Axial compression of circular cylindrical bar with coaxial subsurface cylindrical crack of finite length

A fracture stability of a circular cylindrical bar with a coaxial surface cylindrical crack subjected to an axial compression is considered. A state of subcritical initial strain is assumed. A non-classical fracture criterion is based on a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.