Coupled Environment Fracture Model Research Articles

The Role of Determinism in the Prediction of Corrosion Damage

This paper explores the roles of empiricism and determinism in science and concludes that the intellectual exercise that we call “science” is best described as the transition from empiricism (i.e., observation) to determinism, which is the philosophy that the future can be predicted from the past based on the natural laws that are condensations of all previous scientific knowledge. This transition (i.e., “science”) is accomplished by formulating theories to explain the observations and models that are based on those theories to predict new phenomena. Thus, models are the computational arms of theories, and all models must possess a theoretical basis, but not all theories need to predict. The structure of a deterministic model is reviewed, and it is emphasized that all models must contain an input, a model engine, and an output, together with a feedback loop that permits the continual updating of the model parameters and a means of assessing predictions against new observations. This latter feature facilitates the application of the “scientific method” of cyclical prediction/assessment that continues until the model can no longer account for new observations. At that point, the model (and possibly the theory, too) has been “falsified” and must be discarded and a new theory/model constructed. In this regard, it is important to stress that no amount of successful prediction can prove a theory/model to be “correct”, because theories and models are merely the figments of our imagination as developed through imperfect senses and imperfect intellect and, hence, are invariably wrong at some level of detail. Contrariwise, a single failure of a model to predict an observation invalidates (“falsifies”) the theory/model. The impediment to model building is complexity and its impact on model building is discussed. Thus, we employ instruments such as microscopes and telescopes to extend our senses to examining smaller and larger objects, respectively, just as we now employ computers to extend our intellects as reflected in our computational prowess. The process of model building is illustrated with reference to the deterministic Coupled Environment Fracture Model (CEFM) that has proven to be highly successful in predicting crack growth rate in metals and alloys in contact with high-temperature aqueous environments of the type that exist in water-cooled nuclear power reactor primary coolant circuits.

Customization of the coupled environment fracture model for predicting stress corrosion cracking in Alloy 600 in PWR environment

The coupled environment fracture model (CEFM) has been modified and calibrated to predict crack growth rate (CGR) in Alloy 600 under typical PWR primary coolant conditions. The customized CEFM provides quantitative predictions of the effects of stress intensity factor, hydrogen concentration, yield strength, and temperature on CGR in Alloy 600 in PWR primary coolant environments, as well as explaining the dominating mechanism of stress corrosion cracking (SCC) in this alloy. The importance of the mechanical properties, such as yield strength and stress intensity factor, as identified previously from Artificial Neural Network (ANN) analysis of CGR data in the literature, has been confirmed theoretically. The success in explaining the intergranular stress corrosion cracking (IGSCC) of Alloy 600, argues that the CEFM, which was originally developed to describe IGSCC in sensitized stainless steels, is equally applicable for describing IGSCC in Alloy 600.

Theoretical aspects of stress corrosion cracking of Alloy 22

Theoretical aspects of the stress corrosion cracking of Alloy 22 in contact with saturated NaCl solution are explored in terms of the Coupled Environment Fracture Model (CEFM), which was calibrated upon available experimental crack growth rate data. Crack growth rate (CGR) was then predicted as a function of stress intensity, electrochemical potential, solution conductivity, temperature, and electrochemical crack length (ECL). From the dependence of the CGR on the ECL and the evolution of a semi-elliptical surface crack in a planar surface under constant loading conditions it is predicted that penetration through the 2.5-cm thick Alloy 22 corrosion resistant layer of the waste package (WP) could occur 32,000 years after nucleation. Accordingly, the crack must nucleate within the first 968,000 years of storage. However, we predict that the Alloy 22 corrosion resistant layer will not be penetrated by SCC within the 10,000-year Intermediate Performance Period, even if a crack nucleates immediately upon placement of the WP in the repository.

An advanced coupled environment fracture model for hydrogen-induced cracking in alloy 600 in PWR primary heat transport environment

A theoretical model for hydrogen-induced cracking (HIC) has been developed to estimate the inter-granular crack growth rate (CGR) in Alloy 600 in aqueous environments. In this model, crack growth is assumed to occur by anodic dissolution at the crack tip with the combined effect of nucleation and growth of voids ahead of the crack tip along a grain boundary, and linkage with the main crack due to stress-induced fracture of the remaining ligaments. Under proper electrochemical conditions, hydrogen evolution at the crack tip results in atomic hydrogen diffusing ahead of the crack tip followed by recombination in voids to generate a pressure within a void that increases with time. The hydrogen pressure adds to the hydrostatic stress on the void due to mechanical loading, resulting in an increase in void rupture frequency and hence in the CGR. Calculations were performed for Alloy 600 in PWR heat transport circuit for different electrochemical and mechanical conditions. The calculated results indicate that the hydrogen evolution at the crack tip under PWR conditions has a significant effect on the CGR.

On the shape of stress corrosion cracks in sensitized Type 304 SS in Boiling Water Reactor primary coolant piping at 288 °C

Evolution of the shape of surface cracks in sensitized Type 304 SS in Boiling Water Reactor primary coolant circuit piping at the reactor operating temperature of 288°C is explored as a function of various environmental variables, such as electrochemical potential (ECP), solution conductivity, flow velocity, and multiplier for the oxygen reduction reaction (ORR) standard exchange current density (SECD), using the coupled environment fracture model (CEFM). For this work, the CEFM was upgraded by incorporating Shoji’s model for calculating the crack tip strain rate and more advanced expressions were used for estimating the stress intensity factor for semi-elliptical surface cracks. This revised CEFM accurately predicts the dependence of the crack growth rate on stress intensity factor and offers an alternative explanation for the development of semi-elliptical cracks than that provided by fracture mechanics alone. The evolution of surface crack semi-elliptical shape depends strongly upon various environmental variables identified above, and the CEFM predicts that the minor axis of the ellipse should be oriented perpendicular to the surface, in agreement with observation. The development of the observed semi-elliptical cracks with the minor axis perpendicular to the surface is therefore attributed to the dependence of the crack growth rate on the electrochemical crack length.

Prediction of crack growth rate in Type 304 stainless steel using artificial neural networks and the coupled environment fracture model

A crack growth rate (CGR) database has been developed to train an artificial neural network (ANN). The trained ANN and the extended coupled environment fracture model (CEFM) were used to predict the CGR in Type 304SS as a function of each of the principal variables of the system. The ANN revealed the underlying relationships that map the dependencies of the CGR on the various input independent variables. A sensitivity analysis revealed that IGSCC in sensitized Type 304SS in high temperature aqueous environments is primarily electrochemical in character. Comparison between the ANN-predicted CGR and CEFM-predicted CGR reveal good agreement.

Customization of the CEFM for predicting stress corrosion cracking in lightly sensitized Al–Mg alloys in marine applications

The Coupled Environment Fracture Model (CEFM) has been modified and calibrated to predict crack growth rate (CGR) in aluminum marine alloys. The customized CEFM provided quantitative predictions of the effects of O2, electrochemical potential, stress intensity factor, and conductivity on CGR in lightly sensitized AA5083-H321 in 3.5 wt.% NaCl solution, as well as explaining the development of a semi-elliptical surface cracks. The importance of the properties of the external environment, such as conductivity, oxidant/reductant concentration, and the kinetics of the cathodic reactions on the surfaces external to the crack has been confirmed. Crack growth is attributed to a sequence of microfracture events at the crack front, the frequency of which is determined by the mechanical conditions that exist at the crack tip, as governed by the stress intensity while the microfracture dimension is determined by hydrogen-induced fracture, with the CGR being the product of these two quantities. The success in explaining the intergranular stress corrosion cracking (IGSCC) of aluminum alloys, argues that the basic concept of the CEFM, that the internal and external environments are strongly coupled, is sound and that the CEFM, which was originally developed to describe IGSCC in sensitized stainless steels is equally applicable for describing IGSCC in lightly sensitized aluminum alloys.

On the Shape of Stress Corrosion Cracks in Water-Cooled Nuclear Power Reactor Piping

The evolution of the shape of surface cracks in sensitized Type 304 SS in Boiling Water Reactor primary coolant at 288 oC was explored as a function of the corrosion potential and stress intensity using the Coupled Environment Fracture Model (CEFM). The revised CEFM that incorporates Shoji’s model for calculating the crack tip strain rate and more advanced expressions for estimating the stress intensity factor for semi-elliptical surface cracks provides more accurate prediction of the dependence of the crack growth rate on stress intensity factor and offers an alternative explanation for the development of semi-elliptical cracks than that provided by fracture mechanics. The evolution of the shape of surface cracks depends strongly upon environmental variables, such as the corrosion potential, predicting that the minor axis of the ellipse should be oriented perpendicular to the surface due to the dependence of the crack growth rate on the electrochemical crack length.

The effect of acetic acid on the stress corrosion cracking of 3.5NiCrMoV turbine steels in high temperature water

The effects of acetic acid on the stress corrosion cracking (SCC) susceptibility of ASTM A470/471 turbine disk/rotor steels (3.5NiCrMoV) were evaluated. Thus, this study investigated the possibility of corrosion damage to turbine components due to acidified, early condensates containing acetic acid, which is a common impurity in steam cycle systems. Constant extension rate tests (CERTs) were carried out in aqueous solutions containing acetic acid at various concentrations (pH 3–5) at 150 °C to ascertain the susceptibility in terms of strain to failure and reduction in area upon fracture. Acetic acid significantly affects the SCC susceptibility of the turbine steels with the susceptibility increasing with increasing acetic acid concentration, except at the very highest concentration at which excessive dissolution led to crack blunting. The SCC susceptibility test results were analyzed using the CEFM (Coupled Environment Fracture Model), and it is shown that this model accounts for the experimentally–observed relationships between the SCC growth rate and the concentration of the acetic acid in terms of the conductivity of the solution.

The effect of dielectric coatings on igscc in sensitized type 304 ss in high temperature dilute sodium sulfate solution

Zirconium dioxide(ZrO 2) coatings were applied to sensitized Type 304SS C(T) crack growth rate specimens and to small coupons for corrosion potential measurements via electrophoretic deposition. The interfacial resistance of the coatings was evaluated by electrochemical impedance spectroscopy (EIS). Electrochemical corrosion potentials (ECPs) of un-coated and coated samples were measured against an external pressure balanced reference electrode (EPBRE) in dilute Na 2SO 4 (0.0005 m) solution at 288°C, and it was found that the ECP of the coated samples were consistently 200 to 400 mV more negative than that of uncoated samples. A coated C(T) specimen and an identical, uncoated specimen were exposed simultaneously under load in a refreshed autoclave, in order to measure the crack growth rates. The results from the long-term experiments (400 hours) showed that the surface coatings reduced the IGSCC crack growth rate (CGR) by a factor of more than 10. The reduction in crack growth rate and the negative shift in the ECP were found to scale with interfacial resistance as predicted by the Coupled Environment Fracture Model and the Mixed Potential Model, respectively, assuming that the exchange current density for oxygen reduction scales inversely with the interfacial resistance.

Theoretical Estimation of Crack Growth Rates in Type 304 Stainless Steel in Boiling-Water Reactor Coolant Environments

Abstract The coupled-environment fracture model (CEFM)for intergranular stress corrosion cracking (IGSCC) of sensitized type 304 (UNS S30400) stainless steel (SS) in light-water reactor (LWR) heat-...

Determination of the fate of the current in the stress corrosion cracking of sensitized type 304SS in high temperature aqueous systems

The experimental work reported in this paper was designed to resolve the question concerning the fate of the current that is generated during crack growth in engineering alloys in power plant environments. Two limiting possibilities exist: the cathodic processes that consume the positive ion current generated at the crack tip reside within the confines of the crack; or they reside on the external surfaces. Experiments were conducted which made use of sensitized type 304 stainless steel (SS) compact specimens C(T) that had been modified to provide external surfaces that are isolated from the specimen, so that the current flowing between the crack and the external cathode could be readily monitored. This was done by coating the C(T) specimens with baked-on polytetrafluoroethylene so that only the crack (after fatigue precracking) was exposed to the environment. Cathodes were then mounted on the sides of the C(T) specimen and the current was monitored as the stress intensity and water chemistry were varied. The experiments reported here clearly demonstrate that current flows from the crack to the external cathode during crack propagation in sensitized type 304SS in pure water at the elevated temperatures typical of light water reactor heat transport systems. Thus, in spite of the high resistivity of the environment, the cathodic reaction is not restricted to the flanks of the crack or to the crack mouth, but occurs predominantly on the external surfaces, as postulated in the coupled environment fracture model. New insight has been gained into the physical mechanism of crack growth in high temperature aqueous environments.