@misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms}, series = {Journal of Pressure Vessel Technology}, volume = {141}, journal = {Journal of Pressure Vessel Technology}, number = {3}, doi = {10.1115/1.4042853}, pages = {031206-1 -- 031206-10}, abstract = {After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic-plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified determination of accumulated strains to satisfy design code requirements}, series = {International Journal of Pressure Vessels and Piping}, volume = {171}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2019.01.014}, pages = {92 -- 103}, 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. In addition, the strain range is required for performing fatigue analyses in case of plastic shakedown. However, little guidance is usually provided by Design Codes on how the accumulated strains and strain ranges are to be calculated, and some of the guidelines implemented in Design Codes are not well founded and may therefore be misleading. This is, for example, true for the ASME B\&PV Code, Section III. Of course, strains and strain ranges can be determined by means of incremental elastic-plastic analyses, which require to go step-by-step through many cycles of a given load histogram until the state of shakedown is reached. This is rather costly in terms of engineering time and numerical effort. As an alternative, simplified methods can be adopted, e.g. the Simplified Theory of Plastic Zones (STPZ) as used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and illustrated by some examples. 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 and plastic shakedown at the cost of few linear elastic analyses.}, 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} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Ratcheting caused by moving loads}, series = {International Journal of Advanced Structural Engineering}, volume = {9}, journal = {International Journal of Advanced Structural Engineering}, number = {2}, issn = {2008-6695}, pages = {139 -- 152}, abstract = {Progressive deformation (ratcheting) can occur as a response to variable loads as soon as the elastic limit is exceeded. If this is the case, strains and displacements accumulate in the event of cyclic loading in each load cycle. Widely known as triggers for ratcheting and already being considered in some design codes are configurations, in which a structure is subjected to at least two different types of load, namely a constant load (the primary load) and a superimposed cyclic load. In this paper, another mechanism that generates ratcheting is introduced. It can be attributed solely to the effect of a single load. In the simplest case, this can be explained by the successive activation of (an infinite number of) plastic hinges if a load of constant magnitude is moved in space. The increments of strains and displacements can decrease or increase from cycle to cycle, when the material is hardening, or if elastic foundation is present, or if the equilibrium condition is formulated for the deformed system (second-order theory) or if "large" rotations are taken into account (third-order theory).}, 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} } @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} } @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} } @misc{HuebelWilluweitRudolphetal., author = {H{\"u}bel, Hartwig and Willuweit, Adrian and Rudolph, J{\"u}rgen and Ziegler, Rainer and Lang, Hermann and Rother, Klemens and Deller, Simon}, title = {Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check}, series = {International Journal of Pressure Vessels and Piping}, journal = {International Journal of Pressure Vessels and Piping}, number = {116}, issn = {0308-0161}, doi = {doi:10.1016/j.ijpvp.2014.01.003}, pages = {10 -- 19}, abstract = {As elastic-plastic fatigue analyses are still time consuming the simplified elastic-plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (Ke factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with Ke correction, b) direct methods for the determination of stabilized elastic-plastic strain ranges and c) incremental elastic-plastic methods for the determination of stabilized elastic-plastic strain ranges. The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka's method) and - for comparison - the established Twice-Yield method. The Twice-Yield method is explicitly addressed in ASME Code, Section VIII, Div. 2. Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed. Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic-plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic-plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication.}, language = {en} } @inproceedings{HuebelRudolphRotheretal., author = {H{\"u}bel, Hartwig and Rudolph, J{\"u}rgen and Rother, Klemens and Ziegler, Rainer and Willuweit, Adrian and Lang, Hermann and Deller, Simon}, title = {Performance Study of the Simplified Theory of Plastic Zones for the Fatigue Check}, series = {Proceedings of PVP2013, ASME 2013 Pressure Vessels and Piping Conference, Paris, 2013}, booktitle = {Proceedings of PVP2013, ASME 2013 Pressure Vessels and Piping Conference, Paris, 2013}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5564-5}, doi = {10.1115/PVP2013-97137}, pages = {1 -- 9}, abstract = {As elastic-plastic fatigue analyses are still time consuming the simplified elastic-plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (Ke-factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with Ke correction, b) direct methods for the determination of stabilized elastic-plastic strain ranges and c) incremental elastic-plastic methods for the determination of stabilized elastic-plastic strain ranges. The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka's method). Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed. Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic-plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic-plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication.}, language = {en} }