Open Access

ABSTRACT

Higher-Order Stress and Size Effects Due to Self Energy of Geometrically Necessary Dislocations

by N. Ohno¹, D. Okumura¹

1 Department of Mechanical Science and Engineering, Nagoya University, Nagoya 464-8603, Japan

The International Conference on Computational & Experimental Engineering and Sciences 2007, 4(4), 207-214. https://doi.org/10.3970/icces.2007.004.207

Abstract

The self energy of geometrically necessary dislocations (GNDs) is considered to inevitably introduce the higher-order stress work-conjugate to slip gradient in single crystals. It is pointed out that this higher-order stress stepwise changes in response to in-plane slip gradient and thus directly influences the onset of initial yielding in polycrystals. The self energy of GNDs is then incorporated into the strain gradient theory of Gurtin (2002). The resulting theory is applied to model crystal grains of size D, leading to a D-1-dependent term with a coefficient determined by grain shape and orientation. It is thus shown that the self energy of GNDs induced by slip gradient accounts for the grain size dependence of initial yield stress and also the dislocation cell size dependence of flow stress in the submicron to several micron range of grain and cell sizes.

---