Application of strain gradient plasticity theory to model Charpy impact energy of functionally graded steels using modified stress–strain curve data

Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic and carbon steels with appropriate thickness as electrode. Charpy impact energy of the specimen has been studied and modeled regarding the mechanism-based strain gradient plasticity theory. The hardness of each layer was related to the density of the dislocations of that layer and then by using a linear relation, the predicted hardness was related to its corresponding yield stress. Afterwards; by assuming Holloman relation for the corresponding stress–strain curves, tensile strengths and tensile strains of the constituent layer were determined via numerical method. By using load–displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress–strain curves from uniaxial tensile tests were modified. Charpy impact energy each layer was related to the corresponding area under modified stress–strain curve of that layer and finally by applying the rule of mixtures, Charpy impact energy of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.