1,721,632 research outputs found
Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading
No full textIn some cases of engineering interest, the contribution of the higher order stress terms (besides the stress intensity factors and the T-stress) is not negligible in the crack tip stress field. The main aim of the present investigation is to present a set of equations for accurately describing the crack tip stress components particularly for those cases where the modes I and II stress intensity factors used in combination with the T-stress component, are unable to capture with satisfying precision the complete stress field ahead the crack tip. The case of a plate with a central crack under mixed mode (I + II) loading is discussed to show the different contributions of the higher order terms in the overall stress field. The second example deals with a thin welded lap joint characterized by a jointing face width to thickness ratio d/t ranging from 0.5 to 5. The third example investigates the case of an inclined crack departing from the slit tip of a welded lap joint. The strain energy averaged over a control volume can be analytically evaluated with high precision by taking into account only four additional terms besides KI, K II and T. Finally, the averaged SED is used to provide a demarcation line between the elastic and the elastic-plastic behaviors as well as to create a possible bridging with the CJP (Christopher, James and Patterson) model. © 2012 Elsevier Ltd. All rights reserved
Analytical models for fatigue life prediction of metals in the stress life approach
Full text linkQuesta tesi fornisce una raccolta di modelli stress-life (S/N) per la valutazione della vita a fatica di componenti metallici sia lisci che intagliati sottoposti a sollecitazioni di ampiezza sia costante che variabile. Il documento è suddiviso in cinque capitoli, il primo è una panoramica della fatica in generale e, nello specifico, degli strumenti necessari nei capitoli successivi. Nel capitolo 2 la transizione di da intaglio di tipo "crack like" a "blunt" è adattata all'approccio stress-life attraverso la teoria delle distanze critiche, quindi viene definita una nuova curva S/N modellante tale transizione. Il capitolo 3 si basa sul nuovo modello di curva S/N per il carico a fatica ad ampiezza variabile, dimostrando che la valutazione della vita a fatica in queste condizioni può essere eseguita attraverso uno shift costante della curva di Wöhler se si adotta la regola del danno cumulativo lineare. Il metodo è abbastanza generale poiché non è necessario ipotizzare vincoli specifici sulla della storia di carico in quanto il fattore di shift tiene conto degli effetti di tensione media, sebbene siano chiari i limiti della regola del danno cumulativo lineare alla base del lavoro. Si è anche osservato che, adottando una regola di danneggiamento cumulativo bilineare, il modello introduce in maniera naturale il concetto di limite di fatica, pur mantenendo costante il fattore di shift già definito. I modelli proposti sono stati validati sperimentalmente attraverso i dati del programma di test SAE Keyhole, disponibili pubblicamente online all'indirizzo https://www.efatigue.com/benchmarks/SAE_keyhole/SAE_keyhole.html.
Il capitolo 4 discute i limiti di validità dell regola del danno cumulativo lineare, prestando particolare attenzione al suo rapporto con le leggi di propagazione di cricca del tipo "Paris generalizzato". In particolare, il capitolo dimostra come il supporre danno cumulativo lineare corrisponda esattamente all'integrare una legge di potenza della sollecitazione e delle dimensioni della cricca in forma di legge di Paris o Walker. Ergo, questo risultato è valido anche per tensione media diversa da zero, ma non considera né la sequenza di applicazione del carico né effetti di chiusura della cricca. Di conseguenza, nonostante alcune chiare limitazioni, non si prevede alcuna differenza in termini di accuratezza tra l'applicazione di una del danno cumulativo lineare rispetto all'integrazione di un'equazione di propagazione della cricca. Infine, il capitolo 5 presenta un'indagine sui vantaggi dell'applicazione di una curva S/N a quattro parametri (forse più realistica rispetto ad una pura legge di potenza) ottenuta direttamente ipotizzando che la curva a due parametri corrisponda alla derivata prima della precedente nel suo punto di flesso. L'accuratezza della nuova curva è stata dunque confrontata con la legge di potenza troncata utilizzando una campagna sperimentale di dati di fatica su acciaio e lega di alluminio condotta dal National Advisory Committee for Aeronautics (NACA).This Thesis provides a collection of stress-life (S/N) models for fatigue life evaluation of both pristine and notched metallic components. The document is subdivided into five Chapters, the first being a Literature Overview of fatigue in general, and, in the specific, of the tools needed in the subsequent Chapters. In Chapter 2 the “crack like to blunt” notch transition is adapted to the stress-life approach using the theory of the critical distances, therefore a new S/N curve to model this transition is defined. Chapter 3 relies on the new S/N curve model for variable amplitude fatigue loading by demonstrating that fatigue life assessment under these conditions can be performed through a constant shift of the Wöhler curve if adopting a linear damage accumulation rule. The method is quite general since there is no need of hypothesizing specific constraints on loading history as the shift accounts for mean stress effects, albeit suffering from the weaknesses of the underlying linear damage accumulation rule. The models proposed have been experimentally validated through the SAE Keyhole test program data, publicly available online at https://www.efatigue.com/benchmarks/SAE_keyhole/SAE_keyhole.html.
Chapter 4 discusses the limits of validity of a linear damage accumulation rule, giving special attention to its relationship with crack propagation laws of the generalized Paris type. Specifically, the Chapter proves that supposing a linear damage accumulation exactly corresponds to integrating a power law of the stress and the crack size in the form of Paris’ or Walker’s law. Ergo, this result is valid even for non-zero mean stress, yet neither accounting for load sequence nor for crack closure is considered. Thenceforth, despite some clear limitations, no difference in terms of accuracy is expected between the application of a linear damage accumulation rule vs. integration of a crack growth equation. Finally, Chapter 5 presents an investigation of the advantages in the application of a (maybe more realistic) four parameters S/N curve directly obtained postulating that the two parameters curve corresponds to the first derivative of the former one in its inflection point. The accuracy of the new curve is compared with the former employing an experimental campaign fatigue data on steel and aluminum alloy conducted by the National Advisory Committee for Aeronautics (NACA)
A criterion based on the local strain energy density for the fracture assessment of cracked and V-notched components made of incompressible hyperelastic materials
No full textThe present contribution is devoted to the theoretical and numerical study of the elasto-static fields at a vertex notch under mode I loading. The analysis is based on the plane deformation hyperelasticity theory for an incompressible Mooney-Rivlin material. While for cracked components some contributions can be found in the recent and past literature, studies on V-notched components are instead very limited. The aim of this paper is to partially fill this lack, providing a fracture criterion for the assessment of components weakened by sharp V-notches. In the first part of the paper, a brief description of the analytical frame available for V-notches in hyperelastic material is reported. A Williams' type diagram reporting the degree of singularity for a material obeying a Mooney-Rivlin behavior is present. The asymptotic stress field and the local strain energy density are investigated by means of non-linear finite element analyses. In the second part of the paper, a criterion based on the local energy is proposed and successfully applied to a set of experimental data taken from the literature. Future works are surely necessary to validate the criterion considering more sets of data from sharp and blunt V-notches
Brittle Fracture of Rounded V-Notches in Isostatic Graphite under Static Multiaxial Loading
No full textWhile a large bulk of experimental results from cracked specimens of polycrystalline graphite under pure modes of loading, in particular under mode I loading, can be found in the literature, only a very limited number of tests have been carried out on notches. At the best of the author knowledge dealing with the specific case of V-notches under mixed mode loading (tension + torsion) no results can be found in the literature. With the aim to fill this lack, the problem of mixed mode (I + III) brittle fracture of polycrystalline graphite is investigated systematically here for the first time. The present study considers cylindrical specimens weakened by circumferential notches characterized by different acuities. A new complete set of experimental data is provided considering different geometrical configurations by varying the notch opening angle and the notch tip radius. The multiaxial static tests have been performed considering different values of the mode mixity ratio (i.e. the ratio between the nominal stress due to tension and that due to torsion loading). A criterion based on the local strain energy density previously applied by the same authors only to pure modes of loading is extended here to the case of tension and torsion loadings applied in combination. The proposed criterion allows a sound assessment of the fracture loads
A simplified extension of the Crack Analogue model for fretting fatigue with varying normal load
No full textThe stress concentration induced by fretting is studied with a simple "Crack Analogue" model (CA), vaguely inspired by the original CA proposed by MIT 20 years ago, "improved" by the first author to take into account simply both contact loads and bulk stresses loads, and even the case of finite stress concentration in the so-called "Crack Like Notch Analogue" (CLNA) model. We suggest here a very crude extension to include the case of varying normal load, where we don't attempt to solve the contact mechanics problem rigorously, only providing an estimate of the equivalent Stress Intensity Factor from the instantaneous load and contact area. Even this results in a problem which has no equivalent in standard fatigue, since it corresponds to a "crack" that is oscillating in size at each cycle. This defines the cycles of stress in the actual material points in the fretted area, but the uncertainties in the approximations suggest that only some limit cases should be approaches this way: for example, when the peaks of tangential load are obtained at about a "mean contact area" (out-of-phase loading) then the original CLNA model could be used
Framing Effects
Full text linkThis chapter introduces two kinds of one-place TSIMs representing, respectively, belief activated in working memory and belief left passively stored in long-term memory. The distinction between the two sorts of belief is shown to help with the modelling of a typical form of the well-known framing effect, whereby people can have different attitudes towards logically or necessarily equivalent propositions. The chapter introduces a semantics for active and passive topic-sensitive belief to represent and reason about, agents whose belief states can be subject to framing effects. The analysis of framing calls for a precise characterization of the sense in which framed agents are logically non-omniscient given that they can believe exactly one of two intensionally equivalent propositions even when they are fully on top of the relevant subject matters and, in a ‘dormant’ sense, they are even aware of the equivalence. The formal framework here combines topic-sensitivity with ideas from subset space semantics
Probabilities, Indicatives, and Relevance
Full text linkThis chapter combines topic-sensitivity and probabilities to provide an account of the acceptability conditions of (simple) indicative conditionals, i.e. indicatives with no further indicatives embedded in the antecedent or consequent. The account is in the spirit of the so-called Adams’ Thesis, in that the acceptability of a simple indicative is tied to the corresponding conditional probability; and in line with the Ramsey Test, whereby we assess conditionals by evaluating the consequent on the supposition of the antecedent. But it fixes the empirical and theoretical shortcomings of Adams’ Thesis by adding a relevance constraint for acceptability, where relevance is understood, again, as topic-sensitivity: we accept a simple indicative ‘If φ, then ψ’ to the extent that p(ψ|φ), the conditional probability of ψ given φ, is high, provided ψ is fully on-topic with respect to the topic of φ, plus that of background assumptions which matter for getting the consequent. The chapter presents a probabilistic logic for simple indicatives in terms of Popper functions, arguing that its (in)validities are both plausible and in line with empirical results on how people reason with conditionals
Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy
No full textThe main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading. © 2010 Elsevier Ltd
Modelling and fatigue assessment of steel rollers with failure occurring at the weld root based on the local strain energy
No full textAbstractWeldments geometry with failures occurring at the weld toe or at the weld root cannot, by its nature, be precisely defined. Parameters such as bead shape and toe or root radius vary from joint to joint even in well-controlled manufacturing operations. The worst case configuration can be achieved by modelling as a sharp, zero radius, notch both the toe and the weld root. The intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). For steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch, units for NSIFs are the same as conventional SIF used in LEFM. The different dimensionality of NSIFs for different notch opening angles does not allow a direct comparison of failures occurring at the weld toe or at the weld root. In order to overcome the problem related to the variability of the V-notch opening angle, a simple scalar quantity, i.e. the value of the strain energy density averaged in the structural volume surrounding the notch tip, has been introduced. This energy is given in closed form on the basis of the relevant NSIFs for modes I, II and III. The radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes being equal to 0.28 mm for welded joints made of steel.The local-energy based criterion is applied here to steel welded rollers produced by Rulmeca subjected to prevailing mode I (with failures at the weld root). The aim of the paper is firstly to describe the employed methodology for the fatigue assessment and secondly to show the first synthesis of fatigue data by means of local SED for a specific geometry
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