Longitudinal Fracture Analysis of Continuously Inhomogeneous Beams Undergoing General Planar Motion

This paper is devoted to longitudinal fracture in continuously inhomogeneous non-linear elastic beam structures which undergo general planar motion. First, a unified approach for treatment of the problem is presented assuming law of planar motion in general form. The acceleration of an arbitrary point in the beam is determined also in general form. This acceleration is used for obtaining the components of inertia forces continuous field in the beam. The forces of inertia in concentrated masses on the beam surfaces are also obtained and used when deriving solution of the strain energy release rate in general form. An example for application of this solution is presented. The strain energy release rate is confirmed by the J integral. It is investigated how the longitudinal fracture in a beam that undergoes general planar motion is affected by factors as location of the crack along the beam thickness, length of crack, length of the beam, and the material inhomogeneity along the beam thickness and length.