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1
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EN
The rigid-plastic model for the single grain is developed in which the velocity gradient is split into two parts connected with crystallographic slip and micro-shear bands respectively. For crystallographic slip the regularized Schmid law proposed by Gambin is used. For the micro-shear bands the framework with the function fMS that accounts for the contribution of this mechanism into the total plastic deformation described by Pecherski is applied. Different constitutive equations for the plastic spin due to two considered mechanisms of plastic deformation are used. The presented model is applied to simulate crystallographic texture evolution in the polycrystalline element.
PL
Opracowano sztywno-plastyczny model pojedynczego ziarna,w którym tensor gradientu prędkości został rozbity na dwie części związane odpowiednio z poślizgiem krystalograficznym i mikropasmami ścinania. Dla poślizgu krystalograficznego zastosowano regulryzowane prawo Schmida zaproponowane w pracy [8]. Dla mikropasm ścinania użyto formalizmu rozwiniętego w [18], gdzie uwzględnia się ich udział w przyroście deformacji plastycznej poprzez funkcje fMS. Zastosowane zostały różne równania konstytutywne dla części spinu plastycznego wywołanych rozważanymi dwoma mechanizmami deformacji plastycznej. Zaprezentowany model wykorzystano w symulacji rozwoju tekstury krystalograficznej w elemencie polikrystalicznym
EN
Finite element computations of metal forming often involve large deformations so that the mesh degenerates and a remeshing procedure is required. When microstructural variables are attached to the nodes or integration points of the mesh, they have to be transported from the old mesh to the new one by using an interpolation technique. Such interpolation of microstructure variables automatically induce numerical errors, and in many cases, may even have no physical meaning. In this paper two strategies of transport based on the Lagrangian particles concept are presented. They can be applied to a wide range of discretized microstructures. As an example, the transport of the variables of a polycrystalline plasticity model is used for simulations of uniaxial compression of a reference aluminium sample. Various numerical strategies are compared in terms of the accuracy of the description of the evolving mechanical anisotropy.
PL
W obliczeniach metodą elementów skończonych często mamy do czynienia z dużymi odkształceniami siatki i wymagana jest jej aktualizacja (remeshing). Jeżeli w punktach całkowania lub w węzłach określone są parametry mikrostruktury, muszą one zostać przeniesione ze starej siatki do nowej. Stosowane są w tym celu metody interpolacji. Interpolacja zmiennych opisujących mikrostrukturę wprowadza błędy numeryczne i, w wielu przypadkach, może nie mieć fizycznego znaczenia. W pracy przedstawiono dwie strategie przekazywania oparte na idei cząstek Lagrange'a. Metody te mogą zostać zastosowane do szerokiego zakresu dyskretyzowanych mikrostruktur. Przeniesienie zmiennych modelu krystalicznej plastyczności zastosowano do symulacji osiowosymetrycznego ściskania próbki z aluminium przedstawiono w pracy jako przykład. Różne strategie numeryczne są porównane odnośnie dokładności opisu rozwijającej się w materiale mechanicznej anizotropii.
3
Content available remote Formation of texture inhomogeneity in severely plastically deformed copper
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EN
The development of the crystallographic texture in copper subjected to severe plastic deformation (SPD) by means of high pressure torsion (HPT) and equal-channel angular pressing (ECAP) was experimentally investigated and analyzed by means of computer modelling. It was demonstrated, that the texture developed in HPT and ECAP Cu is characterized by significant inhomogeneity. Therefore, the analysis focused on the study of the texture distribution and its inhomogeneity in sample space. The detailed texture analysis, based on the X-ray diffraction technique, led to important observations concerning the localization of the maximum texture gradient and the regularity of its changes related to the parameters of the applied deformation. The obtained results provided the basis for certain conclusions concerning complex texture changes in SPD Cu.
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Crystallographic texture is the only factor essentially influencing plastic anisotropy in annealed pure metals and single phase alloys. Therefore, the extreme states of anisotropy can be defined using the quantitatively evaluated texture. The macroisotropy condition in polycrystalline metals constitutes a limit which can be approached when diminishing the sharpness of texture. On the other hand perfect single crystal can be estimated as the opposite limit of plastic anisotropy. It has been shown that the deviation from the limiting state influences the mechanical behaviour of real single crystals and poly crystalline samples with a close-to-random orientation. This finding motivates the introduction of the notion of "texture" in real single crystals.
PL
W pracy scharakteryzowano, na podstawie źródeł literaturowych i badań własnych, anizotropię właściowości plastycznych stopów Al-Li z uwzględnieniem ich tekstury krystalicznej i morfologicznej. Przeprowadzono analizę indywidualnego i łącznego wplywu tych tekstur na anizotropię właściwości badanych stopów. Przedstawiono także wyniki badań o charakterze ogólnym, podsumuwujące złożone oddziaływanie obu rodzajów tekstury. Przedmiotem analizy jest anizotropia właściwości plastycznych wyrobów z różnych gatunków stopów Al otrzymanych różnymi technikami wytwarzania. Większość prac z tego zakresu dotyczy wpływu tekstury krystalicznej na zjawisko anizotropii (np. Hirsch, Lucke, 1988; Bacroix, Jonas, 1988a, b; Juul Jensen i in., 1988; Bowen, 1990; Hirsch, 1990; Engler, Lucke, 1991; Barlat i in., 1992; Maurice, Driver, 1997; Hu i in., 1998; Park, 1999; Kalidindi, 2001; Rabbe i in., 2002). Znacznie mniej prac dotyczyło tekstury morfologicznej mającej istotny wpływ na anizotropię właściwości plastycznych (Lipinski i in., 1987; Kim, Lee, 1993; Hargarter i in., 1998; Barlat, Liu, 1998; Choi i in., 2000). Dlatego w pracy podjęto próbę ustalenia i usystematyzowania oddzielnego i łącznego wpływu wymienionych tekstur na anizotropię właściwości plastycznych materiałów dla wybranej grupy stopów Al-Li. W badaniach własnych udowodniono znaczenie wpływu składowej tekstury typu mosiądzu ({ 112 }
EN
The study, based on the author's own experiments and on literature reports, is concerned with the anisotropy of the plastic properties of selected Al-Li alloys with account of their crystallographic and morphological textures. The effect of these two textures, each individually and the two jointly, on the anisotropy of the properties of the alloys was analysed. The results of the analysis are also discussed in their general aspects and the complex effect of the two kinds of texture is comprehensively described. The anisotropy of the plastic properties was examined in various kinds of the Al-Li alloys produced by various techniques. Most literature reports were concerned with the effect of the crystallographic texture al one upon the anisotropy of the alloys (e.g. Hirsch, Liicke, 1988; Bacroix, Jonas, 1988a, b; JulI Jensen et al., 1988; Bowen, 1990; Hirsch, 1990; Engler, Liicke, 1991; Barlat et al., 1992; Maurice, Driver, 1997; Hu et al., 1998; Park, 1999; Kalidindi, 2001; Rabbe et al., 2002), and only a smalI number of them discussed the effect of the morphological texture (Lipinski et al., 1987; Kim, Lee, 1993; Hargarter et al., 1998; Barlat, Liu, 1998; Choi et al., 2000). This is the reason why the present study was aimed at investigating and systematising the individual and joint effects of these two textures. In the author' s own experiments, it has been demonstrated that the brass ({ 112 ) <110>) component of the texture of the Al-Li alloys has a substantial effect upon the anisotropy of their plastic properties (e.g. Engler et al., 1991, 1992 - Al, A2; Mizera, Driver, 1999 - A4; Mizera, 2002 - A 7). By determining the crystalline orientation of the individual grains of the alloy, the mechanism of the formation of this texture component was described and the possibilities of restricting its share in the overall alloy texture was discussed (Mizera, Driver, 1993 A3, Mizera, 2002 - A 7). The role of the crystallographic texture gradient in the formation of the plastic anisotropy of the Al-Li alloys was also analysed. It has been indicated that to describe properly the course of plastic deformation, its existing models should be modified, and/or new models should be developed, such that would take into account the real texture gradient which exists within the treated parts over their entire cross-section (Mizera et al., 2000, 2002 A5, A6). The effect of the morphological texture upon the anisotropy of the plastic properties of the Al-Li aJloys was also analysed (Mizera et al., 1996 - A8, Mizera, 1999 - A9; Mizera, Kurzydlowski, 2001a, b - A 10, All). A method was proposed that permits describing quantitatively this texture and determining its contribution to the formation of the plastic properties of the alloys (Ciupiński et al., 2001 - Al2). The analysis of the joint effect of the crystallographic and morphological textures upon the anisotropy of the plastic properties of the Al-Li alloys shows that, in order to control these properties, the grains that form the individual texture components should be ascribed certain geometrical features (Mizera et al. 2001a, b - A13, A14).
EN
Austenitic stainless steels are widely used in industry, from heavy industry and power generation to precision mechanics and electronics, accounting for about 2/3 of the stainless steels produced. The stability of austenite influences the properties and behaviour of these steels during deformation and annealing. This paper presents the results of research into austenitic metastable phase X5CrNi1810 steel, which was subjected to cold rolling (in the range of 5 to 80%) and then annealing (at temperatures of 500-900°C). The research focused mainly on changes in crystallographic texture parameters occurring during the analysed processes. It was found that the observed development of the deformation texture is complex due to the fact that several processes take place simultaneously. Namely, the deformation of austenite, the transformation of austenite into martensite, and the deformation of the resulting martensite. The texture of the deformed austenite was similar to the texture of the alloy type {112}<110>. After 80% deformation, the Goss-type {110}<001> texture component showed the highest intensity. The lack of {112}<111> orientation in the texture was due to the fact that this orientation changes to the {112}<110> martensite orientation as a result of the γ→α’ phase transition. Annealing of the deformed steel at 500°C led to an increase in the degree of texturing (sharpening of the texture), which was related to the improvement of the texture in this temperature range. Above 600°C, the degree of texturing decreased, which is directly related to the α’→γ reverse transformation and the subsequent recrystallization process. Magnetic studies indicate an increasing proportion of the magnetic phase α’ (martensite) together with an increasing degree of deformation. For deformation of 80%, the amount of magnetic phase reached a value of more than 33%. However, after annealing at a temperature of 800°C, there is no martensite in the structure, which indicates that, in these heat treatment conditions, the complete reverse transformation of martensite into austenite has already taken place.
EN
It is well admitted that machining processes can introduce residual stresses at the surface of machined workpieces and can modify significantly the microstructure and texture in a small volume c1ose to the surface. Such changes are important in controlling the corrosion behaviour of these workpieces in the presence of an aggressive environment and the initiation of fracture processes. Therefore, it is of major importance to quantify residual stresses and texture components and to determine the machining-induced microstructure to understand and predict the corrosion behaviour of modified surfaces. In the present paper, particular attention was paid to pure copper considered as a modeling system. The influence of the nose radius of the tool, the cutting speed and the lubricant on the surface stress field and the surface texture was quantified by means of XRD techniques. On the other band, the microstructural modifications at !be specimen surface and in depth were evaluated using scanning electron microscopy. The electrochemical behaviour of modified surfaces were studied from local measurements in 1M NaClO4 using the electrochemical microcell technique.
8
Content available remote Non-destructive testing of FGM-MADE structural elements
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EN
Non-destructive testing of materials with laminar and gradient structure is one of priority research of temporary surface engineering. In that field crystallographic texture and residual stresses analysis in near-the-surface areas of structural elements become more and more useful. Recently introduced and verified experimentally the X-ray texture tomography (XTT) represents a non-invasive method of investigating the texture of the near-the-surface areas on X-ray penetration depth, usually up to 100 µm. It allows to localize the texture changes occurring under the sample surface to a certain definite depth. The study gives a review on application the XTT to analysis of a functionally graded material (FGM) as a non-conventional investigation its inhomogeneous structure. Principles of the XTT method for determination of texture depth-profile of the FGM-made layers are also presented. The nature of texture formation in the substrate/deposit composition is discussed.
PL
Nieniszczące badania materiałów o strukturze warstwowej oraz gradientowej są jednym z priorytetowych kierunków rozwoju współczesnej inżynierii powierzchni, a analiza tekstury krystalograficznej i naprężeń własnych w obszarach przypowierzchniowych elementów konstrukcyjnych staje sie coraz bardziej użyteczna w tym zakresie. Opracowana ostatnio rentgenowska tomografia teksturowa (RTT) reprezentuje nieniszczącą metodę badań tekstury obszarów przypowierzchniowych o grubości porównywalnej z głębokością penetracji promieni rentgenowskich, zwykle do 100 µm. Pozwala ona zlokalizować zmiany tekstury zachodzące pod powierzchnią próbki do określonej głębokości. W pracy opisano zastosowanie RTT w analizie funkcjonalnych materiałów gradientowych cechujących się niejednorodną strukturą. Podano również zasady stosowania RTT w ocenie profilu głębokościowego tekstury materiałów gradientowych. Przedyskutowano wpływ podłoża na formowanie się tekstury warstwy w materiale warstwowym.
EN
The main purpose of the paper is to present a method which allows taking into account the anisotropic properties of dynamo steel sheets. An additional aim is to briefly present anisotropic properties of these sheets which are caused by occurrences of some textures. In order to take into account textures occurring in dynamo sheets, a certain sheet sample is divided into elementary segments. Two matrix equations, describing changes of the magnetic field, are transformed to one non-linear algebraic equation in which the field strength components are unknown. In this transformation the flux densities assigned to individual elementary segments are replaced by functions of flux densities of easy magnetization axes of all textures occurring in the given dynamo sheet. The procedure presented in the paper allows determining one non-linear matrix equation of the magnetic field distribution; in this equation all textures occurring in a dynamo sheet are included. Information about textures occurring in typical dynamo sheets may be used in various approaches regarding the inclusion of anisotropic properties of these sheets, but above all, the presented method can be helpful in calculations of the magnetic field distribution in anisotropic dynamo sheets.
EN
The article presents the results of residual stress analysis in selected metal-metal joints manufactured by conventional welding and explosive merging. The X-ray diffraction technique applied for advanced stress-texture measurements and data processing revealed directions and values of the principal stresses and their configuration on the surface of the examined structural elements. The obtained stress topography of the joint intersections indicates a possible path of potential cracking formed during the exploitation process and thus it becomes a very useful tool in the diagnostics of structural elements.
PL
W pracy opisano badania i uzyskane wyniki analizy naprężeń własnych przeprowadzone dla wybranych połączeń metal-metal wytworzonych przez konwencjonalne spawanie oraz łączenie wybuchowe. Pomiary naprężeń oraz tekstury dokonane techniką dyfrakcji rentgenowskiej, jak i zastosowane odpowiednie procedury obliczeniowe pozwoliły zidentyfikować kierunki i wartości naprężeń głównych oraz ich konfigurację w badanych elementach konstrukcyjnych. Topografia naprężeń w wybranych obszarach badanych połączeń wskazuje możliwą drogę potencjalnej destrukcji złączy w procesie ich eksploatacji. Charakterystyki naprężeniowo-teksturowe uzyskane w oparciu o technikę dyfrakcji rentgenowskiej okazują się bardzo przydatnym narzędziem w diagnostyce elementów konstrukcyjnych, szczególnie takich jak przedmiotowe złącza.
11
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EN
Regardless of the origin of structure irregularities of materials, recognizing its spatial distribution in a sample or constructing elements is a great research problem. One of the most effective and non-destructive tools in this range is the X-ray diffraction technique assisted by appropriate experimental method and data processing. The work presents the results of investigations of planar distribution of crystallographic texture and stress irregularities manifested by changes of diffraction effects registered by X-ray technique. As an example, the introduced method is tested on titanium rod after severe plastic deformation process.
PL
ldentyfikacja przestrzennego rozkładu niejednorodności struktury materiału, bez względu na przyczyny ich powstania, stanowi istotny problem badawczy. Jednym z najbardziej efektywnych i nieniszczących narzędzi badawczych w tym zakresie jest technika dyfrakcji rentgenowskiej. W niniejszej pracy zaprezentowano wyniki badań rozkładu planarnego tekstury krystalograficznej i naprężeń własnych przejawiających się w zmianie charakterystyki odbić dyfrakcyjnych. Wprowadzona metoda topografii tekstury i naprężeń własnych została przetestowana na prętach tytanu poddanych silnemu odkształceniu plastycznemu.
EN
Integral structural parts of titanium alloy have high material removal rate, high machining difficulty and need multi-step machining to form the final geometry. The crystallographic texture of machined surface layer will affect the surface quality and the mechanical performance of machined parts from the microstructural aspect. Therefore, high requirements for finish machining surface quality and a reasonable high-quality machining surface-oriented process adjustment method need to be explored. In this paper, the surface quality controlling methods of titanium alloy machining are theoretically analyzed, two machining process adjustment methods in terms of multi-step cutting and prestressed cutting are proposed, and the finite element simulation of multi-step cutting and prestressed cutting was carried out. According to the principle of crystallographic texture and the obtained shear strain and strain rate data by finite element simulation, the crystallographic texture of surface layer materials processed by single-step cutting, single-step prestressed cutting, multi-step cutting and prestressed multi-step cutting were simulated by viscoplastic self-consistent (VPSC) texture simulation program. The influence of cutting process adjustment method on the texture polar figures (texture type and texture density) and crystallographic orientation distribution function (ODF) diagram of machined surface was analyzed. Moreover, the experimental comparisons and validations of simulated results were conducted by orthogonal cutting tests and microstructural texture measurements by using electron backscatter diffraction (EBSD) technique.
EN
This paper presents some results of the influence of severe plastic deformation on the microstructure evolution, grain refinement aspect, and mechanical properties of ultra-low carbon steel. Ti-stabilized experimental IF steel was deformed at a room temperature with unconventional SPD process—dual rolls equal channel extrusion (DRECE). Mechanical properties and structure of ferritic steel in initial state and after selected steps of deformation were investigated. The mechanical properties were determined by static tensile tests carried out at a room temperature and microhardness research. The structural investigations involved using scanning transmission electron microscopy observations, electron back scattered diffraction and measurements of the crystallographic texture. The DRECE process affects the evolution of the structure. The microstructural investigations revealed that the processed strips exhibited a dislocation cell and grain structures with mostly low angle grain boundaries. The electron backscattering diffraction (EBSD) examination showed that the processed microstructure is homogeneous along the strips thickness. The mechanical properties of the DRECE-processed IF steel strips increased with an increase the number of passes.
14
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Experimental investigations of texture formation processes were conducted in selected zones of cross section of bulk billets, subjected to equal channel angular (ECA) pressing. Pure Cu and Ti with fcc and hcp lattices, respectively were chosen as investigated materials. There was considered a case of 12 ECA pressing passes (route Bc). The angle of channels’ intersection during ECA pressing was 90°. ECA pressing rate was 6 mm/s. In the case of Cu deformation was carried out at room temperature and in the case of Ti it was elevated to 450°C. Experimental tests were carried out by means of X-ray diffraction technique. For both investigated materials, the incomplete back-reflection pole figures in selected areas of prepared samples were registered. The texture functions calculated on the basis of such incomplete pole figures enabled to calculate both the complete and inverse pole figures, and to perform the qualitative and quantitative texture analysis. Conclusions on texture homogeneity during ECA pressing of bulk Cu and Ti ingots were drawn.
PL
Eksperymentalne badania procesu tworzenia tekstury przeprowadzono w wybranych obszarach przekroju poprzecznego litych próbek poddanych wyciskaniu w kanale kątowym (ECA) o przekroju kwadratowym. Materiałami wybranymi do badań były Cu i Ti o strukturze odpowiednio fcc i hcp. Rozważano przypadek 12 przepustów wyciskania (droga Bc), przy czym kąt zakrzywienia kanału wynosił 90°. Szybkość wyciskania wynosiła 6 mm/s. W przypadky Cu deformacje przeprowadzono w temperaturze pokojowej, podczas gdy Ti w 450°C. Badania tekstury uzyskanych materiałów przeprowadzono metodą dyfrakcji rentgenowskiej. Wyznaczono niekompletne figury biegunowe wybranych obszarów uzyskanych próbek. Obliczone na podstawie niekompletnych figur biegunowych funkcje tekstury umożliwiły obliczenie kompletnych i odwrotnych figur biegunowych oraz pozwoliły na jakościową i ilościowa analizę tekstury. Wyciągnieto wnioski o jednorodności tekstury podczas wyciskania ECA sztabek Cu i Ti.
15
Content available remote Formation of crystallographic texture during severe plastic deformation
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EN
The current paper represents the results of recent investigations, aimed at revealing of regularities and establishing of crystallographic texture evolution mechanisms during equal-channel angular pressing (ECAP). Pure Cu was used as material for investigation. The investigations were conducted with the help of computer simulation. The variable parameter was the friction coeffcient. Accumulated strain fields, as well as strain rate gradients, were calculated using the variation-diffrence method (VDM) and the simplest isotropic material model. The strain rate gradients from the VDM program served as input parameters for the viscous-plastic self-consistent model (VPSC), simulating the texture formation processes. Results of modeling are compared to experimental texture measurements.
PL
W pracy przedstawiono wyniki najnowszych badań dotyczących prawidłowości mechanizmu formowania się tekstury krystalograficznej czystej miedzi podczas wyciskania w kanale kątowym (ECAP). Parametrem zmiennym był współczynnik tarcia. Badania wsparto symulacją komputerową. Za pomoca metody wariacyjno-różniczkowej (VDM) oraz uproszczonego modelu materiału izotropowego obliczono skumulowane pola odkształceń i gradienty prędkości odkształcenia. Gradienty prędkości odkształcenia z programu VDM posłużyły jako parametry wejściowe dla samouzgodnionego, visko- plastycznego modelu (VPSC) symulującego proces formowania się tekstury.Wyniki modelowania porównano z doświadczalnymi pomiarami tekstury.
EN
The substructure anisotropy of real textured metal materials was studied by use of the X-ray method of Generalized Pole Figures. Substructure states of rolled material along different directions form an extremely wide spectrum. Three laws of substructure anisotropy were revealed for the first time. The 1st law describes the distribution of residual deformation effects in textured materials, the 2nd law concerns variation of lattice parameters in metal products due to elastic microstrains and the 3d law considers non-uniformity of the lattice condition in connection with sign of residual microstrains.
PL
Anizotropia substruktury w metalach posiadających teksturę krystalograficzną była badana za pomocą rentgenowskiej metody uogólnionych figur biegunowych. Stany substruktury walcowanego materiału wzdłuż rożnych kierunków stanowią bardzo szerokie spektrum. Po raz pierwszy zostały przedstawione trzy prawa anizotropii substrukturalnej. Pierwsze prawo opisuje szczątkowe efekty odkształcenia w teksturowanych materiałach w zależności od orientacji ziaren. Drugie prawo dotyczy zmienności parametrów sieci krystalicznej w wyrobach metalowych w wyniku elastycznych mikronaprężeń. Trzecie prawo dotyczy niejednorodności stanu sieci krystalicznej w związku ze znakiem mikronaprężeń szczątkowych.
PL
W serii trzech artykułów przeanalizowano literaturę dotyczącą walcowania asymetrycznego oraz wpływu tego procesu na teksturę i mikrostrukturę metali. W obecnej pracy przedstawiono wpływ asymetrii walcowania na teksturę i mikrostrukturę miedzi, aluminium tytanu i stali. Zamieszczono także podsumowanie cyklu publikacji oraz analizę możliwości zastosowania walcowania asymetrycznego w praktyce technologicznej.
EN
A literature review on asymmetric rolling has been done and presented in a series of three consecutive papers. The effect of rolling asymmetry on technological parameters and the product texture and microstructure was presented. The present paper concern the asymmetry effect on crystallographic texture and microstructure of copper, aluminum, titanium and steels. A summary of the publication cycle and possibilities for the asymmetric rolling application in technological practice are provided.
EN
This paper discusses the mechanical properties, microstructure and crystallographic texture of light alloys made on the base of aluminium, magnesium and lithium. An acoustic emission (AE) technique was applied to detect the moment of twinning or slip activation during compression and channel – die tests to extend the comprehension on the nature of the plastic deformation processes occurring in the investigated alloys.
EN
The present work aims to model the influence of microstructural features of Ti-6Al-4V titanium alloy on its mechanical behavior. A multi-scale approach based on crystal plasticity is considered. The elasto-viscoplastic constitutive equations of Meric-Cailletaud are modified to take into consideration the effect of the grain size by introducing the Hall-Petch relationship at the local scale. This modified model is coupled with finite element calculations under small strain assumption to simulate the monotonic mechanical behavior of Ti-6A-4V at local and global scales. It is shown that the mechanical behavior of Ti-6Al-4V is drastically dependent upon the material features. Strong crystallographic texture can result in the formation of hardened and less hardened areas. Moreover, by increasing the grain size scattering, the heterogeneously deformed areas are multiplied. By decreasing the average grain size, the yield strength increases. It is observed that the effects of grain size, grain size scattering and crystallographic texture are coupled.
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