Effect of spatial translational motion on lengthwise fracture in functionally graded beams

Beam-like structural members and components manufactured by functionally graded materials are widely applied in up-to-date aeronautical and aerospace engineering. Being parts of various flying apparatuses (helicopters, aircrafts, spacecrafts, etc.) these structural members very often are involved in different types of nonuniform spatial motion in the time of their service. This fact indicates the importance of studying the fracture behavior of the structural members and components with taking into account the inertia loading in the conditions of spatial motion. The present paper analyzes the effects of spatial translational motion on lengthwise fracture in functionally graded beams with non-linear elastic behavior. The beams under consideration are executing spatial translational motion with acceleration along the three axes in the space. The law of motion of the beams is known. The paper is focused particularly on deriving the strain energy release rate (SERR) in the beams acted upon by the inertia loading. The content of this paper is presented in the following consequence. First, the SERR problem in beams executing spatial translational motion is treated generally. Determination of accelerations and inertia loads along the three axes of the beam is considered. Then solution of an example is presented in detail. Finally, results illustrating the effects of spatial translational motion, material inhomogeneity and distribution of material density in the beam structure on the SERR are displayed in various graphs. A comparison in terms of the SERR between plane translation and spatial translation motion is presented. In context of this comparison, the effect of thickness to width ratio of the beam is evaluated.