Multiscale modeling of fracture in barium titanate: Fracture toughness estimation and modified G-Criterion

This study explores fracture physics for Barium Titanate using multiscale modeling and connects the fracture physics to failure criterion, i.e. G-Criterion. The specimen is devided into three regions: (1) far field, modeled by classical fracture mechanics; (2) near field, modeled by Atomistic Field Theory (AFT) and Generalized Atomistic Finite Element Method (GAFEM); and (3) crack tip, modeled by molecular dynamics (MD). The interaction between the near field and crack tip region is described by full blown interatomic forces. The interatomic potential used for deriving interatomic forces is modified Columb-Buckingham potential, which has a remedy term to avoid Buckingham Catastrophe. Mode I, Mode II and several different cases of mixed mode fracture are studied and the corresponding fracture toughnesses are estimated. Fracture toughness is associated with the instability of MD simulation at the crack tip region. A modified G-Criterion model is also developed to provide a design principles from a multiscale perspective. Simulation results agree with the newly proposed modified G-Criterion model.