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Variational modelling of cavitation and fracture in nonlinear elasticityHenao Manrique, Duvan Alberto January 2009 (has links)
Motivated by experiments on titanium alloys of Petrinic et al. (2006), which show the formation of cracks through the growth and coalescence of voids in ductile fracture, we consider the problem of formulating a variational model in nonlinear elasticity compatible both with cavitation and the appearance of discontinuities across two-dimensional surfaces. As in the model for cavitation of Müller and Spector (1995) we address this problem, which is connected to the sequential weak continuity of the determinant of the deformation gradient in spaces of functions having low regularity, by means of adding an appropriate surface energy term to the elastic energy. Based upon considerations of invertibility, we derive an expression for the surface energy that admits a physical and a geometrical interpretation, and that allows for the formulation of a model with better analytical properties. We obtain, in particular, important regularity results for the inverses of deformations, as well as the weak continuity of the determinants and the existence of minimizers. We show, further, that the creation of surface can be modeled by carefully analyzing the jump set of the inverses, and we point out some connections between the analysis of cavitation and fracture, the theory of SBV functions, and the theory of Cartesian currents of Giaquinta, Modica, and Soucek. In addition to the above, we extend previous work of Sivaloganathan, Spector and Tilakraj (2006) on the approximation of minimizers for the problem of cavitation with a constraint in the number of flaw points, and present some numerical results for this problem.
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Nízkocyklové a vysokocyklové únavové vlastnosti ADI / Low Cycle and High Cycle Fatigue Properties of Austempered Ductile IronZapletal, Josef January 2011 (has links)
The thesis is focused on assessment of fatigue behaviour of austempered ductile iron with nodular graphite. Optimal period of transformation was determined based on the best combination of stress and strain characteristics established by tensile test. Cyclic response and low-cycle fatigue life were studied under both stress-control and longitudinal strain-control mode at room temperature. For both modes, shapes of cyclic hardening curves are dependent on stress amplitude. Cyclic deformation curves (CDC) were fitted by power regression function. Results were compared with CDC established by multiple step test in both modes with verification of the influence of cyclic creep (high stress levels, stress-control mode). Experimental data of S-N curves are in agreement with the Manson-Coffin and the Basquin law. Fatigue and cyclic parameters were compared. Fatigue life time in high-cycle fatigue region was determined. Experimental data were fitted by suitable regression functions. Regression parameters and fatigue limit were established by means of each regression function. Experimental data in low- and high-cycle fatigue regions were used to construct S-N curve and to determine relevant parameters. Discontinuity of experimental data was not observed. Low-cycle fatigue behaviour was predicted. Approximation of tolerance bands was realized in high-cycle and both high and low cycle fatigue regions.
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Ductile fracture criteria in multiaxial loading – theory, experiments and application / Ductile fracture criteria in multiaxial loading – theory, experiments and applicationŠebek, František Unknown Date (has links)
Práce se zabývá tvárným lomem, který je výsledkem víceosého kvazi-statického monotónního namáhání doprovázeného rozsáhlými plastickými deformacemi, přičemž pro degradaci materiálu je uvažován lokální přístup. Ve výpočtech o rozvoji poškození rozhodují použité mezní podmínky tvárného lomu. Tyto byly teoreticky studovány v úvodu práce a po výběru vhodné mezní podmínky byl stanoven postup kalibrace. Dále byl rozpracován plán měření a realizovány zkoušky při pokojové teplotě na slitině hliníku 2024-T351, zahrnující tah, krut a tlak, pro studium rozvoje poškození a věrohodnou kalibraci vybraného fenomenologického modelu tvárného porušování, vyjádřeného pomocí lomového přetvoření a závislého na hydrostatickém tlaku a deviátoru tenzoru napětí. Mezní podmínka tvárného lomu byla posléze svázána s podmínkou plasticity. Plasticita byla pro zkoumaný materiál uvažována ve tvaru zohledňujícím i stav třetího invariantu deviátoru tenzoru napětí. Celý navržený přístup, plně aplikovatelný na víceosé úlohy, byl implementován pomocí uživatelské rutiny do komerčního programu založeného na explicitní variantě metody konečných prvků. V závěru práce je předložena aplikace navrženého přístupu k modelování tvárného porušování v podobě verifikace na vybraných zkušebních testech, z níž plynou závěry a doporučení pro další práci.
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Caracterização das propriedades mecânicas e metalúrgicas do aço API 5L X 80 e determinação experimental de curvas J-R para avaliação da tenacidade a fratura. / Experimental investigation of ductile crack growth in an API 5L X80 pipeline steel using J-R curves.Silva, Maurício de Carvalho 29 October 2004 (has links)
Caracterizar propriedades de resistência à propagação de trinca em materiais dúcteis é um elemento central em métodos de avaliação de integridade estrutural de dutos destinados ao transporte de gás, petróleo e seus derivados que utilizam os aços ARBL. Sendo assim, o objetivo deste trabalho foi estudar as propriedades de fratura dúctil do aço API 5L X80, através da obtenção da curva de resistência à propagação estável de defeitos (curvas J-R) do material. O ensaio de tenacidade à fratura para obtenção da curva J-R foi conduzido utilizando a técnica do corpo-de-prova único (single specimen) empregando o método da flexibilidade no descarregamento (unloading compliance), segundo a norma de ensaios ASTM E1820-96. Os corpos-de-prova compactos C(T) apresentaram espessura B=15mm, largura W=2B e uma relação aproximada entre o tamanho de trinca (a) e a largura, a/W=0,6. O ensaio foi conduzido numa máquina universal de ensaios (MTS) servo-controlada e capacidade máxima de 250kN. Adicionalmente, foram conduzidos ensaios convencionais de tração (limite de escoamento 550MPa, limite de resistência 676MPa e alongamento total em 50mm 27%), ensaios de impacto Charpy (energia absorvida de 220J à 0ºC sentido longitudinal) e análises metalográficas (microestrutura refinada composta por ferrita, colônias de perlita e presença do constituinte MA). Tais caracterizações permitirão uma maior precisão na comparação da curva J-R do aço API 5L X80 em estudo com estudos futuros de tenacidade à fratura. / Assessments of crack growth resistance in ductile materials play a key role in structural integrity procedures for high strength, low alloy (HSLA) pipeline steels commonly employed in gas and petroleum trasmission systems. This work presents an investigation of the ductile tearing properties for an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves (J-R curves) for the material. Testing of the X80 pipeline steel employed compact tension (C(T)) fracture specimens to determine the J-R curves based upon the unloading compliance method using a single specimen technique in accordance with the ASTM E1820 standard procedure. The C(T) specimens have thickness B=15mm, width W=2B and a ratio between crack size (a) and width, a/W=0,6. The experimental tests utilized a 250 kN MTS universal machine. Conventional tensile tests were also performed to determine the tensile properties for the tested material: yield strength of 550MPa, tensile strength of 676MPa and elongation of 27% (gage length of 50 mm). The Charpy V-notch impact tests also provided and absorbed energy of 220J at 0ºC. The metallographic analysis showed colonies of perlite and MA constituent islands in a ferrite matrix. This experimental characterization provides additional toughness and mechanical data against which the general behavior of X80 class pipeline steel can be compared.
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CARACTERIZAÇÃO MECÂNICA E TRANSIÇÃO FRÁGIL-DÚCTIL EM MATERIAIS VITROCERÂMICOSMathias, Ivan 01 April 2015 (has links)
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Previous issue date: 2015-04-01 / Fundação Araucária de Apoio ao Desenvolvimento Científico e Tecnológico do Paraná / In this work two vitreous systems are studied, the lithium disilicate (LS2) and sodiumcalcium-silica with stoichiometry 2Na2O.CaO.3SiO2 (2N1C3S) and the glassceramics
formed from these by heat treatment. Several properties were determined for the two systems as a function of crystallized volume fraction, from glass to fully
crystallization (100%), highlighting the fracture toughness and the brittle-ductile transition, with the last two determined only for the LS2 glass-ceramic. Hardness and
elastic modulus were obtained for the two glass-ceramics and their values increase with the crystallized volume fraction in the glass ceramic, with the exception of
hardness of 2N1C3S, which has its maximum for the crystallized volume fraction of 9%. Thermal expansion coefficients were determined and are larger in the LS2 glassy phase and in the 2N1C3S crystalline phase, thereby generating mean residual stresses obtained by Selsing model of -76 MPa for the LS2 (compression in the crystal) and 232 MPa for the 2N1C3S (traction in the crystal). The indentation fracture toughness was also determined for the two systems using the Anstis' and Niihara's models. The results show an increase of indentation fracture toughness
with the crystalline volume fraction for LS2 glass-ceramic and also a dependence with indentation load. As for the 2N1C3S glass-ceramic, indentation fracture toughness
are reduced at intermediate crystalline fractions, which is attributed to residual stresses arising from the difference between the thermal expansion mismatch between the glass and the crystalline phases. LS2 glass-ceramic flexural strength increases with the crystalline fraction, from 103 ± 3 MPa for the glass to 260 ± 20 MPa for the fully crystallized sample. Without the removal of the crystallization surface layer, this value rises to 290 ± 20 MPa. The increase in flexural strength in the first 20% of the crystallized fraction is more pronounced. As the size of the precipitates was kept constant, this increase can be related only to the increase in the crystallized fraction. The residual stress in the matrix, the critical radius of
spontaneous cracking of the crystals and the crack mean free path between the precipitates were considered in the analysis of the increase in flexural strength. The existence of pores in the samples was a factor that limited its resistance. The fracture toughness (KDTIC) a function of the crystallized fraction was determined for LS2 glassceramics using the double torsion technique. It was found that KDTIC increases with the crystallized fraction, from 0.75 MPa.m1/2 for the glass to about 3.50 ± 0.05
MPa.m1/2 for the fully crystallized sample, a significant increase of approximately five times. Several factors were analyzed as possible causes of the increase in KDTIC. The
experimental data are better adjusted with a recently proposed model with one adjustable parameter that relates the ratio of the crystal and glass areas to the
crystallized volume fraction. The brittle-ductile transition (BDT) of LS2 glass and glass-ceramic samples (39% crystallized volume fraction) were determined for three
different strain rates. BDT temperatures were determined for each strain rate.Activation energies of BDT for the glass and glass-ceramic were obtained, which were 5.2 ± 0.2 eV and 7 ± 2 eV. It was found that BDT activation energy in glass resembles the activation energy of the LS2 viscous flow, thus concluding the BDT in LS2 is governed by viscous flow of the glass matrix. Finally, the fact of the activation energy of the glass ceramic be larger than the glass was attributed to the fact that the viscosity of the vitreous matrix is "hindered" by the presence of crystalline
precipitates. A viscosity model of a rigid spheres composite was used as an analogy to explain this observation. / No presente trabalho são estudados dois sistemas vítreos, o dissilicato de lítio (LS2) e o soda-cal-sílica de estequiometria 2Na2O.CaO.3SiO2 (2N1C3S), bem como os
vitrocerâmicos formados a partir destes através de tratamentos térmicos. Diversas propriedades foram determinadas para os dois sistemas em função da fração
cristalizada, desde vidro até os 100%, com destaque para a tenacidade à fratura e a transição frágil-dúctil, sendo estas últimas determinadas somente para o LS2. Dureza
e módulo de elasticidade foram obtidos para os dois sistemas e seus valores aumentam com a fração volumétrica cristalizada no vitrocerâmico, com exceção da
dureza no 2N1C3S, que tem seu máximo para a fração cristalizada de 9%. Os coeficientes de expansão térmica foram determinados e são maiores na fase vítrea
do LS2 e na fase cristalina do 2N1C3S, gerando assim tensões residuais médias obtidas pelo modelo de Selsing de -76 MPa para o LS2 (compressiva no cristal) e
232 MPa para o 2N1C3S (trativa no cristal). A tenacidade à fratura por indentação (KC) foi determinada também para os dois sistemas, sendo utilizados os modelos de
Anstis e Niihara. Os resultados mostram um aumento com a fração cristalina para o LS2 e também uma dependência com a carga utilizada no teste. Já para o 2N1C3S,
os valores de KC sofrem uma redução em frações cristalinas intermediárias, comportamento atribuído às tensões residuais oriundas da diferença entre os
coeficientes de expansão térmica e anisotropias elásticas do material. Os ensaios de resistência à flexão mostraram que para o LS2 a resistência aumenta com a fração
cristalina, passando de 103 ± 3 MPa para o vidro para 260 ± 20 MPa para a amostra totalmente cristalizada. Se não removermos a camada de cristalização superficial,
este valor sobe para 290 ± 20 MPa. O aumento da resistência à flexão nos primeiros 20% da fração cristalizada é mais pronunciado. Como o tamanho dos precipitados foi mantido constante, esse aumento pode ser relacionado apenas ao aumento na fração cristalizada. A tensão residual na matriz, o raio crítico dos cristais para
trincamento espontâneo e o livre caminho médio da trinca entre os precipitados foram considerados na análise do aumento da resistência à flexão. A existência de
poros nas amostras foi um fator que limitou a sua resistência. Caso amostras sem poros fossem feitas, um aumento em torno de 20 a 30% da resistência seria obtido. A tenacidade à fratura (KDTIC) foi determinada para o LS2 pela técnica de torção dupla em função da fração cristalizada. Foi verificado que KDTIC aumenta com a fração cristalizada, passando de 0,75 MPa.m1/2 para o vidro para cerca de 3,50 ±0,05 MPa.m1/2 para a amostra totalmente cristalizada, um aumento significativo de
aproximadamente cinco vezes. Diversos fatores foram apontados como possíveis causas do aumento da tenacidade e foi verificado que os fatores considerados de
forma isolada não são suficientes para descrever completamente o aumento na tenacidade. Os dados experimentais são melhor ajustados com um modelo de um parâmetro de ajuste recentemente proposto que relaciona a razão entre as áreas dos cristais e do vidro na superfície de fratura com a fração cristalizada. A transição
frágil-dúctil (TFD) de amostras vítreas e vitrocerâmica (39% fração cristalizada) de LS2 foram determinadas para três taxas de deformação. Foram determinadas as
temperaturas de TFD para cada uma das taxas e foi verificada uma dependência com a taxa de deformação. Foram calculadas as energias de ativação para a TFD
no vidro e vitrocerâmico, sendo elas de 5,2 ± 0,2 eV e 7 ± 2 eV. Verificou-se que a energia de ativação da TFD no vidro se assemelha a energia de ativação do
escoamento viscoso do LS2, concluindo assim que a TFD no LS2 é governada pelo escoamento viscoso da matriz vítrea. Por fim, o fato da energia de ativação do
vitrocerâmico ser maior que do vidro foi atribuída ao fato de que a viscosidade da matriz vítrea seria "dificultada" pela presença dos precipitados cristalinos. Um modelo de viscosidade de um compósito com esferas rígidas foi utilizado como analogia para explicar essa observação.
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Déformation et rupture dans les roches tendres et les sols indurés : comportement homogène et localisationBésuelle, Pierre 23 June 1999 (has links) (PDF)
La localisation des déformations sous forme de bandes de cisaillement dans des roches tendres et des sols indurés est étudiée par une approche expérimentale et théorique :<br /><br />L'étude expérimentale porte sur trois matériaux de caractéristiques différentes : un grès des Vosges, une siltite du Gard et une marne tendre de Beaucaire. On décrit d'abord la mise en opération d'une cellule triaxiale à haute pression et le développement d'une instrumentation de mesure des déformations. On présente ensuite une campagne d'essai sur un grès des Vosges jusqu'à des confinements de 60 MPa. L'étude concerne le comportement homogène de la roche sur des chemins de compression, extension et isotropes, la détection de la localisation, la caractérisation des structures localisées par une observation macroscopique, des mesures tomodensitométriques et une analyse microstructurale quantitative. Sur une siltite du Gard, plus raide que le grès, une étude de l'évolution de la fracturation de l'initiation jusqu'à la ruine de l'éprouvette est menée en utilisant la stéréophotogrammétrie de faux relief. Pour la marne de Beaucaire, le comportement normalement consolidé est exploré en réalisant des mesures de perméabilité au cours de la déformation, en régime isotrope ou déviatoire.<br /><br />L'étude théorique présente la nouvelle loi CloE Roche développée spécifiquement pour les roches tendres à partir du modèle de lois incrémentales non-linéaires hypoplastiques CloE. Elle prend en compte une dépendance du comportement en volume vis-à-vis de la contrainte moyenne. L'identification de la loi est réalisée sur le grès des Vosges. Une analyse paramétrique d'un critère explicite de bifurcation en mode localisé prévoyant le moment d'apparition et l'inclinaison des bandes de cisaillement est réalisée pour obtenir un calage des résultats théoriques de bifurcation sur les expériences. Cette démarche illustre l'esprit de la loi, qui considère les observations de localisation comme un élément de calage de ses paramètres.
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Accommodation du mouvement relatif entre l'Inde et la Sonde depuis la faille de Sagaing (Birmanie) jusqu'à la Syntaxe Est HimalayenneSocquet, Anne 19 December 2003 (has links) (PDF)
Dans cette thèse, sont présentées la façon dont est accommodé le mouvement relatif entre les blocs Inde et Sonde à l'actuel ainsi que l'évolution de la déformation de la Zone de Cisaillement Est Indienne depuis le cénozoïque.<br />J'ai utilisé une approche pluridisciplinaire, basée sur la combinaison de la géodésie spatiale et de la géologie structurale, pour répondre à ces questions. Le GPS (Global Positioning System) permet de quantifier les déplacements relatifs des plaques ainsi que les mouvements intra-continentaux instantanés. La cartographie de failles à partir d'images satellitaires et les données structurales de terrain permettent d'identifier les structures tectoniques sur lesquelles ces déplacements ont été accommodés au cours du temps, ainsi que le type de déformation qui leur est associé.<br />J'ai pu contraindre le pôle de rotation entre les plaques Inde et Sonde. Leur mouvement relatif à la frontière n'est pas accommodé sur une seule faille isolée, mais sur plusieurs structures discrètes affectant une bande large d'environ 500 km, correspondant géographiquement à la Birmanie. La faille de Sagaing, intersismiquement bloquée, n'accommode que 18 mm/an en décrochement dextre. La partie restante de la déformation est sans doute prise dans le prisme indo-birman, aussi bien en décrochement qu'en chevauchement.<br />Au nord, le système partitionné birman se connecte à la Syntaxe Est Himalayenne. La transition entre ces deux systèmes est assurée, au Yunnan Occidental (Chine), par la rotation de microblocs le long de failles sénestres NE-SW, depuis le pliocène.<br />Auparavant, entre l'éocène et le miocène, la zone de cisaillement Shan Scarp - Gaoligong Shan constituait la limite majeure dextre entre l'Inde et l'Indochine tandis que les massifs de l'Ailao / Diangcan Shan et de la Chong Shan étaient cisaillés en sénestre, autorisant un déplacement du bloc Indochinois vers le SE.
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Constraint Effects On Stationary Crack Tip Fields In Ductile Single CrystalsPatil, Swapnil D 11 1900 (has links)
In order to understand and predict the fracture behaviour of polycrystalline materials from a fundamental perspective, it is important to first investigate plastic deformation at a crack tip in a ductile single crystal. In this context, it may be noted that when the crack opening displacement is much less than the grain size, the crack tip fields are entirely contained in a single grain. Further, some key structural components are being fabricated in single crystal form. For example, blades in high pressure turbines of jet engines are made of single crystals of Nickel-based superalloys. In view of the above considerations, a combined experimental and computational study of the crack tip stress and strain fields in FCC single crystal is carried out in the present work.
The effect of constraint level, which is characterized by the T-stress under mode I, plane strain small scale yielding conditions, on the near-tip response is first analyzed for a crystal orientation in which the crack plane coincides with (010) and ¯the crack front lies along[101]direction. A family of finite element solutions are generated by employing a boundary layer approach within continuum crystal plasticity framework. The results show that the near-tip deformation field, especially the development of kink and slip shear bands, is sensitive to the constraint level. On imposition of negative T-stress, a significant drop in the hydrostatic stress level is noticed in the region ahead of the tip. This suggests loss of crack tip constraint with negative T-stress, which is akin to isotropic plastic solids. The reason for the loss of crack tip constraint is traced to the occurrence of an elastic sector near the notch tip. The results also show that a two-parameter (such as K-T or J-Q) characterization of near-tip fields is necessary to accommodate different constraint levels in FCC single crystals.
The results of the boundary layer formulation are used to guide the construction of asymptotic solutions near the crack tip corresponding to various constraint levels in elastic-perfectly plastic FCC single crystal. Two families of alternate asymptotic solutions are constructed by introducing an elastic near-tip sector. These families of stress fields are parameterized by the normalized opening stress ahead of the tip, τA22/τo, where τo is the critical resolved shear stress, and a quantity (p) which characterizes the coordinates of the point where elastic unloading commences in stress plane. The results show that the stress distribution corresponding to each member of these families, as well as the trajectories in stress plane as the crack tip is traversed, agree well with finite element results for a certain value of T-stress.
In order to validate the above numerical and analytical solutions, the nature of crack tip deformation in aluminium single crystals is examined experimentally in a high constraint three point bend (TPB) specimen and in a low constraint single edge notch tensile (SENT) geometry. These experiments provide evidence, based on in-situ Electron Back Scattered Diffraction (EBSD) of the existence of kink shear bands (involving lattice rotation) exactly as predicted by Rice [J.R. Rice, Mech. Mater. 6 (1987) 317] and the present finite element analysis. The experimental investigation of a low constraint SENT geometry is also supplemented by 3D finite element computations based on continuum crystal plasticity. These computational results enable assessment of 3D effects near the tip.
Finally, the effects of different lattice orientations (especially ones for which the slip systems are not symmetric with respect to the notch line) on the near-tip fields are studied pertaining to various constraint levels. The results obtained for different orientations show that the near-tip deformation field is sensitive to the constraint level. The stress distribution and the size and shape of plastic zone near the notch tip are also strongly influenced by the level of T-stress. It is clearly established that ductile single crystal fracture geometries, would progressively lose stress triaxiality with increase in negative T-stress irrespective of lattice orientation. Also, the near-tip field is shown to be part of a family which can be characterized by two parameters (such as K – T or J - Q).
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Multi-scale simulation of crack propagation in the ductile-brittle transition region / Mehrskalensimulation der Rissausbreitung im spröd-duktilen ÜbergangsbereichHütter, Geralf 03 September 2013 (has links) (PDF)
In the present thesis the crack propagation in the ductile-brittle transition region is studied on two scales with deterministic models. In the macroscopic model the ductile failure is described by a non-local Gurson-model whereas the discrete void microstructure is resolved around the crack tip in the microscopic model. The failure by cleavage is not evaluated by means of a post-processing criterion but is modeled equivalently using a cohesive zone model on both scales. Thus, cleavage is not a priori identified with unstable crack propagation but the transition between stable and unstable mode of propagation is a result of the simulation. The problem of handling completely failed material within the framework of non-local damage models is pointed out. A method to overcome this problem is proposed and successfully applied.
The case of contained plastic yielding at the crack tip is addressed with a modified-boundary layer model. The macroscopic simulations reproduce many features which are known from experiments like the formation of stretch zones, cleavage after initial ductile tearing, pop-ins with crack arrest, among others. The microscopic simulations substantiate the understanding of the macroscopically observed behavior.
Systematic parameter studies are performed. Starting with considerations on the limit cases like pure ductile failure or the lower-ductile brittle transition region allows to separate the effects of the different constitutive parameters. Based on these results, a methodology is proposed to extract the macroscopic material parameters from experiments. This scheme is successfully applied to experimental data from literature. The results show that the behavior of a low-constraint specimen can be reliably predicted with the parameters extracted from a high-constraint specimen. / In der vorliegenden Arbeit wird die Rissausbreitung im spröd-duktilen Übergangsbereich auf zwei Skalen mittels deterministischer Modelle untersucht. Das duktile Versagen wird im makroskopischen Modell durch ein nichtlokales Gurson-Modell beschrieben, während im mikroskopischen Modell die Porenmikrostruktur im Bereich um die Rissspitze diskret aufgelöst wird. Das mögliche Versagen durch Spaltbruch wird nicht, wie üblich, nachträglich durch ein spannungsbasiertes Kriterium bewertet. Stattdessen wird der Spaltbruch auf beiden Skalen durch ein Kohäsivzonenmodell abgebildet. Somit wird die Spaltbruchinitiierung nicht a priori mit instabiler Rissausbreitung gleichgesetzt. Vielmehr ist die Stabilität der Rissausbreitung ein Ergebnis der Simulationen. Außerdem wird das Problem der der Handhabung vollständig ausgefallenen Materials im Rahmen nichtlokaler Schädigungsmodelle herausgestellt. Es wird eine Methode vorgestellt, dieses Problem zu behandeln und erfolgreich angewendet. In den Simulationen wird der Fall vollständig eingebetteten, plastischen Fließens untersucht. Die Simulationen mit dem makroskopischen Modell geben viele Effekte wieder, die aus Experimenten bekannt sind. Dazu zählen die Ausbildung von Stretchzonen, die Spaltbruchinitiierung nach anfänglichem, duktilem Reißen oder lokale Instabilitäten mit Rissarrest. Die mikroskopischen Simulationen tragen zum Verständnis des makroskopisch beobachteten Verhaltens bei. In der vorliegenden Arbeit werden systematische Parameterstudien durchgeführt. Zunächst werden Grenzfälle wie das rein duktile Versagens oder der Spaltbruch in Abwesenheit der Mikroporen untersucht, um die Einflüsse der einzelnen Materialparameter abzugrenzen. Ausgehend von diesen Ergebnissen wird eine Prozedur vorgeschlagen, die Materialparameter des makroskopischen Modells Schritt für Schritt aus Experimenten zu bestimmen. Diese Prozedur wird erfolgreich auf experimentelle Daten aus der Literatur angewendet. Die Ergebnisse zeigen, dass es das entwickelte Modell erlaubt, das Verhalten einer Bruchmechanikprobe mit geringer Dehnungsbehinderung an der Rissspitze mit denjenigen Materialparametern vorherzusagen, die an Proben mit einer hohen Dehnungsbehinderung ermittelt wurden.
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Effect Of Free-Volume On The Fracture And Fatigue Of Amorphous AlloysRaghavan, R 07 1900 (has links)
Bulk metallic glasses (BMGs) are a new class of structural materials and exhibit unique combinations of mechanical properties. As a result, their mechanical behavior has been an active area of scientific pursuit in the recent past and considerable emphasis has been paid to understand plastic deformation in them. It is now well accepted that shear transformation zones (STZs), aided by free volume, are the fundamental carriers of plasticity. At a microscopic level, deformation at low temperatures and high stresses tends to localize into shear bands. Most BMGs posses high fracture toughness despite high yield strengths and poor global ductility. However, the micro-mechanisms of fracture and fatigue in this new class of materials are not fully understood yet. The overall objective of this study is to provide insights into the fracture and fatigue response of amorphous alloys, which is important both from scientific and technological perspectives. The key questions we seek to answer through this study are the following. Do amorphous alloys undergo a ductile-brittle transition (DBT), and if so what are the reasons for it? What are the parameters that influence fatigue crack initiation in amorphous alloys and whether fatigue life can be improved by surface treatments? A related question is whether the BMGs are susceptible to deformation-induced crystallization (DIC). A Zr-based BMG, Zr41.2Ti13.75Cu12.5Ni10Be22.5 was utilized to conduct this study. By comparing the fracture and fatigue behaviors in the as-cast and annealed states {annealing was carried out below the glass transition temperature (Tg) because of established embrittlement effects}, we seek to provide answers for the questions posed above.
We begin by examining the influence of temperature on the toughness of BMGs. Impact toughness measurements show that the annealed samples, which are brittle at room temperature, recover the lost toughness beyond a critical temperature (TDB) and exhibit a sharp DBT. However, the hardness remains unaffected across the TDB. Fractography reveals nano-scale patterning and cleavage fracture in the brittle state, while the formation of thick vein-patterns and shear fracture are characteristics of the ductile state of the annealed samples. We explore various micro-mechanistic possibilities for explaining the features of this transition, including a critical Poisson’s ratio-toughness correlation.
Next, to understand the origins of fatigue crack initiation, we study the un-notched fatigue response of as-cast and sub-Tg annealed Zr-based BMG specimens. Because of embrittlement and nano-crystallization at the crack initiation region, the annealed specimens exhibit a lower fatigue life than the as-cast specimens. Shot-peening of the as-cast specimens did not exhibit significant improvement in their fatigue performance because of competing effects between the compressive residual stress field (CRSF) and deformation-induced softening. To further investigate surface and repeated loading effects, the tribological response of the as-cast Zr-based BMG was compared with specimens annealed above and below the Tg. A good correlation between the hardness (increasing as a function of the annealing temperature) and wear rate was obtained. The formation and peeling of the oxide layer formed during testing was the primary wear mechanism in all the specimens.
Lastly, crystallization was observed within the deformed region of the as-cast Zr-based BMG repeatedly scratched with a sharp diamond indenter. But, transmission electron microscopy (TEM) does not reveal any evidence of crystallization within the indents formed within an electron transparent film formed by laser deposition of the as-cast Zr-based BMG. Absence of crystallization in deformed regions obtained by designing critical experiments, which avoid artifacts generated during sample preparation, suggests that the occasional observation of DIC might be an exception rather than the rule in BMGs.
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