Viscous and Frictional Strength of the Lithospheric Mantle: Microstructural
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Plastic Deformation of Single Crystals
Plastic Deformation of Single Crystals 27-750 Texture, Microstructure & Anisotropy A.D. Rollett With thanks to Prof. H. Garmestani (GeorgiaTech), G. Branco (FAMU/FSU) Last revised: 11th Feb. ‘14 Single Crystal Plasticity, A.D.Rollett, Carnegie Mellon Univ., 2014 2 Objective • The objective of this lecture is to explain how single crystals deform plastically. • Subsidiary objectives include: – Schmid Law – Critical Resolved Shear Stress – Lattice reorientation during plastic deformation • Note that this development assumes that we load each crystal under stress boundary conditions. That is, we impose a stress and look for a resulting strain (rate). Single Crystal Plasticity, A.D.Rollett, Carnegie Mellon Univ., 2014 3 Why is the Schmid factor useful? • The Schmid factor is a good predictor of which slip or twinning system will be active, especially for small plastic strains (< 5 %). • It has been used to analyze the plasticity of ordered intermetallics, especially Ni3Al and NiAl. • It has been used to analyze twinning in hexagonal metals, which is an essential deformation mechanism. • Some EBSD software packages will let you produce maps of Schmid factor. • Schmid factor has proven useful to visualize localization of plastic flow as a precursor to fatigue crack formation. • Try searching with “Schmid factor” (include the quotation marks). Single Crystal Plasticity, A.D.Rollett, Carnegie Mellon Univ., 2014 4 Bibliography • U.F. Kocks, C. Tomé, H.-R. Wenk, Eds. (1998). Texture and Anisotropy, Cambridge University Press, Cambridge, UK: Chapter 8, Kinematics and Kinetics of Plasticity. • C.N. Reid (1973). Deformation Geometry for Materials Scientists. Oxford, UK, ISBN: 1483127249, Pergamon. • Khan and Huang (1999), Continuum Theory of Plasticity, ISBN: 0-471-31043-3, Wiley. -
Dislocation Multiplication by Cross-Slip and Glissile Reaction in a Dislocation Based Continuum Formulation of Crystal Plasticity
Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity Markus Sudmannsa, Markus Strickerc, Daniel Weyganda, Thomas Hochrainerb, Katrin Schulza,∗ aInstitute for Applied Materials, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany bInstitut f¨urFestigkeitslehre, Technische Universit¨atGraz, Kopernikusgasse 24, 8010 Graz, Austria cInstitute of Mechanical Engineering, Ecole´ Polytechnique F´ed´erale de Lausanne, CH-1015, Switzerland Abstract Modeling dislocation multiplication due to interaction and reactions on a mesoscopic scale is an important task for the physically meaningful description of stage II hardening in face-centered cubic crystalline materials. In recent Discrete Dislocation Dynamics simulations it is observed that dislocation multiplication is exclusively the result of mechanisms, which involve disloca- tion reactions between different slip systems. These findings contradict multiplication models in dislocation based continuum theories, in which density increase is related to plastic slip on the same slip system. An application of these models for the density evolution on individual slip systems results in self-replication of dislocation density. We introduce a formulation of dislo- cation multiplication in a dislocation based continuum formulation of plasticity derived from a mechanism-based homogenization of cross-slip and glissile reactions in three-dimensional face- centered cubic systems. As a key feature, the presented -
Some Aspects of Cross-Slip Mechanisms in Metals and Alloys Daniel Caillard, J.L
Some aspects of cross-slip mechanisms in metals and alloys Daniel Caillard, J.L. Martin To cite this version: Daniel Caillard, J.L. Martin. Some aspects of cross-slip mechanisms in metals and alloys. Journal de Physique, 1989, 50 (18), pp.2455-2473. 10.1051/jphys:0198900500180245500. jpa-00211074 HAL Id: jpa-00211074 https://hal.archives-ouvertes.fr/jpa-00211074 Submitted on 1 Jan 1989 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. J. Phys. France 50 (1989) 2455-2473 15 SEPTEMBRE 1989, 2455 Classification Physics Abstracts 62.20H Some aspects of cross-slip mechanisms in metals and alloys D. Caillard (1) and J. L. Martin (2) (1) Laboratoire d’Optique Electronique du CNRS, B.P. 4347, F-31055 Toulouse Cedex, France (2) Institut de Génie Atomique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland (Reçu le 6 mars 1989, accepté sous forme définitive le 24 mai 1989) Résumé. 2014 Des modèles ont été proposés pour décrire le glissement dévié des dislocations dans les métaux de structure CFC et HC. On montre comment ces modèles se sont développés et comment des résultats expérimentaux récents confirment leurs prédictions. -
Grain Size and Solid Solution Strengthening in Metals
Grain Size and Solid Solution Strengthening in Metals A Theoretical and Experimental Study Dilip Chandrasekaran Doctoral Dissertation Division of Mechanical Metallurgy Department of Materials Science and Engineering Royal Institute of Technology SE-100 44 Stockholm, Sweden Stockholm 2003 ISBN 91-7283-604-0 ISRN KTH/MSE--03/54--SE+MEK/AVH Akademisk avhandling, som med tillstånd av Kungliga Tekniska Högskolan i Stockholm, framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 21 november kl 10.00 i sal K1, Teknikringen 56, Kungliga Tekniska Högskolan, Stockholm. Fakultetsopponent Dr. Torben Leffers, Forskningscenter Risö, Roskilde, Danmark. ” Dilip Chandrasekaran 2003 ii ABSTRACT The understanding of the strengthening mechanisms is crucial both in the development of new materials with improved mechanical properties and in the development of better material models in the simulation of industrial processes. The aim of this work has been to study different strengthening mechanisms from a fundamental point of view that enables the development of a general model for the flow stress. Two different mechanisms namely, solid solution strengthening and grain size strengthening have been examined in detail. Analytical models proposed in the literature have been critically evaluated with respect to experimental data from the literature. Two different experimental surface techniques, atomic force microscopy (AFM) and electron backscattered diffraction (EBSD) were used to characterize the evolving deformation structure at grain boundaries, in an ultra low-carbon (ULC) steel. A numerical model was also developed to describe experimental features observed locally at grain boundaries. For the case of solid solution strengthening, it is shown that existing models for solid solution strengthening cannot explain the observed experimental features in a satisfactory way. -
Asthenosphere–Lithospheric Mantle Interaction in an Extensional Regime
Chemical Geology 233 (2006) 309–327 www.elsevier.com/locate/chemgeo Asthenosphere–lithospheric mantle interaction in an extensional regime: Implication from the geochemistry of Cenozoic basalts from Taihang Mountains, North China Craton ⁎ Yan-Jie Tang , Hong-Fu Zhang, Ji-Feng Ying State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, P.O. Box 9825, Beijing 100029, PR China Received 25 July 2005; received in revised form 27 March 2006; accepted 30 March 2006 Abstract Compositions of Cenozoic basalts from the Fansi (26.3–24.3 Ma), Xiyang–Pingding (7.9–7.3 Ma) and Zuoquan (∼5.6 Ma) volcanic fields in the Taihang Mountains provide insight into the nature of their mantle sources and evidence for asthenosphere– lithospheric mantle interaction beneath the North China Craton. These basalts are mainly alkaline (SiO2 =44–50 wt.%, Na2O+ K2O=3.9–6.0 wt.%) and have OIB-like characteristics, as shown in trace element distribution patterns, incompatible elemental (Ba/Nb=6–22, La/Nb=0.5–1.0, Ce/Pb=15–30, Nb/U=29–50) and isotopic ratios (87Sr/86Sr=0.7038–0.7054, 143Nd/ 144 Nd=0.5124–0.5129). Based on TiO2 contents, the Fansi lavas can be classified into two groups: high-Ti and low-Ti. The Fansi high-Ti and Xiyang–Pingding basalts were dominantly derived from an asthenospheric source, while the Zuoquan and Fansi low-Ti basalts show isotopic imprints (higher 87Sr/86Sr and lower 143Nd/144Nd ratios) compatible with some contributions of sub- continental lithospheric mantle. The variation in geochemical compositions of these basalts resulted from the low degree partial melting of asthenosphere and the interaction of asthenosphere-derived magma with old heterogeneous lithospheric mantle in an extensional regime, possibly related to the far effect of the India–Eurasia collision. -
Seismic Velocity Structure of the Continental Lithosphere from Controlled Source Data
Seismic Velocity Structure of the Continental Lithosphere from Controlled Source Data Walter D. Mooney US Geological Survey, Menlo Park, CA, USA Claus Prodehl University of Karlsruhe, Karlsruhe, Germany Nina I. Pavlenkova RAS Institute of the Physics of the Earth, Moscow, Russia 1. Introduction Year Authors Areas covered J/A/B a The purpose of this chapter is to provide a summary of the seismic velocity structure of the continental lithosphere, 1971 Heacock N-America B 1973 Meissner World J i.e., the crust and uppermost mantle. We define the crust as 1973 Mueller World B the outer layer of the Earth that is separated from the under- 1975 Makris E-Africa, Iceland A lying mantle by the Mohorovi6i6 discontinuity (Moho). We 1977 Bamford and Prodehl Europe, N-America J adopted the usual convention of defining the seismic Moho 1977 Heacock Europe, N-America B as the level in the Earth where the seismic compressional- 1977 Mueller Europe, N-America A 1977 Prodehl Europe, N-America A wave (P-wave) velocity increases rapidly or gradually to 1978 Mueller World A a value greater than or equal to 7.6 km sec -1 (Steinhart, 1967), 1980 Zverev and Kosminskaya Europe, Asia B defined in the data by the so-called "Pn" phase (P-normal). 1982 Soller et al. World J Here we use the term uppermost mantle to refer to the 50- 1984 Prodehl World A 200+ km thick lithospheric mantle that forms the root of the 1986 Meissner Continents B 1987 Orcutt Oceans J continents and that is attached to the crust (i.e., moves with the 1989 Mooney and Braile N-America A continental plates). -
Investigation with Cellular-Automaton Simulations
Delft University of Technology Topological aspects responsible for recrystallization evolution in an IF-steel sheet – Investigation with cellular-automaton simulations Traka, Konstantina; Sedighiani, Karo; Bos, Cornelis; Galan Lopez, Jesus; Angenendt, Katja; Raabe, Dierk; Sietsma, Jilt DOI 10.1016/j.commatsci.2021.110643 Publication date 2021 Document Version Final published version Published in Computational Materials Science Citation (APA) Traka, K., Sedighiani, K., Bos, C., Galan Lopez, J., Angenendt, K., Raabe, D., & Sietsma, J. (2021). Topological aspects responsible for recrystallization evolution in an IF-steel sheet – Investigation with cellular-automaton simulations. Computational Materials Science, 198, [110643]. https://doi.org/10.1016/j.commatsci.2021.110643 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. Computational Materials Science 198 -
The Distribution of Water in the Continental Lithospheric Mantle and Its Implications for the Stability of Continents
Invited Review Geology November 2013 Vol.58 No.32: 38793889 doi: 10.1007/s11434-013-5949-1 The distribution of water in the continental lithospheric mantle and its implications for the stability of continents XIA QunKe* & HAO YanTao CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China Received January 14, 2013; accepted May 14, 2013; published online July 11, 2013 The lithospheric mantle is one of the key layers controlling the stability of continents. Even a small amount of water can influence many chemical and physical properties of rocks and minerals. Consequently, it is a pivotal task to study the distribution of water in the continental lithosphere. This paper presents a brief overview of the current state of knowledge about (1) the occurrence of water in the continental lithospheric mantle, (2) the spatial and temporal variations of the water content in the continental litho- spheric mantle, and (3) the relationship between water content and continent stability. Additionally, suggestions for future re- search directions are briefly discussed. water, nominally anhydrous minerals, continental lithospheric mantle, continent stability Citation: Xia Q K, Hao Y T. The distribution of water in the continental lithospheric mantle and its implications for the stability of continents. Chin Sci Bull, 2013, 58: 38793889, doi: 10.1007/s11434-013-5949-1 The lithospheric mantle is the lowermost part of continental continental lithospheric mantle is tightly related to its vis- plates; its viscosity contrast with the underlying astheno- cosity and stability [23,25–28]. -
Plate Tectonics
Plate tectonics tive motion determines the type of boundary; convergent, divergent, or transform. Earthquakes, volcanic activity, mountain-building, and oceanic trench formation occur along these plate boundaries. The lateral relative move- ment of the plates typically varies from zero to 100 mm annually.[2] Tectonic plates are composed of oceanic lithosphere and thicker continental lithosphere, each topped by its own kind of crust. Along convergent boundaries, subduction carries plates into the mantle; the material lost is roughly balanced by the formation of new (oceanic) crust along divergent margins by seafloor spreading. In this way, the total surface of the globe remains the same. This predic- The tectonic plates of the world were mapped in the second half of the 20th century. tion of plate tectonics is also referred to as the conveyor belt principle. Earlier theories (that still have some sup- porters) propose gradual shrinking (contraction) or grad- ual expansion of the globe.[3] Tectonic plates are able to move because the Earth’s lithosphere has greater strength than the underlying asthenosphere. Lateral density variations in the mantle result in convection. Plate movement is thought to be driven by a combination of the motion of the seafloor away from the spreading ridge (due to variations in topog- raphy and density of the crust, which result in differences in gravitational forces) and drag, with downward suction, at the subduction zones. Another explanation lies in the different forces generated by the rotation of the globe and the tidal forces of the Sun and Moon. The relative im- portance of each of these factors and their relationship to each other is unclear, and still the subject of much debate. -
The Mid-Lithospheric Discontinuity Caused by Channel Flow in the Cratonic Lithosphere
The Mid-Lithospheric Discontinuity caused by channel flow in the cratonic lithosphere Haibin Yang *a, b, Irina M. Artemieva c,d,e, Hans Thybo e,f,g a. School of Earth Sciences, University of Melbourne, Melbourne, Australia b. Research School of Earth Sciences, Australian National University, Canberra, Australia c. Department of Geophysics, Stanford University, Stanford, CA 94305, USA d. Section of Oceanic Dynamics, GEOMAR Helmholtz Center for Ocean Research, Kiel 24148, Germany e. State Key Laboratory of Geological Processes and Mineral Resources, School of Earth Sciences, China University of Geosciences, Wuhan, China f. Eurasia Institute of Earth Science, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey g. Centre for Earth Evolution and Dynamics (CEED), University of Oslo, Blindern, 0316 Oslo, Norway Corresponding author: Haibin Yang Email: [email protected] This is a non-peer reviewed preprint submitted to EarthArXiv. 1 Abstract Stable cratons with a thick (> 200 km) and cold lithosphere form rheologically strong plates that move atop a ductile asthenospheric mantle. Various types of seismic observations show the presence of a potentially rheologically weak zone at depths of ca. 80 – 150 km termed the Mid-Lithosphere Discontinuity (MLD). While various mechanisms may explain the MLD, the dynamic processes leading to the seismic observations are unclear. We propose that the MLD can be caused by channel flow in the lower lithosphere, triggered by negative Rayleigh-Taylor instabilities at cratonic margins in the Archean, when the mantle was hotter than at present. Presence of a chemically distinct, low-density cratonic lithospheric root is required to initiate the process. Numerical modeling shows that the top of the channel flow creates a shear zone at a depth comparable to the globally observed seismic MLD. -
Origin and Evolution of Asthenospheric Layers
Two mechanisms of formation of asthenospheric layers L. Czechowski and M. Grad Institute of Geophysics, Faculty of Physics, University of Warsaw Ul. Pasteura 5, 02-093 Warszawa, Poland Phone: +48 22 5532003 E-mail: [email protected] Corresponding author: Leszek Czechowski: [email protected] The theory of plate tectonics describes some basic global tectonic processes as a result of motion of lithospheric plates. The boundary between lithosphere and asthenosphere (LAB) is defined by a difference in response to stress. Position of LAB is determined by: (i) the ratio (melting temperature)/( temperature) and (ii) an invariant of the stress tensor. We consider the role of these both factors for origin and decay of asthenosphere. We find that the asthenosphere of shear stress origin could be a transient, time-dependent feature. Key words: asthenosphere, evolution, LAB, origin of asthenosphere 1. Introduction The plate tectonics theory describes some of the basic tectonic processes on the Earth as motion of lithospheric plates. The plates are moved by large-scale thermal convection in the mantle. The lithosphere is mechanically resistant. Its thickness varies from ~50 to ~250 km. The lithosphere is underlain by the asthenosphere. The boundary between the lithosphere and the asthenosphere (LAB) is defined by a difference in response to stress: the asthenosphere deforms viscously. The bulk of asthenosphere is not melted (1), but at the deformation rate typical for the mantle convection (about 10-14 s-1) it behaves as a fluid with the viscosity η of about 5 1019 kg m-1 s-1. The mantle below has higher effective viscosity (e.g. -
The Mechanics of Ice
COLD REGIONS SCIENCE AND ENGINEERING Monograph ll-C2b THE MECHANICS OF ICE John W. Glen December 1975 GB 2401 CORPS OF ENGINEERS, U.S. ARMY .U58m COLD REGIONS RESEARCH AND ENGINEERING LABORATORY no.ll-C2b HANOVER, NEW HAMPSHIRE 1975 Approved for public release; distribution unlimited. 5 fl rolomis The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized docume* s. 0 Unclassified BUREAU OF RECLAMATION pENVER UBRARY C/ 92099625 ^ Y REPORT DOCUMENTATION PAGE ...............Q ? n Q 9 f i ? 5 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPt_______________ - ..------------ Monograph II-C2b -> 5. TYPE OF REPORT ft PERIOD COVERED 4. TITLE (end Subtitle) j m MECHANICS OF ICE 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER*» 7. AUTHORf» European Research Office r J.W. Glen ,r Contract DAJA37-68-C*0208 £ ■ '« • ' 1 "• - TO. PROGRAM ELEMENT, PROJECT, TASK 9. PERFORMING ORGANIZATION NAME AND ADDRESS AREA ft WORK UNIT NJUMBERS Dr. John W. Glen Department of Physics ^ DA Project 1T062112A130 University of Birmingham ( ^ Task 01 ____ Birmingham. England ____; '____ ; _______ — 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Office, Chief of Engineers ^ December 1975 u 13. n u m b er o f p a g e s ' Washington, D.C. 47 14. MONITORING AGENCY NAME ft ADDRESS*?/ different from Controlling Office) 15. SECURITY CLASS, (of thie report) UvS ^Army Cold Regions Research and Engineering Laboratory-^ Unclassified Hanover, New Hampshire 03755 15«. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of thla Report) Approved for public release; distribution unlimited.