Modeling charpy impact energy property changes using a bayesian method

Abstract

Surveillance schemes that monitor the effect of neutron irradiation on reactor pressure vessel materials employ Charpy impact specimens that are periodically withdrawn and tested as a function of test temperature. The resulting Charpy impact absorbed energy curves have been modeled by a threeparameter relationship with the same functional form as the Burr distribution function. The parameters of the Burr distribution function have been represented as a function of irradiation variables: dose and temperature. The method of maximum likelihood estimation has been used to obtain estimates of model parameters together with their standard errors. A method is presented for the evaluation of uncertainties in Charpy impact energy curves and temperature shifts resulting from irradiation damage. A sampling approach, based on Bayesian inference and employing Markov chain Monte Carlo (MCMC) simulation, has been used to quantify the uncertainties. The main idea of MCMC sampling is to generate the distributions of the model parameters by successive random sampling from the multivariate normal distribution. Illustrative results are presented for irradiated submerged arc weld metal.

Interpretation of Charpy impact energy characteristics by microstructural evolution of dynamically compressed specimens in three tempered martensitic steels

“…The toughness of steels is often predicted by a simplified semi-empirical formula obtained from the correlation of fracture speed with crack propagation speed [9,10]. In the case of the high-strength steels such as tempered martensitic steels, however, the correlation of Charpy USE with fundamental fracture process or crack speed is less obvious [11][12][13].…”

The use of multiscale materials modelling within the UK nuclear industry

“…Windle and co-workers [5] used a Burr distribution function to describe these data. Here, the variation of Charpy impact energy, C , with test temperature T i is given by:…”

Absorbed impact energy and mode of fracture: A statistical description of the micro-structural dispersion

“…When testing several, nominally identical samples, it is commonly observed that in the transition region, the absorbed energy values are largely scattered [4] whereas different plateau values, brittle (lower shelf) and ductile (upper shelf), are obtained from dynamic or static mechanical tests [5]. Moreover, this dispersion is characteristic of all the kinds of experimental determinations of the fracture toughness whereas for a given material T DBT values are sample-size dependent.…”

“…Macroscopic modeling of the impact test has been devoted to the derivation of reasonable forms for fitting the experimental results and for obtaining estimates of models parameters and of the associated standard errors [4,6,7]. However, no generally accepted distribution function has been proposed accounting for the variability in the proportions of brittle and ductile fracture stemming from the dispersion in the microstructures of the samples.…”