Effects of Periodic Loading on Longitudinal Fracture in ‎Viscoelastic Functionally Graded Beam Structures‎

This paper analyzes the effects of periodic external loading on the longitudinal fracture of a beam structure made of linear viscoelastic material. A longitudinal crack splits the cracked part of the beam into left-hand and right-hand crack arms. The beam is under a bending moment applied at the free end of the right-hand crack arm. The bending moment varies periodically with time. The material of the beam is continuously inhomogeneous (functionally graded) along the thickness. Thus, the modulus of elasticity and the coefficient of viscosity of the material vary continuously in transversal direction of the beam. The balance of the energy in the beam under periodic bending moment is analyzed in order to derive the strain energy release rate for the longitudinal crack. The solution is verified by deriving the strain energy release rate by analyzing of the compliance of the beam subjected to periodic bending moment. An investigation is carried-out by applying the solutions obtained in order to evaluate the effects of the parameters of the periodic loading on the strain energy release rate.