Modeling fracture toughness of ferritic and austenitic functionally graded steel based on the strain gradient plasticity theory

Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic stainless steels and plain carbon steel with appropriate thickness as electrode. Fracture toughness of the specimen in terms of JIC was studied and modeled regarding the mechanism-based strain gradient plasticity theory. The yield stress of each layer was related to the density of the dislocations of that layer and assuming Holloman relation for the corresponding stress–strain curves, tensile strengths of the constituent layers were determined via numerical method. Fracture toughness of each layer was related to the corresponding area under stress–strain curve of that layer and finally by applying the rule of mixtures, fracture toughness of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.