Abstract
The mechanical behavior near the doubly periodic crack tips for orthotropic composite materials plate subjected to antiplane shear loading is studied. This is done by complex function theory and conformal mapping of the Jacobi elliptic function with the help of boundary conditions. The analytical solution of the crack-tips stress intensity factor and the expression of stress fields are obtained. Numerical examples are given to analyze the impact of the different transverse spacing, longitudinal spacing, and the ratio of cracks periods on stress intensity factors. The results show that the crack-tip field increases with reducing either the transverse spacing or the longitudinal spacing. At the same time, the crack-tip field increases with the decrease of the ratio of cracks periods. This shows that the distribution form makes an important effect on the crack-tip field, but the crack density parameter is not the only cause.
Highlights
Fiber reinforced composite materials are used widely and are characterized by the proportion of small, specific strength and large specific modulus, but there are usually many microcracks, microholes in the process of fatigue damage
In 2011, Xiao et al [10] obtained the exact solution to the antiplane problem of doubly periodic conducting rigid line inclusions of unequal size in piezoelectric materials
This research contributes to the understanding of the interaction between multiple cracks contained in the composite materials
Summary
Fiber reinforced composite materials are used widely and are characterized by the proportion of small, specific strength and large specific modulus, but there are usually many microcracks, microholes in the process of fatigue damage. The more important value of doubly periodic crack model is that it provides the limit properties of interference between multiple cracks in the process from disorder to order. This problem is solved by the superposition method, the single-cell method, and numerical methods. Chang et al [11] discussed the anti-plane problem of doubly periodic cracks in the infinite homogeneous piezoelectric materials using conformal mapping and elliptic function and calculated the stress intensity factor and stress field in a closed form solution. This research contributes to the understanding of the interaction between multiple cracks contained in the composite materials
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