Anti-plane Problem For Elastic Interaction Of Interface And Arbitrary Crack In Bimaterial

The elastic interaction between cracks and interface, and elastic interaction effect among interfacial defects are greatly significant subjet in the fields of solid mechanics and materials science. Investigation on this subject is of theoretical significance and application value which will help to understand the to the complex material research of the strengthening and toughness of composite materials. This paper originally applies the continuous dislocation model method (CDMM) to the elastic interaction of arbitrary cracks and interface cracks or interfacial rigid lines in bimaterials under remote antiplane load.First of all, we adopt both analytical continuation of complex variable function method and analysis of complex stress function's singularity principal part to convert the problem of screw dislocation interaction with the related interface into the Riemann-Hilbert boundary value problem.The corresponding basic solution is provided by means of generalized Liouville theorem, Cauchy integration theorem and Residue theorem. Secondly, we use CDMM to establish the singular integral equation applying to work over both the random crack against interface and interface flaws (including interface cracks and interface rigid line inclusion) of bimaterial. Finally, we creatively employ different integral principles under mentioned relevant circumstance to simplify the singular integral equation into algebraic equation set and easily get the numerical solution to the problem.In this way, we can respectively obtain both circular inhomogeneity internal-external elastic interference solution of anti-plane loaded complex material with arbitrary shape cracks, and elastic interference solution of biphase material's random crack against interface crack, or interface rigid line inclusions. We can also calculate the stress intensity factor at the tip of defect, and then induce some mutual interference laws of bimaterial with cracks and interface defects.The results show that:a) under a given longitudinal shear load, the stress intensity factor K 3 at the crack tip increases as the elastic modulus of matrix decreases, and the crack length increases;b) in biphase material, the internal cracks of soft matrix are easy to propagate, while those of hard matrix are opposite;c) K 3 increases as the elastic ratio of matrix which contains the bimaterial internal crack grows;d) K 3 increases as the ratio of crack length and interface crack length a/b grows;e) the angle change of cracks has less impact on K 3, but still K 3 increases as the angle grows;f) the stress intensity of matrix crack increases as the internal interface rigid line of biphase material elongates, and the stress intensity factor tends to minimum value when the shear modulus goes to 1;g) the angle between matrix crack and rigid line has less impact on K 3, but still K 3 increases as the angle grows; in composite material, internal cracks have intensive disturbance effect on both interface linear crack interference effect and linear rigid line inclusion interference effect.The analysis method and solution can be used to settle the correspond problems of practical project. The examples used in this paper contain a lot of previously know results which can be shown to be special cases.