A numerical method is proposed to obtain individual stress intensity factor in circular arc-shaped interfacial crack. The method is based on the path-independency of L integral and $M_L$ integral witch involves tow independent equilibrium fields, from witch each stress intensity factor at the crack tip may be evaluated from the displacements and stresses remote from the crack tip. Some numerical examples are presented to compare the accuracy of this method to the well known "method of extrapolation". It is found that the accurate values of each individual stress intensity factor $k_1$ and $k_2$ are obtained based on the present method without using very find meshes or singular elements at the crack tip.
The effect of contact between the crack faces of an arc-shaped crack lying along the interface of a circular elastic inclusion embedded in an infinite matrix under remote uniaxial tension is examined by finite element method. It is seen that as the subtended angle of crack and the modulus of the inclusion increase the influence of contact on the stress intensity factors, energy release rate and crack energy, which means the change of potential energy due to crack, becomes larger. Also it is found that the influence of contact on the crack energy is negligible when the crack subtended angle of crack is smaller than about $60^0$.
Theoretical estimates on the basis of the self-consistent method are made for the elastic moduli of unidirectionally fiber-reinforced composite having circular arc-shaped interfacial cracks. It is assumed that a single fiber having circular arc-shaped crack is embedded in a matrix of the effective elastic moduli to be sought, which is guided by the self-consistent method. Results are identified in terms of three parameters, i.e., crack density, η, fiber volume fraction, $V_f$, and representative crack angle $θ_0$. It is found that the stiffening effect of fiber in transverse plane disappers as the subtended angle of crack becomes larger than a certain value.
