A critical assessment of theories of strain gradient plasticity
By A. G. Evans, J. W. Hutchinson. 2009
226 citations recorded by the source corpus.
Theories to extend plasticity to the micron scale have been in existence for over a decade, complemented by a growing body of experimental data. Here, materials and mechanics aspects of two prominent strain gradient theories of plasticity, due to Nix and Gao and to Fleck and Hutchinson, are assessed within the context of simple bending. Differences between the theories are highlighted. The theories predict different trends relative to the size dependence of initial yielding and rate of hardening. The dislocation mechanics underpinning the two theories is addressed. Distinctions between lower-order theories and higher-order theories are also drawn, emphasizing the flexibility of higher-order theories to solve problems for a wide range of boundary conditions, especially those where, locally, the dislocations are blocked (pile up) and the plastic strain is zero.
Subfields: Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/6bc4a678f21ceacc9dcc84f86e291b5a44c7acf2
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In Materials Chemistry
Citations in the corpus
- Protocols for the Optimal Design of Multi‐Functional Cellular Structures: From Hypersonics to Micro‐Architected Materials (2011, background): “63 Regardless of the differences, central to both theories is the concept of geometrically necessary dislocations (GND), initially introduced by Ashby.”
- Gradient plasticity in gradient nano-grained metals (2016, background): “More interestingly, the gradient plastic strains arise under an overall uniform deformation of the GNG sample, and they stand in contrast to the widely studied strain-gradient plasticity induced by imposing a non-uniform deformation such as torsion [30], bending [31], and indentation [32].”
- A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier (2009, methodology): “One possibility is to write these contributions to the free energy in terms of scalar invariants of the arguments, as has been done for a deformation theory of plasticity by Fleck and Willis (2004), and Aifantis and Willis (2005, 2006).”
- Guidelines for Constructing Strain Gradient Plasticity Theories (2015, background): “Some preliminary results [17] along these lines for an elementary, nondilute distribution of geometrically necessary dislocations suggest that f ðe PÞ is not quadratic but nearly linear in e P.”
- Synergetic Strengthening by Gradient Structure (2014, background): “[34–37] First, the gradient structure spans a macroscopic length of hundreds of grains, which is much larger than the grain size scale typically considered by the conventional strain gradient plasticity.”
- Size effects in the bending of thin foils (2009, methodology): “These values lie within the expected range [7,5].”