Relationship between energy release rate and microstructures in Cosserat continuum
Toriyama Toshiyuki
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 aij and the Rieman-Christoffel curvature tensor Rijkl which is equivalent to the disclination density tensor qij. On the other hand, Kluge and Gunther introduced the tensors aij and qij 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 Kluge and Gunther. 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. Key Words:Cosserat continuum, energy release rate, energy momentum tensor, dislocation, disclination, Peach-Koetler force