摘要
This paper presents a new description for brittle solids with micro- cracks under plane strain assumption.The basic idea is to extend the conservation laws such as the J_j-vector and M-integral analysis used in single crack problems to strongly interacting crack problems.The M-integral contains two distinct parts.One of them is a summation from the well-known relation between the M-integral and the stress intensity factors(SIF)at both tips of each crack.The other,called as the additional contribution,is obtained from the two components of the J_j-vector and the coordinates of each microcrack center in a global system.Of great significance is the clarification of the confusion about the dependence of the M-integral on the origin selection of global coordinates,provided that the vector vanishes at infinity and that the closed contour chosen to calculate the integral and the vector encloses all the microcracks completely.The M-integral is equivalent to the decrease of the total potential energy of the microcracking solids with the strong interaction being taken into account.The M-integral analysis,from a physical point of view,does play an important role in evaluating the damage level of brittle solids with strongly interacting microcracks.
This paper presents a new description for brittle solids with micro- cracks under plane strain assumption.The basic idea is to extend the conservation laws such as the J_j-vector and M-integral analysis used in single crack problems to strongly interacting crack problems.The M-integral contains two distinct parts.One of them is a summation from the well-known relation between the M-integral and the stress intensity factors(SIF)at both tips of each crack.The other,called as the additional contribution,is obtained from the two components of the J_j-vector and the coordinates of each microcrack center in a global system.Of great significance is the clarification of the confusion about the dependence of the M-integral on the origin selection of global coordinates,provided that the vector vanishes at infinity and that the closed contour chosen to calculate the integral and the vector encloses all the microcracks completely.The M-integral is equivalent to the decrease of the total potential energy of the microcracking solids with the strong interaction being taken into account.The M-integral analysis,from a physical point of view,does play an important role in evaluating the damage level of brittle solids with strongly interacting microcracks.
基金
The project supported by the National Natural Science Foundation of China(19891180)
