This version is available at https://strathprints.strath.ac.uk/52828/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the University of Leicester, Leicester, LE1 7RH, UK AbstractA novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo-mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared to the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology.
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 loadinteraction 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.
This paper introduces a new approach based upon the Linear Matching Method in order to obtain the ratchet limit of structures subjected to an arbitrary thermo-mechanical load history. This method varies from the traditional Linear Matching Method ratchet analysis, where the cyclic load history is decomposed into cyclic and constant components, instead calculating the ratchet limit with respect to a proportional cyclic load variation, as opposed to an additional constant load. The shakedown and limit load boundaries are initially obtained for the given structure, followed by the utilisation of a bisection procedure in order to calculate an approximate ratchet boundary based upon a predefined magnitude of ratchet strain per cycle. The method also yields the total and plastic strain ranges based upon perfect plasticity, for low-cycle fatigue post-processing considerations. The effects of analysing the ratcheting mechanism of structures undergoing a cyclic primary load that varies proportionally with a cyclic secondary load can be seen to lead to modified and less conservative ratchet boundaries compared to the traditional Bree solution in which the thermal ratcheting requirement (NB-3222.5) of ASME III is based upon. This paper introduces the theory, numerical implementation and verification of the proposed method via a series of example problems.
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