On the analysis of longitudinal fracture in functionally graded rods performing non-uniform rotational movement

Various components of mechanisms and devices that are extensively used in a variety of aerospace and aeronautical applications frequently perform different kinds of movement with acceleration. According to D'Alembert's principle, the acceleration induces forces of inertia that have to be taken into account when analyzing various problems in the area of strength, fracture, stability, durability, reliability, etc. of components of load-bearing engineering structures, machines, mechanisms and devices. Having in mind that functionally graded materials are widely applied for manufacturing of high performance structures in modern aerospace industry, analyzing fracture behaviour of functionally graded structural members represents a problem of the present day. The goal of this paper is to analyze longitudinal fracture in functionally graded rods which perform non-uniform rotational movement around a pinned support. Non-linear viscoelastic rods that are functionally graded along the thickness and length are considered. The problem of determination of the strain energy release rate (SERR) in rods with a longitudinal crack under the action of distributed forces of inertia induced by the normal and tangential acceleration is treated generally (in essence, this is a dynamic problem). The distribution of the forces of inertia in the rod is analyzed. An application of the general approach for solving a particular problem is presented. The solution is confirmed by the integral J. The influence of various parameters of the model is studied. For instance, the influence of the ratio of the values of material parameters on the upper and lower surface of the rotating beam on the SERR is studied in detail. It is found that the SERR is very sensitive with respect to these ratios. A practical application of the solution for determining the boundary value of the parameter involved in the rotation law and the boundary crack length is presented.