Kohonen mapping of the crack growth under fatigue loading conditions of stainless steels in BWR environments and of nickel alloys in PWR environments

Abstract In this study, crack growth rate data under fatigue loading conditions generated by Argonne National Laboratories and published in 2006 were analyzed [O.K. Chopra, B. Alexandreanu, E.E. Gruber, R.S. Daum, W.J. Shack, Argonne National Laboratory, NUREG CR 6891-series ANL 04/20, Crack Growth Rates of Austenitic Stainless Steel Weld Heat Affected Zone in BWR Environments, January, 2006; B. Alexandreanu, O.K. Chopra, H.M. Chung, E.E. Gruber, W.K. Soppet, R.W. Strain, W.J. Shack, Environmentally Assisted Cracking in Light Water Reactors, vol. 34 in the NUREG/CR-4667 series annual report of Argonne National Laboratory program studies for Calendar (Annual Report 2003). Manuscript Completed: May 2005, Date Published: May 2006], and reported by DoE [B. Alexandreanu, O.K. Chopra, W.J. Shack, S. Crane, H.J. Gonzalez, NRC, Crack Growth Rates and Metallographic Examinations of Alloy 600 and Alloy 82/182 from Field Components and Laboratory Materials Tested in PWR Environments, NUREG/CR-6964, May 2008]. The data collected were measured on austenitic stainless steels in BWR (boiling water reactor) environments and on nickel alloys in PWR (pressurized water reactor) environments. The data collected contained information on material composition, temperature, conductivity of the environment, oxygen concentration, irradiated sample information, weld information, electrochemical potential, load ratio, rise time, hydrogen concentration, hold time, down time, maximum stress intensity factor ( K max ), stress intensity range (Δ K max ), crack length, and crack growth rates (CGR). Each position on that Kohonen map is called a cell. A Kohonen map clusters vectors of information by ‘similarities.’ Vectors of information were formed using the metal composition, followed by the environmental conditions used in each experiments, and finally followed by the crack growth rate (CGR) measured when a sample of pre-cracked metal is set in an environment and the sample is cyclically loaded. Accordingly, one experiment will result in a long vector of data containing information such as [Fe, wt%], [Cr, wt%], [Temperature, T ], [Electrochemical potential, ECP], [ K max ], [Conductivity, k ], [CGR], etc. In that long data-vector, CGR is only one component of the vector. To ‘increase’ the importance of the CGR over the other components of the data-vectors, ‘functional links’ or functions of the CGR (as powers, logarithms, etc.) are added to each one of the vectors, resulting in longer vectors. The trained Kohonen map cells adopt ‘average’ values from all of the vectors stored in that cell. Accordingly, each Kohonen cell is ‘represented’ by and ‘average’ vector. The ‘average’ vectors representing each one of the Kohonen trained cells are topologically arranged on the map surface; i.e. ‘high crack growth rates’ vectors are stored on cells far apart of ‘low crack growth rates’ cells. Each of the parameters forming the vector can be investigated; maps of the trends of each parameter were drawn and those maps were compared to the maps of the CGRs. This paper presents the results by means of 3-dimensional figures that show the beneficial and detrimental effects that each of the variables considered has on the CGR on austenitic stainless steel weld heat affected zones in BWR environments and on nickel alloy welds in PWR environments. Data-mining methodologies (including clustering analysis) are useful to extract information from data. ‘Nuclear waste’ belongs to a category of subjects that are extremely complicated, mainly because many electrochemical and material-related phenomena can occur simultaneously. Stress corrosion cracking can be present among the corrosion problems faced by nuclear waste storage. The data-mining on ‘the effect of material composition and environment on the CGRs’ (presented in this paper – in our knowledge used by first time in the area of nuclear waste) is to be used by the reader as an example of a methodology that can be adopted for other problems encountered in the nuclear waste industry and for which data are available.