Strain gradient plasticity under non-proportional loading

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and the increments of strains and their gradients. The specific versions of the theories examined coincide for proportional straining. Implications stemming from the differences in formulation of the two classes of theories are explored for two basic examples having non-proportional loading: (i) a layer deformed into the plastic range by tensile stretch with no constraint on plastic flow at the surfaces followed by further stretch with plastic flow constrained at the surfaces and (ii) a layer deformed into the plastic range by tensile stretch followed by bending. The marked difference in predictions by the two theories suggests that critical experiments will be able to distinguish between them.

[1]  Norman A. Fleck,et al.  A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier , 2009 .

[2]  Norman A. Fleck,et al.  A phenomenological theory for strain gradient effects in plasticity , 1993 .

[3]  Peter Gudmundson,et al.  A unified treatment of strain gradient plasticity , 2004 .

[4]  John W. Hutchinson,et al.  Generalizing J2 flow theory: Fundamental issues in strain gradient plasticity , 2012, Acta Mechanica Sinica.

[5]  B. D. Reddy,et al.  The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 2: single-crystal plasticity , 2011 .

[6]  C. F. Niordson,et al.  Strain gradient effects on cyclic plasticity , 2010 .

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

[8]  Morton E. Gurtin,et al.  A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations , 2005 .

[9]  N. A. Flecka,et al.  A reformulation of strain gradient plasticity , 2001 .

[10]  Lallit Anand,et al.  Thermodynamics applied to gradient theories involving the accumulated plastic strain : The theories of Aifantis and Fleck and Hutchinson and their generalization , 2009 .

[11]  B. D. Reddy,et al.  The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity , 2011 .

[12]  Huajian Gao,et al.  Strain gradient plasticity , 2001 .

[13]  J. R. Willis,et al.  A mathematical basis for strain-gradient plasticity theory — Part I : Scalar plastic multiplier , 2008 .

[14]  Hans Muhlhaus,et al.  A variational principle for gradient plasticity , 1991 .

[15]  Viggo Tvergaard,et al.  An alternative treatment of phenomenological higher-order strain-gradient plasticity theory , 2010 .

[16]  N.,et al.  A PHENOMENOLOGICAL THEORY FOR STRAIN GRADIENT EFFECTS IN PLASTICITY , 2002 .

[17]  C. F. Niordson,et al.  A numerical basis for strain-gradient plasticity theory: Rate-independent and rate-dependent formulations , 2014 .

[18]  Mgd Marc Geers,et al.  A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity , 2006 .