Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media

About: This article is published in Journal of Engineering Materials and Technology-transactions of The Asme.The article was published on 1977-01-01 and is currently open access. It has received 5981 citations till now. The article focuses on the topics: von Mises yield criterion & Nucleation.

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CONTINUUM
THEORY OF
DUCfILE
RUPTURE
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NUCLEATION AND
GROWTH:
- PART 1
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YIELD
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U.S. Energy Research and
MASTER
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Technical
Report No. 39
E (11-1)3084/39 September 1975
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Part I - Yield Criteria and Flow Rules
for Porous Ductile Media
by A. L. Gurson
Division of Engineering, Brown University, Providence, Rhode Island 02912
September 1975
Abstract
Widely used constitutive laws for engineering materials assume plastic
incompressibility, and no effect on yield of the hydrostatic component of
stress. However, void nucleation and growth (and thus bulk dilatancy) are
commonly observed in some processes which are characterized by large local
plastic flow, such as ductile fracture. The purpose of this work is to develop
approximate yield criteria and flow rules for porous (dilatant) ductile materials,
showing the role of hydrostatic stress in plastic yield and void growth. Other
elements of a constitutive theory for porous ductile materials, such as void
nucleation, plastic flow and hardening behavior, and a criterion for ductile
fracture will be discussed in Part II of this series.
The yield criteria are approximated through an upper bound approach. Sim-
plified physical models for ductile porous materials 6ggregates of voids and
ductile matrix) are employed, with the matrix material idealized as rigid-perfectly
plastic and obeying the von Mises yield criterion. Velocity fields are developed
for the matrix which conform to the macroscopic flow behavior of the bulk
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material. Using a distribution of macroscopic flow fields and working through
a dissipation integral, upper bounds to the macroscdpic stress fields required
for yield are calculated. Their locus in stress space forms the yield locus.
It is shown that normality holds for this yield locus, so a flow rule
results. Approximate functional forms for the yield loci are developed.