Modeling charpy impact energy property changes using a bayesian method

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I.

INTRODUCTION

THE fracture toughness of ferritic steels increases and the mechanism of fracture changes from brittle to ductile as the temperature increases. An increase in the temperature of this transition may occur during service as a result of neutron irradiation and thermal ageing. Surveillance schemes employ Charpy impact specimens that are periodically withdrawn for impact testing to evaluate the ductile-to-brittle transition temperature for different neutron irradiation dose levels. It is then necessary to infer the changes in the fracture toughness using an empirical correlation with changes observed in Charpy impact energy properties. Charpy impact energy properties are evaluated by testing specimens over a wide range of temperatures and measuring the energy absorbed to fracture. There is a trend for Charpy impact absorbed energy values to increase as the test temperature increases, and this can be described by a sigmoidal curve that levels off to almost a constant value at the top and bottom. The lower and upper plateau are referred to as the lower and upper shelves and are associated with brittle, usually cleavage, and ductile fracture mechanisms, respectively. The rising part of the curve is the transition region, which is associated with a mixture of both types of failure mechanisms. It is possible to relate the rise in the Charpy impact energy to an increase in the proportion of ductile fracture, which is often expressed as a percentage. When a large number of nominally identical specimens are tested at the same temperature in the transition region, the resulting values of Charpy impact absorbed energy exhibit larger scatter than on the upper and R. MOSKOVIC, Research Officer, is with Magnox Electric plc, Gloucestershire GL13 9PB, United Kingdom. P.L. WINDLE, Senior Lecturer, is with the Royal Naval College, London SE10 9NN, United Kingdom. A.F. SMITH, Professor and Department Head, is with the Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom. Manuscript submitted October 11, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS A

lower shelves. The increase in the scatter is linked to the variability in the proportions of brittle and ductile fracture from specimen to specimen. Most of the variability can be accounted for by microstructural heterogeneity of the steel. This is particularly true for weld metal steels. For such materials, when tested at a given test temperature, there is a range of observed Charpy impact energy values, rather than a unique value. Hence, to fit a mean curve to the data, it would be appropriate to average over a number of Charpy impact energy values. In practice, the batches of specimens irradiated to a given dose level rarely contain more than ten specimens. Each of these is tested at a different temperature in order to establish the temperature variability of Charpy impact absorbed energy. Interpretation of such data can be most effectively accomplished by statistical modeling involving a regression analysis. As noted earlier, the shape of the C