Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Strain gradient plasticity: Theory and experiment

Strain gradient plasticity

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.

Mechanism-based strain gradient plasticity— I. Theory

SUMMARY Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.

Gradient enhanced damage for quasi-brittle materials

A class of phenomenological strain gradient plasticity theories is formulated to accommodate more than one material length parameter. The objective is a generalization of the classical J2 3ow theory of plasticity to account for strain gradient e4ects that emerge in deformation phenomena at the micron scale. A special case involves a single length parameter and is of similar form to that proposed by Aifantis and co-workers. Distinct computational advantages are associated with this class of theories that make them attractive for applications requiring the generation of numerical solutions. The higher-order nature of the theories is emphasized, involving both higher-order stresses and additional boundary conditions. Competing members in the class of theories will be examined in light of experimental data on wire torsion, sheet bending, indentation and other micron scale plasticity phenomena. The data strongly suggest that at least two distinct material length parameters must be introduced in any phenomenological gradient plasticity theory, one parameter characterizing problems for which stretch gradients are dominant and the other relevant to problems when rotation gradients (or shearing gradients) are controlling. Flow and deformation theory versions of the theory are highlighted that can accommodate multiple length parameters. Examination of several basic problems reveals that the new formulations predict quantitatively similar plastic behavior to the theory proposed earlier by the present authors. The new formulations improve on the earlier theory in the manner in which elastic and plastic strains are decomposed and in the representation of behavior in the elastic range. ? 2001 Elsevier Science Ltd. All rights reserved.

http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/143.pdf

E.C. Alfantis

Papers

A variational principle for gradient plasticity

Oscillatory fracture in polymeric materials