Analytical approach to calculate bending, longitudinal and torsional local stiffness of an asymmetric circumferential crack with contact condition

In this paper, bending, longitudinal and torsional stiffness of an eccentric circumferential crack is investigated with taking into account contact condition on the crack surfaces based on fracture mechanics. Although several researches have analyzed stress intensity factors of symmetric circumferential crack, the stiffness of an asymmetric circumferential crack in different directions (along and perpendicular to eccentricity) regarding contact condition has not been studied by an analytical method until now. In this paper we aim to describe behavior of eccentric circumferential crack under axial loading and establish a relation between axial force and the resulting displacement vector. The twisting angle of asymmetric circumferential crack due to torsional loading is also calculated and compared to twisting angle of a symmetric crack. In order to simulate the local bending stiffness in the contact condition, nonlinear governing equations of bending stiffness associated to cracked beam section is developed by dividing it to strip elements and utilizing stiffness equations related to noncontact condition. It is validated by 3D finite element (FE) nonlinear model. Results show a significant compatibility between presented analytical and 3D FE methods. Moreover results of simulations show that without taking into account contact condition, axial, torsional and bending stiffness of symmetric and asymmetric circumferential crack are equal and radius of un-cracked area is the only influential factor.