TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms T2 - Journal of Pressure Vessel Technology N2 - 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. KW - Ratcheting KW - moving loads KW - cyclic loads KW - strain accumulation KW - hardening Y1 - 2019 UR - http://pressurevesseltech.asmedigitalcollection.asme.org/article.aspx?articleid=2725462 U6 - https://doi.org/10.1115/1.4042853 VL - 141 IS - 3 SP - 031206-1 EP - 031206-10 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Simplified determination of accumulated strains to satisfy design code requirements T2 - International Journal of Pressure Vessels and Piping N2 - 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. KW - Simplified elastic-plastic analysis KW - Simplified theory of plastic zones (STPZ) KW - Zarka's method KW - Shakedown KW - Ratcheting KW - Cyclic loading KW - Accumulated strains KW - Strain range KW - Residual stress Y1 - 2019 UR - https://www.sciencedirect.com/science/article/pii/S0308016118304617 U6 - https://doi.org/10.1016/j.ijpvp.2019.01.014 SN - 0308-0161 VL - 171 SP - 92 EP - 103 ER - TY - CHAP A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Simplified Analysis of Strains Accumulated in the State of Elastic Shakedown Considering Multi-Parameter Loadings T2 - ASME 2018 Pressure Vessels and Piping Conference, Volume 3B: Design and Analysis, Prague, Czech Republic, July 15–20, 2018 N2 - 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. KW - pipe bend KW - cyclic loading KW - simplified theory of plastic zones Y1 - 2018 UR - http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2711770 SN - 978-0-7918-5163-0 U6 - https://doi.org/10.1115/PVP2018-84070 PB - ASME CY - New York, NY ER - TY - CHAP A1 - Vollrath, Bastian A1 - Hübel, Hartwig ED - Podgórski, Jerzy ED - Borowa, Ewa-Błazik ED - Be̜c, Jarosław T1 - Determination of post-shakedown quantities of a pipe bend via the simplified theory of plastic zones compared with load history dependent incremental analysis T2 - Computer methods in mechanics (CMM2017), proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017 N2 - 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. KW - Simplified Theory of Plastic Zones KW - pipe bend KW - cyclic loading KW - plastic shakedown KW - post-shakedown quantities Y1 - 2018 SN - 978-0-7354-1614-7 U6 - https://doi.org/10.1063/1.5019119 PB - AIP Publishing CY - Melville, New York ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Ratcheting caused by moving loads T2 - International Journal of Advanced Structural Engineering N2 - 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). KW - Ratcheting KW - Progressive deformation KW - Shakedown KW - Traveling load KW - Moving temperature front Y1 - 2017 UR - http://link.springer.com/article/10.1007/s40091-017-0154-0/fulltext.html SN - 2008-6695 SN - 2008-3556 VL - 9 IS - 2 SP - 139 EP - 152 ER - TY - CHAP A1 - Vollrath, Bastian A1 - Hübel, Hartwig ED - Burczynski, Tadeusz T1 - Determination of post-shakedown quantities of a pipe bend via the Simplified Theory of Plastic Zones compared with load history dependent incremental analysis T2 - 22nd International Conference on Computer Methods in Mechanics, CMM2017 N2 - 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. KW - Simplified Theory of Plastic Zones KW - pipe bend KW - cyclic loading KW - multiaxial ratcheting KW - post-shakedown quantities Y1 - 2017 SN - 978-83-7947-264-2 SP - MS11-1 EP - MS11-2 CY - Lublin ER - TY - CHAP A1 - Hübel, Hartwig A1 - Vollrath, Bastian ED - Meschke, Günther ED - Freitag, Steffen ED - Birk, Carolin ED - Menkenhagen, Jochen ED - Ricken, Tim T1 - Das Phänomen Ratcheting - Auswirkung plastischen Materialverhaltens bei ortsveränderlicher Belastung T2 - Baustatik - Baupraxis 13, 20.-21. März 2017, Bochum N2 - Bei Belastungsänderungen kann eine progressive Deformation (Ratcheting) auftreten, sobald plastische Beanspruchungen im Tragwerk existieren. Dann akkumulieren sich Dehnungen und Verformungen im Falle zyklischer Belastung in jedem Belastungszyklus. Dieser Vorgang begrenzt die Lebensdauer eines Tragwerks, ist aber unabhängig von einer eventuell ebenfalls auftretenden Ermüdungsschädigung als eigenständige mögliche Schadensursache zu betrachten. Bekannt als Auslöser von Ratcheting und in manchen Regelwerken bereits berücksichtigt sind Konfigurationen, bei denen ein Tragwerk mindestens zwei unterschiedlichen Belastungsarten unterworfen ist, nämlich einer konstanten Belastung (der Primärlast) und einer überlagerten zyklischen Belastung. Selbst wenn letztere klein ist und für sich alleine keine plastischen Deformationen hervorruft, kann sie durch Zusammenwirkung mit der Primärlast dennoch eine progressive Deformation in Gang setzen. In der vorliegenden Arbeit wird ein weiterer, Ratcheting erzeugender Mechanismus vorgestellt, der allein auf ortsveränderliche Wirkung einer einzelnen Lastgröße zurück zu führen ist. Im einfachsten Fall lässt sich dieser erklären durch die sukzessive Aktivierung von (gegebenenfalls unendlich vielen existierenden) Fließgelenken. Die Inkremente der Dehnungen und Verformungen können von Zyklus zu Zyklus ab- oder zunehmen, wenn die Verfestigung des Werkstoffs berücksichtigt wird, elastische Bettung vorliegt, die Formulierung des Gleichgewichts am verformten System erfolgt (Theorie II. Ordnung) oder die wahre Verformungsgeometrie (Theorie III. Ordnung) berücksichtigt wird. KW - Ratcheting KW - progressive Deformation KW - Wanderlast KW - Plastizieren Y1 - 2017 SN - 978-3-00-055827-6 SP - 189 EP - 196 PB - Ruhr-Universität Bochum CY - Bochum ER - TY - VIDEO A1 - Hübel, Hartwig T1 - Ratcheting in der Strukturmechanik N2 - Es wird Ratcheting von Werkstoffermüdung abgegrenzt und beides in den Zusammenhang von rechnerischen Lebensdauer-Nachweisen gestellt. Struktur-Ratcheting wird detailliert anhand eines Zweistab-Modells erläutert. Die Rolle der Werkstoff-Verfestigung wird exemplarisch durch eingebettete Animationen für die Endzustände "elastisches Einspielen" und "plastisches Einspielen" aufgezeigt. KW - Ratcheting KW - Lebensdaueranalysen KW - Einspielen KW - Shakedown Y1 - 2016 UR - http://videoserver.hs-lausitz.de/index.php/kmc/preview/partner_id/111/uiconf_id/6709515/entry_id/0_g2klee05/delivery/http ER - TY - BOOK A1 - Hübel, Hartwig T1 - Simplified Theory of Plastic Zones N2 - 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. KW - plasticity KW - ratcheting KW - shakedown KW - progressive deformation KW - cyclic loading KW - limit load KW - simplified analysis Y1 - 2016 UR - http://www.springer.com/de/book/9783319298733 SN - 978-319-29873-3 SN - 978-3-319-29875-7 U6 - https://doi.org/10.1007/978-3-319-29875-7 PB - Springer International Publishing CY - Cham ET - 1. Auflage ER - TY - GEN A1 - Hübel, Hartwig T1 - Simplified Theory of Plastic Zones for cyclic loading and multilinear hardening T2 - International Journal of Pressure Vessels and Piping N2 - 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. KW - Simplified Theory of Plastic Zones KW - Shakedown KW - Ratcheting KW - cyclic loading KW - progressive deformation KW - elastic-plastic strain range Y1 - 2015 UR - http://www.sciencedirect.com/science/article/pii/S0308016115000289 U6 - https://doi.org/10.1016/j.ijpvp.2015.03.002 SN - 0308-0161 IS - 129-130 SP - 19 EP - 31 ER -