Taking into account the inertia terms in lengthwise fracture analysis of moving bars

As known, when structural members and components perform motion with acceleration they are subjected to influence of inertia terms. These terms play an important role when assessing different aspects of the behavior of engineering structures. This paper treats the problem of the lengthwise fracture behavior of continuously inhomogeneous bars which move in horizontal direction and at the same time rotate around a longitudinal axis. Particular attention is paid to the problem of determining the inertia terms that act upon the bars. Since the bars under consideration are continuously inhomogeneous in both longitudinal and transversal directions, the mass per unit area change continuously along the length and thickness of the bars. The inertia terms also change continuously in the length and thickness directions. The bars have non-linear elastic behavior. The parameters of the non-linear constitutive law used in this paper change continuously along the bars length and thickness. The integral J is applied for analyzing the lengthwise fracture in the bars under the forces of inertia. The strain energy release rate (SERR) is derived for verification of the integral J. The effects of the parameters of the laws for motion of the bars on the lengthwise fracture are evaluated and reported in form of diagrams presenting the change of the integral J. Assessments of the influence of the change of the mass per unit area and the parameters of the constitutive law along the length and thickness of the bars on the lengthwise fracture are made too.