Nonlocal plasticity effects on interaction of different size voids

Abstract A nonlocal elastic–plastic material model is used to show that the rate of void growth is significantly reduced when the voids are small enough to be comparable with a characteristic material length. For a very small void in the material between much larger voids the competition between an increased growth rate due to the stress concentrations around the larger voids and a reduced growth rate due to the nonlocal effects is studied. The analyses are based on an axisymmetric unit cell model with special boundary conditions, which allow for a relatively simple investigation of a full three dimensional array of spherical voids. It is shown that the high growth rate of very small voids predicted by conventional plasticity theory is not realistic when the effect of a characteristic length, dependent on the dislocation structure, is accounted for.

[1]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[2]  Jonas Faleskog,et al.  Micromechanics of coalescence—I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids , 1997 .

[3]  V. Tvergaard.  Influence of voids on shear band instabilities under plane strain conditions , 1981 .

[4]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

[5]  John L. Bassani,et al.  Incompatibility and a simple gradient theory of plasticity , 2001 .

[6]  Amit Acharya,et al.  Lattice incompatibility and a gradient theory of crystal plasticity , 2000 .

[7]  Alan Needleman,et al.  Void growth and coalescence in porous plastic solids , 1988 .

[8]  C. F. Niordson,et al.  Nonlocal plasticity effects on the tensile properties of a metal matrix composite , 2001 .

[9]  C. F. Niordson,et al.  Nonlocal plasticity effects on fibre debonding in a whisker-reinforced metal , 2002 .

[10]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity—II. Analysis , 2000 .

[11]  F. A. McClintock,et al.  A Criterion for Ductile Fracture by the Growth of Holes , 1968 .

[12]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[13]  A. Needleman.  Void Growth in an Elastic-Plastic Medium , 1972 .

[14]  Amit Acharya,et al.  On Non-Local Flow Theories that Preserve the Classical Structure of Incremental Boundary Value Problems , 1996 .

[15]  Viggo Tvergaard,et al.  Analysis of tensile properties for a whisker-reinforced metal-matrix composite , 1990 .

[16]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[17]  C. Hom.  Three-dimensional finite element analysis of plastic deformation in a whisker- reinforced metal matrix composite , 1992 .

[18]  J. Hutchinson,et al.  Cavitation instabilities in a power hardening elastic-plastic solid , 1992 .

[19]  V. Tvergaard.  Effect of thickness inhomogeneities in internally pressurized elastic-plastic spherical shells , 1976 .

[20]  Norman A. Fleck,et al.  A reformulation of strain gradient plasticity , 2001 .

[21]  V. Tvergaard.  On localization in ductile materials containing spherical voids , 1982, International Journal of Fracture.

[22]  A. Pineau,et al.  IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials : proceedings of the IUTAM symposium held in Sèvres, Paris, France, 29 August - 1 September 1995 , 1996 .

[23]  V. Tvergaard.  Interaction of very small voids with larger voids , 1998 .

[24]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity— I. Theory , 1999 .

[25]  J. Hutchinson.  Plasticity at the micron scale , 2000 .

[26]  Viggo Tvergaard,et al.  Effect of void size difference on growth and cavitation instabilities , 1996 .