\(M\)-integral analysis for a two-dimensional metal/ceramic bimaterial solid with extending subinterface microcracks (Q1401651)

In this paper, based on the M-integral analysis, the problem of an infinite metal/ceramic bimaterial solid with growing subinterface cracks is investigated. Mutual crack shielding and amplification effects due to the microcrack interaction are analyzed, assuming that the growth of the microcracks to be self-similar. The considered global coordinate system is selected such that the contribution of the microcracks to the M-integral can be evaluated. The numerical results for the stress intensity factors (SIFs) as well as the J-integrals are computed on the basis of the Muskhelishvili's theory, using the pseudo-traction method. A test example considers two co-linear cracks of the same length, which are parallel to the interface. Then, two finite microcracks of the same length are considered (one is parallel to the interface and other locates under angle to the first microcrack). As the bimaterial, Cu/Al2O3 is studied and the brittle material occupies the half-plane with microcracks. For different crack extensions the normalized M-integral is computed versus the increment of the microcrack length, demonstrating crack shielding and amplification effects. It is shown, there exists a relation between the growth of the M-integral and the decrease of the effective stiffness of the brittle component. The analysis of the microcrack interaction effect is carried out, using a parameter, depending on SIFs and fracture toughnesses of I and II Modes. It is shown an existence of mutual amplification and shielding effects for different microcrack orientations. These effects are dependent on the crack increment and the geometry of the microcrack arrangement. To analyze the effects on the stability of the bimaterial solid due to the existence of the ductile phase, the results for the bimaterial are compared with those of the homogeneous brittle solid. It is shown, that the shielding effect of the cracks in the homogeneous solid is stronger than that in the bimaterial solid, leading to lower stability of the material with ductile phase compared to the homogeneous brittle material.