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Yield Functions for Porous Materials with Cubic Symmetry Using Different Definitions of Yield
Author(s) -
McElwain D. L. S.,
Roberts A. P.,
Wilkins A. H.
Publication year - 2006
Publication title -
advanced engineering materials
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 114
eISSN - 1527-2648
pISSN - 1438-1656
DOI - 10.1002/adem.200600075
Subject(s) - cubic crystal system , materials science , scaling , yield (engineering) , hydrostatic equilibrium , yield surface , finite element method , discretization , porosity , dimensionless quantity , void (composites) , geometry , mechanics , mathematical analysis , mathematics , thermodynamics , composite material , condensed matter physics , physics , constitutive equation , quantum mechanics
Plastic yield criteria for porous ductile materials are explored numerically using the finite‐element technique. The cases of spherical voids arranged in simple cubic, body‐centred cubic and face‐centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple‐cubic and body‐centred cubic arrays – in contrast to the famous Gurson‐Tvergaard‐Needleman (GTN) formula – while there is no such dependence for face‐centred cubic arrays within the accuracy of the finite‐element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield‐function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body‐centred and face‐centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.