Elastic-plastic creep response of structures under composite time history of loading

Abstract

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. Starting with the principle of virtual work, exact equilibrium equations are derived for a stepwise Lagrangian formulation. The resulting equilibrium equations are then specialized to the incremental Piola-Kirchhoff stress computation and to small incremental strain formulation. Classical plasticity theory is used to develop a novel method based on the concept of ‘plastic stress’ for consideration of inelastic behavior. It is shown that the material's stress-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors, and by linear interpolation between any two breakpoints in the load history. Efficient criteria for load incrementation in the form of a fraction of the total ‘plastic stress’ for any sequence of two load history break points are developed and made an internal function of the program. This saves the user significant hardship when faced with guessing the load increment for an unknown state of the solution at any of the load history breakpoints. The ‘plastic stress’ load vector concept is utilized with interation and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. In summary, the new results of this work are the efficient handling of an arbitrary load history, introduction of the ‘plastic stress’ concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the ‘plastic stress’ concept, and development of a computer code capable of solving practical three-dimensional problems.