@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} } @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{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Das Ph{\"a}nomen Ratcheting - Auswirkung plastischen Materialverhaltens bei ortsver{\"a}nderlicher Belastung}, series = {Baustatik - Baupraxis 13, 20.-21. M{\"a}rz 2017, Bochum}, booktitle = {Baustatik - Baupraxis 13, 20.-21. M{\"a}rz 2017, Bochum}, editor = {Meschke, G{\"u}nther and Freitag, Steffen and Birk, Carolin and Menkenhagen, Jochen and Ricken, Tim}, publisher = {Ruhr-Universit{\"a}t Bochum}, address = {Bochum}, isbn = {978-3-00-055827-6}, pages = {189 -- 196}, abstract = {Bei Belastungs{\"a}nderungen 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 unabh{\"a}ngig von einer eventuell ebenfalls auftretenden Erm{\"u}dungssch{\"a}digung als eigenst{\"a}ndige m{\"o}gliche Schadensursache zu betrachten. Bekannt als Ausl{\"o}ser von Ratcheting und in manchen Regelwerken bereits ber{\"u}cksichtigt sind Konfigurationen, bei denen ein Tragwerk mindestens zwei unterschiedlichen Belastungsarten unterworfen ist, n{\"a}mlich einer konstanten Belastung (der Prim{\"a}rlast) und einer {\"u}berlagerten zyklischen Belastung. Selbst wenn letztere klein ist und f{\"u}r sich alleine keine plastischen Deformationen hervorruft, kann sie durch Zusammenwirkung mit der Prim{\"a}rlast dennoch eine progressive Deformation in Gang setzen. In der vorliegenden Arbeit wird ein weiterer, Ratcheting erzeugender Mechanismus vorgestellt, der allein auf ortsver{\"a}nderliche Wirkung einer einzelnen Lastgr{\"o}ße zur{\"u}ck zu f{\"u}hren ist. Im einfachsten Fall l{\"a}sst sich dieser erkl{\"a}ren durch die sukzessive Aktivierung von (gegebenenfalls unendlich vielen existierenden) Fließgelenken. Die Inkremente der Dehnungen und Verformungen k{\"o}nnen von Zyklus zu Zyklus ab- oder zunehmen, wenn die Verfestigung des Werkstoffs ber{\"u}cksichtigt wird, elastische Bettung vorliegt, die Formulierung des Gleichgewichts am verformten System erfolgt (Theorie II. Ordnung) oder die wahre Verformungsgeometrie (Theorie III. Ordnung) ber{\"u}cksichtigt wird.}, language = {de} } @misc{Huebel, author = {H{\"u}bel, Hartwig}, title = {Ratcheting in der Strukturmechanik}, abstract = {Es wird Ratcheting von Werkstofferm{\"u}dung abgegrenzt und beides in den Zusammenhang von rechnerischen Lebensdauer-Nachweisen gestellt. Struktur-Ratcheting wird detailliert anhand eines Zweistab-Modells erl{\"a}utert. Die Rolle der Werkstoff-Verfestigung wird exemplarisch durch eingebettete Animationen f{\"u}r die Endzust{\"a}nde "elastisches Einspielen" und "plastisches Einspielen" aufgezeigt.}, language = {de} } @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 = {Vereinfachte Fließzonentheorie : auf Grundlage der Zarka-Methode}, edition = {1. Auflage}, publisher = {Springer Vieweg}, address = {Wiesbaden}, isbn = {978-3-658-07921-5}, doi = {10.1007/978-3-658-07922-2}, pages = {318}, abstract = {F{\"u}r eine Lebensdauervorhersage ver{\"a}nderlich belasteter Tragwerke, etwa des Anlagen- und Maschinenbaus sowie des Bauingenieurwesens, werden die zyklisch akkumulierten Verzerrungen und ggf. auch die elastisch-plastischen Dehnschwingbreiten ben{\"o}tigt. Die Vereinfachte Fließzonentheorie (VFZT) ist eine direkte Methode, die Absch{\"a}tzungen dieser und aller anderen mechanischen Gr{\"o}ßen im elastischen und im plastischen Einspielzustand liefert. Das vorliegende Buch stellt die VFZT ausf{\"u}hrlich dar und legt Wert darauf, dass sich nicht nur Wissenschaftler, sondern auch in der Praxis t{\"a}tige Ingenieure sowie Studierende h{\"o}herer Semester ein Bild von den M{\"o}glichkeiten und Grenzen machen k{\"o}nnen. Zahlreiche Abbildungen und Anwendungsbeispiele unterst{\"u}tzen das Verst{\"a}ndnis.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Theoretische Grundlagen und Anwendung der Zarka-Methode}, series = {Workshop "Vereinfachte Erm{\"u}dungsnachweise" Erlangen, 20.06.2008}, booktitle = {Workshop "Vereinfachte Erm{\"u}dungsnachweise" Erlangen, 20.06.2008}, pages = {62}, abstract = {Die Zarka-Methode zur vereinfachten Berechnung elastisch-plastisch beanspruchter Tragwerke wird vorgestellt. Ihre historische Entwicklung und ihr theoretisches Fundament werden dargelegt. An einigen Beispielen (Lochscheibe, dickwandiger Zylinder unter Innendruck, Griffith-crack, Bree-Modell) wird die Notwendigkeit ihrer Weiterentwicklung belegt, aber auch ihr Potential zur Absch{\"a}tzung sog. post-shakedown quantities mittels weniger linear elastischer Analysen.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Methoden des regelkonformen vereinfachten Erm{\"u}dungs- und Ratcheting-Nachweises}, series = {Workshop „Vereinfachte Erm{\"u}dungsnachweise", Erlangen, 2008}, booktitle = {Workshop „Vereinfachte Erm{\"u}dungsnachweise", Erlangen, 2008}, pages = {46}, abstract = {Die theoretische Basis des vereinfachten Erm{\"u}dungsnachweises im deutschen, US-amerikanischen, franz{\"o}sischen und japanischen kerntechnischen Regelwerk wird aufgezeigt. Insbesondere wird Kritik ge{\"u}bt am Faktor Ke. Mehrere alternative Berechnungsmethoden werden aufgezeigt (H{\"u}bel, Roche, Seshadri, Zarka). Die theoretische Basis des vereinfachten Ratcheting-Nachweises in den Regelwerken durch Begrenzung der Dehnungen wird kritisch gew{\"u}rdigt, insbesondere die des Bree-Diagramms.}, language = {de} } @misc{Huebel, author = {H{\"u}bel, Hartwig}, title = {Bemerkungen zur Ausnutzung plastischer Querschnitts- und Systemreserven}, series = {Stahlbau}, volume = {72}, journal = {Stahlbau}, number = {12}, doi = {10.1002/stab.200303010}, pages = {844 -- 852}, abstract = {Plastische Tragreserven werden im Stahlbau h{\"a}ufig planm{\"a}ßig in Anspruch genommen und zumindest auf der Bewertungsseite (Verfahren Elastisch - Plastisch der DIN 18800) oder zus{\"a}tzlich auch auf der Ermittlungsseite der Beanspruchungen (Verfahren Plastisch - Plastisch) quantitativ ber{\"u}cksichtigt. In diesen Nachweisverfahren lauern jedoch einige Gefahren, die nicht immer leicht zu erkennen sind. Einige davon werden in diesem Beitrag angesprochen.}, language = {de} } @inproceedings{KretzschmarHuebel, author = {Kretzschmar, Andreas and H{\"u}bel, Hartwig}, title = {Fortschritte bei der Vereinfachten Fließzonentheorie}, series = {5. Lausitzer FEM-Symposium, Cottbus, 2003}, booktitle = {5. Lausitzer FEM-Symposium, Cottbus, 2003}, abstract = {Die im Rahmen eines aFuE-Vorhabens gewonnenen Erkenntnisse und die daraus abgeleiteten Weiterentwicklungen der Vereinfachten Fließzonentheorie werden vorgestellt und durch Beispiele illustriert.}, language = {de} } @techreport{Huebel, author = {H{\"u}bel, Hartwig}, title = {Berechnung akkumulierter Dehnungen nach der Vereinfachten Fließzonentheorie auf der Grundlage der Zarka-Methode bei zyklischer Belastung (Ratcheting-Nachweis)}, publisher = {FH Lausitz}, address = {Cottbus}, pages = {150}, abstract = {Es wird eine Vereinfachte Fließzonentheorie zum Nachweis gegen Ratcheting (progressive Deformation) vorgestellt. Sie beruht auf der Zarka-Methode und gestattet nicht nur festzustellen, ob die Struktur infolge zyklischer Belastung elastisch oder plastisch einspielt (qualitativer Nachweis), sondern auch die Bestimmung der mit dem Einspielen verbundenen elastisch-plastischen Dehnungen und Verformungen (quantitativer Nachweis). Der vorliegende Bericht stellt eine Erweiterung zum Vorg{\"a}ngervorhaben SR 2221 dar, das (unter anderem) bereits eine Variante der Zarka-Methode zur Berechnung elastisch-plastischer Dehnschwingbreiten (Faktor Ke) zum Inhalt hatte. Die der Vereinfachten Fließzonentheorie zugrunde liegenden Annahmen und die Vorgehensweise bei ihrer Anwendung f{\"u}r einen Ratcheting-Nachweis werden dargestellt und kritisch diskutiert. Umfangreiche Beispielrechnungen erl{\"a}utern die Methode.}, language = {de} } @techreport{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie zur Berechnung von Erm{\"u}dung und Ratcheting}, abstract = {Es wird der Stand der Entwicklung der Vereinfachten Fließzonentheorie dargestellt, und wie die VFZT konform mit dem KTA-Regelwerk angewendet bzw. weiter ausgebaut werden k{\"o}nnte. Dies betrifft die Ermittlung des Faktors Ke f{\"u}r vereinfachte Erm{\"u}dungsanalysen sowie die Ratcheting-Nachweisf{\"u}hrung, um erstmals bestehende L{\"u}cken im Regelwerk schließen zu k{\"o}nnen, weil die VFZT unabh{\"a}ngig ist von der speziellen Bauteilgeometrie und der Belastungsart.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Trial Application of Zarka´s Method under Cyclic Loading}, series = {EUROMECH 385, Aachen, September 10, 1998}, booktitle = {EUROMECH 385, Aachen, September 10, 1998}, pages = {4}, abstract = {If a mechanical structure is to be designed for operation under cyclic loading, primarily two kinds of failure must be guarded against: (1) low cycle fatigue which may occur due to strains cycling between two states (controlled by the strain range exceeding twice the yield limit); (2) ductility exhaustion which may occur due to accumulating strain from one load cycle to another. These two kinds of failure are local failure modes so that strains need to be calculated and then assessed by comparison with code allowables such as the 1\%, 2\% and 5\% strain limits set by the ASME nuclear codes. Elastic-plastic strains can be calculated by incremental (or step-by-step or evolutive) analyses. Unfortunately, this can be extremely costly if thousands of cycles are required to achieve shakedown. Therefore, simplified elastic-plastic analysis methods are desired allowing to obtain specific information at reduced effort, nevertheless accounting for the main features controlling strain such as kinematic hardening. Zarka's method, early versions of which are available since twenty years, appears promising to provide both strain ranges and accumulated strains in the saturated cycle, i.e. after shakedown has been achieved. However, several attempts to use this method in the nuclear industry failed to qualify the method as a reliable analysis tool. This was due to several reasons: (1) the publications describing the method were written in a highly scientific language the design engineers in industry were not familiar with; (2) in some cases Zarka's method provided excellent results (compared with incremental analyses), but bad ones in others. Nevertheless, there remained some interest to uncover the potential of this method. For that purpose some calculations are performed for simple configurations of structure and loading (so that the structural response can be interpreted relatively easily). More insight into the performance of the method may thus be gained in terms of computational steps to be followed, the numerical effort required, the quality of the results obtained, and the sensibility with respect to material data and load level. The basic idea of Zarka's method is to redefine the elastic-plastic problem by an equivalent elastic problem with suitably defined modified elastic material parameters and initial strains. This requires estimating (and iteratively improving) the geometry of the plastic zone and of transformed internal variables. A particular class of material models is admitted, the simplest of which is the linear kinematic hardening model.}, language = {en} } @book{GrandemangeHuebelOrsinietal., author = {Grandemange, J. M. and H{\"u}bel, Hartwig and Orsini, M. and Schramm, K. and Smith, N. G.}, title = {Improved Design-by-Analysis Procedures for LWR Design Codes}, publisher = {Commission of the European Communities}, address = {Luxembourg}, isbn = {92-828-4191-X}, pages = {VII, 89}, abstract = {The European Fast Reactor (EFR) collaboration with the EFR Associates Design and Construction Rules Committee, and the R\&D Agreement (AGT9B) produced significant developments in design-by-analysis procedures for high temperature plant. Many of these developments are judged to be relevant to the non-creep conditions of LWR plant, and for this reason, the CEC DGXI Working Group Codes and Standards supported this study to review and make recommendations on their potential application for improving LWR design code procedures. The topics considered are judged to be those where the most significant and relevant developments have been made and the list, although not exhaustive, is as follows: - Negligible creep criteria - Design-by-analysis procedures for weldments - Shakedown design rules - Design-by-analysis methods for tubeplates - Buckling rules - Interaction diagrams for assessing ratcheting - Rules for the prevention of elastic follow-up in piping - Strain range enhancement - Constitutive equations for inelastic analysis - Margins on Level D criteria - Zarka's method}, language = {en} }