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A rationally based yield criterion for work hardening materials

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Sommario

Si considera lo sviluppo di una razionale condizione di plasticità per materiali con incrudimento. Nel tentativo di costruire una sola funzione analitica per rappresentare il comportamento plastico del materiale, la matematica della meccanica dei continui è combinata con considerazioni statiche onde definire una condizione di plasticità che tenga conto dell'implicita inomogeneità nella distribuzione di sforzi e deformazioni in un aggregato policristallino.

Si propone un modello matematico che prende in considerazione inclusioni sferiche anisotrope avvolta da materiale elastoplastico. La condizione di plasticità derivata da questo modello è basata su tre considerazioni principali, (a) argomenti che involvono il valore locale della densità di energia di deformazione al taglio, (b) la soluzione di Eshelby per lo sforzo locale che agisce su ogni inclusione sferica in una matrice infinita e (c) la statistica dei valori estremi.

Si dà un esempio sulla capacità del criterio di plasticità di interpretare i risultati ottenuti su tubi di alluminio sottile precaricato nello spazio tensione-torsione.

Summary

The paper is concerned with the development of a rationally based yield criterion for work hardening materials. In an attempt to construct a single analytical function to represent yield behaviour the mathematics of continuum mechanics is combined with a statistical argument to produce a yield criterion which takes into account the inherent inhomogeneity of stress and strain distribution throughout a polycrystalline aggregate.

A mathematical model is proposed which consists of spherical, anisotropic inclusions embedded in an elastic-plastic matrix. The yield criterion derived from this model is based on three main considerations, (a) arguments involving the local value of shear strain energy density, (b) Eshelby's solution for the local stress acting on a spherical inclusion in an infinite matrix and (c) the statistics of extreme values.

An example is given on the fitting of the yield criterion to the results of thin-walled aluminium tubes prestrained in tensiontorsion space.

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Abbreviations

A ijkl :

anisotropy tensor

A 0 :

anisotropy parameter

b :

constant

c :

work hardening modules

C ijkl :

parameter governing inclusion density

e ij :

local elastic strain

E ij :

aggregate elastic strain

e ij P :

local plastic strain

E ij P :

aggregate plastic strain

G :

clastic shear modulus

H ijkl :

Hookean elastic tensor

I ijkl :

isotropic tensor

k, K :

constants governing strain distribution and inclusion density

L ijkl :

distortion parameter

m :

Bauschinger parameter

δ ij :

Kronecker delta

λ ij :

statistical strain distribution parameter

ϑ :

Poisson's ratio

σ ij :

aggregate stress

μ, λ :

parameters associated with the Laplace probability density function.

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Authors and Affiliations

  1. University of Melbourne, Australia

    John Francis Williams (Lecturer in Mechanical Engineering)

  2. University of New South Wales, Australia

    Noel Levin Svensson (Professor of Mechanical Engineering)

Authors
  1. John Francis Williams
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Williams, J.F., Svensson, N.L. A rationally based yield criterion for work hardening materials. Meccanica 6, 104–114 (1971). https://doi.org/10.1007/BF02151650

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