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Probabilistic aspects of fatigue: Pressurized nuclear power reactor components
Probabilistic j~acture mechanics
293
PROBABILISTIC ASPECTS OF F A T I G U E : P R E S S U R I Z E D NUCLEAR POWER REACTOR COMPONENTS P. M. Scott, UKAEA For over a decade now, there has been increasing interest in probabilistic assessments of failure rates, however small, of pressurized nuclear power reactor components. The Marshall Study Group on PWR pressure vessel integrity ~ summarized the objectives of this type of analysis as follows: (1) To verify that failure probabilities are less than some acceptable limit based on the assessed consequences of failure. (2) To indicate which factors the failure probabilities are sensitive to, thereby allowing effort t o be concentrated on them. (3) To estimate gains in reliability which may follow from improved design, construction, operation and inspection. The growth of cracks by fatigue is an important element of such calculations, although many probabilistic failure assessments have included a deterministic calculation of fatigue crack growth. Any attempt to include fatigue crack growth as a distributed quantity requires details of the anticipated stress spectrum over the design life, an estimate of the initial defect distribution, the fatigue crack growth properties and a failure criterion. The initial defect distribution and failure criteria are major issues in their own right and not specific to the fatigue crack growth problem. These are not discussed further here, and we concentrate on those issues specific to fatigue crack growth. The assumed stress spectrum is usually based on a forecast of the operational duty of a power station, modified by experience from plant monitoring. In general, the differences in stress levels experienced during normal, upset and test cycles are not so large that either the stress cycle sequence or stress cycle interaction effects have any major effect on the outcome of fatigue crack growth calculations. For plane strain conditions, a 25% or greater change in the maximum stress or crack-tip stress intensity between successive cycles is necessary for any significant acceleration for retardation of crack growth rates due to plastic flow at the crack tip. Such changes in stress level between successive stress cycles are not a normal feature of nuclear power reactor operations which reduces or even eliminates any influence of this phenomenon on the estimated distribution of final crack sizes. By contrast, the variance in fatigue crack growth rates as a function of cyclic stress intensity factor as a material property has been shown to have a marked influence on probabilistic calculation on nuclear pressure vessels. Some care is required to ensure that the mean and standard deviation in the
294
T. Jutla
cychc crack growfla rhte, da/d~V,'at ar~y given c3/clic stress~ inten~ty, AK, are correctly estimated. To this end, there has been much recent activity in the development of databases for fatigue crack in pressure vessel steels and in their statistical analYsis. This is discussed in more detail below. Guidance on fatigue crack growth equations for nuclear pressure vessel steels and their use is available in the ASME Nuclear Pressure Vessel Code (Section XI, Appendix A). The code makes a distinction between dry buried cracks and internal surface-breaking cracks exposed to aqueous coolant. Laboratory measurements under both conditions have been made extensively in recent years and a database known as the EPRI Data Base on Environment Assisted Cracking (EDEAC) has been developed in parallel. 2 In addition, a new computer program known as the Fatigue Data Analysis Code (FATDAC), 3 has been specifically developed to process EDEAC and provide sensible models and statistical analysis of the data. Analysis of fatigue crack growth data in ferritic pressure vessel steels under dry conditions has presented no significant problems with regard to the availability of sensible physical models such as that represented by the familiar Paris equation. However, considerable care and effort has proved necessary in the development of F A T D A C to ensure that scatter about the mean of the fatigue crack growth data is correctly estimated. At the heart of F A T D A C is a statistical software package which derives the minimum number of da/dN, AK pairs which, when numerically integrated, minimizes the error between the observed and calculated crack length as a function of stress cycles. It turns out to be a c o m m o n problem that investigators overestimate the precision of their crack length measurements, such that when the data is differentiated to determine da/dN, spuriously high estimates of the variance in da/dN are then made. With the aid of EDEAC and F A T D A C , a new dry crack growth equation has been derived in which, in addition to AK, three other parameters, the cyclic frequency, the stress ratio and the temperature, have been modelled. 3 This is important for probabilistic calculations, as it also provides a soundly based estimate of the mean and standard deviation in crack growth rates. New assessments of fatigue crack growth in stainless steels have also been published recently. 4 In the case of internal surface-breaking cracks, the possibility of environmental effects on crack growth must be considered. The present ASME Section XI Appendix A code provides statistically derived equations for corrosion fatigue crack growth based on data available around 1979. The equations are 95% global confidence limits on the mean of the data, and provide no information on the frequency of extreme events. Thus the equations represent a factored mean and, as such, must not be used for probabilistic calculations. In deterministic calculations, safety factors are introduced elsewhere in the assessment process.
Probabilistic fracture mechanics
295
Corrosion fatigue of pressure vessel steels in water reactor coolants is a complex problem, but one in which considerable progress has been made in understanding the circumstances under which large environmental effects can occur, and how they can be avoided. 5 It has been found necessary to develop a time-based approach to the analysis of corrosion fatigue data rather than the traditional crack growth per cycle method. 6 This is quite a radical departure and is the subject of much current investigation. Undoubtedly, distinctions will have to be made between those circumstances under which environmental enhancement of the rate of crack growth occurs and those under which it does not. Then, with the aid of E D E A C and F A T D A C , these separated data groups can be analysed, and proper statistically based descriptions derived. In conclusion, it is clear that significant progress has been made in developing databases on fatigue crack growth in pressure boundary steels for water reactors, and in their statistical analysis. For the case of corrosion fatigue crack growth, further work remains to be done to determine the mean and variance of the data when analysed according to new time-based models of crack growth. These are important steps towards improved probabilistic analysis of fatigue crack growth in pressurized nuclear components.
References I. Marshall, W. An assessment of the integrity of PWR pressure vessels, UKAEA, 1982. 2. Rungta, R., Mindlin, H. and Gilman, J. D. Applications of EPRI data base on environmentally assisted cracking in the nuclear industry, Mat. Perjbrm., November 1986, pp. 43 52. 3. Eason, E. D., Andrew, S. P. and Warmbrodt, S. B. FATDAC--an interactive fatigue and corrosion fatigue data analysis code, A S M E Winter Meeting, Miami, November 1985. 4. James, L. A. and Jones, D. P. Fatigue crack growth correlations for austenitic stainless steels in air, ASME PVP No. 99 .from 'Predictive Capabilities in Environmentally Assisted Cracking', 1985. 5. Cullen, W. H. Proc. 2nd lAEA Specialists' Meeting on 'Subcritical Crack Growth', Sendai, Japan, 1985; NUREG/CP-O067, 1986. 6. Gilman, J. D. Application model for predicting corrosion fatigue crack growth in reactor pressure vessel steels in LWR environments, ASME Winter Annual Meeting, Miami, November 1985. F A T I G U E IN A I R C R A F T S T R U C T U R E S J. B. Young, Cranfield Institute o f Technology Fatigue loading on aircraft structures is produced mainly by gusts, manoeuvres, landing and ground loads. Fatigue life estimation is based on
293
PROBABILISTIC ASPECTS OF F A T I G U E : P R E S S U R I Z E D NUCLEAR POWER REACTOR COMPONENTS P. M. Scott, UKAEA For over a decade now, there has been increasing interest in probabilistic assessments of failure rates, however small, of pressurized nuclear power reactor components. The Marshall Study Group on PWR pressure vessel integrity ~ summarized the objectives of this type of analysis as follows: (1) To verify that failure probabilities are less than some acceptable limit based on the assessed consequences of failure. (2) To indicate which factors the failure probabilities are sensitive to, thereby allowing effort t o be concentrated on them. (3) To estimate gains in reliability which may follow from improved design, construction, operation and inspection. The growth of cracks by fatigue is an important element of such calculations, although many probabilistic failure assessments have included a deterministic calculation of fatigue crack growth. Any attempt to include fatigue crack growth as a distributed quantity requires details of the anticipated stress spectrum over the design life, an estimate of the initial defect distribution, the fatigue crack growth properties and a failure criterion. The initial defect distribution and failure criteria are major issues in their own right and not specific to the fatigue crack growth problem. These are not discussed further here, and we concentrate on those issues specific to fatigue crack growth. The assumed stress spectrum is usually based on a forecast of the operational duty of a power station, modified by experience from plant monitoring. In general, the differences in stress levels experienced during normal, upset and test cycles are not so large that either the stress cycle sequence or stress cycle interaction effects have any major effect on the outcome of fatigue crack growth calculations. For plane strain conditions, a 25% or greater change in the maximum stress or crack-tip stress intensity between successive cycles is necessary for any significant acceleration for retardation of crack growth rates due to plastic flow at the crack tip. Such changes in stress level between successive stress cycles are not a normal feature of nuclear power reactor operations which reduces or even eliminates any influence of this phenomenon on the estimated distribution of final crack sizes. By contrast, the variance in fatigue crack growth rates as a function of cyclic stress intensity factor as a material property has been shown to have a marked influence on probabilistic calculation on nuclear pressure vessels. Some care is required to ensure that the mean and standard deviation in the
294
T. Jutla
cychc crack growfla rhte, da/d~V,'at ar~y given c3/clic stress~ inten~ty, AK, are correctly estimated. To this end, there has been much recent activity in the development of databases for fatigue crack in pressure vessel steels and in their statistical analYsis. This is discussed in more detail below. Guidance on fatigue crack growth equations for nuclear pressure vessel steels and their use is available in the ASME Nuclear Pressure Vessel Code (Section XI, Appendix A). The code makes a distinction between dry buried cracks and internal surface-breaking cracks exposed to aqueous coolant. Laboratory measurements under both conditions have been made extensively in recent years and a database known as the EPRI Data Base on Environment Assisted Cracking (EDEAC) has been developed in parallel. 2 In addition, a new computer program known as the Fatigue Data Analysis Code (FATDAC), 3 has been specifically developed to process EDEAC and provide sensible models and statistical analysis of the data. Analysis of fatigue crack growth data in ferritic pressure vessel steels under dry conditions has presented no significant problems with regard to the availability of sensible physical models such as that represented by the familiar Paris equation. However, considerable care and effort has proved necessary in the development of F A T D A C to ensure that scatter about the mean of the fatigue crack growth data is correctly estimated. At the heart of F A T D A C is a statistical software package which derives the minimum number of da/dN, AK pairs which, when numerically integrated, minimizes the error between the observed and calculated crack length as a function of stress cycles. It turns out to be a c o m m o n problem that investigators overestimate the precision of their crack length measurements, such that when the data is differentiated to determine da/dN, spuriously high estimates of the variance in da/dN are then made. With the aid of EDEAC and F A T D A C , a new dry crack growth equation has been derived in which, in addition to AK, three other parameters, the cyclic frequency, the stress ratio and the temperature, have been modelled. 3 This is important for probabilistic calculations, as it also provides a soundly based estimate of the mean and standard deviation in crack growth rates. New assessments of fatigue crack growth in stainless steels have also been published recently. 4 In the case of internal surface-breaking cracks, the possibility of environmental effects on crack growth must be considered. The present ASME Section XI Appendix A code provides statistically derived equations for corrosion fatigue crack growth based on data available around 1979. The equations are 95% global confidence limits on the mean of the data, and provide no information on the frequency of extreme events. Thus the equations represent a factored mean and, as such, must not be used for probabilistic calculations. In deterministic calculations, safety factors are introduced elsewhere in the assessment process.
Probabilistic fracture mechanics
295
Corrosion fatigue of pressure vessel steels in water reactor coolants is a complex problem, but one in which considerable progress has been made in understanding the circumstances under which large environmental effects can occur, and how they can be avoided. 5 It has been found necessary to develop a time-based approach to the analysis of corrosion fatigue data rather than the traditional crack growth per cycle method. 6 This is quite a radical departure and is the subject of much current investigation. Undoubtedly, distinctions will have to be made between those circumstances under which environmental enhancement of the rate of crack growth occurs and those under which it does not. Then, with the aid of E D E A C and F A T D A C , these separated data groups can be analysed, and proper statistically based descriptions derived. In conclusion, it is clear that significant progress has been made in developing databases on fatigue crack growth in pressure boundary steels for water reactors, and in their statistical analysis. For the case of corrosion fatigue crack growth, further work remains to be done to determine the mean and variance of the data when analysed according to new time-based models of crack growth. These are important steps towards improved probabilistic analysis of fatigue crack growth in pressurized nuclear components.
References I. Marshall, W. An assessment of the integrity of PWR pressure vessels, UKAEA, 1982. 2. Rungta, R., Mindlin, H. and Gilman, J. D. Applications of EPRI data base on environmentally assisted cracking in the nuclear industry, Mat. Perjbrm., November 1986, pp. 43 52. 3. Eason, E. D., Andrew, S. P. and Warmbrodt, S. B. FATDAC--an interactive fatigue and corrosion fatigue data analysis code, A S M E Winter Meeting, Miami, November 1985. 4. James, L. A. and Jones, D. P. Fatigue crack growth correlations for austenitic stainless steels in air, ASME PVP No. 99 .from 'Predictive Capabilities in Environmentally Assisted Cracking', 1985. 5. Cullen, W. H. Proc. 2nd lAEA Specialists' Meeting on 'Subcritical Crack Growth', Sendai, Japan, 1985; NUREG/CP-O067, 1986. 6. Gilman, J. D. Application model for predicting corrosion fatigue crack growth in reactor pressure vessel steels in LWR environments, ASME Winter Annual Meeting, Miami, November 1985. F A T I G U E IN A I R C R A F T S T R U C T U R E S J. B. Young, Cranfield Institute o f Technology Fatigue loading on aircraft structures is produced mainly by gusts, manoeuvres, landing and ground loads. Fatigue life estimation is based on