Academic literature on the topic 'Anisotropic steels'

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Journal articles on the topic "Anisotropic steels"

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Niazi, M. S., V. Timo Meinders, H. H. Wisselink, C. H. L. J. ten Horn, Gerrit Klaseboer, and A. H. van den Boogaard. "A Plasticity Induced Anisotropic Damage Model for Sheet Forming Processes." Key Engineering Materials 554-557 (June 2013): 1245–51. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.1245.

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The global fuel crisis and increasing public safety concerns are driving the automotive industry to design high strength and low weight vehicles. The development of Dual Phase (DP) steels has been a big step forward in achieving this goal. DP steels are used in many automotive body-in-white structural components such as A and B pillar reinforcements, longitudinal members and crash structure parts. DP steels are also used in other industrial sectors such as precision tubes, train seats and Liquid Petroleum Gas (LPG) cylinders. Although the ductility of DP steel is higher than classical high strength steels, it is lower than that of classical deep drawing steels it has to replace. The low ductility of DP steels is attributed to damage development. Damage not only weakens the material but also reduces the ductility by formation of meso-cracks due to interacting micro defects. Damage in a material usually refers to presence of micro defects in the material. It is a known fact that plastic deformation induces damage in DP steels. Therefore damage development in these steels have to be included in the simulation of the forming process. In ductile metals, damage leads to crack initiation. A crack is anisotropic which makes damage anisotropic in nature. However, most researchers assume damage to be an isotropic phenomenon. For correct and accurate simulation results, damage shall be considered as anisotropic, especially if the results are used to determine the crack propagation direction. This paper presents an efficient plasticity induced anisotropic damage model to simulate complex failure mechanisms and accurately predict failure in macro-scale sheet forming processes. Anisotropy in damage can be categorized based on the cause which induces the anisotropy, i.e. the loading state and the material microstructure. According to the Load Induced Anisotropic Damage (LIAD) model, if the material is deformed in one direction then damage will be higher in this direction compared to the other two orthogonal directions, irrespective of the microstructure of the material. According to Material Induced Anisotropic Damage (MIAD) model, if there is an anisotropy in shape or distribution of the particles responsible for damage (hard second phase particles, inclusions or impurities) then the material will have different damage characteristics for different orientations in the sheet material. The LIAD part of the damage model is a modification of Lemaitre’s (ML) anisotropic damage model. Modifications are made for damage development under compression state and influence of strain rate on damage, and are presented in this paper. Viscoplastic regularization is used to avoid pathological mesh dependency. The MIAD part of the model is an extension of the LIAD model. Experimental evidence is given of the MIAD phenomenon in DP600 steel. The experimental analysis is carried out using tensile tests, optical strain measurement system (ARAMIS) and scanning electron microscopy. The extension to incorporate MIAD in the ML anisotropic damage model is presented in this paper as well. The paper concludes with a validation of the anisotropic damage model for different applications. The MIAD part of the model is validated by experimental cylindrical cup drawing wheras the LIAD part of the model is validated by the cross die drawing process.
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Szumiata, Tadeusz, Paweł Rekas, Małgorzata Gzik-Szumiata, Michał Nowicki, and Roman Szewczyk. "The Two-Domain Model Utilizing the Effective Pinning Energy for Modeling the Strain-Dependent Magnetic Permeability in Anisotropic Grain-Oriented Electrical Steels." Materials 17, no. 2 (January 11, 2024): 369. http://dx.doi.org/10.3390/ma17020369.

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This paper presents a newly proposed domain wall energy-based model of the 2D strain dependence of relative magnetic permeability in highly grain-oriented anisotropic electrical steels. The model was verified utilizing grain-oriented M120-27s electrical steel sheet samples with magnetic characteristics measured by an automated experimental setup with a magnetic yoke. The model’s parameters, identified in the differential evolution-based optimization process, enable a better understanding of the interaction between stress-induced anisotropy and magnetocrystalline anisotropy in electrical steels. Moreover, the consequences of the simplified description of grain-oriented magnetocrystalline anisotropy are clearly visible, which opens up the possibility for further research to improve this description.
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Niazi, M. S., H. H. Wisselink, and T. Meinders. "Validation of Modified Lemaitre’s Anisotropic Damage Model with the Cross Die Drawing Test." Key Engineering Materials 488-489 (September 2011): 49–52. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.49.

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Dual Phase (DP) steels are widely replacing the traditional forming steels in automotive industry. Advanced damage models are required to accurately predict the formability of DP steels. In this work, Lemaitre’s anisotropic damage model has been slightly modified for sheet metal forming applications and for strain rate dependent materials. The damage evolution law is adapted to take into account the strain rate dependency and negative triaxialities. The damage parameters for pre-production DP600 steel were determined. The modified damage models (isotropic and anisotropic) were validated using the cross die drawing test. The anisotropic damage model predicts the crack direction more accurately.
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van den Berg, F. D., and H. T. Ploegaert. "Strain Dependence of Magnetic Anisotropy in Low-Carbon Production Steels." Materials Science Forum 495-497 (September 2005): 1475–84. http://dx.doi.org/10.4028/www.scientific.net/msf.495-497.1475.

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The magnetic parameters of steel depend on the mutual orientation of the applied magnetic field, the (applied) stress and the crystalline structure. The magnetic anisotropy can be modeled in terms of the magneto-elastic and magneto-crystalline energy distributions. By investigation of the magnetic anisotropic behaviour of steels with respect to stress, a rapid, nondestructive and possibly non-contact measurement of the residual stress can be devised that can find application in manufacturing, machining, forming and life-time assessment of steel and steel components. Reliability, robustness and versatility will constitute the main challenges to further develop these techniques for common industrial applications.
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Toribio, Jesús, Beatriz González, Juan Carlos Matos, and F. J. Ayaso. "Anisotropic Fracture Behaviour of Progressively Drawn Pearlitic Steel." Key Engineering Materials 452-453 (November 2010): 1–4. http://dx.doi.org/10.4028/www.scientific.net/kem.452-453.1.

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This paper analyses the differences in fracture behaviour of two cold drawn pearlitic steels with different degree of strain hardening: a slightly drawn bar and a heavily drawn wire. The load-displacement curve F-u was analysed in the two cases, with special emphasis in the characteristic points of the plot: the load defining the end of linear behaviour (Fe), the final fracture load (Fmax) and, in the heavily drawn steel, the pop-in load (FY). Results demonstrate that slightly drawn steels exhibit isotropic fracture behaviour with crack propagation along its own plane (mode I propagation). On the other hand, heavily drawn steels exhibit a markedly anisotropic fracture behaviour with crack deflection (mixed mode propagation), and vertical fracture embryos suddenly appear associated with the pop-in instant. This special fracture mode is a consequence of the markedly oriented microstructure of the heavily drawn steel.
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Panich, Sansot. "Constitutive Modeling of Advanced High Strength Steels Characterized by Uniaxial and Biaxial Experiments." Advanced Materials Research 849 (November 2013): 207–11. http://dx.doi.org/10.4028/www.scientific.net/amr.849.207.

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Anisotropic plastic behavior of advanced high strength steel sheets of grade DP780 and DP980 were investigated using three different yield functions, namely, the von Mises, Hills 48 and Barlat2000 (Yld2000-2d) criteria. Uniaxial tensile and balanced biaxial (hydraulic bulge) tests were conducted for the examined steels in order to characterize flow behavior and plastic anisotropy for different stress states. Additionally, disk compression and In-plane biaxial tension tests were performed for obtaining balanced r-value of DP780 and DP980, respectively. All these data were used to determine the anisotropic coefficients. According to the different yield criteria, yield stresses and r-values for different directions were calculated corresponding to these yield criteria. The results were compared with experimental data. It was found that the Yld2000-2d model precisely predict well with experimental data than the other models.
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Steuwer, Axel, Javier Roberto Santisteban, Philip J. Withers, Lyndon Edwards, and Mike E. Fitzpatrick. "In situdetermination of stresses from time-of-flight neutron transmission spectra." Journal of Applied Crystallography 36, no. 5 (September 8, 2003): 1159–68. http://dx.doi.org/10.1107/s0021889803013748.

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The pulsed neutron transmission diffraction technique exploits the sharp steps in intensity (Bragg edges) appearing in the transmitted spectra of thermal neutrons through polycrystalline materials. In this paper the positions of these edges acquired by the time-of-flight (TOF) technique are used to measure accurately the interplanar lattice distances to a resolution of Δd/d≃ 10−4of specimens subjected toin situuniaxial tensile loading. The sensitivity of the method is assessed for elastically isotropic (b.c.c. ferritic) and anisotropic (f.c.c. austenitic) polycrystalline specimens of negligible and moderately textured steels. For the more anisotropic austenitic steel, the elastic anisotropy is studied with regard to a Pawley refinement, and compared with previous results from conventional neutron diffraction experiments on the same material. It is shown that the method can be used to determine anisotropic strains, diffraction elastic constants, the residual and applied stress state as well as the unstrained lattice parameter by recording transmission spectra at different specimen inclinations, by complete analogy with the sin2ψ technique frequently used in X-ray diffraction. The technique is shown to deliver reliable measures of strain even in the case of moderate texture and elastic anisotropy.
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YONEDA, KEISHI, AKIO YONEZU, HIROYUKI HIRAKATA, and KOHJI MINOSHIMA. "ESTIMATION OF ANISOTROPIC PLASTIC PROPERTIES OF ENGINEERING STEELS FROM SPHERICAL IMPRESSIONS." International Journal of Applied Mechanics 02, no. 02 (June 2010): 355–79. http://dx.doi.org/10.1142/s1758825110000536.

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This study proposes a method of reverse analysis to estimate the anisotropic plastic properties of engineering steels by spherical indentation. The method takes into consideration materials that obey the work-hardening law and show in-plane anisotropic yield stress. Finite element analysis was first carried out to compute the indentation behavior of such materials, showing that a permanent impression exhibited an anisotropic shape which was strongly dependent on the orthotropic axis. Based on the anisotropy of the impression geometry, we developed a simple approach to determine the yield stress, work-hardening exponent and yield stress ratio. The approach consists of several functions related to the parameters of two impression geometries, produced by dual spherical indentations with different indentation forces. Since the present method uses only two impression geometries and does not necessitate indentation force — displacement curves (indentation curves), it is a particularly useful technique to evaluate "indistinguishable materials" which are special sets of materials with distinct plastic properties, yet yield almost identical indentation curves.
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Toribio, Jesús, and Francisco-Javier Ayaso. "Cleavage Stress Producing Notch-Induced Anisotropic Fracture and Crack Path Deflection in Cold Drawn Pearlitic Steel." Metals 11, no. 3 (March 9, 2021): 451. http://dx.doi.org/10.3390/met11030451.

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The fracture performance of axisymmetric notched samples taken from pearlitic steels with different levels of cold-drawing is studied. To this end, a real manufacture chain was stopped in the course of the process (on-site in the factory), and samples of all intermediate stages were extracted from the initial hot-rolled bar (not cold-drawn at all) to the final commercial product (prestressing steel wire). Thus, the drawing intensity or straining level (represented by the yield strength) is treated as the key variable to elucidate the consequences of manufacturing on the posterior fracture issues. On the basis of a materials science approach, the clearly anisotropic fracture behavior of heavily drawn steels (exhibiting deflection in the fracture surface) is rationalized on the basis of the markedly oriented pearlitic microstructure of the cold-drawn steel that influences the operative micromechanism of fracture. In addition, a finite element analysis of the stress distribution at the fracture instant allows the computation of the cleavage annular stress required to produce anisotropic fracture behavior and thus crack path deflection associated with mixed-mode cracking. Results show that such a stress is the variable governing initiation and propagation of anisotropic fracture by cleavage (a specially oriented and enlarged cleavage fracture) appearing along the wire axis direction in the case of sharply-notched samples of heavily drawn pearlitic steels.
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Toribio, Jesús, Beatriz González, and Juan Carlos Matos. "Anisotropic Fatigue & Fracture Behaviour in Hot-Rolled and Cold-Drawn Pearlitic Steel Wires." Key Engineering Materials 713 (September 2016): 103–6. http://dx.doi.org/10.4028/www.scientific.net/kem.713.103.

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This paper analyses the role of cold drawing in the fatigue and fracture behaviour of pearlitic steels with distinct drawing degree (a hot rolled bar and a commercial prestressing steel wire). Fatigue crack growth develops globally in mode I and locally in mixed mode in both steels, the micro-crack deflection angle depending on the drawing degree. With regard to fracture behaviour, it takes place in mode I in the hot-rolled bar and in mixed mode (with a strong component of mode II) in the case of the cold-drawn wire, so that strength anisotropy appears in the drawn steel and a sort of directional toughness can be defined.
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Dissertations / Theses on the topic "Anisotropic steels"

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Moverare, Johan J. "Microstresses and anisotropic mechanical behaviour of duplex stainless steels /." Linköping : Univ, 2001. http://www.bibl.liu.se/liupubl/disp/disp2001/tek699s.pdf.

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Wei, Jianfei [Verfasser]. "Anisotropic Distortion of High Alloyed Tool Steels During Gas Quenching and Tempering / Jianfei Wei." Aachen : Shaker, 2004. http://d-nb.info/117261458X/34.

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Menard, Corentin. "Imagerie ultrasonore dans des aciers anisotropes dont les propriétés élastiques sont incertaines : application au contrôle des assemblages soudés du domaine nucléaire." Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG027.

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En contrôle non-destructif par ultrasons, la qualité de l’imagerie échographique repose sur l’adéquation entre le modèle direct de propagation des ondes élastiques et la propagation dans le milieu physique. C’est notamment le cas des structures anisotropes, comme les soudures en acier du domaine nucléaire, où la méconnaissance de l’anisotropie au moment de l’inspection peut conduire à des images très dégradées et inexploitables. Cette dégradation est d’autant plus marquée que l’anisotropie d’une soudure est fortement inhomogène en raison de la croissance dendritique de la matière au moment de son refroidissement. La fiabilité des diagnostics en imagerie ultrasonore requiert alors de bien connaître les propriétés du matériau au moment de l’inspection.Dans cette thèse, une méthode adaptative basée sur une procédure d’optimisation est étudiée pour améliorer l’imagerie des soudures anisotropes du domaine nucléaire. On s’intéresse notamment à l’imagerie TFM (Total Focusing Method) dont l’intérêt principal est que le mode d’acquisition des signaux ne présuppose aucun a priori sur les propriétés du matériau. Dans la procédure d’optimisation, une première image est calculée à partir d’un modèle de reconstruction isotrope. Si l’image fait apparaître une indication au-dessus du niveau de bruit, un algorithme d’optimisation itère le calcul des images en faisant varier les paramètres du modèle de soudure jusqu’à maximiser l’amplitude de l’écho d’intérêt. Dans ce travail, l’optimisation est validée statistiquement avec des échos simulés, en s’appuyant sur des outils d’apprentissage machine qui permettent d’accélérer les temps de calcul. La procédure est également évaluée expérimentalement sur diverses soudures de complexité croissante. Dans chacun des cas, la procédure produit une image avec un rapport signal/bruit satisfaisant, tout en minimisant les erreurs de localisation des défauts
In non-destructive ultrasound testing, the quality of the imaging relies on the adequacy between a direct model of elastic wave propagation and the propagation in the physical medium. This is particularly the case for anisotropic structures, such as nuclear-domain welds, for which not knowing the anisotropy at the time of inspection can lead to severly degraded and unusable images. This degradation is all the more marked as the anisotropy of a weld is highly inhomogeneous, due to the dendritic growth of the material during its cooling. The reliability of an array imaging diagnosis therefore requires a good knowledge on the material at the time of inspection.In this thesis, an adaptive method based on an optimization procedure is studied in order to improve the imaging in nuclear anisotropic welds. We are especially interested in TFM (Total Focusing Method) imaging, whose acquisition principle does not rely on any foreknowledge on the material properties. In the optimization procedure, a first image is computed with an isotropic reconstruction model. If the image shows an indication above the noise level, an optimization algorithm iterates image computations by varying the parameters of the model that describes the structure, until the amplitude of the echo of concern is maximized. The optimization is statistically validated with simulated data, using machine learning tools to speed up computation times. This method is also evaluated experimentally on different welds of increasing complexity. In each case, the procedure produces an image with a high level of signal-to-noise ratio, while minimizing the defect localization error
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Cyril, Nisha S. "Anisotropy and Sulfide Inclusion Effects on Tensile Properties and Fatigue Behavior of Steels." Connect to full text in OhioLINK ETD Center, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=toledo1198808409.

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Thesis (M.S.)--University of Toledo, 2007.
Typescript. "Submitted as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering." "A thesis entitled"--at head of title. Bibliography: leaves 204-209.
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Fard, Samad Moemen Bellah. "Modelling anisotropy in electrotechnical steels." Thesis, Cardiff University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263551.

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Xue, Xin. "Modelling and control of twist springback in lightweight automotive structures with complex cross-sectional shape." Doctoral thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/17766.

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Doutoramento em Engenharia Mecânica
Este trabalho é dedicado à investigação dos mecanismos / fontes de retorno elástico torsional em estruturas automóveis leves e à identificação de formas de controlar este problema. Em primeiro lugar, para garantir uma correta modelação do retorno elástico torsional, foram utlizados os resultados de vários ensaios do material, incluindo diferentes solicitações de carga/descarga, assim como a utilização de modelos constitutivos adequados. O comportamento mecânico dos materiais submetidos a trajetórias simples e complexas de carga é descrito utilizando leis de encruamento e critérios de plasticidade anisotrópicos. Foi desenvolvido um novo dispositivo de ensaios de corte para os aços DP para realização de ensaios de inversão de carga. Foram realizados testes cíclicos de carga-descarga-carga de tração uniaxial e biaxial assim como testes de dobragem em três pontos em material pré -deformado com vista à determinação da degradação do módulo de elasticidade com o aumento de deformação plástica. O efeito da trajetória de deformação na determinação do valor inicial do módulo de elasticidade e a sua degradação foram registados e analisados. Em segundo lugar, foram selecionados como casos de estudo dois processos clássicos de deformação plástica de metais, nomeadamente embutidura de chapas de aço DP e dobragem por matriz rotativa de tubos de alumínio de parede fina e secção assimétrica, devido ao seu evidente efeito de retorno elástico torsional. Foi proposta uma definição melhorada de retorno elástico torsional baseada nos eixos principais de inércia da secção transversal. A relação entre o momento de torção e ângulo de torção foi introduzida para explicar a ocorrência de retorno elástico torsional. Para melhorar a robustez dos modelos numéricos, foram realizadas várias técnicas de modelação, incluindo a identificação de coeficiente de atrito, a restrição de acoplamento da superfície para mandril flexível utilizando um elemento conector articulado, e a correlação de imagens digitais. O mecanismo de retorno elástico torsional foi analisado tendo em conta a evolução de estado plano de tensão e a trajetória de deformação nos componentes após a enformação por deformação plástica. Em terceiro lugar, foi analisada e discutida a sensibilidade dos modelos constitutivos de materiais no que diz respeito à precisão da previsão do retorno elástico torsional. Além disso, foi investigada a influência dos parâmetros do processo de embutidura profunda (direção de material, “blank-piercing” e lubrificação) e dos parâmetros numéricos do processo de dobragem de tubos (restrição dos limites do mandril flexível e atrito nas zonas de contacto) no retorno elástico torsional. Finalmente, foram propostas duas estratégias de controlo para o processo de embutidura profunda, com base no raio da curvatura da matriz variável e na posição dos freios, para reduzir o retorno elástico torsional de duas peças “Cchannel” e “P-channel”, respetivamente. No caso de dobragem de tubos, o controlo do retorno elástico torsional foi alcançado pela otimização da função do mandril e inclusão de um assistente de impulso de carga. Estas estratégias de controlo, baseadas em FEA, apresentam-se como métodos alternativos para a redução do momento torsor e do retorno elástico torsional em termos de aplicações específicas.
This work is devoted to the investigation of the mechanism/source of twist springback in lightweight automotive structures and to the identification of ways to control this problem. Firstly, to ensure accurate twist springback modelling, a reliable test data of material behaviours under various loading /unloading conditions as well as appropriate constitutive models are necessary. The anisotropic yield criteria and hardening models were adopted to characterize the material behaviours under monotonic and complex strain paths. An enhanced simple shear device was developed to obtain the stress-strain behaviour under reversal loading of DP steels. Uniaxial and biaxial loadingunloading- loading cycle tests and the proposed three-point bend test with prestrained sheets, were conducted to determine the elastic modulus degradation with the increase of plastic strain. A significant effect of the loading strategy on the determination of the initial and the degradation of elastic modulus was observed and discussed. Secondly, two typical metal forming processes, namely deep drawing of DP steel sheets and mandrel rotary draw bending of asymmetric thin-walled aluminium alloy tube, were selected as case studies due to their evident twist springback. A more reasonable definition of twist springback with respect to the principal inertia axes of the cross-sections was proposed. The relationship between torsion moment and twist angle was introduced to explain the occurrence of twist springback. Several key modelling techniques including the friction coefficient identification, surface-based coupling constraint for flexible mandrel using HINGE connector element and digital image correlation were performed for improving the robustness of the numerical models. The mechanism of twist springback was analysed from the evolution of in-plane stress and deformation history in the components after forming. Thirdly, the sensitivities of material constitutive models to the accuracy of twist springback prediction were analysed and discussed. The influence of deep drawing process parameters (material direction, blank piercing and lubrication) and numerical parameters of tube bending (boundary constraint for flexible mandrel and interfacial friction) on twist springback are provided. Finally, two control strategies for deep drawing process, based on variable die radius and partial draw bead design, were proposed to reduce the twist springback of the C-channel and the P-channel, respectively. In case of tube bending, the control of twist springback was reached by the optimization of mandrel nose placement and inclusion of push assistant loading. These FEAbased control strategies appear to be alternative methods to reduce the unbalance torsion moment and the twist springback in terms of particular case.
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Daniel, Dominique. "Prediction of elastic and plastic anisotropy in deep drawing steels." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74533.

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Yield stresses and r-values were measured as a function of inclination with respect to the rolling direction on thirty-one steels selected from high strength low alloy (HSLA), Al-killed (AKDQ), interstitial free (IF1 and IF2) and rimmed (RIM) types. Modul-r and electromagnetic acoustic (EMAT) techniques were employed to determine the elastic anisotropy in terms of the angular variation of Young's modulus and the ultrasonic velocities, respectively. Orientation distribution functions (ODF's) were also measured for these steels in their as-received states and after deformation in tension and in drawing. The various initial textures and their evolutions along the latter strain path are analyzed in terms of the 4- and 6-ear behaviours commonly observed during the forming of cylindrical cups.
The series expansion method was employed for predicting the elastic and plastic anisotropies from the initial texture data. Comparison with the experimental measurements of Young's modulus indicates that the so-called elastic energy method can accurately reproduce the elastic anisotropy if the single crystal elastic constants are appropriately chosen within their ranges of uncertainty. The systematic evaluation of various grain interaction models for predicting the polycrystal plastic anisotropy reveals that the "pancake" relaxed constraint model is a more accurate predictor of the behaviour than the Taylor, Sachs-Kochendorfer, or other relaxed constraint models. The best quantitative agreement is obtained when the critical resolved shear stress (CRSS) ratio for glide on the $ {112 } langle 111 rangle$ and $ {110 } langle 111 rangle$ systems is 0.95 (except for the AKDQ and IF2 grades, for which values of 0.90 and 1.0, respectively, are preferred).
The ODF coefficients of order greater than 4 were evaluated and calculated non-destructively from the anisotropy of the ultrasonic velocities of the lowest order symmetrical Lamb (S$ sb{ rm o}$) and shear horizontal (SH$ sb{ rm o}$) waves propagating in the rolling plane. The elastic energy method was employed, together with a decomposition of the texture into the principal preferred orientations. The calculated pole figures based on the ODF coefficients obtained in this way are similar to those derived from complete X-ray data. It is shown that the plastic properties of commercial deep drawing steels are predicted more accurately when the 4th and 6th order ODF coefficients are employed than when only the 4th order ones are used.
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Baselli, Silvia. "Study of the anisotropic sintering shrinkage of green iron and stainless steel." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/267476.

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Powder metallurgy (PM) is a near net-shape technology that guarantees excellent dimensional control and surface finishing in the production of parts with complex shapes. Press and sinter is the conventional PM process. The powder mix is compacted into rigid dies to obtain the so called green part that is subsequently sintered to promote the formation of metallic bonding between the powder particles. The differences in terms of geometrical and dimensional features between the green compact and the final part are related to the dimensional variations occurring during sintering, therefore, to preserve the cost effectiveness of the process, their in-depth knowledge is crucial. In this context, post- sintering machining should be limited to the realization of geometrical details that cannot be directly obtained through uniaxial cold compaction or to achieve strict tolerances required by specific applications. The dimensional changes in sintering that may be either shrinkages or swellings are affected by many parameters and, among them, we can consider: material, presence of lubricant and additives, green density, compaction strategy, sintering temperature and time, atmosphere, heating and cooling rate. Furthermore, the dimensional variations along the direction parallel to compaction (longitudinal, axial) are different from the dimensional variations in the compaction plane (transversal, radial) causing an anisotropy that depends, in addition to the mentioned parameters, on the geometry and the dimension of the part. At present, in absence of an adequate designing tool to account for the anisotropy, engineers rely on empirical methods often based on the trial-and-error approach.
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Baselli, Silvia. "Study of the anisotropic sintering shrinkage of green iron and stainless steel." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/267476.

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Powder metallurgy (PM) is a near net-shape technology that guarantees excellent dimensional control and surface finishing in the production of parts with complex shapes. Press and sinter is the conventional PM process. The powder mix is compacted into rigid dies to obtain the so called green part that is subsequently sintered to promote the formation of metallic bonding between the powder particles. The differences in terms of geometrical and dimensional features between the green compact and the final part are related to the dimensional variations occurring during sintering, therefore, to preserve the cost effectiveness of the process, their in-depth knowledge is crucial. In this context, post- sintering machining should be limited to the realization of geometrical details that cannot be directly obtained through uniaxial cold compaction or to achieve strict tolerances required by specific applications. The dimensional changes in sintering that may be either shrinkages or swellings are affected by many parameters and, among them, we can consider: material, presence of lubricant and additives, green density, compaction strategy, sintering temperature and time, atmosphere, heating and cooling rate. Furthermore, the dimensional variations along the direction parallel to compaction (longitudinal, axial) are different from the dimensional variations in the compaction plane (transversal, radial) causing an anisotropy that depends, in addition to the mentioned parameters, on the geometry and the dimension of the part. At present, in absence of an adequate designing tool to account for the anisotropy, engineers rely on empirical methods often based on the trial-and-error approach.
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Somkun, Sakda. "Magnetostriction and magnetic anisotropy in non-oriented electrical steels and stator core laminations." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/55184/.

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Magnetostriction is a source of vibration and acoustic noise of electrical machines and it can be highly anisotropic even in non-oriented electrical steel. Understanding of magnetostriction under magnetisation and stress conditions present in stator core laminations can help predict the core vibration and radiated noise. Anisotropy of magnetostriction of a 0.50 mm thick non-oriented steel investigated in Epstein strips cut at angles to the rolling direction was much higher than the anisotropy of its magnetic and elastic properties because magnetostriction arises directly from magnetic domain processes. Magnetostriction of a disc sample of the 0.50 mm thick steel was measured under ID and 2D magnetisation and compared with that of a 0.35 mm thick steel with different anisotropy level. A 2D magnetostriction model and an analytical simple domain model were used to explain the experimental results. 2D magnetostriction is dependent on the magnetostrictive anisotropy and the ratios of the transverse to longitudinal magnetostriction. AC magnetostriction measured in the disc samples was larger than in the Epstein strips due to the form effect. An induction motor model core was constructed from the 0.50 mm thick steel for measurements of localised flux density and deformation. Core deformation due to Maxwell forces was calculated. Magnetostriction and specific power loss of the core material under magnetisation conditions present in the core was measured. The localised loss in the stator teeth, tooth roots and back iron differed from their average value by 52%, 19% and 36% due to the magnetic anisotropy. Magnetostriction was estimated to be about 55% and 80% of the radial deformation at the tooth root and back iron regions respectively. Stator teeth deformed asymmetrically and the magnitude of the space harmonics increased due to the magnetostrictive anisotropy. The measurement results inferred that 2D magnetostriction can be predicted from the magnetostrictive anisotropy and vice versa. Also, core deformation and vibration of large machines, where segmented stator core laminations are used, can be estimated analytically with the knowledge of 2D magnetostriction of the core material.
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Books on the topic "Anisotropic steels"

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Page, J. H. R. Low Anisotropy Non-oriented Electrotechnical Steels. European Communities / Union (EUR-OP/OOPEC/OPOCE), 1990.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Cosmological perturbations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0061.

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This chapter describes the first steps toward an understanding of large structures, which are observed in the universe at all scales—galaxies, groups of galaxies, and galactic clusters. It does so by studying the evolution of perturbations at linear order in Friedmann–Lemaître spacetimes. To simplify the discussion, the chapter limits the scope to the textbook case where the spatial sections of the background space are Euclidean (K = 0), and anisotropic perturbations and entropy perturbations are absent. This basically means that the matter reduces to a single fluid. The relativistic and Newtonian theories of cosmological perturbations differ. Finally, the chapter discusses the limit in which they converge.
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Book chapters on the topic "Anisotropic steels"

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Mirone, G. "Optical: Numerical Determination of the Flow Curves of Anisotropic Steels and Failure Prediction." In Conference Proceedings of the Society for Experimental Mechanics Series, 267–76. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00876-9_33.

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Zhang, Haiming, Qian Li, Dongkai Xu, and Zhenshan Cui. "A Virtual Laboratory Based on Full-Field Crystal Plasticity Simulations to Predict the Anisotropic Mechanical Properties of Advanced High Strength Steels." In The Minerals, Metals & Materials Series, 155–64. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06212-4_14.

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Boehler, J. P. "Anisotropic Hardening of Rolled Sheet-Steel." In Applications of Tensor Functions in Solid Mechanics, 123–39. Vienna: Springer Vienna, 1987. http://dx.doi.org/10.1007/978-3-7091-2810-7_7.

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Toribio, Jesús, Beatriz González, and Juan-Carlos Matos. "Strength Anisotropy in Prestressing Steel Wires." In Materials with Complex Behaviour II, 259–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-22700-4_15.

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Parks, D. M., and R. G. Stringfellow. "Strain-Induced Transformation Plasticity in Metastable Austenitic Steels." In Anisotropy and Localization of Plastic Deformation, 516–19. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3644-0_120.

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Minachi, A., and R. B. Thompson. "Ultrasonic Wave Propagation in Inhomogeneous, Anisotropic Cast Stainless Steel." In Review of Progress in Quantitative Nondestructive Evaluation, 1967–74. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4615-3742-7_108.

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Petrov, Roumen, Leo Kestens, and Yvan Houbaert. "Toughness Anisotropy in Intercritically Rolled Steel Plates." In Materials Science Forum, 1499–504. Stafa: Trans Tech Publications Ltd., 2005. http://dx.doi.org/10.4028/0-87849-975-x.1499.

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Gerstein, Gregory, Florian Nürnberger, and Hans Jürgen Maier. "Evolution of Void Shape Anisotropy in Deformed BCC Steels." In EPD Congress 2016, 173–79. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48111-1_20.

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Gerstein, Gregory, Florian Nürnberger, and Hans Jürgen Maier. "Evolution of Void Shape Anisotropy in Deformed BCC steels." In 2016 EPD Congress, 173–79. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781119274742.ch20.

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Yoshida, F., M. Itoh, and M. Ohmori. "Yielding of Mild Steel after Hydrostatic Pressurization." In Anisotropy and Localization of Plastic Deformation, 425–28. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3644-0_99.

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Conference papers on the topic "Anisotropic steels"

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Chwastek, Krzysztof, Artur Wodzynski, Ajay P. S. Baghel, and Shrikrishna V. Kulkarni. "Anisotropic properties of electrical steels." In 2015 16th International Conference on Computational Problems of Electrical Engineering (CPEE). IEEE, 2015. http://dx.doi.org/10.1109/cpee.2015.7333328.

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Clements, B. E. "Investigation of the Observed Anisotropic Fracture in Steels." In Shock Compression of Condensed Matter - 2001: 12th APS Topical Conference. AIP, 2002. http://dx.doi.org/10.1063/1.1483595.

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Volenik, K., V. Novak, J. Dubsky, P. Chraska, and K. Neufuss. "Compressive Behaviour of Plasma Sprayed High-Alloy Steels." In ITSC 1998, edited by Christian Coddet. ASM International, 1998. http://dx.doi.org/10.31399/asm.cp.itsc1998p0671.

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Abstract The mechanical properties of plasma sprayed metals and alloys are important in most applications. It a posttreatment by forming of plasma deposited coatings is required, their response to compressive loading is decisive. This paper is concerned with the compressive behaviour of two high-alloy steels sprayed by a water stabilized plasma gun. Martensitic (13.2 % Cr) and austenitic (19.6 % Cr, 11.6 % Ni) steels were plasma sprayed onto plain steel substrates. Small cube-shaped test samples were cut out of thick coatings by an electrospark technique. Compressive load was applied along axes parallel and perpendicular to the substrate and coating surfaces. In addition, comparative samples of bulk steels produced by conventional metallurgy were tested. The compressive behaviour of the as-sprayed martensitic steel was anisotropic at room temperature, i.e. dependent on the orientation of the compression axis. As a result of compression, the splat shapes changed in a manner depending on the orientation of the compression axis. The room temperature compression tests showed that the yield stress of this steel was decreased and the anisotropy was reduced by annealing after plasma spraying. At room temperature, the anisotropy of the as-sprayed austenitic steel and the effect of annealing were less pronounced in comparison with the martensitic steel. Very low values of the yield stress were observed in both steels compressed at the annealing temperature. In spite of the presence of oxide films enveloping each splat, the coatings were prone to considerable plastic deformation, in particular if compressed along the axis perpendicular to the surface.
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Hart, James D., Nasir Zulfiqar, Joe Zhou, and Keith Adams. "Extension of a Material Model for Pipeline Steels." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90489.

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Pipeline steel stress-strain curves obtained from tension and compression testing of longitudinally and circumferentially oriented specimens of the pipe wall can be significantly different e.g., the pipe material is anisotropic. The anisotropic behavior can result from the manufacturing process (e.g., due to cold expansion of UOE pipe) and can also be influenced by strain aging effects (e.g., due to heated application of pipe coating materials). As described in previous work, the Mroz multilinear kinematic hardening plasticity theory has the ability to accurately model different types of anisotropic pipe material behavior including relatively “sharp” uniaxial circumferential tension response and relatively well-rounded uniaxial longitudinal tension and compression response. The stress-strain curve fitting is accomplished by essentially selecting the sizes and initial positions of elliptical von Mises yield functions in stress-space. A previously developed and published 8-parameter model is well-suited for fitting a matched pair of longitudinal tension (LT) and hoop tension (HT) stress-strain curves as might typically be available from a strain-based pipeline design project. Fitting a pair of “target” LT-HT stress-strain curves is accomplished using a “2-root” fitting procedure where the roots correspond to locations where the yield functions intercept the stress axes in two-dimensional (longitudinal-hoop) stress space. In this paper, the previously described 8-parameter/2-root fitting procedure is extended to a 10-parameter/3-root fitting procedure for situations where a matched “triple” of pipe steel stress-strain curves are available (e.g., LT, HT and longitudinal compression or LC). This extension allows for analysis of strain-based design conditions using an analytical pipe steel, which provides an accurate representation of the uniaxial longitudinal and circumferential stress-strain response of the pipeline material. This paper reviews the 8-parameter/2-root fitting procedure and outlines the extension to the 10-parameter/3-root fitting approach including example application.
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Guan, Weimin, Di Zhang, Mu Yang, Yanhui Gao, and Kazuhiro Muramatsu. "Hybrid Laminated Iron Core Models Based on Isotropic and Anisotropic Silicon Steels." In 2018 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD). IEEE, 2018. http://dx.doi.org/10.1109/asemd.2018.8559039.

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Garion, C. "Anisotropic Constitutive Model of Strain-Induced Phenomena in Stainless Steels at Cryogenic Temperatures." In ADVANCES IN CRYOGENIC ENGINEERING: Transactions of the International Cryogenic Materials Conference - ICMC. AIP, 2004. http://dx.doi.org/10.1063/1.1774565.

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Roll, Karl, Alexander Faust, and Lutz Keßler. "Deep Drawing Simulation Of High And Ultrahigh Strength Steels Under Consideration Of Anisotropic Hardening." In MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes. AIP, 2007. http://dx.doi.org/10.1063/1.2740917.

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El Shawish, Samir, Leon Cizelj, and Igor Simonovski. "Evolution of Crystal Orientations in Plastically Deformed Steels: Role of Constitutive Models Used in Finite Element Simulations." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-16767.

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Stainless steel is a commonly used material in safety-important components of nuclear power plants. In order to study degradation mechanisms in stainless steels, like crack initiation and propagation, it is important to characterize the degree of plastic strain on microstructural level. One way to estimate local plastic strain is by measuring local crystal orientations of the scanned surfaces: the electron backscatter diffraction (EBSD) measurements on stainless steel revealed a strong correlation between the spread of crystal orientations within the individual grains and the imposed macroscopic plastic strain. Similar behavior was also reproduced by finite element simulations where stainless steel was modeled by an anisotropic elasto-plastic constitutive model. In that model the anisotropic Hill’s plasticity function for yield criteria was used and calibrated against the EBSD measurements and macroscopic tensile curve. In this work the Hill’s phenomenological model is upgraded to a more sophisticated crystal plasticity model where plastic deformation is assumed to be a sum of crystalline slips in all activated slip systems. The hardening laws of Peirce, Asaro and Needleman and of Bassani and Wu are applied in crystal plasticity theory and implemented numerically within the user subroutine in ABAQUS. The corresponding material parameters are taken from literature for 316L stainless steel. Finite element simulations are conducted on the analytical Voronoi tessellation with 100 grains and initial random crystallographic orientations. From the simulations, crystal and modified crystal deformation parameters are calculated, which quantify mean and median spread of crystal orientations within individual grains with respect to central grain orientation. The results are compared to EBSD measurements and previous simulations performed with Hill’s plasticity model.
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Pleta, Abram D., Matthew C. Krugh, Chetan Nikhare, and John T. Roth. "An Investigation of Anisotropic Behavior on 5083 Aluminum Alloy Using Electric Current." In ASME 2013 International Manufacturing Science and Engineering Conference collocated with the 41st North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/msec2013-1244.

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Due to more stringent environmental regulations, the demand for strong, lightweight metal alloys, such as AA 5083, has increased. In sheet metal forming, aluminum is preferred over higher density steels to manufacture such parts; however the in-plane anisotropic behavior of AA 5083 alloy greatly affects its formability. Previous researchers have found that mechanical properties of metallic materials can be influenced by DC electrical current, a research area known as Electrically-Assisted Manufacturing (EAM). The research herein is focused on characterizing the in-plane anisotropic behavior of AA 5083 alloy with and without DC current application, while it is loaded in the uniaxial direction. Furthermore, the effects of EAM on Lueder’s banding will also be investigated.
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Hart, James D., Nasir Zulfiqar, and Joe Zhou. "Evaluation of Anisotropic Pipe Steel Stress-Strain Relationships Influence on Strain Demand." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90495.

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Buried pipelines can be exposed to displacement-controlled environmental loadings (such as landslides, earthquake fault movements, etc.) which impose deformation demands on the pipeline. When analyzing pipelines for these load scenarios, the deformation demands are typically characterized based on the curvature and/or the longitudinal tension and compression strain response of the pipe. The term “strain demand” is used herein to characterize the calculated longitudinal strain response of a pipeline subject to environmentally-induced deformation demands. The shape of the pipe steel stress-strain relationship can have a significant effect on the pipe strain demands computed using pipeline deformation analyses for displacement-controlled loading conditions. In general, with sufficient levels of imposed deformation demand, a pipe steel stress-strain curve with a relatively abrupt or “sharp” elastic-to-plastic transition will tend to lead to larger strain demands than a stress-strain curve with a relatively rounded elastic-to-plastic transition. Similarly, a stress-strain curve with relatively low strain hardening modulus characteristics will tend to lead to larger strain demands than a stress-strain curve with relatively high strain hardening modulus characteristics. High strength UOE pipe can exhibit significant levels of anisotropy (i.e., the shapes of the stress-strain relationships in the longitudinal tension/compression and hoop tension/compression directions can be significantly different). To the extent that the stress-strain curves in the different directions can have unfavorable shape characteristics, it follows that anisotropy can also play an important role in pipeline strain demand evaluations. This paper summarizes a pipeline industry research project aimed at evaluation of the effects of anisotropy and the shape of pipe steel stress-strain relationships on pipeline strain demand for X80 and X100 UOE pipe. The research included: a review of pipeline industry literature on the subject matter; a discussion of pipe steel plasticity concepts for UOE pipe; characterization of the anisotropy and stress-strain curve shapes for both conventional and high strain pipe steels; development of representative analytical X80 and X100 stress-strain relationships; and evaluation of a large matrix of ground-movement induced pipeline deformation scenarios to evaluate key pipe stress-strain relationship shape and anisotropy parameters. The main conclusion from this work is that pipe steel specifications for high strength UOE pipe for strain-based design applications should be supplemented to consider shape-characterizing parameters such as the plastic complementary energy.
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Reports on the topic "Anisotropic steels"

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Hart and Zulfiqar. L52324 Characterization of Anisotropic Pipe Steel Stress-Strain Relationships Influence On Strain Demand. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), November 2011. http://dx.doi.org/10.55274/r0010014.

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This report summarizes a PRCI research project aimed at evaluation of the effects of anisotropy and the shape of pipe steel stress-strain relationships on pipeline strain demand for X80 and X100 UOE pipe. The research included: a review of pipeline industry literature on the subject matter; a discussion of pipe steel plasticity concepts for UOE pipe; characterization of the anisotropy and stress-strain curve shapes for both conventional and high strain pipe steels; development of representative analytical X80 and X100 stress-strain relationships; and evaluation of a large matrix of ground-movement induced pipeline deformation scenarios to evaluate key pipe stress-strain relationship shape and anisotropy parameters. One goal of this research was to apply the findings toward guidance for supplemental pipe material specifications aimed at minimizing undesirable effects of anisotropy and stress-strain curve shape on pipe deformations under displacement-controlled loads.
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Ahmed, Salahuddin, and Michael T. Anderson. Task 1 Final Report, Theoretical/Mathematical Modeling of Ultrasonic Wave Propagation in Anisotropic Polycrystalline Stainless Steels. Office of Scientific and Technical Information (OSTI), April 2009. http://dx.doi.org/10.2172/968202.

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Foeken, van, and Gresnigt. L51809 Buckling and Collapse of UOE Manufactured Steel Pipes. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), November 1998. http://dx.doi.org/10.55274/r0010236.

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In the past 20 years, much research has been conducted into buckling and collapse of pipelines under external pressure, bending or tension and combinations. Also many finite element analyses have been performed into the behavior of pipelines under these loads. The available test results show considerable scatter, which is considered to be caused by variations in the stress-strain relationship, the anisotropy of the steel, the Bauschinger effect, the geometrical deviations, the residual stresses, the test conditions, etc. The manufacturing method (seamless, UO, UOE) has a considerable influence on these properties and on the collapse and local buckling resistance. In this project, design formulations for collapse and buckling with appropriate safety factors, calibrated against experimental and numerical models using probabilistic methods, have been selected for a practical range of design considerations. The project consisted of three parts: experiments, probabilistic calculations, and finite element calculations.
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Gelles, D. S., and T. Shibayama. Analysis of stress-induced Burgers vector anisotropy in pressurized tube specimens of irradiated ferritic-martensitic steel: JLF-1. Office of Scientific and Technical Information (OSTI), September 1998. http://dx.doi.org/10.2172/330623.

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Friedman, Shmuel, Jon Wraith, and Dani Or. Geometrical Considerations and Interfacial Processes Affecting Electromagnetic Measurement of Soil Water Content by TDR and Remote Sensing Methods. United States Department of Agriculture, 2002. http://dx.doi.org/10.32747/2002.7580679.bard.

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Time Domain Reflectometry (TDR) and other in-situ and remote sensing dielectric methods for determining the soil water content had become standard in both research and practice in the last two decades. Limitations of existing dielectric methods in some soils, and introduction of new agricultural measurement devices or approaches based on soil dielectric properties mandate improved understanding of the relationship between the measured effective permittivity (dielectric constant) and the soil water content. Mounting evidence indicates that consideration must be given not only to the volume fractions of soil constituents, as most mixing models assume, but also to soil attributes and ambient temperature in order to reduce errors in interpreting measured effective permittivities. The major objective of the present research project was to investigate the effects of the soil geometrical attributes and interfacial processes (bound water) on the effective permittivity of the soil, and to develop a theoretical frame for improved, soil-specific effective permittivity- water content calibration curves, which are based on easily attainable soil properties. After initializing the experimental investigation of the effective permittivity - water content relationship, we realized that the first step for water content determination by the Time Domain Reflectometry (TDR) method, namely, the TDR measurement of the soil effective permittivity still requires standardization and improvement, and we also made more efforts than originally planned towards this objective. The findings of the BARD project, related to these two consequential steps involved in TDR measurement of the soil water content, are expected to improve the accuracy of soil water content determination by existing in-situ and remote sensing dielectric methods and to help evaluate new water content sensors based on soil electrical properties. A more precise water content determination is expected to result in reduced irrigation levels, a matter which is beneficial first to American and Israeli farmers, and also to hydrologists and environmentalists dealing with production and assessment of contamination hazards of this progressively more precious natural resource. The improved understanding of the way the soil geometrical attributes affect its effective permittivity is expected to contribute to our understanding and predicting capability of other, related soil transport properties such as electrical and thermal conductivity, and diffusion coefficients of solutes and gas molecules. In addition, to the originally planned research activities we also investigated other related problems and made many contributions of short and longer terms benefits. These efforts include: Developing a method and a special TDR probe for using TDR systems to determine also the soil's matric potential; Developing a methodology for utilizing the thermodielectric effect, namely, the variation of the soil's effective permittivity with temperature, to evaluate its specific surface area; Developing a simple method for characterizing particle shape by measuring the repose angle of a granular material avalanching in water; Measurements and characterization of the pore scale, saturation degree - dependent anisotropy factor for electrical and hydraulic conductivities; Studying the dielectric properties of cereal grains towards improved determination of their water content. A reliable evaluation of the soil textural attributes (e.g. the specific surface area mentioned above) and its water content is essential for intensive irrigation and fertilization processes and within extensive precision agriculture management. The findings of the present research project are expected to improve the determination of cereal grain water content by on-line dielectric methods. A precise evaluation of grain water content is essential for pricing and evaluation of drying-before-storage requirements, issues involving energy savings and commercial aspects of major economic importance to the American agriculture. The results and methodologies developed within the above mentioned side studies are expected to be beneficial to also other industrial and environmental practices requiring the water content determination and characterization of granular materials.
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