Дисертації з теми "Continual damage"

Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.02.09 – динаміка та міцність машин (13 – механічна інженерія). – Національний технічний університет "Харківський політехнічний інститут", Міністерство освіти та науки Харків, 2019. Актуальність. Машинобудівні конструкції, що застосовуються в енергетиці, працюють в умовах інтенсивних циклічних навантажень та дії агресивних зовнішніх або робочих середовищ. Тривала експлуатація конструкцій у таких умовах призводить до корозійного зношення або формування об’ємних дефектів на робочих поверхнях, стоншення стінок корпусних деталей тощо. Це призводить до появи зон додаткової набутої локалізації напружено-деформованого стану (НДС) у елементах конструкцій, що здатні суттєво відрізнятись від проектних значень, та разом із циклічним характером навантаження призводить до інтенсивного накопичення втоми матеріалу і викликає відмову. Несвоєчасне їх виявлення може стати причиною виникнення аварійних ситуацій, екологічних катастроф, завдати суттєвих споживчих збитків. Прогнозування показників надійності елементів таких конструкцій є актуальною проблемою, вирішення якої дає можливість попередити їх раптові відмови, спланувати ремонтні роботи, оцінити експлуатаційні ризики тощо. Метою дослідження є розробка розрахункових підходів до прогнозування надійності та оцінки залишкового ресурсу елементів конструкцій, що використовуються в транспортуванні енергоносіїв та в енергетичному машинобудуванні, та які мають набуті пошкодження корозійної природи на основі статистичної оцінки концентрації напружено-деформованого стану і процесів накопичення втоми. При розв’язанні сформульованих на основі вказаної мети завдань було удосконалено підхід до оцінки надійності елементів конструкцій, які використовуються в транспортуванні енергоносіїв та енергетичному машинобудуванні з корозійно пошкодженими ділянками, які дозволяють спрогнозувати можливий розвиток корозійних пошкоджень процеси накопичення втоми, що мають наступну наукову новизну: Отримані нові закономірності, щодо впливу об’ємних дефектів корозійної природи на концентрацію напружень в елементах конструкцій, які використовуються при транспортуванні енергоносіїв та в енергетичному машинобудуванні за різних параметрів цих дефектів на криволінійних ділянках конструкцій; 1. Вперше отримані статистичні оцінки щодо можливої варіації концентрації напружень в елементах конструкцій, які використовуються при транспортуванні енергоносіїв та в енергетичному машинобудуванні в умовах прогнозу можливого стохастичного розвитку корозії у часі та з урахуванням експлуатаційної варіації циклічного навантаження. 2. Знайшли подальший розвиток статистичні моделі та методи оцінки процесу розвитку пошкоджуваності при багато- та мало-цикловій втомі, що на відміну від існуючих моделей враховують випадкову зміну параметрів НДС в часі, яка викликана формуванням концентрації напружень навколо об’ємних поверхневих дефектів. 3. Вперше встановлено закономірності впливу наявності корозійних дефектів різного ступеня розвитку на прогноз надійності залишкового ресурсу елементів конструкційна основі удосконалених статистичних моделей оцінки процесу накопичення втомних пошкоджень. З використанням розробленого підходу до прогнозування надійності елементів конструкцій були вирішені наступні практичні задачі: 1. Визначено параметри пошкоджуваності та кількість циклів до відмови коліна трубопроводу з тривимірним поверхневим дефектом середніх розмірів з урахуванням експлуатаційної варіації навантаження, які мають значення в межах від 1 до 50 циклів (до 1,5 років) при максимально можливому навантажені та від 70 до 470 циклів (від 2 до 10 років) при мінімальному навантажені у трубопроводі з дефектом середніх розмірів, А у випадку дефекту, що стохастично розвивається кількість циклів до відмови складає від 42 до 700 (від 14 місяців до 20 років) при максимально можливому навантаженні. 2. Досліджено вплив композиційного бандажу на ресурс трубопроводу з дефектом середніх розмірів. Проведені розрахунки для визначення раціональних розмірів композиційного бандажу для криволінійної частини трубопроводу з дефектом із середніми розмірами. Визначено значення внутрішнього тиску, при якому еквівалентні напруження досягають границі міцності у трубопроводі з бандажем різної товщини (від 25 мм до 175 мм). Встановлено, що при наявності бандажу 75 мм при глибині дефекту менше ніж 40 % від товщини трубопроводу еквівалентні напруження зменшуються на 10 % та при максимально можливому навантаженні не виникають пластичні деформації. У випадку глибини дефекту більше ніж 40 % від товщини трубопроводу у трубопроводі еквівалентні напруження зменшуються від 25% до 50% при різних розмірах дефекту відповідно та дорівнюють границі плинності Кількість циклів до відмови при використанні композиційного бандажу збільшилась у 100 разів, що робить можливою подальшу експлуатацію трубопроводу. 3. Проведено оцінку залишкової міцності насоса, який використовується в енергетичному машинобудуванні з урахуванням зменшення товщини стінок корпусних деталей від ерозійно-корозійного зносу. Визначено НДС конструкції при стоншенні стінок корпусу від 10% до 30%, яке можливо при тривалій експлуатації. Отримані значення кількості циклів до відмови при урахуванні накопичення втомних пошкоджень та впливу експлуатаційного зносу конструкції. Об’єктом дослідження є процеси накопичення нелокалізованої втомної пошкоджуваності, а також вплив наявності та розвитку у часі локалізованих корозійних дефектів на міцність та надійність елементів конструкцій, які використовуються при транспортуванні енергоносіїв та в енергетичному машинобудуванні. Предмет дослідження – показники надійності, а також ймовірнісні характеристики параметрів НДС та втомної пошкоджуваності, які накопичуються в елементах конструкцій, що досліджуються, з урахуванням наявності та прогнозу стохастичного розвитку корозійних дефектів в них. Основна частина дисертації включає Вступ, Розділ 1 – "Аналіз сучасних підходів до вирішення задач надійності елементів конструкцій з набутими пошкодженнями", Розділ 2 – "Теоретичні основи моделювання елементів конструкцій з дефектами корозійного типу", Розділ 3 – "Імовірнісне оцінювання міцності та надійності трубопроводів із корозійними дефектами та прогноз їх залишкового ресурсу", Розділ 4 – "Аналіз можливості підвищення надійності конструкції шляхом використання композитних ремонтних накладок", Розділ 5 – "Оцінка залишкового ресурсу корпусних елементів насосів енергетичної системи" та Висновки, а також містить 72 рисунки та 18 таблиць. У Вступі обґрунтовано актуальність теми дисертації, сформульовано її мету і задачі, визначено об’єкт, предмет і методи дослідження, наукову новизну та практичну значущість роботи. У Розділі 1 представлено аналіз робіт, які спрямовані на прогнозування надійності елементів конструкцій у машинобудуванні, здійснено аналіз науково-технічної літератури щодо дослідження корозійно пошкоджених елементів конструкцій, що використовуються в транспортуванні енергоносіїв та в енергетичному машинобудуванні. Виділено основні методи для визначення залишкового ресурсу конструкцій, які використовуються в транспортуванні енергоносіїв та енергетичному машинобудуванні та мають набуті в експлуатації дефекти. Проаналізовано підходи до оцінки накопичення втомної пошкоджуваності. У Розділі 2 представлено теоретичні основи розв’язання задачі статистичної оцінки елементів конструкцій із пошкодженнями, зокрема, оцінка прогнозованих габаритних розмірів дефектів при статистичному моделюванні та визначено методологію дослідження. Наведено вирішення задачі пружно-пластичного деформування з кінематичним зміцненням при кусково-лінійній діаграмі деформування. Визначено залежності кінетики росту розмірів корозійного дефекту у трьох напрямах у часі, а також, що його габаритні розміри у фіксований момент часу, випадкові та підпорядковуються лог-нормальному закону розподілення. В рамках континуальної механіки пошкоджуваності удосконалені методи оцінки надійності та прогнозу залишкового ресурсу пошкоджених ділянок елементів конструкцій. У Розділі 3 розроблено параметричні математичні моделі визначення напружено-деформованого стану криволінійної частини трубопроводу за наявності тривимірного поверхневого дефекту корозійного характеру. Здійснено дослідження особливостей формування концентрації напружень в пошкоджених ділянках елементів конструкцій із урахуванням експлуатаційної варіації навантаження та стохастичного характеру розвитку корозійного пошкодження. З використанням розробленого підходу до прогнозування надійності елементів конструкцій визначено параметри пошкоджуваності та кількість циклів до відмови коліна трубопроводу з тривимірним поверхневим дефектом, що розвивається у часі із урахуванням експлуатаційної варіації навантаження. У Розділі 4 досліджено вплив композиційного бандажу на ресурс трубопроводу з дефектом. Для визначення раціональних розмірів композиційного бандажу проведено розрахунки криволінійної частини трубопроводу з дефектом з розмірами, які були отримані під час діагностики трубопроводу, що знаходиться в експлуатації. Здійснені розрахунки для визначення раціональних розмірів композиційного бандажу для криволінійної частини трубопроводу з дефектом із середніми розмірами. Відповідно до розробленої математичної моделі накопичення втомних пошкоджень визначено кількість циклів до відмови при використанні композиційного бандажу на криволінійній частині трубопроводу з дефектом середніх розмірів. У Розділі 5 здійснено оцінку залишкової міцності насоса, який використовується в енергетичному машинобудуванні з урахуванням зменшення товщини стінок корпусних деталей від ерозійно-корозійного зносу. На основі розробленої математичної моделі накопичення втомних пошкоджень та з використання отриманих результатів об НДС конструкції визначено параметр пошкоджуваності для усіх можливих рівнів стоншення стінки конструкції. Проведено дослідження щодо оцінки надійності даних конструкцій з урахуванням ерозійно-корозійного зносу. У Висновках зазначено науково-практичні задачі, що були розвязані в роботі, викладені найбільш важливі наукові та практичні результати, надані рекомендації щодо впровадження результатів дослідження.
Thesis for granting the Degree of Candidate of Technical sciences in specialty 05.02.09 – Dynamics and Strength of Machines (13 – Mechanical Engineering). – National Technical University, "Kharkiv Polytechnical Institute", 2019. Machine-building structures used in power engineering are worked under conditions of intense cyclic loading and the action of aggressive external or working environments. Long-term using of structures in such conditions is led to corrosion or formation of volumetric defects on working surfaces, thinning of the walls of hull parts and other. It can have led to the appearance of additional zones of localization of deformed state in structural elements that can be differ significantly from the design values, and together with the cyclic nature of the load can led to an intensive accumulation of fatigue of the material and failure. Untimely detection of that defects caused of emergencies, environmental disasters, and cause significant consumer losses. Predicting the reliability of elements of such structurals is an urgent problem whose solution makes it possible to prevent them from sudden failures, to plan repair work, to evaluate operational risks, and so on. The aim of the work is to develop computational approaches to predicting the reliability and estimation of the residual life of structural elements used in energy transportation and power engineering, which have acquired corrosive nature defects based on a statistical evaluation of the stress-strain concentration and fatigue accumulation processes. For solving the tasks formulated on the basis of the stated aim, the approaches to the estimation of the reliability of structural elements used in transportation of energy carriers and power engineering with corrosion-damaged areas has been improved, which are allowed to predict the possible development of corrosion damages and the processes of accumulation of fatigue, which have the follow scientific novelty: 1. New regularities have been obtained concerning the effect of volumetric defects of corrosive nature on the concentration of stresses in structural elements used in the transport of energy carriers and in power engineering under different parameters of these defects in curvilinear sections of structures. 2. For the first time, statistical estimate has been obtained regarding the possible variation of stress concentration in structural elements used in energy transportation and in power engineering in the conditions of forecast of possible stochastic development of corrosion in time and taking into account operational variation of cyclic loading. 3. The statistical models and methods of estimating the process of development of damage in multi- and small-cycle fatigue have been developed, which, unlike the existing models, are taken into account the random change of the deformed state parameters over time, which is caused by the formation of stress concentrations around volumetric surface defects. 4. For the first time have been established the regularities of the influence of corrosion defects of various degrees of development on the prediction of the reliability of the residual life of structural elements based on the improved statistical models of the estimation of the process of fatigue damage accumulation. Using the developed approach to predict the reliability of structural elements, the following practical problems were solved: 1. The parameters of damage and the number of cycles to failure of the elbow of the pipeline with three-dimensional surface defect of the average sizes were defined, with taking into account operational variation of load, which have values in the range from 1 to 50 cycles (up to 1.5 years) at the maximum possible load and from 70 to 470 cycles (2 to 10 years) at minimum load in the pipeline with a defect of medium size, And in the case of a defect stochastically developing number of cycles to failure is from 42 to 700 (from 14 months to 20 years) at the maximum possible load. 2. The effect of composite bandage on the mean-sized pipeline resource was investigated. Calculations have been made for determine the rational dimensions of the composite bandage for the curved portion pipeline with the mean-sized defect. The value of the internal pressure at which equivalent stresses reach the strength limits in the pipeline with a bandage of different thickness (from 25 mm to 175 mm) was determined. It is established that in the presence of a 75 mm bandage with a defect depth of less than 40% of the thickness of the pipeline, the equivalent stresses are reduced by 10% and plastic deformation does not occur at the maximum load. In the case of a defect depth is greater than 40% of the pipeline thickness in the pipeline, the equivalent stresses are reduced from 25% to 50% at different defect sizes, respectively, and equal to the yield strength. The number of cycles to failure when using a composite bandage has increased 100 times, which is making possible for the pipeline to be operated further. 3. Estimation of the residual strength of the pump used in power engineering has been made, taking into account the reduction of the wall thickness of the body parts in consequence from erosion-corrosion wear. The design deformed state was determined when the walls of the housing are thinned from 10% to 30%, which is possible for long-term operation. The values of the number of cycles to failure were obtained with taking into account the accumulation of fatigue damage and the impact of operational wear of the structure. The object of the study is the processes of accumulation of non-localized fatigue damage, as well as the influence of the presence of localized corrosion defects which is development over time on the strength and reliability of structural elements used in energy transportation and in power engineering. The subject of the study is the reliability indicators, as well as the probabilistic characteristics of the parameters of the deformed state and fatigue damage, which are accumulated in the elements of the investigated structures, taking into account the presence and prediction of stochastic development of corrosion defects in it. The main part of the dissertation includes Introduction, Section 1 – "Analysis of modern approaches to solving the problems of reliability of structural elements with acquired damage", Section 2 – "Theoretical bases of modeling elements of structures with corrosion defects", Section 3 – "Probability assessment of strength and reliability of pipeline with corrosion defects and the prediction of their residual life-time", Section 4 – "Analysis of the possibility of improving the reliability of the structure by using composite bandage", Section 5 – "Assessment of the residual life-time of the housing elements of pumps of the energy system" and Conclusions, and also contains 74 figures and 18 tables. The introduction substantiates the relevance of the dissertation topic, formulates its aim and objectives, defines the object, subject and methods of research, scientific novelty and practical significance of the work. Section 1 is presented the analysis of works aimed at predicting the reliability of structural elements in mechanical engineering, the analysis of scientific and technical literature on the study of corrosion-damaged structural elements used in energy transportation and in power engineering. The main methods for determining the residual life-time of structures used in energy transportation and power engineering and which have acquired defects were identified. Approaches to the estimation of fatigue accumulation were analyzed. Section 2 is presented the theoretical foundations for solving the problem of statistical estimation of structural elements with defects, in particular, the estimation of the predicted overall defect sizes in statistical modeling, and a research methodology is defined. The solution of the problem of elastic-plastic deformation with kinematic hardening at a multi-linear deformation diagram is presented. The dependences of the kinetics of growth of the corrosion defect sizes in three directions in time are determined, and also that its overall dimensions at a fixed moment of time are random and obey the log-normal distribution law. Within the framework of continuous damage mechanics, methods of reliability estimation and prediction of residual life-time of damaged sections of structural elements have been improved. In Section 3 the parametric mathematical models for determining the stress-strain state of the curved part of the pipeline in the presence of a three-dimensional surface defect of corrosive character are developed. The peculiarities of stress concentration formation in the damaged parts of structural elements were studied, taking into account the operational variation of the load and the stochastic nature of the development of corrosion defect. Using the developed approach to predicting the reliability of structural elements, the parameters of damage and the number of cycles to failure of the pipeline elbow with volumetric defect, which develops over time with taking into account the operational variation of the load, were determined. Section 4 is investigated the effect of composite bandage on a life-time of pipeline with defect. In order to determine the rational dimensions of the composite bandage, calculations of the curved part of the pipeline with defect with the dimensions obtained during the diagnostics of the pipeline in operation were performed. Calculations were made to determine the rational dimensions of the composite bandage for the curved portion of the mean-sized defect pipeline. According to the developed mathematical model of accumulation of fatigue damage, the number of cycles to failure using a composite bandage on a curved part of a pipeline with a defect of medium size was determined. Section 5 is assessed the residual strength of the pump used in power engineering with taking into account the reduction of the wall thickness of the body parts from erosion-corrosion wear. On the basis of the developed mathematical model of accumulation of fatigue damage and using the results obtained on the deformed state of the structure, the parameter of damage for all possible levels of thinning of the wall of the pump was determined. Research to evaluation the reliability of these structures, taking into account erosion-corrosion wear has been carried out. The conclusions are summared the scientific and practical problems that have been solved in the paper, outlined the most important scientific and practical results, and provided recommendations for the implementation of the research results.

In this thesis, the mechanical behavior of a timber joint has been studied. The main task is to model the mechanical behavior of the joint as good as possible. To be able to solve the numerical instabilities of the timber joints, a deeper look needs to be done to the modelling of the wooden material and the steel wood contact. For this thesis a previously developed 3D numerical damage model of wood has been studied. This model has been elaborated by Sandhaas(2012) and it describes crack initiation and propagation of the material based on the concepts of continuum damage mechanics. The basic material model of wood has been implemented as a user material in the UMAT subroutine of ABAQUS. The developed model is giving some numerical instabilities due to the extreme distortion of the elements. During this thesis the model has been enhanced in order to be able to represent the mechanical behavior of wood as good as possible and solve the problem of the model. The modelling outcomes were compared to the results obtained by experimental tests (ref. to Sandaas,2012).The results showed that the first model, a tension test parallel-to grain, had been enhanced. Indeed the results got closer to the experimental value than the original model’s results did. The second model represented a timber joint with slotted-in steel plate with a dowel. The analysis were done with different wood spieces (spruce, beech and azobè). Regarding the spruce, the analysis reached fairly accurate results concerning the capacity load but they were less precise regarding the displacement and the stiffness. The prediction quality was rather poor for the other two species, beech and azobè. It is necessary to find other ways to further enhance the model.Even today a model that is able to represent all three fields (stiffness, capacity load and displacement) accurately doesn’t exist. Good results of one of these lead to bad results of the others. Modelling wood then still represents an evolving challenge.

A three-dimensional, phenomenological, tensorial, isotropic, damage model is developed in the framework of continuum damage mechanics for materials whose behavior is governed by elastic deformation coupled with damage. The model was then extended to include isotropic damage for anisotropic materials, as well as rate-dependency behavior caused by damage evolution. The shortcomings of the commonly used scalar variable, as representative of isotropic damage are discussed. It is shown that isotropic damage is best represented by an isotropic tensor of rank four. The damage evolution equations are postulated using strain tensor invariants, based on decomposition of strain energy. The model simulates well the results of static and dynamic uniaxial tension tests on quasiisotropic laminated graphite-epoxy obtained in this study and results, from literature, of uniaxial compression tests on quartzite rock.
To determine the material parameters used in the model and to validate the model, a set of material and structural tests, testing a laminate containing a hole, were performed under static and dynamic loading conditions. A tensile version of the Hopkinson bar, suitable for testing of laminated composite materials, is developed to perform dynamic tests. A pulse duration of 200--250 microseconds and peak strain rates of up to 350 s--1 are obtained. Tests performed on a quasi-isotropic lay-up of graphite-epoxy show good repeatability. Comparison of Hopkinson bar tests results with results of tests performed at a quasi-static rate on a hydraulic test machine shows the rate-dependency of this lay-up of graphite-epoxy. Tensile strength and fracture strain are found to be higher for dynamic testing.
The model was evaluated for structural analysis, by implementing the model into a finite element code and analysing a laminate containing a hole. Two techniques are investigated in evaluating the model for structural analysis: stress limiter and mesh limiter. The model is found to be objective with respect to the mesh size. The predicted failure loads using both techniques conform well to the experiments and to the results obtained using one of the existing models.

The present work focuses on the formulation of a Continuum Damage Mechanics model for nonlinear analysis of masonry structural elements. The material is studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic continuum. The orthotropic behaviour is simulated by means of an original methodology, which is based on nonlinear damage constitutive laws and on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. It is based on establishing a one-to-one mapping relationship between the behaviour of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictitious space and the results are transported to the real field. The application of this idea to strain-based Continuum Damage Models is rather innovative. The proposed theory is a generalization of classical theories and allows us to use the models and algorithms developed for isotropic materials. A first version of the model makes use of an isotropic scalar damage model. The adoption of such a simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a damage model for orthotropic materials able to reproduce the overall nonlinear behaviour, including stiffness degradation and strain-hardening/softening response. The relationship between the two spaces is expressed in terms of a transformation tensor which contains all the information concerning the real orthotropy of the material. A major advantage of this working strategy lies in the possibility of adjusting an arbitrary isotropic criterion to the particular behaviour of the orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be modelled in such a way that totally different mechanical responses can be predicted along the material axes. The aforementioned approach is then refined in order to account for different behaviours of masonry in tension and compression. The aim of studying a real material via an equivalent fictitious solid is achieved by means of the appropriate definitions of two transformation tensors related to tensile or compressive states, respectively. These important assumptions permit to consider two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the fictitious space makes use of two scalar variables, which monitor the local damage under tension and compression, respectively. Such a model, which is based on a stress tensor split into tensile and compressive contributions that allows the model to contemplate orthotropic induced damage, permits also to account for masonry unilateral effects. The orthotropic nature of the Tension-Compression Damage Model adopted in the fictitious space is demonstrated. This feature, both with the assumption of two distinct damage criteria for tension and compression, does not permit to term the fictitious space as “isotropic”. Therefore, the proposed formulation turns the original concept of “mapping the real space into an isotropic fictitious one” into the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry. The model is fully formulated for the 2-dimensional case. However, it can be easily extended to the 3-dimensional case. It provides high algorithmic efficiency, a feature of primary importance when analyses of even large scale masonry structures are carried out. To account for this requisite it adopts a strain-driven formalism consistent with standard displacement-based finite element codes. The implementation in finite element programs is straightforward. Finally, a localized damage model for orthotropic materials is formulated. This is achieved by means of the implementation of a crack tracking algorithm, which forces the crack to develop along a single row of finite elements. Compared with the smeared cracking approach, such an approach shows a better capacity to predict realistic collapsing mechanisms. The resulting damage in the ultimate condition appears localized in individual cracks. Moreover, the results do not suffer from spurious mesh-size or mesh-bias dependence. The numerical tool is finally validated via a finite element analysis of an in-plane loaded masonry shear wall.

L'objectif de ce travail est de proposer un modèle de comportement avec endommagement ductile pour la simulation des procédés de mise en forme de tôles minces qui peut bien représenter le comportement des matériaux sous des trajets de chargement complexes en grandes déformations plastiques. Basé sur la thermodynamique des processus irréversibles, les équations de comportement couplé à l’endommagement tiennent compte des anisotropies initiales et induites, de l’écrouissage isotrope et cinématique et de l’endommagement isotrope ductile. Les effets de fermeture des microfissures, de triaxialité des contraintes et de l’angle de Lode sont introduits pour influencer l’évolution de l’endommagement sous une large gamme de triaxialité des contraintes. La distorsion de la surface de charge est introduite via un tenseur déviateur qui gouverne la distorsion de la surface de charge. A des fins de comparaison, les courbes limites de formage sont tracées basées sur l’approche M-K.Des essais sont conduits sur trois matériaux pour les besoins d’identification et de validation des modèles proposés. L’identification utilise un couplage entre le code ABAQUS et un programme MATLAB via un script en langage Python. Après l’implémentation numérique du modèle dans ABAQUS/Explicite et une étude paramétrique systématique, plusieurs procédés de mise en forme de structures minces sont simulés. Des comparaisons expériences-calculs montrent les performances prédictives de la modélisation proposée
The objective of this work is to propose a “highly” predictive material model for sheet metal forming simulation which can well represent the sheet material behavior under complex loading paths and large plastic strains. Based on the thermodynamics of irreversible processes framework, the advanced fully coupled constitutive equations are proposed taking into account the initial and induced anisotropies, isotropic and kinematic hardening as well as the isotropic ductile damage. The microcracks closure, the stress triaxiality and the Lode angle effects are introduced to influence the damage rate under a wide range of triaxiality ratios. The distortion of the yield surface is described by replacing the usual stress deviator tensor by a ‘distorted stress’ deviator tensor, which governs the distortion of the yield surfaces. For comparisons, the FLD and FLSD models based on M-K approach are developed.A series of experiments for three materials are conducted for the identification and validation of the proposed models. For the parameters identification of the fully coupled CDM model, an inverse methodology combining MATLAB-based minimization software with ABAQUS FE code through the Python script is used. After the implementation of the model in ABAQUS/Explicit and a systematic parametric study, various sheet metal forming processes have been numerically simulated. At last, through the comparisons between experimental and numerical results including the ductile damage initiation and propagation, the high capability of the fully coupled CDM model is proved

Dans une première partie de cette thèse, l’indentation du verre par des sphères rigides a été analysée numériquement. Un modèle d’endommagement continu anisotrope a été implanté dans un code de calculs par éléments finis pour étudier l’endommagement du verre. Trois zones ont été mises en évidence : la première est liée à la fissure conique, la deuxième à la fissure médiane et la troisième à la déformation permanente. Les directions des fissures prédites via le critère de densité d’énergie minimale ont été trouvées en très bon accord avec ceux déterminées expérimentalement dans la littérature. Le modèle utilisé dans l’analyse statique a été étendu aux cas dynamiques dans une deuxième partie de cette thèse. Une attention particulière a été portée sur la fissure conique. Un modèle d’endommagement simplifié (seulement gouverné par la contrainte principale maximale) couplé à la technique de désactivation des éléments a été utilisé pour suivre la propagation de la fissureconique sans présumer du site d’initiation. Dans une dernière partie de cette thèse, le phénomène d’érosion du verre a été étudié expérimentalement (par sablage) et numériquement. Le modèle implanté a été utilisé pour expliquer les observations expérimentales, en particulier la dépendance de l’enlèvement de matière vis-à-vis de la taille des projectiles, la distance inter-projectiles, la vitesse d’impact, l’angle d’impact et le nombre d’impacts. En modélisant plusieurs tailles et vitesse de projectiles en accord avec les paramètres expérimentaux connus, la simulation numérique d’un seul impact a prédit une quantité de matière enlevée en très bon accord avec celui mesuré expérimentalement par profilométrie
In a first part of this thesis, the indentation of glass bulk was numerically analyzed using small-sized rigid spheres loaded normally. An anisotropic continuum damage mechanics (CDM) model was implemented into a finite element program to study the damage pattern in glass. The CDM-based model pointed out three explicit sites for damage initiation: the first for cone crack, the second for median crack and the third for permanent deformation. The directions of crack propagation predicted via the criterion of minimum strain energy density were found in very good agreement with those experimentally obtained in the literature. The CDM framework used in the static modeling was extended to the dynamic cases in a second part of this thesis. A particular attention was paid to the cone crack pattern. A simplified CDM-based model (only governed by the maximum principal stress) coupled with the vanishing element technique was employed to follow the cone crack propagation without presuming the initiation site. In the last part of this thesis, the phenomenon of glass erosion was studied from experimental (sandblasting) and numerical approaches. The implemented CDMbased model was used to explain the experimental observations, especially the dependence of material removal on projectile size, inter-projectile spacing, velocity, angle and number of impacts. By modeling various projectile sizes and velocities according to those used in the experiments, the numerical simulation of a single impact predicted an amount of material removal in very good agreement with that measured experimentally using a profilometer

Thesis (Ph. D.)--West Virginia University, 2010.
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A local isotropic damage coupled hyperelastic-plastic framework is formulated in principal axes where thermo-mechanical extensions are also addressed. It is shown that, in a functional setting, treatment of many damage growth models, including ones originated from phenomenological models (with formal thermodynamical derivations), micro-mechanical models or fracture criteria, proposed in the literature, is possible. Quasi-unilateral damage evolutionary forms are given with special emphasis on the feasibility of formulations in principal axes. Local integration procedures are summarized starting from a full set of seven equations which are simplified step by step initially to two and finally to one where different operator split methodologies such as elastic predictor-plastic/damage corrector (simultaneous plastic-damage solution scheme) and elastic predictor-plastic corrector-damage deteriorator (staggered plasticdamage solution scheme) are given. For regularization of the post peak response with softening due to damage and temperature, Perzyna type viscosity is devised. Analytical forms accompanied with algorithmic expressions including the consistent material tangents are derived and the models are implemented as UMAT and UMATHT subroutines for ABAQUS/Standard, VUMAT subroutines for ABAQUS/Explicit and UFINITE subroutines for MSC.Marc. The subroutines are used in certain application problems including numerical modeling of discrete internal cracks, namely chevron cracks, in direct forward extrusion process where comparison with the experimental facts show the predicting capability of the model, isoerror map production for accuracy assessment of the local integration methods, and development two novel necking triggering methods in the context of a damage coupled environment.

Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.02.09 – динаміка та міцність машин. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2016. Дисертаційна робота присвячена вирішенню науково-прикладної проблеми, яка полягає у створенні розрахункових методів визначення ресурсу машинобудівних елементів конструкцій з гумо-кордними композитами та їх складовими. У роботі запропоновано моделі накопичення втомної пошкоджуваності в матеріалах, що вивчаються, при їх циклічному деформуванні на скінченних рівнях деформацій в рамках теорії континуальної механіки пошкоджуваності, з урахуванням одночасного протікання процесів деградації їх властивостей внаслідок старіння. Встановлено характеристики пружності, міцності та опору втомі типових гумових матеріалів та гумо-кордних композитів, а також закономірності їх зміни внаслідок старіння на основі проведеного комплексу експериментальних досліджень. Сформульовано підхід до створення ієрархічної системи розрахункових скінчено-елементних моделей різного масштабу розгляду гумо-кордних композиційних елементів машин. Запропоновано СЕ моделі автомобільних пневматичних шин, багатошарових амортизаційних прокладок, гумо-кордних тороїдальних компенсаторних муфт, що враховують особливості їх тривимірної багатошарової конструкції, криволінійну ортотропію механічних властивостей. Із використанням розроблених моделей досліджено особливості формування функціонально-експлуатаційних характеристик зазначених елементів машинобудівних конструкцій, а також проведено прогнозування їх надійності.
The thesis is presented for scientific degree of doctor of technical sciences, speciality 05.02.09 – Dynamics and strength of machines. – National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2016. The thesis deals with a solution of a scientific and practical problem of devel-opment of computational methods of determination of mechanical engineering elements life-time with rubber-cord composites and their components based on creation of probabilistic mathematical models describing fatigue damage accumulation and scientific-based approaches for definition of characteristics of a deformed state in those structural elements. The work offers improved probabilistic models of the fatigue damage accumu-lation in the subject materials under cyclic deformation with finite strain amplitudes in the framework of continuum damage mechanics. The appropriate models take into account a random scatter of the material fatigue resistance characteristics, along with simultaneous passing of stochastic processes of material properties degradation caused by natural aging. The approaches are developed for determination of the probability characteristics of the machine elements fatigue damage and life-time considering presence of possible operational random variation of the characteristics of the deformed state. New analytical formulations have been obtained for the determination of a onedimensional probability density function for the process of damage fatigue accumulation basing on the offered mathematical models. A relation between the characteristics of the classical S-N curve and parameters of a fatigue damage kinetic equation within the offered model has been found. It allows to determine the required material damage parameters basing on the known experimental data. A series of experimental researches has been carried out for identification of the characteristics of elasticity, strength and fatigue resistance parameters for a typical rubber-like materials and rubber-cord composites. The study has been performed for specimens before and after artificial aging. Regularities of changes in the characteristics of the materials caused by aging have been analysed. A methodological approach is formulated for creation of a hierarchical system of FE models with a different scale of rubber-cord elements representation. In the framework of the approach: macro-models integrally represent the composite as orthotropic homogeneous material that makes it possible to solve practical problems, considering the main design features, operational conditions etc. Micro-level models allow to estimate internal concentration of stresses and strains in the rubber-cord composites.Basing on this approach a number of hierarchical systems of FE models have been developed for automobile pneumatic tires, multilayer amortizing cushion, rubber-cord toroidal compensatory tubes and hoses that take into account the peculiarities of their three-dimensional multi-layer internal structure and curve-linear orthotropy of mechanical properties. A formation of functional performance of the mentioned engineering designs along with characteristics of their reliability have been analysed basing on the developed models. The lifetime forming features of the pneumatic tires and toroidal tubes with different service loading have been studied along with the influence of the intensity of the aging process. It has been developed an informational system that allows to automate the creation process of geometrical and computational FE models of pneumatic tires for a wide class of their sizes and design variations. The informational system is developed as integrated software based on the existing CAD/CAE programs.

Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.02.09 – динаміка та міцність машин. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2016. Дисертаційна робота присвячена вирішенню науково-прикладної проблеми, яка полягає у створенні розрахункових методів визначення ресурсу машинобудівних елементів конструкцій з гумо-кордними композитами та їх складовими. У роботі запропоновано моделі накопичення втомної пошкоджуваності в матеріалах, що вивчаються, при їх циклічному деформуванні на скінченних рівнях деформацій в рамках теорії континуальної механіки пошкоджуваності, з урахуванням одночасного протікання процесів деградації їх властивостей внаслідок старіння. Встановлено характеристики пружності, міцності та опору втомі типових гумових матеріалів та гумо-кордних композитів, а також закономірності їх зміни внаслідок старіння на основі проведеного комплексу експериментальних досліджень. Сформульовано підхід до створення ієрархічної системи розрахункових скінчено-елементних моделей різного масштабу розгляду гумо-кордних композиційних елементів машин. Запропоновано СЕ моделі автомобільних пневматичних шин, багатошарових амортизаційних прокладок, гумо-кордних тороїдальних компенсаторних муфт, що враховують особливості їх тривимірної багатошарової конструкції, криволінійну ортотропію механічних властивостей. Із використанням розроблених моделей досліджено особливості формування функціонально-експлуатаційних характеристик зазначених елементів машинобудівних конструкцій, а також проведено прогнозування їх надійності.
The thesis is presented for scientific degree of doctor of technical sciences, speciality 05.02.09 – Dynamics and strength of machines. – National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2016. The thesis deals with a solution of a scientific and practical problem of devel-opment of computational methods of determination of mechanical engineering elements life-time with rubber-cord composites and their components based on creation of probabilistic mathematical models describing fatigue damage accumulation and scientific-based approaches for definition of characteristics of a deformed state in those structural elements. The work offers improved probabilistic models of the fatigue damage accumu-lation in the subject materials under cyclic deformation with finite strain amplitudes in the framework of continuum damage mechanics. The appropriate models take into account a random scatter of the material fatigue resistance characteristics, along with simultaneous passing of stochastic processes of material properties degradation caused by natural aging. The approaches are developed for determination of the probability characteristics of the machine elements fatigue damage and life-time considering presence of possible operational random variation of the characteristics of the deformed state. New analytical formulations have been obtained for the determination of a onedimensional probability density function for the process of damage fatigue accumulation basing on the offered mathematical models. A relation between the characteristics of the classical S-N curve and parameters of a fatigue damage kinetic equation within the offered model has been found. It allows to determine the required material damage parameters basing on the known experimental data. A series of experimental researches has been carried out for identification of the characteristics of elasticity, strength and fatigue resistance parameters for a typical rubber-like materials and rubber-cord composites. The study has been performed for specimens before and after artificial aging. Regularities of changes in the characteristics of the materials caused by aging have been analysed. A methodological approach is formulated for creation of a hierarchical system of FE models with a different scale of rubber-cord elements representation. In the framework of the approach: macro-models integrally represent the composite as orthotropic homogeneous material that makes it possible to solve practical problems, considering the main design features, operational conditions etc. Micro-level models allow to estimate internal concentration of stresses and strains in the rubber-cord composites.Basing on this approach a number of hierarchical systems of FE models have been developed for automobile pneumatic tires, multilayer amortizing cushion, rubber-cord toroidal compensatory tubes and hoses that take into account the peculiarities of their three-dimensional multi-layer internal structure and curve-linear orthotropy of mechanical properties. A formation of functional performance of the mentioned engineering designs along with characteristics of their reliability have been analysed basing on the developed models. The lifetime forming features of the pneumatic tires and toroidal tubes with different service loading have been studied along with the influence of the intensity of the aging process. It has been developed an informational system that allows to automate the creation process of geometrical and computational FE models of pneumatic tires for a wide class of their sizes and design variations. The informational system is developed as integrated software based on the existing CAD/CAE programs.

This dissertation presents the development of an anisotropic viscoplastic continuum damage model to describe the permanent deformation of asphalt pavements. The model is developed to account for several phenomena that influence the permanent deformation of Asphalt Concrete (AC) at high temperatures. These phenomena include strain rate dependency, confining pressure dependency, dilation, aggregate friction, anisotropy, and damage. The model is based on Perzyna's theory of viscoplasticity with Drucker-Prager yield function modified to account for the microstructure anisotropy and damage. A parametric study was conducted to study the effect of key factors such as inherent anisotropy and damage on the model response. A preliminary investigation was conducted to demonstrate the capabilities of the model and its sensitivity to changes in the microstructure distribution and loading conditions. The model was used to describe laboratory experimental measurements obtained from the Federal Highway Administration (FHWA) Accelerated Loading Facility (ALF). The model had a good match with these experimental measurements. In particular, using the damage parameter, the model was able to capture the point at which AC experienced tertiary creep in a static creep test. A comprehensive experiment was conducted to systematically determine the model parameters and the evolution laws that describe AC hardening, anisotropy, and damage. The experiment consisted of a set of compressive triaxial strength tests conducted at three confining pressures and five strain rates. Based on these experimental measurements, the model was modified to include a nonassociated flow rule. The model was shown to capture the experimental measurements very well. Furthermore, an experiment was conducted to capture and characterize damage evolution in AC due to permanent deformation. AC specimens were loaded using a triaxial compression setup to four predefined strain levels at three confining pressures. X-Ray computed tomography and image analysis techniques were used to capture and characterize the evolution of cracks and air voids in the deformed specimens. Damage was found to be a localized phenomenon in the sense that there exists a critical section in an AC specimen that is mainly responsible for failure. The results of the damage experiment supported the damage evolution function proposed in the viscoplastic model.

Dans les générateurs de vapeur des centrales nucléaires à eau pressurisée, les tuyauteries sont soumises à des chargements thermique et mécanique, qui sont variables et divisés en deux régimes différents : la fatigue oligocyclique et la fatigue gigacyclique. Les aciers au carbone – manganèse, type A42, A48 et Tu48 (normes françaises) sont souvent utilisés dans de telles applications. Les propriétés du matériau manifestent certains caractères spéciaux en mécanique et métallurgie comme le vieillissement dynamique conduisant à une augmentation de la valeur de la contrainte maximale et une diminution de la ductilité à la température 200 ℃. Le comportement en fatigue oligocyclique et gigacyclique sont étudiés à température ambiante et 200 ℃. Des essais de fatigue cumulée ont été mis en oeuvre pour étudier l’effet du cumul de dommage combinant des cycles de fatigue oligocyclique suivis de cycles en fatigue gigacyclique. Tous les résultats sont analysés en utilisant la mécanique de l’endommagement des milieux continus et l’analyse microfractographique. Les cycles d’hystérésis en fatigue oligocyclique sont dus à la déformation plastique de durcissement cinématique, ils peuvent être décrits par sous le modèle d’Armstrong – Frederick ; le durcissement isotrope est utile pour prédire l’évolution de l’amplitude de contrainte. Mais avec l’augmentation de la déformation plastique accumulée, le dommage ne peut être négligé. Le modèle de Chaboche d’endommagement par fatigue est utilisé pour décrire l’évolution des dommages oligocyclique et il est étendu au régime gigacyclique. Un modèle de fatigue cumulée des dommages a été développé à partir du modèle de Chaboche et appliqué à l’estimation des dommages de fatigue pour décrire le comportement de l’évolution de la contrainte en fonction du nombre de cycles. En fatigue oligocyclique à la température de 200 ℃, l’acier A48 est sensible au phénomène de vieillissement dynamique et il apparaît un durcissement secondaire, qui peut être prédit par la théorie des dislocations et est simulé dans la thése. L’analyse des surfaces de rupture est effectuée par fractographie au Microscope Electronique à Balayage pour les essais en oligocyclique, gigacyclique et cumul. En fatigue oligocylique, la fissure est initiée en surface. En fatigue gigacyclique, certaines fissures sont initiées sur des inclusions situées à l’intérieur d’éprouvettes
In steam generators of nuclear power plants, typical pipes components are subjected to thermal and mechanical loading which are variable and divided into two different regimes: low cycle fatigue and gigacycle fatigue. Carbon-manganese steels A42, A48 and Tu48 steels (French standards) are often used in such applications. The material properties manifest some special characters in mechanics and metallurgy such as Dynamic Strain Aging, increasing UTS values in 200℃ temperature domain. The LCF and VHCF behaviors are investigated respectively by test method at room temperature and 200℃. The cumulative fatigue tests are implemented through referencing the load as prior LCF following gigacycle fatigue from the steam generator pipes thermal loads in order to obtain the performance of material under accumulated fatigue damage. All the test results are analyzed by using plastic mechanics, continuums damage mechanics and microscopic analysis. Hysteresis loops are due to plastic deformation in LCF which is the effect of kinematic hardening and they can be described by Armstrong – Frederick form models; the isotropy hardening is used to predict the evolution of stress amplitude in LCF. But with rising of accumulated plastic deformation, the damage can not be neglected. The Chaboche fatigue damage model is applied to describe the damage evolution of LCF and extended to VHCF regime. The cumulative fatigue damage model is extended from Chaboche model and applies to the estimation cumulative fatigue damage. The constitutive relationship and isotropy rule are coupled with fatigue damage model that can describe the whole fatigue behavior. In 200℃ for LCF, A48 is sensitive to dynamic strain aging and its secondary hardening behavior is important which can be predicted by dislocation theory and is simulated in the paper. The fractographic analysis is performed by SEM for LCF, VHCF and cumulative fatigue tests. The LCF crack is initiated in surface. Some of cracks of VHCF are given birth from the inclusions located at interior of sample

Two topics involving irradiation damage in alpha-iron have been considered. First, damage cascades representative of those that would be induced by radiation have been simulated using molecular dynamics (MD). The number and type of defects produced are compared for pure iron and iron with a small hydrogen concentration. Second, the inter- action energy between point defects and line dislocations has been calculated for a number of configurations, using both molecular statics methods and calculations based on linear elastic continuum theory and the dipole force tensor. Results from both methods are com- pared. Results from these two topics are relevant for predicting macroscopic behaviors such as creep and plasticity in reactor structural materials.

Fatigue performance modeling is one the major topics in asphalt concrete modeling work. Currently the only standard fatigue test available for asphalt concrete mixtures is the flexural bending fatigue test, AASHTO T-321. There are several issues associated with flexural fatigue testing, the most important of which are the stress state is not uniform but varies over the depth of the specimen and equipment for fabricating beam specimens is not widely available. Viscoelastic continuum damage (VECD) fatigue testing is a promising alternative to flexural fatigue testing. Different researchers have successfully applied the VECD model to asphalt concrete mixtures using constant crosshead rate direct tension test. However, due to the load level limitation of the new coming Asphalt Mixture Performance Tester (AMPT) testing equipment, there is an immediate need to develop a model that can characterize fatigue performance quickly using cyclic test data. In this study, a simplified viscoelastic continuum damage model developed at NCSU is applied to various North Carolina mixtures, which are used in the NCDOT HWY-2007-7 MEPDG local calibration project. It is shown that the simplified VECD model can predict fatigue tests fairly accurately under various temperature conditions and strain levels. It is also shown that the model can be further utilized to simulate both the strain controlled direct tension fatigue test and the traditional beam fatigue test. In this thesis, simulation results are presented. Conclusions regarding the applicability of the new model are advanced as well as suggestions for further work.

The effect of the element length is examined in modelling crack growth in fatigue loading of an adhesive joint. This is done for a cohesive element using an expression for the damage evolution developed at the University of Skövde which is implemented using the UMAT subroutine in the FE-solver Abaqus. These analyses are done for pure mode I loading by analysing a DCB-specimen loaded by a pure moment. An expression is developed in which the critical element length is dependent on the geometry of the specimen (in the form of the wave number of the adhesive joint), the element length, the material properties of the adhesive (in form of the material parameters , , ), the load applied (in form of the stress in the crack tip), the time step used in the analysis and the crack growth rate. It is shown that the results converge by decreasing the element length and the time step used. Therefore an expression for the crack growth rate as a function of the remaining parameters can be determined. Another expression is thereafter developed for the element length needed in order to get a crack growth rate within a certain range of the critical element length. The results show a regular pattern but are not monotone. Therefor two different definitions of the critical element length are tested, either by defining the critical element length as the point where the error is greater than an arbitrary boundary of 1 % of a converged result or where a least square approximation of the error is within 1 % of the converged results. The first method shows a highly irregular result which makes it difficult to develop an expression out of these results. The second method on the other hand gives results that are predictable enough to develop a function out of them. This is done using a regression analysis with all parameters of a third order expression in order to get an expression.

Une méthode de couplage continu-discret a été développée pour simuler les mécanismes complexes d'endommagement de la silice soumise à un choc laser de haute puissance. Dans un premier temps, une classification des méthodes numériques existantes a été faite pour choisir celles les mieux adaptées à la simulation du comportement sous choc de la silice. Comme résultat de cette classification, deux méthodes ont été retenues: la méthode des éléments discrets (DEM) et la méthode des éléments naturels contraints (CNEM). Ces méthodes sont alors couplées en se basant sur la technique dite "Arlequin". Puis, un modèle numérique permettant de tenir compte des différents phénomènes qui caractérise le comportement de la silice sous haute pression a été développé. Pour bien caractériser les mécanismes de fissuration de la silice à l'échelle microscopique, un nouveau modèle de rupture a été développé dans ce travail. Finalement, ces deux modèles, modèle de comportement et modèle de rupture, ont été intégrés dans la méthode du couplage pour simuler d'un point de vue mécanique le choc laser sur un échantillon en silice.

Built on top of a consistent continuum damage mechanics (CDM) damage representation formulation, a novel damage evolution law based on the concept of damage driving force is proposed for modelling the evolution of matrix damage in UD composites. This damage evolution law has the advantage of allowing different damage evolution constants to be associated with different loading modes (corresponding to the fracture modes in Fracture Mechanics) when dealing with mixed-mode loading conditions, which avoids the unrealistic assumption in many existing theories that different loading modes make the same contribution to damage evolution. A new CDM model for UD composites is developed incorporating this damage evolution law. Thanks to the laminate test cases designed and conducted in this project, it is found that the damage initiation and propagation related material constants can be determined using these tests. These damage-related material constants served as inputs to the UD composite CDM model. Apart from the tests on laminates, detailed experimental investigation was carried out regarding damage in two types of layer-to-layer interlock 3D woven composites which are reinforced by IM7 carbon fibre (CF) and E-glass fibre (GF), respectively. The experimental data obtained and the damage processes recorded for these 3D woven composites can serve as a good reference for future interest in this area, since currently only limited studies are available in the literature regarding damage in this type of 3D woven composites. The new UD composite CDM model is applied to predict intra-laminar damage in laminates and intra-tow damage in the 3D woven composites. Compared to the experimental results, it is found that the model produced satisfactory predictions but lacking the capability to predict a severe stress-strain nonlinearity caused by shear. A new pragmatic continuum damage model is developed to capture the damage effect of inter-tow cracks in the 3D woven composites caused by warp direction tensile loading. This model works in conjunction with the intra-tow damage predicted by the aforementioned UD composite CDM model. With the successful development of these damage models, a novel damage modelling methodology for textile composites is made possible and implemented in conjunction with the UnitCells© composite characterisation tool and the artificial neural network tool developed. Through the artificial neural network for data interpolation, the constitutive behaviour of textile composite incorporating the effect of damage can be interpolated for any load combination, which is then readily available for engineering applications.

In a recent investigation conducted by the United States Air Force, the mechanical failure of the aileron lever, manufactured from 2014-T6 aluminum, caused the fatal mishap of a T-38 trainer aircraft. In general the locations of cracks are unknown and must be determined by simulation. In this study we propose to use a continuum damage modeling approach to determine the degradation and damage in a material as the number of cycles of loading increases. This approach successfully predicts the location of crack initiation, propagation path, and propagation rate. A stress-based model in conjunction with the successive initiation technique is utilized. Successive initiation is based on the idea that damage will accrue in a material. Each element inside a new material will have a value of 0 damage assigned to it. Over time, the damage that occurs due to stresses on individual elements will add until the damage reaches a value of 1. At that point, failure of the element will occur. A code was developed in ANSYS that can draw, mesh, and apply appropriate forces on the aileron lever for successive runs. By using the S-N curve for the 2014-T6 aluminum material, the material damage constants are found. This stress-based damage model is then used to determine the state of damage in each element. Each time the elements are stressed, a particular amount of damage will occur. When an element reaches a specific amount of damage, ANSYS will "kill" the element, resulting in the element no longer adding to the stiffness matrix of the material. Variability is a common occurrence in all aspects of engineering such as manufacturing, testing, and loading. A Monte Carlo simulation is used to determine the sensitivity of the results to variability of input parameters by ± 15%. Input parameters include loads, material properties and damage model constants. The Monte Carlo simulation indicates the only significant input in the initiation life of the material is the exponential value in the stress-based fatigue life equation. Material properties and load variations in the ± range will not significantly change the life prediction results.

Une méthode de couplage continu-discret a été développée pour simuler les mécanismes complexes d'endommagement de la silice soumise à un choc laser de haute puissance. Dans un premier temps, une classification des méthodes numériques existantes a été faite pour choisir celles les mieux adaptées à la simulation du comportement sous choc de la silice. Comme résultat de cette classification, deux méthodes ont été retenues: la méthode des éléments discrets (DEM) et la méthode des éléments naturels contraints (CNEM). Ces méthodes sont alors couplées en se basant sur la technique dite "Arlequin". Puis, un modèle numérique permettant de tenir compte des différents phénomènes qui caractérise le comportement de la silice sous haute pression a été développé. Pour bien caractériser les mécanismes de fissuration de la silice à l’échelle microscopique, un nouveau modèle de rupture a été développé dans ce travail. Finalement, ces deux modèles, modèle de comportement et modèle de rupture, ont été intégrés dans la méthode du couplage pour simuler d'un point de vue mécanique le choc laser sur un échantillon en silice
A discrete-continuum coupling approach has been developed to simulate the laser-induced damage in silica glass. First, a classification of the different numerical methods has been performed to select the ones that best meet the objectives of this work. Acting upon this classification, the Discrete Element Method (DEM) and the Constrained Natural Element Method (CNEM) have been retained. Subsequently, a coupling approach between these methods has been proposed. This approach is based on the Arlequin technique. In the second part, a numerical model of the silica glass mechanical behavior has been developed to better characterize the silica glass response under highly dynamic loadings and particularly loading generated by a laser beam. To correctly characterize the silica glass cracking mechanisms, a new fracture model has been proposed in this work. Finally, all these developments have been used to simulate the laser-induced damage in silica glass

It is well known that the formation and propagation of microcracks within concrete is anisotropic in nature, and has a degrading effect on its mechanical performance. In this thesis an anisotropic damage mechanics model is formulated for concrete which can predict the behavior of the material subjected to monotonic loading, fatigue loading, and freeze-thaw cycles. The constitutive model is formulated using the general framework of the internal variable theory of thermodynamics. Kinetic relations are used to describe the directionality of damage accumulation and the associated softening of mechanical properties. The rate independent model is then extended to cover fatigue loading cycles and freeze-thaw cycles. Two simple softening functions are used to predict the mechanical properties of concrete as the number of cyclic loads as well as freeze-thaw cycles increases. The model is compared with experimental data for fatigue and freeze-thaw performance of plain concrete.
DOT-MPC grant
Department of Civil Engineering, North Dakota State University

Cette thèse est dédiée à l’étude du comportement élasto-plastique des matériaux polycristallins multiphasés ainsi que de l’endommagement ductile à différentes échelles. Les hétérogénéités microscopiques ont une influence importante sur la réponse mécanique macroscopique des matériaux. Et l’endommagement ductile est encore difficile à mesurer aux échelles fines. Cette thèse traite des problématiques suivantes : 1. L’évolution du comportement des phases et des grains sous chargements jusqu’à la rupture.2. L’influence de l’hétérogénéité intrinsèque au niveau micro, sur le comportement macroscopique des matériaux biphasés.3. L’influence de la striction et de l’endommagement sur le comportement de familles d’orientation de grains.4. La mesure indirecte de l’endommagement échelle fine par diffraction. Afin d’enquêter sur ces questions, l’acier duplex et le titane biphasé sont testés. La diffraction est utilisée pour effectuer des mesures in situ non-destructive au cours d’essais de traction et jusqu’à la rupture. Des simulations sont réalisées grâce à un modèle auto-cohérent élasto-plastique, dans lequel est introduite la modélisation de l’endommagement ductile. Les données expérimentales aux différentes échelles y sont comparées. En outre, des tests de nano-indentation et observation micrographiques sont effectués pour observer l’évolution spatiale des propriétés mécaniques des phases le long de la striction et jusqu’à la surface de rupture
The thesis is dedicated to the study of elasto-plastic behavior of multiphase polycrystalline materials and ductile damage at different scales. The microscopic heterogeneities have important influence on the macroscopic mechanical behavior of materials. Ductile damage is still difficult to measure at small scales. The following issues are the main topic involved in this thesis: 1. The evolution of mechanical behavior in phases and groups of grains, under external load until fracture.2. The influence of intrinsic heterogeneity on the macroscopic behavior of two-phase materials.3. The influence of necking and ductile damage, on the behavior of grains with different orientation families.4. The indirect measurement of ductile damage at small scales by diffraction. To answer these questions, duplex steels and two-phase titanium are tested. The diffraction method is used to perform in situ measurements during tensile test until fracture. Predictions are carried out by an elasto-plastic self-consistent model, in which ductile damage have been integrated. Experimental data on different scales are compared with these predictions. In addition, nano-indentation tests are carried out to study the evolution of phases’ mechanical properties along the neck until fracture edge. Microscopic images were also taken in order to observe the fracture surfaces of studied materials

A three-dimensional finite element code to analyze coupled thermomechanical deformations of composites has been developed. It incorporates geometric nonlinearities, delamination between adjoining layers, and damage due to fiber breakage, fiber/matrix debonding, and matrix cracking. The three damage modes are modeled using the theory of internal variables and the delamination by postulating a failure envelope in terms of the transverse stresses; the damage degrades elastic moduli. The delamination of adjoining layers is simulated by the nodal release technique. Coupled nonlinear partial differential equations governing deformations of a composite, and the pertinent initial and boundary conditions are first reduced to coupled ordinary differential equations (ODEs) by the Galerkin method. These are integrated with respect to time with the Livermore solver for ODEs. After each time step, the damage in an element is computed, and material properties modified. The code has been used to analyze several static and transient problems; computed results have been found to compare well with the corresponding test results. The effect of various factors such as the fiber orientation, ply stacking sequence, and laminate thickness on composite's resistance to shock loads induced by underwater explosions has been delineated.
Ph. D.

This thesis describes the development of computational analysis techniques for weldments which contain three different material regions (Parent Material, Weld Material and Heat Affected Zone) and which exhibit different creep behaviour. The different strain rate behaviour of the three regions and the growth of creep continuum damage lead to local stress redistribution and to complex states of stress which can greatly enhance the accumulation of creep damage. A review of literature is presented which covers weldment design methodology and the associatedm etallurgy. The shortcomingso f design and assessmenct odes for pipe vessels, and the need for approximate methods of lifetime estimation, are revealed, indicating the need for further research in these areas. The development of the Continuum Damage Mechanics (CDM) method is presented, which is a physically based technique for the analysis of the creep behaviour of materials and engineering structures. Previous works are also reviewed showing that the CDM method can be used to accurately describe the behaviour of weldments providing the constitutive equations are available which describe the deformation and rupture of materials. Since the research is concerned with the analysis of the creep rupture of welded pressure vessels and pipes using the CDM method, previous research is reviewed regarding the creep behaviour of weldments and 'the determination of constitutive equations for different weldment material phases. A review is also presented of different solution techniques for solving systems of equations and for minimising the bandwidth and profile of matrix. The modification is described of the two-dimensional (2D) solver, Damage XX- 2D, to extend its capability to three-dimensional (3D), together with the techniques required to satisfy plastic incompressibility using a special brick arrangement of tetrahedral elements. The Three-dimensional CDM Finite Element Solver is known as Damage XX-3D. The 3D finite element theory and the co-ordinate transformation techniques are outlined for the solution of axi-symmetricengineering problems. The technique for the removal of failed finite elements is described for both of the two-dimensional and the three-dimensional analyses. The restart facility and the associated data output strategy are developed to help to minimise the loss of result data files, in the case of an accidental power cut to computers. These methods also allow a complete analysis to be divided into individual smaller analyses. Two numerical solution methods, with different storage schemes, for sets of linear algebraic equations have been developed and validated against results obtained independently using a commercial Finite Element package Abaqus (version 5.6-1). A damage averaging technique is developed to reduce the number of iterations required for the solution of three-dimensional problems which have large number of degrees of freedom; and also to preserve the symmetry of creep CDM solutions for axi-symmetric two-dimensional analyses. The creep CDM solutions obtained using Damage XX-3D are compared with the solutions obtained using Damage XX-2D Axi-symmetric analysis, and good agreement has been obtained for lifetimes and failure mechanisms. Applications of Damage XX-3D, are presented for the analysis of the high temperaturec reep behaviour of a CrossweldedT estpiece,t he Cylinder-SphereP ipe Intersection (Flank Section) subjected to an internal pressure, and Butt-welded ferritic steel pipe subjected to a combined internal pressure and a global bending moment. Finally, a three-dimensional Finite Element CDM Solver has been developed which is computationally fast and efficient, and which yields predictions which have been validated against independent solutions. IV

The thesis describes the development of a new continuum damage mechanics (hereafter, CDM) model for the deformation and failure of brittle matrix composites reinforced with continuous fibres. The CDM model is valid over sizes scales large compared to the spacing of the fibres and the dimensions of the damage. The composite is allowed to sustain damage in the form of matrix micro-cracking, shear delamination, tensile delamination and fibre failure. The constitutive equations are developed by decomposing the composite compliance into terms attributable to the fibre and matrix, and modelling the competing failure modes by intersecting failure surfaces based on maximum stress theory. The fibres are treated as being weakly bonded to the matrix so that the fibres only transmit axial loads, and fail in tension. The matrix is modelled as isotropic linear elastic and is treated as transversely-isotropic after damage has initiated. The effect of multiple matrix cracking on the stiffness was determined from experimental data, while failure was modelled by a rapid decay in the load bearing capacity. Although the model is motivated largely to proportional loading, matrix unloading and damage closure has been modelled by damage elasticity. During compression, the matrix stiffness is identical to the undamaged state with the exception that the fibres are assumed not to transmit compressive loads. The model was implemented computationally through a FORTRAN subroutine interfaced with the ABAQUS/Standard finite element solver. The CDM model was validated by comparing experimental and computational results of test specimens with unidirectional and balanced 0°-90° woven fibres of a brittle matrix composite, fabricated from polyester fibres in a polyester matrix. This composite system exhibits low elastic mismatch between fibres and matrix, and has similar non-dimensionalised stress-strain response to a SiC/SiC composite proposed for the exhaust diffuser unit of the Rolls-Royce EJ200 aero-engine.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O presente trabalho da modelagem da fadiga plástica oligocíclica de barras também conhecida na literatura como fadiga de baixo ciclo. O modelo unidimensional proposto é desenvolvido a partir dos princípios básicos da Mecânica do Dano Contínuo. Seu principal objetivo é considerar a influencia de vários fenômenos complexos – como a história da deformação plástica, a viscosidade, o endurecimento e o amolecimento cíclico induzido pela deformação plástica acumulada – na vida da estrutura. As equações constitutivas, usadas ao longo do trabalho, formam um sistema de equações diferenciais ordinárias não-lineares e, para um conjunto de condições iniciais dado, a solução é aproximada usando-se um método preditor corretor de quarta ordem com passo variável. O modelo proposto é estudado através da análise da vida de uma barra de aço inoxidável 316L submetida a carregamentos de tensão não monotonicos à temperatura ambiente (20 graus Celsius). Para carregamentos de tensão cíclica com amplitude constante e tensão média nula, as vidas computadas encontram-se em muita boa concordância com aquelas obtidas pelo método E – N clássico. Uma das principais vantagens do modelo proposto é que pode ser facilmente estendido a um contexto tridimensional, o que só pode ser feito no método E – N mediante fortes hipóteses, restritivas. Espera-se assim, que no futuro, este modelo de dano contínuo possa ser usado como uma ferramenta simples e acurada no projeto de estruturas mecânicas, tornando-as mais baratas, seguras e confiáveis.
The present work is concerned with the modeling of the low-cycle fatigue of elasto-viscoplastic bars. The proposed unidimensional model is developed in the framework of the Continuum Damage Mechanics and takes into account the influence of many complex pehnomena (such as the history of plastic deformation, the viscosity and the cyclic hardening induced by the cumulated plastic doformation) in the life of the structure. The resulting governing equations form a nonlinear system of ordinary differential equations and, for a given set of initial conditions, the solution is approximated by using a fourth order predictor-corrector finite difference schme with variable time steps. The proposed model is checked by analysing the life of a 316L stainless steel bar subjected to non monotonic loadings at room temperature (20 degress Celsius). For cyclic stress loadings with constant amplitude and zero men stress, the computed lifes are in very good agreement to those obtained by the classical E – N method. One of the main features of the proposed model is that it can be easily extended to a tridimensional context, what is not an easy task in the case of the classical methods. So, in the future, this continuum damage model may be used as an reasonably simple tool in the sesign of mechanical structures making them more safer and reliable.

Components in advanced gas cooled reactor (AGR) operating at elevated temperatures in the range of 500-650°C are typically susceptible to the initiation and growth of cracks due to creep. Type 316H stainless steel steam headers after a long term service are susceptible to reheat cracking in the vicinity of the weld driven by the presence of welding residual stresses. For this reason, this research has focused on developing pragmatic numerical methods for predicting creep crack growth behaviour of welded components containing residual stresses, using a simplified continuum damage and fracture mechanics method. The work presented had three main aims. The first was to derive a comprehensive set of plastic η factors for standard fracture mechanics geometries containing welds. The impetus for this was to improve material crack growth characterisation for welds by improving the creep C* solutions for these geometries that are presently recommended in standard codes of practice for creep crack growth testing. The second part was to experimentally examine appropriate creep material properties for as-received and service-exposed 316H stainless steels containing welds for use in numerical modelling and predictive methods for creep crack growth in a real component. The third was to develop and validate a simplified method of simulating residual stresses and creep crack growth behaviour in an ex-service AISI 316H weld header with reheat cracking. This approach simulates the presence of residual stresses using appropriate loading and boundary conditions in actual components that undergo reheat cracking without the need to develop full weld simulations to quantify them. The creep crack growth behaviour was studied using two methods based on the theories of fracture mechanics and continuum damage mechanics. Fracture mechanics parameter C* was firstly used to examine the approximate crack growth rate using the reference stress approach and approximate NSW model. The second method was to predict long term cracking by using a simplified continuum damage mechanics model, with a consideration of stress relaxation. For this purpose, a simplified multi-axial ductility exhaustion model was developed and implemented in an Abaqus user subroutine, taking into account the changes in the ex-service creep properties and the effect of reduction in creep ductility under low loads and long term operation at service temperatures. Resulting from the findings, the task was to identify the geometric and the material reasons of how and why the crack growth follows a path of least resistance and higher constraint which did not necessarily mean growing through the welds or the heat affected zone region.