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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v2.i3.30
24 pages

Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory

Rashid K. Abu Al-Rub
Department of Civil Engineering, Catholic University of America, Washington, DC 20064, USA
George Voyiadjis
Louisiana State University


The enhanced 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. The later cannot predict the size effects since it does not posses an intrinsic length scale. To assess the size effects, it is indispensable to incorporate an intrinsic material length parameter l into the constitutive equations. However, the full utility of gradient-type theories hinges on one's ability to determine the constitutive length-scale parameter l that scales the gradient effects. Thus, the definition and magnitude of the intrinsic length scale are keys to the development of the new theory of plasticity that incorporates size effects. The classical continuum plasticity is also 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: those that are initially randomly or statistically distributed, which are referred to as statistically stored dislocations (SSDs), and those formed to account for the additional strengthening mechanism associated with the deformation gradients, which are referred to as geometrically necessary dislocations (GNDs). In this work two micromechanical models to assess the coupling between SSDs and GNDs are discussed. One in which the SSDs and GNDs are simply summed (model-I) and one in which, implicitly, their accompanying strength are added (model-II). These two dislocation interaction models, which are based on Taylor's hardening law, are then used to identify the deformation-gradient-related intrinsic length-scale parameter l in terms of measurable microstructural physical parameters. The paper also presents a method for identifying the material intrinsic length parameter l from micro hardness results obtained by conical or pyramidal indenters.