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...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.展开更多
The explicit formulation of the J2-integral in anisotropic bodies and its application in microcrack shielding problems are discussed. With analytical treatments and numerical examinations, it is proved that there is a...The explicit formulation of the J2-integral in anisotropic bodies and its application in microcrack shielding problems are discussed. With analytical treatments and numerical examinations, it is proved that there is a redistribution law for the remote J-integral in a discrete model of microcrack shielding problems, i.e. the projected conservation law of the Jk-vector. In this law, the J2-integral which was disregarded by Herrmann (1981) is proved to be of the same significance as the J1-integral. It is also concluded that the two energy dissipative processes due to the mi crocrack damage, i. e. the reduction in the effective moduli and the release of residual stresses, can be described by using the dissipation of the remote J-integral spreading across the microcrack damage zone.展开更多
The stress shielding effect of profuse microcracks at the tip of a macroscopic stationary mode Ⅰ crack is studied. The analysis method adopted combines the micromechanical approach with the effective elastic med...The stress shielding effect of profuse microcracks at the tip of a macroscopic stationary mode Ⅰ crack is studied. The analysis method adopted combines the micromechanical approach with the effective elastic medium approach. The anisotropic constitutive relation of the effective elastic medium is based on the DMG damage model developed by the authors for microcrack weakened brittle materials undergoing damage in form of elastic modulus degradation as a result of stable microcrack growth. The stress and strain fields at the crack tip and the condition of path independence of J integral in the damage zone are discussed under some reasonable approximations. A modified J integral method is thereby proposed to calculate the ratio of near tip to remote stress intensity factors and compared with the conventional method of J conservation.展开更多
基金The project supported by the National Natural Science Foundation of China(19891180)
文摘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Project supported by the National Natural Science Foundation of China.
文摘The explicit formulation of the J2-integral in anisotropic bodies and its application in microcrack shielding problems are discussed. With analytical treatments and numerical examinations, it is proved that there is a redistribution law for the remote J-integral in a discrete model of microcrack shielding problems, i.e. the projected conservation law of the Jk-vector. In this law, the J2-integral which was disregarded by Herrmann (1981) is proved to be of the same significance as the J1-integral. It is also concluded that the two energy dissipative processes due to the mi crocrack damage, i. e. the reduction in the effective moduli and the release of residual stresses, can be described by using the dissipation of the remote J-integral spreading across the microcrack damage zone.
文摘The stress shielding effect of profuse microcracks at the tip of a macroscopic stationary mode Ⅰ crack is studied. The analysis method adopted combines the micromechanical approach with the effective elastic medium approach. The anisotropic constitutive relation of the effective elastic medium is based on the DMG damage model developed by the authors for microcrack weakened brittle materials undergoing damage in form of elastic modulus degradation as a result of stable microcrack growth. The stress and strain fields at the crack tip and the condition of path independence of J integral in the damage zone are discussed under some reasonable approximations. A modified J integral method is thereby proposed to calculate the ratio of near tip to remote stress intensity factors and compared with the conventional method of J conservation.
