@misc{Huebel, author = {H{\"u}bel, Hartwig}, title = {Simplified Theory of Plastic Zones for cyclic loading and multilinear hardening}, series = {International Journal of Pressure Vessels and Piping}, journal = {International Journal of Pressure Vessels and Piping}, number = {129-130}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2015.03.002}, pages = {19 -- 31}, abstract = {The Simplified Theory of Plastic Zones (STPZ) is a direct method based on Zarka's method, primarily developed to estimate post-shakedown quantities of structures under cyclic loading, avoiding incremental analyses through a load histogram. In a different paper the STPZ has previously been shown to provide excellent estimates of the elastic-plastic strain ranges in the state of plastic shakedown as required for fatigue analyses. In the present paper, it is described how the STPZ can be used to predict the strains accumulated through a number of loading cycles due to a ratcheting mechanism, until either elastic or plastic shakedown is achieved, so that strain limits can be satisfied. Thus, a consistent means of estimating both, strain ranges and accumulated strains is provided for structural integrity assessment as required by pressure vessel codes. The computational costs involved typically consist of few linear elastic analyses and some local calculations. Multilinear kinematic hardening and temperature dependent yield stresses are accounted for. The quality of the results and the computational burden involved are demonstrated through four examples.}, language = {en} } @book{Huebel, author = {H{\"u}bel, Hartwig}, title = {Simplified Theory of Plastic Zones}, edition = {1. Auflage}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-319-29873-3}, doi = {10.1007/978-3-319-29875-7}, pages = {316}, abstract = {For a life prediction of structures subjected to variable loads, frequently encountered in mechanical and civil engineering, the cyclically accumulated deformation and the elastic-plastic strain ranges are required. The Simplified Theory of Plastic Zones (STPZ) is a direct method which provides the estimates of these and all other mechanical quantities in the state of elastic and plastic shakedown. The STPZ is described in detail, with emphasis to the fact that not only scientists but engineers working in practice and advanced students are able to get an idea of the possibilities and limitations of the STPZ. Numerous illustrations and examples are provided to support your understanding.}, language = {en} } @inproceedings{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Determination of post-shakedown quantities of a pipe bend via the Simplified Theory of Plastic Zones compared with load history dependent incremental analysis}, series = {22nd International Conference on Computer Methods in Mechanics, CMM2017}, booktitle = {22nd International Conference on Computer Methods in Mechanics, CMM2017}, editor = {Burczynski, Tadeusz}, address = {Lublin}, isbn = {978-83-7947-264-2}, pages = {MS11-1 -- MS11-2}, abstract = {The Simplified Theory of Plastic Zones (STPZ) may be used to determine post-shakedown quantities such as strain ranges and accumulated strains. The principles of the method are summarized succinctly and the practical applicability is shown by the example of a pipe bend subjected to internal pressure and cyclic in-plane bending.}, language = {en} } @inproceedings{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified Analysis of Strains Accumulated in the State of Elastic Shakedown Considering Multi-Parameter Loadings}, series = {ASME 2018 Pressure Vessels and Piping Conference, Volume 3B: Design and Analysis, Prague, Czech Republic, July 15-20, 2018}, booktitle = {ASME 2018 Pressure Vessels and Piping Conference, Volume 3B: Design and Analysis, Prague, Czech Republic, July 15-20, 2018}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5163-0}, doi = {10.1115/PVP2018-84070}, pages = {10}, abstract = {In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. However, this requirement is sometimes tied to misleading prerequisites, and little guidance is provided on how the strains accumulated in the state of shakedown can be calculated. Incremental elastic-plastic analyses which require to go step-by-step through many cycles of a given load histogram are rather costly in terms of engineering time and numerical effort. As an alternative, the Simplified Theory of Plastic Zones (STPZ) is used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and exemplarily applied to a simplification of a pipe bend and a straight pipe, both subjected to combinations of several loads which vary independently from each other so that a multidimensional load domain is represented. It is shown that the Simplified Theory of Plastic Zones is well suited to provide reasonable estimates of strains accumulated in the state of elastic shakedown at the cost of few linear elastic analyses.}, language = {en} } @inproceedings{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Determination of post-shakedown quantities of a pipe bend via the simplified theory of plastic zones compared with load history dependent incremental analysis}, series = {Computer methods in mechanics (CMM2017), proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017}, booktitle = {Computer methods in mechanics (CMM2017), proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017}, editor = {Podg{\´o}rski, Jerzy and Borowa, Ewa-Błazik and Be̜c, Jarosław}, publisher = {AIP Publishing}, address = {Melville, New York}, isbn = {978-0-7354-1614-7}, doi = {10.1063/1.5019119}, abstract = {The Simplified Theory of Plastic Zones (STPZ) may be used to determine post-shakedown quantities such as strain ranges and accumulated strains at plastic or elastic shakedown. The principles of the method are summarized. Its practical applicability is shown by the example of a pipe bend subjected to constant internal pressure along with cyclic inplane bending or/and cyclic radial temperature gradient. The results are compared with incremental analyses performed step-by-step throughout the entire load history until the state of plastic shakedown is achieved.}, language = {en} }