Artificial Neural Network Modelling of In-Reactor Diametral Creep of Zr2.5%Nb Pressure Tubes of Indian PHWRs

Highlights

• An ANN model is developed to predict the in-reactor diametral creep in Zr–2.5%Nb.

• Database from pressure tubes of Indian PHWRs have been used.

• The developed ANN model can efficiently predict diametral creep of pressure tubes.

• O cont and mech properties play important role in determining diametral creep rate.

Abstract

A model is developed to predict the in-reactor diametral creep in the Zr–2.5%Nb pressure tube of Indian Pressurized Heavy Water power reactors (PHWR) using Artificial Neural Network (ANN). The inputs of the neural network are alloy composition of the tube (concentration of Nb, O, N and Fe), mechanical properties (YS, UTS, %EL), temperature and fluence whereas diametral creep rate is the output. Measured diametral creep rate data from the sampled pressure tubes operating in Indian PHWRs at Rajasthan Atomic Power Station (RAPS 2), Kakrapar Atomic Power Station (KAPS 2) and Kaiga Generating Station (KGS) are employed to develop the model. A three-layer feed-forward ANN is trained with Levenberg–Marquardt training algorithm. It has been shown that the developed ANN model can efficiently and accurately predict the diametral creep of pressure tube. Results show the high significance of O concentration and mechanical properties in determining diametral creep rate.

Introduction

Zr–2.5Nb alloy in cold-worked and stress-relieved (CWSR) condition is being used as pressure tubes in the Pressurized Heavy Water Reactors (PHWR). Pressure tubes used in Indian PHWRs are manufactured from extruded hollow billets that have been given a beta-quench treatment. They are nominally extruded around 800 °C, stress-relieved at 480 °C for 3 h followed by a two-stage pilgering reduction involving an intermediate stress-relief at 550 °C for 6 h and then followed by a steam autoclave at 400 °C for 36 h. The extreme environment (e.g. high pressure, temperature and fast neutron flux) within the PHWR core induces dimensional changes (deformation) in pressure tubes which affect their useful service-life. The current state of understanding of the in reactor deformation and its engineering implications have recently been reviewed by Holt (2008). It is widely believed that three mechanisms namely irradiation growth, thermal creep and irradiation creep are primarily responsible for dimensional changes of pressure tubes in PHWR (Holt, 2008, Christodoulou et al., 1996, Ibis and Holt, 1980). The deformation produced by aforementioned mechanisms manifests as elongation, diametral expansion, sag and wall thinning of pressure tube and the extent of this is dependent on exposure. Diametral creep may lead to the flow by-pass and the penalty to critical heat flux for fuel rods, longitudinal creep may lead to missing bearing support for end fitting provided in the lattice tube, and sagging may lead to interference with in-core components and potential contact between the pressure tube and calandria tube. In order to ensure integrity, safe and reliable operation and economic performance of the reactor, it is important to understand the factors that govern these mechanisms of deformation as well as to predict reliably the rate of deformation of pressure tubes. Several research and development efforts have been made in the past to understand the factors which influence the mechanisms of in-reactor deformation and its rate with the objectives to provide engineering solutions and to mitigate the mechanisms of degradation. As regards the rate of deformation, it is found that a host of variables such as neutron fluence, irradiation temperature, chemical composition and pre-irradiation material history (metallurgical texture, grain size/shape, extent of cold work, etc.) influence the in-reactor deformation. In order to reliably predict the deformation rate, all these variables must be simultaneously considered. A reliable mechanistic model incorporating effects of each variable to predict deformation rate appears to be unrealistic and is therefore not attempted to model the in-reactor deformation rate of pressure tubes. However phenomenological models (Holt, 2008, Christodoulou et al., 1996, Ibis and Holt, 1980, Ross-Ross and Hunt, 1968) have been attempted with some success. In recent years, ANN approach has been found to be very useful for modeling complicated materials science problems that are difficult to articulate using analytical and mechanistic models. ANN has been successfully used to model different types of metallurgical problems e.g. flow curve analysis (Kapoor et al., 2005, Mandal et al., 2006), Hume-Rothery’s rule (Zhang et al., 2008), correlation between processing parameters and physical and mechanical properties (Aijun et al., 2004, Malinov et al., 2001), irradiation hardening (Kemp et al., 2006), etc. In our earlier paper (Sarkar et al., 2013) we have used ANN to model the axial elongation data of pressure tubes.

The objective of this investigation is to ascertain suitability of ANN technique to train and predict diametral creep of pressure tubes used in different Indian PHWRs. For this purpose a large data base on diametral creep of pressure tubes of various reactors (which used Zr–2.5Nb of different origins) has been considered with a view to identify the variables which influence the diametral expansion most. The investigation described here is a part of an extensive research programme being carried out for gaining an understanding of in-reactor deformation processes. Further research is being carried out to identify the role of processing route, microstructure, and texture on the in-reactor dimensional changes.