Growth of yield front in thermo-mechanically loaded non-uniform bars using an iterative variational method

Abstract

The aim of this study is to investigate the growth of yield front in post-elastic domain of a thermo-mechanically loaded non-uniform bar with clamped ends. The problem is solved through an extension of the variational method in post-elastic regime. It is assumed that yield stress is the only physical parameter dependent on temperature variation of the bar and all other material properties remain constant corresponding to the value at ambient temperature. The bar is axisymmetric, and during thermal loading, its plane cross sections remain plane maintaining axisymmetry. This analysis of the energy-based variational formulation is carried out by Galerkin’s principle, using a linear combination of sets of orthogonal coordinate functions which satisfy prescribed boundary conditions. The approximate solution additionally needs an iterative technique to find the growth in yield front for the type of prescribed temperature field. The solution algorithm is actualized with the assistance of MATLAB^® computational simulation software. Uniform, linear and parabolic types of temperature distribution over the length of the bar are assumed, and some numerical results in dimensional form are presented and discussed for a clamped-clamped mild steel bar. The temperatures corresponding to onset of yielding and total collapse are considered as markers of yield limit and collapse loads. The temperatures and limit load factors for different bar geometries and temperature distributions are provided. The results reveal that the thermo-elasto-plastic deformation of clamped bar is significantly influenced by the effect of geometry parameters and by the nature of thermal load.