Analytical solution for the axisymmetric problem of a penny-shaped crack under internal pressure in a multi-layer composite

Abstract

The axisymmetric problem of a multi-layer composite with a penny-shaped crack, which is parallel to the interface between elastic layers, in the center plane is considered. It is assumed that each elastic layer, which has a unique elastic constant, is perfectly bonded to its adjacent elastic layers. The multi-layer composite is subjected to uniform internal pressure on the crack surface. The dual integral equations obtained for the problem are reduced to an infinite system of simultaneous equations by expressing the normal displacements on the crack surface as an appropriate series function. The boundary conditions between adjacent elastic layers can be generally formulated using the transfer matrix method. Numerical results were obtained in hard- and soft-layer composite systems, for which the elastic properties of each layer linearly increase and decrease towards the crack plane, respectively. This study shows not only the results of the mode I stress intensity factor at the crack tip, but also the distribution of normal stress and displacement at the crack plane. Furthermore, sandwich structures composed of three materials with different mechanical properties were considered. Numerical calculations show several conclusions that a stiffer layer should be placed father away from the crack surface to decease the stress intensity factor and the hardness of the middle layer contributes to the stress intensity factor for the sandwich structures.

Keywords

• stress intensity factor
• multi-layer composites
• penny-shaped crack
• elasticity
• transfer matrix method