Dissertations / Theses on the topic 'Notch stress intensity factors'

This diploma thesis deals with influence of a notch on stress-strain states at the front of cracks by shear modes. Starting with fracture mechanics and its division, followed by stress intensity factor and calculate its by finite element method. Calculation is solved for two types of notches, U-notched and V-notched, both notches were modeled parametrically so their geometry was changeable and stress intensity factor were calculated for all configurations. Subsequently was solved next calculation of stress intensity factor but for shaft without notch. Finally, was evaluated influence of notch on stress intensity factor. Software for finite element method has been used ANSYS. Others calculation was provided in software MATLAB

This research focuses on the stress analysis of periodic notches by using the strain energy density approach. Bolts, screws and rotary-shouldered connections, as examples of periodic notched components, play an important role in the performance of the machinery. The contents are related to two-dimensional (2D), as well as three-dimensional (3D) modeling of periodic notches both in the case of round and sharp notches. The analyses are based on the numerical modeling of periodic notches with linear elastic assumption of the material. The simple analytical expressions for the notch stress intensity factors (NSIFs) of periodic sharp notches, as well as theoretical stress concentration factors (SCFs) of periodic blunt notches are obtained. Using the strain energy density (SED) approach, the coarse mesh in the finite element models is used and compared with the results obtained from the fine meshing. In fact, using SED approach, the averaged strain energy in a control volume allows using the coarse meshes in order to determine the NSIFs and SCFs of notched components precisely. In the case of 3D analysis, the thickness effects with particular attention on coupling modes, which due to Poisson effect are automatically generated, are studied. These modes can have a significant effect on the structural integrity of mechanical components. In addition, two collaborative industry projects with: Officine Meccaniche Zanetti s.r.l. and Omera s.r.l. are successfully implemented.
Questa ricerca si concentra su "Analisi delle sollecitazioni di intagliati periodici utilizzando l'approccio di densità di energia di deformazione", si è occupato di problematiche relative alla modellazione bidimensionale e tridimensionale di intagli periodici raccordati e a spigolo vivo. Bulloni, viti e connessioni rotanti spalle, come esempi di componenti intagliati periodiche, svolgono un ruolo importante nelle performance delle macchine. L'attività ha coinvolto prevalentemente la modellazione numerica in campo elastico ed ha permesso di ottenere delle semplici espressioni per la stima dei fattori d’intensificazione delle tensioni (NSIFs) e dei fattori teorici di concentrazione delle tensioni (SCFs) in funzione di tutti i parametri geometrici considerati. Le analisi numeriche sono state effettuate in prima battuta con mesh fitte e successivamente con mesh molto rade. Nel secondo caso l’energia di deformazione mediata in un volume di controllo ha permesso di determinare con precisione i fattori tensionali di riferimento e alcune espressioni per l’applicazione diretta a problematiche simili. Nel caso tridimensionale sono stati studiati e analizzati gli effetti legati allo spessore con particolare riferimento ai modi accoppiati che vengono automaticamente generati per effetto Poisson e che possono incidere in modo rilevante sull’integrità strutturale di componenti meccanici. I risultati raggiunti sono stati applicati a casi aziendali con due collaborazioni tutt’ora in atto con Officine Meccaniche Zanetti e Omera formalizzate in progetti di ricerca in cui il dottorando è stato il principale protagonista.

Předkládaná dizertační práce se zabývá stanovením hlavních členů Williamsova asymptotického rozvoje popisujícího rovinné elektro-elastické pole v okolí piezoelektrických bi-materiálových vrubů a trhlin na rozhraní za použití rozšířeného Lechnického-Eshelbyho-Strohova formalismu v návaznosti na čistě anizotropní pružnost. Je ukázáno, že rozšířený Lechnického-Eshelbyho-Strohův formalismus představuje spolu s moderními programovacími koncepty v jazyku Python efektivní a také praktický nástroj pro lomovou analýzu piezoelektrických bi-materiálů. Teoretická část práce popisuje aspekty anizotropní pružnosti a její návaznost na piezoelektrické materiály. Základní rovnice zaměřené na speciální typy monoklinických materiálů, které umožňují oddělení rovinného a anti-rovinného problému, jsou vyjádřeny pomocí komplexních potenciálů. V praktické části práce je sestaven problém vlastního hodnot pro bi-materiálový vrub, na jehož základě jsou stanoveny exponenty singularity a pomocí dvoustavového -integrálu také zobecněné faktory intenzity napětí. Veškeré vztahy a numerické procedury jsou následně rozšířeny na problém piezoelektrických bi-materiálových vrubů a podrobně prozkoumány v uvedených příkladech. Zvláštní pozornost je věnována přechodu asymptotického řešení téměř zavřených vrubů a trhlin na rozhraní. Vliv směru polarizace na asymptotické řešení je také zkoumán. Přesnost stanovení zobecněných faktorů intenzity napětí je testována srovnáním asymptotického řešení a řešení získaného pomocí metody konečných prvků s velmi jemnou sítí konečných prvků. Na závěr je formalismus modifikován pro nepiezoelektrické materiály.

The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a notch-tip is modelled accurately in the FFEM using a few unknowns, leading to reduction of the computational cost.The analytical expressions of displacements and stresses around a notch tip are derived for different cases of notch problems: in-plane (modes I and II) conditions and out-of-plane (mode III) conditions for isotropic and bi-material notches. These expressions, which are eigenfunction series expansions, are then incorporated into the FFEM to carry out the transformation of the displacements of the singular nodes and to compute the notch SIFs directly without the need for post-processing. Different numerical examples of notch problems are presented and results are compared to available published results and solutions obtained by using other numerical methods.A strain energy approach (SEA) is also developed to extract the notch SIFs from finite element (FE) solutions. The approach is based on the strain energy of a control volume around the notch-tip. The strain energy may be computed using commercial FE packages, which are only capable of computing SIFs for crack problems and not for notch problems. Therefore, this approach is a strong tool for enabling analysts to compute notch SIFs using current commercial FE packages. This approach is developed for comparison of the FFEM results for notch problems where available published results are scarce especially for the bi-material notch cases.A very good agreement between the SEA results and the FFEM results is illustrated. In addition, the accuracy of the results of both procedures is shown to be very good compared to the available results in the literature. Therefore, the FFEM as a stand-alone procedure and the SEA as a post-processing technique, developed in this research, are proved to be very accurate and reliable numerical tools for computing the SIFs of a general notch in isotropic homogeneous and bi-material plates.

Presented diploma thesis is concerned with problems of a stress singularity exponent and a generalized stress intensity factor determination, by dint the stress field in the vicinity of the stress concentrator can be consecutively determined. This task is possible to sectionalize into three parts. The first part summarizes basic information about linear anisotropic materials, deals with fundamentals of the linear elastic fracture mechanics and introduces its generalization to the case of the generalized stress intensity factors. The second part is dedicated to a special theory of anisotropic elasticity - Lekhnitskii-Eshelby-Stroh formalism (LES). Furthermore, a theory of the psi-integral is introduced, by dint the stress intensity factor is determined. The final part applies the LES theory and the psi-integral to the concrete material configuration of a crack on the bimaterial interface, a special example of a sharp bimaterial notch. By means of analytical-numerical algorithm in ANSYS and Silverforst FNT95 software the stress singularity exponents and generalised stress intensity factors are consecutively computed.

The master thesis is focused on estimation of crack propagation origin from sharp V-notch. Stress distribution around the tip of the V-notch is described on the base of generalized linear elastic fracture mechanics. The change of the stress singularity exponent caused by geometry of the V-notch and the vertex singularity is taken into account. The first part of the work is devoted to the estimation of the stress singularity exponent of the V-notch either from stress distribution around the tip of the V-notch or by using analytical solution. Formerly derived stability criteria are applied in the second part of the work. The origin of the crack propagation is estimated for several experimental specimens. The aim of this thesis is to compare the available experimentally observed data with results obtained using those criteria based on the application of generalized linear elastic fracture mechanics developer at the Institute of Physics of Materials Academy of Sciences of the Czech Republic. The finite element code Ansys and mathematical software Matlab were used for the necessary calculations.

The presented diploma thesis deals with a problem of a generalized stress intensity factor determination and a consecutive study of stress distribution around the bimaterial notch tip, combining analytical and numerical methods. This task is possible to sectionalize into three parts. The first part is dedicated to the fundamentals of the linear fracture mechanics and the mechanics of composite materials. The second part deals with methods of anisotropic plane elasticity solution. Pursuant to the solution the computational models in the third part are created. The first model makes for determination of a singularity exponent eigenvalue by dint of Lekhnitskii-Eshelby-Stroh formalism. The second model makes for determination of the generalized stress intensity factor using psi-integral method, which is based on the Betti reciprocal theorem. All needed calculation are performed in the software ANSYS 12, Maple 12 and Silverforst FTN95. Results will be compared with the values obtained from a direct method of the generalised stress intensity factor determination.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
A partir das equações de Williams e Creager foi desenvolvido um método híbrido, que acopla fotoelasticidade a um método numérico-computacional para determinação a dos fatores de intensificação de tensões (FIT) em placas planas sujeitas aos Modos I e II de abertura, com ou sem arredondamento na raiz do entalhe. Às equações propostas acopla-se um polinômio completo que representa uma tensão não-singular (sigma). Assim feito é possível a determinação dos coeficientes KI, KI e termos de sigma. Três programas de computador foram desenvolvidos para as formulações (Williams ou Creager): O primeiro: a partir da configuração das franjas isocromáticas, obtém-se KI e KII e os termos relativos à tensão não singular. O segundo: o desvio relativo a cada ordem de franja é determinado a partir dos termos acima. O terceiro: a partir dos valores determinados regenera-se as franjas isocromáticas para compara-las com as originais. As formulações foram testadas em modelos de barras com trincas e entalhes (com e sem arredondamento na raiz) e seus resultados comparados com dados disponíveis na literatura. Os fatores de influência na determinação de KI e KII, estudados foram: a quantidade de pontos e o ângulo delimitador da região de coleta de dados, bem como a influência dos termos referentes ao campo não singular e alguns aspectos do método numérico implementado. Como aplicação estudou-se o caso do corpo de prova tipo Charpy, onde, a partir das equações de Creager e dos valores de KI e KII assim determinados, pôde-se obter o valor de Kt para uma dada geometria.
A hybrid method coupling photoelasticity to a numerical-computational method which implements the William s (modes I and II) and Creager s (mode I) equations has been developed to determine the mixed-mode stress intensity factors in sharp notches and blunt cracks. The equations take into account the presence or not of a radius in the tip of the notch. To the proposed equations was added a complete polynomial, which represents the non-singular stress field. Three computational programs were developed for both formulations (William s and Creager): one to determine KI, KII and the non-singular terms, the second to evaluate the error between the actual situation and the results obtained and the third to regenerate the isochromatic fringes. The method has been tested in bars with cracks and notches (taking or not into account the existence of the radius at the depth of the notch) and the results were compared to experimental and analytical data found in the literature. Factors which have influence on the determination of KI, KII, were discussed: the number of data points and sector angle where those points are collected as well as the influence of the number of non-singular terms and some aspects of the numeric method. Two applications were studied: Charpy type test specimen under tension and bending and a beam with deep simetrycal grooves. With the values of KI and KII obtained by the Creager s equations one can determine the valeu of sigma x and sigma y in the analyzed situation, as well as the Kt value.

The drive of the aerospace industry to use better materials to save weight and increase the performance of the components has been the principal motive to create new materials like Titanium Metal Matrix Composites (Ti-MMC). The Ti-MMCs were designed to combine high stiffness with low weight. Most aerospace components are exposed to fatigue loads during their operation life, hence extensive research has been carried out to investigate the behaviour of Ti-MMC under fatigue loading. During fatigue of Ti-MMC in four point bend specimens, two cracks grow quazisymmetrical at an angle relative to the normal direction of the notch. It is clear therefore that Mode I and Mode II are present in the specimen. Solutions for predicting the Stress Intensity Factor (SIF) for TI-MMC under these load conditions have not been carried out before and presents difficulties, both analytically and experimentally. Some experimental technique like Stereo-Imaging Technique (Sin, Scanning electron microscope (SEM), Laser interferometry displacement gage system and mechanical extensometer have been used to calculate the SIF in Ti-MMC specimens by measuring the Crack Open Displacement COD during the fatigue crack propagation, but these technique have limited measuring capabilities. However, the Moire interferometry technique gives very sensitive and detailed data, due to its ability to measure the full field displacements near the crack tip. Moire Interferometry was applied in this thesis to calculate KI and KII using different analytical methods, for fatigue crack growth in unidirectional Metal Matrix Composite. The composite considered was Textron SCS-6ffi-6-4 and the bend was carried out in four point bending at room temperature. Zero load ratio and four different load ranges were considered. Two finite element models were also developed to predict the crack path direction and to calculate the SIFs. The results obtained from FE models and from the experimental technique show good correlation. The experimental results though show that the SIFs do not reduce in a linear manner but have several stages of crack retardation which is believed to be due to fibres becoming active in bridging behind the crack tip. The results presented are unique in that very little data on SIFs in Ti-MMC material is available and the effect of off-axis cracks on the KI and KII SIFs has not been addressed until now.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
FINANCIADORA DE ESTUDOS E PROJETOS
Foi desenvolvido um método computacional para a determinação dos fatores de intensidade de tensão, para os modos de abertura I e II, a partir de configurações de franjas isocromáticas. O método se caracteriza pela generalização na formulação do campo de tensões na vizinhança da ponta de trinca, que busca determinar, além dos fatores de intensidade de tensão, alguns parâmetros significativos do campo de tensões não singular, associados a diferentes geometrias, que interferem no campo singular, próximo à trinca. Um programa de computador foi desenvolvido para a obtenção KI, KII e dos demais fatores considerados. O erro das respostas pode ser calculado a partir das diferentes opções de saída do programa. O método foi testado em modelos de barras com trincas a 90 e 45 graus e os resultados comparados com dados experimentais e analíticos disponíveis na literatura. Como fatores de influência na determinação de KI e KII forma estudados: a quantidade e a posição dos pontos de coleta de dados, e o número de parâmetros considerados no campo não singular. Foram analisados ainda, como exemplo de aplicação ainda, como exemplo de aplicação, três modelos de solda de topo com trincas a 45 e 90 graus com diferentes posicionamentos em relação ao reforço de solda.
A computational method has been developed to determine mixed-mode stress intensity factors from isochromatic fringe patterns. The method proposes a general formulation of the stress field around a crack tip. It searches to obtain not only the stress intensity factors but also all the other non-singular stress field parameters, associated to different geometries, which interfere with the singular field near the crack. The method has been tested in bars with 90 and 45 degree cracks and the results, compared to experimental and analytical data found in literature. Three factors influencing in KI and KII determination have been studied: the quantity of data collecting points, its position and number of parameters considered in the non-singular field. Three models of transverse butt welded joints with 45 and 90 degrees cracks placed in different positions relative to weld reinforcement, have been analyzed as application examples.

In steel megastructures welding is a widely used and accepted joining technique. However, welds are geometrical discontinuities, resulting in severe local stress gradients, which strongly affect the fatigue strength of components. Advanced fatigue assessments are usually based on the local stress and strain state in the close neighborhood of such stress raisers. Despite this, current standards are lacking in giving a real guidance on how to perform a reliable fatigue assessment. Still, most of them do not refer to any local concept and lead to the nominal stress method. Even so, no recommendations exist on how to derive the nominal stress from a finite element (FE) model and it is left to the engineering assessment of a designer to establish which nominal stress is the right one. Within this framework, the present Ph.D. thesis, focused on making the fatigue assessment of large steel structures possible, is divided into ten chapters. Purposes of this thesis are both giving scientific contributions to advanced local approaches for fatigue assessment and developing a method fully compliant with current standards, in order to be employed in the industrial context. In the first chapter, a general introduction and the state of the art on fatigue design of welded structures are presented, with the aim to clarify the motivations of the present research work. In the second chapter, the adopted local approaches, namely the notch stress intensity factor (NSIF) based approach, the averaged strain energy density (SED) criterion and the peak stress method (PSM), are briefly introduced and described along with their theoretical frameworks. The third chapter deals with the fatigue behavior of large-scale welded cover plates, for which non uniform fatigue classification is highlighted at standards’ level. Through the application of the SED approach and adopting both bi-dimensional and three-dimensional FE models, parameters which mainly affect the fatigue strength are identified and alternatives to those provided by standards are proposed. Experimental data of four geometric variants are successfully summarized into a unique scatter band in terms of SED, regardless of the weld geometry. The suitability of the SED approach and of the related design curve to perform the fatigue assessment of welded cover plates is, therefore, not proven wrong. The fourth chapter is focused on the local SED numerical computation. Its principal drawback, consisting in the need of a specific control volume centered on a notch tip (i.e. at the weld toe and at the weld root in case of welded joints), within which the strain energy density has to be averaged, is overcome by using coarse meshes completely free-generated. The method and its limitations are formalized. For the sake of generality, some practical applications are given by using both Ansys® and Straus7® FE software. Robustness in terms of insensitivity to mesh pattern, mesh refinement and FE formulation are proven advantages of the method. The fifth chapter establishes a link between local stress fields, near weld toes and roots, and the nominal stress components evaluated at a proper distance from the weld. An analytical relationship between such distance and the loaded plate thickness is provided. A criterion to estimate SED values, both at the weld toe and at the weld root, as well as a posteriori the related NSIFs, as an explicit function of the nominal load components (membrane loads, shear loads and bending moments) is also presented. The proposed method is suitable for automation to perform the large number of fatigue assessments that a nowadays complex steel structure requires. However, the current lack of normative compliance of both SED and NSIF approaches can be a possible obstacle in industrial applications. That is why in the sixth chapter a method, scientifically and normatively compliant, to improve the classical nominal stress approach for welded structures, which is still the most widely accepted and recognized in standards, is proposed. The methodological problem of the nominal stress definition is overcome through an original, finite element based approach, which takes into account both membrane and bending effects. An experimental validation is presented and the implications in fatigue design of large steel structures are discussed. The seventh and eighth chapters present a finite element post-processor, developed to perform the almost automatic fatigue assessment of a large structure. The post-processor is compatible with Straus7® finite element solver and it is based on shell models to be suitable for large assemblies. Many of the findings of the present research work are automated: local SED and NSIF approaches are implemented, as well as the modified nominal stress and, finally, the classical nominal stress and hot spot stress approaches. A very good agreement between “manually” performed assessments, both through global and local approaches, and those rapidly performed by using the post-processor is found. Further good agreement is found between expected fatigue lives estimated through the local SED approach and those estimated through the modified nominal stress, in the presence of bending stresses. The ninth chapter deals with the rapid estimation of residual notch stress intensity factors (R-NSIFs), due to the welding process, by using the PSM and Sysweld® FE dedicated software. First, the calibration of the PSM in Sysweld® environment is presented; afterwards, practical applications of the PSM to evaluate the R-NSIFs are illustrated. Finally, the tenth chapter presents some overall concluding remarks, in order to discuss the main obtained results.
Nelle megastrutture in acciaio la saldatura è una tecnica di giunzione ampiamente utilizzata. Tuttavia, le saldature rappresentano delle discontinuità geometriche e introducono elevati gradienti tensionali locali che influiscono negativamente sulla resistenza a fatica dei componenti. Secondo la letteratura scientifica recente, le analisi di resistenza a fatica più avanzate si basano sugli stati di tensione o deformazione locali calcolati in prossimità dei punti singolari. Ciononostante, le normative vigenti mancano di fornire una guida reale su come eseguire tali stime della resistenza fatica: la maggior parte di esse non fa riferimento agli approcci locali e prevede l'impiego del metodo della tensione nominale. Tuttavia, non esistono raccomandazioni su come ottenere la tensione nominale mediante un modello agli elementi finiti ed è demandato alla capacità ingegneristica del progettista stabilire quale sia quella adeguata. In questo contesto, la presente tesi di dottorato, focalizzata sul rendere possibile la stima della resistenza a fatica delle grandi strutture in acciaio, è divisa in dieci capitoli. Scopo della tesi è sia fornire un contributo scientifico ad alcuni tra i più avanzati approcci locali per la stima della resistenza fatica, che sviluppare un metodo pienamente conforme alle normative vigenti, al fine di poter essere impiegato nel contesto industriale. Il primo capitolo rappresenta l'introduzione generale sul tema trattato, lo stato dell'arte in materia di progettazione a fatica delle strutture saldate e le motivazioni della presente ricerca. Nel secondo capitolo vengono introdotti gli approcci locali adottati e le loro basi teoriche: l'approccio basato sui fattori di intensificazione delle tensioni (NSIF), il criterio della densità di energia di deformazione (SED) e il metodo della tensione di picco (PSM). Il terzo capitolo riguarda la caratterizzazione a fatica dei coprigiunti saldati, tipicamente impiegati come rinforzo nelle travi da ponte, per i quali è stata evidenziata una non uniforme classificazione a fatica a livello normativo. Mediante l'impiego dell'approccio locale SED e adottando modelli agli elementi finiti sia bidimensionali che tridimensionali, sono stati isolati i parametri che influiscono sensibilmente la resistenza e proposte soluzioni ottimizzate rispetto a quelle fornite dalle normative. I dati sperimentali ottenuti testando a fatica quattro differenti soluzioni geometriche sono sintetizzati con successo in un'unica banda di dispersione in termini di SED, indipendentemente dalla geometria della saldatura. L'approccio locale SED e la relativa curva di progettazione si sono dimostrati quindi adatti a stimare la resistenza a fatica dei coprigiunti saldati in acciaio. Il quarto capitolo è incentrato sul calcolo numerico del SED. La principale criticità dell'approccio, rappresentata dalla necessità di uno specifico il volume di controllo localizzato all'apice di un intaglio strutturale (al piede e alla radice dei cordoni di saldatura, nel caso dei giunti saldati), entro il quale l'energia di deformazione deve essere calcolata e mediata, è superata mediante l'utilizzo di maglie di calcolo (mesh) rade e generate in maniera completamente automatica da un generico algoritmo di meshatura. La soluzione proposta e le relative limitazioni di applicabilità sono stati formalizzati. La robustezza in termini di insensibilità alla tipologia di mesh, alla sua raffinatezza e alla formulazione degli elementi finiti sono alcuni dei vantaggi provati. La generalità del metodo è dimostrata anche mediante alcune applicazioni pratiche con l'impiego di differenti software agli elementi finiti. Il quinto capitolo stabilisce un collegamento tra i campi di tensione locali, in prossimità del piede e della radice dei cordoni di saldatura, e le componenti di tensione nominale valutate ad una adeguata distanza dalla saldatura stessa. Nel capitolo viene fornita una relazione analitica tra tale distanza e lo spessore della piastra caricata; inoltre, viene presentato un criterio per stimare il valore del SED, sia al piede che alla radice dei cordoni di saldatura, e, a posteriori, i relativi NSIFs, come esplicita funzione delle componenti di tensione nominale (sollecitazione membranale, flessionale e tagliante). Tale metodo si presta all'automatizzazione e, quindi, a condurre l'enorme quantità di verifiche a fatica richieste per una complessa struttura saldata in acciaio. Tuttavia, l'attuale mancanza di conformità normativa degli approcci locali SED e NSIF rappresenta un possibile ostacolo nelle applicazioni industriali. Per questo motivo nel sesto capitolo viene proposto un metodo, conforme alle normative vigenti e alla letteratura scientifica, per modificare il classico approccio nominale, che tuttora è il metodo di riferimento ampiamente accettato e riconosciuto. Il problema metodologico della definizione di tensione nominale in un modello agli elementi finiti viene superato attraverso un approccio originale che tiene conto sia degli effetti membranali che di quelli di flessionali. Viene presentata una validazione sperimentale e vengono discusse le implicazioni nella progettazione a fatica delle grandi strutture in acciaio. I capitoli settimo e ottavo presentano un post-processore ad elementi finiti, sviluppato per automatizzare l'analisi della resistenza a fatica di una struttura di grandi dimensioni. Il post-processore è basato sul solutore ad elementi finiti Straus7® ed è compatibile con modelli di tipo shell per essere adatto ai grandi assiemi strutturali. Molte delle proposte illustrate nella presente tesi sono state quindi automatizzate: gli approcci locali SED e NSIF, il metodo della tensione nominale modificato e, infine, gli approcci classici basati sulla tensione nominale e di hot spot. È inoltre mostrato un ottimo accordo tra le analisi condotte "manualmente", sia attraverso approcci globali che locali, e quelle eseguite rapidamente utilizzando il post-processore, riscontrando generalmente un ottimo accordo tra la vita a fatica stimata mediante l'approccio locale SED e quella stimata attraverso il metodo della tensione nominale modificata. Il nono capitolo tratta la stima rapida dei fattori di intensificazione delle tensioni residue (R-NSIFs), conseguenti al processo di saldatura, utilizzando il PSM e il software agli elementi finiti dedicato Sysweld®. Innanzitutto, viene presentata la calibrazione del PSM in ambiente Sysweld®; quindi vengono illustrate alcune applicazioni pratiche. Infine, il decimo capitolo riporta alcune osservazioni conclusive di carattere generale e la discussione dei principali risultati ottenuti.

This thesis presents a study about the determination of the stress intensity factors in cracked sheets with riveted stiffeners. Stress intensity factors are determined with both analytical method and finite element method for different combination of rivet/stringer spacing and stringer to sheet stiffness ratio. Analytical part of the thesis is a replication of the original study of Poe which assumes rigid rivet connections with no stringer offset. In the analytical part, the whole systems of equations of Poe are re-derived, and it is shown that there are two typographical errors in the expressions for the calculation of the influence coefficients of the cracked sheet and the stringer. Major objective of the analytical part is to develop a computer code which calculates the variation of the normalized stress intensity factor with the crack length for any combination of rivet/stringer spacing and stringer to sheet stiffness ratio. Analytical part of the study also covers the effect of broken stiffener on the stress intensity factor of the cracked sheet. The stress intensity factors of stiffened cracked sheets are calculated by the finite element method by incorporating fastener flexibility and stringer offset. Finite element solutions are performed by Franc2D/L and Abaqus, and comparisons are made. The effect of geometry, fastener flexibility, and stringer offset on the stress intensity factors are studied by presenting normalized stress intensity factor versus crack length curves. Finally, as a case study a sample damage tolerant stiffened panel is designed according to FAR 25 safety criteria. Experiments are performed for determining mechanical and crack growth properties of Al 2124 which is used as the material in the case study. Present study showed that the most significant effect on the stress intensity factor is seen when stringer-cracked sheet offset is included in the analysis model.

Vickers hardness indentations on AI2O3 were studied comprehensively. Beneath indentation, there is a well-defined interface between the plastic zone and the elastic region and the radius of the plastic zone is close to half the indentation diagonal length. The residual stress field around the indentations has been measured by optical fluorescence microscope (FLM) scans. Yoffe's stress model predicted higher stresses than the experimental stress results. the radial crack lengths were measured by FLM scans, and the optical microscope (OM) and SEM methods for crack length measurements were found to significantly underestimate the crack lengths. Post indentation slow crack growth was found on the radial cracks were determined. The radial-median crack system was found for alumina indentations. Lateral cracks were also found for all the indentations, and their depths were close to the half diagonal lengths. the lateral cracks joined the tips of the radial cracks and had the similar growth rates to the radial cracks. The indentation parameters of SiC and 3Y-TZP indentations were also measured. Lateral cracking was observed beneath in SiC indentations but not in case of 3Y-TZP. The depth of the lateral crack of the SiC indentation was found to be close to the half diagonal length. the residual stresses and surface profiles around SiC and 3Y-TZP indentations were measured. the lateral crack lengths of the SiC determined from the surface profiles were close to the radial crack lengths. For TZP indentations, the highest volume fraction of the monoclinic zirconia phase was found near the edge of the indentations. Surface uplifts around indentations were found to have the profiles matching with distributions of the volume fraction of the monoclinic phase. A new Vickers indentation residual stress model has been presented using assumptions based on the experimental findings on alumina indentations. The main novelty of the model is that it predicts the stresses in the presence of cracking, and is therefore testable. The residual stress model has successfully predicted the stress fields around the polycrystalline alumina and SiC indentations but failed on TZP indentations because of the lack of lateral cracking and the tetragonal-to-monoclinic phase transformation. From the residual stress model, a new formula for the indentation stress intensity factor K was derived, which provided good results for threshold stress intensity factor, K10, on alumina, and fracture toughness, KIC, for SiC, and Si3N4. Three adjustable parameters can be added to strengthen existing model.

A finite element program utilizing singularity-enriched elements was developed to determine the stress-intensity factors for an arbitrary V-notch in a linear elastic orthotropic beam. The special elements allow computation of the stress-intensity factors without recourse to an extremely fine element mesh. An application of the program was made to wood. A pilot experiment involving rectangular end-notched wood beams verified the program as well as demonstrated the utility of the program in predicting failure loads due to rapid crack propagation emanating from V-notches. The effect of varying wood properties on the V-notch stress-intensity factor was examined. A procedure to establish the failure surface encompassing V-notches and cracks under all loading conditions using the program is presented.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

This thesis introduces an alternative method to evaluate Stress Intensity Factors (SIFs) in computational fracture mechanics directly, using the Extended Dual Boundary Element Method (XBEM) for 2D problems. A novel auxiliary equation introduced which enforces displacement continuity at the crack tip to yield a square system. Additionally, the enrichment method has been extended to 3D, so that the J-integral with XBEM and a direct technique are used to evaluate SIFs. This includes a complete description of the formulation of enrichment functions, a substitution of the enriched form of displacement into boundary integral equations, treatment of singular integrals, assembly of system matrices and the introduction of auxiliary equations to solve the system directly. The enrichment approach utilizes the Williams expansions to enrich crack surface elements for accurate evaluation of stress intensity factors. Similar to other enrichment methods, the new approach can yield accurate results on coarse discretisations, and the enrichment increases the 2D problem size by only two degrees of freedom per crack tip. In the case of 3D, the number of the new degrees of freedom depends on the desired number of crack front points where SIFs need to be evaluated. The auxiliary equations required to yield a square system are derived by enforcing continuity of displacement at the crack front. The enrichment approach provides the values of singular coefficients KI, KII and KIII directly in the solution vector; without any need for postprocessing such as the J-integral. Numerical examples are used to compare the accuracy of these directly computed SIFs to the J-integral processing of both conventional and XBEM approximations.

The AASHTO LRFD design specifications and the AASHTO manual for bridge evaluation are consistently revised using knowledge of previous bridge failures. Although modern steel structures are designed to resist fatigue cracking from service loads, cracks in the tension flanges of steel bridge girders have been observed as a result of stress concentrations, design errors, welding quality control, and vehicular impacts. Cracks can grow in size with time and active cyclic live loads and may result in a member fracture. Fracture is a dangerous limit state which occurs with little to no warning. One method to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around the crack tip. Finding SIFs for a cracked geometry may help an engineer to determine the fracture potential based on crack dimensions found during the inspection. Rolled I-beam and steel plate girders are extensively used as bridge superstructure members to efficiently carry live loads. This research was focused on determining Stress Intensity Factors (SIFs) of partially cracked I-sections using Finite Element Analysis. Two different tension flange crack profiles were studied: edge cracks, and full-width cracks. The SIF solutions were further used to study the fracture behavior and stress redistribution in the partially cracked flexural I-shaped members.
Master of Science
Steel is one of the fundamental materials used in the construction of bridge structures, and steel girder bridges are one of the most common types of bridge structures seen in the United States. Past bridge failures have helped engineers to understand shortcomings in design specifications, and AASHTO codes have been developed and revised over the years to reflect an improved understanding and evolution of engineering behavior. Engineers must make sure that a design is robust enough for functional use of the component during its service life. It is also equally important to understand the potential chances of failure and make the structure strong enough to overcome any failure mechanisms. Fracture is one structural failure mode which occurs with little to no warning and hence is very dangerous. One efficient way to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around a crack tip. Fracture literature is available which describes different methods of determining SIFs for cracked members. However, there are no solutions available to find a SIF of a partially cracked flexural I-shaped members. This research was focused on determining Stress Intensity Factors and studying the fracture behavior of partially cracked I-sections using Finite Element Analysis. The resulting SIF solutions were further used to study the fracture behavior and stress redistribution in partially cracked flexural I-shaped members.

The goal of this research was to extend the investigation into a method to represent and analyze the stress field around two parallel edge cracks in a finite body. The Westergaard-Schwarz method combined with the local collocation method was used to analyze different cases of two parallel edge cracks in a finite body. Using this method a determination of when two parallel edge cracks could be analyzed as isolated single edge cracks was determined Numerical experimentation was conducted using ABAQUS. It was used to obtain the coordinate and stress information required in the local collocation method. The numerical models were created by maintaining one crack at a fixed length while varying the length of the second crack as well as the separation distance of the two cracks. The results obtained through the local collocation method were compared with the finite element obtained J-Integrals to verify the accuracy of the results. The results obtained in the analysis showed that the major factor in determining when the second crack’s stress field has to be considered was the crack separation distance. It was found that a reduction in the second crack’s length did not have a significant effect on overall stress intensity factors of the fixed crack. A larger change in the opening mode stress intensity factor can be seen by varying the crack separation distance. As well as seeing a steady reduction in shear mode stress intensity factors as the crack separation was increased. The results showed that after a certain crack separation distance the two cracks could be analyzed separately without introducing significant error into the stress field calculations.

An investigation into the influence of cracks in bonded specimens is conducted. Photoelastic specimens containing a bondline are subjected to a constant displacement boundary condition created by bonded end grips. Specimens containing various crack orientations are analyzed to determine stress intensity factors at the induced crack tips. Specimens containing interface and sub-interface cracks were investigated. Two global geometries were used in this investigation, square and rectangular. The constant displacement boundary condition was induced on the specimen through dead weights hung from bonded aluminum end grips. Stress intensity factors were determined using photoelastic techniques. The stress intensity factors were examined to determine trends in the results as a function of changes in geometry. The effects of the induced boundary condition, the specimen geometry, and the bondline were investigated. The results from this investigation were compared to known solutions with a similar specimen geometry. These tests exhibited influences from the bondline, the boundary conditions, and the specimen geometry. The bondline tended to decrease the stress intensity factor for specimens with small crack lengths and tended to increase the stress intensity factor for specimens containing long crack lengths. As the crack length increased so too did the stress intensity factor. A reduction in the bondline to crack distance with sub-interface crack specimens caused a reduction in the stress intensity factor. A reduction in the global height of the specimen caused a reduction in the stress intensity factor also. The results from this investigation will aid in the understanding of the influence of interface and sub-interface cracks in bonded specimens.
Master of Science

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O presente trabalho visa determinar, experimentalmente,Fatores de Intensidade de Tensões, KI e KII em barras e tubos, submetidos à tração, com trincas situadas: I) Junto ao pé do cordão de solda em barras planas soldadas ortogonalmente com relações comprimento de trinca, a, largura da barra, B, a/B igual a 0,1 e a/B igual a 0,2. II) Próximo à raiz da solda em tubos unidos a 90 graus com relações comprimento de trinca, espessura do tubo principal, t, a/t igual a 0,1; a/t igual a 0,2; a/t igual a 0,3. III) Barras e tubos simples (sem uniões soldadas) tendo as relações a/B igual a 0,1; 0,2; 0,3 e a/t igual a 0,1; 0,2; 0,25 e 0,3. Nos modelos planos, foi feito um estudo comparativo entre espécimes que possuíam entalhes usinados para simular as trincas e espécimes onde forma propagadas trincas de fadiga. Os resultados para as barras forma obtidos utilizando-se a técnica fotoelástica bidimensional e para os tubos, o método tridimensional de congelamento de tensões e corte em fatias. Nas barras os dados coletados foram submetidos aos programas CRACK e FLAW, e nos tubos, apenas ao programa FLAW, para determinação dos valores de KI e KII.
This work aims to determine Stress Intensity Factors KI and KII for bars and tubes loaded in tension with the following geometry: I) T Join bars with cracks located near the weld toe. Relations between crack length, a, and bar width, B, were: a/B equal 0.05; a/B equal 0.1 a/B equal 0.2. II) Tubes with T joints with cracks located at the weld toe. The relations between crack length and tube thickness, t, were: a/t equal 0.1; a/t equal 0.2 and a/t equal 0.3. III) Plains bars with ratios a/B equal 0.05; a/B equal 0.1 and a/B equal 0.2. IV) Plains tubes with ratios a/t of 0.1, 0.2, 0.25 and 0.3. A comparative study was made between plane models that had artificial machined cracks and those that had natural fatigue cracks. Results for bars were obtained employing two-dimensional Photoelasticity technique and for tubes, the three-dimensional stress freezing and slicing method was used. To generate KI and KII, the collected data were submitted to FLAW and CRACK computer programs in the case of bars, while for tubes, only the FLAW program was used.

Nous proposons dans ce manuscrit une nouvelle méthode pour prendre en compte l’effet du gradient en Fretting-fatigue. Les champs mécaniques présents à proximité du front de contact sont décrits à travers des facteurs d’intensité non locaux. L’objectif est d’aboutir à une description du champ de vitesse sous la forme d’une somme de termes exprimés chacun comme le produit d’un facteur d’intensité (Is, Ia, Ic), qui dépend des chargements macroscopiques appliqués à l’ensemble et d’une fonction de forme (ds, da, dc), qui est liée à la géométrie locale du contact. Cette description est obtenue à travers un processus non intrusif de post-processing des résultats obtenus avec des calculs à éléments finis. De plus, elle a été pensée pour être implémentée dans un contexte industriel. En pratique, pour chaque chargement macroscopique et pour chaque géométrie, il est possible de calculer un ensemble de facteurs d’intensité non locaux qui permettent de décrire les champs mécaniques locaux près du front de contact. Cette description non locale a l’avantage d’être (i) indépendante de la géométrie du contact employé et (ii) utilisable dans des modèles à éléments finis utilisés dans l’industrie qui sont caractérisés par des maillages plus grossiers par rapport à ceux utilisés pour étudier le fretting-fatigue dans des milieux académiques. Une étude est menée pour vérifier que les facteurs d’intensité non locaux peuvent être utilisés pour transposer les résultats expérimentaux d’une géométrie à une autre
In this manuscript a new method to describe the stress gradient effect in fretting-fatigue is proposed. It is based on the description of the mechanical fields arising close to the contact edges through nonlocal intensity factors. For this purpose, the kinetic field around the contact ends is partitioned into a summation of multiple terms, each one expressed as the product between intensity factors, Is, Ia, Ic, depending on the macroscopic loads applied to the mechanical assembly, and spatial reference fields, ds, da, dc, depending on the local geometry of the part. This description is obtained through nonintrusive post-processing of FE computation and is conceived in order to be easily implementable in the industrial context. As a matter of fact, for any given macroscopic load and geometry, a set of nonlocal intensity factors is computed that permits to characterize the mechanical fields close to the contact edges. Such nonlocal description has the advantage of being (i) geometry independent so that the nonlocal intensity factors can be used to compare laboratory test with real-scale industrial assembly, (ii) applicable to industrial FE models usually characterized by rougher meshes compared to the ones used to describe fretting-fatigue in the academic context. The procedure is applied to fretting-fatigue test data in order to verify whether the nonlocal intensity factors can be used to transpose experimental results to different contact geometries from the one in which they have been obtained

This thesis introduces a three-dimensional (3D) finite element (FE) formulation to model the linear elastic deformation of fractured media under tensile and compressive loadings. The FE model is based on unstructured meshes using quadratic tetrahedral elements, and includes several novel components: (i) The singular stress field near the crack front is modeled using quarter-point tetrahedral finite elements. (ii) The frictional contact between the crack faces is modeled using isoparametric contact discretization and a gap-based augmented Lagrangian method. (iii) Accurate stress intensity factors (SIFs) of 3D cracks computed using the two novel approaches of displacement correlation and disk-shaped domain integral. The main contributions in the FE modeling of 3D cracks are: (i) It is mathematically proven that quarter-point tetrahedral finite elements (QPTs) reproduce the square root strain singularity of crack problems. (ii) A displacement correlation (DC) scheme is proposed in combination with QPTs to compute SIFs from unstructured meshes. (iii) A novel domain integral approach is introduced for the accurate computation of the pointwise $J$-integral and the SIFs using tetrahedral elements. The main contributions in the contact algorithm are: (i) A square root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. (ii) A gap-based augmented Lagrangian algorithm is introduced for updating the contact forces obtained from the penalty method to more accurate estimates. The results of contact and stress intensity factors are validated for several numerical examples of cubes containing single and multiple cracks. Finally, two applications of this numerical methodology are discussed: (i) Understanding the hysteretic behavior in rock deformation; and (ii) Simulating 3D brittle crack growth. The results in this thesis provide significant evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

The main objective of this study is to evaluate mixed mode stress intensity factors for inclined embedded cracks in functionally graded materials. Fracture analysis of inclined cracks requires the calculation of both Mode I and Mode II stress intensity factors ( I K , II K ). In this study, k J -integral is used to calculate I K and II K . Equivalent domain integral approach is utilized to evaluate the k J - integral around the crack tip. The present study aims at developing a finite element model to study inclined crack problems in graded media under thermomechanical loading. A two dimensional finite element model is developed for inclined cracks located in a functionally graded medium. Structural and thermal problems are solved using two dimensional finite elements namely 8- noded triangles. Material properties are sampled directly at the integration points of the elements, as required by the numerical integral evaluation. The main results of the study are the stress intensity factors at the crack tip for functionally graded materials subjected to thermomechanical loading.

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Tese (Doutoramento)
IPEN/T
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

A virtual testing of double cantilever beam interlaminar fracture toughness sandwich specimens under different types of dynamic loads and loading rates is considered. The nonlinear dynamic response of those sandwich specimens being fractured during the test is numerically examined using the two-dimensional finite element model within the ABAQUSTM code. The interaction integral method is exploited to extract the dynamic stress intensity factor. Cohesive elements allocated along the face/core interface are used to simulate the dynamic fracturing of the specimens.

Structural health monitoring (SHM) is the process of using measurements of a structureâ s response to known excitations and trying to determine if damage has occurred to the structure. This also fits the description of non-destructive evaluation (NDE). The main difference is that NDE takes place while the structure is out of service and SHM is intended to take place while the structure is in service. As such, SHM provides the opportunity to provide early warning against structural failure. This thesis intends to advance the state of the art in SHM by examining two approaches to SHM: vibration based and impedance based, and to associate these with the NDE method of stress intensity factors. By examining these methods the goal is to try and answer some of the important questions in SHM process. The first is to experimentally validate a crack model and to see how small of a crack can be detected by vibration methods. The second is to use the concept of stress intensity factor to perform an SHM type of measurement to determine the remaining life of a structure once the impedance method has determined that damage has occurred. The measurement system considered consists of using several different piezoceramic materials as self-sensing actuators and sensors. The structures are a simple beam and a more complex lug element used in aircraft applications. The approach suggested here is to use the impedance and vibration methods to detect crack initiation and then to use the proposed stress intensity method to measure the stress intensity factor of the structure under consideration.
Master of Science

This thesis details an experimental study on the determination of the fracture parameters for a crack located at the interface between two dissimilar materials using the method of photoelasticity. The interface is potential1y an inherent weak spot of any composite material, structure"or adhesively bonded joint. Accurate description of the state of stress at the crack tip is required for strength prediction. The concept of the complex stress intensity factor is used to characterise the elastic crack tip stress field for an interface crack. Complex stress intensity factors and their moduli have been measured experimental1y for standard bimaterial crack geometries using the wel1 established technique of photo elasticity. Bimaterial specimens comprising aluminium al10y and epoxy resin components were used. This creates a large material mismatch at the interface and al10ws data to be col1ected from the epoxy component of the specimen using transmission photoelasticity. An automated ful1 field photoelastic technique was developed to significantly reduce the data col1ection time. The technique comprises elements from the approaches of three wavelength and phase stepping photoelasticity and is a significant improvement on techniques previously available. Stress intensity factors were determined by fitting a theoretical stress field solution for the bimaterial crack to the experimental data. A computational routine automatical1y selects the region of best fit between the experimental data and the theoretical solution. This data is then used to determine the complex stress intensity factor and its modulus value. In order to provide a robust fit between the experimental data and the theoretical field solution a weighting function was incorporated into the routine. The measured bimaterial stress intensity factors are compared with those determined experimental1y for equivalent homogeneous specimens made from epoxy resin. The differences between the two are then discussed. The experimental results agree with the wel1 known concept that tension and shear effects are inherently coupled at the crack tip. However, the effects of changing the load angle with respect to the interface also demonstrate that some contrasts exist with known numerical solutions.

Semi-circular specimens (SCB) under three point-bending which are commonly used for fracture testing of rocks were used here for fracture mechanics tests. A total of 65 specimens were tested by using Ankara andesite rock. Investigations including the effects of initial notch thickness, different loading span ratios (S/R), flattened loading end, and little dimensional variations when preparing the specimens were carried out. Stress intensity factors for specimens with different geometries were computed individually by using a 3D finite element program ABAQUS. Specimens with a preliminary notch thickness varying from 0.84 to 3.66 mm were tested under three point bending. For a second group of specimens loading span was changed and fracture toughness variation was studied. Another change in the specimen geometry was made by machining a flat loading end at the upper load application point. Fracture toughness values were computed using the stress intensity values computed from numerical modeling and failure loads from the experiments. It was found that up to 2 mm fracture toughness was not affected by variations in the thickness of preliminary notches. Fracture toughness was not affected by changing the loading span. For specimens with flat loading ends, fracture toughness was about 16% lower than the value found from regular SCB type specimens loaded at a point at the top by a steel roller. As a result of about 46 experiments average fracture toughness of Ankara Gö
lbasi andesite was found as 1.36 MPa .

Modified Ring specimens are of the shape of discs having a hole inside and flattened ends. These specimens are used for determination of Mode I fracture toughness. Finite element program, named ABAQUS, is used for numerical modeling for finding stress intensity factors. Varying disc geometries were used for the experiments and numerical modeling in which size of the flat ends, radius of the hole inside, and external radius of the specimen were varied. Experiments were done by using pink Ankara andesite. Effects of internal hole radius, external disc radius and size of the flat ends on both stress intensity factor and fracture toughness were studied. In order to compare the results, fracture tests with semi-circular specimens under three point bending (SCB) were also performed. From a similar previous study, fracture toughness values of gray andesite were recalculated and compared to the fracture toughness values of pink andesite for varying geometrical factors. Size effect studies were performed as well for varying diameter of core specimens.Fracture toughness values of andesite were found to increase with increasing specimen size. Fracture toughness of 100 mm specimens was determined as 1.11±
0.07 MPa&
#8730
m, whereas fracture toughness of 75 mm specimens was 0.96±
0.08 MPa&
#8730
m. 100 mm or larger diameter specimens were suggested for the fracture toughness determination with the modified ring tests.