Completed Projects
Brief description
Simplified yield zone theory (SLT) is used for the simplified estimation of state variables of elastically-plastically loaded structures, especially under cyclic loading. These are usually obtained using incremental elastic-plastic analyses for a finite element model of the structure over many loading cycles. The VFZT, on the other hand, allows the approximate determination of the structural behavior in the steady state in a simplified manner. With only a few linear elastic analyses, an estimate of the accumulated strain, the strain amplitude, the deformation state, etc. can be obtained.
So far, however, the VFZT is only available for calculations according to first-order theory, in which the deformations must be so small that it is sufficient to formulate the equilibrium conditions on the undeformed system. However, it is obvious that in structures that can develop a ratcheting mechanism, second-order geometric effects also occur as a result of the progressive deformation, which make it necessary to formulate the equilibrium conditions on the deformed system (second-order theory). A second-order VFZT is therefore to be developed as part of the project.
An example is a pipe bend under in-plane bending (modeled in the adjacent figure as a simplified half torus shell), in which downward forces ensure that the maximum stress is generated by circumferential bending near the crown. If an internal pressure exists at the same time, its stiffening effect ensures a reduction in the bending stresses according to the second-order theory.
Author
Maximilian Zobel, M. Sc.
Prof. Dr.-Ing. Hartwig Hübel
Funding institution
DFG, Project HU 1734/5-1
Keywords
fatigue, ratcheting, simplified elastic-plastic analysis
Brief description
The simplified yield zone theory (VFZT) is used for the simplified estimation of state variables of elastically-plastically loaded structures. In particular, it is intended to reduce the sometimes immense numerical effort for a computational fatigue analysis under cyclic loading. This includes, above all, the determination of the strain amplitude required for a fatigue analysis and the strain accumulation in the in-game state required for a ratcheting check.
An example of strain accumulation is a two-span beam under cyclic traveling load (see adjacent figure). The ratcheting mechanism can be traced back to a large number of flow joints opening and closing one after the other at different points until, due to the hardening of the material, the in-growth state is reached after approx. 40 cycles.
In the project, the focus was placed on accelerating the calculation process, expanding the range of applications and increasing the performance of the VFZT. The research results were published in seven peer-reviewed publications and conference papers.
Author
B. Vollrath, M. Sc.
Prof. Dr.-Ing. H. Hübel
Funding Institution
DFG,
project HU 1734/2-1
Funding Period
01.01.2016 - 30.06.2020
Keywords
fatigue, ratcheting, simplified elastic-plastic analysis
Peer-reviewed publications:
[1] Hübel, H.; Vollrath, B.: Ratcheting caused by moving loads. International Journal of Advanced Structural Engineering 9, Heft 2, 2017, S. 139 - 152, https://doi.org/10.1007/s40091-017-0154-0.
[2] Vollrath, B.; Hübel, H.: Determination of post-shakedown quantities of a pipe bend via the simplified theory of plastic zones compared with load history dependent incremental analysis. In: COMPUTER METHODS IN MECHANICS (CMM2017): Proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017. AIP Conference Proceedings, S. 120004-1 - 120004-12, https://doi.org/10.1063/1.5019119.
[3] Hübel, H.; Vollrath, B.: Simplified Analysis of Strains Accumulated in the State of Elastic Shakedown Considering Multi-Parameter Loadings. In: Volume 3: Design and Analysis. ASME 2018 Pressure Vessels & Piping Conference, July 15-20, 2018, Prague, Czech Republic. American Society of Mechanical Engineers, S. 1 - 10, https://doi.org/10.1115/PVP2018-84070.
[4] Hübel, H.; Vollrath, B.: Simplified determination of accumulated strains to satisfy design code requirements. International Journal of Pressure Vessels and Piping 171, 2018, S. 92 - 103, https://doi.org/10.1016/j.ijpvp.2019.01.014.
[5] Hübel, H.; Vollrath, B.: Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms. Journal of Pressure Vessel Technology 141, 2019, Heft 3, S. 214 - 223, https://doi.org/10.1115/1.4042853.
[6] Vollrath, B.; Hübel, H.: Direct Analysis of Post-Shakedown Quantities With the STPZ Considering Multi-Parameter Loading. In: Volume 3: Design and Analysis. ASME 2019 Pressure Vessels & Piping Conference, San Antonio, Texas, USA, July 14 - 19, 2019. American Society of Mechanical Engineers, S. 1 - 7, doi.org/10.1115/PVP2019-93268.
[7] Vollrath, B.; Hübel, H.: Efficient Fatigue and Ratcheting Computation in Case of Multi-Parameter Loading. In: Volume 2: Codes and Standards. ASME 2020 Pressure Vessels & Piping Conference, Minneapolis, Minnesota, USA, July 19 - 24, 2020, PVP2020-21089. American Society of Mechanical Engineers (paper accepted).