Trial Application of Zarka´s Method under Cyclic Loading

  • If a mechanical structure is to be designed for operation under cyclic loading, primarily two kinds of failure must be guarded against: (1) low cycle fatigue which may occur due to strains cycling between two states (controlled by the strain range exceeding twice the yield limit); (2) ductility exhaustion which may occur due to accumulating strain from one load cycle to another. These two kinds of failure are local failure modes so that strains need to be calculated and then assessed by comparison with code allowables such as the 1%, 2% and 5% strain limits set by the ASME nuclear codes. Elastic-plastic strains can be calculated by incremental (or step-by-step or evolutive) analyses. Unfortunately, this can be extremely costly if thousands of cycles are required to achieve shakedown. Therefore, simplified elastic-plastic analysis methods are desired allowing to obtain specific information at reduced effort, nevertheless accounting for the main features controlling strain such as kinematic hardening. Zarka’s method, early versions ofIf a mechanical structure is to be designed for operation under cyclic loading, primarily two kinds of failure must be guarded against: (1) low cycle fatigue which may occur due to strains cycling between two states (controlled by the strain range exceeding twice the yield limit); (2) ductility exhaustion which may occur due to accumulating strain from one load cycle to another. These two kinds of failure are local failure modes so that strains need to be calculated and then assessed by comparison with code allowables such as the 1%, 2% and 5% strain limits set by the ASME nuclear codes. Elastic-plastic strains can be calculated by incremental (or step-by-step or evolutive) analyses. Unfortunately, this can be extremely costly if thousands of cycles are required to achieve shakedown. Therefore, simplified elastic-plastic analysis methods are desired allowing to obtain specific information at reduced effort, nevertheless accounting for the main features controlling strain such as kinematic hardening. Zarka’s method, early versions of which are available since twenty years, appears promising to provide both strain ranges and accumulated strains in the saturated cycle, i.e. after shakedown has been achieved. However, several attempts to use this method in the nuclear industry failed to qualify the method as a reliable analysis tool. This was due to several reasons: (1) the publications describing the method were written in a highly scientific language the design engineers in industry were not familiar with; (2) in some cases Zarka’s method provided excellent results (compared with incremental analyses), but bad ones in others. Nevertheless, there remained some interest to uncover the potential of this method. For that purpose some calculations are performed for simple configurations of structure and loading (so that the structural response can be interpreted relatively easily). More insight into the performance of the method may thus be gained in terms of computational steps to be followed, the numerical effort required, the quality of the results obtained, and the sensibility with respect to material data and load level. The basic idea of Zarka's method is to redefine the elastic-plastic problem by an equivalent elastic problem with suitably defined modified elastic material parameters and initial strains. This requires estimating (and iteratively improving) the geometry of the plastic zone and of transformed internal variables. A particular class of material models is admitted, the simplest of which is the linear kinematic hardening model.show moreshow less

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Metadaten
Author: Hartwig HübelORCiDGND
URL:https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16096.pdf
Title of the source (English):EUROMECH 385, Aachen, September 10, 1998
Document Type:Conference Proceeding
Language:English
Year of publication:1998
Tag:Bree-tube; Ratcheting; Shakedown; Zarka's method
Number of pages:4
Faculty/Chair:Fakultät 6 Architektur, Bauingenieurwesen und Stadtplanung / FG Baustatik, Stahlbau, FEM
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