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Solutions for Fully Plastic Conditions

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Plasticity and Fracture

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 244))

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Abstract

The concept of limit-load analysis is presented which allows for an analytical assessment of the critical load for fully plastic conditions, the “collapse” load, in incremental plasticity. It is suited as approximation of the ultimate load of a structure if instability or fracture can be excluded or as reference load in some fracture assessment procedures. Theorems and extremum principles based on Drucker’s postulates of stability have been established which provide upper and lower bounds of the collapse load. Analytical solutions for plane strain plastic flow can be obtained by the method of characteristics. This approach is known as slip line theory and is generally suited for calculating plastic limit loads of fracture mechanics specimens.

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References

  1. Alexander JM, Komoly TJ (1962) On the yielding of a rigid/plastic bar with an Izod notch. J Mech Phys Solids 10:265–275

    Article  Google Scholar 

  2. Brocks W, Burth K (1977) Über den Zusammenhang von Elementstabilität und Systemstabilität von Tragwerken aus elastischem und elastisch–plastischem Werkstoff”. Forsch Ingenieurwes 43:190–198

    Article  Google Scholar 

  3. Burth K, Brocks W (1992) Plastizität - Grundlagen und Anwendungen für Ingenieure. Vieweg, Braunschweig

    Google Scholar 

  4. Drucker DC (1950) Some implications of work hardening and ideal plasticity. Q Appl Math 7:411–418

    Article  MathSciNet  MATH  Google Scholar 

  5. Drucker DC (1951): A more fundamental approach to plastic stress-strain relations. In: Proceedings of 1st US Nat Congr Appl Mech, ASME, pp 487–491

    Google Scholar 

  6. Drucker DC (1959) A definition of stable inelastic material. Trans ASME, J Appl Mech, pp 101–106

    MATH  Google Scholar 

  7. Drucker (1964) On the postulate of stability of materials in the mechanics of continua. J Mécanique 3:235–249

    MathSciNet  Google Scholar 

  8. Drucker DC, Prager W, Greenberg HJ (1952) Extended limit design theorems for continuous media. Q Appl Mech 9:382–389

    MathSciNet  MATH  Google Scholar 

  9. EN1993 (2004) Eurocode 3: design of steel structures. European Committee for Standardization

    Google Scholar 

  10. Ewing DJF (1968) Plastic yielding of V-notched tension bars with circular roots. J Mech Phys Solids 16:91–98

    Google Scholar 

  11. Ewing DJF (1968) Calculations of the bending of rigid/plastic notched bars. J Mech Phys Solids 16:205–213

    Google Scholar 

  12. Ewing DJF, Hill R (1967) The plastic constraint of V-notched tension bars. J Mech Phys Solids 15:115–125

    Google Scholar 

  13. Freudenthal AM, Geiringer H (1958) The mathematical theories of the slip-line field in plane plastic flow, Handbook of Physics VI. Springer, Berlin

    Google Scholar 

  14. Green AP (1956) The plastic yielding of shallow notched bats due to bending. J Mech Phys Solids 4

    Google Scholar 

  15. Green AP, Hundy BB (1956) Initial plastic yielding in notch bend tests. J Mech Phys Solids 4

    Google Scholar 

  16. Hencky H (1923) Über einige statisch bestimmte Fälle des Gleichgewichts in plastischen Körpern. Z angew Math Mech 3:211–251

    Article  MATH  Google Scholar 

  17. Hill R (1949) The plastic yielding of notched bars under tension. Quart J Appl Math 2:40–52

    Article  MathSciNet  MATH  Google Scholar 

  18. Johnson W, Sowerby R, Venter RD (1982) Plane strain slip line fields for metal deformation. a source book and bibliography. Pergamon, Oxford

    Google Scholar 

  19. Justusson JW, Phillips A (1966) Stability and convexity in plasticity. Acta Mech 2:251–267

    Article  Google Scholar 

  20. Lianis G, Ford H (1958) Plastic yielding of single notched bars due to bending. J Mech Phys Solids 7

    Google Scholar 

  21. Maier G, Drucker DC (1966) Elastic-plastic continua containing unstable elements obeying normality and convexity relations. Schweiz Bauztg 84:447–450

    Google Scholar 

  22. Maier G, Drucker DC (1973) Effects of geometry change on essential features of inelastic behavior. Proc ASCE 99:819–834

    Google Scholar 

  23. Palmer AC, Maier G, Drucker DC (1967) Normality relations and convexity of yield surfaces for unstable materials or structural elements. J Appl Mech 34:464–470

    Article  Google Scholar 

  24. Phillips A, Sierakowski RL (1965) On the concept of the yield surface. Acta Mech 1:29–35

    Article  MATH  Google Scholar 

  25. Prager W, Hodge PG (1954) Theorie ideal plastischer Körper. Springer, Wien

    Book  MATH  Google Scholar 

  26. Wilshaw TR, Pratt RP (1966) On the plastic deformation of Charpy specimens prior to general yield. J Mech Phys Solids 14

    Google Scholar 

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Authors and Affiliations

  1. Technical Faculty, Christian Albrecht University Kiel, Geesthacht, Germany

    Wolfgang Brocks

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  1. Wolfgang Brocks
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Correspondence to Wolfgang Brocks .

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Brocks, W. (2018). Solutions for Fully Plastic Conditions. In: Plasticity and Fracture. Solid Mechanics and Its Applications, vol 244. Springer, Cham. https://doi.org/10.1007/978-3-319-62752-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-62752-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62751-9

  • Online ISBN: 978-3-319-62752-6

  • eBook Packages: EngineeringEngineering (R0)

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