Parameter Sensitivity Analysis of Pit Initiation at Single Sulfide Inclusions in Stainless Steel
Parameter Sensitivity Analysis of Pit Initiation at Single Sulfide Inclusions in Stainless Steel
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DOI：
10.1149/1.1638384
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发表时间：
2004-02
影响因子：
3.9
通讯作者：
M. Kamrunnahar;R. Braatz;R. Alkire
中科院分区：
文献类型：
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作者：
M. Kamrunnahar;R. Braatz;R. Alkire
采用敏感性分析方法，结合不锈钢中MnS夹杂物附近腐蚀坑形成的数学模型，研究了物理化学参数与电位分布和浓度分布的关系。采用中心差分有限差分法计算灵敏度。孔洞形成的数学模型包括20个组分加电势和13个物理化学参数，包括表面化学反应和电化学反应的速率常数以及均相反应的平衡常数。结果表明，电势和浓度分布对含硫包裹体电化学溶解速率的Tafel斜率最敏感，对均相反应平衡系数的变化最不敏感。电化学反应溶解硫化物包裹体的速率常数也很重要。该程序为选择最重要的参数、设计关键实验和选择最符合实验数据的假设提供了第一步。不锈钢的点蚀~SS！是一种局部现象，可能始于各种类型的表面位置，包括硫化物包裹体。人们对点蚀的兴趣很高，因为这通常是导致缝隙腐蚀、腐蚀疲劳、应力腐蚀开裂和涂层失效的第一步。启动发生的各种机制是一个长期感兴趣的课题，人们越来越多地借助数学模型来研究它。虽然有不同的建模方法，但我们在这里重点介绍一种方法，其中与机制相关的潜在物理现象由物种之间的反应、传输和平衡的连续介质方程表示。虽然复杂腐蚀系统的数值模拟可以提供有用的见解，但也需要额外的数值方法。在这项工作中，我们主要关注不确定性的评估。例如，通过与实验数据的比较来验证模型需要指定腐蚀机理假设，而文献提供了多种合理的选择！以及系统参数的值-其中一些可能很难或不可能直接测量！因此出现了各种各样的不确定性。这项工作的动机是应用数值分析工具来确定与一个特定的机制假说相关的最敏感的参数。这样的工具可以用来解决这样的问题：系统的哪些属性对其观察到的行为负责？反驳或证实一个模型最有希望的实验是什么？几个假设中哪一个最符合来自不同来源的实验数据？硫化物包裹体的作用已被广泛研究。硫化物夹杂物在点蚀过程中起着重要的作用。不同的研究人员已经用一系列实验技术研究了点蚀的开始，以澄清硫化物夹杂溶解早期阶段的各种事件，例如，参考文献。1-3！和坑洞的增长。在硫化物包裹体的溶解过程中发现了含硫物种，并在硫化物溶解过程中的不同位置进行了4-8和pH测量。9研究了外加机械应力对凹坑萌生的影响。10最近，使用电化学微池获得了硫化物包裹体附近的电化学数据和化学成分。11，12在本工作中，我们详细考虑了一个特定机制的数学模型，该机制被开发来模拟电化学微电池中SS中单个MnS夹杂物的凹坑起始。13该模型检验了以下假设：在氯化物存在的情况下，由于硫代硫酸盐离子积累到临界浓度以上，SS的钝化导致凹坑的形成，并且包裹体的溶解速度是由氯化物催化的。该模型用于预测点蚀过程中点蚀电位随时间和距离的变化，以及单个夹杂物的点蚀电位与氯化物浓度的关系。本工作的重点是应用数值方法来评估参数敏感性，并用一种机制假设来演示它们的使用。在这项工作中，耦合的非线性方程组报告
Sensitivity analysis methods were used in conjunction with a mathematical model for corrosion pit initiation in the vicinity of MnS inclusions in stainless steel to investigate the relationship between physicochemical parameters and the potential and concentration distributions. The finite difference method with central differences was used to calculate sensitivities. The mathematical model of pit initiation included 20 species plus the potential and 13 physicochemical parameters including rate constants for chemical and electrochemical surface reactions and equilibrium constants for homogeneous reactions. It was found that the potential and concentration profiles are most sensitive to the Tafel slope of the rate of electrochemical dissolution of sulfur-containing inclusions and least sensitive to changes in the equilibrium coefficients of the homogeneous reactions. The rate constant for the electrochemical reaction for dissolution of sulfide inclusions was also found to be significant. The procedure provides a first step toward selecting the most important parameters, designing critical experiments, and selecting the hypothesis that best fits experimental data. Pitting corrosion of stainless steel ~SS! is a localized phenomenon that may initiate at various types of surface sites including sulfide inclusions. Interest in pitting corrosion is high because it is often a first step leading to crevice corrosion, corrosion fatigue, stress-corrosion cracking, and failure of coatings. The various mechanisms by which initiation occurs, a subject of longstanding interest, have increasingly been investigated with the aid of mathematical models. While there are various modeling approaches, we focus here on an approach where the underlying physical phenomena associated with the mechanisms are expressed by continuum equations for reaction, transport, and equilibration among species. Although numerical simulation of complex corrosion systems can provide useful insight, there is also the need for additional numerical methods. In this work we focus on the assessment of uncertainty. For example, the validation of models by comparison with experimental data requires specification of the hypothesis of corrosion mechanism ~of which the literature provides multiple reasonable choices! as well as values for the system parameters ~some of which may be difficult or impossible to measure directly!. Various kinds of uncertainty therefore arise. The motivation for the present work is to apply numerical analysis tools to identify the most sensitive parameters associated with one particular hypothesis of mechanism. Such tools may find use in addressing questions such as: What properties of a system are responsible for its observed behavior? What is the most promising experiment to refute or confirm a model? Which of several hypotheses best agrees with experimental data from heterogeneous sources? The role of sulfide inclusions has been widely investigated. Sulfide inclusions play an important role in the initiation of pitting corrosion. Various researchers have studied initiation of pitting corrosion with a range of experimental techniques to clarify various events during early stages of sulfide inclusion dissolution, ~e.g., Ref. 1-3! and pit growth. Sulfur-containing species have been detected during dissolution of sulfide inclusions, 4-8 and pH measurements have been taken at various locations during sulfide dissolution. 9 The influence of applied mechanical stress on pit initiation has been investigated. 10 More recently, an electrochemical microcell was used to obtain electrochemical data and chemical composition at the vicinity of the sulfide inclusions. 11,12 In the present work we consider in detail a mathematical model of one particular mechanism developed to simulate pit initiation at a single MnS inclusion in SS within an electrochemical microcell. 13 The model examined the hypotheses that pit initiation occurs by depassivation of SS as a result of accumulation of thiosulfate ions above a critical concentration in the presence of chloride, and that the rate of inclusion dissolution was catalyzed by chloride. The model was used to predict the variation of potential in time and distance during the pit initiation and also to predict the dependence of pitting potential on the chloride concentration for a single inclusion. The emphasis in the present work is to apply numerical procedures for assessment of parameter sensitivity and to demonstrate their use with one hypothesis of mechanism. In this work, the system of coupled nonlinear equations reported