Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior - Part I: Model Presentation

A new multiscale model is proposed by a "model synthesis" approach, as the first attempt to clarify the relationship between microstructures of steel and macroscopic brittle crack propagation and arrest behavior. The first part of the present paper shows the model presentation. The multiscale model consists of two models: (1) a microscopic model to simulate cleavage fracture in the grain scale and (2) a macroscopic model to simulate brittle crack propagation and arrest behavior in the steel plate scale. In both the models, we utilize the same framework, where a simple two-dimensional domain discretization is employed but a three-dimensional crack propagation can be effectively modeled. The discretized unit cells in the microscopic model correspond to the grain size. On the other hand, the discretized unit cells in the macroscopic model correspond to the entire domain of the microscopic model. The microscopic model proposed by Aihara and Tanaka is basically employed except the integration with the macroscopic model. The effective surface energy, which is used for the integration between microscopic and macroscopic models, is assumed as the plastic work to form tear-ridge. The proposed model synthesis for multiscale model as an integrated macroscopic model is performed by systematically incorporating (1) the preparatory macroscopic finite element analysis and (2) the Monte Carlo simulation of microscopic analysis into (3) the macroscopic analysis for brittle crack propagation and arrest in steel plate. The integration procedure is implemented by the assignment of physical quantities based on interpolation methods as a one-way coupling algorithm for simplification.