A critical assessment of theories of strain gradient plasticity

A G Evans and J W Hutchinson

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.

Break-down of Hall-Petch

August 8, 2007

Title: The strongest size

Authors: A. S. Argon; S. Yip

Source: Philosophical Magazine Letters, Volume 86, Issue 11 November 2006 , pages 713 – 720

Abstract:
The well known break-down of the Hall-Petch effect of the rise of the plastic resistance with decreasing grain size in polycrystalline metals, when the grain size drops into the nanometre range resulting in a peak plastic resistance at a grain size of about 12-15 nm, is explained by considering two alternative and complementary rate mechanisms of plasticity, grain boundary shear and dislocation plasticity, each contributing to the overall strain rate in proportion to the volume fraction of the material in which they operate. In the model for a given applied strain rate it is shown that the plastic resistance reaches a maximum at a grain size of about 12.2 nm in Cu when the two mechanisms contribute to the overall strain rate equally, defining the so-called strongest size.