Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory

Abstract

The enhanced strain-gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. To assess the size effects it is indispensable to incorporate an intrinsic material length parameter into the constitutive equations. However, the full utility of gradient-type theories hinges on one’s ability to determine the constitutive length-scale parameter. The classical continuum plasticity is unable to predict properly the evolution of the material flow stress since the local deformation gradients at a given material point are not accounted for. The gradient-based flow stress is commonly assumed to rely on a mixed type of dislocations: statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs). In this work a micromechanical model to assess the coupling between SSDs and GNDs, which is based on the Taylor’s hardening law, is used to identify the deformation-gradient-related intrinsic length-scale parameter in terms of measurable microstructural physical parameters. This work also presents a method for identifying the length-scale parameter from micro-indentation tests.