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 - 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 - 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 - 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 - Willuweit, Adrian A1 - Rudolph, Jürgen A1 - Ziegler, Rainer A1 - Lang, Hermann A1 - Rother, Klemens A1 - Deller, Simon T1 - Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check T2 - International Journal of Pressure Vessels and Piping N2 - 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. KW - Simplified Theory of Plastic Zones KW - Simplified elastic-plastic fatigue analyses KW - Zarka's method KW - Thermal cyclic loading KW - elastic-plastic strain range Y1 - 2014 UR - http://www.sciencedirect.com/science/article/pii/S0308016114000143 U6 - https://doi.org/doi:10.1016/j.ijpvp.2014.01.003 SN - 0308-0161 IS - 116 SP - 10 EP - 19 ER - 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 - Bieniussa, Klaus W. A1 - Reck, Hans A1 - Hübel, Hartwig T1 - Determination of more realistic Ke,r-factors for simplified elastic–plastic analysis T2 - Nuclear Engineering and Design N2 - According to the relevant KTA-Rules, e.g. KTA 3201.2, strain correction factors — Ke-factors — have to be used in the fatigue analysis of pressurised components if the strain intensity ranges are determined by elastic analyses, and if in this case the range of primary plus secondary stress intensity exceeds a certain limit. This limit is three times the design stress intensity value, Sm, and thus approximately corresponds to twice the value of the 0.2% strain limit. The relations given in the above-mentioned rules to determine the Ke-factors for considering plastification have proved to be very conservative in many cases compared with the strain intensity ranges that were determined by complete elastic–plastic analyses. In order to improve the validity of the fatigue analysis, the topic of `Performance of fundamental work to prepare concrete proposals for realistic Ke,r-factors (strain correction factors) to consider plastification at large strain amplitudes' was one of the subjects of the BMU project SR 2063. In summary, the result was that the proposed realistic Ke,r-factors present a real alternative to the Ke-factors of the regulations; the latter serve a mostly conservative registration of the observed elastic–plastic strain but cannot be explained in terms of physics and are not formulated in a manner adequately specific of any material. The exemplary verification calculations that have been performed so far show, furthermore, that the proposed realistic Ke,r-factors can be easily determined and also deliver sufficiently conservative results. This new method therefore has great potential which, however, still has to continue to be verified by further calculations before it can be included in the KTA-Rules. KW - strain correction factor KW - KTA KW - Ke-factor KW - fatigue analysis Y1 - 1997 SN - 0029-5493 VL - 174 IS - 3 SP - 343 EP - 352 ER - TY - GEN A1 - Hübel, Hartwig T1 - Bemerkungen zur Ausnutzung plastischer Querschnitts- und Systemreserven T2 - Stahlbau N2 - Plastische Tragreserven werden im Stahlbau häufig planmäßig in Anspruch genommen und zumindest auf der Bewertungsseite (Verfahren Elastisch - Plastisch der DIN 18800) oder zusätzlich auch auf der Ermittlungsseite der Beanspruchungen (Verfahren Plastisch - Plastisch) quantitativ berücksichtigt. In diesen Nachweisverfahren lauern jedoch einige Gefahren, die nicht immer leicht zu erkennen sind. Einige davon werden in diesem Beitrag angesprochen. KW - Ratcheting KW - progressive Deformation KW - plastische Tragreserven Y1 - 2003 U6 - https://doi.org/10.1002/stab.200303010 VL - 72 IS - 12 SP - 844 EP - 852 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 -