T
Fracture toughness is expressed in terms of an elastic-plastic stress intensity factor, KJc, that is derived from the J-integral calculated at fracture.
Ferritic steels are inhomogeneous with respect to the orientation of individual grains. Also, grain boundaries have properties distinct from those of the grains. Both contain carbides or nonmetallic inclusions that can act as nucleation sites for cleavage microcracks. The random location of such nucleation sites with respect to the position of the crack front manifests itself as variability of the associated fracture toughness (13). This results in a distribution of fracture toughness values that is amenable to characterization using statistical methods.
Distributions of KJc data from replicate tests can be used to predict distributions of KJc for different specimen sizes. Theoretical reasoning (9), confirmed by experimental data, suggests that a fixed Weibull slope of 4 applies to all data distributions and, as a consequence, standard deviation on data scatter can be calculated. Data distribution and specimen size effects are characterized using a Weibull function that is coupled with weakest-link statistics (14). An upper limit on constraint loss and a lower limit on test temperature are defined between which weakest-link statistics can be used.
The experimental results can be used to define a master curve that describes the shape and location of median KJc transition temperature fracture toughness for 1T specimens (15). The curve is positioned on the abscissa (temperature coordinate) by an experimentally determined reference temperature, To. Shifts in reference temperature are a measure of transition temperature change caused, for example, by metallurgical damage mechanisms.
Tolerance bounds on KJc can be calculated based on theory and generic data. For added conservatism, an offset can be added to tolerance bounds to cover the uncertainty associated with estimating the reference temperature, To, from a relatively small data set. From this it is possible to apply a margin adjustment to To in the form of a reference temperature shift.
For some materials, particularly those with low strain hardening, the value of To may be influenced by specimen size due to a partial loss of crack-tip constraint (5). When this occurs, the value of To may be lower than the value that would be obtained from a data set of KJc values derived using larger specimens.
As discussed in 1.3, there is an expected bias among To values as a function of the standard specimen type. The magnitude of the bias may increase inversely to the strain hardening ability of the test material at a given yield strength, as the average crack-tip constraint of the data set decreases (16). On average, To values obtained from C(T) specimens are higher than To values obtained from SE(B) specimens. Best estimate comparison indicates that the average difference between C(T) and SE(B)-derived To values is approximately 10 °C (2). However, individual C(T) and SE(B) datasets may show much larger To
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