A Cosserat bond-based correspondence model and the investigation of microstructure effect on crack propagation

Microstructure plays a significant role in the fracture behavior of the material. To analyze the microstructure effect on crack propagation, a peridynamic model named Cosserat bond-based correspondence model (CBBCM) is proposed based on the Cosserat continuum theory and bond-based correspondence model. In CBBCM, the peridynamic (PD) force and moment are obtained by Cosserat constitutive equations through the relation between PD forces/moment and the stress/couple stress. Such relation is derived according to the bond relation of the Cosserat peridynamic model. To validate the proposed CBBCM, three numerical examples are presented, and the comparison shows good agreement between the CBBCM and the experimental observation and numerical results. The numerical convergence studies of m-convergence and δ-convergence are made to demonstrate the proposed CBBCM. The microstructure effect of crack propagation is analyzed by applying different Cosserat shear modulus and internal length scales in the simulation. The results indicate that the Cosserat shear modulus has an impact on the crack propagation and the crack propagates slower with a greater Cosserat shear modulus. The internal length scale has little impact on the crack path and only influences the local damage distribution.