Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2021 | OriginalPaper | Chapter

7. FE Simulation Results

Authors : Christian B. Silbermann, Matthias Baitsch, Jörn Ihlemann

Published in: Introduction to Geometrically Nonlinear Continuum Dislocation Theory

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter presents numerical solutions of the initial boundary value problem for a continuously dislocated single crystal under plane shear deformation. To this end, the in-house finite element simulation code explained in the preview chapter is adopted. The simulation results are discussed in the light of the theory of complex, pattern forming systems. Additionally, the convergence behavior of the FE solution is examined and numerical challenges are highlighted.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Numerical Solution with the Finite Element Method
next chapter Outlook
Appendix
Available only for authorised users
Footnotes
1
The dislocation density in the inactive SS 1 is zero as expected and is therefore not depicted.
 
2
The also frequently observed arrangement of dipoles (dislocations of different signs) at \(45^\circ \) cannot be reproduced with theories that only take GNDs into account [10].
 
3
Even without the thermal problem being considered, the necessary entropy outflow exists by the implicit assumption that all dissipated energy is transferred via heat flow.
 
4
The associated finite elements are called superparametric [18]. If the polynomial degree equals 1, the well-known bilinear functions result.
 
5
Note that this condition is sufficient but not necessary for a reliable and effective finite element scheme [19, 20].
 
Literature
1.
Koster, M., Le, K.C.: Formation of grains and dislocation structure of geometrically necessary boundaries. Mater. Sci. Eng. A 643, 12–16 (2015)CrossRef
2.
Koster, M., Le, K.C., Nguyen, B.D.: Formation of grain boundaries in ductile single crystals at finite plastic deformations. Int. J. Plast. 69, 134–151 (2015)CrossRef
3.
Silbermann, C.B., Shutov, A.V., Ihlemann, J.: Modeling the evolution of dislocation populations under non-proportional loading. Int. J. Plast. 55, 58–79 (2014)CrossRef
4.
Hughes, D.A., Hansen, N.: High angle boundaries formed by grain subdivision mechanisms. Acta Materialia 45(9), 3871–3886 (1997)CrossRef
5.
Zahn, D., Tlatlik, H., Raabe, D.: Modeling of dislocation patterns of small- and high-angle grain boundaries in aluminum. Comput. Mater. Sci. 46(2), 293–296 (2009)CrossRef
6.
Shutov, A.V., Kuprin, C., Ihlemann, J., Wagner, M.F.X., Silbermann, C.: Experimentelle Untersuchung und numerische Simulation des inkrementellen Umformverhaltens von Stahl 42CrMo4. Materialwiss. Werkstofftech. 41(9), 765–775 (2010)CrossRef
7.
Silbermann, C.B., Ihlemann, J.: Geometrically linear continuum theory of dislocations revisited from a thermodynamical perspective. Arch. Appl. Mech. 88(1–2), 141–173 (2017)
8.
Läpple, V.: Werkstofftechnik Maschinenbau : theoretische Grundlagen und praktische Anwendungen. Verl. Europa-Lehrmittel, Haan Gruiten (2013)
9.
Hull, D., Bacon, D.J.: Introduction to Dislocations, 5th edn. Butterworth-Heinemann, Amsterdam (2011)
10.
Sangid, M.D.: The physics of fatigue crack initiation. Int. J. Fatigue 57, 58–72 (2013)CrossRef
11.
Ebeling, W.: Chaos, Ordnung, Information: Selbstorganisation in Natur und Technik, vol. 74. Harri Deutsch Verlag (1989)
12.
Haken, H.: Die Selbststrukturierung der Materie: Synergetik in der unbelebten Welt, German edn. Vieweg, Wiesbaden (1990)
13.
Nicolis, G., Prigogine, I., Rebhan, E.: Die Erforschung des Komplexen : Auf dem Weg zu einem neuen Verständnis der Naturwissenschaften. Piper, München, Zürich (1987)
14.
Mánica, M.A., Gens, A., Vaunat, J., Ruiz, D.F.: Nonlocal plasticity modelling of strain localisation in stiff clays. Comput. Geotech. 103(July), 138–150 (2018)CrossRef
15.
Conti, S., Hackl, K. (eds.): Analysis and Computation of Microstructure in Finite Plasticity. Springer, Berlin (2015)
16.
Horn, T., Silbermann, C.B., Frint, P., Wagner, M.F.X., Ihlemann, J.: Strain localization during equal-channel angular pressing analyzed by finite element simulations. Metals 8(1), 55+ (2018)
17.
Roters, F., Eisenlohr, P., Bieler, T.R., Raabe, D.: Crystal Plasticity Finite Element Methods in Materials Science and Engineering. Wiley, New York (2010)
18.
Szabó, B.A., Babuska, I.: Finite Element Analysis. Wiley, New York (2008)
19.
Bathe, K.J.: The inf–sup condition andits evaluation for mixed finite element methods. Comput. Struct. 79(2), 243–252 (2001)
20.
Bathe, K.J.: Finite-Elemente-Methoden. Springer, Berlin (2002)
Metadata
Title
FE Simulation Results
Authors
Christian B. Silbermann
Matthias Baitsch
Jörn Ihlemann
Copyright Year
2021
Book
Introduction to Geometrically Nonlinear Continuum Dislocation Theory

Print ISBN: 978-3-030-63695-1

Electronic ISBN: 978-3-030-63696-8

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-63696-8_7

Premium Partners

    Image Credits