@techreport{Huebel, author = {H{\"u}bel, Hartwig}, title = {Anwendung der Vereinfachten Fließzonentheorie auf der Grundlage der Zarka-Methode mit einem Finite-Elemente-Programm}, pages = {38}, abstract = {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 fr{\"u}heren Unterauftr{\"a}gen zum Vorhaben SR 2298 vorgestellt und ihre Leistungsf{\"a}higkeit durch umfangreiche Beispielrechnungen relativ einfacher Strukturen mittels Handrechnung belegt. F{\"u}r 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 erf{\"u}llen, um eine Implementierung zu gestatten. Anhand beispielhafter Anwendungen wird gezeigt, dass die Vereinfachte Fließzonentheorie auch auf Finite-Elemente-Modelle anwendbar ist.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie mit ANSYS}, series = {1. Lausitzer FEM-Symposium, Cottbus, 12. November 1999}, booktitle = {1. Lausitzer FEM-Symposium, Cottbus, 12. November 1999}, pages = {10}, abstract = {Es wird die Vereinfachte Fließzonentheorie als Weiterentwicklung der Zarka-Methode vorgestellt sowie ihre Implementierung in das FE-Programm ANSYS. Anwendungsbeispiele belegen die gute Ergebnisqualit{\"a}t bei gleichzeitig geringem Berechnungsaufwand f{\"u}r die Ermittlung der plastischen Dehnschwingbreite und der akkumulierten plastischen Verzerrungen bei zyklischer Belastung.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie f{\"u}r Erm{\"u}dungs- und Ratcheting-Nachweise}, series = {25. MPA-Seminar, Stuttgart, 7. und 8. Oktober 1999}, booktitle = {25. MPA-Seminar, Stuttgart, 7. und 8. Oktober 1999}, pages = {20}, abstract = {Die Vereinfachte Fließzonentheorie gestattet bei zyklischer Belastung die n{\"a}herungsweise Ermittlung der elastisch-plastischen Dehnungsschwingbreite und der durch einen Ratcheting-Mechanismus akkumulierten Verzerrungen sowie aller daraus ableitbaren Gr{\"o}ßen 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 Einfl{\"u}sse aus der unterschiedlichen Querdehnungszahl im Elastischen und im Plastischen zu ber{\"u}cksichtigen. 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 N{\"a}herung abgesch{\"a}tzt werden k{\"o}nnen.}, language = {de} } @inproceedings{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie mit ANSYS}, series = {17. CAD-FEM Users' Meeting, 8. Oktober 1999 in Sonthofen (Allg{\"a}u)}, booktitle = {17. CAD-FEM Users' Meeting, 8. Oktober 1999 in Sonthofen (Allg{\"a}u)}, pages = {10}, abstract = {Die Vereinfachte Fließzonentheorie beruht auf der Zarka-Methode und gestattet die n{\"a}herungsweise 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 f{\"u}r Zyklus inkrementell durchrechnen zu m{\"u}ssen. Als Berechnungsaufwand fallen lediglich einige modifizierte linear elastische Analysen sowie „lokale" Berechnungen an, so daß gegen{\"u}ber den herk{\"o}mmlichen inkrementellen Berechnungen nach der exakten Fließzonentheorie ein erheblicher Gewinn an Rechenzeit m{\"o}glich ist. Bei einigen Beispielrechnungen wurde nur etwa 1/10.000 der Rechenzeit ben{\"o}tigt, um sowohl die Dehnungsschwingbreite (zur Ermittlung der Erm{\"u}dungsausnutzung) als auch die akkumulierten Verzerrungen (f{\"u}r einen Ratcheting-Nachweis) in guter N{\"a}herung absch{\"a}tzen zu k{\"o}nnen. 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.}, language = {de} } @techreport{StangeHuebel, author = {Stange, Maren and H{\"u}bel, Hartwig}, title = {Verifikation der Vereinfachten Fließzonentheorie - bei Anwendung der Finite Elemente Methode (subroutine f{\"u}r ANSYS)}, publisher = {FH Lausitz}, address = {Cottbus}, pages = {5, 34, 42}, language = {de} } @techreport{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie zur Berechnung von Erm{\"u}dung und Ratcheting}, abstract = {Es wird der Stand der Entwicklung der Vereinfachten Fließzonentheorie dargestellt, und wie die VFZT konform mit dem KTA-Regelwerk angewendet bzw. weiter ausgebaut werden k{\"o}nnte. Dies betrifft die Ermittlung des Faktors Ke f{\"u}r vereinfachte Erm{\"u}dungsanalysen sowie die Ratcheting-Nachweisf{\"u}hrung, um erstmals bestehende L{\"u}cken im Regelwerk schließen zu k{\"o}nnen, weil die VFZT unabh{\"a}ngig ist von der speziellen Bauteilgeometrie und der Belastungsart.}, language = {de} } @misc{Huebel, author = {H{\"u}bel, Hartwig}, title = {Erh{\"o}hungsfaktor Ke zur Ermittlung plastischer Dehnungen aus elastischer Berechnung}, series = {Technische {\"U}berwachung}, volume = {35}, journal = {Technische {\"U}berwachung}, number = {6}, issn = {1434-9728}, pages = {268 -- 278}, abstract = {Im Zuge einer Erm{\"u}dungsanalyse plastisch beanspruchter Komponenten von Kernkraftwerken werden Dehnungserh{\"o}hungsfaktoren Ke zur Ermittlung der plastischen Dehnschwingbreite aus elastisch berechneten Beanspruchungen verwendet. Ausgehend von einer Kritik an der derzeit {\"u}blichen Vorgehensweise nach ASME Code wird eine Modifikation vorgeschlagen. Der Vorschlag basiert wie der Ke-Faktor des ASME Code (der auch von diversen KTA-Regeln {\"u}bernommen worden ist) auf dem Konzept eines einfachen Faktors. Er beseitigt die potentielle Unkonservativit{\"a}t des ASME Code bei Kerben (Rundungsradien) und reduziert gleichzeitig dessen {\"U}berkonservativit{\"a}t in vielen anderen Anwendungsbereichen, indem drei unterschiedliche Effekte ber{\"u}cksichtigt und individuelles Werkstoffverhalten erfasst werden k{\"o}nnen. Zudem beruht er im Gegensatz zu Ke-ASME auf m{\"o}glichst realit{\"a}tsnahen 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 ung{\"u}nstigsten Orientierung eines Schnittes durch die Wand, die i. allg. nicht einfach zu identifizieren ist, entf{\"a}llt. Eine Reihe detaillierter elastisch-plastischer Vergleichsrechnungen f{\"u}r hinsichtlich Bauteilgeometrie und Belastung typische Problemstellungen bei schnellen und Leichtwasserreaktoren best{\"a}tigen die Konservativit{\"a}t des Vorschlages. Es wird ein Potential zur weiteren Reduzierung der Konservativit{\"a}t bei Anwendung auf Bauteile von Leichtwasserreaktoren im Rahmen eventueller zuk{\"u}nftiger Entwicklungsarbeiten aufgezeigt.}, language = {de} } @inproceedings{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Das Ph{\"a}nomen Ratcheting - Auswirkung plastischen Materialverhaltens bei ortsver{\"a}nderlicher Belastung}, series = {Baustatik - Baupraxis 13, 20.-21. M{\"a}rz 2017, Bochum}, booktitle = {Baustatik - Baupraxis 13, 20.-21. M{\"a}rz 2017, Bochum}, editor = {Meschke, G{\"u}nther and Freitag, Steffen and Birk, Carolin and Menkenhagen, Jochen and Ricken, Tim}, publisher = {Ruhr-Universit{\"a}t Bochum}, address = {Bochum}, isbn = {978-3-00-055827-6}, pages = {189 -- 196}, abstract = {Bei Belastungs{\"a}nderungen kann eine progressive Deformation (Ratcheting) auftreten, sobald plastische Beanspruchungen im Tragwerk existieren. Dann akkumulieren sich Dehnungen und Verformungen im Falle zyklischer Belastung in jedem Belastungszyklus. Dieser Vorgang begrenzt die Lebensdauer eines Tragwerks, ist aber unabh{\"a}ngig von einer eventuell ebenfalls auftretenden Erm{\"u}dungssch{\"a}digung als eigenst{\"a}ndige m{\"o}gliche Schadensursache zu betrachten. Bekannt als Ausl{\"o}ser von Ratcheting und in manchen Regelwerken bereits ber{\"u}cksichtigt sind Konfigurationen, bei denen ein Tragwerk mindestens zwei unterschiedlichen Belastungsarten unterworfen ist, n{\"a}mlich einer konstanten Belastung (der Prim{\"a}rlast) und einer {\"u}berlagerten zyklischen Belastung. Selbst wenn letztere klein ist und f{\"u}r sich alleine keine plastischen Deformationen hervorruft, kann sie durch Zusammenwirkung mit der Prim{\"a}rlast dennoch eine progressive Deformation in Gang setzen. In der vorliegenden Arbeit wird ein weiterer, Ratcheting erzeugender Mechanismus vorgestellt, der allein auf ortsver{\"a}nderliche Wirkung einer einzelnen Lastgr{\"o}ße zur{\"u}ck zu f{\"u}hren ist. Im einfachsten Fall l{\"a}sst sich dieser erkl{\"a}ren durch die sukzessive Aktivierung von (gegebenenfalls unendlich vielen existierenden) Fließgelenken. Die Inkremente der Dehnungen und Verformungen k{\"o}nnen von Zyklus zu Zyklus ab- oder zunehmen, wenn die Verfestigung des Werkstoffs ber{\"u}cksichtigt wird, elastische Bettung vorliegt, die Formulierung des Gleichgewichts am verformten System erfolgt (Theorie II. Ordnung) oder die wahre Verformungsgeometrie (Theorie III. Ordnung) ber{\"u}cksichtigt wird.}, language = {de} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Ratcheting caused by moving loads}, series = {International Journal of Advanced Structural Engineering}, volume = {9}, journal = {International Journal of Advanced Structural Engineering}, number = {2}, issn = {2008-6695}, pages = {139 -- 152}, abstract = {Progressive deformation (ratcheting) can occur as a response to variable loads as soon as the elastic limit is exceeded. If this is the case, strains and displacements accumulate in the event of cyclic loading in each load cycle. Widely known as triggers for ratcheting and already being considered in some design codes are configurations, in which a structure is subjected to at least two different types of load, namely a constant load (the primary load) and a superimposed cyclic load. In this paper, another mechanism that generates ratcheting is introduced. It can be attributed solely to the effect of a single load. In the simplest case, this can be explained by the successive activation of (an infinite number of) plastic hinges if a load of constant magnitude is moved in space. The increments of strains and displacements can decrease or increase from cycle to cycle, when the material is hardening, or if elastic foundation is present, or if the equilibrium condition is formulated for the deformed system (second-order theory) or if "large" rotations are taken into account (third-order theory).}, language = {en} } @inproceedings{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Determination of post-shakedown quantities of a pipe bend via the Simplified Theory of Plastic Zones compared with load history dependent incremental analysis}, series = {22nd International Conference on Computer Methods in Mechanics, CMM2017}, booktitle = {22nd International Conference on Computer Methods in Mechanics, CMM2017}, editor = {Burczynski, Tadeusz}, address = {Lublin}, isbn = {978-83-7947-264-2}, pages = {MS11-1 -- MS11-2}, abstract = {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.}, language = {en} } @inproceedings{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Determination of post-shakedown quantities of a pipe bend via the simplified theory of plastic zones compared with load history dependent incremental analysis}, series = {Computer methods in mechanics (CMM2017), proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017}, booktitle = {Computer methods in mechanics (CMM2017), proceedings of the 22nd International Conference on Computer Methods in Mechanics, Lublin, Poland, 13-16 September 2017}, editor = {Podg{\´o}rski, Jerzy and Borowa, Ewa-Błazik and Be̜c, Jarosław}, publisher = {AIP Publishing}, address = {Melville, New York}, isbn = {978-0-7354-1614-7}, doi = {10.1063/1.5019119}, abstract = {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.}, language = {en} } @inproceedings{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified Analysis of Strains Accumulated in the State of Elastic Shakedown Considering Multi-Parameter Loadings}, series = {ASME 2018 Pressure Vessels and Piping Conference, Volume 3B: Design and Analysis, Prague, Czech Republic, July 15-20, 2018}, booktitle = {ASME 2018 Pressure Vessels and Piping Conference, Volume 3B: Design and Analysis, Prague, Czech Republic, July 15-20, 2018}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5163-0}, doi = {10.1115/PVP2018-84070}, pages = {10}, abstract = {In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. 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.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified determination of accumulated strains to satisfy design code requirements}, series = {International Journal of Pressure Vessels and Piping}, volume = {171}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2019.01.014}, pages = {92 -- 103}, abstract = {In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. In addition, the strain range is required for performing fatigue analyses in case of plastic shakedown. However, little guidance is usually provided by Design Codes on how the accumulated strains and strain ranges are to be calculated, and some of the guidelines implemented in Design Codes are not well founded and may therefore be misleading. This is, for example, true for the ASME B\&PV Code, Section III. Of course, strains and strain ranges can be determined by means of incremental elastic-plastic analyses, which require to go step-by-step through many cycles of a given load histogram until the state of shakedown is reached. This is rather costly in terms of engineering time and numerical effort. As an alternative, simplified methods can be adopted, e.g. the Simplified Theory of Plastic Zones (STPZ) as used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and illustrated by some examples. It is shown that the Simplified Theory of Plastic Zones is well suited to provide reasonable estimates of strains accumulated in the state of elastic and plastic shakedown at the cost of few linear elastic analyses.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms}, series = {Journal of Pressure Vessel Technology}, volume = {141}, journal = {Journal of Pressure Vessel Technology}, number = {3}, doi = {10.1115/1.4042853}, pages = {031206-1 -- 031206-10}, abstract = {After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic-plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed.}, language = {en} } @misc{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Efficient Fatigue and Ratcheting Computation in Case of Multi-Parameter Loading}, series = {ASME 2020 Pressure Vessels \& Piping Conference : August 3, 2020 Virtual, Online}, journal = {ASME 2020 Pressure Vessels \& Piping Conference : August 3, 2020 Virtual, Online}, isbn = {978-0-7918-8381-5}, doi = {10.1115/PVP2020-21089}, pages = {7}, abstract = {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.}, language = {en} } @misc{Huebel, author = {H{\"u}bel, Hartwig}, title = {Plastic Limit Analysis Using the Simplified Theory of Plastic Zones}, series = {Journal of pressure vessel technology}, volume = {143}, journal = {Journal of pressure vessel technology}, number = {2}, issn = {1528-8978}, doi = {10.1115/1.4049643}, pages = {12}, abstract = {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.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Effect of stress stiffness on elastic-plastic strain range}, series = {International Journal of Pressure Vessels and Piping}, volume = {192}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2021.104421}, abstract = {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.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified Theory of Plastic Zones in the state of elastic shakedown with stress stiffening}, series = {European Journal of Mechanics - A/Solids}, volume = {95}, journal = {European Journal of Mechanics - A/Solids}, issn = {0997-7538}, doi = {10.1016/j.euromechsol.2022.104613}, pages = {15}, abstract = {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.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Ratcheting and strain ranges in the shakedown state with stress stiffening using the Simplified Theory of Plastic Zones}, series = {International Journal of Pressure Vessels and Piping}, volume = {199}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2022.104727}, pages = {1 -- 11}, abstract = {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.}, language = {en} } @misc{VollrathHuebel, author = {Vollrath, Bastian and H{\"u}bel, Hartwig}, title = {Direct Analysis of Elastic-Plastic Strain Ranges and Accumulated Strains Considering Stress Stiffening}, series = {ASME 2022 Pressure Vessels \& Piping Conference}, journal = {ASME 2022 Pressure Vessels \& Piping Conference}, isbn = {978-0-7918-8614-4}, doi = {10.1115/PVP2022-84241}, abstract = {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.}, language = {en} } @book{Huebel, author = {H{\"u}bel, Hartwig}, title = {Vereinfachte Fließzonentheorie : auf Grundlage der Zarka-Methode}, edition = {2., {\"u}berarbeitete Auflage}, publisher = {Springer Vieweg}, address = {Wiesbaden}, isbn = {978-3-658-41832-8}, doi = {10.1007/978-3-658-41833-5}, pages = {XXI, 409}, abstract = {F{\"u}r eine Lebensdauervorhersage ver{\"a}nderlich belasteter Tragwerke, etwa des Anlagen- und Maschinenbaus sowie des Bauingenieurwesens, werden die zyklisch akkumulierten Verzerrungen und ggf. auch die elastisch-plastischen Dehnschwingbreiten ben{\"o}tigt. Die Vereinfachte Fließzonentheorie (VFZT) ist eine direkte Methode, die Absch{\"a}tzungen dieser und aller anderen mechanischen Gr{\"o}ßen im elastischen und im plastischen Einspielzustand liefert. Das vorliegende Buch stellt die VFZT ausf{\"u}hrlich dar und legt Wert darauf, dass sich nicht nur Wissenschaftler, sondern auch in der Praxis t{\"a}tige Ingenieure sowie Studierende h{\"o}herer Semester ein Bild von den M{\"o}glichkeiten und Grenzen machen k{\"o}nnen. Zahlreiche Abbildungen und Anwendungsbeispiele unterst{\"u}tzen das Verst{\"a}ndnis.}, language = {de} }