TY - BOOK A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie : auf Grundlage der Zarka-Methode N2 - Für eine Lebensdauervorhersage veränderlich belasteter Tragwerke, etwa des Anlagen- und Maschinenbaus sowie des Bauingenieurwesens, werden die zyklisch akkumulierten Verzerrungen und ggf. auch die elastisch-plastischen Dehnschwingbreiten benötigt. Die Vereinfachte Fließzonentheorie (VFZT) ist eine direkte Methode, die Abschätzungen dieser und aller anderen mechanischen Größen im elastischen und im plastischen Einspielzustand liefert. Das vorliegende Buch stellt die VFZT ausführlich dar und legt Wert darauf, dass sich nicht nur Wissenschaftler, sondern auch in der Praxis tätige Ingenieure sowie Studierende höherer Semester ein Bild von den Möglichkeiten und Grenzen machen können. Zahlreiche Abbildungen und Anwendungsbeispiele unterstützen das Verständnis. KW - Vereinfachte Fließzonentheorie KW - Shakedown KW - Ratcheting KW - progressive Deformation KW - Plastizieren KW - zyklische Belastung Y1 - 2015 UR - http://www.springer.com/gp/book/9783658079215 SN - 978-3-658-07921-5 U6 - https://doi.org/10.1007/978-3-658-07922-2 PB - Springer Vieweg CY - Wiesbaden 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 - 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 - GEN A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie T2 - Bauingenieur N2 - Es wird eine vereinfachte Fließzonentheorie vorgestellt, mit der das plastische Verhalten eines Tragwerks berechnet werden kann. Sie lässt sich nicht nur auf Stabwerke, sondern auch auf Flächentragwerke unter beliebiger Belastung anwenden. Das zugrunde gelegte Werkstoffgesetz ist bilinear, wodurch Verfestigung erfasst werden kann. Die Theorie beruht auf dem Konzept transformierter interner Variabler nach Zarka, mit dem das plastische Problem in ein geeignet formuliertes elastisches Problem überführt wird. Damit fällt oft nur eine weitere elastizitätstheoretische Berechnung an mit modifizierten elastischen Werkstoffparametern und mit (in Form von Anfangsdehnungen) modifizierter Belastung. Das Ergebnis kann gegebenenfalls iterativ verbessert werden, bis das "exakte" Ergebnis erreicht ist. Mehrere Beispiele erläutern die Methode. KW - Vereinfachte Fließzonentheorie KW - Fließgelenktheorie KW - Shakedown KW - Dehnungsakkumulation KW - Dehnschwingbreite Y1 - 1998 SN - 0005-6650 VL - 73 IS - 11 SP - 492 EP - 502 ER - TY - CHAP A1 - Hübel, Hartwig T1 - Trial Application of Zarka´s Method under Cyclic Loading T2 - EUROMECH 385, Aachen, September 10, 1998 N2 - 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. KW - Zarka's method KW - Ratcheting KW - Shakedown KW - Bree-tube Y1 - 1998 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16096.pdf ER - TY - BOOK A1 - Grandemange, J. M. A1 - Hübel, Hartwig A1 - Orsini, M. A1 - Schramm, K. A1 - Smith, N. G. T1 - Improved Design-by-Analysis Procedures for LWR Design Codes N2 - 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 KW - Shakedown KW - Tubeplates KW - Buckling KW - Ratcheting KW - Elastic follow-up KW - Strain range enhancement KW - Zarka's method Y1 - 1998 SN - 92-828-4191-X PB - Commission of the European Communities CY - Luxembourg ER - TY - GEN A1 - Hübel, Hartwig T1 - Basic Conditions for Material and Structural Ratcheting T2 - Nuclear Engineering and Design N2 - This paper is intended to provide an overview of different aspects of ratcheting under cyclic loading below the creep range. It distinguishes between material ratcheting and structural ratcheting, each being characterized by several different phenomena which appear in different configurations of materials, states of stress, structural geometries and loadings. The systematic compilation of these phenomena presented in the paper may help to improve understanding between material researches, developers of inelastic methods of analysis, structural analysts and design code committees. Above all, a certain degree of knowledge about the different mechanisms of ratchetting is important for a structural analyst to be able to choose an appropriate analytical method for assessing the ratcheting phenomena involved in a specific design problem. KW - Shakedown KW - Material Ratcheting KW - Structural Ratcheting Y1 - 1996 UR - http://www.sciencedirect.com/science/article/pii/0029549395011366 U6 - https://doi.org/10.1016/0029-5493(95)01136-6 SN - 0029-5493 VL - 162 IS - 1 SP - 55 EP - 65 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 - 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 - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Simplified Theory of Plastic Zones in the state of elastic shakedown with stress stiffening T2 - European Journal of Mechanics - A/Solids N2 - Cyclic loading may cause elastic-plastic strains to accumulate if a ratcheting mechanism is present. After a number of cycles, strain accumulation may cease so that a state of either elastic or plastic shakedown is reached. Determination of strains and other quantities in the state of shakedown (post-shakedown quantities) by means of incremental analyses is costly. Direct methods such as the Simplified Theory of Plastic Zones (STPZ) aim at providing estimates of the post-shakedown quantities, bypassing cycle-by-cycle analyses. If geometric effects such as stress stiffening play a role, determination of accumulated strains even becomes more complicated. The STPZ has been further developed in order to account for the combination of plasticity and stress stiffening with respect to elastic shakedown. The theory is described and illustrated using examples such as a pipe bend subjected to cyclic in-plane bending. The implications of cyclic as opposed to constant stress stiffness are discussed. The effect of stress stiffening on ratcheting interaction diagrams (RID), separating regions of elastic and plastic shakedown in the space of loading parameters, is discussed. KW - Cyclic strain accumulation KW - Shakedown KW - Ratcheting KW - Post-shakedown quantities KW - Stress stiffening KW - Geometric effects KW - Second order effects KW - Progressive buckling KW - Zarka's method Y1 - 2022 U6 - https://doi.org/10.1016/j.euromechsol.2022.104613 SN - 0997-7538 VL - 95 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Ratcheting and strain ranges in the shakedown state with stress stiffening using the Simplified Theory of Plastic Zones T2 - International Journal of Pressure Vessels and Piping N2 - The behavior of elastic-plastic structures under cyclic loading can be determined by incremental elastic-plastic analyses where a given load histogram is analysed cycle-by-cycle until shakedown is achieved. Many cycles may be required for this, if a ratchet mechanism is causing plastic strains to accumulate in each cycle until either elastic or plastic shakedown is achieved. The complexity of the elastic-plastic response of a structure is further increased if geometric effects are present. It may be very costly to get the accumulated strains and strain ranges in the state of shakedown by incremental analyses so that simplified or direct methods have been developed as an alternative. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the required quantities in the state of elastic and plastic shakedown within the framework of the 1st order theory, i.e., if the equilibrium conditions are satisfied for the undeformed structure. It is shown in this paper, how the STPZ can be expanded to capture 2nd order effects introduced by the equilibrium of the deformed structure. Some examples are used to demonstrate its applicability and the quality of the results, but also its limitations with respect to determining the accumulated strains and elastic-plastic strain ranges. KW - Simplified theory of plastic zones KW - Cyclic strain accumulation KW - Shakedown KW - Ratcheting KW - Post-shakedown quantities KW - Stress stiffening Y1 - 2022 U6 - https://doi.org/10.1016/j.ijpvp.2022.104727 SN - 0308-0161 VL - 199 SP - 1 EP - 11 ER - TY - BOOK A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie : auf Grundlage der Zarka-Methode N2 - Für eine Lebensdauervorhersage veränderlich belasteter Tragwerke, etwa des Anlagen- und Maschinenbaus sowie des Bauingenieurwesens, werden die zyklisch akkumulierten Verzerrungen und ggf. auch die elastisch-plastischen Dehnschwingbreiten benötigt. Die Vereinfachte Fließzonentheorie (VFZT) ist eine direkte Methode, die Abschätzungen dieser und aller anderen mechanischen Größen im elastischen und im plastischen Einspielzustand liefert. Das vorliegende Buch stellt die VFZT ausführlich dar und legt Wert darauf, dass sich nicht nur Wissenschaftler, sondern auch in der Praxis tätige Ingenieure sowie Studierende höherer Semester ein Bild von den Möglichkeiten und Grenzen machen können. Zahlreiche Abbildungen und Anwendungsbeispiele unterstützen das Verständnis. KW - Plastizieren KW - Ratcheting KW - Shakedown KW - Vereinfachte Fließzonentheorie KW - progressive Deformation KW - zyklische Belastung Y1 - 2023 SN - 978-3-658-41832-8 SN - 978-3-658-41833-5 U6 - https://doi.org/10.1007/978-3-658-41833-5 PB - Springer Vieweg CY - Wiesbaden ET - 2., überarbeitete Auflage ER -