Comparison of the linear matching method to Rolls Royce's hierarchical finite element framework for ratchet limit analysis

This paper provides a direct comparison between the Linear Matching Method (LMM) and the numerical procedures currently being employed within the Rolls-Royce Power Engineering (plc) Hierarchical Finite Element Framework (HFEF) for the assessment of shakedown and ratcheting behaviour. These numerical methods include the application of Direct Cyclic Analysis (DCA), utilised in an automated search procedure for load-interaction plot generation and the recently developed Hybrid procedure. The Hybrid procedure is based on a similar premise to the LMM in that the load history is decomposed into cyclic and constant components. The LMM allows for the direct evaluation of shakedown and ratchet limits to be obtained in a traditional Bree load interaction format, along with the subsequent maximum plastic strain range for low-cycle fatigue considerations. Three problems have been used for comparison in this paper; the classic Bree cylinder, a nozzle-in-sphere with a cold media injection transient typical of nuclear power plant loading and a pressurised two-bar structure for multi-axial failure analysis. The accuracy of each method has been verified using ABAQUS step-by-step inelastic analysis. The variations in the implementation strategies associated with each method have also been discussed along with computational efficiency and effectiveness, which show that the LMM has the significant potential to improve analysis speeds via obtaining the ratchet limit boundary directly for a specified level of cyclic loading, instead of conducting an iterative search procedure.