型. 该模型仍然是基于实验统计的经验模型,故不能反应裂纹尖端的变形状态,以及疲劳过程中裂尖的弹塑性扩展机理. 最近,Dong等[22,50]将近场动力学被与离散位错动力学(DDD)相结合,发展出的DDD-PD模型在模拟材料弹塑性开裂时,无需预设裂纹扩展路径和内聚力区域,裂纹扩展路径由位错与裂纹的相互作用自动确定,在今后的工作中我们可以采用该模型来理解疲劳裂纹扩展中的韧脆循环转变机制,也可以将DDD-PD模型与近场动力学腐蚀模型相结合,从物理机制出发模拟研究材料的腐蚀疲劳行为.
本文将近场动力学疲劳演化模型与腐蚀损伤模型相结合,建立了新的近场动力学腐蚀疲劳模型. 该新模型可以模拟腐蚀疲劳过程中复杂的界面演化、表面损伤和裂纹扩展等不连续问题. 模型考虑了应力分布演化与腐蚀演化之间的相互作用关系,并在生成腐蚀损伤时引入了随机性以体现腐蚀前沿产物与几何形貌的非均质性,反映由材料结构非均质引起的应力集中所造成的局部腐蚀加速.
采用本文建立的腐蚀疲劳模型,我们数值模拟研究了紧凑拉伸试件完整的腐蚀疲劳破坏过程,分析了腐蚀环境与疲劳载荷相互作用引起的疲劳寿命降低现象. 数值结果表明:腐蚀疲劳裂纹裂纹萌生位置呈现一定随机性,但总是在预期的缺口高应力区域萌生;施加低载荷时,腐蚀环境导致的疲劳性能劣化更为明显;当腐蚀疲劳进入裂纹扩展阶段后,裂纹扩展代替腐蚀作用成为主导地位,腐蚀疲劳从腐蚀损伤主导逐步转变为疲劳损伤主导,标志着裂纹的快速扩展与试件即将失效. 此外,基于该模型的数值算例揭示了循环载荷的加载频率对腐蚀疲劳寿命有显著的影响,加载频率较低时,每次循环载荷之间腐蚀作用的时间更长,从而导致腐蚀损伤的加剧,最终使得裂纹萌生寿命降低且裂纹扩展加快.
  • 国家自然科学基金面上项目(12372208)
  • 中央高校基本科研业务费专项资金(2021GCRC021)
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2024年第45卷第3期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.003
  • 接收时间:2024-01-16
  • 首发时间:2026-04-01
  • 出版时间:2024-06-25
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  • 收稿日期:2024-01-16
基金
国家自然科学基金面上项目(12372208)
中央高校基本科研业务费专项资金(2021GCRC021)
作者信息
    1华中科技大学航空航天学院工程力学系,武汉,430074
    2长沙理工大学土木工程学院,长沙,410114
    3工程结构分析与安全评定湖北省重点实验室,武汉,430074

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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
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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