Mechanics of Periodic Film Cracking in Bilayer Structures Under Stretching

In a bilayer structure consisting of a stiff film bonded to a soft substrate, the stress in the film is much larger when the rigidity of the film is much higher than that of the substrate so that film cracking is a common phenomenon in bilayer structures such as flexible electronics and biological tissues. In this paper, a theoretical model is developed to analyze the normal stress distribution in the structure to explain the mechanism of the formation of periodic crack patterns. The effects of geometrical and material parameters are systematically discussed. The analytical result agrees well with finite element analysis, and the prediction of spacing between cracks agrees with experiments from the literature.

An Analysis of Mode III Doubly Periodic Crack-Tip Field of Orthotropic Composite Materials

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.