Effect of thermal loading on post elastic behaviour of axisymmetric bar and rotating disk

Abstract

The present thesis investigates the elasto-plastic behaviour of axisymmetric bars and rotating disks subjected to mechanical and thermal loads. In case of bars, the loading is uniaxial and the problem is essentially one-dimensional. A one dimensional problem is attributed by the presence of one-dimensional fields, e.g., stress, strain, displacement, etc. In case of rotating disks, the loading is in-plane and the presence of radial and tangential stress field makes the problem two-dimensional. In this class also the basic problem is defined in terms of radial displacement field. Hence, the mathematical analysis of axisymmetric bar and disk problems are quite similar. In the present thesis problem, the material of construction is assumed to be of two types, (a) isotropic and homogeneous and (b) isotropic and functionally graded. The elastic analysis of bar and rotating disk is solved upto limit (yield) state using total minimum potential energy principle. The limit elastic study is then extended to post-elastic domain to investigate the effect of material non-linearity of the performance of the structures. The post-elastic investigation of axisymmetric bar and rotating disk is addressed using an extension and application of minimum potential energy principle in Hencky’s total deformation theory of plasticity In this case, the strain energy is computed from hydrostatic and deviatoric stress-strain components. The von-Mises yield criterion and its associated flow rule assuming linear strain hardening (bilinear) material behaviour is adopted for the present work. The study on the extension of the linear strain hardening model for multiple straight line segments is also carried out. The entire formulation for all the simulation studies of the present thesis work is displacement based and the unknown displacement field is approximated by finite linear combination of admissible orthogonal coordinate functions and unknown coefficients. The set of functions come from a suitably selected start function and the higher order orthogonal functions are generated numerically by using Gram Schmidt orthogonalization scheme. The solution algorithm is actualized with the assistance of MATLAB® computational simulation software. The elasto-plastic analysis of statically indeterminate non-uniform bars subjected to concentrated axial load has been performed using an iterative variational method. The elastoplastic behaviour of thermo-mechanically loaded non-uniform bars is also studied. The results obtained for these one dimensional problems are in good agreement with the available results and with the results generated by a known finite element package, Abaqus. Some of the results xxxii presented for these problems showing the effect of geometry parameters like aspect ratio, slenderness ratio and the type of taperness. In the present thesis, the effect of disk geometries and temperature distribution on the thermo elastic stresses and deformation states has been carried out. The effect of temperature on various material properties is also studied. Limit angular speed of the disks is calculated under thermo-mechanical loading and reported in dimensional form as limit peripheral speed and dimensionless form as normalized limit angular speed. The elasto-plastic analysis of FGM disk under thermo-mechanical loading is also addressed in the present work. The material of the FG disk is considered to be metal-ceramic composite with a continuous variation of volume fraction of metal and ceramic along the radial direction. The results obtained from the present numerical method have been compared with benchmark results and good agreement is observed establishing the validity of the proposed methodology. Some of the results presented for these problems are new of their kind and may serve as benchmarks for further study. It is believed that the outcome of the present simulation embodied in the thesis will be helpful for both industrial design development and academic point of view.