Emilio Martinez Paneda

Abstract:

Experiments have shown that metallic materials display strong size effects at the micron and sub-micron scales, with smaller being stronger. Such size effects have been attributed to geometrically necessary dislocations (GNDs) associated with inhomogeneous plastic flow and, since the earlier seminal works of Aifantis, several continuum strain gradient plasticity (SGP) theories have been developed in order to incorporate some length-scale parameters in the constitutive equations. These size effects are especially significant in fracture problems as the plastic zone adjacent to the crack tip is physically small and contains strong spatial gradients of deformation. Finite element (FE) simulations have shown that GNDs near the crack tip promote strain-hardening, leading to a much higher stress level in the vicinity of the crack than that predicted by classical plasticity. Moreover, recent numerical studies revealed that the domain ahead of the crack where strain gradients significantly influence crack tip fields could be one order of magnitude higher when finite strains are taken into account. In this work, the influence of the plastic strain gradient on the fracture process of metallic materials is evaluated within the finite deformation theory by means of both mechanism-based and phenomenological SGP theories. The relation between material parameters and the physical length over which gradient effects prominently enhance crack-tip stresses is identified and quantified. Physical implications of the results are discussed and the relevance of accounting for size effects in the modelization of damage is thoroughly examined. Several numerical tools are evaluated with the aim of integrating SGP modeling in a robust numerical framework.