Analytical solution to the problem of disk cracking in functionally gradient space

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

“…The problem of a crack in the transversely isotropic layer (Sakamoto et al, 1999(Sakamoto et al, , 1989Tsai, 1982) has been related to the anisotropy of composites such as multi-layer materials. Aizikovich et al (2010Aizikovich et al ( , 2009 considered the problem of an inhomogeneous medium whose mechanical properties vary continuously (modeled on FGMs). Aizikovich et al (2015) extended the analytical procedure of previous studies to the problem of an inhomogeneous layer with a penny-shaped crack.…”

“…The penny-shaped crack is assumed to have internal pressure applied to its surface. The penny-shaped crack problem subjected to internal pressure has been studied by many researchers (Aizikovich et al, 2015(Aizikovich et al, , 2010(Aizikovich et al, , 2009Lowengrub and Sneddon, 1974;Sakamoto, 2003;Sakamoto et al, 1999Sakamoto et al, , 1989Selvadurai, 2000;Sneddon, 1946) because the problem is equivalent to the essential crack problem of elastic materials subjected to a uniform axial stress according to superposition principle for theory of linear elasticity. The reason of considering the crack subjected to internal pressure is that the crack problem can be formulated as a mixed boundary value problem (Selvadurai, 2000).…”