Exact elasto-plastic analysis of rotating disks made of functionally graded materials

Presented in this paper is an exact closed-form analytical solution for elasto-plastic deformations and stresses in a rotating disk made of functionally graded materials (FGMs) in which the elasto-perfectly-plastic material model is employed. As for the yield criterion, the well-known Tresca’s model is used. The material properties are assumed to vary according to the power law whereas the Poisson’s ratio is kept constant. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit angular speed, displacement and stresses versus the radial direction. Moreover, the effect of increasing the angular speed on the propagation of the plastic zone is investigated. This analysis reveals that the plasticity can occur in different regions of the disk. To the best of authors’ knowledge, so far all previous exact solutions for the elasto-plastic analysis of FGM disks address the case of constant material density. The novelty of this work is to present an exact solution by taking into account the variation of density. The results show that the variation of density has a significant influence on the distribution of deformations and stresses. Furthermore, the effect of changing Poisson’s ratio on the value of the critical material parameter is demonstrated.