Elasto-plastic analysis of thermo-mechanically loaded functionally graded disks by an iterative variational method

Abstract

The present work concentrates on the propagation of elastic-plastic front of functionally graded rotating disk under centrifugal and thermal load in post-elastic regime. The modeling of FGM is done for continuous distribution of ceramic and metal constituents along the radial direction by using power law variation of volume fraction. Minimum total potential energy principle in Hencky’s deformation theory of plasticity is used to obtain the governing equations in post-elastic regime. By using von-Mises yield criterion and assuming bilinear material behaviour, the solution of the unknown displacement field is achieved from the governing equation in an iterative manner. The solution algorithm is implemented by using MATLAB® computational simulation software. A comparative study is carried out for the present mathematical model for some reduced problems and good agreement is found. The effect of material parameters, disk geometries and types of temperature distribution field on the elasto-plastic performance of FG disk is investigated and some numerical results are presented in dimensionless form. The angular speeds and temperatures corresponding to yield initiation and plastic collapse are provided for different disk geometries, material parameters and temperature distributions. The effects of the problem parameters on the limiting angular speeds, limiting temperatures and the corresponding limit load factors are provided. Keywords: Variational method, Yield front, Deformation theory, Functionally graded disk, Thermal load, Limit load factor