Analytical Investigation of Yielding in Rotating Functionally Graded Disks with Variable Thickness Using the Tresca Criterion

This study examines the onset of plastic deformation in a spinning disk with non-uniform thickness by utilizing the Tresca failure criterion. The research focuses on a Functionally Graded Material (FGM) designed through spatially varying material properties and is conducted within the framework of small deformation theory under plane stress conditions. The radial dependence of parameters such as stiffness, density, and yield limit is described using power-law expressions, while Poisson’s ratio remains constant due to its limited fluctuation across different substances. An analytical solution is derived for the governing equation of motion. Additionally, the influence of the disk’s geometric profile on stress distribution is investigated, considering both the material gradation and cross-sectional variation. The disk’s thickness follows a power-law distribution along the radial direction. Various yield initiation scenarios and subsequent plastic zone formations are analyzed. The findings are compared with results from prior studies on homogeneous and graded disks of uniform thickness to ensure accuracy. The study demonstrates that allowing thickness to vary radially has a pronounced impact on both stress behavior and the point at which yielding begins, offering insights into optimized disk configurations.