A re-assessment of parameter tuning for the Beremin model using the toughness scaling technique

A commonly employed technique to tune the Weibull parameters within the Beremin cleavage model is an iterative scheme using a maximum likelihood method applied to available fracture data. For reliable results, this can require results from a large number of specimens, which is rarely practicable. Recently, a new tuning method has been proposed which seeks to scale the history of Weibull stress of one geometry onto that of another. This possesses a number of advantages over maximum likelihood schemes since reliable predictions can be obtained from fewer experimental results. The technique has been applied to fracture data from two specimen geometries over a range of temperatures, and compared with results obtained from the maximum likelihood method. The technique has been extended to allow tuning of a single, temperature-independent, value of the Weibull modulus, m. Results from the two methods are similar, and it is shown that reliable results can be obtained from the toughness scaling method with as few as five specimens. A three-parameter Weibull model is also tuned, and in general the results show better predictions of the ‘tails’ of the probability distribution functions than with a two-parameter model.