FG Baustatik, Stahlbau, FEM
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- Ratcheting (15)
- Vereinfachte Fließzonentheorie (12)
- Shakedown (9)
- Zarka-Methode (7)
- Dehnschwingbreite (6)
- KTA (6)
- Zarka's method (6)
- cyclic loading (5)
- Simplified Theory of Plastic Zones (4)
- progressive Deformation (4)
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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.
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.
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.
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.
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).
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.
Das Phänomen Ratcheting - Auswirkung plastischen Materialverhaltens bei ortsveränderlicher Belastung
(2017)
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.
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.
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.
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.
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.
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.
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.
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. 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.
Die Grundlagen der Vereinfachten Fließzonentheorie (VFZT) werden dargestellt. Für einige praxisnahe Beispiele aus dem Bereich der Kerntechnik wird die VFZT zur Ermittlung der Dehnschwingbreite und der akkumulierten Verzerrungen im Einspielzustand heran gezogen. Die Bewegungen des Spannungsbildvektors aufgrund veränderlicher Belastung werden anschaulich animiert im deviatorischen Hauptspannungsraum dargestellt. Die Entwicklung der Dehnungsakkumulation wird für zahlreiche Belastungszyklen im Spannungs-Dehnungs-Diagramm sowie im Dehnungshistogramm animiert dargestellt.
Die Implementierung der Zarka-Methode als User-Subroutine in ANSYS wird vorgestellt. Ihr Ausbau-Potential zur Erfassung temperaturabhängiger Streckgrenzen und die Praxisrelevanz hiervon in Hinblick auf die Abschätzung elastisch-plastischer Beanspruchungen in zyklisch belasteten Tragwerken werden aufgezeigt. Anhand zahlreicher Animationen wird für einen thermozyklisch belasteten Behälterstutzen das thermische und das Strukturverhalten veranschaulicht und die Qualität der Zarka-Methode im Vergleich zu einer inkrementellen Analyse dargestellt.
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 Abschätzung sog. post-shakedown quantities mittels weniger linear elastischer Analysen.
Die theoretische Basis des vereinfachten Ermüdungsnachweises im deutschen, US-amerikanischen, französischen und japanischen kerntechnischen Regelwerk wird aufgezeigt. Insbesondere wird Kritik geübt am Faktor Ke. Mehrere alternative Berechnungsmethoden werden aufgezeigt (Hübel, Roche, Seshadri, Zarka). Die theoretische Basis des vereinfachten Ratcheting-Nachweises in den Regelwerken durch Begrenzung der Dehnungen wird kritisch gewürdigt, insbesondere die des Bree-Diagramms.
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.