Abstract
A wide range of stress states has been generated using axisymmetric and plane strain notched tensile specimens which have been analysed by elastic-plastic finite element analysis. Observations of voids on metallographic sections have been combined with calculated deformation histories and the hole growth equations to determine the local conditions for hole nucleation and the strength of the particle-matrix interface. These calculations show that nucleation is a statistical event for which the radial stress at the particle/matrix interface has been determined. Subsequent calculations give the local conditions at void coalescence in the average material and in statistical inhomogeneities. The statistics of the inclusion distribution determine the size scale over which void coalescence must occur in order to create a crack-like defect.
Résumé
En utilisant des éprouvettes de traction entaillées axisymétriques soumises à état plan de déformation, analysées par éléments finis élasto-plastiques, on a pu élaborer une gamme importante d'états de tension. En combinant les observations de lacunes de section métallographique avec l'histoire des déformations calculées et des équations de croissance d'une cavité, on a déterminé les conditions locales qui président à la croissance de cavité et à la résistance de l'interface particule-matrice. Ces calculs montrent que l'apparition de cavités est un évènement statistique pour lequel la contrainte radiale à l'interface particule-matrice a pû être déterminé. Des calculs subséquents fournissent les conditions locales qui conduisent à la -coalescence de lacunes dans un matériau standard et pour des conditions d'inhomogénéité statistiquement réparties. La statistique de distribution des inclusions détermine l'échelle au delà de laquelle une coalescence de porosités peut se produire et crée un défaut assimilable `a une fissure.
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Abbreviations
- a :
-
semi-major axis of elliptical void, radius at minimum cross-section of notch tensile specimen
- b :
-
semi-minor axis of elliptical void
- E :
-
uniaxial elastic modulus
- e :
-
matrix strain
- H :
-
aggregate hardening rate
- J :
-
intermediate variable in void equations
- K :
-
intermediate variable in void equations
- L :
-
intermediate variable in void equations
- M :
-
eccentricity of elliptical void
- n :
-
power hardening index
- P(x):
-
probability of nucleation at a radial stress x
- r :
-
distance of void from specimen axis
- R :
-
mean radius of elliptical void, tip radius of notch
- s :
-
matrix stress deviator V volume
- ε:
-
aggregate stress
- σ:
-
matrix stress
- ø:
-
yield function
- p:
-
plastic component
- -(overbar):
-
effective, representative or equivalent value
- 0:
-
initial value, initial yield value in uniaxial tension
- m:
-
mean value
- y:
-
current yield value in uniaxial tension
- ∞:
-
remote value
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Thomson, R.D., Hancock, J.W. Ductile failure by void nucleation, growth and coalescence. Int J Fract 26, 99–112 (1984). https://doi.org/10.1007/BF01157547
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DOI: https://doi.org/10.1007/BF01157547