Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness, J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters, J and Q, suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. Full-field finite element calculations show that the J-Q field dominates over physically significant size scales, i.e., it describes the environment in which brittle and ductile failure mechanisms are active. The material's fracture resistance is characterized by a toughness locus, Jc(Q), which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q =0) to low constraint conditions (Q < 0). Contents Section No.

This study applies recent advances in probabilistic modelling of cleavage fracture to predict the measured fracture behaviour of surface crack plates fabricated from an A515‐70 pressure vessel steel. Modifications of the conventional, two‐parameter Weibull stress model introduce a non‐zero, threshold parameter (σw‐min ). The introduction of σw‐min brings numerical predictions of scatter in toughness data into better agreement with experimental measurements, and calibration of this new parameter requires no additional experimental data. The Weibull modulus (m) and scaling parameter (σu ) are calibrated using a new strategy based on the toughness transferability model, which eliminates the non‐uniqueness that arises in calibrations using only small‐scale yielding toughness data. Here, the Weibull stress model is calibrated using toughness data from deep‐notch C(T) and shallow‐notch SE(B) specimens, and is then applied to predict the measured response of surface crack plates loaded in different combinations of tension and bending. The model predictions accurately capture the measured distributions of fracture toughness values.

Experimental studies demonstrate a significant effect of specimen size, a/W ratio and prior ductile tearing on cleavage fracture toughness values (Jc) measured in the ductile-to-brittle transition region of ferritic materials. In the lower-transition region, cleavage fracture often occurs under conditions of large-scale yielding but without prior ductile crack extension. The increased toughness develops when plastic zones formed at the crack tip interact with nearby specimen surfaces which relaxes crack-tip constraint (stress triaxiality). In the mid-to-upper transition region, small amounts of ductile crack extension (often < 1-2 ram) routinely precede termination of the J-Aa curve by brittle fracture. Large-scale yielding, coupled with small amounts of ductile tearing, magnifies the impact of small variations in microscale material properties on the macroscopic fracture toughness which contlJbutes to the large amount scatter observed in measured Jc-values. Previous work by the authors described a micromechanics fracture model to correct measured Jc-values for the mechanistic effects of large-scale yielding. This new work extends the model to also include the influence of ductile crack extension prior to cleavage. Ductile crack extensions of 10-15 × the crack-tip opening displacement at initiation are considered in plane-strain, finite element computations. The finite element results demonstrate a significant elevation in crack-tip constraint due to macroscopic "sharpening" of the extending tip relative to the blunt tip at initiation of growth. However, this effect is offset partially by the additional plastic deformation associated with the increased applied J required to grow the crack. The initial a/W ratio, tearing modulus, strain hardening exponent and specimen size interact in a complex manner to define the evolving near-tip conditions for cleavage fracture. The paper explores development of the new model, provides necessary graphs and procedures for its application and demonstrates the effects of the model on fracture data sets for two pressure vessel steels (A533B and A515).