A Comparison of Weibull and βIcAnalyses of Transition Range Data

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Abstract
Specimen size effects on KJc data scatter in the transition range of fracture toughness have been explained by extremal (weakest link) statistics. In this investigation, compact specimens of A533 Grade B steel were tested in sizes ranging from ½TC(T) to 4TC(T) with sufficient replication to obtain good three-parameter Weibull characterization of data distributions. The optimum fitting parameters for an assumed Weibull slope of four were calculated. Extremal statistics analysis was applied to the ½TC(T) data to predict median KJc values for 1TC(T), 2TC(T), and 4TC(T) specimens. The distributions from experimentally developed 1TC(T), 2TC(T), and 4TC(T) data tended to confirm the predictions. However, the extremal prediction model does not work well at lower-shelf toughness. At -150°C, the extremal model predicts a specimen size effect where in reality there is no size effect.Another model that has potential for dealing with data scatter effects in the transition range is the Irwin βc-βIc relationship. This model uses breakdown in constraint as the argument for specimen size effects and suggests that data sets can be transposed from one size to another by operating on each individual datum with the following equation KIc=KJcβIc/βcBoth models predict about the same distributions for specimens larger than 1TC(T), and only the extremal statistical model can predict correctly the smaller specimen distribution. With the βc-βIc relationship, the limitation appears to be that βc ⩽ π must not be exceeded. Therefore, both the statistical and βIc models have limitations for their use. This study explores these limitations and makes specimen size requirement recommendations on KJc data.

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