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Research Opportunities in Corrosion Science and Engineering C Corrosion Modeling The purpose of a corrosion model is to predict an outcome. As such, a model can test or express a theoretical hypothesis in order to increase understanding of a phenomenon. Models are useful only if they are validated and provide reasonable outcomes so that predictions can be tested. In this framework, models are particularly valuable tools to gain knowledge and insight relatively quickly for assessing difficult, complex corrosion problems. It is challenging to predict the result when, for example (1) structural materials are placed in a corrosive environment that can cause several degradation modes to interact with one another,(2) in-service stress conditions cause acceleration of the corrosion rate, or (3) the environment varies dynamically in its corrosion potential. Once validated, corrosion models can support a variety of analyses, such as estimating the required interval between maintenance and repair actions, gauging the effectiveness of various corrosion mitigation approaches, aiding in the selection of materials and coatings, and performing sensitivity analysis regarding the basic assumptions and the initial and boundary conditions used in a corrosion analysis. The word “model” is itself ambiguous, and there is no uniform terminology to define models. Basically, a model is considered to be a representation of some object, behavior, or system that one wants to understand. Models are abstract vehicles for learning about the world. With a well-developed model, significant parts of scientific investigation could be carried out the results are verified by experiments. The validity of a model rests not only on its fit to empirical observations but also on its ability to extrapolate to situations or data beyond those originally
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Research Opportunities in Corrosion Science and Engineering described in the model. The first step in the scientific method is to formulate a hypothesis or theory. A hypothesis is an educated guess or logical conclusion from known facts, which is then compared against all available data. If the hypothesis is found to be consistent with known facts, it is called a theory. Most theories explain observed phenomena, predict the results of future experiments, and can be presented in mathematical form. When a theory is found to be always correct over the course of many years, it is eventually referred to as a scientific law. But theories do not provide the algorithms for the construction of a model; models provide the algorithms needed to support a theory. A theory may be incompletely specified in the sense that it imposes certain general constraints. There are many different types of models used across the scientific disciplines, although there is no uniform terminology to classify them. The most familiar are physical models, such as scale replicas. Algorithms constitute another, completely different type of model. A computer simulation is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system. Frequently, computer simulations are needed to solve a difficult set of equations describing the governing laws of the system (in the case of deterministic models) or to handle a very large amount of data and/or heuristic knowledge (in the case of data-mining-based models).1 In situations in which the underlying model is well confirmed and understood, computer experiments potentially could replace real experiments, which is especially useful when data collection is difficult and expensive. Computer simulations could also be heuristically important; for example, they may suggest new theories, models, and hypotheses based on a systematic exploration of a model’s parameter space.2,3 Several different taxonomies can be used to describe problems in corrosion science: static and dynamic, well and poorly understood, and simple and difficult. For the problems that are well understood, simple, and static, models either exist or can be readily developed to describe the corrosion behavior and to make predictions. Dynamic systems are usually more difficult to model, especially if the evolution of the dynamic behavior is poorly understood. Models can be based in some understanding of the phenomenon or can be based entirely on mined data. 1 P. Humphreys, Extending Ourselves: Computational Science, Empiricism, and Scientific Method, Oxford University Press, Oxford, U.K., 2004. 2 S. Hartmann, Models as a tool for theory construction: Some strategies of preliminary physics, pp. 49-67 in Theories and Models in Scientific Processes (W.E. Herfel, W. Krajewski, I. Niiniluoto, and R. Wójcicki, eds.), Studies in the Philosophy of the Sciences and the Humanities, Volume 44, Rodopi, The Netherlands, 1995. 3 S. Hartmann, The world as a process. Simulations in the natural and social sciences, pp. 77-100 in Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View (R. Hegselmann, U. Mueller, and K.G. Troitzsch, eds.), Series A: Philosophy and Methodology of the Social Sciences, Kluwer Academic Publishers, The Netherlands, 1996.
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Research Opportunities in Corrosion Science and Engineering The success of a model will depend strongly on the relevance and accuracy of the data collected, the level of understanding of the key parameters, and the observed knowledge. One of the perennial debates in the philosophy of science has to do with realism: What aspects of science, if any, truly represent the real world? “Idealization” is a very important part of mathematical models. The degree to which a model has positive analogies is typically described by how “realistic” the model is; i.e., the idea is that more realistic models contain more truth than other models. Model complexity involves a trade-off between the simplicity and the accuracy of the model. It is important to recognize that in addition to the measured observations, the data will contain biases and beliefs inherent in the method used for collecting the data, and uncertainties and inaccuracies due to measurement limitations. For difficult corrosion problems, models built from the bottom up are realistic—models tied to experimental empirical data and observations of a particular system. Deterministic models are derived in a top-down manner from abstract laws and are typically less realistic but more general. Accordingly, there are two complementary approaches for developing corrosion models and predicting corrosion damage: Empirical models based on what has been measured or experienced, and Deterministic models based on known and established natural laws. Within these two classes of models, there exist numerous subclasses. For example, within the empirical class, there are functional models, in which (discrete) data are represented by continuous mathematical functions or by approximations that sometimes follow a natural law. Within the broad class of deterministic models there can exist definite models that yield a single output for a given set of input values; and probabilistic models, in which the inputs are distributed, resulting in a distributed output from which the probability of an event occurring can be estimated.4 Also, as mentioned above, there are other possible ways to classify models: Linear versus nonlinear: If all the operators in a mathematical model present linearity, the resulting mathematical model is defined as linear. Otherwise, a model is considered to be nonlinear. 4 G. Engelhardt and D.D. Macdonald, Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation, Corrosion Science 46(11):2755-2780, 2004.
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Research Opportunities in Corrosion Science and Engineering Static versus dynamic: A static model does not account for the element of time, whereas a dynamic model does. Pure “determinism” is an ideal concept that is probably never achieved in reality and thus integrating deterministic and empirical models could provide the most effective method for predicting corrosion damage.