Artigos de revistas: "Shear localizations"

1

Chang, L. "On the Shear Bands and Shear Localizations in Elastohydrodynamic Lubrication Films". Journal of Tribology 127, n.º 1 (1 de janeiro de 2005): 245–47. http://dx.doi.org/10.1115/1.1843157.

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Lee, J. H., e Y. Zhang. "A Finite-Element Work-Hardening Plasticity Model of the Uniaxial Compression and Subsequent Failure of Porous Cylinders Including Effects of Void Nucleation and Growth—Part II: Localization and Fracture Criteria". Journal of Engineering Materials and Technology 118, n.º 2 (1 de abril de 1996): 169–78. http://dx.doi.org/10.1115/1.2804883.

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In Part I [1] of this paper, Gurson’s mixed hardening plasticity model with strain and stress-controlled nucleations, was used in a large deformation finite element program to study the plastic flow and damage in the uniaxial compression of cylinders under sticking friction. Due to low stress triaxiality at the bulge of the cylinders, it was found that localization may occur before void coalescence. In this paper, necessary conditions of localizations are analyzed for the axial compression of porous cylinders under sticking friction. Shear band type of localization with a normal mode of fracture has been predicted for the majority of the cases studied. Various existing localization conditions and fracture criteria are assessed using the results from the simulation. The maximum shear stress at failure is approximately constant and a constant critical damage can not be found.

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Voyiadjis, George Z., Amin H. Almasri, Danial Faghihi e Anthony N. Palazotto. "Analytical solution for shear bands in cold-rolled 1018 steel". Journal of the Mechanical Behaviour of Materials 20, n.º 4-6 (1 de junho de 2012): 89–102. http://dx.doi.org/10.1515/jmbm-2012-0001.

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AbstractCold-rolled 1018 (CR-1018) carbon steel has been well known for its susceptibility to adiabatic shear banding under dynamic loadings. Analysis of these localizations highly depends on the selection of the constitutive model. To deal with this issue, a constitutive model that takes temperature and strain rate effect into account is proposed. The model is motivated by two physical-based models: the Zerilli and Armstrong and the Voyiadjis and Abed models. This material model, however, incorporates a simple softening term that is capable of simulating the softening behavior of CR-1018 steel. Instability, localization, and evolution of adiabatic shear bands are discussed and presented graphically. In addition, the effect of hydrostatic pressure is illustrated.

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Kudryashov, N. A., R. V. Muratov e P. N. Ryabov. "The collective behavior of shear strain localizations in dipolar materials". Applied Mathematics and Computation 338 (dezembro de 2018): 164–74. http://dx.doi.org/10.1016/j.amc.2018.06.005.

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Deliveris, A. V., I. E. Zevgolis e N. C. Koukouzas. "NUMERICAL MODELLING OF SLOPE STABILITY IN OPEN PIT LIGNITE MINES: A COMPARATIVE STUDY". Bulletin of the Geological Society of Greece 50, n.º 2 (27 de julho de 2017): 671. http://dx.doi.org/10.12681/bgsg.11773.

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Slope stability of an open pit lignite mine was studied using numerical methods (FEM and FDM), by means of three different software packages whose performance was compared and similarities - differences were identified. Plane strain analyses were performed using the shear strength reduction technique under drained conditions and Mohr-Coulomb constitutive models. Based on the results, all three programs demonstrated qualitatively a good agreement in the determination of safety factors and the kinetics of the collapse mechanisms. Small differences were observed in terms of shear strains localizations. Important differences were evident in the development of plastic (shear) and tensile failure indicators. Nevertheless, the problem under examination may be addressed satisfactorily by all three programs.

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Rice, James R. "Heating, weakening and shear localization in earthquake rupture". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, n.º 2103 (21 de agosto de 2017): 20160015. http://dx.doi.org/10.1098/rsta.2016.0015.

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Field and borehole observations of active earthquake fault zones show that shear is often localized to principal deforming zones of order 0.1–10 mm width. This paper addresses how frictional heating in rapid slip weakens faults dramatically, relative to their static frictional strength, and promotes such intense localization. Pronounced weakening occurs even on dry rock-on-rock surfaces, due to flash heating effects, at slip rates above approximately 0.1 m s −1 (earthquake slip rates are typically of the order of 1 m s −1 ). But weakening in rapid shear is also predicted theoretically in thick fault gouge in the presence of fluids (whether native ground fluids or volatiles such as H 2 O or CO 2 released by thermal decomposition reactions), and the predicted localizations are compatible with such narrow shear zones as have been observed. The underlying concepts show how fault zone materials with high static friction coefficients, approximately 0.6–0.8, can undergo strongly localized shear at effective dynamic friction coefficients of the order of 0.1, thus fitting observational constraints, e.g. of earthquakes producing negligible surface heat outflow and, for shallow events, only rarely creating extensive melt. The results to be summarized include those of collaborative research published with Nicolas Brantut (University College London), Eric Dunham (Stanford University), Nadia Lapusta (Caltech), Hiroyuki Noda (JAMSTEC, Japan), John D. Platt (Carnegie Institution for Science, now at *gramLabs), Alan Rempel (Oregon State University) and John W. Rudnicki (Northwestern University). This article is part of the themed issue ‘Faulting, friction and weakening: from slow to fast motion’.

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Prakash, Aditya, Tawqeer Nasir Tak, Namit N. Pai, S. V. S. Narayana Murty, P. J. Guruprasad, R. D. Doherty e Indradev Samajdar. "Slip band formation in low and high solute aluminum: a combined experimental and modeling study". Modelling and Simulation in Materials Science and Engineering 29, n.º 8 (11 de novembro de 2021): 085016. http://dx.doi.org/10.1088/1361-651x/ac3369.

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Abstract Direct ex situ observations related slip band formation with deformed microstructures in commercial AA1050 and AA2219. The samples from both grades had similar grain sizes (∼250 μm) and nearly random crystallographic textures. However, AA2219 contained significantly more solute. Slip bands, on the internal long transverse (LT) plane in split channel die specimens, were characterized by primary spacings (λ) of 2–9 μm, heights (Z) of 160–360 nm and secondary shear strains ( γ LT S ). Higher deformation temperatures for both grades increased λ, decreased, Z and r e d u c e d γ LT S . At all deformation temperatures, AA1050 had smaller λ and higher Z, while AA2219 showed higher γ LT S . In-grain misorientations, but not residual strains, were larger in grains with finer λ in AA1050, but less so in AA2219. Discrete dislocation dynamics (DDD) simulations reported realistic slip bands with slip localizations. The simulations, initiated with static obstacles and sources, led to dislocation interactions and junction formation. The probability of junction stabilization (p) determined the ratio of dynamic sources to obstacles. Slip band formation appeared to be an outcome of the release of piled up dislocations leading to dislocation avalanches. Slip localization increased weakly with finer active slip plane spacing (λ *), giving higher dynamic obstacle strengths and densities, but strongly with smaller p. In particular, the DDD simulations captured experimental patterns of higher slip localizations and dislocation densities in low solute aluminum with finer λ *.

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Boulahia, R., Taoufik Boukharouba, Fahmi Zaïri, M. Naït-Abdelaziz, J. M. Gloaguen, R. Seguela e J. M. Lefebvre. "Successive Translucent and Opaque Shear Bands Accompanied by a Pronounced Periodic Waves Observed in a Polypropylene (PP) Processed by Single ECAE Pass". Advanced Materials Research 423 (dezembro de 2011): 12–25. http://dx.doi.org/10.4028/www.scientific.net/amr.423.12.

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The equal channel angular extrusion (ECAE) is an ingenious severe plastic deformation process used to modify texture and microstructure without reducing sample cross-section. The ECAE of polypropylene (PP) was conducted under various extrusion velocities and back-pressure levels using a 90° die. The application of single ECAE pass to PP was meticulously investigated at room temperature. The ECAE-induced deformation behaviour was examined in relation to the load versus ram displacement curves. Depending on extrusion conditions, PP displayed various types of plastic flow. For ram velocities beyond 4.5 mm/min, severe shear bands consisting of successive translucent and opaque bands were observed, accompanied on the top surface by more or less pronounced periodic waves. Although the application of a back-pressure significantly reduced the wave and shear-banding phenomena, slightly inhomogeneous shear deformation was still observed. Shear bands were only suppressed by decreasing extrusion velocity. The strain-induced crystalline microstructure was investigated by X-ray scattering. Shear-banded samples exhibited a strong texturing of the (hk0) planes along the shear direction in the translucent bands whereas perfect crystalline isotropy appeared in the opaque bands. Application of backpressure and/or reducing ram velocity resulted in uniform texturing along the extruded sample. Yet, texturing changed from single shear to twin-like shear orientation about the shear direction. Mechanical properties changes of the extruded specimens due to back-pressure and extrusion velocity effects were analyzed via uniaxial tensile tests. The tensile samples displayed multiple strain localizations in shear-banded materials whereas quite homogeneous deformation appeared for non-banded ones. These effects were connected with the crystalline texturing. The results also revealed significant increase in the strain hardening after ECAE. Full-field strain was measured under tensile loading using an optical strain measuring technique based upon Digital image correlation technique, suitable for large deformation, which confirms these effects.

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Katoh, Kazuo, e Yasuko Noda. "Distribution of Cytoskeletal Components in Endothelial Cells in the Guinea Pig Renal Artery". International Journal of Cell Biology 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/439349.

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The cytoskeletal components of endothelial cells in the renal artery were examined by analysis of en face preparations under confocal laser scanning microscopy. Renal arterial endothelial cells were shown to be elongated along the direction of blood flow, while stress fibers ran perpendicular to the flow in the basal portion. Focal adhesions were observed along the stress fibers in dot-like configurations. On the other hand, stress fibers in the apical portion of cells ran along the direction of flow. The localizations of stress fibers and focal adhesions in endothelial cells in the renal artery differed from those of unperturbed aortic and venous endothelial cells. Tyrosine-phosphorylated proteins were mainly detected at the sites of cell-to-cell apposition, but not in focal adhesions. Pulsatile pressure and fluid shear stress applied over endothelial cells in the renal artery induce stress fiber organization and localization of focal adhesions. These observations suggest that the morphological alignment of endothelial cells along the direction of blood flow and the organization of cytoskeletal components are independently regulated.

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10

Abed, Farid H., e George Z. Voyiadjis. "Adiabatic Shear Band Localizations in BCC Metals at High Strain Rates and Various Initial Temperatures". International Journal for Multiscale Computational Engineering 5, n.º 3-4 (2007): 325–49. http://dx.doi.org/10.1615/intjmultcompeng.v5.i3-4.120.

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11

Kim, Hyeong-Ki, Chang-Geun Cho, Sun-Ju Lee, Young Hak Lee e Taehoon Kim. "Structural Performance and Reinforcement Improvement of Structural Walls Using Strain-Hardening Cementitious Composites". Sustainability 13, n.º 7 (24 de março de 2021): 3607. http://dx.doi.org/10.3390/su13073607.

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Reinforced concrete (RC) shear walls are effective in improving lateral stiffness and load-carrying capacity under earthquake and wind loads. According to the level of seismic design, however, the spacing of reinforcing steel bars should be very narrow and complicated, with tight spacing of tied bars, as is the case with seismically special RC shear wall design. The purpose of this study was to investigate the applicability of strain-hardening cementitious composites (SHCCs) in structural walls in order to improve structural performance as well as the complications with reinforcement details. The SHCC was mixed, and mechanical tests showed that the SHCC exhibited high ductile tensile strains above 2.0%, while sustaining the tensile stress after cracks and developing multiple microcracks, avoiding crack localizations. Six specimens of RC and reinforced SHCC structural walls were designed and manufactured with varying reinforcement details, and experiments on wall specimens were carried out under transverse wall-loading tests. These experiments demonstrated that the use of SHCC in structural walls, despite minimum use of reinforcement ratios, showed improved responses to minimize damage and failure caused by localized cracks under bending and shear to compared with the use of normal reinforcement ratios in RC walls.

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12

Tejchman, Jacek. "Comparative FE-studies of shear localizations in granular bodies within a polar and non-local hypoplasticity". Mechanics Research Communications 31, n.º 3 (maio de 2004): 341–54. http://dx.doi.org/10.1016/j.mechrescom.2003.11.009.

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Ebrahimian, Babak, Asadollah Noorzad e Mustafa I. Alsaleh. "Effects of periodic fluctuations of micro-polar boundary conditions on shear localizations in granular soil-structure interaction". International Journal for Numerical and Analytical Methods in Geomechanics 36, n.º 7 (11 de março de 2011): 855–80. http://dx.doi.org/10.1002/nag.1031.

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14

Sun, Yujun, Taoyuan Fan, Chunjing Zhou e Zhonghai Wu. "The Evolution of Stress and Strain around the Bayan Har Block in the Tibetan Plateau". Journal of Earthquakes 2015 (8 de dezembro de 2015): 1–10. http://dx.doi.org/10.1155/2015/971628.

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With the constraint of GPS observation, the tectonic deformation of the Bayan Har block and its periphery faults is investigated based on an elastoplastic plane-stress finite element model. The results show that the elastic model cannot explain the current GPS observation in the Bayan Har block. When East Kunlun fault and Yushu-Xianshuihe fault are under plastic yield state or high strain localization, the calculated velocities fit well with the observation values. It indicates that most of the current shear deformations or strain localizations are absorbed by these two large strike-slip faults. In addition, if the recurrence intervals of large earthquakes are used to limit the relative yield strength of major faults, the order of entering the plastic yield state of the major faults around Bayan Har block is as follows. The first faults to enter the yield state are Yushu-Xianshuihe faults and the middle segment of East Kunlun faults. Then, Margaichaka-RolaKangri faults (Mani segment) and Heishibeihu faults would enter the yield state. The last faults to enter the yield state are the eastern segment of East Kunlun faults and Longmenshan faults, respectively. These results help us to understand the slip properties of faults around the southeastward moving Bayan Har block.

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15

Kim, Jongmin, Sunyoung Ahn, Young-Gyu Ko, Yong Chool Boo, Sung-Gil Chi, Chih-Wen Ni, Young-Mi Go, Hanjoong Jo e Heonyong Park. "X-linked inhibitor of apoptosis protein controls α5-integrin-mediated cell adhesion and migration". American Journal of Physiology-Heart and Circulatory Physiology 299, n.º 2 (agosto de 2010): H300—H309. http://dx.doi.org/10.1152/ajpheart.00180.2010.

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The association of integrins with caveolin-1 regulates cell adhesion. However, the vascular ramifications of this association remain to be clearly determined. We recently reported that the X chromosome-linked inhibitor of apoptosis protein (XIAP)-caveolin-1 interaction is critical to endothelial cell survival. Thus, we hypothesized that XIAP performs a crucial function in integrin/caveolin-1-mediated endothelial cell survival. In this study, we demonstrated that XIAP is recruited into the α5-integrin complex via caveolin-1 binding and mediates cell adhesion. We also determined that XIAP is critical to shear stress-stimulated ERK activation in an α5-integrin-dependent manner but is not important to VEGF-induced ERK activation. This differential activation of ERK is partly attributable to unique localizations of the receptors. Furthermore, we confirmed that XIAP is an essential molecule in the efficient recruitment of focal adhesion kinase (FAK) into the α5-integrin-associated complex. This α5-integrin-caveolin-1-XIAP-FAK multicomplex regulates endothelial cell migration via a mechanism that involves shear-dependent ERK activation. Together, our results indicate that XIAP stabilizes the α5-integrin-associated focal adhesion complex, thereby further regulating endothelial cell adhesion and migration. The findings of this study provide us with greater insight into the molecular mechanisms underlying the control of vascular function by integrins.

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Tandon, Vipin, Ki-Seong Park, Rajesh Khatirkar, Aman Gupta e Shi-Hoon Choi. "Evolution of Microstructure and Crystallographic Texture in Deformed and Annealed BCC Metals and Alloys: A Review". Metals 14, n.º 2 (25 de janeiro de 2024): 149. http://dx.doi.org/10.3390/met14020149.

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Dislocation slips, twinning, shear banding (SBs), strain localization, and martensite formation are a few deformation modes that are activated in BCC metals and alloys. Strain, strain rate, and deformation temperature are other parameters that determine the activation of deformation modes in BCC alloys. This review focuses on several BCC alloys, such as beta-titanium (β-Ti), tantalum (Ta), and ferritic stainless steels (FSSs), all of which exhibit differences in deformation behavior. These alloys often undergo thermo-mechanical processing (TMP) to enhance their mechanical properties. TMP leads to the evolution of deformation-induced products, such as SBs, strain-induced martensite (SIM), strain localizations, and mechanical/deformation twins (DTs) during plastic deformation, while also influencing crystallographic texture. The deformation modes in β-Ti depend upon the stability of the β-phase (i.e., β-stabilizers); low-stability alloys show the formation of SIM along with slips and twins, whereas in highly stable β-Ti alloys, only slip+twin modes are observed as the primary deformation mechanisms. In the case of Ta, slip activity predominantly occurs on {110} planes, but it can also occur on planes with the highest resolved shear stress. The breakdown of Schmid’s law or non-Schmid behavior for Ta and Ta-W alloys has been discussed in detail. The cold rolling (CR) of FSSs results in the formation of ridges, which is an undesirable phenomenon leading to very low formability. The microstructures of the rolled sheets consist of elongated ferrite grains with in-grain SBs, which are preferentially formed in the γ-fiber-oriented grains. The formation of finer grains after recrystallization improves both the mechanical properties and ridging resistance in FSS. Therefore, this review comprehensively reports on the impact of TMP on the microstructural and crystallographic texture evolution during the plastic deformation and annealing treatment of β-Ti, Ta alloys, and FSSs in BCC materials, using results obtained from electron microscopy and X-ray diffraction.

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Gobernado, Patricia, Roumen H. Petrov, Jaap Moerman, Carla Barbatti e Leo Kestens. "Origin of the {h 1 1 }<1/h,1,2> Fiber in Single Phase Ferrite Steels". Materials Science Forum 715-716 (abril de 2012): 134–39. http://dx.doi.org/10.4028/www.scientific.net/msf.715-716.134.

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In the present work, the oriented nucleation origin of the recrystallized {h11}<1/h,1,2> fibre is characterized. Aiming to investigate the substructural evolution of <110>//RD fibre grains and {001}<110> grains in particular, a detailed microstructure and texture analysis is performed by high resolution orientation scanning microscopy on a cross-rolled sample. The reason to work with cross-rolled material is the increased incidence of rotated cube orientations after cross rolling. The present data have revealed the presence in the deformed substructure of a crystallite volume that has rotated towards the {311}<136> component in the interior of <110>//RD fibre grains as a result of a grain fragmentation process. Preliminary simulations of the deformation texture suggested that the observed orientation fragmentation might be produced by strain localizations of a shear band nature.

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Kibitkin, Vladimir, Nickolai Savchenko, Mikhail Grigoriev, Andrey Solodushkin, Alexander Burlachenko, Ales Buyakov, Anna Zykova, Valery Rubtsov e Sergei Tarasov. "Digital Image Correlation Characterization of Deformation Behavior and Cracking of Porous Segmented Alumina under Uniaxial Compression". Ceramics 6, n.º 1 (9 de janeiro de 2023): 102–31. http://dx.doi.org/10.3390/ceramics6010008.

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In this study, the two-dimensional digital image correlation (DIC) technique has been applied to sequences of images taken from the surfaces of porous, segmented alumina samples during uniaxial compression tests. The sintered alumina was structurally composed of polycrystalline alumina grains with interior ~3–5-μm pores, a network of discontinuities that subdivided the sample into ~230 μm segments, and ~110 μm pores located at the discontinuity network nodes. Bimodal pore structure and the segment boundaries were the results of the evaporation and the outgassing of the paraffin and ultra-high-molecular-weight polyethylene admixed with alumina powder via slip casting. Only partial bonding bridges between the segments were formed during a low-temperature sintering at 1300 °C for 1 h. A special technological approach made it possible to change the strength of the partial bonding bridges between the segments, which significantly affected the deformation behavior ceramics during compression. The subpixel accuracy of the DIC results was achieved using an interpolation scheme for the identification functional. The vector fields obtained in the experiment made it possible to characterize the processes of deformation and destruction of a porous, segmented alumina using the strain localization in situ maps, cardinal plastic shear, and circulation of vector fields. The use of these characteristics made it possible to reveal new details in the mechanisms of deformation and destruction of segmented ceramics. The localizations of damage were identified and related to the characteristic structural heterogeneities of the tested porous segmented ceramics.

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Gupta, Aman, e Shi-Hoon Choi. "Self-Annealing Phenomena in the Cold-Rolled and Cryo-Rolled Copper Alloys: A Review". Journal of Physics: Conference Series 2635, n.º 1 (1 de novembro de 2023): 012015. http://dx.doi.org/10.1088/1742-6596/2635/1/012015.

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Abstract Severely deformed copper (Cu) alloys showed the self-annealing behaviour when exposed at room temperature (RT) for a prolonged time. This phenomenon results in the evolution of self-annealed grains, dislocations annihilations, and a decrease in the strength. The present review work addresses the evolution of self-annealed microstructures in room-temperature-rolled (RTR) and cryogenic-rolled (CR) Cu alloys, including various grades of Cu alloys such as ETP Cu, Cu-Fe-P, Cu-Sn-Mg alloys that were studied in terms of RT softening. Static recrystallization (SRX) at room temperature (RT) was observed in the highly deformed RTR and CR Cu alloy samples. Both discontinuous SRX (DSRX) and continuous SRX (CSRX) were responsible for the nucleation of small grains at RT. Particle-stimulated nucleation (PSN) also contributed to small-grain formations around Cu2O particles in ETP Cu. However, no PSN was reported for the Cu-Fe-P and Cu-Sn-Mg alloys. The formation of strain localizations (SLs) and shear bands (SBs) was observed in the deformed Cu alloys; these sites were preferred for grain nucleation during RT recrystallization.

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Sornette, A., D. Sornette e P. Evesque. "Frustration and disorder in granular media and tectonic blocks: implications for earthquake complexity". Nonlinear Processes in Geophysics 1, n.º 4 (31 de dezembro de 1994): 209–18. http://dx.doi.org/10.5194/npg-1-209-1994.

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Abstract. We present exploratory analogies and speculations on the mechanisms underlying the organization of faulting and earthquake in the earth crust. The mechanical properties of the brittle lithosphere at scales of the order or larger than a few kilometers are proposed to be analogous to those of non-cohesive granular media, since both systems present stress amplitudes controlled by gravity, and shear band (faulting) localization is determined by a type of friction Mohr-Coulomb rupture criterion. here, we explore the implications of this correspondence with respect to the origin of tectonic and earthquake complexity, on the basis of the existing experimental data on granular media available in the mechanical literature. An important observation is that motions and deformations of non-cohesive granular media are characterized by important fluctuations both in time (sudden breaks, avalanches, which are analogous to earthquakes) and space (strain localizations, yield surfaces forming sometimes complex patterns). This is in apparent contradiction with the conventional wisdom in mechanics, based on the standard tendency to homogenize, which has led to dismiss fluctuations as experimental noise. On the basis of a second analogy with spinglasses and neural networks, based on the existence of block and grain packing disorder and block rotation "frustration", we suggest that these fluctuations observed both at large scales and at the block scale constitute an intrinsic signature of the mechanics of granular media. The space-time complexity observed in faulting and earthquake phenomenology is thus proposed to result form the special properties of the mechanics of granular media, dominated by the "frustration" of the kinematic deformations of its constitutive blocks.

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Xiang, Jiajie, Yuxuan Zheng, Jiang Li e Zhanqiu Tan. "Mechanical Response of CNT/2024Al Composite to Compression and Tension at Different Strain Rates". Metals 13, n.º 2 (28 de janeiro de 2023): 254. http://dx.doi.org/10.3390/met13020254.

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Compressive and tensile properties of a carbon nanotube (CNT) reinforced 2024Al composite are investigated under quasi-static and dynamic compression as well as quasi-static tension, along three different directions (extrusion, normal and transverse directions). Upon compression, yield and fracture strengths of the composite show negligible strain rate effect and mechanical anisotropy as manifested in the compressive stress–strain curves. Fractography and profilometry show that fracture surfaces are rough shear fracture planes for quasi-static compression; however, smooth conical fracture surfaces are observed for dynamic compression as a result of more homogeneous damage nucleation and growth, leading to high ductility under high strain rate loading. Pronounced mechanical anisotropy is observed for the composite under quasi-static tensile loading. Ductility or fracture strain is the highest along the normal direction, because debonding along the particle and lamellar interfaces is suppressed along this direction. In situ optical imaging along with digital image correlation is utilized to obtain the deformation dynamics of the composite along the three different directions. Stripe-shaped strain localizations appear in the strain fields along the extruded and tangential directions, while the strain fields are approximately uniformly distributed along the normal direction, consistent with the stress–strain curves.

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An, Xuanyi, Ping Ye, Jiayun Liu, Chao Tian, Shunshan Feng e Yongxiang Dong. "Dynamic Fracture and Fragmentation Characteristics of Metal Cylinder and Rings Subjected to Internal Explosive Loading". Materials 13, n.º 3 (8 de fevereiro de 2020): 778. http://dx.doi.org/10.3390/ma13030778.

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Dynamic fracture and fragmentation characteristics of explosively driven rings and cylinders are important issues in the field of weapon effectiveness and protection. However, the comparison of fracture characteristics between metal cylinder and rings, and the fracture characteristics of the metal shells at different axial positions, are rarely touched. In the present work, a recovery tank was used to collect fragments, and witness plates were used to investigate the fragment spatial distributions. Before the test, the representative positions of metal shells were plated with copper layers to locate the original position of the recovered fragments. After the test, scanning electron microscopy and optical microscope were used for characterizing the microstructure of the recovered fragments from different positions. Then, the recovered fragments were weighed and measured to investigate their mass and size characteristics. In addition, numerical simulation was used to further investigate the fracture mechanisms of explosively driven cylinders and rings. It was found that the projection angle axial distribution of the fragments for the metal cylinder was similar to that of the fragments for the metal rings. However, the fracture characteristics of the metal rings were significantly different from those of the metal cylinder. The adiabatic shear band played a key role in the fracture process of the metal cylinder, whereas the adiabatic shear band had little chance to initiate in the fracture process of the metal rings because the metal rings could deform uniformly with much fewer strain localizations due to their much lower length. The fracture surfaces of the fragments from different positions of the metal cylinder were very smooth, whereas dimples were found in the fracture surfaces of the fragments from different positions of the metal rings. The mass distribution of the fragments from the metal rings was more uniform than that of the fragments from the metal cylinder, and the circumferential rupture strains of the metal rings were much larger than those of the metal cylinder.

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Wan, Chang-Feng, Li-Gang Sun, Hai-Long Qin, Zhong-Nan Bi e Dong-Feng Li. "A Molecular Dynamics Study on the Dislocation-Precipitate Interaction in a Nickel Based Superalloy during the Tensile Deformation". Materials 16, n.º 18 (9 de setembro de 2023): 6140. http://dx.doi.org/10.3390/ma16186140.

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In the present paper, the dislocation-precipitate interaction in the Inconel 718 superalloy is studied by means of molecular dynamics simulation. The atomistic model composed of the ellipsoidal Ni3Nb precipitate (γ″ phase) and the Ni matrix is constructed, and tensile tests on the composite Ni3Nb@Ni system along different loading directions are simulated. The dislocation propagation behaviors in the precipitate interior and at the surface of the precipitate are characterized. The results indicate that the dislocation shearing and bypassing simultaneously occur during plastic deformation. The contact position of the dislocation on the surface of the precipitate could affect the penetration depth of the dislocation. The maximum obstacle size, allowing for the dislocation shearing on the slip planes, is found to be close to 20 nm. The investigation of anisotropic plastic deformation behavior shows that the composite system under the loading direction along the major axis of the precipitate experiences stronger shear strain localizations than that with the loading direction along the minor axis of the precipitate. The precipitate size effect is quantified, indicating that the larger the precipitate, the lower the elastic limit of the flow stress of the composite system. The dislocation accumulations in the precipitate are also examined with the dislocation densities given on specific slip systems. These findings provide atomistic insights into the mechanical behavior of nickel-based superalloys with nano-precipitates.

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Shawki, T. G. "An Energy Criterion for the Onset of Shear Localization in Thermal Viscoplastic Materials, Part II: Applications and Implications". Journal of Applied Mechanics 61, n.º 3 (1 de setembro de 1994): 538–47. http://dx.doi.org/10.1115/1.2901493.

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Necessary and/or sufficient conditions for the onset of shear flow localization in thermal viscoplastic materials were derived by Shawki (1994) through the analysis of a one-dimensional model of dynamic simple shear with velocity-controlled boundaries. In the former work, an energy-based viewpoint of localization allows for the association of the positive rate of change of the total kinetic energy of the absolute perturbations with the onset of shear strain localization. Here, we derive explicit conditions for the onset of shear localization without the need to obtain exact linear solutions. Explicit localization conditions are then applied to a number of empirical constitutive descriptions of material response. The effects of inertia, heat conduction, thermal softening, strain hardening, and strain rate sensitivity as regards the onset of shear localization are thoroughly discussed. Furthermore, the validity of conclusions based on a constant homogeneous solution is quantified together with the validity of conclusions based on a quasi-static approximation. Moreover, we examine the inadequacy of the notion of asymptotic stability for shear localization in the presence of heat conduction effects. A critical wavelength threshold is derived, for a general description of material response, below which perturbations will not grow. This threshold may also serve as a lower bound for shear band thickness.

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25

Meyers, Marc A., Zezhou Li, Shiteng Zhao, Bingfeng Wang, Yong Liu e Peter K. Liaw. "Shear localization of fcc high-entropy alloys". EPJ Web of Conferences 183 (2018): 03028. http://dx.doi.org/10.1051/epjconf/201818303028.

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Dynamic behavior of the single phase (fcc) Al0.3CoCrFeNi and CoCrFeMnNi high-entropy alloys (HEAs) was examined. The combination of multiple strengthening mechanisms such as solid solution hardening, cutting forest dislocation, as well as mechanical nano-twinning leads to a high work-hardening rate, compared with conventional alloys. The resistance to shear localization was studied by dynamicallyloading hat-shaped specimens to induce forced shear localization. However, no adiabatic shear band could be observed for Al0.3CoCrFeNi HEA at a large shear strain ~1.1. Additionally, shear localization of the CoCrFeMnNi HEA was only found at an even larger shear strain ~7 under dynamic compression. It is therefore proposed that the combination of the excellent strain-hardening ability and modest thermal softening of these two kinds of high-entropy alloys gives rise to remarkable resistance to shear localization, which makes HEAs excellent candidates for impact resistance applications.

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26

Duan, Chun Zheng, Wei Sen Kong, Zhao Xi Wang e Min Jie Wang. "Adiabatic Shear Localization in High Speed Cutting of Hardened Steel". Applied Mechanics and Materials 55-57 (maio de 2011): 983–87. http://dx.doi.org/10.4028/www.scientific.net/amm.55-57.983.

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The formation and development of adiabatic shear localization in serrated chips have great significance to study of mechanism of high speed cutting. This paper investigates the theory prediction and experimental verification of the critical cutting speed of adiabatic shear localization, distribution of adiabatic shear band in serrated chip and the geometry of adiabatic shear band during high speed cutting of hardened steel. The results indicated that the theoretical prediction of critical cutting speed is consistent with the experimental results.With the increase of cutting speed, the width and spacing of adiabatic shear bands in the serrated chips decrease linearly. There are two types of adiabatic shear bands during the formation and development of adiabatic shear localization, i.e. the deformation shear band and the transformed shear band.

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Peirs, J., P. Verleysen, W. Tirry, L. Rabet, D. Schryvers e J. Degrieck. "Dynamic shear localization in Ti6Al4V". Procedia Engineering 10 (2011): 2342–47. http://dx.doi.org/10.1016/j.proeng.2011.04.386.

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Kim, Young Woo, e D. L. Bourell. "Microscopic shear localization in nickel". Metallurgical Transactions A 19, n.º 8 (agosto de 1988): 2041–48. http://dx.doi.org/10.1007/bf02645207.

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Walley, S. M. "Shear Localization: A Historical Overview". Metallurgical and Materials Transactions A 38, n.º 11 (13 de setembro de 2007): 2629–54. http://dx.doi.org/10.1007/s11661-007-9271-x.

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Li, Hong Ru, Fei Feng e Qing Wang. "Application of Structural Loess Binary-Medium Mode in Localization Shear Band". Applied Mechanics and Materials 204-208 (outubro de 2012): 825–32. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.825.

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Based on the theory of breakage mechanics,the structural loess are conceptualized as binary －medium model consisting of bonding brick and frictional band. Shear band is structural loess’ breakage, localization band sprout and development is dynamic process that bonding brick is translating into frictional band.Application of double parameter breakage ratio binary-medium mode of structural loess,simulated the process of structural loess localization band sprouting and expanding with the numerical simulations method,studied localization shear band shape、speciality and law under different disfigurement project,found that the strain localization on a shear band of structural soil at originally is some sets discontinuous little local breakage area step by step developed、 connected and formed the shape of whole destruct with the external load increased,appeared dilatation softening phenomena under the especial disfigurement. Combining binary-medium mode with general finite element,solved the question of localization shear band softening,visual reappeared the course of the local shear band germination and progress.

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31

Su, Ming-Yao, Wei-Han Zhang, Yuan-Yuan Tan, Yan Chen, Hai-Ying Wang e Lan-Hong Dai. "Microstructural Evolution of Shear Localization in High-Speed Cutting of CoCrFeMnNi High-Entropy Alloy". Metals 13, n.º 4 (24 de março de 2023): 647. http://dx.doi.org/10.3390/met13040647.

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Shear localization is one of the most important failure mechanisms subjected to high-strain-rate deformation and has significant effects on the process, plastic deformation, and catastrophic failure of a material. Shear localization was observed in serrated chips produced during the high-speed cutting of the CoCrFeMnNi high-entropy alloy. Electron backscatter diffraction was performed to systematically investigate microstructural evolution during shear banding. The elongation and subdivision of the narrow grains were observed in the areas adjacent to the shear band. The microstructure inside the shear band was found to be composed of equiaxed ultrafine grains. The results reveal that grain subdivision and dynamic recrystallization might have significant roles in the microstructural evolution of shear bands. These results offer key insights into our understanding of shear localization and high-speed machining behavior for high entropy alloys.

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32

Chang, L. "A Parametric Analysis of the Thermal Shear Localization in Elastohydrodynamic Lubrication Films". Journal of Tribology 128, n.º 1 (30 de agosto de 2005): 79–84. http://dx.doi.org/10.1115/1.2125968.

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Experiments and computer simulations have revealed some unusual results of elastohydrodynamic lubrication (EHL) associated with a high degree of thermally induced inhomogeneous shear across the lubricant film, or thermal shear localization. The results include the development of a sizable film dimple in the central EHL region and a dramatic reduction in EHL traction. In this study, a theoretical analysis is carried out to determine the conditions under which the thermal shear localization may develop in EHL films. For a Newtonian lubricant obeying the Barus law of viscosity, a dimensionless group-parameter is identified that fully governs the degree of the thermal inhomogeneous shear. Results are presented that show the critical range of values of this parameter corresponding to the onset of the shear localization. The analysis is also extended to lubricants with non-Newtonian behavior. Results suggest that the same dimensionless group-parameter may be used to measure the degree of the shear localization when the lubricant viscosity in the parameter is replaced by an effective viscosity that accounts for the non-Newtonian effect.

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Wang, Lican, Rongqian Chen, Yancheng You, Zhengwu Chen e Ruofan Qiu. "Effects of Shear Layer Characteristics on Acoustic Propagation and Source Localization". Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, n.º 6 (dezembro de 2019): 1148–57. http://dx.doi.org/10.1051/jnwpu/20193761148.

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The shear layer characteristics of an open-jet acoustic wind tunnel are of key importance on measurements of aeroacoustics. The effects of thickness, spreading angle and strength of shear layer on acoustic propagation and source localization are investigated through the mean/spreading shear layer with a self-similar velocity distribution. Based on the shear flow, the acoustic propagation is computed by the linearized Euler equations via a source term, and then source localization is obtained from beamforming technique combined with the theory of Amiet. Results show that the numerical method can precisely capture the refraction and reflection after sound traversing shear layer. The thickness, spreading angle and strength of the shear layer exerts little effects on the refracted region where sound wave nearly vertical incident, while mainly influence the corresponding up/downstream region in terms of phase change. Increment of thickness, spreading angle and strength of the shear layer increases the acoustic difference between the shear layer with and without thickness, and produces a larger error of source localization downstream of the actual position.

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Wang, Chuanbin, Junjie Wang, Jianian Hu, Shanglin Huang, Yi Sun, Youlin Zhu, Qiang Shen e Guoqiang Luo. "Shear Localization and Mechanical Properties of Cu/Ta Metallic Nanolayered Composites: A Molecular Dynamics Study". Metals 12, n.º 3 (27 de fevereiro de 2022): 421. http://dx.doi.org/10.3390/met12030421.

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With their excellent mechanical properties, Cu/Ta metallic nanolayered composites (MNCs) are extensively applied in aerospace and nuclear industry facilities. However, shear localization severely disrupts the ability of these materials to deform uniformly, attracting many researchers. The necessary time and length conditions of experiments limit the investigation of shear localization; thus, relevant studies are insufficient. The molecular dynamics simulation perfectly corresponds to the short duration and high strain rate of the deformation process. Therefore, in this study, we used molecular dynamics simulations to explore the effect of layer thickness on the shear localization of Cu/Ta MNCs with Kurdjumov–Sachs (KS) orientation–related interfaces. Our research demonstrates that shear localization occurs in samples with layer thicknesses below 2.5 nm, resulting in an inverse size effect on the flow strength. The quantitative analysis indicates that the asymmetry of dislocations in the slip transmission across the interface causes interface rotation. This activates dislocations parallel to the interface to glide beyond the distance of individual layer thicknesses, eventually forming shear bands. Both interface rotation and sliding dominate the plastic deformation in the shear band region. In addition, the dislocation density and amorphous phase increase with decreasing layer thickness.

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Shawki, T. G. "An Energy Criterion for the Onset of Shear Localization in Thermal Viscoplastic Materials, Part I: Necessary and Sufficient Initiation Conditions". Journal of Applied Mechanics 61, n.º 3 (1 de setembro de 1994): 530–37. http://dx.doi.org/10.1115/1.2901492.

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Necessary and/or sufficient conditions for the onset of shear flow localization in thermal viscoplastic materials are derived. Initiation of shear band formation is examined through the analysis of a one-dimensional model of dynamic simple shear with velocity-controlled boundaries. An exact energy estimate is derived for the fully nonlinear initial boundary value problem which illustrates the weak effect of elasticity as regards the onset of localization. The existence, uniqueness and well-posedness properties of a spatially homogeneous solution are also examined. A unique homogeneous solution is shown to exist for the dynamic simple shear problem with velocity controlled and thermally insulated boundaries. The former solution is also shown to be the unique static solution of the simple shear problem, with no elastic or heat conduction effects, consistent with the foregoing boundary conditions. A linear system of equations is derived for the perturbations superposed on the reference, time-dependent homogeneous (static) solution. A discussion regarding the notions of instability and localization motivates the introduction of a novel localization criterion, based on an appropriately selected energy norm, that takes full account of the time variation of the homogeneous solution. Taking advantage of the admissible spatial form of the perturbations together with the foregoing criterion allows for the association of the positive rate of change of the total kinetic energy of the absolute perturbations with the onset of shear strain localization.

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Rodríguez-Martínez, J. A., G. Vadillo, D. Rittel, R. Zaera e J. Fernández-Sáez. "Dynamic recrystallization and adiabatic shear localization". Mechanics of Materials 81 (fevereiro de 2015): 41–55. http://dx.doi.org/10.1016/j.mechmat.2014.10.001.

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El'kin, V. M. "Plastic flow localization in simple shear". Journal of Applied Mechanics and Technical Physics 33, n.º 5 (1992): 751–55. http://dx.doi.org/10.1007/bf00852212.

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Bose, A. "Shear localization in tungsten heavy alloys". Metal Powder Report 47, n.º 11 (novembro de 1992): 53. http://dx.doi.org/10.1016/0026-0657(92)90955-e.

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39

Osovski, S., e D. Rittel. "Microstructural heterogeneity and dynamic shear localization". Applied Physics Letters 101, n.º 21 (19 de novembro de 2012): 211901. http://dx.doi.org/10.1063/1.4767654.

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Warner, D. H., e S. N. Mathaudhu. "Influence of Microcracking on Shear Localization". Journal of Engineering Mechanics 137, n.º 10 (outubro de 2011): 691–98. http://dx.doi.org/10.1061/(asce)em.1943-7889.0000269.

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41

Sheikh-Ahmad, J., e J. A. Bailey. "Flow Instability in the Orthogonal Machining of CP Titanium". Journal of Manufacturing Science and Engineering 119, n.º 3 (1 de agosto de 1997): 307–13. http://dx.doi.org/10.1115/1.2831108.

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An experimental and analytical investigation of flow instability and shear localization in the orthogonal machining of grade 2 commercially pure titanium was made. A criterion for thermo-plastic instability was developed from torsion test results and applied to the analysis of the chip formation process. It was shown that flow instability followed by flow localization occurs when machining titanium at all cutting speeds and that a transition in the chip type from uniform to segmented does not occur. Orthogonal machining experiments were conducted in the speed range from 8.75 × 10−5 to 3.20 m/s for various depths of cut and the shear strain in the chip was calculated. It was shown that shear localization occurred in the chip formation process when the uniform shear strain involved in producing a chip segment reached a critical value and that this critical shear strain correlates fairly well with the instability shear strain predicted by the thermo-plastic instability criterion.

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42

Shawki, T. G. "The Phenomenon of Shear Strain Localization in Dynamic Viscoplasticity". Applied Mechanics Reviews 45, n.º 3S (1 de março de 1992): S46—S61. http://dx.doi.org/10.1115/1.3121391.

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This article addresses shear flow localization during high rates of deformation of thermal viscoplastic materials. An overview of several efforts towards an improved understanding of shear band formation is given. This paper aims at extracting a unified framework towards the analysis of shear band formation for the considered class of deformations. For this purpose, we present a number of rigorous exact solutions for the one–dimensional simple shearing deformation of a general class of thermal viscoplastic material response. These solutions are used as benchmarks for the validation of both analytical and computational procedures. The interactive roles of inertia, rate–sensitivity, heat conduction, perturbation geometry, boundary conditions, thermal softening, strain hardening and constitutive description as regards the initiation and further intensification of flow localization are thoroughly addressed. We also examine the delicate questions concerning the notion of shear localization and the related mathematical characterization, length and time scales as well as the connection between localization and catastrophic failure.

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43

Guan, Xinran, Shoujiang Qu, Hao Wang, Guojian Cao, Aihan Feng e Daolun Chen. "Adiabatic Shear Localization in Metallic Materials: Review". Materials 17, n.º 21 (1 de novembro de 2024): 5365. http://dx.doi.org/10.3390/ma17215365.

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In advanced engineering applications, there has been an increasing demand for the service performance of materials under high-strain-rate conditions where a key phenomenon of adiabatic shear instability is inevitably involved. The presence of adiabatic shear instability is typically associated with large shear strains, high strain rates, and elevated temperatures. Significant plastic deformation that concentrates within a adiabatic shear band (ASB) often results in catastrophic failure, and it is necessary to avoid the occurrence of such a phenomenon in most areas. However, in certain areas, such as high-speed machining and self-sharpening projectile penetration, this phenomenon can be exploited. The thermal softening effect and microstructural softening effect are widely recognized as the foundational theories for the formation of ASB. Thus, elucidating various complex deformation mechanisms under thermomechanical coupling along with changes in temperatures in the shear instability process has become a focal point of research. This review highlights these two important aspects and examines the development of relevant theories and experimental results, identifying key challenges faced in this field of study. Furthermore, advancements in modern experimental characterization and computational technologies, which lead to a deeper understanding of the adiabatic shear instability phenomenon, have also been summarized.

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44

Bair, S., F. Qureshi e W. O. Winer. "Observations of Shear Localization in Liquid Lubricants Under Pressure". Journal of Tribology 115, n.º 3 (1 de julho de 1993): 507–13. http://dx.doi.org/10.1115/1.2921667.

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A High Pressure Flow Visualization Cell has been designed and constructed to perform a fundamental investigation of the deformation behavior of liquid lubricants under lubricated concentrated contact conditions. A pressure of 0.3 GPa and a shear stress between parallel plates of about 25 MPa has been demonstrated. Time averaged velocity profiles show no continuous slip either in the bulk or at walls. Localized slip at shear bands inclined to the walls was demonstrated to occur during nonlinear shear response. The number of shear bands increases with shear rate (and shear stress) from as few as one at the onset of non-Newtonian flow until the shear region is essentially filled with bands with a spatial periodicity of 7 μm. Bands are typically inclined 19 deg off the solid surfaces in a direction which reduces the compressive normal stress due to shear on the plane of the band.

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45

Wang, X. B. "Temperature-Dependent Shear Strain Localization of Aluminium-Lithium Alloy in Uniaxial Compression Using Zerilli-Armstrong and Gradient Plasticity Models". Materials Science Forum 519-521 (julho de 2006): 789–94. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.789.

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Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) is introduced into Zerilli-Armstrong model based on the framework of thermally activated dislocation motion. Effect of initial temperature on the distributions of plastic shear strain and deformation in adiabatic shear band (ASB), the axial compressive stress-axial compressive strain curve, the shear stress-average plastic shear strain in ASB curve and the plastic shear strain corresponding to the occurrence of shear strain localization is investigated. The axial deformation within aluminum-lithium alloy specimen in uniaxial compression in strain-hardening stage is considered to be uniform. Beyond the peak compressive stress, a single ASB with a certain thickness determined by internal length is formed and intersects the specimen. The axial plastic deformation is decomposed into uniform deformation and localized deformation due to the shear slip along ASB. Lower temperature leads to earlier occurrence of shear strain localization, i.e., lower critical plastic compressive strain, steeper post-peak shear stress-average plastic shear strain in ASB curve, higher peak shear stress and more apparent shear strain localization. The calculated distributions of plastic shear strain and deformation in ASB are highly nonuniform due to the microstructural effect, as cannot be predicted by classical elastoplastic theory applicable to completely homogenous material. The predicted average plastic shear strains in ASB for different widths of ASB agree with the measured values for under-aged Al-Li alloy at 298K and at strain rate of approximately 103s-1.

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46

Hatem, T. M., e M. A. Zikry. "Shear pipe effects and dynamic shear-strain localization in martensitic steels". Acta Materialia 57, n.º 15 (setembro de 2009): 4558–67. http://dx.doi.org/10.1016/j.actamat.2009.06.028.

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Gray, G. T., K. S. Vecchio e V. Livescu. "Compact forced simple-shear sample for studying shear localization in materials". Acta Materialia 103 (janeiro de 2016): 12–22. http://dx.doi.org/10.1016/j.actamat.2015.09.051.

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Kuroda, Mitsutoshi. "Effects of Crystallographic Texture on Plastic Flow Localization". Key Engineering Materials 340-341 (junho de 2007): 211–16. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.211.

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In this study, effects of typical texture components observed in rolled aluminum alloy sheets (i.e. Copper, Brass, S, Cube and Goss texture components) on plastic flow localization are studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic-viscoplastic continuum slip constitutive relation. First, forming limits of thin sheet set by sheet necking are predicted using a Marciniak–Kuczynski (M–K-) type approach. It is shown that only the Cube texture component yields forming limits higher than that for a random texture in the biaxial stretch range. Next, three-dimensional shear band analyses are performed, using a three-dimensional version of M–K-type model, but the overall deformation mode is restricted to a plane strain state. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. It is concluded that the Cube texture component is said to be a shear band free texture, while some texture components exhibit significantly low resistance to shear band formation. Finally, shear band developments in plane strain pure bending of sheet specimens with the typical textures are studied.

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49

Jenkins, James T. "Localization in Granular Materials". Applied Mechanics Reviews 43, n.º 5S (1 de maio de 1990): S194—S195. http://dx.doi.org/10.1115/1.3120803.

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Ebrahimian, Babak. "Evolution of Shear Localization in an Elasto-Plastic Cosserat Material under Shearing". Key Engineering Materials 577-578 (setembro de 2013): 21–24. http://dx.doi.org/10.4028/www.scientific.net/kem.577-578.21.

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Numerical investigations of shear localization evolution within a layer of granular material under large monotonic shearing are presented. Here, micro-polar (Cosserat) continuum approach is applied within the framework of elasto-plasticity to remove the numerical difficulties of localization modeling encountered in classical continuum. The micro-polar kinematical boundary conditions are used to model the rotation resistance of soil grains along the interface between granular layer and surface of adjoining structure. The finite element results show that shear localization takes place from the beginning of shearing and appears parallel to the direction of shearing, close to the boundary with less restriction of particle rotation. Furthermore, the state variables tend towards asymptotical stationary condition in large shear deformations.

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