@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} } @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} } @book{MaierComiCoriglianoetal., author = {Maier, Giulio and Comi, Claudia and Corigliano, Alberto and Perego, Umberto and H{\"u}bel, Hartwig}, title = {Bounds and Estimates on Inelastic Deformations}, publisher = {Commission of the European Communities}, address = {Luxembourg}, isbn = {92-827-5006-X}, pages = {286}, abstract = {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 Ladev{\`e}ze 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.}, language = {en} } @inproceedings{KretzschmarHuebel, author = {Kretzschmar, Andreas and H{\"u}bel, Hartwig}, title = {Fortschritte bei der Vereinfachten Fließzonentheorie}, series = {5. Lausitzer FEM-Symposium, Cottbus, 2003}, booktitle = {5. Lausitzer FEM-Symposium, Cottbus, 2003}, abstract = {Die im Rahmen eines aFuE-Vorhabens gewonnenen Erkenntnisse und die daraus abgeleiteten Weiterentwicklungen der Vereinfachten Fließzonentheorie werden vorgestellt und durch Beispiele illustriert.}, language = {de} } @inproceedings{KretzschmarHuebel, author = {Kretzschmar, Andreas and H{\"u}bel, Hartwig}, title = {Implementierung der Vereinfachten Fließzonentheorie in ANSYS}, series = {Conference Proceedings of 20. CAD-FEM Users' Meeting 2002}, booktitle = {Conference Proceedings of 20. CAD-FEM Users' Meeting 2002}, publisher = {CAD-FEM}, address = {Grafing bei M{\"u}nchen}, pages = {1 -- 10}, language = {de} } @book{HuebelZeibig, author = {H{\"u}bel, Hartwig and Zeibig, H.}, title = {State-of-the-Art of Simplified Methods to Account for Elastic Follow-up in Creep}, publisher = {Commission of the European Communities}, address = {Luxembourg}, isbn = {92-827-5009-4}, pages = {103}, abstract = {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).}, language = {en} } @misc{HuebelWilluweitRudolphetal., author = {H{\"u}bel, Hartwig and Willuweit, Adrian and Rudolph, J{\"u}rgen and Ziegler, Rainer and Lang, Hermann and Rother, Klemens and Deller, Simon}, title = {Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check}, series = {International Journal of Pressure Vessels and Piping}, journal = {International Journal of Pressure Vessels and Piping}, number = {116}, issn = {0308-0161}, doi = {doi:10.1016/j.ijpvp.2014.01.003}, pages = {10 -- 19}, abstract = {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.}, language = {en} } @inproceedings{HuebelWilluweitRudolphetal., author = {H{\"u}bel, Hartwig and Willuweit, Adrian and Rudolph, J{\"u}rgen and Ziegler, Rainer and Lang, Hermann and Rother, Klemens and Deller, Simon}, title = {Performance study of the simplified theory of plastic zones and the Twice Yield method for the fatigue check}, series = {Proceedings of ANSYS Conference \& 31th CADFEM Users' Meeting, Mannheim, 2013}, booktitle = {Proceedings of ANSYS Conference \& 31th CADFEM Users' Meeting, Mannheim, 2013}, abstract = {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.}, language = {en} } @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} }