Dissertations / Theses on the topic 'Grinding, Finite Element Method, Residual Stresses'
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Mahdi, Mofid. "A NUMERICAL INVESTIGATION INTO THE MECHANISMS OF RESIDUAL STRESSES INDUCED BY SURFACE GRINDING." University of Sydney, Mechanical, 1998. http://hdl.handle.net/2123/413.
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Abstract Grinding introduces unavoidable residual stresses of significant but unknown magnitudes. The effect of residual stresses in surface integrity is related to the nature of the residual stresses which relies purely on the process parameters and the workmaterial properties. It is a well-known fact that the fatigue strength of a ground component is increased by introducing compressive stresses. On the other hand, fatigue cracks may originate at regions of maximum tensile stress and usually at the surface of the material. Moreover, stress corrosion cracking is another consequence of critical surface tensile stress. Added to that, the residual stresses may result in dimension alteration and surface distortion, particularly for thin products such as plates. The beneficial effects of compressive residual stresses have been widely recognized in industry. The wise application of such a principle would bring about improved economical use of parts subjected to fatigue loading and aggressive environmental conditions. Therefore a better understanding of residual stress mechanisms is necessary to increase the dimensional accuracy and improve the surface integrity of ground elements, particularly for parts with high precision and manufactured by automated production lines. Consequently, the development of reliable models for predicting residual stresses is of great value in reducing the amount of measurements and experimental tests of residual stresses. Unfortunately, little effort has been devoted so far to develop appropriate models to take into account grinding conditions, workmaterial properties and boundary conditions. This thesis aims to investigate the residual stress mechanisms induced by grinding in terms of grinding parameters. In order to obtain a full understanding, both the roles of individual factors causing residual stresses (i.e. mechanical, thermal and phase transformation) and their couplings were carefully studied with the aid of the finite element method. The studies include: (1) residual stresses due to thermal grinding conditions, (2) residual stresses due to iso-thermal mechanical grinding conditions, (3) coupling of thermo-mechanical conditions, (4) coupling of thermo-phase transformation, and (5) the full coupling of all the factors. It is found that under sole thermal grinding conditions, the heat flux associated with up-grinding may lead to a higher grinding temperature compared with that of down-grinding. A constant flux introduces the least temperature rise if the total grinding energy is the same. Higher convection heat transfer not only decreases the grinding temperature but also makes the temperature rise occur mainly within a thin surface layer. A similar effect can be achieved by applying higher table speeds. When the grinding temperature is less than the austensing temperature, surface residual stresses are tensile. The heat generated within the grinding zone causes a very non-uniform temperature field in the workpiece. The part of the workmaterial subjected to a higher temperature rise expands more significantly and causes compressive stresses because of the restraint from its surrounding material that expands less. When the surface heat flux moves forward, the material outside the grinding zone contracts under cooling. Since the workmaterial has been plastically deformed during thermal loading, the contraction is restrained and thus a tensile stress field is generated locally. If a workpiece material experiences a critical temperature variation in grinding, phase transformation takes place and a martensite layer appears in the immediate layer underneath the ground surface. It was found that the growth of martensite develops a hardened zone with a higher yield stress that expands with the movement of the heat flux. A tensile surface residual stress is then developed. When the volume growth of material takes place during phase change, compressive residual stresses may also be generated. Under iso-thermal grinding conditions, it was found that plane stress is mainly compressive regardless of the distribution of surface traction and the direction of the tangential grinding force. With up-grinding, the residual stress in the grinding direction is always tensile. However, down-grinding may yield compressive surface residual stresses if the magnitude of the ratio of horizontal to vertical grinding forces is sufficiently large. Moreover, it is noted that discrete surface traction, which is more reasonable in terms of simulating the individual cutting of abrasive grits, would bring about more complex residual stress distribution that is very sensitive to the combined effect of individual cutting grits. If thermal and mechanical grinding conditions are coupled, a state free from residual stresses may be achieved if grinding heat is low and either the convection heat transfer or the table speed is high. However, it is found that the full coupling of the mechanical deformation, the thermal deformation and deformation by phase change results in tensile residual stresses. The effects of cooling and mechanical traction in this case however are minor. In summary, the research of this thesis explored the following: (a) grinding temperature development in terms of a wide range of grinding parameters together with the effect of temperature-dependent material properties, (b) the origin and onset of irreversible deformation due to mechanical loading, thermal loading and phase change under critical grinding conditions, (c) the effects of individual residual stress mechanisms and their partial and full couplings, and (d) the selection of grinding conditions to achieve beneficial residual stresses. Finally, based on the new findings in this research, a more comprehensive methodology is suggested for further study.
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Shah, Syed Mushtaq Ahmed. "Prediction of residual stresses due to grinding with phase transformation." Phd thesis, INSA de Lyon, 2011. http://tel.archives-ouvertes.fr/tel-00679816.
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Grinding is a commonly used finishing process to produce components of desired shape, size and dimensional accuracy. The ultimate goal is to have the maximum workpiece quality, minimum machining time and high economic efficiency by making a selective adaptation of the possible process strategy and chosen parameter selection. The focus of this study arose from a limitation that challenges the grinding industry. The production rate of the ground parts is generally constrained by surface topography and subsurface damage appearing as residual tensile stress, localized burns, and phase transformation induced micro and macro-cracking. This motivates the need for a reliable numerical modelling to simulate the grinding process. The numerical model sought should be able to predict not only the required grinding residual stresses but also the deformation history. The objective of this thesis is to build up a reliable finite element model for grinding-induced residual stress analysis and thus to explore thoroughly the mechanisms in terms of grinding conditions. The variations of the residual stresses and strains at integration points have been examined, and the effects of the friction coefficient (µ), Peclet number (Pe), non dimensional heat transfer coefficient (H) and different magnitudes of input heat flux (Q) on both the microstructure and the residual stress state are analyzed. Finally, based on the new findings in this research, a more comprehensive methodology is suggested for further study.
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Garza-Delgado, Abelardo. "A study of casting distortion and residual stresses in die casting." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1196175848.
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Al-Zkeri, Ibrahim Abdullah. "Finite element modeling of hard turning." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1181928433.
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Philander, Oscar. "Mathematical modelling of welding : sensitivity of residual stresses and thermal dilatations on welding parameters." Thesis, Peninsula Technikon, 1998. http://hdl.handle.net/20.500.11838/2227.
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Thesis (MTech (Mechanical Engineering))--Peninsula Technikon, 1998.In South Africa, the determination of residual stress distribution and undesirable metallurgical phase fractions that are formed in components during welding are been dealt with in a destructive or semi-destructive manner. This dissertation is an attempt at enhancing the acquisition of residual components found in welded structures. It shows how finite element methods can be used to obtain these results. TIG welding is modeled as a thermo-mechano-metallurgical (TMM) problem. The mathematical and finite element models for welding described in this study is based on the work performed by Ronda and Oliver. These models has not yet fully been incorporated into any of the existing computational tools and therefor, a commercial computational software program, SYSWELD 2, was employed to perform the welding simulations. The Leblond material models are incorporated into this software program, and the model that is used for this study is described in this text. Computational simulations were performed to study the effects that the sensitivity of welding parameters would have on the resulting shape and size of Heat Affected Zones, depth and width of penetration, temperature fields, metallurgical solid phase fractions, as well as residual stress distribution and deformation. The results of these simulations were compared to laboratory experiments.
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Maczugowski, Maciej. "Numerical simulation of residual stresses in a weld seam : An application of the Finite Element Method." Thesis, Linnéuniversitetet, Institutionen för maskinteknik (MT), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-65867.
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Articulated haulers are fundamental equipment to transport material. The load carrying structure on a hauler consists mainly of welded frames. During welding of the frames high residual stress will be introduced. These stresses may have a significant impact on the fatigue life of the frames. This is the reason for having good knowledge of the weld residual stresses. The finite element method was used to calculate the residual stress distributions in a butt weld and a T-join weld. Simulation of the welding process with thermal and mechanical analysis was prepared by means of welding GUI implemented in LS-PrePost. The welding simulation is a computer intensive operation with high CPU time. That is why it is important to investigate which process factors that have the largest impact on welding simulation results. The aim of this thesis is to investigate the correlation between designed models in FEA software with published results of weld residual stress measurements and conclude which parameters should be mainly taken into consideration.
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Badr, Elie Antoine. "Estimation of residual stresses induced by autofrettage with an experimental evaluation of the autofrettage process in crossbores of positive displacement pumps /." Access abstract and link to full text, 1994. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9500703.
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Liou, Jiann-Haw. "Study of stress developments in axi-symmetric products fabricated by forging and machining /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9737869.
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Long, Xin. "Finite element analysis of residual stress generation during spot welding and its affect on fatigue behavior of spot welded joints." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4171.
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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 13, 2006) Vita. Includes bibliographical references.
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Awang, Mokhtar. "The effects of process parameters on steel welding response in curved plates." Morgantown, W. Va. : [West Virginia University Libraries], 2002. http://etd.wvu.edu/templates/showETD.cfm?recnum=2682.
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Thesis (M.S.)--West Virginia University, 2002.Title from document title page. Document formatted into pages; contains xiv, 133 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 83-85).
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Meňhert, Samuel. "Vliv modelu zpevnění na výsledky simulace kosoúhlého rovnání." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401548.
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This diploma thesis deals with simulation of cross-roll straightening using computational modeling with finite element method in software ANSYS. The main goal of this thesis is to quantify the influence of inaccurate knowledge of mechanical properties on the straightening process and correct setting of machine. It also aims for comparison of hardening models and their influence on the final curvature and residual stresses in the cross section of the bar.
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Torkaman, Hamid. "Modeling and Analysis of the Shot Peening Process : a Study of the Residual Stresses in an Insert using the Finite Element Method." Thesis, Linnéuniversitetet, Institutionen för maskinteknik (MT), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-77322.
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Cutting tool inserts are often coated with thin layers either through chemical vapor deposition (CVD) or physical vapor deposition (PVD) processes. In order to have a better wear resistance cutting tools are mostly subjected to post-coating treatment processes. Shot peening is one of the processes that is used to improve the fatigue life of metallic components. In this study, the finite element (FE) method is employed to model the elastic-plastic deformation and development of residual stress distributions in a cutting tool after the impact of a shot medium. To carry out the work, CVD coated cemented carbide has been chosen to be the workpiece (insert), and the coatings of the chosen insert are Titanium Carbo Nitride (TiCN) and Aluminum Oxide (Al2O3). Aim of the study is to model a single impact in the shot peening process on a surface of a coated cemented carbide insert while simulating the plastic deformation of the materials. In addition, the objective of the study is also to understand and explain the mechanics of shot peening process and find applicable mechanical properties of the materials for FE modeling. Conjugately, the influence of shot peening process parameters (e.g. velocity, diameter or shape of the peening media) on residual stress distribution has been investigated and the results obtained were compared to the one observed from experiment. The modeling in the study is carried out both with and without initial residual stresses in the materials. The initial residual stresses are estimated by applying a thermal load to the model. The results show that the compressive residual stresses achieved while shot peening by an edge-shaped medium are significantly higher at the surface (i.e. in a coated layer) than compared to a globular medium. In contrast, it is observed that the compressive residual stresses in the cemented carbide are significantly higher and deeper when shot peened with globular medium than the edge-shaped medium. Furthermore, the results of parameteric study demonstrate that the smaller medium induces higher residual stresses at the surface (i.e. in a coated layer) than in the cemented carbide. In contrast, it is observed that the bigger medium induces less residual stresses at the surface (i.e. in a coated layer) and higher residual stresses deeper in the cemented carbide. Whereas, it is observed that the higher residual stresses at the surface (i.e. in a coated layer) and in the cemeneted carbide can be achieved simultaneously by shot peens having a higher velocity. Residual stress profiles modelled in this report correlate with data from previous studies. This study has been carried out at Sandvik Coromant, Edge and Surfaces department in Stockholm, Sweden.
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Dawkins, Jeremy James. "Influence of crystallographic orientation in normal and sliding contacts." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24713.
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Shih, Yi-Pu. "The stress patterns and residual stresses developed in curved die upsetting." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1175883679.
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Golestanian, Hossein. "Modeling of process induced residual stresses and resin flow behavior in resin transfer molded composites with woven fiber mats /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9841293.
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Barban, Leonardo Manesco. "Análise numérico-computacional das tensões térmicas induzidas pela soldagem." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/3/3151/tde-23122014-143431/.
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A soldagem é o processo de união mais utilizado na fabricação de equipamentos pela indústria mecânica. Devido à introdução de calor durante o processo de soldagem, dependente do posicionamento da tocha e consequentemente do tempo, dilatações e contrações não uniformes produzem tensões térmicas no componente em questão, as quais permanecem como residuais ao final do processo, ao se atingir o equilíbrio térmico. O entendimento da formação e comportamento destas tensões se torna importante, pois na presença de carregamentos externos, a integridade estrutural do elemento mecânico pode ser comprometida. Portanto, este estudo visa analisar o comportamento destas tensões térmicas, avaliando ao final a magnitude e distribuição das tensões residuais, tendo como ferramenta o método dos elementos finitos. Inicialmente são apresentados os principais processos de soldagem envolvendo a fusão de materiais por meio de arco elétrico, sendo possível com base em uma explicação teórica, observar e entender a formação das tensões oriundas destes processos. Na sequência uma revisão bibliográfica contendo as principais técnicas para modelamento deste problema pelo método dos elementos finitos é apresentada, navegando por conceitos da análise térmica, que envolve o estudo das temperaturas e mecânica, a qual avalia as tensões formadas. Com toda parte teórica consolidada, um caso exemplo é analisado, simulando desta maneira um processo GTAW pelo programa computacional ANSYS, e comparando os resultados numéricos com os dados experimentais e numéricos obtidos na literatura. Ao final da simulação conclui-se que o modelo analisado reproduz fielmente a distribuição de temperaturas durante o processo e também estima corretamente as tensões residuais na chapa soldada, mostrando que a simulação de processos de soldagem utilizando o método dos elementos finitos se apresenta como uma ferramenta alternativa a indústria no aprimoramento de processos existentes ou desenvolvimento de novos.Welding is the most used joining process in equipment manufacture by mechanical industry. Due to heat application during welding, varying with torch position and therefore by time, non-uniform expansion and contraction produces thermal stresses, which remains as residual when the component reaches thermal equilibrium. Formation and behavior of these stresses understanding becomes important since on external forces presence the mechanical piece may have it structural integrity compromised. This study aims to analyze thermal stress behavior due to welding evaluating residual stress magnitude and distribution at the process end by the finite element method. First of all fusion welding process by an electric arc are presented and a theoretical explanation about thermal stresses formation during welding is shared. Next is shown a bibliographic research with main techniques to model these problems using the finite element method, including thermal analysis, which involves temperature distribution study, and structural analysis that evaluate resulting stresses. With all theoretical background consolidated an example case of a GTAW process is studied utilizing ANSYS software, comparing numerical results with experimental and numerical data obtained in literature. It is possible to conclude that analyzed model accurately reproduces temperature distribution and also residual stress in the welded specimen proving that a welding process simulation via finite element method is an alternative tool for industry purposes on improving existing process and developing new ones.
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Mondardo, Milena Macarini. "Análise da influência de parâmetros do processo de trefilação de barras cilíndricas de aço AISI 1045 via simulação numérica computacional." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/61069.
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Este trabalho objetiva fazer uma análise do processo de trefilação através do uso de simulação computacional e avaliar a influência de variáveis do processo como lubrificante (coeficiente de atrito) e ângulo de fieira, bem como, verificar a eficácia da simulação na previsão de força, de temperatura e das tensões residuais. Foi realizado um trabalho experimental que envolveu a determinação do coeficiente de atrito através do ensaio do anel e a determinação das curvas de escoamento que foram retiradas de amostras trefiladas de um processo real. Efetuaram-se os cálculos das tensões do processo usando dados de curvas de escoamento e equações da literatura, posteriormente realizaram-se simulações computacionais que foram comparadas aos resultados obtidos através dos cálculos. Também se usou, adicionalmente, a simulação otimizada para avaliar as tensões residuais a fim de averiguar estes resultados de tensões residuais, comparando-os com resultados experimentais obtidos via difração de nêutrons para as mesmas barras que foram extraídas do processo industrial. Observou-se que a curva de escoamento do material é determinante para a obtenção de resultados confiáveis. A simulação foi boa para a estimativa da força, mas ainda apresenta limitações quanto à previsão de tensões residuais.This paper aims to analyze the drawing process using simulation and evaluate the influence of process variables such as lubricant (friction coefficient) and angle of die as well as verify the effectiveness of simulation to preview the drawing force, temperature and residual stresses. Experimental work was carried out involving the determination of friction coefficient by means of the ring test and determination of flow curves by compression tests. The calculations of the stress of the process using data from the flow curves and equations from the literature have been carried out. Later on the experimental results were compared to the simulated results. It was also used in addition, the optimized simulation to evaluate the residual stresses and the results were then compared with experimental results obtained by neutron diffraction for the same bars that were extracted from the industrial process. The results are very influenced by the flow stress curve chosen. The simulation was satisfactory for the estimation of the drawing force but must be improved for a better estimation of residual stresses.
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Marini, Michelangelo. "Numerical models for the simulation of shot peening induced residual stress fields: from flat to notched targets." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/266179.
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Shot peening is a cold-working surface treatment, basically consisting in pelting the surface of the to-be-treated component with a high number of small hard particles blown at relatively high velocity. This causes the plasticization of the surface layer of the substrate, and the generation of a compressive residual stress field beneath the component surface. The surface topology modification can be beneficial for coating adhesion, and the work hardening enhances the fretting resistance of components, but the most commonly appreciated advantage of the process is the increased fatigue resistance in the treated component, due to the compressive residual stress which inhibits the nucleation and propagation of fatigue cracks. In spite of its widespread use, the mechanisms underlying the shot peening process are not completely clear. Many process parameters are involved (material, dimension, velocity of the shots, coverage, substrate mechanical behavior) and their complex mutual interaction affects the success of the process as well as the jeopardizing of any beneficial effect due to the increased surface roughness. Experimental measurements are excessively expensive and time-costly to deal with the wide variability of the process parameters, and their feasibility is not always granted. The effect of shot peening is indeed particularly effective where geometrical details (e.g. notches or grooves) act as stress raisers and where the direct measurement of residual stresses is very difficult. Nonetheless, the knwoledge of the effects of the treatment in this crictical locations would be extremely useful for the quantitative assessment of the effect of shot peening and, ultimately, for the optimization fo the process as well as its complete integration in the design process. The implementation of the finite element method for the simulation of shot peening has been studied since many years. In this thesis the simulation of shot peening is studied, in order to progress towards a simulation approach to be used in the industrial practice. Specifically, the B120 micro shot peening treatment performed with micrometric ceramic beads is studied, which has proven to be very effective of aluminum alloys, such as the aeronautical grade Al7075-T651 alloy considered in this work. The simulation of shot peening on a flat surface is addressed at first. The nominal process parameters are used, to include stochastic variability of the shot dimensions and velocity. A MatLab routine based on the linearization of the impact dent dimension, on the shot dimension and velocity is used to assess the coverage level prior to the simulation and predict the number of shots to full coverage. To best reproduce the hardening phenomena of the substrate material under repeated impacts, the Lemaitre-Chaboche model is tuned on cyclic strain tests. Explicit dynamic finite element simulations are carried out and the statistical nature of the peening treatment is taken into account. The results extracted from the numerical analyses are the final surface roughness and residual stresses, which are compared to the experimentally measured values. A specific novel procedure is devised to account for the effect of surface roughness and radiation penetration in the in-depth residual stress profile. In addition, a static finite element model is devised to assess the concentration effect exerted by the increased surface roughness on an external stress. The simulation of shot peening on an edge is then addressed as a first step towards more complex geometries. Since the true peening conditions are not known in this locations, a synergistic discrete element - finite element method approach is chosen for the correct modelization of the process. A discrete element model of the peening process on a flat surface is used to tune the simulation on the nominal process parameters, i.e. mass flow rate and average shot velocity, and to assess the nozzle translational velocity. Discrete element simulations are used to simulate the process when the nozzle turns around the edge tip. To lower the computing cost, the process is linearized into static-nozzle simulations at different tilting angles. The number of impacting shots and their impact velocity distribution are used to set up the finite element simulations, from which the resulting residual stress field is obtained. In addition to the realistic simulation, two simplified simulation approaches for the practical industrial use are devised. The resulting residual stress fields are compared with the reference residual stress field computed using thermal fields in a finite element simulation, tuned with experimental XRD measurements. The effect of the dimension of the fillet on the edge tip is studied by modifying the finite element model of shot peening on an edge. 3 different fillet radii (up to 40 um) are considered, on the basis of experimental observations. The resulting residual stress field are compared to analyze the effect of the precise geometry of the substrate. Lastly, the simplified simulation approach devised in the case of the edge is used to simulate shot peening on the root of a notch. The resulting residual stress field is again compared to the reconstructed reference one.
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Murugaratnam, Kovthaman. "A refined numerical modelling technique for Shot Peening." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:43e0fa12-bf49-425b-9ba6-6b93adaa8a7e.
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Compressive residual stresses (CRS) are beneficial for enhancing the fatigue life of metal components. Shot Peening (SP) is an industrial cold working process that is applied to induce a field of CRS and modify the mechanical properties of the metal component. The SP process involves impacting a surface with tiny shots with forces sufficient to create plastic deformation. The process is governed by a number of important parameters such as the shot size, angle of attack, initial velocity, mass flow rate and the distance from the shot nozzle to the surface being peened. The relationship between the optimal peening outcome, particularly the residual stress distribution of the treated surface, and the peening parameters is still unknown and needs to be investigated further. Manufacturers are interested in producing a uniform peening process for complex geometries which optimises the SP parameters. Modelling the process is complex as it involves the interaction of a metallic surface with a large number of shots of very small diameter. Conventionally, such problems are solved using finite element software to predict stresses and strains of a single shot impact then applying superposition. At the moment there are no Finite Element Method (FEM) modelling solutions involving more than tens of shots. The number of shots and elements required for such a modelling process made the approach unfeasible prior to the work described herein. The objective of this work is to develop an appropriate numerical modelling approach that can better simulate the real SP process. The model will be provided by combining Discrete Element Method (DEM) with FEM. The DEM is employed to get a distribution of impact velocities over space and time which are then implemented into a FEM analysis. A discrete element model with randomly distributed steel shots bombarding a steel component at various velocities has been developed as benchmark example. With this model the SP shot - shot interaction, the shot - target interaction, the surface coverage, angle of impingement, shot size, impact velocity and the overall shot flow can be parametrically studied in details and with little computational effort. The novel approach also proposes a new method to dynamically change the coefficient of restitution for repeated impacts during the simulation and predicts the CRS more effectively. The effects of SP on different materials of relevance to gas turbine engine components will be investigated in order to improve the understanding of the interaction between the shots and the targeted material. Initially, an uncoupled analysis was peforned, in order to assess the capabilities of the two modelling systems, DEM and FEM, to delivery an improved solutuion when combining two commercially available codes. This parametric analysis is performed using the state-of-the-art Discrete Element (DE) application EDEM. In the subsequent part of this work, a dynamic Finite Element (FE) application Abaqus will be used to investigate single shot impacts and to obtain the residual stress distribution. This gives us a prescribed residual stress distribution and peening coverage. A Combined DEM/FEM tool (DEST) is proposed that eliminates any manual pre-processing required for linking/coupling, eliminating the use of two different applications and provide an integrated solution for the simulation of the Shot Peening process. In the subsequent chapter, the implementation of essential tools for the enchanced modelling of Shot Peening process functionalities, such as the nozzle, bounding box, coverage and intensity is described. A number of computational improvements are also implemented to reduce the computation time. The existing binary search is enhanced to self-balancing search tree and further improved to allow insertion and deletion of elements. A bounding box feature which removes shots that move out of the domain during the course of the simulation is also implemented. Experiments featuring single shot impacts are performed to gain better understanding the deformation process in the target material subjected to impact conditions to those occurring in the production peening. The single shot impacts are experimentally examined using SEM and EBSD. During final chapter, case studies are performed to compare the results of the simulations with large-scale experimental work. The coverage of peening of single and multiple nozzles with different angle of impingements are assessed. Finally, possible directions for further research concerning the accurate quantification of material responses to SP are identified in the report.
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Martins, Jairo Aparecido. "Analise de tensões residuais em valvulas estampadas por meio da difração de raios-X e do metodo de elementos finitos." [s.n.], 2004. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264486.
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Orientadores: Sergio Tonini Button, Lisandro Pavie CardosoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: A evolução dos materiais, de seus processos de transformação e de diversos componentes mecânicos vêm requerendo cada vez mais o desenvolvimento de técnicas e métodos para sua análise. A transformação de materiais por deformação plástica origina tensões internas chamadas tensões residuais que podem vir a alterar a resposta do componente e/ou sistema quando em uso. Este trabalho tem como objetivo a análise dessas tensões residuais em válvulas dinâmicas estampadas por difração de raios- X e pelo método de elementos finitos. Dentro deste contexto, foi desenvolvido um método alternativo ao usual sen2", para a determinação de tensões residuais por difração de raios- X em pequenas áreas, esse utiliza o método de análise da difração de raios-X usualmente empregada na determinação de tensões residuais em filme finos . Os resultados obtidos na difração de raios-X mostraram-se compatíveis com o processo de deformação estudado e também com os resultados da simulação numérica pelo método de elementos finitos. A comprovação prática desses resultados deu-se pela realização de ensaios de durabilidade em bancada por flexão alternada reversa de uma válvula dinâmica nas seguintes condições de fabricação: a) estampada, b) estampada e deformada plasticamente em regiões de alta solicitação mecânica e c) estampada, deformada plasticamente e com um processo abrasivo adicional empregado para a eliminação de regiões potencialmente danosas ao componente previamente verificadas na simulação. Os resultados obtidos nesses ensaios comprovaram a validade dos métodos empregados para a análise das tensões residuais
Abstract: The continuous development of engineering materials, the new manufacturing processes, and the more complex mechanical parts have required constandy improvement of techniques and methods able to make analyses fast and easy. Metal forming with dimensional changes by plastic deformation results internal stresses, named residual stresses, which can significandy a:ffect the mechanical performance of parts and systems. The main objective of this work is to develop a method to analyze the residual stresses in stamped dynamical valves by X-ray diffraction and by the finite element method. In this context it was developed a sin2", alterna tive method based on the method common1y applied to the determination of residual stresses in metallic thin fUms. The results obtained from X-ray diffraction are coherent to those obtained in the stamping processes and in the simulation by the finite element method. These results were also compared to results from fatigue tests carried out with a laboratory bench (cantilever alterna te reversed bending) with dynamic valves in the conditions: a) as blanked , b) blanked and plastica11y deformed on the regions subjected to high 10005, and c) blanked, plastica11y deformed and grinded to eliminate potential dangerous regions as revea1ed in the simulation. The results obtained in the fatigue tests confumed the validity of the methods applied in this work to analyze the residual stresses
Doutorado
Materiais e Processos de Fabricação
Doutor em Engenharia Mecânica
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SOARES, MARIA da C. B. V. "Influencia das tensoes residuais no comportamento em fadiga e fratura de ligas metalicas." reponame:Repositório Institucional do IPEN, 1998. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10668.
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Tese (Doutoramento)
IPEN/T
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Medeiros, Iury Zottele. "Modelagem optomecânica de fibras ópticas microestruturadas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259176.
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Orientador: Hugo Enrique Hernández FigueroaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: Atualmente as fibras ópticas microestruturadas (FOMs) estão sendo cada vez mais exploradas por possuírem geometricamente um maior grau de liberdade em seu projeto, além da possibilidade do uso de materiais não usados em fibras convencionais, proporcionando características ópticas antes inalcançáveis. Sendo assim, através do uso do programa para obtenção de modos de propagação pelo método dos elementos finitos totalmente vetorial disponível no grupo do Prof. Dr. Hugo E. H. Figueroa, foram apresentadas técnicas de simulação em FOMs multimodais, as quais foram implementadas em FORTRAN e adicionadas ao programa principal. Neste trabalho também foi estudado os esforços mecânicos gerados pelo o uso de diferentes materiais na constituição da FOM em seu processo de fabricação. Tais esforços são conhecidos como tensão residual térmica e proporcionam variações anisotrópicas dos índices de refração dos meios que compõem as FOMs. Primeiramente o cálculo das tensões residuais foi feito analiticamente para uma geometria generalizada de FOM, e então tratando-as como uma pertubação no modo propagante analisado anteriormente pelo programa de análise modal. Por ultimo foi implementado um código para o cálculo estimativo da birrefringência de fase e de grupo levando em conta os esforços mecânicos induzidos no processo de fabricação, portanto o objetivo final foi alcançado
Abstract: Nowadays micro-structured optical fibers (MOFs) are being increasingly exploited since they have a greater geometrical flexibility in its project, in addition to the possibility of using un-conventional materials, providing optical features unreachable before. Therefore, a full-vectorial finite element modal solver developed by Prof. Dr. Hugo E. H. Figueroa's group was used, since it has already proved its efficiency. New techniques for multimodal MOFs simulation were presented, they were implemented using FORTRAN and then added to the main program to make the search for the propagation constants easier. Mechanical stress was also studied. It is generated by the use of different materials whithin the MOF constitution, in its manufacturing process. These stresses are known as thermal residual stresses and they provide variations of the anisotropic refractive indexes of the MOFs media. First, the calculation of the residual stresses was done analytically for a general geometry of MOF, and then they were treated as perturbations in the propagating mode, discussed previously by the full-vectorial finite element modal solver. Finally a code was implemented to estimate the phase and group birefringence, considering the mechanical stresses induced in the manufacturing process, therefore the ultimate goal was achieved
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica
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Sonde, Abayomi Emmanuel. "Etude et modélisation de procédés innovants de mise en compression de surfaces : Traitements de surface par cavitation et par impulsions électromagnétiques." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI015/document.
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Les procédés de traitement de surface tels que le grenaillage sont utilisés pour introduire des contraintes résiduelles de compression dans les matériaux métalliques. Cela permet de prévenir l'initiation et la propagation des fissures afin d'augmenter la durée de vie en fatigue des pièces mécaniques. Les limites et inconvénients des procédés actuels généralement utilisés pour cette fin sont connus et ont été mis en avant dans plusieurs études. Il s'agit d'une modification importante de l'état de surface (rugosité), une profondeur traitée limitée, des difficultés de mise en œuvre, etc. Aussi, de nouveaux procédés permettant d'obtenir des résultats équivalents voire meilleurs tout en évitant ces problèmes suscitent un intérêt grandissant. Le traitement de surface par cavitation (cavitation peening) et la mise en compression par impulsions électromagnétiques font partie de ces procédés innovants dont la modélisation a fait l'objet de cette thèse. Le traitement de surface par cavitation consiste à générer un jet d'eau submergé contenant des bulles de cavitation et dirigé vers la surface à traiter. La principale difficulté dans la modélisation du cavitation peening est la détermination du chargement mécanique sur la surface provenant de l'implosion des bulles de cavitation. L'effondrement des bulles peut se faire de manière sphérique ou non-sphérique suivant leur proximité de la paroi solide. Des modèles analytiques et numériques ont donc été élaborés pour étudier la dynamique des bulles et déterminer l'onde de pression due à une bulle sphérique d'une part, et la pression d'impact du micro-jet (bulle asphérique) d'autre part. Ces deux types de sollicitations ont été comparés et un modèle macroscopique pour le traitement par cavitation a été dérivé, en s'appuyant sur une simulation numérique du jet de cavitation. Une comparaison avec des résultats expérimentaux a été effectuée et a montré la pertinence du modèle proposé. En ce qui concerne le traitement par impulsions électromagnétiques, il consiste à générer un puissant champ magnétique transitoire par induction dans la pièce de matériau conducteur. Les contraintes résiduelles proviennent de la déformation plastique créée par les forces de Laplace à l'intérieur du matériau. Un modèle numérique couplant l'électromagnétisme et la mécanique des solides a été mis en place pour la simulation du procédé. Grâce à une étude d'optimisation, ce modèle a permis d'obtenir les paramètres électriques nécessaires pour arriver à mettre en compression des matériaux de type alliage de base nickel ou d'aluminium par cette méthode. Les profondeurs de la mise en compression calculées sont théoriquement par calcul plus élevées que celles obtenues avec les méthodes classiques de traitement de surface. Une étude de l'influence des différents paramètres a été faite et a montré que le procédé peut être contrôlé de manière relativement aisée en variant l'intensité et la pseudo-fréquence du courant traversant l'inducteurSurface treatments methods like shot peening are used to introduce compressive residual stresses in metallic materials. The compressive stresses prevent the initiation and growth of cracks and hence improve the fatigue life of mechanical parts. The drawbacks and limitations of the existing processes generally used for this purpose are known and have been highlighted in many studies. These are, among others, an important surface modification (roughness), a limited compressive depth, difficulties in execution, debris and contamination problems, etc. Therefore, the interest in new surface treatment methods, which permit to obtain equivalent or even better compressive results while avoiding the previous problems, are growing. Cavitation peening and electromagnetic pulse peening are part of these innovative processes which modeling is the aim of this PhD thesis. Cavitation peening is a process of surface treatment which acts by the generation of cavitation bubbles near the workpiece surface. The modeling of this process is challenging because of the complexity of cavitation phenomenon and the main problematic point is the determination of the mechanical loading on the material due the bubbles collapse. In this thesis, an approach of modeling for cavitation peening based on the study of the dynamics of cavitation bubbles is proposed. Spherical and aspherical collapse of bubbles near a solid surface are studied by some numerical and analytical models. These two sources of loading pressures have been compared and a macroscopic model for cavitation peening have been derived by associating the numerical simulation of the cavitation jet and the localization of the cavitation zone. The comparison between the final residual stress profile calculated with the proposed model and the experimental results were satisfactory. Electromagnetic pulse peening (EMP) is a contactless process of surface treatment which could be used to introduce compressive residual stresses in conductive materials, by the generation of a high transient electromagnetic field. Laplace forces induced in the material by magnetic induction are the source of the material plastic deformation and compressive residual stresses introduction. To predict the EMP results, a numerical model have been built for the process simulation. The model, based on finite element method, coupled successfully electromagnetic and mechanical phenomena by using a sequential-coupled approach. It was proven theoretically, by the study of a reference case, that compressive residual stresses could be induced in metallic materials like nickel-based (Inconel) or aluminum alloys by the means of the present process. It was also shown by the calculations that much higher compressive depths than those of conventional peening processes could be achieved. The parametric study exhibited the influence of the maximum current intensity and frequency which affect both the compressive depth and the maximum residual stress
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Novotný, Lukáš. "Návrh a realizace experimentálního zařízení pro určování zbytkové napjatosti ohýbaných vzorků." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382570.
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The master thesis is focused to design and realization of experimental equipment for researching of residual stress determination for specimen with non-uniform distribution stress along the depth. Literature search study of problematic was performed and it was used for elaboration of chapters about origin of residual stress, their classification and chapters about methods, which are used for measuring of residual stress and their determination. The following part explains the design of experimental equipment and stress-strain analysis of selected parts of this equipment. Then the final design of equipment is presented, including complete production drawings, and it’s explained final assembling of experimental equipment. Final chapter is devoted to examinable loading of specimen.
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Cheng, Wentao. "In-plane shrinkage strains and their effects on welding distortion in thin-wall structures." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124049585.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xx, 268 p.; also includes graphics (some col.). Includes bibliographical references (p. 256-268). Available online via OhioLINK's ETD Center
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Silva, Evandro Cardozo da. "Analise numerica do processo corformação de chapas metalicas por jateamento de esferas." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264439.
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Orientadores: Sergio Tonini Button, Renato PavanelloTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: O grande desafio do engenheiro no processo de jateamento de esferas, é obter o perfil da tensão residual e a deformação final da peça com precisão. Pois a solução analítica, os resultados experimentais e as simulações numéricas, que possam ser validados, ainda não são totalmente dominados, devido a complexidade do problema de contato dinâmico não linear do impacto que envolve várias disciplinas da elasticidade e plasticidade estática e dinâmica. É preciso reconhecer os vários parâmetros que influenciam o processo e obter um modelo de simulação numérica 3D de elementos finitos (EF) dinâmica e estática, utilizando ferramentas comerciais consagradas, que tenha relativa precisão e possa ser validado ao se caracterizar a tensão residual mecânica induzida e conseqüente deformação. O estudo de modelos estáticos de carregamento equivalente são limitados pela precisão da temperatura e pressão que da a forma final da peça. No modelo de EF elasto-plástico dinâmico 3D do impacto simples, identifica-se que a camada deformada plasticamente, a tensão residual superficial e sub-superficial são influenciados significativamente pelas características da esfera. Além disso, a separação entre as esferas no impacto simultâneo alteram o desenvolvimento da região plástica. Modelos de impactos múltiplos são implementados com base nestes resultados para a condição de impacto concentrado e disperso de forma semialeatória para modelos reduzidos da peça discretizada
Abstract: Shot peen forming presents a great challenge to engineers to get a precise residual stress and the correct final plastic strain distribution within the formed parts. Because there is not a complete knowledge on analytical solutions, experimental results and numerical simulations are commonly used due to the complex dynamic contact of nonlinear impact problems that involve many disciplines on static and dynamic elasticity and plasticity. Therefore, it is essential to know the parameters that affect the process to obtain a static and dynamic 3D finite element (FE) numerical model to simulate peen forming using powerful FE commercial codes that have relative precision and give results that can be validated and consequently induced mechanical residual stress and consequent deformation can be characterized. The study of equivalent static load models are limited by the precision of temperature and pressure to calculate the correct deformed shape. In the elastic-plastic 3D dynamic FE model with a single impact, the shot characteristics influence the thickness plasticity, and the superficial and under surface residual stress. Besides, the separation distance between adjacent shots changes the development of the plastic region. Multiple shot impacts models are implemented based in these results for concentrate and partial randomic dispersed impact conditions to reduce the models of the target
Doutorado
Materiais e Processos de Fabricação
Doutor em Engenharia Mecânica
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Taro, Mandikizinoyou. "Modélisation et simulation des procédés de mise en compression des surfaces à très grandes vitesses de déformation par méthode semi-analytique." Thesis, Lyon, INSA, 2015. http://www.theses.fr/2015ISAL0105/document.
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La défaillance des pièces mécaniques est très souvent initiée par un défaut de surface. Par conséquent, la génération de contraintes résiduelles compressives sur des pièces mécaniques via une déformation plastique hétérogène améliore la tenue en fatigue et augmente la durée de vie des pièces. Parmi les procédés permettant d'introduire des contraintes résiduelles dans les pièces, le traitement par choc laser est plus intéressant à plusieurs titres. D'une part, il permet de produire des pressions en surface du matériau de l'ordre de 1 à 6 GPa sur de courtes durées d'impulsion allant de 3 à 30 nanosecondes. D'autre part, il offre la possibilité d'introduire des contraintes résiduelles de compression sur une certaine profondeur tout en conservant l'état initial de la pièce traitée. Ainsi, les simulations numériques par réalisation de modèles simples permettent de cerner les physiques mises en jeux. Dans cette perspective, la méthode semi-analytique offre d'énormes avantages, notamment la simplicité des modèles et la réduction des temps de calcul. Cependant, cette méthode n’a jamais été étendue aux problème dynamiques. Dans cette thèse la méthode semi-analytique a été étendue aux problèmes dynamiques et le modèle mis en place été appliqué pour la simulation du procédé de choc LaserThe failure of the mechanical parts is very often initiated by a surface defects. Consequently, the generation of compressive residual stresses on mechanical parts by introducing a heterogeneous plastic strain improves the resistance to fatigue and increases the lifetime of the parts. Among the processes making it possible to introduce residual stresses into the parts, the laser shock peening is more interesting for several reasons. On the one hand, it makes it possible to produce pressures on the surface of material of about 1 to 6 going GPa over short pulse times from 3 to 30 nanoseconds. In addition, he gives the opportunity of introducing residual stresses of compression on a certain depth while preserving the initial state of the treated part. The numerical simulation becomes necessary to determine the best physical phenomena involved. Thus, the semi-analytical method offers a lot of advantages, in particular the simplicity of the models and the computation times saving. This method was never extended to the dynamic problems. In this thesis the semi-analytical method was extended to the dynamic problems and the model implemented is applied for the simulation of the Laser process of shock
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Boyer, Vincent. "Modélisation du grenaillage d’un alliage de nickel avec prise en compte de l’écrouissage et de la microstructure." Thesis, Troyes, 2017. http://www.theses.fr/2017TROY0030.
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Le grenaillage de précontrainte est un procédé de traitement de surface répandu dans le domaine industriel permettant d’augmenter la durée de vie en fatigue d’une pièce mécanique. Ce procédé demeure néanmoins empirique en raison de mécanismes mal maitrisés liés à la dissipation des contraintes résiduelles.Pour ces raisons, les disques de turbine haute pression forgés en Inconel 718 produits par Safran Aircraft Engines sont grenaillés sans que le procédé ne soit intégré à la phase de dimensionnement, à des fins purement conservatives. Les impératifs de compétitivité et de sécurité créent le besoin d’un modèle prédictif du procédé et du gain en durée de vie pour une pièce à géométrie complexe. Cette thèse est rattachée au projet CONDOR (CONtrainte, DimensiOnnement Relaxation) qui se donne pour objectif de répondre à ce besoin. Le présent travail en est la première étape, et a pour but de mettre en place un modèle numérique rendant compte de l’écrouissage généré au cours du procédé. Ce paramètre a une influence de premier ordre sur la relaxation des contraintes résiduelles.Une caractérisation poussée du matériau, tenant compte du comportement visqueux de l’Inconel 718 est réalisée, permettant, la mise en place d’un modèle numérique de grenaillage. Ce modèle prédit l’état de contrainte résiduelle et d’écrouissage, et offre une vision statistique des résultats. Une vaste campagne expérimentale de mesure par DRX sur éprouvettes grenaillées a permis de corréler le modèle. Celui-ci est ensuite utilisé afin de caractériser l’état mécanique post-grenaillageShot-peening in a surface treatment used in the industry to enhance fatigue life of a mechanical part. Nonetheless, this process remains empirical as complex phenomena linked with residual stress relaxation are not well understood yet. For these reasons, peening step of turbine disks produced by Safran Aircraft Engines, made in Inconel 718, is not considered in the dimensioning phase of the part. Today there is a need for a precise prediction of the process and the life enhancement of peened parts. This thesis is part of the CONDOR project, the objective of which is to answer this need. This work is the first step, and its goal is to build a numerical model of shot-peening able to predict the work-hardening state after the process. In fact this parameter is known to have an important role in the relaxation of residual stress.Complete assessment of the mechanical behavior of Inconel 718 is first proposed. Then the numerical model is built, able to adress the stress and work-hardening state of the peened part. A statistical approach is also proposed. An important XRD experimental campaign on peened sampled was led to correlate the model. Finally, the simulation is used to predict the mechanical state after shot-peening
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Capron, Adélie. "Towards the predictive FE analysis of a metal/composite booster casing’s thermomechanical integrity." Doctoral thesis, Universite Libre de Bruxelles, 2020. https://dipot.ulb.ac.be/dspace/bitstream/2013/314767/5/contratAC.pdf.
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In response to serious environmental and economic concerns, the design and production of aircrafts have been changing profoundly over the past decades with the nose-to-tail switch from metallic materials to lightweight composite materials such as carbon fibre reinforced plastic (CFRP). In this context, the present doctoral research work aimed to contribute to the development of a CFRP booster casing, a real innovation in the field initiated and conducted by Safran Aero Boosters. More specifically, this thesis addresses the matter of joining metal/CFRP hybrid structures, which are prone to possibly detrimental residual stresses.The issue is treated with an approach combining experimental characterisation and finite element (FE) simulations. The multi-layered system’s state of damage was systematically examined on hundreds of micrographs, and the outcome of this study is presented under the form of a statistical analysis. Further, the defects’ 3D morphology is investigated by incremental polishing. A number of thermal and mechanical properties are measured by diverse physical tests on part of the constituent materials, i.e. the aerospace grade RTM6 epoxy resin, the structural Redux 322 epoxy film adhesive, and AISI 316L stainless steel. They are used as input data in a FE model of the multilayer that is developed and progressively refined to obtain detailed residual stress fields after thermal loading. These results are compared to experimental data acquired by X-ray diffraction stress analysis and with the curvature-based Stoney formula. Cohesive elements are placed at specific locations within the FE model to allow simulating progressive damage. Peel tests, mode I, mode II and mixed mode I/II fracture tests are thus performed in view of measuring the joint toughness. The results of these tests are discussed and the presence of residual stress in the fracture specimens is highlighted. Key information for the calibration of the cohesive law is finally identified via inverse FE analysis of the mode I test, this being a significant step in the process of building a damage predictive FE model of the multi-layered system.Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Štegnerová, Kateřina. "Popis šíření trhlin v polích silně nehomogenních a reziduálních napětí." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-399210.
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This Ph.D. thesis was written under the supervision of Assoc. Prof. Luboš Náhlík, Ph.D. and Assoc. Prof. Pavel Hutař, Ph.D. Thesis is focused mainly on application of generalized linear elastic fracture mechanics, which allows description of crack behaviour propagating from general singular stress concentrators, such as material interfaces or sharp V-notches, and verification of validity of used fracture criteria. The obtained results were used in the next part of the thesis, which deals with the issue of crack propagating in ceramic composites, where the stress distribution field is strongly influenced by the existence of material interface and presence of residual stresses, that arise during manufacturing process of composite.
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Maricic, Luke A. "Thermo-mechanical Behaviour of Turbine Disc Assembly in the Presence of Residual Stresses." Thesis, 2013. http://hdl.handle.net/1807/43135.
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A comprehensive three dimensional coupled thermo-mechanical finite element study is performed on turbine blade attachments in gas turbine engines. The effects of the self-generated centrifugal forces of the disc and the associated blades, thermal loads, and shot peening residual are all considered in this thesis. Three aspects of the work were accordingly examined. The first was concerned with the coupled thermo-mechanical stress analysis and load sharing between the teeth of the fir-tree root. The second was devoted to the development of a complete model incorporating the effect of shot peening residual stresses upon the developed stress state. The effectiveness of shot peening treatment in response to cyclic thermo-mechanical loadings at the contact interface has also been studied. The third was concerned with the validation of some aspects of the developed models analytically using closed form solutions and experimentally using photoelasticity.