A statistical sampling approach for measurement of fracture toughness parameters in a 4330 steel by 3-D femtosecond laser-based tomography

A new approach using statistically random material volume sampling has been developed to model the variability of fracture toughnesses in steels. A recently developed femtosecond laser-based serial sectioning (FSLSS) technique was utilized to collect 3-D datasets showing the distribution of titanium nitride (TiN) phases in a 4330 high strength steel. Random volumes were sampled from widely spaced regions within the bulk steel specimen. Plastic zone sized volumes were sampled from the 3-D reconstructions to produce statistically representative volume elements containing TiN particles. Fracture toughness was calculated for 48 different plastic zone sized volumes using two different toughness models. Weibull analysis was performed to relate the modeled fracture toughness to the probability of occurrence. Variability in the fracture toughness gave a Weibull modulus of m = 1.4–1.5, similar to the variability measured in 22 bulk sample specimens analyzed by Ruggieri et al. for a similar steel.