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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
61

Constitutive Modeling and Life Prediction in Ni-Base Superalloys

Shenoy, Mahesh M. 01 June 2006 (has links)
Microstructural features at different scales affect the constitutive stress-strain response and the fatigue crack initiation life in Ni-base superalloys. While numerous efforts have been made in the past to experimentally characterize the effects of these features on the stress-strain response and/or the crack initiation life, there is a significant variability in the data with sometimes contradictory conclusions, in addition to the substantial costs involved in experimental testing. Computational techniques can be useful tools to better understand these effects since they are relatively inexpensive and are not restricted by the limitations in processing techniques. The effect of microstructure on the stress-strain response and the variability in fatigue life were analyzed using two Ni-base superalloys; DS GTD111 which is a directionally solidified Ni-base superalloy, and IN100 which is a polycrystalline Ni-base superalloy. Physically-based constitutive models were formulated and implemented as user material subroutines in ABAQUS using the single crystal plasticity framework which can predict the material stress-strain response with the microstructure-dependence embedded into them. The model parameters were calibrated using experimental cyclic stress-strain histories. A computational exercise was employed to quantify the influence of idealized microstructural variables on the fatigue crack initiation life. Understanding was sought regarding the most significant microstructure features using explicit modeling of the microstructure with the aim to predict the variability in fatigue crack initiation life and to guide material design for fatigue resistant microstructures. Lastly, it is noted that crystal plasticity models are often too computationally intensive if the objective is to model the macroscopic behavior of a textured or randomly oriented 3-D polycrystal in an engineering component. Homogenized constitutive models were formulated and implemented as user material subroutines in ABAQUS, which can capture the macroscale stress-strain response in both DS GTD111 and IN100. Even though the study was conducted on two specific Ni-base superalloys; DS GTD111 and IN100, the objective was to develop generic frameworks which should also be applicable to other alloy systems.
62

Supercritical Gas Cooling and Near-Critical-Pressure Condensation of Refrigerant Blends in Microchannels

Andresen, Ulf Christian 14 December 2006 (has links)
A study of heat transfer and pressure drop in zero ozone-depletion-potential (ODP) ‎refrigerant blends in small diameter tubes was conducted. The azeotropic refrigerant ‎blend R410A (equal parts of R32 and R125 by mass) has zero ODP and has properties ‎similar to R22, and is therefore of interest for vapor compression cycles in high-‎temperature-lift space-conditioning and water heating applications. Smaller tubes lead to ‎higher heat transfer coefficients and are better suited for high operating pressures.‎ Heat transfer coefficients and pressure drops for R410A were determined experimentally ‎during condensation across the entire vapor-liquid dome at 0.8, 0.9xPcritical and gas ‎cooling at 1.0, 1.1, 1.2xPcritical in three different round tubes (D = 3.05, 1.52, 0.76 mm) ‎over a mass flux range of 200 < G < 800 kg/m2-s. A thermal amplification technique was ‎used to accurately determine the heat duty for condensation in small quality increments ‎or supercritical cooling across small temperature changes while ensuring low ‎uncertainties in the refrigerant heat transfer coefficients. ‎ The data from this study were used in conjunction with data obtained under similar ‎operating conditions for refrigerants R404A and R410A in tubes of diameter 6.22 and ‎‎9.40 mm to develop models to predict heat transfer and pressure drop in tubes with ‎diameters ranging from 0.76 to 9.40 mm during condensation. Similarly, in the ‎supercritical states, heat transfer and pressure drop models were developed to account for ‎the sharp variations in the thermophysical properties near the critical point.‎ The physical understanding and models resulting from this investigation provide the ‎information necessary for designing and optimizing new components that utilize R410A ‎for air-conditioning and heat pumping applications.‎
63

Atomistic Characterization and Continuum Modeling of Novel Thermomechanical Behaviors of Zinc Oxide Nanostructures

Kulkarni, Ambarish J. 09 October 2007 (has links)
ZnO nanowires and nanorods are a new class of one-dimensional nanomaterials with a wide range of applications in NEMS. The motivation for this work stems from the lack of understanding and characterization of their thermomechanical behaviors essential for their incorporation in nanosystems. The overall goal of this work is to develop a fundamental understanding of the mechanisms controlling the responses of these nanostructures with focus on: (1) development of a molecular dynamics based framework for analyzing thermomechanical behaviors, (2) characterization of the thermal and mechanical behaviors in ZnO nanowires and (3) development of models for pseudoelasticity and thermal conductivity. The thermal response analyses show that the values of thermal conductivity are one order of magnitude lower than that for bulk ZnO due to surface scattering of phonons. A modified equation for phonon radiative transport incorporating the effects of surface scattering is used to model the thermal conductivity as a function of wire size and temperature. Quasistatic tensile loading of wires show that the elastic moduli values are 68.2-27.8% higher than that for bulk ZnO. Previously unknown phase transformations from the initial wurtzite (WZ) structure to graphitic (HX) and body-centered-tetragonal (BCT-4) phases are discovered in nanowires which lead to a more complete understanding of the extent of polymorphism in ZnO and its dependence on load triaxiality. The reversibility of the WZ-to-HX transform gives rise to a novel pseudoelastic behavior with recoverable strains up to 16%. A micromechanical continuum model is developed to capture the major characteristics of the pseudoelastic behavior accounting for size and temperature effects. The effect of the phase transformations on the thermal properties is characterized. Results obtained show that the WZ→HX phase transformation causes a novel transition in thermal response with the conductivity of HX wires being 20.5-28.5% higher than that of the initial WZ-structured wires. The results obtained here can provide guidance and criteria for the design and fabrication of a range of new building blocks for nanometer-scale devices that rely on thermomechanical responses.
64

Methodology for predicting microelectronic substrate warpage incorporating copper trace pattern characteristics

McCaslin, Luke 09 July 2008 (has links)
The current trend in electronics manufacturing is to decrease the size of electronic components while attempting to increase processing power and performance. This is leading to increased interest in thinner printed wiring boards and finer line widths and wire pitches. However, mismatches in the thermomechanical properties of materials used can lead to warpage, hindering these goals. Warpage can be problematic as it leads to misalignments during package assembly, reduced tolerances, and a variety of operational failures. Current warpage prediction techniques utilize isotropic volume averaging to estimate effective material properties in layers of copper mixed with interlayer dielectric material. However, these estimates do not provide material properties with sufficient accuracy to predict warpage, as they contain no information about the orientation of the copper traces. This thesis describes the development of a new technique to predict the warpage of a particular substrate. The technique accounts for both the trace pattern planar density and planar orientation in determining effective orthotropic material properties for each layer of a multi-layer substrate. Starting with the trace pattern image, this technique first divides the trace pattern into several smaller areas for a given layer of the substrate and then uses image processing techniques to determine the copper percentage and average trace orientation in each small area. The copper percentage and average trace direction orientation are used in conjunction with the material properties of copper and the dielectric material to calculate the effective orthotropic material properties of each smaller area of the substrate. A finite-element model is then created where each layer is represented as a concatenation of several small areas with independent directional properties, and such a model is then subjected to sequential thermal excursion as seen in the actual fabrication process. The results from the models have been compared against experimental data with a great degree of accuracy. The modeling technique and the results obtained clearly demonstrate the need for the proposed subdivisional orthotropic material property calculations, as opposed to homogeneous isotropic properties typically used for each layer in computational simulations, as these more accurate directional properties are capable of predicting warpage with higher accuracy.
65

Stucture and thermomechanical behavior of nitipt shape memory alloy wires

Lin, Brian E. 10 April 2009 (has links)
The objective of this work is to understand the structure-property relationships in a pseudoelastic composition of polycrystalline NiTiPt (Ti-42.7 at% Ni-7.5 at% Pt). Structural characterization of the alloy includes grain size determination and texture analysis while the thermo-mechanical properties are explored using tensile testing. Variation in heat treatment is used as a vehicle to modify microstructure. The results are compared to experiments on Ni-rich NiTi alloy wires (Ti-51.0 at% Ni), which are in commercial use in various biomedical applications. With regards to microstructure, both alloys exhibit a <111> fiber texture along the wire drawing axis, however the NiTiPt alloy's grain size is smaller than that of the Ni-rich NiTi wires, while the latter materials contain second phase precipitates. Given the nanometer scale grain size in NiTiPt and the dispersed, nanometer scale precipitate size in NiTi, the overall strength and ductility of the alloys are essentially identical when given appropriate heat treatments. Property differences include a much smaller stress hysteresis and smaller temperature dependence of the transformation stress for NiTiPt alloys compared to NiTi alloys. Potential benefits and implications for use in vascular stent applications are discussed.
66

Materiais compósitos à base de gesso contendo eva (Etileno Acetato de Vinila) e vermiculita: otimização de misturas e propriedades termomecânicas / Composite materials based gypsum containing eva (ethilene vinil acetate) and vermiculite: optimization of mixtures and thermomechanical properties

Oliveira, Marilia Pereira de 29 May 2009 (has links)
Made available in DSpace on 2015-05-08T15:00:03Z (GMT). No. of bitstreams: 1 parte1.pdf: 2195747 bytes, checksum: 603940fe9313a5c16903650901059e36 (MD5) Previous issue date: 2009-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Gypsum is a building material older than is known. Some of their properties they confer advantages such as fire resistance, thermal and acoustic insulation. By virtue of being a ligand less aggressive environment than Portland cement, its use should be encouraged and new applications studied. This work aims to study the physical-mechanical and thermal composite gypsum with the addition of vermiculite and waste of the footwear industry (EVA). The development of these composites has as its purpose the production of elements of thermal protection coating on walls. In the initial stage were investigated physical and mechanical properties of these composites. To determine the influence of levels of EVA and vermiculite, and ratio water/plaster in the physical and mechanical properties of composites in the fresh and hardened were incorporated into five different percentages of the materials with the three ratios water/plaster. A basic composition of each composite was determined by multivariate analysis. Then the composite was optimized its matrix modified with the partial replacement of gypsum by ceramic waste and lime and studied its physical and mechanical properties as well as aspects related to durability. Finally they were certain the thermal properties of composites with waste gypsum and gypsumvermiculite waste-EVA and proposed a constructive element for use in masonry lining and examined its thermal performance. The results indicated that the incorporation of ceramic waste and lime into matrix gypsum of the composites improved their optimized mechanical properties and their performance in relation to water by surface treatment. The theoretical study has shown that proposed plates reduce the heat load incident on mansory. / O gesso é um dos materiais de construção mais antigos que se tem conhecimento. Algumas de suas propriedades lhe confere vantagens como, resistência ao fogo, isolamentos térmico e acústico. Em virtude de ser um ligante menos agressivo ao ambiente que o cimento Portland, seu uso deve ser incentivado e novas aplicações estudadas. Este trabalho teve como objetivo estudar as propriedades físico-mecânicas e térmicas de compósitos à base de gesso com a incorporação de vermiculita e de resíduos da indústria de calçados (EVA). O desenvolvimento destes compósitos tem como propósito a produção de elementos de revestimento para proteção térmica de alvenarias. Na etapa inicial foram pesquisadas as propriedades físicas e mecânicas desses compósitos. Para determinar a influência dos teores de resíduo de EVA e vermiculita e da relação água/gesso nas propriedades físicomecânicas dos compósitos no estado fresco e endurecido foram incorporados cinco percentuais diferentes dos materiais com três relações água/gesso. Uma composição básica de cada compósito foi determinada através de análise estatística multivariada. Em seguida o compósito otimizado teve sua matriz modificada com a substituição parcial do gesso por resíduo cerâmico e cal e estudadas suas propriedades físico-mecânicas, bem como aspectos relacionados à durabilidade. Finalmente foram determinadas as propriedades térmicas do gesso e do compósito gesso com vermiculita e gesso com EVA e proposto um elemento construtivo para aplicação em revestimento interno de alvenarias bem como analisado teoricamente seu desempenho térmico. Os resultados deste trabalho indicaram que a incorporação de resíduo cerâmico e cal à matriz de gesso dos compósitos otimizados melhoraram suas propriedades mecânicas bem como seu desempenho em relação à água mediante o tratamento superficial. O estudo teórico demonstrou que as placas propostas reduzem a carga térmica incidente em alvenarias.
67

Thermomechanical processing of eutectoid steels: strategies to improve the microstructure of the hot rolled strips

Caruso, Matteo 30 October 2013 (has links)
Eutectoid steel strips are designed for the production of parts for intensive use such as clutches, seat slides, and springs as they exhibit<p>excellent strength levels and wear resistance. These properties arise from the unique morphology of lamellar pearlite which can be considered<p>as a self-laminated nanoscale composite. However, a spheroidization annealing step is nowadays necessary to improve the cold forming properties before further cold rolling steps.<p>This thesis is aimed at improving the tensile ductility of the hot rolled products of eutectoid composition in order to eliminate the intermediate<p>annealing step. Two strategies are proposed.<p>The first is to transpose the concept of controlled rolling developed for HSLA to<p>eutectoid steels. Through a strict adjustment of the austenite processing and of the cooling strategy, it is possible to improve the ductility<p>of the final lamellar microstructure. The way the processing parameters influence the hot deformation of austenite, the eutectoid transformation and of the subsequent spheroidization annealing is deeply<p>investigated. It is found that refinement and pancaking of austenite<p>is beneficial as it reduces the pearlite block size improving the total<p>tensile elongation. Accelerated cooling is of paramount importance to<p>achieve fine Interlamellar spacing (ILS), which lead to high strength<p>levels and accelerate spheroidization during subsequent annealing.<p>The second approach involves intercritical or warm deformation. Warm processing of eutectoid steels is first explored by torsion testing<p>and then up-scaled to a pilot rolling-line. The interactions between thermomechanical parameters, rolling forces generated and microstructural<p>evolution are carefully scrutinized. During concurrent hot deformation, spheroidization of cementite takes place almost instantaneously<p>in both torsion and rolling. The restoration processes occurring in the ferrite matrix depends on the strain path and the strain rates. Low strain rates (0,1 s−1) and simple shear promotes the formation of a recrystallized-like HABs network of about 3μm in size.<p>Plane strain compression and high strain rates (10 s−1) leads to the formation of a typical recovered dislocation substructure (LABs) of 1μm in size. During annealing, no recrystallization occurs and the LABs substructure remains stable. This substructure influences drammatically the mechanical properties: the strength is very high and the work-hardening behavior is poor due to high recovery rate in the region close to the LABs. However, due to the presence of spheroidized<p>cementite particles the ductility of warm rolled eutectoid steels is higher than that of ultra fine grained low carbon steels. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished
68

Optimisation des propriétés thermomécaniques d’adhésifs polyépoxydes structuraux en conditions extrêmes : relation structure-propriétés / Optimisation of thermomechanical properties of structural epoxy adhesives in extreme conditions : structure-properties relationship

Plouraboué, Thibaud 14 December 2015 (has links)
La démocratisation des technologies du collage dans le domaine aérospatial amène les industriels à exiger des adhésifs toujours plus performants. L’objectif de cette thèse est d’optimiser les propriétés thermomécaniques d’un adhésif polyépoxyde bi-composant qui devra présenter des propriétés structurales entre -150°C et +150°C, tout en respectant des exigences de mise en oeuvre.L’analyse de la littérature et des expériences préliminaires a permis de sélectionner le système polyépoxyde modèle binaire le plus pertinent en termes de réactivité à l’ambiante et de propriétés sur assemblage collé. Pour optimiser la résistance en température élevée de ce système, deux voies ont été explorées : l’incorporation d’époxydes multi-fonctionnalisés pour augmenter la densité de réticulation, et l’utilisation d’amines cycliques qui accroit la rigidité des segments macromoléculaires. Pour améliorer les propriétés de résistance à la propagation de fissure à basse température, les additifs de renforcement montrent un intérêt certain pour la formulation d’adhésifs structuraux polymérisés à température ambiante. Sur la base de ces résultats, plusieurs formulations complexes ont pu être élaborées. Des phénomènes de synergie et d’inhibition entre les différents éléments des formulations ont été constatés, sans pouvoir être totalement compris ce qui met en lumière la difficulté de prévoir le comportement d’adhésifs complexes, à l’image des formulations commerciales.Ces travaux de thèse ont permis de développer un adhésif structural répondant aux exigences strictes du secteur aérospatial, et de dégager une stratégie de formulation qui pourra être appliquée à d’autres secteurs d’activités. / The democratisation of bonding technologies in aerospace field leads industrials to demand more and more efficient adhesives. The aim of this thesis is to optimise thermomechanical properties of two-component epoxy adhesives which need to preserve structural properties on a large scale of temperature (from -150°C to +150°C) and observing application process requirements.The analysis of scientific literature and preliminary experiments enable to select the most relevant binary epoxy system in terms of reactivity and bonding mechanical properties. To optimise high temperature resistance of this epoxy system, two approaches have been explored: addition of multi-functionalised epoxy resin to extend the crosslink density, and use of cycloaliphatic amines which increase the rigidity of macromolecular segments. To improve crack propagation resistance in low temperature, tougheners reveal an interest to formulate room temperature structural adhesives. On the basis of these results, complex formulations have been developed. Synergy and inhibition phenomenon between the formulation blends have been observed without being able to fully understand them which highlight the difficulty to predict the behaviour of complex adhesives such as commercial formulations.This thesis works allowed to develop a two-component epoxy adhesive formulation which meets aerospace requirements, and to bring about a formulation strategy which could be adapted to others sectors activities.
69

Simulations multi-échelles de matériaux polymères / Multiscale modelling of polymers

Maurel, Gaëtan 24 November 2014 (has links)
Les matériaux polymères sont aussi bien utilisés dans des applications de la vie courante que dans des domaines de haute technologie. Ces matériaux font intervenir des échelles spatiales et temporelles variées et étendues, rendant la modélisation de leurs propriétés inaccessible avec une seule méthode. Cette thèse propose le développement d’une stratégie multi-échelle, couplant ainsi plusieurs niveaux de représentation de la matière. Le but est d’accéder aux propriétés rhéologiques d’un polymère, faisant intervenir des temps de relaxation lents, tout en conservant les caractéristiques chimiques intrinsèques à sa microstructure de façon à pouvoir établir des relations structure-propriétés. Les potentiels d’interaction de l’échelle mésoscopique sont développés à partir des configurations atomistiques. Ils permettent ensuite une reproduction quantitative de plusieurs propriétés structurales du polymère, telles que la masse volumique ou la distance bout à bout. La transférabilité des potentiels mésoscopiques a été étudiée à travers la dépendance des propriétés thermomécaniques en température, en pression et en nature du polymère. À partir de ces potentiels, des simulations hors équilibre ont permis de déterminer des grandeurs caractéristiques comme la masse d’enchevêtrement ou le module élastique. L’approche multi-échelle est étendue à l’interaction polymère-silice, dans le but d’étudier l’impact des facteurs comme le degré de confinement ou la densité de greffage sur les propriétés dynamiques et structurales des chaînes au voisinage de la surface. / Polymer materials are widely used, both for everyday applications and in high-technology products. These materials involves a wide range of time and length scales, making the modelling of their properties challenging by using only one method. This thesis focuses on the development of a multiscale strategy, combining different levels of description of the matter. The aim is to reach the rheological properties of a polymer over a large time scale, while retaining the chemical structure inherent of its microstructure. The investigation of structure-property relationships will then be facilitated. The mesoscopic potentials are developped from atomistic configurations. A quantitative reproduction of several structural properties of the polymer such as density or end to end distance is obtained. Then, the transferability of the potentials has been studied through the dependence of temperature, pressure or polymer structure on thermomechanical properties. By using these potentials, nonequilibrium simulations have been carried out to calculate the entanglement mass and the plateau modulus. The multicale approach has been extended to model the polymer-silica interaction in order to study the impact of the degree of confinement or the grafting density on the dynamical and structural properties of polymer chains close to the surface.
70

Matériaux solide conducteur thermodurcissable : Application aux plaques bipolaires pour pile à combustible / Conducting solid thermosetting material : Application to bipolar plates for fuel cell

Dessertenne, Estelle 21 March 2012 (has links)
Parmi les nouvelles technologies pour l’énergie inscrites dans un contexte de développement durable, les piles à combustible à membrane échangeuse de protons (PEMFC) présentent des aspects séduisants. Toutefois, pour rendre cette technologie compatible avec une application à grande échelle, elle doit répondre à des exigences strictes en termes de coût, performance, et durabilité. Alors que les plaques bipolaires métalliques sont pénalisées par leur résistance à la corrosion et celles en graphite par leurs propriétés mécaniques et leur coût (dû aux phases d’usinage des canaux), les plaques bipolaires composites apparaissent attrayantes en raison de leurs propriétés et performances et de leur coût. Cette thèse s’inscrit dans ce cadre, en proposant un matériau composite à matrice organique de type époxy et charges conductrices de graphite. L’objectif de notre étude consiste à mettre au point un matériau thermodurcissable à base d’une formulation époxyde solide (permettant de contrôler sa chimie et plus particulièrement sa réactivité) fortement chargée en graphite. Deux formulations différentes sont étudiées. La première est à base de prépolymère époxy appelé DGEBA et de dicyandiamide (DDA) comme durcisseur. L’autre formulation étudiée est constituée de DGEBA et de durcisseur : le 3,3’,4,4’-benzophénone dianhydride tétracarboxylique (BTDA). Ces deux formulations ont la particularité d’être très réactives à haute température (180-200°C) caractérisées par des temps de gel très courts (plus petit que 1min) afin d’avoir un temps de cycle de réticulation court pour une industrialisation de la fabrication. De plus, ces mêmes matrices ont montré une bonne stabilité chimique à température ambiante ainsi qu’une bonne stabilité thermique du système réticulé compatible avec la température d’utilisation des piles en fonctionnement. Concernant les réseaux composites résultant de la polymérisation DGEBA/BTDA et DGEBA/DDA, le module au plateau caoutchoutique est dominé par le taux de charge qui est très élevé (85%), celui-ci est ainsi très proche d’un réseau à l’autre et reste supérieur à 1 GPa. Nous constatons une viscosité relativement élevée pour les systèmes fortement chargés, point à prendre en compte lors du procédé de transformation. Enfin, la dernière partie des travaux réalisés concerne l’étude de mélange constitué de la matrice thermodurcissable (DGEBA/DDA/urée) modifiée par un thermoplastique (PEI). L’originalité et l’intérêt de ce travail résident dans l’incorporation de charges conductrices afin que celles-ci puissent se disperser dans la phase continue ou co-continue époxyde-amine lors de la séparation de phase pour limiter la proportion de charges et ainsi la viscosité des systèmes chargés. L’autre intérêt est d’améliorer les propriétés de résistance à la rupture du réseau époxyde TD final grâce à la présence de la phase thermoplastique séparée. / Among the new technologies for energy for sustainable development, PEM fuel cells offer seducing aspects. However, in order to make this technology fit large scale application requirements, it has to comply with stringent cost, performance, and durability criteria. While metal bipolar plates are penalized by their corrosion resistance and those based on graphite by their mechanical properties and cost (due to machining phases of the channels), the composite bipolar plates appear attractive because of their properties, performance and their cost. In such a frame, the goal of this PhD was to propose a composite material based on an epoxy matrix and graphite conductive fillers.The aim of our study was to develop a thermosetting material based on a solid epoxy formulation (to control its chemistry and in particular its reactivity) highly filled with graphite. Two different formulations were studied. The first was based on the epoxy prepolymer DGEBA and dicyandiamine (DDA) as a hardener. The other formulation studied was composed of DGEBA and curing agent: 3,3’,4,4’ benzophenone tetracarboxylic dianhydride (BTDA). Both formulations have the particularity to be very reactive at high temperature (180-200 °C) characterized by very short gel time (less than 1min) to have a short curing cycle for the industrialization of the production. In addition, these matrixes have shown good chemical stability at room temperature and good thermal stability of cross-linked system compatible with the operating temperature of the fuel cell. On composite network resulting from the polymerization DGEBA / BTDA and DGEBA / DDA, the rubbery modulus appears to be dominated by the loading rate, very high (85%), and is above 1 GPa. We see a high viscosity for highly filled systems, point to consider during the process of transformation. The final part of the work concerned the study of blend of the thermosetting matrix (DGEBA / DDA / urea) modified with a thermoplastic (PEI). The originality and interest of this work is the incorporation of conductive fillers so that they can be dispersed in the continuous or co-continuous structure during the phase separation to limit the proportion of charges and and the viscosity of filled systems. The other interest is to improve the properties of tensile strength of the thermosetting epoxy network with the presence of the thermoplastic phase.

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