Dissertations / Theses on the topic 'Kinematic and isotropic hardening'

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Este trabalho apresenta uma teoria de vigas para metais e ligas metálicas a altas temperaturas que leva em conta o endurecimento cinemático e isotrópico induzidos pela plastificação. Apesar da não linearidade das equações constitutivas consideradas, propõe-se uma técnica numérica extremamente simples de solução, válida para diferentes tipos de carregamentos. Desta forma, é possível se fazer a baixo custo uma avaliação das tensões atuantes e das deformações permanentes induzidas por carregamentos complexos, o que é um passo fundamental no estudo da integridade de certos equipamentos industriais.
This work presents a theory of beams for metals and alloys at elevated temperature which takes into account the kinematic and isotropic hardening induced by plastic deformation. In spite of the strong non linearity of the constitutive equations, it is proposed a very simple numerical technique of solution which is valid is valid for any kind of loading. Consequently, the theory allows a low cost analysis of the stresses and strains in many structural elements used in industrial applications.

Le travail s'intéresse aux effets de l'histoire de chargement sur le comportement et la durée de vie en fatigue de deux nuances (THYSSEN et CLI)d'un acier inoxydable austénitique 304L à la température ambiante. Les essais ont été réalisés en utilisant deux catégories d'éprouvettes. Les éprouvettes de la première catégorie (vierges) ont été soumises à des essais classiques de fatigue,alors que celles de la deuxième ont subi, avant les essais de fatigue, un pré-écrouissage monotone ou cyclique en déformation imposée. Les éprouvettes vierges manifestent un adoucissement cyclique suivi d'un durcissement cyclique alors que les éprouvettes pré-écrouies ne présentent qu'un durcissement cyclique. Les résultats montrent une grande influence du pré-écrouissage qui semble bénéfique en contrainte imposée, mais néfaste en déformation imposée,même en présence d'une contrainte moyenne de compression. Ces résultats sont discutés en termes d'évolution cyclique du module d'élasticité, des écrouissages isotropes et cinématiques, et de la densité d'énergie absorbées par cycle, dans différentes configurations : avec ou sans pré-écrouissage, en contrainte ou déformation imposées...

Dans cette thèse nous étudions le comportement de composites visco-élastiques linéaire, élasto-(visco)plastiques à écrouissages cinématique linéaire ou non linéaire et isotrope, ainsi que de composites plastiquement compressibles. Pour cela, nous nous appuyons sur les principes incrémentaux variationnels introduits par Lahellec et Suquet (2007). Nous tirons également parti d’une autre formulation récemment proposée par Agoras et al. (2016), consistant en une double application de la procédure variationnelle de Ponte-Castañeda (1991). La première application de la procédure variationnelle permet, après la résolution de conditions de stationnarité, de linéariser le comportement local en prenant en compte l’écrouissage. Ceci conduit à un Milieu Linéaire de Comparaison (MLC) thermo-élastique avec un champ de polarisation hétérogène par phase. La seconde application traite de l'hétérogénéité de la polarisation et donne lieu à un nouveau MLC thermo-élastique avec un champ de polarisation homogène par phase. Le comportement effectif peut ensuite être estimé par les schémas classiques d'homogénéisation linéaire, ici les bornes de Hashin et shtrikman. Les prévisions du modèle sont comparées aux résultats disponibles dans la littérature pour différents chargements. Un bon accord a été observé entre les prédictions du modèle proposé et les simulations numériques en champs complets. De nouveaux résultats pour les composites élasto-plastiques à écrouissage isotrope et à écrouissages cinématique linéaire ou non linéaire et isotrope sont également fournis. Ils sont en bon accord avec les calculs numériques que nous avons effectués, tant à l’échelle locale que macroscopique
In this thesis we investigate the behavior of linear viscoelastic composites, elasto-(visco)plastic composites with isotropic and linear or nonlinear kinematic hardening and plastically compressible composites. We first rely on the incremental variational principles introduced by Lahellec and Suquet (2007). We also take advantage of an alternative formulation, recently proposed by Agoras et al. (2016), which consists in a double application of the variational procedure of Ponte-Castañeda (1991). The first application of the variational procedure linearizes the local behavior, including hardening, and leads to a thermo-elastic Linear Comparison Composite (LCC) with a heterogeneous polarization field inside the phases. The second one deals with the heterogeneity of the polarization and results in a new thermo-elastic LCC with a per-phase homogeneous polarization field, which effective behavior can then be estimated by classical linear homogenization schemes, the Hashin et shtrikman bounds. The predictions of the model are compared with results available in the literature for different loadings. A good agreement has been observed between the predictions of the proposed model and numerical full field simulations. New results for elasto-plastic composites with isotropic and combined isotropic and linear or nonlinear kinematic hardening are also provided. They are in good agreement with the numerical computations we carried out, at both local and macroscopic scales

Fatique life extension of nuclear powerplants lies in the search for project reserves. This work deals with the evaluation of low-cycle fatigue of nuclear installations of the VVER type and the assessment of the influence of the computational model level. Fatigue tests of austenitic steel using optical method of digital image correlation for which the evaluation procedure is designed and used is performed. Selected model of plasticity with kimenatic (Chaboche) and combinated hardening (Chaboche, Voce) are calibrated from the obtained data. Subsequently, the durability of the test specimen is determined by computational modeling for different material models. From the comparison of the results of fatigue tests with the calculation, the material models suitable for the description of fatigue life and their validity are determined.

Le travail s’intéresse aux effets d’un pré-écrouissage cyclique axial ou en torsion sur le comportement cyclique et la durée de vie en fatigue sous sollicitation axiale à température ambiante d’un acier inoxydable austénitique 304L. Les essais cycliques séquentiels à amplitude de déformation croissante ou décroissante montrent que la courbe cyclique du 304L est non-unique. Cette caractéristique est liée à la persistance de l’état microstructural généré pendant les cycles d’amplitude de déformation maximale de la première séquence. En augmentant le nombre des séquences, l’acier 304L montre une tendance vers une courbe cyclique asymptotique, l’écrouissage semble se stabiliser. Des essais de fatigue sous chargement axial ont été réalisés sur des éprouvettes vierges ou pré-écrouies en traction-compression ou en torsion. Les durées de vie ont été sensiblement réduites pour les éprouvettes pré-écrouies. Ce phénomène est lié à la formation de structures de dislocations denses héritées de la phase de pré-écrouissage. Cependant, l’augmentation de l’amplitude de déformation en fatigue réduit l’effet du pré-écrouissage
This study investigates the effects of loading history on the cyclic stress-strain curve and fatigue behavior of 304L stainless steel at room temperature. Tension-compression tests were performed ont the same specimen under controlled strain, using several loading sequences of increasing or decreasing amplitude. The results showed that fatigue life is significantly reduced by the previous loading history. A previously developed method for determining the effect of prehardening was evaluated. Microstructural analyses were also performed; the microstructures after preloading and their evolution during the fatigue cycles were characterized by TEM. The results of these analyses improve our understanding of the macroscopic properties of 304L stainless steel and can help us identify the causes of failure and lifetime reduction

In this study, a set of rules is established, which when implemented in the modeling of dilatant soils, within the framework of associative plasticity, enables very successful shear and dilatancy predictions. The proposed approach is based on a number of principles, the most important of which are: (1) The plasticity model must have a loading surface that hardens kinematically, and a failure surface that is perfectly plastic. (2) Experimental evidence shows that uniformly deformed sand samples dilate with a constant rate when they reach their ultimate strength value, while critical state is only achieved at very large strains. There is a unique point A on the loading surface that corresponds to the experimentally observed dilatation rate. The hardening rule must, therefore, ensure that the stress point approaches A as it approaches the failure surface. These principles are implemented in a plasticity model and compared to numerous published monotonic and cyclic tests, with varied stress paths, performed on a true triaxial apparatus. The agreement between experimental data and theoretical predictions is excellent.

The pre-failure behaviour of overconsolidated clays is now well known to be highly non-linear and inelastic. Conventional constitutive soil models fail to predict this observed behaviour and recently a family of elasto-plastic soil models, the kinematic hardening models, has been developed to overcome these limitations. The kinematic hardening models allow for plasticity and non-linearity to be invoked within the conventionally defined yield surface, through the introduction of kinematic surfaces. The aim of this thesis is to improve the predictions of the behaviour of overconsolidated clays, particularly the pre-failure behaviour, through the study of elasto-plastic constitutive models based on this concept. Two existing kinematic hardening models, formulated within the framework of critical state soil mechanics, were chosen to be implemented into the Imperial College Finite Element Program (ICFEP), the two-surface model developed by Al-Tabbaa (1987), and the three-surface model developed by Stallebrass (1990). Both models were generalised in order to make their implementation into a finite element code possible. Although these models form a substantial improvement in modelling the behaviour of overconsolidated clays they cannot predict a smooth transition from elastic to elasto-plastic behaviour. This feature of behaviour, which proves to be an important drawback when simulating pre-failure non-linearity, was improved by changing the hardening modulus of each model and in this way two new generalised models were formulated. The implementation of the four models into ICFEP was validated through a number of single finite element analyses. The performance of the models was then evaluated through simulation of a series of laboratory tests on overconsolidated clays and comparison of the predictions with experimental data, where possible. The models were further used in the finite element analyses of two boundary value problems. The first of these modelled an embankment founded on a soft clay deposit. The second boundary value problem involved the analyses of tunnels excavated within the heavily overconsolidated London Clay. An analysis of the twin tunnels beneath St. James's Park, London, constructed as part of the Jubilee Line Extension of the London Underground network, is also presented. The predictions of the models were compared with field data, where available.

Doutoramento em Engenharia Mecânica
In the present work, finite strain elastoplastic constitutive formulations suitable for advanced metallic materials are developed. The main goals are the correct description of the elastoplastic behaviour, including strong plastic anisotropy and cyclic hardening phenomena, in the large strain regime, as well as the development of numerically efficient algorithmic procedures for numerical implementation of the constitutive models into codes of numerical simulation by the Finite Element Method. Two different approaches are used in the derivation of the finite strain constitutive formulations, namely, hypoelasticity and hyperelasticity. On the one hand, regarding the hypoelastic-based model, particular attention is given to the development of computationally effcient forward- and backward-Euler algorithms considering distinct techniques. On the other hand, concerning the hyperelastic-based model, the focus is on the possibility of using any (quadratic or nonquadratic) yield criteria and on a new procedure that ensures that the anisotropy is correctly described in the finite strain regime. Moreover, the constitutive relations are solely expressed in the reference configuration, hence yielding symmetric tensor-valued quantities only. This symmetry, allied to an algorithm that preserves it, is crucial for the computational efficiency of the model's implementation since it reduces the storage effort and the required solver capacities when compared to the model's standard counterparts. For a better description of cyclic hardening phenomena, the developed models and corresponding algorithms, are extended to include several back stresses. This extension is carried out by considering a modified rheological model of nonlinear kinematic hardening and using additional state variables. The capabilities of the developed models for accurate reproduction of the plastic anisotropy and cyclic hardening phenomena are assessed by means of their implementation into material user subroutines of the commercial code Abaqus. The accuracy and computational efficiency of the models and numerical algorithms are compared by means of simulations of benchmarks. These benchmarks allow the models' assessment in the description of, e.g., metal forming defects such as earing and springback, as well as the comparison of the stability and precision of the numerical algorithms.
No presente trabalho, são desenvolvidas formulações constitutivas elastoplásticas para grandes deformações, adequadas a materiais metálicos avançados. Os principais objectivos deste estudo consistem na correcta descrição do comportamento elastoplástico, incluindo anisotropia plástica acentuada e fenómenos de endurecimento cíclico, no regime de grandes deformações, bem como o desenvolvimento de procedimentos algorítmicos eficientes para a implementação numérica dos modelos constitutivos em códigos de simulação numérica pelo Método dos Elementos Finitos. São usadas duas metodologias diferentes na derivação das formulações constitutivas de grandes deformações, nomeadamente, hipoelasticidade e hiperelasticidade. Por um lado, relativamente ao modelo baseado em hipoelasticidade, é dada particular atenção ao desenvolvimento de algoritmos eficientes do ponto de vista computacional, considerando técnicas particulares. Por outro lado, em relação ao modelo baseado em hiperelasticidade, a possibilidade de usar qualquer critério de cedência (quadrático ou não-quadrático) e a apresentação de um procedimento inovador, que garante a correcta descrição da anisotropia na presença de grandes deformaçães, são destacadas. Além disso, as relações constitutivas são expressas unicamente na configuração de referência, resultando no uso de apenas variáveis simétricas de segunda ordem. Esta simetria e o uso de um algoritmo que a preserva são cruciais no que diz respeito à eficiência numérica da implementação do modelo, uma vez que reduz significativamente o espaço de armazenamento e o custo computacional de cálculo, relativamente aos modelos hiperelásticos convencionais. Os modelos, e respectivos algoritmos de integração, são posteriormente alargados ao uso de múltiplos tensores das tensões inversas de modo a permitir uma melhor descrição dos fenómenos de endurecimento cíclico. Para tal, foi considerado um modelo reológico modificado de endurecimento cinemático e usadas variáveis de estado adicionais. O desempenho dos modelos desenvolvidos na reprodução precisa de anisotropia plástica e fenómenos de endurecimento cíclico é avaliado através da sua implementação no código comercial Abaqus usando subrotinas de utilizador. A precisão e eficiência computacional dos modelos e algoritmos desenvolvidos são comparados entre si através de simulações de benchmarks. Estes benchmarks permitem a avaliação dos modelos na descrição de, por exemplo, defeitos na conformação de chapas metálicas, tais como a formação de orelhas e o retorno elástico, bem como a comparação da estabilidade e precisão dos algoritmos numéricos.

A constitutive model based on rate-independent elastoplasticity concepts is developed to simulate the behavior of geologic materials under arbitrary three-dimensional stress paths, stress reversals and cyclic loading. The model accounts for the various factors such as friction, stress path, stress history, induced anisotropy and initial anisotropy that influence the behavior of geologic materials. A hierarchical approach is adapted whereby models of progressively increasing sophistication are developed from a basic isotropic-hardening associative model. The influence of the above factors is captured by modifying the basic model for anisotropic (kinematic) hardening and deviation from normality (nonassociativeness). Both anisotropic hardening and deviation from normality are incorporated by introducing into the formulation a second order tensor whose evolution is governed by the level of induced anisotropy in the material. In the stress-space this formulation may be interpreted as a translating potential surface Q that moves in a fixed field of isotropic yield surfaces. The location of the translating surface in the stress-space, at any stage of the deformation, is given by the 'induced anisotropy' tensor. A measure to represent the level of induced anisotropy in the material is defined. The validity of this representation is investigated based on a series of special stress path tests in the cubical triaxial device on samples of Leighton Buzzard sand. The significant parameters of the models are defined and determined for three sands based on results of conventional laboratory test results. The model is verified with respect to laboratory multiaxial test data under various paths of loading, unloading, reloading and cyclic loading.

Little effort has been made to apply the Critical State Soil Mechanics concept to the prediction of pavement response. The aim of this research is to apply soil mechanics principles, particularly the kinematic hardening concept, to the prediction of the response of lightly trafficked pavements to repeated loading. For this purpose, the finite element critical state program CRISP is used. A comparison is made between the predictions given by the three-surface kinematic hardening (3-SKH) model and a layered elastic analysis BISAR for the resilient deformation produced by repeated loading of a thinly surfaced pavement, and the models are found to be in good agreement. The ability of the 3-SKH model to predict soil behaviour under cyclic loading, and under one-dimensional loading, unloading and reloading is also evaluated. A comparison between model predictions and experimental data obtained by other researchers shows that the 3-SKH model over-predicts the value of K0,nc and hence shear strain during monotonic loading. This problem is magnified when the model is applied to cyclic loading behaviour where large numbers of cycles are involved. The model also predicts an accumulation of negative shear strain with increasing number of cycles under some stress conditions. This will lead to unrealistic predictions of rutting in pavements. However, the model is suitable for obtaining resilient parameters for input to a layered elastic analysis program. A new model, which is a modified version of the 3-SKH model, is therefore proposed by modifying the flow rule and the hardening moduli. This model can correctly predict the value of K0,nc and reduce the amount of shear strain predicted. The model also eliminates the problem of accumulation of negative shear strain with increasing number of cycles. The new model introduces two additional parameters, one of which can be determined by one-dimensional normal compression test, and the other by fitting a set of cyclic loading data. The new model is used to design the required thickness of granular material using the permissible resilient subgrade strain and permanent rut depth criteria during construction. It is found that the new model predicts a realistic granular layer thickness required to prevent excessive rutting, thus showing much promise for use in design of thinly surfaced pavements.

Der Vortrag beschreibt die Grundlagen der Elasto-Plastizität sowie die softwaretechnische Anwendung mit dem FEM-Programm Creo Simulate bzw. Pro/MECHANICA von PTC. Der erste Teil des Vortrages beschreibt die Charakteristika plastischen Verhaltens, unterschiedliche plastische Materialgesetze, Fließkriterien bei mehrachsiger Beanspruchung und unterschiedliche Verfestigungsmodelle. Im zweiten Vortragsteil werden Möglichkeiten und Grenzen der Berechnung elasto-plastischer Probleme mit der Software dargestellt sowie Anwendungstipps gegeben. Im dritten Vortragsteil schließlich werden verschiedene Beispiele vorgestellt, davon besonders ausführlich das Verhalten einer einachsigen elasto-plastischen Zugprobe vor und nach dem Eintreten der Einschnürdehnung
This presentation describes the basics of elasto-plasticity and its application with the finite element software Creo Simulate (formerly Pro/MECHANICA) from PTC. The first part describes the characteristics of plastic behavior, different plastic material laws, yield criteria for multiaxial stress states and different hardening models. In the second part, the opportunities and limitations of analyzing elasto-plastic problems with the FEM-code are described and user information is provided. The last part finally presents different examples. Deeply treated is the behavior of a uniaxial tensile test specimen before and after elongation with necking appears

In den letzten Jahrzehnten hat sich auf dem Gebiet der phänomenologischen Metallplastizität eine schleichende Revolution vollzogen. Dank der gestiegenen Rechenleistung, in Kombination mit ausgereiften numerischen Algorithmen, sind viele technisch relevante Problemstellungen einer zuverlässigen numerischen Analyse zugänglich gemacht worden. Beispielsweise ermöglicht die Metallumformsimulation, als häufigste Anwendung der Plastizitätstheorie, eine Analyse des Eigenspannungszustandes und der Rückfederung in plastisch umgeformten Halbzeugen und Bauteilen. Solche Simulationen sind für die Planung energie- und ressourceneffizienter Herstellungsprozesse sowie für die Ausnutzung der plastischen Tragfähigkeitsreserven von großer Bedeutung. Die Crashtest-Simulation ist die zweithäufigste Anwendung, die in der Automobilindustrie und auch zunehmend im Flugzeugbau eingesetzt wird. Aus der Notwendigkeit, das Verhalten metallischer Werkstoffe auf Bauteilebene hinreichend genau zu beschreiben, resultiert die Motivation für eine breit angelegte Studie zur Materialmodellierung. Dabei führt die beträchtliche Anzahl unterschiedlicher Phänomene und Effekte, die berücksichtigt werden müssen, zu einer großen Vielfalt von Materialmodellen. Da die Lösung komplizierter praktischer Probleme mit einem sehr großen numerischen Aufwand verbunden ist, wird der vorteilhafte phänomenologische Zugang bevorzugt. Bei der Konzeption von neuen phänomenologischen Materialmodellen müssen folgende Aspekte beachtet werden: die Genauigkeit bei der Beschreibung des Materialverhaltens; die Stabilität und Robustheit von zugehörigen numerischen Algorithmen; die numerische Effizienz; die zuverlässige Parameteridentifikation für einen möglichst großen Anwendbarkeitsbereich; die Anschaulichkeit und Einfachheit des Materialmodells. Im Allgemeinen stehen diese Anforderungen an ein "gutes Materialmodell" zwar in einem gewissen Widerspruch zueinander, bilden andererseits aber das Grundgerüst für eine systematische Studie. Obwohl sich die vorliegende Arbeit vordergründig an erfahrene Spezialisten im Bereich der Kontinuumsmechanik wendet, sind die darin präsentierten Modelle und Algorithmen auch für praktisch tätige Berechnungsingenieure von Interesse
In the last decades, a creeping revolution was taking place in the area of the phenomenological metal plasticity. Due to the increased computational power, combined with refined numerical algorithms, many of technically relevant problems are now available for the numerical analysis. In particular, the metal forming simulation is a typical application of the metal plasticity. It enables the analysis of the residual stresses and spring back phenomena in plastically deformed workpieces and components. Such analysis is advantageous for planning of energy and resource-efficient manufacturing and for exploitation of plastic reserves of bearing capacity. The crash test simulation is the second most common application of metal plasticity, highly celebrated in the automotive industry and gaining increasing popularity in the aircraft industry. The need for sufficiently accurate description of metal behaviour on the macroscale motivates wide-ranging studies on material modelling. The large number of different effects and phenomena contributes to the large manifold of material models. The current work deals with the phenomenological approach, due to its great suitability for the solution of practical problems. The following aspects should be taken into account upon the construction of new phenomenological models: the accurate description of the material behaviour, the stability and robustness of the corresponding numerical algorithms, the numerical efficiency, the reliable parameter identification for a sufficiently large application area, the clearness and simplicity of the material models. In general, these requirements imposed on a "good material model" contradict each other. In this work, however, they are complimentary to each other and build a framework for a systematic study. Although this work is written primarily for experts on the continuum mechanics, the presented models and algorithms can be of interest for practically working engineers

Die Arbeit widmet sich dem Fließverhalten von Stählen bei zyklisch inkrementeller Torsion. Dazu werden vergleichend Reineisen und der ferritisch-perlitische Stahl 42CrMo4N bei unterschiedlichen Verformungspfaden betrachtet. Vor allem in zyklischen Torsionsversuchen mit bleibendem Verformungsinkrement je Zyklus werden Fließkurvenverläufe und Verformungsverfestigung analysiert. Die Ergebnisse belegen den Einfluss des lamellaren Zementit auf das Fließverhalten des Stahls 42CrMo4N, während die Eigenschaften des Reineisens von der entstehenden Versetzungszellstruktur bestimmt werden. Die Richtungsabhängigkeit der Fließspannung und die Verläufe der Fließkurven unterscheiden sich für die betrachteten Werkstoffe deutlich. Fließortkurven dienen der quantitativen Beschreibung der Verfestigung. Die Vorgehensweise zu ihrer Ermittlung und ihre Abhängigkeit von den Versuchsbedingungen und den Verformungszuständen werden gezeigt. Bei Reineisen dominieren isotrope, bei dem Stahl 42CrMo4N kinematische Verfestigungsanteile das Fließverhalten
Ferritic-pearlitic steel 42CrMo4N and pure iron under different strain paths are compared regarding their flow behaviour. Mainly in cyclic torsion tests with resulting strain increment per cycle shear stresses and strain hardening are analysed. The results show, that the cementite lamellae determine the flow behaviour of the steel 42CrMo4N, whereas the properties of pure iron are governed by the evolving dislocation cell structure. The dependency of flow stress on the strain direction is different for the two materials. Yield surfaces describe strain hardening quantitatively. The procedure for yield point detection and the dependency of subsequent yield surfaces on experimental conditions and strain states is shown. For pure iron isotropic hardening, for steel 42CrMo4N kinematic strain hardening dominates the flow behaviour

In den letzten Jahrzehnten hat sich auf dem Gebiet der phänomenologischen Metallplastizität eine schleichende Revolution vollzogen. Dank der gestiegenen Rechenleistung, in Kombination mit ausgereiften numerischen Algorithmen, sind viele technisch relevante Problemstellungen einer zuverlässigen numerischen Analyse zugänglich gemacht worden. Beispielsweise ermöglicht die Metallumformsimulation, als häufigste Anwendung der Plastizitätstheorie, eine Analyse des Eigenspannungszustandes und der Rückfederung in plastisch umgeformten Halbzeugen und Bauteilen. Solche Simulationen sind für die Planung energie- und ressourceneffizienter Herstellungsprozesse sowie für die Ausnutzung der plastischen Tragfähigkeitsreserven von großer Bedeutung. Die Crashtest-Simulation ist die zweithäufigste Anwendung, die in der Automobilindustrie und auch zunehmend im Flugzeugbau eingesetzt wird. Aus der Notwendigkeit, das Verhalten metallischer Werkstoffe auf Bauteilebene hinreichend genau zu beschreiben, resultiert die Motivation für eine breit angelegte Studie zur Materialmodellierung. Dabei führt die beträchtliche Anzahl unterschiedlicher Phänomene und Effekte, die berücksichtigt werden müssen, zu einer großen Vielfalt von Materialmodellen. Da die Lösung komplizierter praktischer Probleme mit einem sehr großen numerischen Aufwand verbunden ist, wird der vorteilhafte phänomenologische Zugang bevorzugt. Bei der Konzeption von neuen phänomenologischen Materialmodellen müssen folgende Aspekte beachtet werden: die Genauigkeit bei der Beschreibung des Materialverhaltens; die Stabilität und Robustheit von zugehörigen numerischen Algorithmen; die numerische Effizienz; die zuverlässige Parameteridentifikation für einen möglichst großen Anwendbarkeitsbereich; die Anschaulichkeit und Einfachheit des Materialmodells. Im Allgemeinen stehen diese Anforderungen an ein "gutes Materialmodell" zwar in einem gewissen Widerspruch zueinander, bilden andererseits aber das Grundgerüst für eine systematische Studie. Obwohl sich die vorliegende Arbeit vordergründig an erfahrene Spezialisten im Bereich der Kontinuumsmechanik wendet, sind die darin präsentierten Modelle und Algorithmen auch für praktisch tätige Berechnungsingenieure von Interesse.
In the last decades, a creeping revolution was taking place in the area of the phenomenological metal plasticity. Due to the increased computational power, combined with refined numerical algorithms, many of technically relevant problems are now available for the numerical analysis. In particular, the metal forming simulation is a typical application of the metal plasticity. It enables the analysis of the residual stresses and spring back phenomena in plastically deformed workpieces and components. Such analysis is advantageous for planning of energy and resource-efficient manufacturing and for exploitation of plastic reserves of bearing capacity. The crash test simulation is the second most common application of metal plasticity, highly celebrated in the automotive industry and gaining increasing popularity in the aircraft industry. The need for sufficiently accurate description of metal behaviour on the macroscale motivates wide-ranging studies on material modelling. The large number of different effects and phenomena contributes to the large manifold of material models. The current work deals with the phenomenological approach, due to its great suitability for the solution of practical problems. The following aspects should be taken into account upon the construction of new phenomenological models: the accurate description of the material behaviour, the stability and robustness of the corresponding numerical algorithms, the numerical efficiency, the reliable parameter identification for a sufficiently large application area, the clearness and simplicity of the material models. In general, these requirements imposed on a "good material model" contradict each other. In this work, however, they are complimentary to each other and build a framework for a systematic study. Although this work is written primarily for experts on the continuum mechanics, the presented models and algorithms can be of interest for practically working engineers.

Dissertação de Mestrado Integrado em Engenharia Mecânica apresentada à Faculdade de Ciências e Tecnologia
Esta dissertação teve como principal objetivo a implementação de um modelo constitutivo que caracterizasse a resposta elastoplástica cíclica da liga de alumínio AA 7050-T6 utilizando o software de elementos finitos ADINA®.A modelação do comportamento cíclico da liga foi feita com base em resultados experimentais obtidos através de ensaios de fadiga oligocíclica efetuados em controlo de amplitude de deformação total, entre 0,6% e 1,75%, e com razões de deformação de -1, 0 e 0,5. O modelo aplicado define o comportamento plástico cíclico do material através do critério de cedência de von Mises, de duas leis de encruamento: isotrópico e cinemático, e de uma regra de fluxo associada ao critério de von Mises. Através das leis de encruamento, respetivas ao modelo constitutivo, e pela metodologia abordada por Prates, [20], obteve-se uma aproximação inicial dos parâmetros de encruamento do material, tendo-se procedido com simulações numéricas dos ensaios de fadiga num sólido cúbico tridimensional. Posteriormente efetuou-se o ajustamento dos parâmetros através da análise comparativa entre as curvas de histerese de tensão-deformação experimentais e as resultantes das simulações numéricas, tendo-se conseguido simular com sucesso a resposta cíclica da liga quando solicitada em controlo de amplitude de deformação de 1,5% a 1%, com razão de deformação -1, 0 e 0,5 e de 1,75% e 0,8%, com razão de deformação de -1 e 0. Conclusivamente, o procedimento desenvolvido é suficientemente robusto para simular satisfatoriamente as formas dos circuitos estáveis, assim como, para determinar as densidades de energia de deformação plástica e total para as diferentes amplitudes e razões de deformação.
The main objective of this study was the implementation of a constitutive model able to characterize the cyclic elastoplastic response of the AA 7050-T6 aluminum alloy using the ADINA® finite element software. The modelling of the alloy's cyclic behavior was based on experimental results from low-cycle fatigue tests performed under strain-controlled mode with total strain amplitudes between 0,6% and 1,75% and strain ratios of -1, 0 and 0,5. The model defines the cyclic plastic behavior of the material according to the von Mises yield criterion, a flow rule related to it, and two hardening laws - isotropic and kinematic. Through the respective constitutive model hardening rules and the methodology used by Prates, [20], an initial estimate of the material hardening parameters was obtained, followed by numerical simulations of the fatigue tests on a tridimensional cubic solid.Afterwards, an adjustment was made to the parameters by means of a comparative analysis between the experimental stress-strain hysteresis loops and those obtained from the numerical simulations, resulting in the successful simulation of the alloy’s behavior, of low cyclic fatigue tests, in constant amplitude strain control of 1,5%, 1,25%, 1% (with strain ratios of -1, 0, 0,5), 1,75% and 0,8% (with strain ratios of -1 and 0). In conclusion, the procedure developed is sufficiently accurate to satisfactorily simulate the stable circuits shapes, as well as to determinate the total and plastic strain energy densities for the several amplitude and strain ratios.

碩士
中華科技大學
航空機械系飛機系統工程碩士班
103
This thesis investigates elastic shakedown limit loads and elastic-plastic analysis of structures subjected to cyclic loads made of nonlinear kinematic hardening materials. In the thesis, the step-by-step analysis of the computer code ABAQUS is applied to consider elastic-perfectly plastic and kinematic hardening materials, respectively. Parametric studies are made to study the prediction of shakedown limit loads and the relationship between shakedown limit loads and plastic limit loads. Also, validations and comparisons are made between the results obtained by ABAQUS and MATALB. Moreover, Armstrong-Frederick and Chaboche kinematic hardening models are utilized in the related parametric studies

碩士
國立成功大學
機械工程學系碩博士班
100
Solder is used extensively in electronic devices for electrical interconnection. As a result of the drive for environmental protection, the toxic lead-bearing solder is being replaced with lead-free solder. A critical issue of the lead-free conversion is that reliability information of electronic components and systems using lead-free solder is scarce due to the limited experiences with these new alloys. Under typical temperature cycling conditions, thermomechanical stress-induced solder fatigue cracking is the dominant failure mode in electronic systems. In order to accurately model solder damage under the cyclic loading condition, it is important to characterize the inelastic behavior of solder under cyclic loading condition. In this research the viscoplastic behavior of Sn2.4Ag is considered by using a state variable approach. The most popular viscoplastic model used for considering solder constitutive behavior is the Anand model. The main drawback of the Anand model is that only the isotropic hardening effect is considered, but not the kinematic hardening. In order to overcome this issue, a Chaboche viscoplastic model that considers the kinematic hardening behavior is applied to model the Sn2.4Ag constitutive behavior. The model constants are determined from curve fitting constant strain rate and creep experimental results. A numerical model based on the Chaboche model is applied to simulate several load histories and compared to experimental results and other numerical results obtained from Anand model. It is observed that the Chaboche model could properly describe the transient creep response when the applied load jumps or reverses.

There exists considerable motivation to reduce vehicle weight through the adoption of lightweight materials, such as aluminum alloys, while maintaining energy absorption and component integrity under crash conditions. To this end, it is of particular interest to study the crash behaviour of lightweight tubular hydroformed structures to determine how the forming behaviour affects the axial crush response. Thus, the current research has studied the dynamic crush response of both non-hydroformed and hydroformed EN-AW 5018 and AA5754 aluminum alloy tubes using both experimental and numerical methods. Experiments were performed in which hydroforming process parameters were varied in a parametric fashion after which the crash response was measured. Experimental parameters included the tube thickness and the hydroformed corner radii of the tubes. Explicit dynamic finite element simulations of the hydroforming and crash events were carried out with particular attention to the transfer of forming history from the hydroforming simulations to the crash models. The results showed that increases in the strength of the material due to work hardening during hydroforming were beneficial in increasing energy absorption during crash. However, it was shown that thinning in the corners of the tube during hydroforming decreased the energy absorption capabilities during axial crush. Residual stresses resulting from hydroforming had little effect on the energy absorption characteristics during axial crush. The current research has shown that, in addition to capturing the forming history in the crash models, it is also important to account for effects of material non-linearity such as kinematic hardening, anisotropy, and strain-rate effects in the finite element models. A model combining a non-linear kinematic hardening model, the Johnson-Cook rate sensitive model, and the Yld2000-2d anisotropic model was developed and implemented in the finite element simulations. This combined model did not account for the effect of rotational hardening (plastic spin) due to plastic deformation. It is recommended that a combined constitutive model, such as the one described in this research, be utilized for the finite element study of materials that show sensitivity to the Bauschinger effect, strain-rate effects, and anisotropy.

Die Arbeit widmet sich dem Fließverhalten von Stählen bei zyklisch inkrementeller Torsion. Dazu werden vergleichend Reineisen und der ferritisch-perlitische Stahl 42CrMo4N bei unterschiedlichen Verformungspfaden betrachtet. Vor allem in zyklischen Torsionsversuchen mit bleibendem Verformungsinkrement je Zyklus werden Fließkurvenverläufe und Verformungsverfestigung analysiert. Die Ergebnisse belegen den Einfluss des lamellaren Zementit auf das Fließverhalten des Stahls 42CrMo4N, während die Eigenschaften des Reineisens von der entstehenden Versetzungszellstruktur bestimmt werden. Die Richtungsabhängigkeit der Fließspannung und die Verläufe der Fließkurven unterscheiden sich für die betrachteten Werkstoffe deutlich. Fließortkurven dienen der quantitativen Beschreibung der Verfestigung. Die Vorgehensweise zu ihrer Ermittlung und ihre Abhängigkeit von den Versuchsbedingungen und den Verformungszuständen werden gezeigt. Bei Reineisen dominieren isotrope, bei dem Stahl 42CrMo4N kinematische Verfestigungsanteile das Fließverhalten.
Ferritic-pearlitic steel 42CrMo4N and pure iron under different strain paths are compared regarding their flow behaviour. Mainly in cyclic torsion tests with resulting strain increment per cycle shear stresses and strain hardening are analysed. The results show, that the cementite lamellae determine the flow behaviour of the steel 42CrMo4N, whereas the properties of pure iron are governed by the evolving dislocation cell structure. The dependency of flow stress on the strain direction is different for the two materials. Yield surfaces describe strain hardening quantitatively. The procedure for yield point detection and the dependency of subsequent yield surfaces on experimental conditions and strain states is shown. For pure iron isotropic hardening, for steel 42CrMo4N kinematic strain hardening dominates the flow behaviour.

Tese de doutoramento em Engenharia Mecânica, na especialidade de Produção Tecnologica, apresentada ao Departamento de Engenharia Mecânica da Faculdade de Ciências e Tecnologia da Universidade de Coimbra
O ensaio de expansão biaxial sob pressão hidráulica continua a ser hoje em dia uma ferramenta importante de caracterização do comportamento plástico de chapas metálicas quando sujeitas a grandes deformações plásticas. A informação retirada deste ensaio não só faculta dados adicionais aos da curva tensão-deformação em tração, mas também desempenha um papel importante como informação necessária para a identificação dos parâmetros dos critérios de plasticidade mais avançados. Este trabalho foi realizado recorrendo a simulações numéricas do ensaio de expansão biaxial em matriz circular, com recurso ao programa DD3IMP. Tem como objetivo contribuir para a determinação da curva tensão-deformação de chapas metálicas em tração biaxial, de modo simples e preciso. Durante o ensaio foram analisadas a geometria e outras variáveis do ensaio, tais como, a evolução de pressão, o raio de curvatura e as trajetórias de tensão e de deformação no pólo da calote. Isto permitiu delinear algumas recomendações, de modo a melhorar o procedimento tradicional experimental de determinação da curva de encruamento, e desenvolver novos métodos diretos e inversos com o intuito de simplificar a sua avaliação. O procedimento tradicional de obtenção da curva de encruamento do ensaio de expansão biaxial em matriz circular não toma em consideração a anisotropia do material. Neste estudo analisam-se em pormenor algumas questões, tais como a geometria da calote esférica e as trajetórias de tensão e de deformação no pólo, de modo a compreender as relações entre as diferentes variáveis do ensaio em função da anisotropia do material e para diferentes comportamentos de encruamento. Isto permite uma compreensão aprofundada sobre a precisão na determinação do raio de curvatura e na espessura da chapa no pólo da calote esférica durante o ensaio, com impacto na determinação experimental da curva de encruamento do material. Foram propostos modelos analíticos para que descrevem a evolução do raio de curvatura e da espessura de chapa em função da altura de pólo. Estes modelos são baseados numa ampla análise de comportamentos de materiais, ou seja, para diferentes valores de tensão limite de elasticidade, coeficiente de encruamento, anisotropia, e também para diferentes valores de espessura inicial da chapa e geometrias circulares de matriz. As variáveis analisadas, respeitantes à geometria da matriz, são o raio da matriz e o raio de concordância da matriz. A validação dos modelos analíticos propostos foi realizada com resultados gerados numericamente e experimentais; neste último caso, foram utilizados os existentes na literatura, para várias geometrias de matriz, e os obtidos no âmbito da presente tese, com uma geometria de matriz específica. Esta formulação mostra-se adequada para simplificar a determinação experimental da curva de encruamento recorrendo ao ensaio de expansão biaxial sob pressão hidráulica. Nomeadamente, é possível evitar o procedimento experimental complexo para determinar os valores de tensão e de deformação durante o ensaio, que requer dispositivos específicos para a análise do raio de curvatura e da espessura da chapa no pólo da calote. Por fim, os presentes resultados também mostram que é possível sobrepor as curvas da evolução da pressão em função da altura de pólo e este conhecimento foi utilizado de modo a conceber uma estratégia de análise inversa para identificar os parâmetros da lei encruamento de Swift, baseada no ensaio de expansão biaxial. A sobreposição das curvas de pressão em função da altura de pólo é possível de obter com a utilização de fatores de multiplicação para a pressão e para a altura de pólo, no caso de materiais com o mesmo coeficiente de encruamento independentemente dos restantes parâmetros da lei de encruamento de Swift, da anisotropia e da espessura inicial da chapa. Além disso, a análise da evolução da pressão durante o ensaio mostrou que os valores desses fatores são sensíveis aos parâmetros da lei de Swift e à espessura inicial da chapa, sendo apenas ligeiramente dependentes da anisotropia do material. A metodologia proposta consiste em definir a melhor sobreposição entre os resultados experimentais e de referência, obtidos numericamente para materiais isotrópicos com diferentes valores de coeficiente de encruamento. Esta metodologia foi validada utilizando resultados gerados numericamente e resultados experimentais. Ela permite simplificar o procedimento experimental e não está exposta a erros relacionados com a determinação experimental da deformação no pólo da calote e a utilização da teoria de membrana na avaliação da tensão a partir da análise do raio de curvatura, que é normalmente a principal fonte de erro. The hydraulic bulge test remains nowadays an important tool for characterizing the behaviour of sheet materials submitted to large plastic deformation. Data from this test, not only provides additional information to the tensile stress-strain curve, but also plays an important role as input information when identifying the parameters of the current most advanced yield criteria. The circular hydraulic bulge test is studied by means of finite element simulations, using the in-house code DD3IMP. This work aims to contribute to the easy and accurate evaluation of stress-strain curve of sheet metals in biaxial tension. The geometry and other variables of the test, such as pressure evolution during the test, radius of curvature, strain and stress paths at the pole of the cap, were analysed. This allows to make recommendations in order to improve the traditional experimental procedure for determining the hardening curve, but also the development of new direct and inverse methodologies for simplifying its evaluation. The traditional procedure for obtaining the hardening curve from the circular bulge test does not takes into account the anisotropy of the material. This study analyses in detail issues such as the geometry of the spherical cap and the stress and strain paths at the pole, in order to understand the relationships between different variables of the test as a function of the anisotropy and for different hardening behaviours of the material. This allows the in-depth understanding about the accuracy of the assessment of thickness and radius of curvature at the pole of the spherical cap during the test, with repercussions on the experimental determination of the hardening curve of the material. Analytical models for the radius of curvature and the sheet thickness evolutions with the pole bulge height were proposed. These models are based in an extensive analysis of material Abstract vi behaviours, i.e. different values of yield stress, hardening coefficient, anisotropy, and also different values of initial sheet thickness and geometry of the circular bulge test. The geometric variables analysed are the bulge die radius and the fillet radius of the die. The validation of the proposed analytical models is performed with numerically generated and experimental results; in the latter case, results from literature, with various die geometries, and those obtained in the framework of this thesis, with a specific die geometry, were used. This formulation shows to be appropriate for simplifying the experimental assessment of the hardening curve from the hydraulic bulge test. Namely, it is possible to avoid the complex experimental procedure to determine the stress and strain values during the test, which requires specific devices for evaluating the radius of curvature and the sheet thickness at the pole of the cap. Finally, the current results also showed that it is possible to overlap the curves concerning the evolution of the pressure with the pole height, and this insight was explored in order to build an inverse strategy for identifying the parameters of the Swift hardening law, from the bulge test. The overlapping of these curves can be accomplished by using multiplying factors for the pressure and the pole height, in case of materials with the same hardening coefficient regardless of the remaining parameters of the Swift law, anisotropy and initial thickness of the sheet. Moreover, analysis of the pressure evolution during the test has shown that the values of these factors are sensitive to the parameters of Swift law and the initial sheet thickness, being only slightly dependent of the anisotropy of the material. The proposed methodology consists on choosing the best overlap between the experimental and reference results, numerically obtained for isotropic materials with various values of the hardening coefficient. It was validated using numerical generated and experimental results. The methodology allows simplifying the experimental procedure and additionally is not exposed to experimental errors related to the experimental evaluation of strain at the pole of the bulge and the use of membrane theory approach for assessment of the stress from the radius of curvature, which is usually the major source of error.
The hydraulic bulge test remains nowadays an important tool for characterizing the behaviour of sheet materials submitted to large plastic deformation. Data from this test, not only provides additional information to the tensile stress vs. strain curve, but also plays an important role as input information for identifying the parameters of the current most advanced yield criteria. The circular hydraulic bulge test is studied by means of finite element simulations, using the in-house code DD3IMP. This work aims to contribute to the easy and accurate evaluation of stress vs. strain curve of sheet metals in biaxial tension. Variables of the test, such as pressure evolution during the test, geometry of the cap, including radius of curvature and sheet thickness, strain and stress paths at the pole of the cap, were analysed. This allows to make recommendations in order to improve the traditional experimental procedure for determining the stress vs. strain curve, but also to develop new direct and inverse methodologies for simplifying its evaluation. The traditional procedure for obtaining the stress vs. strain curve from the circular bulge test does not takes into account the anisotropy of the material. The detailed analysis of issues such as the geometry of the spherical cap and the stress and strain paths at the pole, allowed to understand the relationships between such variables of the test, the sheet anisotropy and the different hardening behaviours of the material. The in-depth understanding of these relationships has repercussions on the experimental evaluation of the stress vs. strain curve of materials when using the bulge test, for which recommendations are made. Analytical models for the radius of curvature and the sheet thickness evolutions with the pole bulge height were proposed. These models are based in an extensive analysis of material behaviours, i.e. different values of yield stress, hardening coefficient, anisotropy, and also different values of initial sheet thickness and geometry of the circular bulge test. The analysed geometric variables include the bulge die radius and the fillet radius of the die. The validation of the proposed analytical models is performed both by numerically generated results and experimental results; in the latter case, results were considered not only from literature, having various die geometries, but also from an experimental equipment in the framework of this thesis, having a specific die geometry. This formulation shows to be appropriate for simplifying the experimental assessment of the hardening curve from the hydraulic bulge test. Namely, it is possible to avoid the complex experimental procedure to determine the stress and strain values during the test, which requires specific devices for evaluating the radius of curvature and the sheet thickness at the pole of the cap. Finally, the current results also showed that it is possible to overlap the curves concerning the evolution of the pressure with the pole height, and this insight was explored in order to build an inverse strategy for identifying the parameters of the Swift hardening law, from the bulge test. The overlapping of these curves can be accomplished by using multiplying factors for the pressure and the pole height, which in case of materials with the same hardening coefficient it is independent of the remaining parameters of the Swift law, anisotropy and initial thickness of the sheet. Moreover, the analysis of the pressure evolution during the test has shown that corresponding values of these factors are sensitive to the parameters of Swift law and the initial sheet thickness, being only slightly dependent of the anisotropy of the material. The proposed methodology consisted on choosing the best overlap between the experimental and reference results, which were numerically obtained for isotropic materials with various values of the hardening coefficient. Validation was performed using numerical generated results and experimental results. The methodology allows simplifying the experimental procedure and in addition is not exposed to experimental errors related to the experimental evaluation of strain at the pole and the use of membrane theory approach, for assessment of the stress from the radius of curvature, which is usually the major source of error.
FCT - Pest-C/EME/UI0285/2013