Study On Holes With Edge Cracks And Elasticity Of New Materials

New materials such as piezoelectric materials, quasicrystals and magneto-electro-elastic materials as smart structures and devices are widely used in material science and engineering practice, e.g., aerospace and communication network, etc., due to their excellent multiple fields coupling performance. Many components with holed shape are commonly used in engineering when they connect other structures. However, the inherent brittle weakness of these materials easily results in cracks at the boundary of holes under combined mechanical, electrical and magnetic loads for a long time. The structural model with one or more tiny cracks emanating from holes has become a common units of micro-defects and these defects affects the mechanical properties of materials. Therefore, it is significant to systematically study the initiation and propagation of complicated defects such as cracks originating from holes. Furthermore, the displacement method in the classical elasticity mechanics is extended to the mechanical behavior of an infinitely large quasicrystal elastic layer subjected to gravity and uniform pressure.By using the Stroh-type formalism, Cauchy integral and Residue theorem, the anti-plane problems of cracks originating from holes in new materials are investigated systematically. Firstly, anti-plane problem of an edge crack emanating from a regular triangle hole with smooth vertices in one-dimensional hexagonal quasicrystals was analyzed by introducing a numerical conformal mapping. The expressions of the field intensity factors and the energy release rates near the crack tip were obtained. Numerical examples were conducted to show that the influences of the crack length and the side length of triangle hole, coupling coefficient and mechanical loads of phonon and phason fields on the field intensity factors and the energy release rate.Secondly, by constructing two new numerical conformal mappings, the anti-plane problem of three edge cracks originating from a regular triangle hole and four edge cracks emanating from a square hole in a transversely isotropic piezoelectric solid were investigated. The explicit expressions of the complex potential, field intensity factors, energy release rates and mechanical strain energy release rate near the crack tip were obtained under the assumption that the surfaces of the cracks and hole are electrically permeable and electrically impermeable. Numerical examples were conducted to show the influences of the geometrical parameters of defects and applied mechanical/electric loads on crack growth under two electrically boundary conditions.Thirdly, taking the piezoelectric effect into account, the anti-plane problems of one and three edge cracks emanating from a regular triangle hole and four edge cracks emanating from a square hole in one-dimensional hexagonal piezoelectric quasicrystals were studied. The explicit solutions of the field intensity factors and the energy release rates at the crack tip were obtained. Numerical examples were presented to show the influences of the geometrical parameters of defect, the applied mechanical loads of phonon and phason fields and the electric displacement on the field intensity factor and the energy release rate.Fouthly, one and three edge cracks originating from a regular triangle hole in magneto-electro-elastic(MEE) materials were investigated. The explicit expressions of the complex potential function, field intensity factors and energy release rates near the crack tip are obtained under the assumption of two magneto-electrically boundary conditions that the surfaces of the cracks and hole are fully permeable and fully impermeable. Numerical examples were conducted to show the influences of the geometrical parameters of defects and applied mechanical/electric/magnetic loads on the energy release rate under different magneto-electrical boundary conditions. The result showed that three cracks emanating from a triangle hole were easier to propagate the crack than that of an edge cracks emanating from a regular triangle hole in MEE materials.Finally, the displacement method for solving the space problem in the classical elasticity was applied to the mechanical analysis of infinite quasicrystals elastic layer subjected to gravity and uniform pressure. The analytic solutions of stress and displacement components of the phonon and phason fields were obtained. The influences of uniformly distributed load and coupling elastic constants on the stress and displacement of elastic layer were discussed numerically.