Random-fuzzy model for the ductile/brittle transition

Based on a large number of experimental samples, the influence of stress triaxiality and temperature have been studied on the growth of micro voids and the ductile/brittle transition (DBT) of 40 Cr steel. Ductile and brittle fractures have been investigated simultaneously. The experiments show that the ductile fracture is controlled by the micro void mechanism, and the critical void growth ratio can be used as the criterion of ductile fracture. The brittle fracture was modeled by an embedded penny crack, and a micro stress intensity with a characteristic length could be used as the criterion of the brittle fracture. The DBT is the result of the competition of the two mechanisms, which exists in the fracture of all specimens simultaneously. The distributions of model parameters were measured experimentally on an Instron 1196 test machine. A random model and a random-fuzzy model for DBT were presented. The comparison between the calculated and experimental results shows that the random-fuzzy model can model the DBT satisfactorily.