Abstract
Several concepts concerning with fracture mechanics of materials having microstructures have been considered in last three decades. Especially, Eshelby's proposal of the elegant treatment of the generalized forces which act on elastic singularities made great contribution of this research field. Along with this conception, it is expected that the energy release rate for the material having microstructures can be described by using the generalized forces which act on singular stress fields at crack tip and around lattice defects at crack tip vicinity. This conception was first proposed by Ohnami. Through the series of studies, Ohnami and coworkers suggested that the stress singularities due to lattice defects at crack tip vicinity can be described by the dislocation density tensor αij and the Rieman-Christoffel curvature tensor Rijkl which is equivalent to the disclination density tensor θij. On the other hand, Klüge and Günther introduced the tensors αij and θij into Cosserat continuum to develop the lattice defect theory in it.
The objective of this study is to derive the mathematical formulation for Ohnami's conception with the aid of lattice defect theory developed by Klüge and Günther. The energy release rate was described as the sum of resultant generalized forces which act on singular stress fields at crack tip and around lattice defects at crack tip vicinity in Cosserat continuum.
