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Elastoplasticity

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Mechanical Behaviour of Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 180))

Abstract

Phenomenological descriptions are given of the elasto-plastic behaviour in uniaxial loading. Monotonic and cyclic loadings are then considered. It is shown how this can be generalised in three dimensions. Plastic deformation requires the displacement of dislocations, which are described first in a continuous medium and then in crystallographic structures. The forces on dislocations and their stress and strain fields and energy are introduced. Mutual interactions between dislocations and interaction with interfaces are studied. Twinning is described. Then hardening due to interactions with the crystallographic lattice, dislocation network, grain boundaries, foreign atoms either isolated or in the form of precipitates or inclusions is described. Hardening due to twinning, martensitic transformation and transformation plasticity are described. The case of some steels is given as examples. Fibres reinforcement is introduced. The macroscopic formulation of plastic behaviour is based on single crystal plasticity and this leads to plasticity criteria considering isotropic and kinematic hardening. The limit analysis of structures is studied. The plasticity of heterogeneous materials is introduced.

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Notes

  1. 1.

    Johann Bauschinger (1834–1893) was a German mathematician. He taught mechanics at the Technical University of Munchen.

  2. 2.

    Erich.Schmid (1896–1983) was an Austrian physicist. Walter Boas (1904–1982) was a German-Australian physicist.

  3. 3.

    Geoffrey Ingram Taylor (1886–1975) was an English physicist. Egon Orowan (1902–1989) and Michael Polanyi (1891–1976), Hungarian-British physicists, proved the necessity of the intervention of dislocations to explain plastic deformation at about the same time.

  4. 4.

    Vito Volterra (1860–1940) was an Italian mathematician.

  5. 5.

    Sir Nevill Mott (1905–1996) was a British physicist who won the Nobel Prize.

  6. 6.

    Johannes (Jan) Martinus Burgers (1895–1981) was a Dutch physicist.

  7. 7.

    Frederick Charles Frank (1911–1998) was a British physicist.

  8. 8.

    William B. Shockley (1910–1989) was an American physicist who won the Nobel Prize in 1956 for the invention of the transistor.

  9. 9.

    J.S. Koehler was professor at the University of Illinois and M.Peach was his PhD student.

  10. 10.

    Sir Rudolf Ernst Peierls (1907–1995) was a German born British scientist.

  11. 11.

    Petr Alexandrovitch Rehbinder (1898–1972) was a Russian scientist.

  12. 12.

    Ludwig Boltzmann (1844–1906) was an Austrian physicist.

  13. 13.

    In 1967 Rudolph Peierls claimed that this force should have been called the Orowan-Nabarro force (Rosenfield et al. 1968).

  14. 14.

    Johann Bauschinger (1834–1893) was a German engineer.

  15. 15.

    Eric Ogivie Hall (1925–2009) was a New-Zelander born Australian metallurgist. Norman James Petch (1917–1992) was a British metallurgist. The Hall-Petch equation is named after their independent contributions in the early 1950s to the study of the influence of grain size on the yield strength of polycrystals.

  16. 16.

    Robert L. Coble (1928–1992) was an American materials scientist.

  17. 17.

    Guillaume Piobert (1793–1871) was a French mechanical engineer and scientist who observed and described these bands in 1842 when studying shocks on plates. W.Lüders published his observations in 1860.

  18. 18.

    Albert Portevin (1880–1962) was a French metallurgist. Henry Le Chatelier (1850–1936) was a French chemist.

  19. 19.

    Hidoji Suzuki was a Japanese scientist.

  20. 20.

    André Guinier (1911–2000) was a French physicist; George Dawson Preston (1896–1972) was a British physicist.

  21. 21.

    Hadfield steel contains about 1%C with 11–15% Mn. This austenitic steel is unique in that it combines high toughness and ductility with high work-hardening capacity and good resistance to wear. Sir Robert Hadfield invented this steel in 1882.

  22. 22.

    Edgard C. Bain (1891–1971) was an American metallurgist.

  23. 23.

    Body in white (BIW) refers to the stage, in automobile manufacturing, in which the car body sheet metal components have been welded together, but before moving parts (doors, hoods and deck lids as well as fenders) the motor and chassis assemblies have been added before painting.

  24. 24.

    This subsection does not consider plastic deformation related to twinning or to transformations, which was studied in Sect. 3.4.4.

  25. 25.

    Henri Tresca (1814–1885) was a French mechanical engineer.

  26. 26.

    Christian Otto Mohr (1835–1918) was a German civil engineer.

  27. 27.

    Charles-Augustin de Coulomb (1736–1806) was a French physicist.

  28. 28.

    Richard Edler von Mises (1883–1953) was an Austro-Hungarian scientist and engineer.

  29. 29.

    Maurice Lévy (1838–1910) was a French mathematician and engineer.

  30. 30.

    Ludwig Prandtl (1875–1953) was a German physicist and engineer.

  31. 31.

    Endre Reuss (1900–1968) was a Hungarian mathematician.

  32. 32.

    William Prager (1903–1980) was a German-born US applied mathematician.

  33. 33.

    Heinrich Hencky (1885–1951) was a German engineer.

  34. 34.

    Hilda Geiringer (1893–1973), also known as Hilda von Mises, was an Austrian mathematics professor.

  35. 35.

    George (Georg Oskar) Sachs (1896–1960) was a Russian-born German and American metallurgist.

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Authors and Affiliations

  1. École Centrale de Paris, rue des Envierges 13, 75020, Paris, France

    Dominique François

  2. École des Mines de Paris ParisTech Centre des Matériaux UMR CNRS, 87, 91003, Evry Cedex, France

    André Pineau

  3. Academy of Engineering, Avenue F.D. Roosevelt, 75008, Paris, France

    André Pineau & André Zaoui

  4. Académie des Sciences, 23 Quai de Conti, 75006, Paris, France

    André Zaoui

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François, D., Pineau, A., Zaoui, A. (2012). Elastoplasticity. In: Mechanical Behaviour of Materials. Solid Mechanics and Its Applications, vol 180. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2546-1_3

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