Influence of statistical and constraint loss size effects on cleavage fracture toughness in the transition – A model based analysis

Abstract

A database derived from tests on specimens with a large range of ligament ( b) and thickness ( B) dimensions was systematically analyzed to evaluate constraint loss and statistical size effects on cleavage fracture toughness. The objectives were to: (1) decouple size effects related to constraint loss, mediated by b and B, from those arising from statistical effects, primarily associated with B; and, (2) develop procedures to transfer toughness data to different conditions of constraint and B. The toughness database for a Shoreham pressure vessel steel plate, tested at a common set of conditions, was described in a companion paper. Quantification of constraint loss was based on an independently calibrated 3D finite-element critical stress-area, σ ∗ - [ K J m / K J c ] , model. The measured toughness data, K J m , were first adjusted using computed [ K J m / K J c ] constraint loss factors to the corresponding values for small scale yielding conditions, K J c = K J m / [ K J m / K J c ] . The K J c were then statistically adjusted to a K J r for a reference B r = 25.4 mm. The B adjustment was based on a critically stressed volume criterion, modified to account for a minimum toughness, K min, consistent with modest modifications of the ASTM E 1921 Standard procedure. The combined σ ∗ - [ K J m / K J c ] - K min adjustment procedure was applied to the Shoreham b − B database, producing a homogeneous population of K J r data, generally within the expected scatter. The analysis suggests that: (1) there may be a maximum B beyond which statistical size effects diminish, and (2) constraint loss in the three-point bend specimens begins at a relatively low deformation level. A corresponding analysis, based on a Weibull stress, σ w - [ K J m / K J c ] - K min , adjustment procedure, yielded similar, but somewhat less satisfactory, results. The optimized adjustment procedure was also applied to other K J m data for the Shoreham plate from this study, as well as a large database taken from the literature. The population of 489 K J r data points, covering an enormous range of specimen sizes, geometries and test temperatures, was found to be consistent with the same master curve T 0 = −84 °C derived from the b − B database. Thus, calibrated micromechanical models can be used to treat size and geometry effects on K J m , facilitating using small specimens and data transfer to predict the fracture limits of structures.