Mechanism-based strain gradient plasticity - I. Theory

Citation
H. Gao et al., Mechanism-based strain gradient plasticity - I. Theory, J MECH PHYS, 47(6), 1999, pp. 1239-1263
Citations number
47
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
ISSN journal
0022-5096 → ACNP
Volume
47
Issue
6
Year of publication
1999
Pages
1239 - 1263
Database
ISI
SICI code
0022-5096(199906)47:6<1239:MSGP-I>2.0.ZU;2-N
Abstract
A mechanism-based theory of strain gradient plasticity (MSG) is proposed ba sed on a multiscale framework linking the microscale notion of statisticall y stored and geometrically necessary dislocations to the mesoscale notion o f plastic strain and strain gradient. This theory is motivated by our recen t analysis of indentation experiments which strongly suggest a linear depen dence of the square of plastic flow stress on strain gradient. While such l inear dependence is predicted by the Taylor hardening model relating the fl ow stress to dislocation density, existing theories of strain gradient plas ticity have failed to explain such behavior. We believe that a mesoscale th eory of plasticity should not only be based on stress-strain behavior obtai ned from macroscopic mechanical tests, but should also draw information fro m micromechanical, gradient-dominant tests such as micro-indentation or nan o-indentation. According to this viewpoint, we explore an alternative formu lation of strain gradient plasticity in which the Taylor model is adopted a s a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the densi ty of geometrically necessary dislocations, strictly following the Taylor m odel, and that the plastic flow retains the associative structure of conven tional plasticity. On the mesoscale, the constitutive equations are constru cted by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering mo dels of geometrically necessary dislocations associated with bending, torsi on and 2-D axisymmetric void growth. The new theory differs from all existi ng phenomenological theories in its mechanism-based guiding principles, alt hough the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented i n Part II of this paper. (C) 1999 Elsevier Science Ltd. All rights reserved .