Simplified determination of elastic-plastic accumulated strain for analytical life assessment of structures by means of the Simplified Theory of Plastic Zones based on Zarka's method

• Applicant: Professor Dr.-Ing. Hartwig Hübel
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mechanics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286671283

The lifetime of a structure, operated beyond elastic limits and subjected to varying loads, is dependent on whether a ratcheting mechanism causing an accumulation of stress and strain in successive cycles of loading is developing (progressive deformation) until this process possibly ceases when shakedown is attained. In addition, fatigue is to be considered. Accordingly, the maximum elastic-plastic strain accumulated at the end of a ratcheting process needs to be determined for an analytical assessment of life (for comparison with maximum admissible strains), as well as the effective strain range occurring in subsequent cycles (for determination of fatigue usage factors). Usually, these quantities are obtained by means of incremental elastic-plastic analyses of a finite element model of the structure for many cycles of loading until shakedown is at least approximately achieved, usually associated with a huge computational burden. In contrast to this, the Simplified Theory of Plastic Zones (STPZ) makes use of a reformulation of the elastic-plastic constitutive equations including hardening known from Zarkas method, allowing for estimating some special quantities in some suitable manner. Thus, an approximation of accumulated strains and of strain ranges may be obtained at each location in the structure in the condition of shakedown. Few linear elastic analyses are sufficient, reducing the computational burden remarkably compared to incremental elastic-plastic analyses. Although steel was the material of main focus when developing the STPZ up to now, the basics of the STPZ are independent of a particular material. Accordingly, the potential field of application is widespread, including, for example, civil engineering, plant design and mechanical engineering. First applications give rise to the hope that the STPZ, at least with respect to determining the strain range, is a reasonable compromise between exact but costly cyclic incremental analyses on one hand and the simple and thus weakly based knock-down factors widely used in practical design of structures developing cyclic plasticity (e.g. factor Ke, Neuber method) on the other hand. The object of the project applied is to expand the STPZ in order to achieve a good approximation to the accumulated strains at little computational burden as well, by accelerating the calculation process, expanding its range of applicability and increasing its performance. Since no other simplified methods quantifying accumulated strains founded on sound mechanical background are known so far, this aim is considered to be of great value.

• DFG Programme: Research Grants