Made available in DSpace on 2016-08-18T18:19:27Z (GMT). No. of bitstreams: 1 LUCIENE ARAUJO NASCIMENTO.pdf: 1402629 bytes, checksum: b9ce204098b2c4fe0362b6792a692744 (MD5) Previous issue date: 2010-02-25 / FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO / Austenitic stainless steels have low economic value compared to titanium and its alloys, considered the most resistant to corrosion in biological environment, and for over fifty years are widely used in the manufacture of orthopedic implants, particularly in public health service. Currently the ISO 5832-1 steel (ASTM F 138) is the most used in the manufacture of orthopedic prosthesis, especially the temporary ones. However, because it is susceptible to localized corrosion when in contact with human tissue, it is being gradually replaced by austenitic stainless steel of low carbon and high nitrogen called ISO 5832-9. The same is already used extensively in Europe and the United States, while in Brazil it's use is more recent and smaller scale. This work investigates the behavior of dynamic recrystallization in an ISO 5832-9 steel through hot torsion tests and optical microscopy, for different conditions of temperature, strain and strain rate. It was found through the plastic flow curves of the studied material crystallizes dynamically and that the high value of its apparent activation energy for deformation can be attributed to the presence of a large amount of precipitated particles and nitrogen dissolved in the matrix. Micrographs confirmed that tests carried out at low temperatures reveal a strong retardation of dynamic recrystallization. Moreover, the presence of serrated grain boundaries and nucleation of new grains in the old deformed grain boundaries, are strong indications that the recrystallization occurred by a necklace mechanism. The behavior of the average recrystallized grain size, DDRX, with temperature resembles the behavior of the austenitic grain growth in microalloyed steels. The presence of a minimum in the behavior of DDRX with the strain rate can be attributed to a minimum strain rate required to cause the greatest amount of dynamics precipitation. / Os aços inoxidáveis austeníticos possuem um baixo valor econômico quando comparados ao titânio e suas ligas, considerados os mais resistentes à corrosão em meio biológico, e há mais de cinquenta anos são amplamente utilizados na confecção de implantes ortopédicos, em especial no serviço de saúde pública. Atualmente o aço ISO 5832-1 (ASTM F 138) é o mais utilizado na confecção de próteses ortopédicas, principalmente as temporárias. Entretanto, devido o mesmo ser suscetível à corrosão localizada quando em contato com tecido humano, ele está sendo gradativamente substituído pelo aço inoxidável austenítico de baixo teor de carbono e alto teor de nitrogênio denominado de ISO 5832-9. O mesmo já é utilizado em larga escala na Europa e nos Estados Unidos, enquanto no Brasil a sua utilização é mais recente e em menor escala. Este trabalho investiga o comportamento da recristalização dinâmica em um aço ISO 5832-9, através de ensaios de torção a quente e microscopia ótica, para diferentes condições de temperatura, deformação e taxa de deformação. Foi constatado através das curvas de escoamento plástico que o material estudado recristaliza dinamicamente e, que o alto valor da sua energia de ativação aparente para a deformação pode ser atribuído à presença de uma grande quantidade de partículas de precipitados e ao nitrogênio em solução na matriz. Micrografias confirmam que ensaios realizados a baixas temperaturas revelam um forte retardamento da recristalização dinâmica. Além disso, a presença de contornos de grão serrilhados e nucleação de novos grãos nos antigos contornos de grãos deformados, são fortes indícios de que a recristalização ocorreu por mecanismo colar. O comportamento do tamanho de grão médio recristalizado, DDRX, com a temperatura, se assemelha ao comportamento do crescimento de grão austeníticos de aços microligados. A presença de um mínimo no comportamento do DDRX com a taxa de deformação pode ser atribuído a uma taxa de deformação mínima necessária para que ocorra a maior quantidade de precipitação dinâmica.

Nos últimos anos, devido ao elevado preço do níquel, uma nova série de aços inoxidáveis austeníticos com um menor teor de níquel foi criada. A essa nova série foi dado o nome de série 200. Dentre os aços dessa classe, o AISI 201 tem sido utilizado em aplicações onde a elevada resistência à corrosão não é tão necessária. Neste trabalho de Mestrado investigou-se a formação e a reversão da martensita induzida por deformação em um aço inoxidável austenítico AISI 201 laminado a frio em 20, 40 e 60% de redução em espessura. Das chapas laminadas foram retiradas amostras que foram recozidas em várias temperaturas (200-800oC) por 1 hora. Amostras do material laminado em 60% de redução em espessura também foram recozidas por várias temperaturas (200-800oC) e por vários tempos (5-180min). Com isso, avaliou-se a evolução microestrutural do material durante a laminação frio e durante o recozimento por meio de medidas de microdureza Vickers, microscopias óptica, eletrônica de varredura e eletrônica de transmissão, difração de elétrons retroespalhados, difração de raios X e medidas de magnetização. Além disso, foram realizados cálculos termodinâmicos para a previsão da formação de fases nesse material. Constatou-se que o material de partida não era completamente austenítico, possuindo uma pequena fração de ferrita ? residual em sua microestrutura. Com relação às medidas de magnetização, observou-se que a fração de fase ferromagnética (martensita) aumenta com o aumento da deformação, aumentando a magnetização de saturação (Ms) do material. Para pequenas deformações (20% de redução em espessura) houve a ocorrência de um pico no valor de campo coercivo do material (Hc). Com o aumento da deformação (40 e 60%) os valores de Hc diminuíram. Com relação à reversão da martensita induzida por deformação durante os recozimentos, observou-se que ela ocorre na faixa de temperatura de 500-700oC para o material laminado em 60% de redução em espessura. O comportamento do material nesse estudo corrobora o que tem sido reportado na literatura para os aços da série 300. Entretanto, pouco tem sido publicado com relação às propriedades magnéticas do aço inoxidável austenítico AISI 201, principalmente com relação ao campo coercivo. Neste trabalho também foram realizadas medidas de magnetização durante o recozimento das amostras (condição in situ). Os parâmetros obtidos desses experimentos in situ foram comparados com aqueles obtidos para as amostras recozidas isotermicamente. / In the last years, since nickel price increased, another series of austenitic stainless steel with less amount of nickel has emerged: the series 200. The AISI 201 stainless steel has been used where intermediated corrosion resistance is needed. In this work, the formation of strain-induced martensite and its reversion in an AISI 201 austenitic stainless steel were studied. The material was characterized in terms of microstructure and then cold rolled up to 20, 40 and 60% of thickness reduction. For all degree of reduction, samples were annealed at several temperatures (200-800oC) for 1 hour. Additional samples taken from the 60% cold-rolled material were also annealed at several temperatures (200-800oC) for several times (5-180minutes). The microstructural evolution during cold rolling and annealing was evaluated using microhardness Vikers testing, light optical microscopy, scanning electron microscopy, transmission electron microscopy, electron backscatter diffraction, X-Ray diffraction and magnetization measurements. Phase predictions were also performed using software Thermo-calc©. It was observed that the as-received material was not fully austenitic. It has a small fraction of ?-ferrite within its matrix. The amount of ferromagnetic phase (martensite) increases with increasing deformation. For small deformation (20%), there is a peak in the coercive field of the material (Hc). As deformation increases, Hc values decrease. It was also observed that the martensite reversion takes place at 500-700oC. The behavior of the material is in accordance with what has been reported in the literature for the 300 series. However, only few works have been reported concerning AISI 201 stainless steel and its magnetic properties. In this work, magnetic measurements were also carried out during annealing (in situ condition). The obtained parameters from the in situ magnetic measurements were compared to those ones obtained from the isothermally annealed samples.

Le couplage des traitements de surface mécaniques et thermochimiques a fait l’objet de nombreuses études ces dernières années. L’objectif d’un tel couplage est l’amélioration des cinétiques de diffusion d’espèces chimiques résultant en une augmentation des profondeurs de diffusion, et/ou une diminution de la température du traitement thermochimique sur les matériaux prétraités mécaniquement. Dans cette thèse, le procédé SMAT (Surface Mechanical Attrition Treatment) de nanocristallisation superficiel par déformation plastique sévère a été combiné avec la nitruration plasma sur un acier inoxydable 316L de qualité médicale. Ce procédé duplex permet une amélioration notable sur la capacité de diffusion de l’azote sous la surface de l’acier SMATé. Une étape intermédiaire entre le SMAT et la nitruration plasma a été proposée ; son rôle significatif pour la diffusion de l’azote a été démontré. Ainsi, la comparaison des résultats obtenus après la nitruration plasma sur les échantillons SMATés avec ceux uniquement nitrurés a permis de constater une augmentation jusqu’à 60% de l’épaisseur des couches nitrurées. Par ailleurs, de nombreux moyens de caractérisation ont été mis en œuvre à travers divers essais mécaniques de fatigue et de tribologie. Un modèle numérique multi-échelle de diffusion a également été développé pour simuler les profils de concentration d’azote après traitement duplex. Les profils de concentration d’azote simulés sont en bon accord avec les résultats expérimentaux / Coupled mechanical and thermochemical surface treatments have been the subject of much research effort in recent years. The goal of such a coupling is to improve diffusion kinetics leading to increased penetration depths, and/or to decrease the treatment temperature for mechanically pretreated materials. In this work, SMAT (Surface Mechanical Attrittion Treatment), used to refine the grain size by severe plastic deformation, is combined with plasma nitriding of a 316L medical-grade stainless steel. This duplex process significantly improves nitrogen diffusion. An intermediate treatment between SMAT and plasma nitriding is also proposed and its significant effect on the nitrogen diffusion is demonstrated. Comparisons between nitrided-only samples and duplex-treated samples have shown up to 60% increase of the nitrided layer thickness. In order to better understand the link between the generated microstructures and the mechanical fatigue and tribological responses, the samples have been characterised by many different techniques. Also, a multiscale numerical model of the diffusion process is proposed in order to simulate the nitrogen concentration profiles after duplex treatment. The simulated and experimental profiles correspond rather well

Les pièces métalliques constituant le circuit primaire des installations nucléaires sont élaborées par forgeage à chaud. Pendant ce procédé, les transformations microstructurales induites par la déformation et les recuits déterminent une partie des propriétés mécaniques des produits finaux. L’orientation de la microstructure lors du processus de fabrication nécessite une connaissance précise des mécanismes physiques qui opèrent dans le matériau. Dans le cas de la déformation à chaud de l’acier austénitique 304L, ces modifications microstructurales dépendent de la recristallisation dynamique discontinue (DDRX) et de la recristallisation post-dynamique (PDRX). L’objet de ce projet est : (i) l’étude de la DDRX et de la PDRX dans les conditions de déformation du procédé de forgeage, (ii) l’étude de l’influence d’un ajout de niobium sur ces mécanismes, (iii) la modélisation de ces mécanismes afin de prédire les caractéristiques de la microstructure (moyenne et distribution de la taille des grains) à l’issue d’un procédé multipasses. Dans le cadre de l’étude, les conditions de déformation rencontrées lors du forgeage à chaud sont reproduites à l’aide d’essais de torsion sur des matériaux modèles contenant des teneurs en niobium différentes. La caractérisation et la modélisation des microstructures a permis de comprendre les effets respectifs de la température, de la vitesse de déformation ainsi que de l’ajout de niobium sur les mécanismes de la DDRX et de la PDRX. Dans cette étude, une nouvelle approche semi-topologique de l’hypothèse champs moyens est développée afin de permettre la prédiction de distributions de la taille de grain cohérentes avec les données expérimentales. / Cooling system of nuclear power plants is constituted of metallic parts obtained by hot forging. Thus during the manufacturing process, the microstructural trans- formations induced by the deformation and annealing process define partially the mechanical properties of the final products. A sharp knowledge of the physical mechanisms generated within the material is required to handle the microstructure. In the case of hot deformation of 304L austenitic stainless steel, the microstructural modifications depend on the discontinuous dynamic recrystallization (DDRX) and the post-dynamic recrystallization (PDRX). The aim of this project is: (i) the study of the DDRX and the PDRX under the conditions of deformation inherent in the forging process, (ii) the study of the influence of niobium addition on these mechanisms, (iii) the modeling of these me- chanisms in order to predict the microstructure characteristics (mean grain size and distribution) following a multipass process. As part of the research, the deformation conditions experienced during the hot forging process are replicated through torsion tests with model materials containing various niobium concentrations. Characterization and modeling of microstructures enable to understand the respective e ects of temperature, strain rate as well as niobium addittion on the DDRX and PDRX mechanisms. In this study, a new topological approach of mean-field hypothesis is developed in order to allow the prediction of realistic grain size distributions.

This thesis deals with the influence of process parameters on the contamination level of powder materials produced by mechanical alloying (MA) technology. For this purpose austenitic stainless steel 316 L and equiatomic CoCrFeNi high-entropy alloy (HEA) were prepared by high-energy ball milling. Both materials were milled in argon and nitrogen atmospheres from 5 to 30 hours. Spark plasma sintering method (SPS) was then used for consolidation of chosen powder samples. Chemical analysis of contamination within MA was carried out using combustion analysers for determination of carbon, oxygen, and nitrogen contents after different lengths of milling. Also differences in chemical composition of powder and corresponding bulk samples were measured. The microstructure analysis using scanning electron microscopy (SEM) of both powder and bulk materials was executed with focus on oxide and carbide presence and dispersion. Increasing content of carbon with increasing milling time was observed across all measured samples. This contamination is attributed to using milling vial made of tool steel AISI D2 (containing 1,55 wt. % of carbon). Increase of carbon content within consolidation using SPS was also observed. Milling of specimens using N2 as milling atmosphere caused higher contamination level in both AISI 316 L and HEA compared to milling in argon.

Ce travail porte sur l'élaboration et l'analyse du comportement mécanique d'alliages à distribution bimodale de taille de grains. Les applications concernent les aciers inoxydables austénitiques 304L et 316L. Une approche couplée expérience-modélisation est menée pour comprendre les réponses mécaniques macroscopiques et locales de ces nouveaux alliages en se basant notamment sur l'étude des mécanismes de déformation associés. L'utilisation de deux voies d'élaboration et l'optimisation de leurs paramètres a conduit à l'obtention d'un large choix d'échantillons avec différentes distributions bimodales et différentes proportions de chaque famille de taille de grains. L'influence de ces caractéristiques microstructurales sur le comportement a été analysée sur la base d'essais en traction simple sous chargement monotone ou en charges-décharges alternées. Une base de données étendue de propriétés a ainsi été constituée et des éléments de réponse concernant les mécanismes de déformation propres aux alliages bimodaux ont pu être apportés. La présence de grains de taille conventionnelle (Coarse Grain -CG) au sein d'une matrice à grains ultrafins (UltraFine Grain - UFG) semble favoriser la relaxation d'une partie des contraintes internes de la matrice et tend ainsi à retarder l'endommagement des alliages bimodaux en comparaison aux alliages unimodaux à grains ultrafins. Une modélisation à champs complets selon deux lois de plasticité cristalline tenant compte explicitement d'une longueur interne a été proposée. Sa première motivation est de fournir un outil de prédiction du comportement effectif des alliages bimodaux en fonction de leurs caractéristiques microstructurales. Elle donne par ailleurs accès aux champs locaux et permet d'appuyer les analyses expérimentales en partition des contraintes en montrant à la fois une relaxation partielle des contraintes dans la matrice UFG mais aussi des concentrations de contrainte aux interfaces CG/UFG. / This work is focused on the elaboration and the mechanical behaviour of 304L and 316L austenitic stainless steel alloys with bimodal grain size distribution. The complementary approach between experiments and modelling enables a better understanding of both macroscopic and local mechanical responses and also of the associated deformation mechanisms.The use of two elaboration routes and optimized process parameters results in a wide range of samples with different bimodal grain size distributions. Grain sizes and fractions of each population are modified in order to study the influence of these microstructural characteristics on mechanical behavior. Uniaxial tensile tests are used to realize a database of mechanical properties of bimodal alloys and loading-unloading tests provides valuable informations about deformation mechanisms in these materials. With coarse grains (CG) embedded in an ultrafine grained (UFG) matrix, a relaxation of a part of the internal stresses seems to take place and leads to a delayed embrittlement of bimodal alloys as compared to their unimodal counterparts. Full-field modelling, based on two crystal plasticity laws with an explicit account of an internal length, is proposed. It constitutes a valuable prediction tool of effective properties of bimodal alloys in order, in particular, to study the effect of several microstructural characteristics. An access to local fields is also possible and tend, so far, to show similar results compared to experimental ones : stress relaxation is observed in the UFG matrix as well as stress concentrations at the CG/UFG interfaces.

Thermochemische Randschichthärteverfahren ermöglichen eine ausscheidungsfreie Einlagerung von Kohlenstoff bzw. Stickstoff innerhalb des austenitischen Mischkristalls. Im Zusammenhang mit einer Randschichtbehandlung thermisch gespritzter Schichtsysteme stellen die charakteristischen Strukturmerkmale eine bislang weitgehend unerforschte Einflussgröße für die Beurteilung von Diffusionsprozessen dar. Bei der Verarbeitung von randschichtgehärtetem Pulver durch Verfahren des thermischen Spritzens ist die Phasenstabilität des Spritzzusatzwerkstoffs von übergeordneter Bedeutung. Die beiden Möglichkeiten einer Verfahrenskombination werden für hochgeschwindigkeitsflamm- und atmosphärisch plasmagespritzte Schichtsysteme des Werkstoffs EN 1.4404 durch systematische Prozess- und Parametervariation eingehend betrachtet. Für die einzelnen Schichtsysteme werden Einflussfaktoren struktur- und prozessspezifisch sowie in Abhängigkeit vom Anreicherungsmedium erfasst und im Kontext der Massivwerkstoffreferenz eingeordnet. Die daraus abgeleiteten allgemeingültigen Aussagen zu verfahrenstechnischen Wechselwirkungseffekten ermöglichen eine anwendungsorientierte Verfahrensauswahl bzw. Entwicklungsstrategie. / Thermochemical surface hardening enables a precipitation-free solvation of carbon or nitrogen on interstices of the austenitic crystal lattice. However, the interplay of the diffusion mechanisms with the structural properties of thermal spray coatings has not yet been understood. Thermal spraying of surface-hardened powders is a further opportunity, where the phase stability of the feedstock material is of crucial importance. A process and parameter study is conducted on high velocity oxy-fuel and atmospheric plasma spraying of AISI 316L considering both basic concepts. Structural and process-specific influence factors are examined for the different coating systems in comparison to the bulk material reference. Correlation effects are determined allowing for an application-oriented process selection or development strategy.

In this investigation, the fabrication of functionally graded structures of SS316L to Ni-based alloys were studied, using the novel technique 3D plasma metal deposition. Two Ni-based alloys were used, a heat resistance alloy Ni80-20 and the solid-solution strengthened Ni625. Different configurations were analyzed, for the Ni80-20 a hard transition and a smooth transition with a region of 50% SS316L/50% Ni80-20. Regarding the structures with Ni625, a smooth transition configuration and variations in the heat input were applied. The effect of the process parameters on the geometry of the structures and the microstructures was studied. Microstructure examinations were carried out using optical and scanning electron microscopy. In addition, microhardness analysis were made on the interfaces. In general, the smooth transition of both systems showed a gradual change in the properties. The microstructural results for the SS316L (both systems) showed an austenite matrix with δ-phase. For the mixed zone and the Ni80-20 an austenite (γ) matrix with some M7C3 precipitates and laves phase were recognized. The as-built Ni625 microstructure was composed of an austenite (γ) matrix with secondary phases laves and δ-Ni3Nb, and precipitates M7C3. The mixed zone exhibited the same phases but with changes in the morphology.

This research extended the knowledge of the solid phase transformation and the resulting influence on impact toughness and pitting corrosion resistance in super austenitic stainless steel (SASS) SANICRO® 35. A time-temperature-transformation diagram (TTT diagram) was assembled by performing isothermal heat treatments in the temperature range of 650-1050 °C for different periods of time, ranging from 5 min to 500 min. Microstructural analysis via LOM-DIC, SEM-EDS shows that the nose temperature of dominating σ phase is located in between 900-950 °C. Minor nitrides including π phase and Cr2N with the nose temperature of 900 °C and 850 °C, respectively, were detected after prolonged heat treatment times. Area fraction of precipitates was calculated by analyzing micrographic images in the software ImageJ. Charpy impact tests indicate that the impact toughness degrades with increasing area fraction of precipitates but at a higher rate at the early stage of precipitation. Despite a much-lessened area fraction, fine precipitates decorating the grain boundaries in a continuous pattern impose significant negative effect on impact toughness. Pitting corrosion resistance was indicated by critical pitting temperature (CPT) as per ASTM G150mod (3M MgCl2). Pitting corrosion resistance deteriorated with increasing amount of σ phase due to the Cr- and Mo-depleted surrounding area, but it is more dependent on the distribution pattern of precipitates, as well as the secondary phase type. The lowest CPTs were measured after heat treatment for 500 min at 800 °C and 850 °C where nitrides including Cr2N and π phase were formed and the small precipitates were distributed on grain boundaries continuously. Auxiliary simulation of TTT diagram via TC PRISMA shows drastic variation from experimental results in regard of time scale. The enhancement pre-factor for the interfacial mobility and interfacial energy can be modified to approach the experimental results. / Detta arbete utfördes för att undersöka fasomvandlingar och dess inflytande på slagsegheten och gropfrätningsmotståndet för det superaustenitiska rostfria stålet (SASS) SANICRO® 35. Ett tid-temperatur-transformationsdiagram (TTT-diagram) har tagits fram genom att utföra isotermiska värmebehandlingar mellan 650-1050 °C med olika hålltider från 5-500 minuter. Mikrostrukturanalys genom LOM-DIC, SEM-EDS undersökning visar att nosen för den dominerande σ-fasen ligger mellan 900-950 °C. Mindre nitrider, som π-fas och Cr2N, med nosarna vid 900 °C respektive 850 °C observerades vid längre hålltider. Areafraktionen av utskiljningar beräknades genom analys av mikrobilder med programmet ImageJ. Slagprovning visade att slagsegheten minskar med ökande fraktion utskiljningar men med en tydligare försämring i början av fastransformationen. Trots att de utgör en betydligt mindre areafraktion så kan mindre utskiljningar som följer korngränserna också påverka materialet signifikant negativt. Gropfrätningsmotståndet testades genom att mäta Critical Pitting Temperature (CPT) enligt ASTM G150mod (3M MgCl2). CPT minskade med ökande andel σ-fas p.g.a. den Cr- och Mo-utarmade zon som omger de utskilda partiklarna. Det finns även en stark koppling mellan lägre CPT och distributionen av utskiljningarna samt andra typer av faser. Lägst CPT uppmättes efter 500 minuter vid 800 °C och 850 °C då små nitrider inklusive Cr2N och π-fas bildats längs med stora delar av korngränserna. Simulering av TTT-diagram i TC PRISMA visade en drastisk skillnad i tiden till utskiljning/mängden utskiljningar jämfört med de experimentella resultaten. Diffusionförstärkningsfaktorn (eng. “mobility enhancement pre-factor”) och ytenergin kan minskas för att bättre överensstämma med de experimentella resultaten.

η (eta) nitride, Cr3Ni2SiN, is a precipitate found in high temperature austenitic stainless steel and is not yet included in Thermo-Calc steel database TCFE7. The aim of this thesis is to collect thermodynamic data to enable the addition of η nitride in the databases. Three laboratory melts with varying levels of silicon, chromium and nickel have been aged at 700-1000 °C for 75 h, 300 h and 1200 h and examined by Light Optical Microscopy, Scanning Electron Microscopy, Energy Dispersive Spectroscopy, Wavelength Dispersive Spectroscopy, Electron Backscattered Diffraction and X-ray Powder Diffraction. η nitride is in the studied alloys an equilibrium phase stabilized with nitrogen. Presence of η nitride was confirmed by Energy Dispersive Spectroscopy and X-ray Powder Diffraction. It was found to precipitate in four different ways, at primary grain boundaries, intragranularly, as a "skeleton-like" precipitate and as a border around the occurring Cr2N precipitates. The area fraction of η nitrides increases with longer aging times and is favored by silicon and nickel. The composition of η nitride is not changing regardless of material composition, aging temperature and aging time. The composition of η nitride in all three materials are 8.7-9.7 wt.% silicon, 47-54 wt.% chromium, 1.4-4.1 wt.% iron and 33-36 wt.% nickel. The nitrogen content 2 determined by Wavelength Dispersive Spectroscopy is 2.8-3.2 wt.%. No complete equilibrium was achieved and together with incomplete mixing of the alloying elements during melting, the microstructure is difficult to evaluate. Other precipitates found are Cr2N, π nitride, σ phase and two unidentified phases, M and N. Of these phases at least Cr2N is not an equilibrium phase as it dissolves during aging. Further aging to achieve complete equilibrium is necessary.