Anmelden

Open Access

  • Startseite
  • Suchen
  • Browsen
  • Veröffentlichen
  • Hilfe

Filtern

Autor

  • Zerbst, Uwe (82) (entfernen)

Erscheinungsjahr

  • 2019 (1)
  • 2018 (13)
  • 2017 (13)
  • 2016 (10)
  • 2015 (20)
  • 2014 (13)
  • 2013 (12)

Dokumenttyp

  • Vortrag (31)
  • Zeitschriftenartikel (29)
  • Beitrag zu einem Tagungsband (19)
  • Monografie (1)
  • Buchkapitel (1)
  • Forschungsbericht (1)

Sprache

  • Englisch (43)
  • Deutsch (39)

Referierte Publikation

  • nein (50)
  • ja (32)

Schlagworte

  • Fracture mechanics (16)
  • Fatigue strength (15)
  • Bruchmechanik (12)
  • Schwingfestigkeit (12)
  • Weldments (10)
  • Schadenstoleranz (6)
  • Short crack propagation (6)
  • Short cracks (6)
  • Fatigue crack propagation (5)
  • IBESS (5)
+ weitere

Organisationseinheit der BAM

  • 9.1 Betriebsfestigkeit und Bauteilsicherheit (82) (entfernen)

82 Treffer

  • 1 bis 50
  • CSV
  • RIS
  • 10
  • 20
  • 50
  • 100

Sortieren nach

  • Jahr
  • Jahr
  • Titel
  • Titel
  • Autor
  • Autor
Foreword (2018)
Zerbst, Uwe
The subject of this Special Issue is the fracture mechanics-based determination of the fatigue strength of weldments. Except for one, all papers were written in closer or wider relation to a methodology developed within the framework of the German Project cluster IBESS. Some of them provide background or supplementary information needed in that context but which is also relevant in a wider frame of research activities. The acronym IBESS stands for the topic of this Special Issue (in German: „Integrale Methode zu Bruchmechanischen Ermittlung der Schwingfestigkeit von Schweißverbindungen). Eight partners were involved. The cluster was cooperatively founded by the German Research Foundation (Deutsche Forschungsgemeinschaft) and by the German AiF Network (Arbeitsgemeinschaft industrieller Forschungsvereinigungen) for industrial research.
Schadensentwicklung und Schadenstoleranz von SLM-gefertigten Strukturen (2017)
Zerbst, Uwe ; Hilgenberg, Kai
Unterschiedliche Werkstoffeigenschaften reagieren auf jeweils spezifische Weise auf Gittertyp, Gefüge und Defekte. Für die schadenstolerante Betrachtung von Werkstoff und Bauteil ist das Verständnis dieser Zusammenhänge essentiell. Der Beitrag gibt mit Hinblick auf additiv gefertigte metallische Bauteile mittels Selective Laser Melting einen kurzen, keineswegs vollständigen Überblick über Faktoren, die die Steifigkeit, Festigkeit, Duktilität, Zähigkeit, Ermüdungsrissausbreitung und Schwingfestigkeit beeinflussen. Es wird aufgezeigt, wie die bruchmechanische Betrachtung zur Quantifizierung der Zusammenhänge beitragen kann.
Damage development and damage tolerance of structures manufactured by selective laser melting - a review (2017)
Zerbst, Uwe ; Hilgenberg, Kai
The additive manufacturing technology of Selective Laser Melting (SLM) experiences a rapid development within an increasing marked of quite different application fields. The properties of SLM materials and structures are influenced by a number of tech-nological parameters such as the metal powder (particle size, homogeneity, cleanliness), the laser tool (power, beam diameter, pulse lengths), the scanning operation (speed, sequence and orientation of melting paths), parameters of the over-all equipment (design and preheating of the base plate, currents and turbulence in the protective gas atmosphere) and, last not least, the hatching strategy including the build-up direction of the structure with respect to the loading direction of the component. For the perspective use of SLM structures as load carrying, safety-relevant components the knowledge of their mechanical properties is necessary. It is essential to understand these in the context of the manufacturing-related features and at the back-ground of the basic characteristics of metallic materials: crystal lattice, microstructure and material defects. The paper provides an overview on factors which affect the mechanical parameters stiffness, strength, ductility, toughness, fatigue crack propagation and fatigue strength in the context of selective laser melting.
Referenzlastlösungen für die Ermittlung der elastisch-plastischen Rissspritzenbeanspruchung in Platten-Strukturen unter Zug-, Biege-, kombinierter Zug-Biege- und zweiaxialer Zugbelastung (2014)
Zerbst, Uwe
Schwingfestigkeit und Bruchmechanik (2017)
Zerbst, Uwe
Um bruchmechanisch Schwingfestigkeiten ermitteln zu können, sind einige Voraussetzungen erforderlich: (a) Das Wachstum sowohl langer als auch mechanisch und physikalisch kurzer Risse muss adäquat beschrieben werden. Das erfordert die Anwendung elastisch plastischer Konzepte zur Beschreibung der zyklischen Rissspitzenbeanspruchung sowie die Modellierung des graduellen Aufbaus der Rissschließeffekte im Kurzrissbereich. (b) Es müssen physikalisch sinnvolle Ausgangsrissgrößen für die bruchmechanische Analyse bestimmt werden. (c) Bei Spannungen oberhalb der Dauerfestigkeit respektive der Versagensspannung bei 107 Lastwechseln muss gegebenenfalls Mehrfachrisswachstum berücksichtigt werden. Der Vortrag diskutiert diese Punkte und zeigt Lösungswege auf.
Fracture mechanics as a tool in failure analysis (2014)
Zerbst, Uwe
Non-destructive testing and fracture mechanics - A short discussion (2016)
Zerbst, Uwe ; Heckel, Thomas ; Carboni, M.
A discussion is provided on the relation between non-destructive testing (NDT) and fracture mechanics. The basic tasks behind this are to guarantee the safety of a component at a potential hazard loading event, to specify inspection intervals or, alternatively, of demands on NDT for a fixed inspection regime, to plan accompanying measures for cases of temporary continued operation of structures in which cracks have been detected, and, finally, fatigue strength considerations which take into account initial defects.
Extended parametric equations for weld toe stress concentration factors and through-thickness stress distributions in butt-welded plates subject to tensile and bending loading (2016)
Madia, Mauro ; Kiyak, Yusuf ; Zerbst, Uwe
Based on a large set of 2D finite element analyses, parametric equations for weld toe stress concentration factors and through-thickness stress profiles are provided for butt-welded plates. These cover Single-Vand Double-V joints subject to tensile and bending loading. Compared to the most widespread solutions in the literature, which have also been tested against the finite element data in this work, the application range is extended particularly with respect to the weld toe radius(0.1≤ρ≤4 mm)andangle(10 °≤α≤60 °). Furthermore, two values of excess weld metal are considered (h=0.75;2.5mm). The analyses are performed for a plate thickness of 10 mm. Besides the extended validity range, the proposed equations show also an improved accuracy compared to the existing solutions.
IBESS - ein DFG/AiF-Clusterprojekt: Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen (2013)
Zerbst, Uwe
Anwendung bruchmechanischer Werkstoffkennwerte in der Bauteilbewertung. Grundlagen, spezielle Aspekte, Regelwerke (2013)
Zerbst, Uwe
Application of the cyclic R-curve method in notch fatigue analysis (2016)
Madia, Mauro ; Zerbst, Uwe
The paper deals with the prediction of the fatigue Limit of notched specimens. Some authors in the literature have shown that this issue can be solved by employing an approach based on critical distances, others used elastic fracture mechanics. In this paper the fatigue limit of notched specimens is given by the non-propagating condition of mechanically small surface cracks. According to the so-called cyclic R-curve method, the crack driving force of a growing small crack is compared to its resistance force, which incorporates the gradual build-up of crack closure. The fatigue limit is determined by that applied nominal stress, for which the tangency condition of crack driving and resistance force is satisfied. The approach has been modified to incorporate plasticity effects in the mechanically short crack Regime and it has been applied to a mild and a high-strength steel, in case of an infinite plate with circular hole under remote tensile stress. The method has been successfully applied to the evaluation of fatigue notch-sensitivity in case of surface roughness.
The IBESS model – Elements, realisation and validation (2018)
Madia, Mauro ; Zerbst, Uwe ; Beier, T. ; Schork, B.
The work presents the procedure developed within the German research project IBESS, which allows for the fracture mechanics-based prediction of the fatigue strength of welded joints under constant amplitude loading. Based on the experimental observations of the crucial failure mechanisms, the approach focuses on the short crack propagation, where elastic-plastic fracture mechanics and the build-up of closure effects must be considered as well as the variability of the local geometry at the weld toe and the modelling of multiple crack interaction. Analytical solutions are provided for the approximation of the through-thickness stress profiles at the weld toe and for the determination of the crack driving force in the form of a plasticity-corrected stress intensity factor range ∆K_p. Proposals for the determination of the initial crack size and the crack closure factor are also included. The approach is validated against a large number of experimental data, which comprises fatigue tests on individual cracks monitored by heat tinting and beach-marking techniques, as well as stress life curves. Three kinds of welded joints, two steels of significant different strengths and three stress ratios are considered. The results show that the procedure provides good estimations of the statistical distribution of the fatigue strength of welded joints both for the finite and infinite life regime. Furthermore, the predictions are compared with available benchmark data for structural steels.
Fatigue and fracture of weldments - The IBESS approach for the determination of the fatigue life and strength of weldments by fracture mechanics analysis (2019)
Zerbst, Uwe ; Madia, Mauro ; Schork, B. ; Hensel, J. ; Kucharczyk, P. ; Tchoffo Ngoula, D. ; Tchuindjang, D. ; Bernhard, J. ; Beckmann, C.
The acronym IBESS stands for "Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen" which, translated from German, means "integral fracture mechanics determination of the fatigue strength of welds". the method introduced in this study is the outcome of a German Research cluster in which eight partners were involved. A list of them is found at the end this study. The IBESS method is characterized by a number of partially novel aspects and elements of fracture mechanics applied to the evaluation of fatigue stength of welds. The most important ones are: (a) Determination of fatigue crack propagation for mechanically/physically short and long cracks. (b) Determination of an elastic-plastic crack driving force for the treatment of mechanically short cracks. To that purpose an analytical expression for the cyclic J-integral was developed and validated against finite element results. (c) The gradual build-up of the crack closure phenomenon is determined by using cyclic R-curves which describe the crack size dependency of the fatigue crack propagation threshold in the physically short crack growth regime. (d) A physically meaningful initial crack size is defined for total life consideration. It is based on a two-criteria approach. Based on a cyclic R-curve analysis, the crack size at crack arrest is determined as a lower bound. If, however, a pre-existing crack-like defect is larger than this, its dimensions define the initial crack size. (e) Multiple crack propagation at the weld toe is considered. (f) In conjunction with this, the variation of the weld toe geometry is considered in a stochastic model. (g) As a result, both the fatigue limit (defined for 107 loading cycles) and the finite life (high cycle) fatigue S-N curve are obtained statistically. (h) At various analysis steps, parametric equations have been developed which allow for analytical calculations instead of complete stochastic analyses based on finite elements which are unrealistic even at present. (i) The method has been validated with a large number of S-N curves including two materials, three weldment types with two geometries, each referring to differnt manufacturing technologies and the as-welded and stressrelieved state. (j) Althrough not finally solved, an extended discussion is provided on the issue of welding residual stresses including their redistribution under cyclic loading. (k) A number of simplifications is proposed at lower analyses levels which, however, partly lack complete validation by now.
Fatigue strength and fracture mechanics - A general perspective (2018)
Zerbst, Uwe ; Madia, Mauro ; Vormwald, M. ; Beier, T.
Common fracture mechanics based fatigue considerations are usually limited to the residual lifetime determination of so-called long cracks. The extension of this concept to the total lifetime, as in the S-N curve approach, requires an adequate description of short crack propagation which cannot be based on the Delta K concept, and it must consider the crack closure phenomenon as well as its gradual build-up at the short crack stage. Further, it has to provide a meaningful definition of initial crack dimensions and a solution for the multiple crack problem at stress levels higher than the fatigue limit as it is specific for some configurations such as weldments. This paper aims at a discussion of all these points and offers possible solutions which are illustrated by examples taken from the German IBESS project on fracture mechanics based determination of the fatigue strength of weldments, the results of which will be discussed in more detail in this Special issue.
The cyclic R-curve – Determination, problems, limitations and application (2018)
Zerbst, Uwe ; Madia, Mauro ; Maierhofer, J. ; Kolitsch, S. ; Gänser, H.-P. ; Pippan, R.
The so-called cyclic R curve, i.e. the crack size dependence of the fatigue crack propagation threshold in the physically short crack regime, is a key parameter for bringing together fatigue strength and fracture mechanics concepts. Its adequate determination is of paramount importance. However, notwithstanding this relevance, no test guideline is available by now and only very few institutions have spent research effort on cyclic R curves so far. The aim of the present paper is to give an overview on the state-of-the-art. Besides an introduction into the basic principles, the discussion will concentrate on the experimental determination on the one hand and questions of its application on the other hand.
Cyclic J-integral: Numerical and analytical investigations for surface cracks in weldments (2018)
Zerbst, Uwe ; Madia, Mauro ; Tchoffo Ngoula, D. ; Beier, T. ; Vormwald, M.
The cyclic J-integral (∆J-integral) is a crack tip parameter of elastic-plastic fracture mechanics which can be used as governing parameter for the description of fatigue crack growth (FCG) in metallic structures. In this contribution, it is applied for modelling FCG in weldments. The ∆J-integral is determined by means of analytical approximation formulas as well as numerical methods. An analytical solution, which takes into account effects of the local ligament plasticity, was derived. This solution is based on well established methods such as R6, BS7910 and SINTAP which were modified for cyclic loading. It incorporates methods for the description of short crack closure behaviour as well as the well known analytical (long) crack closure function of Newman. A specific code was written to evaluate the ∆J-integral numerically in the course of finite element based crack growth simulations. The code was first validated for an infinite plate with centre crack by applying elastic and elastic-plastic material behaviour. Next, the ∆J-integral was calculated for cracks in various butt and cruciform welded joints. The results were compared with the results of the derived analytical approximation formula. A good accordance was achieved between the results.
Fracture-mechanics-based prediction of the fatigue strength of weldments. Material aspects (2018)
Zerbst, Uwe ; Madia, Mauro ; Gerwien, Peter ; Kucharczyk, P. ; Münstermann, S. ; Schork, B.
Any fracture mechanics based determination of the fatigue strength of weldments requires different input information such as the local weld geometry and material data of the areas the crack is passing through during its propagation. The latter is so far not a trivial task as the fatigue crack is usually initiated at the weld toe at the transition from the weld metal to the heat affected zone and it subsequently propagates through the different microstructures of the latter to eventually grow into the base material and to cause final fracture. This paper describes how the material input information has gained particularly for heat affected zone material by thermo-mechanically simulated material specimens for two steels of quite different static strength. The data comprise the cyclic stress-strain curve, the crack closure effect-corrected crack growth characteristics, long crack fatigue crack propagation thresholds, the dependency of the parameter on the crack length and monotonic fracture resistance. The substantial experimental effort was necessary for the validation exercises of the IBESS approach, however, within the scope of practical application more easily applicable estimating methods are required. For that purpose the paper provides a number of appropriate proposals in line with its check against the reference data from the elaborate analyses.
The effect of the local and global weld geometry as well as material defects on crack initiation and fatigue strength (2018)
Zerbst, Uwe ; Madia, Mauro ; Schork, B. ; Kaffenberger, M. ; Oechsner, M. ; Kucharzcyk, P. ; Hensel, J. ; Bernhard, J. ; Tchuindjang, D.
The paper provides an application of the IBESS approach to the investigation of the influence of various parameters of the global and local weld geometry as well as material defects on the fatigue strength of weldments. For this purpose, the global weld parameters, such as the weld toe radius, the flank angle, the excess weld metal, local secondary notches (in the present study as a measure of surface imperfections) and inclusions sizes have been determined as statistical distributions for different joint types and geometries and two steels of different strengths. The results are in line with literature data and reveal the potential of the theoretical approach to predict the correct trends. The combination with an advanced weld quality system has been demonstrated to be possible.
Analytical flaw assessment (2018)
Zerbst, Uwe ; Madia, Mauro
The paper provides a review on analytical flaw assessment methods with the focus on fracture under monotonic loading and fatigue crack propagation. The first topic comprises linear elastic as well as elastic-plastic fracture mechanics approaches. It essentially follows their historical development. Topics which are separately discussed are reference/Limit loads, the treatment of secondary stresses, strength mismatch, constraint, unstable crack propagation (monotonic R-curve analyses) and statistical aspects. With respect to fatigue crack propagation the analytical treatment of crack closure and constraint and the Determination of the cyclic elastic-plastic crack driving force is discussed. Finally, cyclic Rcurve analyses are briefly addressed.
Fatigue strength and life determination of weldments based on fracture mechanics (2017)
Zerbst, Uwe ; Madia, Mauro ; Beier, H. Th.
The paper provides an overview on the results of a German cluster project on the use of fracture mechanics to the determination of the fatigue strength of weldments with fatigue cracks originating at the weld toes. The approach includes (a) a concept for short crack propagation for which the common ΔK concept is not applicable and the crack closure effects are still being gradually build-up, (b) a method for determining fatigue life relevant initial crack sizes as they are needed in any fracture mechanics analysis and (c) multiple cracking and crack coalescence at load levels higher than the endurance limit. The analyses are stochastically performed. Both, the endurance limit and the finite life branch of the S-N curve are determined. Besides a brief introduction into the approach, validation examples are presented. These comprise different weldment types (butt welds, cross joints and longitudinal stiffened plates), two steels (S355NL and S960QL) of quite different strengths, different weld geometries due to different welding techniques (WIG, MAG), as-welded and stress relieved welds and different stress ratios varying from R = -1 to R = 0.5.
Fatigue strength and fracture mechanics (2017)
Zerbst, Uwe ; Madia, Mauro ; Vormwald, M.
If fracture mechanics shall be applied to the total lifetime respectively the fatigue limit of components (within the meaning of the S-N curve approach) it has to address four challenges: (a) It has to adequately describe so-called short crack propagation, which cannot be based on the common long crack concepts for principle reasons. Since the crack size is in the order of the plastic zone size, the modelling of short crack propagation cannot be based on the common linear elastic Delta K concept. Instead, an elastic-plastic parameter such as the cyclic J integral has to be applied. A second point is that the crack closure concept has to be modified in that the crack opening stress is not a constant, crack size- independent parameter but shows a transient behaviour with increasing short crack size. (b) It has to provide a meaningful definition of the initial crack dimensions as the starting point for an S-N curve relevant (residual) lifetime analysis. This can be based either on the (statistical) size of material defects which can be treated as cracks or by the size of the crack which would arrest subsequent to early crack propagation, whatever is larger. (c) It has to cope with the problem of multiple cracks for load levels higher than the fatigue limit such as it occurs in many applications in the absence of very large initial defects. (d) This requires consequent statistical treatment taking into account variations in the local geometry of the area where crack initiation has to be expected as well as the scatter in the initial crack size and in the material data used for the analyses.
Approximation of the crack driving force for cracks at notches under static and cyclic loading (2017)
Madia, Mauro ; Zerbst, Uwe ; Beier, T. ; Tchoffo Ngoula, D.
The work deals with the efficient calculation of the elastic-plastic crack driving force (J-integral for monotonic loading andΔJ-integral under cyclic loading) for short cracks at notches as essential parameter for the reliable static and fatigue assessment of notched structures. The J- or ΔJ-integral is calculated based on analytical solutions for stress intensity factors, estimated by means of well-known weight function solutions in the case of cracks under power-law stress distributions. A plasticity-correction function is applied to the stress intensity factors to obtain the final expression of the crack driving force. The comparison between analytical solutions and finite element calculations in case of cracks at the weld toe in welded joints shows good agreement.
Fatigue strength and fracture mechanics (2017)
Zerbst, Uwe ; Madia, Mauro ; Vormwald, M.
If fracture mechanics shall be applied to the total lifetime respectively the fatigue limit of components (within the meaning of the S-N curve approach) it has to address four challenges: (a) It has to adequately describe so-called short crack propagation, which cannot be based on the common long crack concepts for principle reasons. Since the crack size is in the order of the plastic zone size, the modelling of short crack propagation cannot be based on the common linear elastic Delta K concept. Instead, an elastic-plastic parameter such as the cyclic J integral has to be applied. A second point is that the crack closure concept has to be modified in that the crack opening stress is not a constant, crack size- independent parameter but shows a transient behaviour with increasing short crack size. (b) It has to provide a meaningful definition of the initial crack dimensions as the starting point for an S-N curve relevant (residual) lifetime analysis. This can be based either on the (statistical) size of material defects which can be treated as cracks or by the size of the crack which would arrest subsequent to early crack propagation, whatever is larger. (c) It has to cope with the problem of multiple cracks for load levels higher than the fatigue limit such as it occurs in many applications in the absence of very large initial defects. (d) This requires consequent statistical treatment taking into account variations in the local geometry of the area where crack initiation has to be expected as well as the scatter in the initial crack size and in the material data used for the analyses.
Schwingfestigkeit und Bruchmechanik (2017)
Zerbst, Uwe ; Madia, Mauro ; Vormwald, M.
Um bruchmechanisch Schwingfestigkeiten ermitteln zu können, sind einige Voraussetzungen erforderlich: (a) Das Wachstum sowohl langer als auch mechanisch und physikalisch kurzer Risse muss adäquat beschrieben werden. Das erfordert die Anwendung elastisch plastischer Konzepte zur Beschreibung der zyklischen Rissspitzenbeanspruchung sowie die Modellierung des graduellen Aufbaus der Rissschließeffekte im Kurzrissbereich. (b) Es müssen physikalisch sinnvolle Ausgangsrissgrößen für die bruchmechanische Analyse bestimmt werden. (c) Bei Spannungen oberhalb der Dauerfestigkeit respektive der Versagensspannung bei 107 Lastwechseln muss gegebenenfalls Mehrfachrisswachstum berücksichtigt werden. Der Vortrag diskutiert diese Punkte und zeigt Lösungswege auf.
Fatigue strength and fracture mechanics of mechanical components (2017)
Zerbst, Uwe
The present paper provides a discussion on all these topics and it offers solutions for it. The authors present an analytical solution of a Delta J based crack driving force based on an R6 type approach but modified for cyclic loading. The gradual build-up of the crack closure effect is modelled by the so-called cyclic R curve which describes the crack size dependency of the fatigue crack propagation threshold in the short crack regime. It is explained how the cyclic R curve is experimentally determined and how it can be estimated by a modified Kitagawa-Takahashi approach.
Defekte als Ursache für das Versagen metallischer Komponenten (2018)
Zerbst, Uwe
Ein Defekt ist „eine Imperfektion …, für die in einer quantitativen Analyse gezeigt werden kann, dass sie Versagen verursacht hat, welches ohne die Imperfektion nicht aufgetreten wäre“. Defekte in diesem Sinn können einerseits Werkstoffimperfektionen wie nichtmetallische Einschlüsse, Poren und Porennester, Nichtdurchschweißungen oder Bereiche defekter Mikrostruktur, andererseits unbeabsichtige geometrische Imperfektionen wie Kratzer, Eindrücke, Korrosionsgrübchen, Einbrandkerben, zu große Oberflächenrauheit u.a. sein. Sie können in der Fertigung, im Betrieb oder auch bei der Wartung entstehen. Nicht jede Imperfektion ist ein Defekt im oben genannten Sinn. Entscheidend ist zumeist nicht, dass an ihr ein oder mehrere Risse initiiert werden, sondern dass wenigstens ein Riss wachstumsfähig bleibt und so innerhalb der projektierten Lebensdauer zum Bruch oder anderweitigem Versagen führt. Aufgrund des begrenzten Umfangs bleibt die vorliegen-de Übersicht beschränkt.
Welding residual stresses as needed for the prediction of fatigue crack propagation and fatigue strength (2018)
Zerbst, Uwe ; Hensel, J. ; Nitschke-Pagel, T. ; Tchoffo Ngoula, D. ; Beier, T.
Welding residual stresses have an impact on the performance of welded structures, on their fracture resistance, their resistance against fatigue crack propagation and, most important, their fatigue strength and fatigue lifetime. The present paper provides an overview on the issue mainly from the point of view of the application of fracture mechanics to the determination of the fatigue strength as the topic of this Special issue. Besides own experimental and theoretical data a comprehensive discussion is provided in that context which includes the definition and interaction of short- and long-range (or reaction) residual stresses, the effect of cyclic mechanical loading and its treatment in fracture and fatigue analyses.
Die zyklische R-Kurve als Kenngröße des Kurzrisswachstums (2018)
Zerbst, Uwe
Unter der zyklischen R-Kurve versteht man die Abhängigkeit des Schwellenwertes gegen Ermüdungsrissausbreitung von der Risstiefe im Kurzrissbereich. Bei Spannungsverhältnissen R = omin/omax < ca. 0,7 erhöht sich der Schwellenwert AKltl ausgehend von einer intrinsischen, werkstoffspezifischen Untergrenze mit zunehmender Risstiefe, bis er einen risslängenunabhängigen Wert erreicht. Ursache ist der graduelle Aufbau unterschiedlicher Rissschließeffekte. Die besondere Bedeutung des Kurzrisswachtums allgemein und der zyklischen R-Kurve speziell besteht darin, dass sie ein physikalisches Bindeglied zwischen der konventionellen Schwingfestigkeit (Wöhlerkurve) und der Bruchmechanik repräsentieren. Der Beitrag befasst sich sowohl mit der experimentellen Ermittlung der zyklischen R-Kurve als auch mit ihrer Anwendung auf Rissarrest im Zusammenhang mit Schwingfestigkeitsbetrachtungen. Die experimentelle Ermittlung der zyklischen R-Kurve erfordert einen experimentellen Aufwand, der deutlich über den der Langrissbruchmechanik hinausgeht. Insbesondere im Anfangsbereich ist eine sehr genaue Messung der Risstiefe erforderlich, was eine Verbesserung etwa der konventionellen Potentialmethode erforderlich macht. Von wesentlicher Bedeutung ist auch, dass der Ausgangsriss vor Beginn des eigentlichen Versuchs keine Rissschließeffekte gesehen haben darf. Realisiert wird das durch eine vorgeschaltete Phase von sog. „Compression Pre-cracking“, d.h. durch Anschwingen komplett im Druckbereich.
Lessons learned on FFS particulary of (short) fatigue crack propagation (2017)
Zerbst, Uwe
The presentation provides a brief overview on results obtained in the context of fracture mechanics based flaw assessment particularly in the context of short crack propagation. Background is the planned updating of international fitness-for-service procedures such as BS 7910. Specific topics addressed are the determination of the cyclic elastic-plastic crack driving force, the description of the gradual build-up of the crack closure phenomenon at the short crack stage, cyclic R curve analysis and residual stresses.
Damage development and damage tolerance of structures manufactured by selective laser melting (2017)
Zerbst, Uwe
The additive manufacturing technology of Selective Laser Melting (SLM) experiences a rapid development within an increasing marked of quite different application fields. The properties of SLM materials and structures are influenced by a number of tech-nological parameters such as the metal powder (particle size, homogeneity, cleanliness), the laser tool (power, beam diameter, pulse lengths), the scanning operation (speed, sequence and orientation of melting paths), parameters of the over-all equipment (design and preheating of the base plate, currents and turbulence in the protective gas atmosphere) and, last not least, the hatching strategy including the build-up direction of the structure with respect to the loading direction of the component. For the perspective use of SLM structures as load carrying, safety-relevant components the knowledge of their mechanical properties is necessary. It is essential to understand these in the context of the manufacturing-related features and at the back-ground of the basic characteristics of metallic materials: crystal lattice, microstructure and material defects. The paper provides an overview on factors which affect the mechanical parameters stiffness, strength, ductility, toughness, fatigue crack propagation and fatigue strength in the context of selective laser melting.
Bruch, Schwingfestigkeit und Ermüdungsrissfortschritt von Schweißverbindungen (2018)
Zerbst, Uwe
Die Präsentation diskutiert Besonderheiten von Schweißnähten bei der Bestimmung der Zähigkeit bei monotoner Belastung, bei der Ermittlung des zyklischen Rissfortschritts und bei der Ermittlung der Gesamtlebensdauer/Schwingfestigkeit mittels moderner bruchmechanischer Methoden. Besonderes Augenmerk liegt auf der Inhomogenität des Werkstoffs in den einzelnen Nahtbereichen, die sich statistisch (stochastische Verteilung von Gefügeschwachstellen) und systematisch (Effekte von Festigkeits-Mismatch) auswirkt. Als weiterer Faktor kommen Schweißeigenspannungen hinzu, bei denen für die bruchmechanische Analyse eine Fallunterscheidung in primäre und sekundäre Eigenspannungen vorgenommen werden muss. Diskstiert werden die Konsequenzen für die Zähigkeitsermittlung und die Bauteilbewertung.
Defects as a root cause for fatigue failure of metallic components (2018)
Zerbst, Uwe
The Topic of the presentationis a discussion on defects which can cause failure in cyclically loaded metallic components. Although also touching Features such as material defects such as pores or micro-shrinkages, etc. and geometric defects such as surface roughness and secondary notches (which are not considered in the design process) which origin in manufacturing, and others the presentation concentrates on non-metallic inclusions. It is prefaced by an introduction to the life cycle of a fatigue crack from initiation up to fracture. Special emphasis is put on the fact that only cracks which are not arrested during one of their distinct Propagation stages can grow to a critical size.
IBESS - an integral method for fracture mechanics-based determination of the fatigue strength of weldments (2017)
Zerbst, Uwe
The paper provides an overview on the results of a German cluster project on the use of fracture mechanics to the determination of the fatigue strength of weldments with fatigue cracks originating at the weld toes. The approach includes (a) a concept for short crack propagation for which the common K concept is not applicable and the crack closure effects are still being gradually build-up, (b) a method for determining fatigue life relevant initial crack sizes as they are needed in any fracture mechanics analysis and (c) multiple cracking and crack coalescence at load levels higher than the endurance limit. The analyses are stochastically performed. Both, the endurance limit as defined for 107 loading cycles and the finite life branch of the S-N curve are determined. Besides a brief introduction into the approach, a wide range of validation examples is presented. These comprise different weldment types (butt welds, cross joints and longitudinal stiffened plates), two steels of quite different strengths, different weld geometries due to different welding techniques (TIG, MAG), as-welded and stress relieved welds and different stress ratios varying from R = -1 to R = 0.5.
Safe life and damage tolerance aspects of railway axles - A review (2013)
Zerbst, Uwe ; Beretta, S. ; Köhler, G. ; Lawton, A. ; Vormwald, M. ; Beier, H.T. ; Klinger, Christian ; Cerný, I. ; Rudlin, J. ; Heckel, Thomas ; Klingbeil, Dietmar
The paper gives an overview on safe life and damage tolerance methods applied to railway axles. It describes failure scenarios due to fatigue crack initiation and propagation. Besides common aspects of design, specific features such as corrosion and impact damage from flying ballast are discussed which may reduce the fatigue strength of axles during service. Potential effects of non-metallic inclusions from the steel manufacturing process are addressed in the context of the very high number of loading cycles railway axles are designed for. With respect to damage tolerance general lines of fracture mechanics residual lifetime analyses are introduced. More specific discussion is provided on aspects such as the threshold value of fatigue crack propagation and reliability aspects of non-destructive inspection.
Structural assessment of railway axles - A critical review (2013)
Zerbst, Uwe ; Klinger, Christian ; Klingbeil, Dietmar
The safety assessment of railway axles is based on a two-stage approach: fatigue strength design and regular inspections which, in terms of a general safety philosophy refer to safe-life and damage tolerance concepts. Starting with a recent failure case, a broken axle of a German high speed train, a discussion is presented on issues of both safety levels. These include ideas for finite life design, the treatment of in-service effects on the fatigue strength due to flying ballast damage and corrosion pits, the effect of corrosion on fatigue crack initiation and propagation, potential effects of non-metallic inclusions in steels, the way to detect them by quality control measures and reliability aspects of non-destructive testing with respect to the detection of fatigue cracks. Proposals are made how the safety level could be further improved.
Bruchmechanisches Modell zur Ermittlung der Schwingfestigkeit von geschweißten und nichtgeschweißten Proben (2013)
Zerbst, Uwe ; Madia, Mauro ; Eufinger, J. ; Bruder, T.
Ermüdungsrisse gehen in technischen Materialien in der Regel von Werkstoffdefekten auf oder nahe der Oberfläche aus. Bei Schweißverbindungen können Schweißnahtdefekte, z. B. oberflächennahe Schlackeneinschlüsse die Risseinleitungsphase erheblich verkürzen, so dass der Hauptteil der Lebensdauer auf die Phase der Kurzriss- und zu geringerem Anteil auf die Langrissausbreitung entfällt. Bei nichtgeschweißten Bauteilen aus technischen Werkstoffen starten Ermüdungsrisse häufig an Einschlüssen, oberflächennahen Poren oder anderen Ungänzen. Einerseits ermöglicht dies prinzipiell die Anwendung bruchmechanischer Methoden zur Ermittlung der Schwingfestigkeit, andererseits müssen die Methoden in der Lage sein, spezielle Aspekte des Kurzrisswachstums wie den graduellen Aufbau des Rissschließeffekts und die lokale Rissspitzenplastizität zu erfassen. Im Beitrag werden ein geeignetes analytisches Modell sowie erste Validierungen an Proben aus verschiedenen Aluminiumlegierungen vorgestellt. Der abschließende Teil des Beitrags geht auf Besonderheiten von Schweißverbindungen (Schweißnahtdefekte, Eigenspannungen etc.) im Kontext des vorgestellten Modells ein. Eine Erweiterung des Modells für Schweißverbindungen aus Stahl wird im Rahmen eines kürzlich gestarteten DFG-AiF-Clusterprojekts erfolgen.
Bruchmechanische Bestimmung der Schwingfestigkeit basierend auf der zyklischen R-Kurve (2015)
Madia, Mauro ; Zerbst, Uwe
Konventionell wird in der Bauteilauslegung zwischen Konzepten der Schwing- und Betriebsfestigkeit auf der einen und der Bruchmechanik auf der anderen Seite unterschieden. Werden in der Schwingfestigkeitsbewertung Gesamtlebensdauern ermittelt, so sind es in der Bruchmechanik Restlebensdauern bei Vorhandensein eines größeren, d.h., bereits zerstörungsfrei auffindbaren Risses. Daneben gibt es seit längerem Bestrebungen, bruchmechanische Ansätze auch für die Ermittlung der Gesamtlebensdauer fruchtbar zu machen. Der besondere Wert einer solchen Kombination besteht darin, dass die Bruchmechanik die explizite theoretische Behandlung von Eingangsparametern (Kerben, Oberflächenrauhigkeit, Mittelspannung, etc.) erlaubt, die in den konventionellen Ansätzen mit vergleichsweise hoher Ungenauigkeit halbempirisch einbezogen werden. Der Beitrag stellt einen von den Autoren entwickelten bruchmechanischen Ansatz zur Ermittlung von Wöhlerkurven vor, der eine Reihe innovativer Merkmale wie die Anwendung der elastischplastischen Bruchmechanik auf kurze Risse, die Ermittlung der Ausgangsrissgröße aus Rissarrestbetrachtungen, die Beschreibung der transienten Entwicklung des Rissschließeffekts mit Hilfe zyklischer R-Kurven (Risslängenabhängigkeit des Schwellenwertes von der Risstiefe), die theoretische Erfassung von Mehrfachrisswachstum bei Lastniveaus oberhalb der Dauerfestigkeit und statistische Aspekte umfasst. Das diskutierte Beispiel ist eine Schweißverbindung (Stumpfnaht) und wurde im Rahmen des laufenden Cluster-Projektes IBESS (Integrale bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen) generiert.
Assessment of ductile cast iron fracture mechanics analysis within licensing of German transport packages (2013)
Komann, Steffen ; Kiyak, Yusuf ; Wille, Frank ; Zerbst, Uwe ; Weber, Mike ; Klingbeil, Dietmar
In the design approval of transport packages for radioactive materials, the mechanical and thermal safety assessment is carried out in Germany by competent authority BAM. In recent years BAM was involved in several licensing procedures of new spent fuel and HLW package designs, where the cask body is of Ductile Cast Iron (DCI). According to IAEA regulations package designs have to fulfill requirements for specific conditions of transport. Type B(U) packages must withstand the defined accident conditions of transport. The temperature range from -40°C up to the operational temperature has to be considered. For the cask material DCI, it is necessary to determine safety against brittle fracture. The German guideline BAM-GGR 007 defines requirements for fracture mechanics of packagings made of DCI. Due to complex cask body structure and the dynamic loading a fracture mechanical assessment by analytical approaches is not always possible. Experience of recent design approval procedures show that the application of numerical calculations are applicable to determine the stresses and stress intensity factors in the cask body. At the first step a numerical analysis has to be done to identify the loading state at the whole cask body. Secondly an analysis of a detail of the cask body is made considering the displacement boundary conditions of the global model. An artificial flaw is considered in this detailed model to calculate the fracture mechanical loading state. The finite element mesh was strongly refined in the area of the flaw. The size of the artificial flaw is based on the ultrasonic inspection acceptance criteria applied for cask body manufacture. The applicant (GNS) developed additional analysis tools for calculation of stress intensity factor and/or J-Integral. The assessment approach by BAM led to the decision to develop own tools to the possibility for independent proof of the results. The paper describes the authority assessment approach for DCI fracture mechanics analysis. The validation procedure incl. the development of own tools is explained. BAM developed a postprocessor to determine the fracture mechanical loads. A horizontal 1 m puncture bar drop test is used to give a detailed description of the assessment procedure.
Fracture mechanics as a tool in failure analysis - Prospects and limitations (2015)
Zerbst, Uwe ; Klinger, Christian ; Clegg, R.
Although fatigue crack propagation and fracture cause a large part of failure events in industrial practice, fracture mechanics in failure analysis seems to be still a side issue. Starting from an introduction into important basic questions of failure analysis and fracture mechanics, the authors specify what kind of questions in failure analysis can be effectively solved by fracture mechanics (and which can't). They illustrate their discussion with a number of 13 case studies from the literature. Much more pronounced than in the design stage the benefit of fracture mechanics in failure analysis depends on its accuracy. This is limited by both, intrinsic factors of the method and the availability and quality of the input information. The authors discuss the various aspects and provide the reader with some background information which, as they believe, will be helpful for better understanding the prospects and limitations of fracture mechanics in failure analysis and the conditions of its application.
About the fatigue crack propagation threshold of metals as a design criterion - A review (2016)
Zerbst, Uwe ; Vormwald, M. ; Pippan, R. ; Gänser, H.-P. ; Sarrazin-Baudoux, C. ; Madia, Mauro
The fatigue crack propagation threshold ΔKth is of paramount importance for any kind of damage tolerant design, but in contrast to this importance, the determination and application of the parameter is not on the firm ground as previously assumed. The paper discusses questions of its experimental determination as well as of its application to components. In both fields, new questions have been raised with the potential to challenge or modify long-standing knowledge. Against this background, the paper is an attempt to systematize the established knowledge as well as questions and open issues.
Der Schwellenwert DKth als Auslegekriterium. Aktuelle Entwicklungen und Fragestellungen (2015)
Zerbst, Uwe ; Madia, Mauro
Bei der Bestimmung der Restlebensdauer zyklisch beanspruchter Bauteile kommt dem Schwellenwert für Ermüdungsrissausbreitung, K111, oft entscheidende Bedeutung zu. Dabei ist seine Anwendung weniger gesichert als bislang angenommen. Der Vortrag diskutiert Fragen der experimentellen Ermittlung des Schwellenwertes sowie seiner Anwendung auf Bauteile. Auf beiden Gebieten haben sich in den letzten Jahren Probleme ergeben, die bestehendes Wissen teilweise wieder in Frage stellen oder modifizieren. Im Beitrag diskutiert werden der Einfluss unterschiedlicher Rissschließmechanismen auf K111, Konsequenzen, die sich daraus hinsichtlich der Ermittlung und Übertragung des Kennwertes ergeben, sowie die Effekte von Einflussgrößen wie Spannungsverhältnis und Rissgröße, aber auch des Werkstoffgefüges und der damit korrelierten mechanischen Eigenschaften.
Imperfektionen für die schwingbruchmechanische Bewertung von Schweißverbindungen (2015)
Schork, B. ; Zerbst, Uwe ; Kucharczyk, P. ; Bernhard, J. ; Kaffenberger, M. ; Baumgartner, J. ; Oechsner, M.
Bruchmechanischen Bewertungsmethoden liegt stets eine tatsachlich vorhandene oder fiktive Anfangsrisslange zu Grunde. Schweißverbindungen sind mit strukturellen Imperfektionen wie beispielsweise lnhomogenitaten in der Mikrostruktur und den Werkstoffeigenschaften behaftet, welche auf der Werkstoffseite berücksichtigt werden können. Imperfektionen wie der Kantenversatz und der Nahtübergangsradius, die als außere geometrische Imperfektionen aufgefasst werden können, haben vor allem Auswirkungen auf den Spannungszustand und werden daher auf der Lastseite erfasst. Innere geometrische Imperfektionen wie Einschlüsse oder Poren, von welchen Risse initiieren und sich ausbreiten, können als Ausgangsrissgröße aufgefasst werden. Im Teilprojekt A1 des Forschungsclusters IBESS wurden außere geometrische Imperfektionen an Schweißverbindungen ermittelt und statistisch ausgewertet. Des Weiteren wurden Schweißverbindungen fraktografisch im Rasterelektronenmikroskop (REM) bezüglich innerer geometrischer Imperfektionen untersucht, jedoch konnten aufgrund der hohen Schweißgütekeine schadigungsrelevanten inneren Imperfektionen (Ausgangsdefekte) detektiert werden. Um dennoch eine Ausgangsrisskonfiguration zu bestimmen, wurden "Heat-Tinting" Versuche eingesetzt, mit denen auf der Bruchflache verschiedene Anrissstadien markiert werden können. Mit dem .Heat-Tinting" Verfahren können sehr kleine Anrisse detektiert und in Abhangigkeit von der Beanspruchung frühe Anrisskonfigurationen ermittelt werden. Des Weiteren haben Zerbst und Madia im Teilprojekt A3 ein Modell entwickelt, mit dem für den Grundwerkstoff mittels zyklischer R-Kurven eine Ausgangsrissgröße rechnerisch ermittelt werden kann. Unter Verwendung der Ergebnisse aus den Versuchen zur Ermittlung der Anrissstadien soll dieses Modell validiert werden, um auch für Schweißverbindungen Anwendung zu finden.
IBESS: Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen - Eine Einführung (2015)
Zerbst, Uwe ; Beier, H.T. ; Nitschke-Pagel, T.
Die Projektbezeichnung IBESS steht für .Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen". Ziel des von acht Partnern vorangetriebenen AiF-DFG-Forschungsclusters IBESS ist die Entwicklung eines Ansatzes zur bruchmechanischen Ermittlung der Schwingfestigkeit von Schweißverbindungen. Die Arbeiten umfassen grundlegende Untersuchungen zum Wachstum und Arrest kurzer Risse, zur Ausbildung und Beeinflussung von Schweißeigenspannungen unter zyklischer Last, zum Einfluss der lokalen Nahtgeometrie auf die Rissausbreitung, zum Mehrfachriss-Phänomen oberhalb des Dauerfestigkeitsniveaus sowie zum Koaleszenzverhalten benachbarter Risse. Die gewonnenen Erkenntnisse fließen in ein analytisches Modell zur Ermittlung der Schwingfestigkeit ein, das physikalisch begründete und mithin sehr viel individuellere Vorhersagen des Ermüdungsverhaltens von Schweißnähten ermöglichen soll, als das auf konventioneller Basis bislang möglich ist. Ein nicht geringer Teil der Aktivitäten des Clusters ist mit der Bereitstellung von Daten zur Validierung befasst. Diese wird auf verschiedenen Ebenen vorgenommen, von der Beschreibung des Wachstuns von Einzelrissen über ihr Zusammenwachsen bis hin zur kompletten Wöhlerkurve. Ziel dieses Vortrags ist ein kurzer Überblick über das IBESS-Gesamtprojekt, das dem Zuhörer eine Einordnung der im IBESS-Vortragsblock vorgestellten Einzelaktivitäten ermöglichen soll.
Assessment of welded joints by fracture mechanics. IBESS - Delevopment of a procedure (2014)
Zerbst, Uwe
The idea to determine the fatigue strength of weldments by means fractuie mechanics was originally based on the empirical observation that the major portion of the fatigue life in weldments is frequently spent in crack propagation. The present paper gives a brief OverView on the basic principles of fracture mechanics-based determination of fatigue strength and on special features which have to be considered for weldments. Based on this Information, the ongoing research project IBESS is introduced and briefly reviewed.
Analytische Beschreibung von Rissarrest, Kurz- und Langrisswachstum in Schweißverbindungen (2015)
Madia, Mauro ; Zerbst, Uwe ; Beier, H.T. ; Schöne, Dieter
Kernstück der angestrebten IBESS-Prozedur ist eine analytische Methode zur bruchmechanischen Beschreibung der Rissausbreitung unter Schwingbelastung. Da man es im Bereich der Schwingfestigkeit mit kurzen Rissen zu tun hat, auf die die etablierten Methoden der Langrissbruchmechanik nicht anwendbar sind, werden Lösungen entwickelt, die es erlauben, sowohl die rissnahen Plastizitätsverhältnisse als auch die mit wachsendem Riss graduell zunehmenden Rissschließeffekte quantitativ zu beschreiben. Unter Einbeziehung der sogenannten zyklischen R-Kurve, deren experimentelle Methodik ebenfalls im Rahmen des Projekts weiterentwickelt wird, ist es zudem möglich, Ausgangsrissgrößen vorherzusagen, die auf Dauerfestigkeitsniveau gerade so noch arretieren würden. Dies erlaubt umgekehrt eine Abschätzung der Dauerfestigkeit an realen Bauteilen wie eben Schweißnähten sowie die statistisch basierte, analytische Vorhersage des Zeitfestigkeitsastes der Wöhlerkurve. Die im Modell berücksichtigten Parameter bzw. deren statistische Verteilung schließen Werkstoffdaten und die lokale Nahtgeometrie (Nachtübergangsradius, Nahtanstiegswinkel, Einbrandkerben oder Oberflächenrauhigkeit) ein. Im Vortrag wird das analytische Modell vorgestellt und vor dem Hintergrund der im IBESS-Cluster bereitgestellten experimentellen Information diskutiert.
Fracture mechanics assessment of welded components at static loading (2015)
Hübner, P. ; Zerbst, Uwe
Special aspects of welded components such as geometrical imperfections, inhomogeneity, strength mismatch and welding residual stresses have to be taken into account in a fracture mechanics analysis since they affect the crack driving force in the component as weil as the fracture resistance of the material. The treatment of components subjected to static loading is based on methods such as the European SINT AP procedure, which has been validated in a nurober of case studies. In the present paper the influence of strength mismatch and residual stresses on the fracture resistance and the assessment of a component are discussed.
Fracture mechanics based assessment of the fatigue strength: approach for the determination of the initial crack size (2015)
Zerbst, Uwe ; Madia, Mauro
In a number of previous papers, the authors have proposed a model for fracture mechanics based prediction of the S-N characteristics of metallic components with large microstructural defects. Here, an extension to materials that do not show large defects onto the fracture surfaces is provided. In such cases, an approach based on a so-called cyclic R-curve analysis is proposed for the determination of the initial flaw size, which has to be used in the calculation of fatigue crack propagation. The principle is explained and demonstrated by a first application to a welded joint.
Einfluss von Save Life- und Schadenstoleranzkonzepten auf die ZfP von Eisenbahnradsatzwellen (2013)
Heckel, Thomas ; Zerbst, Uwe
Reference load solutions for plates with semi-elliptical surface cracks subjected to biaxial tensile loading (2014)
Madia, Mauro ; Arafah, D. ; Zerbst, Uwe
The yield or limit load is a key parameter with respect to the accuracy of flaw assessment based on R6 type procedures such as the R6 routine, the SINTAP and FITNET method, the standard BS 7910 and others. In a number of previous papers two of the present authors proposed the use of a reference load instead of the common limit load, which not only provided more exact fracture mechanics predictions, but showed also a wider and more general application range than the conventional parameter. Here the method has been extended to biaxial tensile loading and it has been successfully validated by a thorough comparison with finite element results and alternative solutions available in the literature.
Schadensentwicklung und Schadenstoleranz von SLM-gefertigten Werkstoffen und Bauteilen (2016)
Zerbst, Uwe
Unterschiedliche Werkstoffeigenschaften reagieren auf jeweils spezifische Weise auf Gittertyp, Gefüge und Defekte. Für die schadenstolerante Betrachtung von Werkstoff und Bauteil ist das Verständnis dieser Zusammenhänge essentiell. Der Beitrag gibt mit Hinblick auf additiv gefertigte metallische Bauteile(Selective Laser Melting) einen kurzen, keineswegs vollständigen Überblick über Faktoren, die die Steifigkeit, Festigkeit, Duktilität, Zähigkeit, Ermüdungsrissausbreitung und Schwingfestigkeit beeinflussen. Es wird aufgezeigt, wie die bruchmechanische Betrachtung zur Quantifizierung der Zusammenhänge beitragen kann
  • 1 bis 50

OPUS4 Logo

  • Kontakt
  • Impressum
  • Sitelinks