Journal ArticleDOI
A constitutive model for plastically anisotropic solids with non-spherical voids
TLDR
In this paper, a variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal sgeroidal void and subjected to uniform boundary deformation.Abstract:
Plastic constitutive relations are derived for a class of anisotropic porous materials consisting of coaxial spheroidal voids, arbitrarily oriented relative to the embedding orthotropic matrix. The derivations are based on nonlinear homogenization, limit analysis and micromechanics. A variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal spheroidal void and subjected to uniform boundary deformation. To obtain closed form equations for the effective yield locus, approximations are introduced in the limit-analysis based on a restricted set of admissible microscopic velocity fields. Evolution laws are also derived for the microstructure, defined in terms of void volume fraction, aspect ratio and orientation, using material incompressibility and Eshelby-like concentration tensors. The new yield criterion is an extension of the well known isotropic Gurson model. It also extends previous analyses of uncoupled effects of void shape and material anisotropy on the effective plastic behavior of solids containing voids. Preliminary comparisons with finite element calculations of voided cells show that the model captures non-trivial effects of anisotropy heretofore not picked up by void growth models.read more
Citations
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Journal ArticleDOI
Failure of metals I : brittle and ductile fracture
TL;DR: In this paper, the first overview of failure of metals is presented, focusing on brittle and ductile failure under monotonic loadings, where the focus is on linking microstructure, physical mechanisms and overall fracture properties.
Book ChapterDOI
Ductile Fracture by Void Growth to Coalescence
TL;DR: In this paper, the authors developed constitutive equations for porous ductile solids based on homogenization theory and developed the most widely known model for spherical and cylindrical voids.
Journal ArticleDOI
Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture
TL;DR: In this paper, an uncoupled non-associated fracture model is proposed which makes use of a stress state dependent weighting function and an anisotropic plastic strain measure, which is obtained from applying the von Mises equivalent plastic strain definition after the linear transformation of the plastic strain tensor.
Journal ArticleDOI
Influence of the Lode parameter and the stress triaxiality on the failure of elasto-plastic porous materials
Kostas Danas,P. Ponte Castañeda +1 more
TL;DR: In this paper, a second-order homogenization model was used to investigate failure in porous elasto-plastic solids under general triaxial loading conditions, where porosity and average pore shape were taken into account.
Journal ArticleDOI
Ductile failure modeling
TL;DR: An overview of the most widely used continuum models for this type of failure can be found in this article, where the authors describe the most commonly used current framework and its limitations discussed.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Journal ArticleDOI
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
Journal ArticleDOI
On the ductile enlargement of voids in triaxial stress fields
James R. Rice,D.M. Tracey +1 more
TL;DR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.