A simplified method of solution for the short cycle creep-plasticity problem

Abstract

This paper describes a method for estimating the long-term effects on structures under cyclic changes of loading. For loads less than a certain critical amplitude (shakedown limit), the stress in the structure will a symptote to a cyclic stationary state consisting of an elastic part in response to the cyclic loading, plus a system of self-equilibrating residuals constant in time. It is shown that corresponding to this cyclic stationary state, the creep energy dissipation per cycle of loading is a maximum. Instead of following the exact time history to reach this state, in this paper it is found by a procedure of successive approximations. It corrects the admissible residual stress distribution at the beginning of a cycle by the creep and plastic strains accumulated over an entire cycle, which are in general not compatible, and requires additional self-equilibrating stresses to give an elastic strain distribution such that the total strain satisfies compatibility. The steady state is reached when no further correction is necessary. Convergence may be accelerated by a suitable choice of initial starting value, and by an artificial choice of the cycle time for the best computational convenience, upon which the steady-state solution can be proved to be independent. The procedure is a powerful device to obtain the cyclic steady-state solution, which will give an upper bound to the creep deformation per cycle and may also be used to find the shakedown limit. The formulation of the procedure in conjunction with the finite element method is given in detail and results of a few examples of the analysis are shown.