The repeated occurrence of environmentally assisted cracking (EAC) in many metallic components subjected to usual design loads and normal service conditions has been costly and common to several industries. Proper quantitative assessment of the EAC damage is essential not only from the safety and reliability point of view but also for the basic economic decision as well. Unfortunately, only little guidance has been offered by the design or inspection codes which is specific to such an assessment. Clearly, there is an engineering need to develop and evaluate comprehensive, reasonably accurate approach(es) to address EAC issues.

In this paper, we discuss an engineering model and its results for the stress corrosion cracking (SCC) of Ni-Cr-Fe Alloy 600 in high purity water. The modeling approach is based on the observation believed to be common to many alloy--environment systems and several likely mechanistic processes leading to the SCC. The observation refers to the fact that a local deformation process repeatedly interrupts the protective qualities offered by the interface between the underlying alloy material and the immediate environment. Also, the fact that significant interaction between the environment and the deformation affects the local development of damage---be it void formation, vacancy migration, microcracking, etc.---is accounted for in the structure of the model that uses strain rate and damage mechanics in engineering sense.

In addition, a framework for adopting the above model or its results is discussed with the focus on addressing the application-specific service conditions, in order to relate these as influence factors. The suggested framework is probabilistic in nature and its purpose is to account for the uncertain and variable nature of the service related influence factors. Introduction

This paper deals with the quantitative evaluation of SCC damage, particularly to illustrate the predictive capabilities of a cumulative type of damage approach based on significant phenomenological observations. The specific application examined in this work deals with the intergranular stress corrosion cracking (IGSCC or SCC for short) of Ni-Cr-Fe Alloy 600 (UNS N06600) in pressurized water reactor environments. This particular SCC has become a generic phenomenon requiring extensive and better assessment than before. The SCC, however, is not limited to this system and several repeated occurrences of SCC in metallic components subjected to usual design loads and normal service conditions continue to be costly and common to several industries (Jones, 1992).

Although the SCC failures or its progression in service components has been one of the dominant modes affecting the design reliability or structural margins, there is to-date very little specific guidance to address this mode through the usual design and inspection codes, especially for a dependable quantitative evaluation. There is a clear need to develop a useful approach or a computational tool to account for this damage mechanism. This paper discusses one possible approach to address this need. The basis and rationale for the type of approach and its emphasis on strain rate are briefly discussed before describing the modeling details. This is followed by the section on results of application of the model to various load--geometric conditions with the purpose of illustrating the predictive capabilities of the model which are also discussed from the point of view of deterministic as well as probabilistic evaluation of the damage and the model parameters.

Strain Rate Dependence of the SCC

In recent years, the importance of deformation mechanics (i.e., local strain rate) has been generally recognized, with increasing emphasis in data interpretation and quantitative evaluation, in relation to SCC of many ductile alloys used in aqueous environments. This is particularly the case where anodic dissolution and/or film-rupture processes are believed to be operative. Similar importance has also been demonstrated in some cases where the basic mechanism may involve effects of the cathodically generated hydrogen (e.g., Scully and Moran, 1988). This basic relation between slow straining and SCC has been shown to be applicable, consistent with many observations from the service and testing, in the case of SCC of Alloy 600 in many aqueous environments (e.g., Garud, 1983; Garud & McIlree, 1995). Also, the strain rate required for sustained SCC damage invariably falls below a low critical value, and this condition is easily generated under the creep information.

Experimental confirmation has been offered by Sung and Was (1991) showing that (a) Alloy 600 does creep around 360 C, and (b) the creep deformation plays an important role in the intergranular cracking in high purity water environment. Another series of tests by Boursier et al. (1992) demonstrated that the creep of Alloy 600 tubing material was responsible for the SCC in primary water environment and that the strain rate was an important variable, rather than the stress, per say. The latter conclusion was based on three comparative tests with the following outcome: (a) Two specimens were subject to the same applied strain rate for 300 hours in water after prestressing, with the only difference being that one specimen was preloaded (rapidly in inert environment and unloaded before straining in water) to a low stress (360 MPa) and the other to a high stress (740 MPa). The latter specimen, during straining, had to be loaded to 850 MPa, as opposed to 510 MPa for the low prestress specimen; however, the highly loaded specimen produced less severe stress corrosion cracking than the other specimen. (b) Third specimen was exposed for 300 hours in water under constant load of 850 MPa, with obviously decreasing creep rate, as opposed to a constant applied strain rate, and it did not result any measurable SCC.

The need and importance of slow straining action for the occurrence of SCC is not limited to the Alloy 600 in primary water environment. For example, the interaction of low temperature creep and aqueous environment has been recently demonstrated for (a) austenitic piping steels in light water reactors (Garud, 1987), (b) duplex stainless steels in a variety of sour environments containing H₂S, CO₂, and Cl^- (vanGelder et al., 1987), (c) ferritic pipeline steel (API 5L X60) in carbonate/bicarbonate environment (Festen, et al., 1990), and (d) austenitic stainless steels in calcium chloride solution (Leinonen, 1996).

It is important to repeat the following points (Garud & Gerber, 1983 and Garud, 1987): (1) in many applications producing the SCC damage, slow strain rates are essential as they allow enough time for environmental action and disrupt the otherwise protective interface (i.e., effectively act as a de-passivating force), (2) the source of strain rates can be steady or cyclic applied loads, the initial (residual) stresses, and the SCC damage process itself, (3) commonly used metallic materials do creep even at low temperatures and low stresses (e.g., Garud, 1987 and Festen, et al., 1990), and (4) the total creep may be negligible by itself but what's important from SCC point of view is the associated slow strain rates over long periods. It is also being generally recognized that the actual mechanistic details may point to a combination of local dissolution and the associated effects of hydrogen, either through enhanced plasticity or through the classical embrittlement, at least for the low-to-medium strength alloys in aqueous environments.

SRDM Formulation

The significance of strain rate in relation to the kinetics of a growing stress corrosion crack was incorporated in an incremental (cumulative) damage formulation called the strain rate damage model (SRDM). The model was developed for the SCC of steam generator tubes, made of Ni-Cr-Fe Alloy 600, in the primary water (high purity, near neutral, about 300 C), e.g., see Garud (1985 and 1990). Strain rate alone, as any other significant factor alone, is not sufficient for the SCC but it is essential and, as a predominant driving force, provides a unified basis for evaluating and correlating different types of loading conditions. The results discussed below illustrate the predictive capabilities, such as the stress-dependence, threshold stress, and crack growth analysis, based on the laboratory type of data. Also, the relation between SRDM and the plausible mechanism, especially involving the film-rupture concept, is obvious and can be exploited for more fundamental aspects of SCC. The cumulative damage concept allows for the accounting of (temporal and spatial) changes in the kinetics of SCC and, phenomenologically, addresses the local interaction between mechanical and environmental damage processes.

Briefly, the model integrates three sets of inter-related concepts:

(1) A damage rate expression describing the local rate of SCC in terms of the local strain-rate and environment--material specific parameters. For example, the following relation was used for Alloy 600:

dDdt = a₀ exp[-Q/RT] (de_net/dt)^f when de_net/dt < de_ucr/dt

where a₀₀, Q, f, and de_ucr/dt are the environment--material specific parameters of the SCC process, T is the absolute temperature, and R is the universal gas constant. dD/dt is the damage growth rate corresponding to the local strain rate de_net/dt.

(2) An effective stress, s(D), that accounts for the extent, D, and growth rate dD/dt of the local SCC damage, whose evolution is given by the following expression:

where _nom is the nominal stress (without the damage), and g₁ and g₂ depend on the geometry and accumulated damage. The effective stress is used to compute the local strain rate d_net/dt, so that the latter is dependent on the rate and accumulation of damage. This computation uses the constitutive relations for material stress--strain response.

(3) The external loads and component geometry are used to compute the nominal stresses and strains through the use of material constitutive relations as well. In this case the same relations are used for local and nominal response, with the implication that the basic material deformation behavior is modified only through the effective stress. It is, however, possible to substitute a different set of constitutive relations for local response, provided such can be independently established. The constitutive relations used in this application for Alloy 600 were developed following the Bodner and Partom approach (Garud, 1985 and 1990).

The above approach is also summarized in the schematic flow-chart shown in Figure 1.

Figure 1 -- SRDM logic diagram (schematic) for cumulative damage approach to quantitative evaluation of SCC failure time and/or crack growth kinetics (Garud, 1990).

For general application of the model the cumulative damage equations are numerically integrated for a given loading history. Currently, the formulation has been used for uniaxial loading conditions such as the constant extension rate and the constant nominal stress, either for a plate, a round bar, or a circular tube geometry.

The environment--material specific damage parameters can be determined from the observations under constant (slow) strain rate tests and the results of simulation using the numerical solution. The main observations used to calibrate the model are: total time to failure and applied strain at failure, covering the strain rates and temperatures of interest. A typical set of these values, derived for the mill-annealed (MA) condition of Alloy 600 tubing application in high purity (de-oxygenated), high temperature water, is as follows (Garud, 1990), when dD/dt is expressed in m/s and d/dt is in 1/s:

Results and Discussion

The application of SRDM to simulate the slow strain rate type of loading condition was covered in the previous publication (Garud, 1990), showing that the model predictions were in agreement with the common trends such as: the reduction in maximum stress, the lowering of failure strain, and the increasing amount (or severity) of SCC with the lowering of applied strain rate. Figure 2 illustrates some of these predictions in comparison with the data trend. Another important trend, also observed for SCC of Alloy 600 under the slow strain rate test conditions, predicted by the model was the need to apply lower strain rate to produce measurable SCC at lower temperatures.

Figure 2 -- Data (points) and SRDM predictions (lines) for constant extension rate loading of Alloy 600 specimens in lithium--borated water at 365 C (Garud, 1990 & 1991).

The stress dependence and temperature dependence as predicted by the model, using the above specific parameters for Alloy 600, were shown to be in good agreement with independent tests and service experience (Garud, 1991_a and 1992); these predictions were also interpreted in terms of the crack growth rate evaluation. More recent application of the same model was to deduce a simple form of stress versus failure time based on these predictions obtained from the simulation of SCC damage growth in a tube under axial stress. These results are shown in Figure 3. It was found useful to express this stress dependence in terms of the applied stress normalized by the respective yield strength (at room temperature, under high strain rate of about 0.0001 1/s). The figure includes predictions for additional material conditions of cold worked (CW), high temperature mill-annealed (HTMA), and thermally treated (TT) after mill-anneal. These predictions were based on an engineering judgment with simple modification of the single model parameter ₀, to illustrate the material sensitivity: these values are 127400, 101922, and 67948, for CW, HTMA, and TT, respectively.

Figure 3 -- Suggested form of the stress-dependence based on the simulations for constant stress condition using the SRDM, and sensitivity to model parameters.

The predicted stress dependence from all of the above simulations for different material conditions can be given by the following logarithmic (or inverse exponential) expression:

where A and represent the environment--material influence for the failure time, t_f, under the stress , normalized by the yield strength _y. The fitted lines are shown in Figure 3 along with the model predictions. The fitted parameters are: A = 1.198, 1.791, 1.733, and 1.730, with = 3808, 1518, 6880, and 15389 days, for CW, MA, HTMA, and TT conditions, respectively. This simplification and the predicted stress dependence has additional benefits: the parameter A appears to be related to the ratio of ultimate to yield strengths for that material condition, and the parameter is related simply to the SCC failure time at yield stress level. The form of the prediction curve is consistent with the expectation that at very low failure times the stress should correspond to the ultimate strength. Also, at the very low stress, below yield, the model predicts a stress threshold as shown previously (Garud and McIlree, 1990). These predictions are in reasonable agreement with recent experimental work on Alloy 600, although in somewhat aggressive environment of 10 percent NaOH (Vaillant, et al., 1995), as shown in Figure 4.

Figure 4 -- Threshold stress predictions (Garud & McIlree, 1990) and test estimates (Vaillant, et al., 1995) for Alloy 600 in high temperature aquueous environments.

When the estimated damage is associated with the crack size it is possible to interpret the results of analysis in terms of the crack growth rate. This interpretation was shown to be consistent with the expected SCC kinetics and the predictions were in good agreement with independently obtained test data on crack growth in Alloy 600 (Garud, 1992 and Garud & McIlree, 1995). The above simplifications and predictive capabilities were recently used to demonstrate the probabilistic evaluation of SCC life of steam generator tubes (Garud and McIlree, 1995). In particular, it was shown that the major part of scatter can be attributed simply to the expected variation in the stress level for these tubes, and the predictions were consistent with the estimated slope on Weibull distribution plot. This probabilistic evaluation was based on the use of deterministic SRDM with assigned statistical variability to the model input. The approach can be generalized through the use of a Monte Carlo simulation procedure to address the variations in other parameters as well as the modeling uncertainty. For this purpose, a calibrated Bayesian method (CA-BALIFE), shown to be useful in another boiler tube application (Basuner, 1988), may be used for the statistical simulation so that the input characteristics can be adjusted based on the additional or new data from the service failure history as well. This approach of integrating the physically based model (i.e. the phenomenon), such as the SRDM, with the inspection results or the service records (i.e. the real world) offers a rational and predictive capability with the appropriate means to reduce the variability and uncertainty in the damage assessment.

The SRDM approach differs from the conventional fracture mechanics application to assess the SCC, and as illustrated above, the predictive capabilities and results are also different. A brief commentary on this difference in emphasis is in order; additional discussion was offered in previous publications (Garud, 1991 and 1992). It is possible that the importance (or kinetics) of local corrosion--deformation (or metal--environment) interaction processes significantly alters with changes in crack size and the associated stress intensity factor. For example, it is unlikely that the environmental influence will be the same through the entire span from practically zero crack length to the development of critical crack for all geometries (Garud, 1992). Likewise, it is more likely that the growth kinetics of an in-situ developed crack (in service) will be significantly different than that of an artificially introduced crack (such as at the beginning of a fracture mechanics type test specimen) of same size or stress intensity, due to the possible difference in the resulting crack tip environment and/or strain-field. Also, the fracture mechanics related SCC work previously reviewed (Garud, 1991_b) showed that the introduction of time-dependent deformation aspects (including creep) in a sub-critical crack growth mechanism often requires additional factors such as the absolute crack size (or net section stress) and the (instantaneous) crack growth rate, which are analogous to the use of D and dD/dt in the above SRDM formulation.

Thus, the breakdown of similitude on account of several significant factors, such as the localized plasticity and its interaction with the local environment (dissolution), crack size influence in determining the local environment, needs to be addressed. At least, the continued use of fracture mechanics parameters, which is fundamentally and practically based on satisfying such a similitude, must be carefully re-evaluated before their generalized application to the synergistic and time-dependent phenomenon of SCC.

Conclusions

This paper presented the strain rate based damage model for quantitative evaluation of SCC and discussed the predictive capabilities illustrating them with results from the slow strain rate tests, constant stress loading on flat plate and tubular geometries, and fracture mechanics type tests. The SRDM formulation specifically accounts for the local interactions between mechanical, microstructural, and electrochemical factors. Although this accounting is phenomenological, the model structure is rational and can be related to the plausible mechanism of SCC that involves repeated and localized passivation and de-passivation caused primarily by the mechanical action. Also, the incremental (or cumulative) nature of the damage evaluation allows for the changes in key factors affecting the SCC kinetics, with time and with the extent of damage incurred at the time.

It is shown that the predicted trends and SCC characteristics are in good agreement with the laboratory type tests and can be related to the service experience. The approach has good links to the plausible mechanistic basis common to several SCC systems which need to be further evaluated. Although the method explicitly accounts for the material deformation characteristics (including creep effects) it is possible to improve the characterization of very local crack-front straining response and its interaction with the dissolution/passivation processes, which may be particularly useful for relatively large crack sizes. Although more systematic work is needed to determine the model parameters for a specific application and to develop it into an engineering tool, the model in its current form is promising for useful quantitative evaluations of SCC damage.

References

Besuner, P. M., Development and Verification of Combined Analysis of Transformer and Boiler Tube Failures, Final Report for New England Electric, APTECH Engineering Service, Sunnyvale, CA, March (1988).

Boursier, J. M., et al. "Stress Corrosion Cracking of Alloy 600 in Water: Influence of Strain Rate on the Different Stages of Cracking," in EUROCORR'92, Vol. II, pp. 11-19, Espoo, June 1-4, (1992).

Festen, M. M., et al., "Low-Temperature Creep of Austenitic-Ferritic and Fully Austenitic Stainless Steels and a Ferritic Pipeline Steel," in Environment-Induced Cracking of Metals (NACE-10), eds. R. P. Gangloff and M. B. Ives, NACE, Houston, TX, pp. 229-232, (1990).

Garud, Y. S., "Intergranular Stress Corrosion Cracking of Ni-Cr-Fe Alloy 600 Tubes in PWR Primary Water---Review and Assessment for Model Development," EPRI NP-3057, Electric Power Research Institute, Palo Alto, CA, (1983).

Garud, Y. S., "Development of a Model for Predicting IGSCC of Alloy 600 in PWR Primary Water," EPRI NP-3791, Electric Power Research Institute, Palo Alto, CA, (1985).

Garud, Y. S., "Significance and Integration of Creep Deformation Modeling in the Quantitative Evaluation of Intergranular SCC at Moderate Temperature," in 10th International Congress on Metallic Corrosion, Vol. III, pp. 2215-2222, CECRI, Karaikudi, India, November 7-11, (1987).

Garud, Y. S., "An Incremental Damage Formulation for SCC and Its Application to Crack Growth Interpretation Based on CERT Data," Corrosion, Vol.46, No.12, pp. 968-974, (1990).

Garud, Y. S., "Incremental Damage Formulation and Its Application to Assess IGSCC Growth of Circumferential Cracks in a Tube," Corrosion, Vol.47, No.7, pp. 523-527, (1991_a).

Garud, Y. S., "Quantitative Evaluation of Environmentally Assisted Cracking: A Survey of Developments and Application of Modeling Concepts," Journal of Pressure Vessel and Technology, ASME, Vol. 113, No. 1, pp. 1-9, (1991_b).

Garud, Y. S., "A Review and Further Applications of the Incremental Damage Approach for SCC Assessments," in ASME PVP-Vol. 241, Fatigue, Fracture, and Risk, ASME, New York, NY, pp. 1-9, (1992).

Garud, Y. S. and T. L. Gerber, "An Engineering Model for Predicting Stress Corrosion Cracking," in Advances in Life Prediction Methods, eds. D. A. Woodford and J. R. Whitehead, ASME, New York, NY, pp. 75-83, (1983).

Garud, Y. S. and A. R. McIlree, "Threshold Stress and Crack Growth Rate Considerations Based on a Strain-Rate Damage Model of IGSCC for Alloy 600,'' in Environment-Induced Cracking of Metals (NACE-10), eds. R. P. Gangloff and M. B. Ives, NACE, Houston, TX, pp. 415-418, (1990).

Garud, Y. S. and A. R. McIlree, "Application of the Strain-rate Damage Model to Simplified and Statistical Predictions of IGSCC", in 7th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems---Water Reactors, eds. A. R. McIlree, et al., NACE, Houston, TX, pp. 947-957, (1995).

Jones, R. H., ed., Stress Corrosion Cracking: Materials Performance and Evaluation, ASM International, Materials Park, OH, (1992).

Leinonen, H., "Stress Corrosion Cracking and Life Prediction Evaluation of Austenitic Stainless Steels in Calcium Chloride Solution," Corrosion, Vol. 52, No. 5, pp. 337-346, (1996).

Scully, J. R. and P. J. Moran, "Influence of Strain on the Environmental Hydrogen-Assisted Cracking of a High-Strength Steel in Sodium Chloride Solution," Corrosion, Vol. 44, No. 3, pp. 176-185, (1988).

Sung, J. K. and G. S. Was, "Intergranular Cracking of Ni-16Cr-9Fe Alloys in High Temperature Water," Corrosion, Vol. 47, No. 11, pp. 824-834, (1991).

Vaillant, F., et al., "Comparative Behavior of Alloy 600 Crack Growth Rate Testing in a PWR Environment," in 7th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems---Water Reactors, eds. A. R. McIlree, et al., NACE, Houston, TX, pp. 219-230, (1995).

van Gelder, K., et al., "The Stress Corrosion Cracking of Duplex Stainless Steel in H₂S/CO₂/Cl^- Environments," Corrosion Science, Vol. 27, No. 10/11, pp. 1271-1279, (1987).