Mechanism-based strain gradient plasticity— I. Theory

Abstract

A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as 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 density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.