Interaction between a Macrocrack and a Cluster of Microcracks by Muskhelishvili’s Complex Potential Method

The interaction between a macrocrack and a cluster of microcracks has been investigated based on Muskhelishvili’s complex potential method. A step-by-step subproblem procedure is used to satisfy the stress boundary conditions on each crack surface. The interactions between a cluster of microcracks and a macrocrack and the interaction among microcracks are analyzed. Three damage configurations as chained, reverse-chained, and randomly distributed microcracks have been designed to simulate the damage around the macrocrack tip. The solution of an infinite elastic plane containing a macrocrack and a cluster of microcracks is presented for the plane subjected to a uniform tensile load. The stress intensity factor (SIF) at the macrocrack tip and the microcrack tips is obtained. The results show that the inclination angle of the microcrack and the distance between the macrocrack and microcracks have a great influence on SIF. When the inclination angle is small, the SIF at microcrack tips may be larger than other inclination angles. These results are helpful to analyze the fracture or damage behaviors of materials.

The coupling interaction of a piezoelectric screw dislocation with a bimaterial containing a circular inclusion

The coupling interaction of a piezoelectric screw dislocation with a bimaterial containing a circular inclusion is investigated by the complex potential method and conformal mapping technique. Explicit series solutions are obtained and then cast into new expressions with the coupling interaction effects separated. The new expressions converge much more rapidly and their one-order approximation formulae have satisfactory accuracy in many cases. According to the generalized Peach–Koehler formula, the image force acting on the screw dislocation is explicitly obtained and numerically studied to reveal the coupling interaction arising from multiple material properties as well as the geometry of inhomogeneous phases. In all regions, the coupling interaction has a significant influence on the number, location and stability of dislocation equilibrium points. In particular, the inclusion can reverse the image force within a region in the material on the other side of the interface.

Some Unexpected Results in the Stress Calculation Around Multiple Holes in an Isotropic Plate Under In-Plane-Loads

The Schwarz alternating method, along with Muskhelishvili’s complex potential method, is used to calculate the stresses around non-intersecting circular holes in an infinite isotropic plate subjected to in-plane loads at infinity. The holes may have any size and may be disposed in any manner in the plate, and the loading may be in any direction. Complex Fourier series, whose coefficients are calculated using numerical integration, are incorporated within a Mathematica program for the determination of the tangential stress around any of the holes. The stress values obtained are then compared to published results in the literature and to results obtained using the finite element method. It is found that part of the results generated by the authors do not agree with some of the published ones, specifically, those pertaining to the locations and magnitudes of certain maximum stresses occurring around the contour of holes in a plate containing two holes at close proximity to each other. This is despite the fact that the results from the present authors’ procedure have been verified several times by finite element calculations. The object of this paper is to present and discuss the results calculated using the authors’ method and to underline the discrepancy mentioned above.

Complex Analysis of Plane Problem of Two-Dimensional Quasicrystals

The fracture behavior of materials and structures are always caused by stress concentration near the defects in materials. This article describes the complex potential method for solving plane problems of quasicrystalline materials with defects. In order to prove effectiveness and success of the method, an example is given, and the results have very important significance in studying two-dimensional quasicrystals.

The Interaction between a Dislocation and Circular Inhomogeneity in 1D Hexagonal Quasicrystals

The interaction between a dislocation and circular inhomogeneity in 1D hexagonal quasicrystals is investigated. By using the complex potential method, explicit solutions of complex potentials are obtained. The image force acting on the dislocation are also derived. The results show that the interface attracts the dislocation inside both the matrix and the inhomogeneity under most condition. The attraction increase with the increase of the elastic constant of phason field and the phonon-phason coupling elastic constant.