TY - CHAP A1 - Hübel, Hartwig A1 - Rudolph, Jürgen A1 - Rother, Klemens A1 - Ziegler, Rainer A1 - Willuweit, Adrian A1 - Lang, Hermann A1 - Deller, Simon T1 - Performance Study of the Simplified Theory of Plastic Zones for the Fatigue Check T2 - Proceedings of PVP2013, ASME 2013 Pressure Vessels and Piping Conference, Paris, 2013 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). 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. Y1 - 2013 SN - 978-0-7918-5564-5 U6 - https://doi.org/10.1115/PVP2013-97137 SP - 1 EP - 9 PB - ASME CY - New York, NY 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 - 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 - 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 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 - RPRT A1 - Hübel, Hartwig A1 - Kretzschmar, Andreas T1 - Vereinfachte elastisch-plastische Berechnung von Stahltragwerken Y1 - 2003 PB - Selbstverlag CY - Cottbus ER - TY - CHAP A1 - Hübel, Hartwig A1 - König, Claus T1 - Vergleich impliziter (ANSYS) und expliziter (ANSYS/LS-DYNA) dynamischer Analysen T2 - Conference Proceedings of 20. CAD-FEM Users' Meeting 2002 Y1 - 2002 SP - 1 EP - 13 PB - CAD-FEM CY - Grafing bei München ER - TY - CHAP A1 - Kretzschmar, Andreas A1 - Hübel, Hartwig T1 - Implementierung der Vereinfachten Fließzonentheorie in ANSYS T2 - Conference Proceedings of 20. CAD-FEM Users' Meeting 2002 Y1 - 2002 SP - 1 EP - 10 PB - CAD-FEM CY - Grafing bei München ER - TY - CHAP A1 - Hübel, Hartwig T1 - Theoretische Grundlagen und Anwendung der Zarka-Methode T2 - Workshop "Vereinfachte Ermüdungsnachweise" Erlangen, 20.06.2008 N2 - 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. KW - Zarka-Methode KW - Ratcheting KW - Dehnschwingbreite KW - Bree-Rohr KW - Griffith-crack Y1 - 2008 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16014.pdf ER - TY - CHAP A1 - Kretzschmar, Andreas A1 - Hübel, Hartwig T1 - Fortschritte bei der Vereinfachten Fließzonentheorie T2 - 5. Lausitzer FEM-Symposium, Cottbus, 2003 N2 - Die im Rahmen eines aFuE-Vorhabens gewonnenen Erkenntnisse und die daraus abgeleiteten Weiterentwicklungen der Vereinfachten Fließzonentheorie werden vorgestellt und durch Beispiele illustriert. KW - Vereinfachte Fließzonentheorie KW - Ratcheting KW - Dehnschwingbreite KW - Dehnungsakkumulation Y1 - 2003 UR - http://www-docs.tu-cottbus.de/ikmz/public/typo3/ubico/5._FEM_Symposium_20031127_Finale.pptx ER - TY - GEN A1 - Hübel, Hartwig A1 - Kretzschmar, Andreas T1 - Use of Zarka's Method at FHL N2 - Es wird ein historischer Abriss der Zarka-Methode gegeben. Ihre Vor- und Nachteile bei der Ermittlung der Strukturantwort monoton oder zyklisch überelastisch beanspruchter Tragwerken werden abgewogen. Erweiterungen, Verbesserungen und Spezialisierungen in Hinblick auf die Vereinfachte Fließzonentheorie werden erläutert und beispielhaft angewendet (thermal stratification, cylindrical shell under axial temperature step). Anforderungen an die Implementierung in eine FE-Umgebung mittels Makros und User-subroutines werden aufgeführt. Ergebnisse eines gemeinsam mit der CUT durchgeführten Benchmarks (Hertz-contact, Bree-tube) werden vorgestellt. KW - Zarka-Methode KW - Vereinfachte Fließzonentheorie KW - Hertz-Kontakt KW - Bree-Rohr Y1 - 2003 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16016.pdf N1 - Vorlesung an der Cracow University of Technology ER - TY - GEN A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie N2 - Es wird auf die historische Entwicklung der Zarka-Methode zur vereinfachten Abschätzuung elastisch-plastischer Beanspruchungen in Tragwerken zurück geblickt, auf ihre theoretischen Grundlagen, auf gute sowie schlechte Anwendungserfahrungen. Es erfolgt ein Ausblick auf die Vereinfachte Fließzonentheorie. KW - Zarka-Methode KW - Vereinfachte Fließzonentheorie Y1 - 2002 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16017.pdf N1 - Ehrenkolloquium zum 60. Geburtstag von Prof. Dr.-Ing. O.T. Bruhns, Bochum ER - TY - CHAP A1 - Hübel, Hartwig T1 - Lebensdauernachweise von KKW-Komponenten mit der VFZT T2 - 12. Lausitzer FEM-Symposium, Cottbus, 2010 N2 - 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. KW - VFZT KW - ratcheting KW - Einspielen KW - Verfestigung KW - Lebensdauer von Tragwerken KW - progressive Deformation KW - Ermüdung Y1 - 2010 UR - https://www.b-tu.de/owncloud/index.php/s/tWYWty3RoX5lKuN UR - https://www.dropbox.com/s/86ibkgisxejh5zc/Vortrag%20H%C3%BCbel%20FEM-Symposium%202010.zip?dl=0 ER - TY - CHAP A1 - Hübel, Hartwig T1 - Exemplarische Anwendung der Zarka-Methode T2 - Workshop "Vereinfachte Ratchetingnachweise", Erlangen, 2009 N2 - 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. KW - Zarka-Methode KW - Behälterstutzen KW - thermozyklische Belastung KW - Dehnschwingbreite Y1 - 2009 UR - https://www.b-tu.de/owncloud/index.php/s/XZsDe7ux2etPzWy UR - https://www.dropbox.com/s/wz0ni4qise96n4k/Vortrag%20H%C3%BCbel%20Workshop%20Erlangen%202009.zip?dl=0 ER - TY - CHAP A1 - Hübel, Hartwig T1 - Methoden des regelkonformen vereinfachten Ermüdungs- und Ratcheting-Nachweises T2 - Workshop „Vereinfachte Ermüdungsnachweise“, Erlangen, 2008 N2 - 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. KW - Ermüdung KW - Ratcheting KW - KTA-Regelwerk KW - Faktor Ke KW - Bree-Diagramm Y1 - 2008 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16013.pdf 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 - CHAP 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 - Proceedings of ANSYS Conference & 31th CADFEM Users‘ Meeting, Mannheim, 2013 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. 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 elastic-plastic fatigue analyses KW - simplified theory of plastic zones KW - Twice Yield method KW - Zarka’s method KW - thermal cyclic loading KW - load-time histories Y1 - 2013 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_15992.pdf ER - TY - RPRT A1 - Hübel, Hartwig T1 - Berechnung akkumulierter Dehnungen nach der Vereinfachten Fließzonentheorie auf der Grundlage der Zarka-Methode bei zyklischer Belastung (Ratcheting-Nachweis) N2 - 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 Vorgängervorhaben 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 für einen Ratcheting-Nachweis werden dargestellt und kritisch diskutiert. Umfangreiche Beispielrechnungen erläutern die Methode. KW - Vereinfachte Fließzonentheorie KW - Ratcheting KW - Einspielen KW - Dehnungsakkumulation KW - Bree-Diagramm KW - KTA Y1 - 1999 PB - FH Lausitz CY - Cottbus 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 - 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 - RPRT A1 - Hübel, Hartwig T1 - Ermittlung realistischer Ke-Faktoren (Plastizierungsfaktoren) als Grundlage für die Präzisierung des kerntechnischen Regelwerkes hinsichtlich der Ermüdungsanalyse N2 - Es werden drei vereinfachte Methoden zur Berechnung elastisch-plastischer Dehnschwingbreiten infolge zyklischer Belastung von Komponenten der Kerntechnik vorgestellt. Es handelt sich um die Methoden von Roche, Seshadri und Zarka. Diese werden mit dem Faktor Ke des KTA-Regelwerks sowie dem im Vorhaben SR 2063 unterbreiteten Vorschlag zu seiner Modifikation verglichen. Die ihnen zugrunde liegenden Annahmen werden kritisch durchleuchtet. Ihre Anforderungen an das Werkstoffgesetz im plastischen Bereich sowie der erforderliche Berechnungsaufwand werden herausgestellt. Einfache Beispielrechnungen zeigen, durch Gegenüberstellung mit den exakten Werten, die erzielbare Genauigkeit. KW - Zarka-Methode KW - Roche-Methode KW - GLOSS-Methode KW - KTA KW - Dehnschwingbreite KW - Ermüdungsanalyse Y1 - 1997 N1 - Vorhaben SR 2221 des Bundesministeriums für Umwelt, Naturschutz und Reaktorsicherheit PB - grm, Merkel CY - Dossenheim ER - TY - BOOK A1 - Maier, Giulio A1 - Comi, Claudia A1 - Corigliano, Alberto A1 - Perego, Umberto A1 - Hübel, Hartwig T1 - Bounds and Estimates on Inelastic Deformations N2 - Design codes require to demonstrate that certain limits of inelastic deformation are not exceeded during the service life of a structure. If the loading is cyclic, inelastic strains may accumulate cycle by cycle and may exceed specified allowables after a number of cycles before a stationary state (elastic or plastic shakedown) is achieved, or the inelastic strains may grow unboundedly due to a ratchetting mechanism. In principle, inelastic deformations can be calculated by performing evolutive (step-by-step) inelastic analyses. These require specific information, which is, however, not always available, such as detailed constitutive modelling and loading history. Furthermore, evolutive inelastic analyses are very costly. Therefore, simplified inelastic analyses are desirable to provide at least partial information about structural behaviour: more specifically, upper bounds on, or estimates of, elastic-plastic-creep deformations. Some simplified methods are envisaged by design codes (as pointed out in Chapter 2). However, they are based on specific configurations of geometry and loading or they adopt heuristic assumptions, the reasonability of which is not always evident for general applicability within the scope of these codes. Accordingly, design codes seem to require improvements. Several simplified methods are reviewed in the present Report and might serve as alternatives to those suggested by design codes. Simplified methods can be grouped in two classes: (a ) procedures intended to determine a safety factor against a critical event of the global structure (such as collapse); (b ) techniques apt to provide information on local quantities (such as inelastic strain) associated to inelastic structural responses. Procedures of class (a ) and some of their recent extensions are briefly surveyed in Chapter 3. Subclasses of category (b ) are discussed in the subsequent Chapters, with emphasis on their operative peculiarities and on their practical usefulness or potentialities. Upper bounds in plasticity (Chapter 4 and Appendix A) can be computed by various approaches, basically by satisfying a set of equations and inequalities and by carrying out some optimisation procedure. To within the consequences of modelling errors, residual post shakedown quantities are guaranteed to be bounded from above: this circumstance is referred to by the adjective "rigorous". A number of bounding inequalities can be proved. Usually, the better (lower) the bound, the more expensive is its computation. However, computational advantages over other simplified approaches can hardly be ascertained in general. Upper bounds in creep (Chapter 5) are based on general rigorous mechanical foundations, but the applications available mostly concern particular cases employing "ad hoc" imaginative, sometimes heuristic assumptions which are not easy to transfer to other cases. Mostly, elastic-perfectly plastic material behaviour and the Bailey-Orowan creep model are assumed. Some simplified methods, such as the British shakedown method (Chapter 6), intend to estimate residual stress fields after elastic shakedown (the British method also, in certain circumstances, after plastic shakedown). They adopt empirically corroborated conjectures, rather than rigorous arguments. Material hardening is neglected. Zarka's method (Chapter 7 and 8 and Appendix B) provides estimates of the mean strain in case of elastic shakedown and, in addition, a lower and an upper estimate of strain range in case of plastic shakedown, by adopting some heuristic assumptions. The validity of these assumptions is difficult to assess in practical applications. Material hardening is required. The method developed by Ladevèze and coworkers (Chapter 9 and Appendix C) is not, strictly speaking, a simplified method, in the sense that it provides the same kind of information as rigorous evolutive analyses. The simplification lies in the solution process, which can be stopped after a few iterations since each one of these concern the whole time interval of interest. Thus estimates are achieved of the structural inelastic response over a large time interval (much larger than the time step in an evolutive analysis). General material models are admitted. None of the simplified methods reviewed in the present Report can directly be recommended for general practical use in nuclear design situations. However, some of them seem to have at least no less potentialities than the methods mentioned so far by design codes. Further work is necessary to clarify the conditions under which they are advantageous. KW - Zarka's method KW - Ladeveze-method KW - simplified methods KW - inelastic deformation KW - shakedown Y1 - 1996 SN - 92-827-5006-X N1 - Nuclear Science and Technology, EUR 16555 EN 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 - BOOK A1 - Hübel, Hartwig A1 - Zeibig, H. T1 - State-of-the-Art of Simplified Methods to Account for Elastic Follow-up in Creep N2 - Engineering structures exposed to high temperature environment exhibit time dependent behaviour due to time dependent material behaviour. In order to avoid full inelastic analyses, simplified inelastic analysis methods are desirable. The concept of elastic follow-up was introduced to allow determination of quantities serving as measure for life assessment of structures subjected to creep conditions without performing full time dependent structural analyses. Various simplified methods are described in the literature to estimate enhancement of creep strain and of creep damage arising from the fact that so-called secondary stresses caused by displacement-controlled loading do not necessarily relax with time in the same way as stresses do that are caused by strain-controlled loading, but rather show some characteristics of stress-controlled loading. After providing a definition of elastic follow-up, the fundamental principles of elastic follow-up are compiled. A parameter "q" is introduced as a measure of elastic follow-up and is derived for some examples. Effects of non-uniform temperature distribution are discussed as well as effects resulting from multiaxial stress states. A number of methods to quantify elastic follow-up by simplified methods adopted by design codes or proposed in the literature are reviewed for general structures (Part I) and for piping (Part II). KW - creep KW - elastic follow-up KW - design codes KW - simplified method Y1 - 1996 SN - 92-827-5009-4 N1 - Nuclear Science and Technology, EUR 16555 EN PB - Commission of the European Communities CY - Luxembourg ER - TY - BOOK A1 - Hübel, Hartwig T1 - Simplified Elastic-Plastic Fatigue Analysis of Smooth Structures N2 - Engineering structures subjected to high cyclic straining necessitating fatigue analysis play an important role in many industries. If the proportionality limit of the material is exceeded, nonlinearity of the material behaviour is to be taken into account. The structural response can then be calculated using either rigorous inelastic analysis methods, where stresses and strains are calculated on a step-by-step basis throughout a given load history, or by employing simplified methods of analysis. In the latter case a plastic strain range enhancement factor Ke is often used to obtain an elastic-plastic strain range based on fictitious elastic stress analyses. Plastic behaviour of simple academic and practical structures is investigated to identify the basic features which determine the factor Ke: (a) geometry of the structure (b) kind of loading (c) load level (d) material behaviour. The factor Ke is quantified for different geometries and kinds of loading. Parameter studies are performed to quantify the effects of load level, material models and hardening characteristics. The background of some factors Ke established in Nuclear Design Codes or proposed in the literature is reviewed. The behaviour of plastic structures can be attributed to global, localised and multiaxiality effects. Global structural effects comprise uniform reduction and redistribution of section forces and moments due to plasticity, including redistribution of stress across a section. Localised effects are concentrated to a very small volume of the material not affecting section forces and moments (e.g. notch effects). Multiaxiality effects arise from different Poisson's ratio associated with elastic and plastic behaviour. Emphasis is laid on global structural effects rather than localised effects due to notches and fillets. Therefore structures exhibiting geometric stiffness discontinuities are considered to be "smooth" in the sense that the specific geometry of the transition between parts of different stiffnesses is disregarded. KW - plastic strain enhancement KW - design codes KW - Ke-factor KW - simplified method Y1 - 1995 SN - 92-826-9833-5 N1 - Nuclear Science and Technology, EUR 16555 EN PB - Publ. of the European Communities CY - Luxembourg ER - TY - CHAP A1 - Bieniussa, Klaus W. A1 - Reck, Hans A1 - Hübel, Hartwig T1 - Ermittlung realistischer Ke,r-Faktoren für vereinfachte elasto-plastische Analyse T2 - Sicherheit und Verfügbarkeit in der Anlagentechnik mit dem Schwerpunkt Maßnahmen zur Absicherung des Langzeitbetriebes von Kernkraftwerken, 21. MPA-Seminar, Stuttgart, 1995, Band 2 N2 - Es werden Ke,r-Faktoren als Dehnungserhöhungsfaktoren für vereinfachte elastisch-plastische Ermüdungsanalysen vorgeschlagen, die realistischer sind als in Regelwerken vorhandene Ke-Faktoren. Letztere dienen einer meistens konservativen Erfassung der auftretenden elasto-plastischen Dehnungen, sie sind aber weder physikalisch nachvollziehbar, noch werkstoffgerecht formuliert. Die bisher exemplarisch durchgeführten Verifikationsrechnungen belegen, dass die vorgeschlagenen realistischen Ke,r-Faktoren leicht bestimmbar sind und zudem ausreichend konservative Ergebnisse liefern. Somit liegt mit dieser neuen Methode ein beachtenswertes Potential vor, das jedoch noch durch weitere Verifikationsrechnungen abgesichert werden muss, bevor es in das KTA-Regelwerk eingebunden werden kann. KW - Ke-Faktor KW - KTA KW - vereinfachte Ermüdungsanalyse Y1 - 1995 SP - S. 49 PB - MPA CY - Stuttgart ER - TY - CHAP A1 - Hübel, Hartwig T1 - Numerical Examples to Compare Zarka’s Method with Evolutive Analyses T2 - ECCM-2001, 2nd European Conference on Computational Mechanics, Cracow, Poland, June 26 - 29, 200, proceedings N2 - Life assessment of a structure subject to cyclic loading rests on quantifying strain accumulated prior to shakedown and the strain range experienced after plastic shakedown has been achieved. Few methods exist to predict these quantities. Zarka's method is one of these methods. It is evaluated by analyzing several examples of structures and comparing the quality of the results obtained and the numerical effort required with evolutive analyses by using a commercial Finite Element program. KW - Zarka's method KW - life assessment KW - shakedown KW - evolutive analysis KW - strain range KW - strain accumulation Y1 - 2001 PB - Vesalius CY - Cracow ER - TY - RPRT A1 - Hübel, Hartwig T1 - Anwendung der Vereinfachten Fließzonentheorie auf der Grundlage der Zarka-Methode mit einem Finite-Elemente-Programm N2 - Die Vereinfachte Fließzonentheorie dient der Berechnung der elastisch-plastischen Beanspruchungen einer Struktur infolge monotoner oder zyklischer Belastung auf der Basis der Zarka-Methode. Sie wurde bereits in den Vorhaben SR 2221, SR 2226 und in früheren Unteraufträgen zum Vorhaben SR 2298 vorgestellt und ihre Leistungsfähigkeit durch umfangreiche Beispielrechnungen relativ einfacher Strukturen mittels Handrechnung belegt. Für realistische und somit kompliziertere Konfigurationen von Bauteilgeometrie und Belastung ist dagegen eine Implementierung der Vereinfachten Fließzonentheorie in ein Finite-Elemente-Programm erforderlich. Dies setzt eine Anpassung der Theorie an diskrete anstelle kontinuierlicher Systeme voraus. Das anzuwendende Finite-Elemente-Programm muß bestimmte Anforderungen erfüllen, um eine Implementierung zu gestatten. Anhand beispielhafter Anwendungen wird gezeigt, dass die Vereinfachte Fließzonentheorie auch auf Finite-Elemente-Modelle anwendbar ist. KW - Vereinfachte Fließzonentheorie KW - Finite Elemente KW - Zarka-Methode Y1 - 2000 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16066.pdf ER - TY - CHAP A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie mit ANSYS T2 - 1. Lausitzer FEM-Symposium, Cottbus, 12. November 1999 N2 - Es wird die Vereinfachte Fließzonentheorie als Weiterentwicklung der Zarka-Methode vorgestellt sowie ihre Implementierung in das FE-Programm ANSYS. Anwendungsbeispiele belegen die gute Ergebnisqualität bei gleichzeitig geringem Berechnungsaufwand für die Ermittlung der plastischen Dehnschwingbreite und der akkumulierten plastischen Verzerrungen bei zyklischer Belastung. KW - Vereinfachte Fließzonentheorie KW - akkumulierte Verzerrungen KW - Dehnschwingbreite KW - zyklische Belastung Y1 - 1999 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16067.pdf ER - TY - CHAP A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie für Ermüdungs- und Ratcheting-Nachweise T2 - 25. MPA-Seminar, Stuttgart, 7. und 8. Oktober 1999 N2 - Die Vereinfachte Fließzonentheorie gestattet bei zyklischer Belastung die näherungsweise Ermittlung der elastisch-plastischen Dehnungsschwingbreite und der durch einen Ratcheting-Mechanismus akkumulierten Verzerrungen sowie aller daraus ableitbaren Größen wie etwa Verformungen im elastischen und plastischen Einspielzustand. Sie beruht auf der Zarka-Methode. Im Gegensatz zu den in den technischen Regelwerken der Anlagentechnik zugelassenen vereinfachten Berechnungsmethoden (wie etwa die Anwendung des Faktors Ke) kann sie neben der Werkstoffverfestigung auch den Einfluß der individuellen Konfiguration von Bauteilgeometrie und Belastungsart auf das plastische Verhalten der Struktur erfassen. Sie ist gleichermaßen geeignet, globale Struktureffekte, lokale Kerbeffekte und Einflüsse aus der unterschiedlichen Querdehnungszahl im Elastischen und im Plastischen zu berücksichtigen. Als Berechnungsaufwand fallen lediglich einige modifizierte linear elastische Analysen sowie „lokale“ Berechnungen an. Eine Reihe von Beispielen zeigt, daß sowohl die Dehnungsschwingbreite als auch die akkumulierten Verzerrungen mit geringem Berechnungsaufwand in guter Näherung abgeschätzt werden können. KW - Vereinfachte Fließzonentheorie KW - shakedown KW - Lebensdaueranalyse Y1 - 1999 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16068.pdf ER - TY - CHAP A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie mit ANSYS T2 - 17. CAD-FEM Users' Meeting, 8. Oktober 1999 in Sonthofen (Allgäu) N2 - Die Vereinfachte Fließzonentheorie beruht auf der Zarka-Methode und gestattet die näherungsweise Ermittlung der elastisch-plastischen Verzerrungen, Spannungen und Verformungen bei monotoner oder zyklischer Belastung. Bei zyklischer Belastung wird sofort der Einspielzustand berechnet, ohne das Belastungshistogramm Zyklus für Zyklus inkrementell durchrechnen zu müssen. Als Berechnungsaufwand fallen lediglich einige modifizierte linear elastische Analysen sowie „lokale“ Berechnungen an, so daß gegenüber den herkömmlichen inkrementellen Berechnungen nach der exakten Fließzonentheorie ein erheblicher Gewinn an Rechenzeit möglich ist. Bei einigen Beispielrechnungen wurde nur etwa 1/10.000 der Rechenzeit benötigt, um sowohl die Dehnungsschwingbreite (zur Ermittlung der Ermüdungsausnutzung) als auch die akkumulierten Verzerrungen (für einen Ratcheting-Nachweis) in guter Näherung abschätzen zu können. Die Vereinfachte Fließzonentheorie wurde mittels einer user-subroutine und einigen Makros in ANSYS implementiert. Es werden die Grundlagen der Vereinfachten Fließzonentheorie dargestellt, ihre Implementierung in ANSYS und einige Beispielrechnungen. KW - Vereinfachte Fließzonentheorie KW - Zarka-Methode KW - ANSYS Y1 - 1999 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16069.pdf ER - TY - RPRT A1 - Stange, Maren A1 - Hübel, Hartwig T1 - Verifikation der Vereinfachten Fließzonentheorie – bei Anwendung der Finite Elemente Methode (subroutine für ANSYS) KW - Vereinfachte Fließzonentheorie KW - ANSYS Y1 - 1999 PB - FH Lausitz CY - Cottbus ER - TY - RPRT A1 - Hübel, Hartwig T1 - Vereinfachte Fließzonentheorie zur Berechnung von Ermüdung und Ratcheting N2 - Es wird der Stand der Entwicklung der Vereinfachten Fließzonentheorie dargestellt, und wie die VFZT konform mit dem KTA-Regelwerk angewendet bzw. weiter ausgebaut werden könnte. Dies betrifft die Ermittlung des Faktors Ke für vereinfachte Ermüdungsanalysen sowie die Ratcheting-Nachweisführung, um erstmals bestehende Lücken im Regelwerk schließen zu können, weil die VFZT unabhängig ist von der speziellen Bauteilgeometrie und der Belastungsart. KW - Vereinfachte Fließzonentheorie KW - Ermüdung KW - Ratcheting KW - KTA Y1 - 1999 UR - https://www-docs.b-tu.de/fg-baustatik-fem/public/ubico/Huebel_Hartwig_16072.pdf ER - TY - GEN A1 - Hübel, Hartwig T1 - Erhöhungsfaktor Ke zur Ermittlung plastischer Dehnungen aus elastischer Berechnung T2 - Technische Überwachung N2 - Im Zuge einer Ermüdungsanalyse plastisch beanspruchter Komponenten von Kernkraftwerken werden Dehnungserhöhungsfaktoren Ke zur Ermittlung der plastischen Dehnschwingbreite aus elastisch berechneten Beanspruchungen verwendet. Ausgehend von einer Kritik an der derzeit üblichen Vorgehensweise nach ASME Code wird eine Modifikation vorgeschlagen. Der Vorschlag basiert wie der Ke-Faktor des ASME Code (der auch von diversen KTA-Regeln übernommen worden ist) auf dem Konzept eines einfachen Faktors. Er beseitigt die potentielle Unkonservativität des ASME Code bei Kerben (Rundungsradien) und reduziert gleichzeitig dessen Überkonservativität in vielen anderen Anwendungsbereichen, indem drei unterschiedliche Effekte berücksichtigt und individuelles Werkstoffverhalten erfasst werden können. Zudem beruht er im Gegensatz zu Ke-ASME auf möglichst realitätsnahen Werkstoffdaten, die eher den Charakter von Mittel- als von Mindestwerten besitzen. Ferner ist die Anwendung dieses Vorschlages insofern einfacher als die des ASME Code, als die Suche nach der ungünstigsten Orientierung eines Schnittes durch die Wand, die i. allg. nicht einfach zu identifizieren ist, entfällt. Eine Reihe detaillierter elastisch-plastischer Vergleichsrechnungen für hinsichtlich Bauteilgeometrie und Belastung typische Problemstellungen bei schnellen und Leichtwasserreaktoren bestätigen die Konservativität des Vorschlages. Es wird ein Potential zur weiteren Reduzierung der Konservativität bei Anwendung auf Bauteile von Leichtwasserreaktoren im Rahmen eventueller zukünftiger Entwicklungsarbeiten aufgezeigt. KW - Ke-Faktor KW - vereinfachte Ermüdungsanalyse KW - Dehnungserhöhung KW - KTA Y1 - 1994 SN - 1434-9728 VL - 35 IS - 6 SP - 268 EP - 278 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 - 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 - 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 - 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 - 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 - 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 - Vollrath, Bastian A1 - Hübel, Hartwig T1 - Efficient Fatigue and Ratcheting Computation in Case of Multi-Parameter Loading T2 - ASME 2020 Pressure Vessels & Piping Conference : August 3, 2020 Virtual, Online N2 - Cyclic and over-elastic loading can lead to an accumulation of plastic strains. If there is a cyclic load, which is driven by a single parameter, the lifecycle design can be very costly in terms of computational effort. If more than one cyclic load parameter is to be taken into account, which is then a multi-parameter loading, this task can become even more complex and costly. To solve this problem efficiently, different techniques are proposed. One of these techniques is based on step-by-step calculations of the strain ranges for a reduced set of loadings. Once these strain ranges are known, the accumulated state for each individual load case can be estimated using the Simplified Theory of Plastic Zones (STPZ), which requires just a few linear elastic analyses. It is shown that cyclic loads, which occur in intervals, can be replaced by interval-free calculations, which reduce the computational effort enormously. All these techniques lead to a procedure, which delivers good estimations in terms of post-shakedown quantities with very low computational effort compared to incremental step-by-step calculations. The results of the STPZ are presented by an example. A thick-walled cylinder is loaded with a constant axial force and subjected to cyclic shear and cyclic internal pressure. In general, for structures exhibiting ratcheting, hundreds or more load cycles must be analysed via step-by-step calculations until the shakedown state is reached. Using the STPZ, post-shakedown quantities, including strain ranges and accumulated strains can be estimated efficiently and the structure can be designed according to the rules of the ASME Codes. The computational effort and the quality of the results of the STPZ are compared with a step-by-step calculation. KW - multi-parameter loading KW - fatigue KW - ratcheting KW - STPZ KW - direct shakedown analysis Y1 - 2020 UR - https://asmedigitalcollection.asme.org/PVP/proceedings-abstract/PVP2020/83815/V001T01A027/1089226 SN - 978-0-7918-8381-5 U6 - https://doi.org/10.1115/PVP2020-21089 ER - TY - GEN A1 - Hübel, Hartwig T1 - Plastic Limit Analysis Using the Simplified Theory of Plastic Zones T2 - Journal of pressure vessel technology N2 - The simplified theory of plastic zones (STPZ) was mainly developed to determine strain ranges and accumulated strains in the state of shakedown at cyclic loading between prescribed levels of loading. Kinematic hardening is an indispensable feature of the STPZ. The plastic limit load, however, is defined for monotonic loading and elastic–plastic material behavior without hardening. Simply assigning a zero value or a numerically very low value of the tangent modulus when applying the STPZ is generally not possible due to arising numerical instabilities. It is, therefore, not immediately obvious how the STPZ can be used to determine the maximum load level that can be applied to a structure without developing a kinematic mechanism. This paper describes the theory and the analysis steps required and provides some illustrative examples. Typically, between one and three linear elastic analyses and some local calculations are required to provide either the exact value or at least a reasonable estimate of a range of the plastic limit load, as well as of the associated stress and strain fields and displacements that are not provided by classical limit analysis. KW - limit load KW - simplified theory of plastic zones Y1 - 2021 U6 - https://doi.org/10.1115/1.4049643 SN - 1528-8978 VL - 143 IS - 2 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Effect of stress stiffness on elastic-plastic strain range T2 - International Journal of Pressure Vessels and Piping N2 - Many pressure vessel and piping components have to withstand high internal pressures and are therefore thick-walled so that geometric effects such as stress stiffening need not be accounted for. However, thin-walled or moderately thick structures may be sensitive to these effects. Design Codes such as the ASME Boiler and Pressure Vessel Code usually provide little guidance on when they are to be accounted for. In the opinion of the authors, this effect deserves more attention. Therefore, the purpose of this paper is to illuminate the effect of stress stiffening by investigating some examples, with particular attention to elastic-plastic strain ranges and the plastic strain range enhancement factor Ke used for fatigue analyses. KW - Ke KW - Elbow KW - Strain range KW - Stress stiffening KW - Plasticity KW - Twice Yield Y1 - 2021 UR - https://www.sciencedirect.com/science/article/pii/S0308016121001174?via%3Dihub U6 - https://doi.org/10.1016/j.ijpvp.2021.104421 SN - 0308-0161 VL - 192 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 - GEN A1 - Vollrath, Bastian A1 - Hübel, Hartwig T1 - Direct Analysis of Elastic-Plastic Strain Ranges and Accumulated Strains Considering Stress Stiffening T2 - ASME 2022 Pressure Vessels & Piping Conference N2 - Many pressure vessel and piping components have to withstand high internal pressures and are therefore thick-walled so that geometric effects such as stress stiffening need not be accounted for. However, thin-walled, or moderately thick structures may be sensitive to these effects. Design Codes such as the ASME Boiler and Pressure Vessel Code usually provide little guidance on when they are to be accounted for. In general, the effects of stress stiffening are difficult to estimate even for experienced engineers and can only be estimated by detailed finite element analyses. In the opinion of the authors, this effect deserves more attention. This is particularly true for simplified elastic-plastic methods for fatigue and ratcheting assessment of structures subjected to cyclic loading. 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 accumulated strains, strain ranges and other quantities in the state of shakedown (post-shakedown quantities) by means of incremental analyses is costly, in particular if geometric effects such as stress stiffening play a role. Direct methods aim at providing estimates of the post-shakedown quantities, bypassing cycle-by-cycle analyses. These methods claim to deliver the post-shakedown quantities with high accuracy and low computational effort. The Simplified Theory of Plastic Zones can account for the combination of plasticity and stress stiffening. The theory is described and illustrated by examples. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the post-shakedown 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. In this paper, the results of elbows subjected to various loading parameters are compared, considering and neglecting stress stiffening. Thus, the results show the influence 2nd order effects can generate. It is further shown that the STPZ can 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, e.g. for a pipe bend subjected to cyclic in-plane bending. KW - STPZ KW - direct methods KW - ratcheting KW - stress stiffening Y1 - 2022 UR - https://asmedigitalcollection.asme.org/PVP/proceedings-abstract/PVP2022/86144/V001T01A020/1149647 SN - 978-0-7918-8614-4 U6 - https://doi.org/10.1115/PVP2022-84241 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 -