13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Meso-scale features and couple stresses in fracture process zone Craig N Morrison1, 3,*, Andrey P Jivkov2, 3, John R Yates3 1 Nuclear FiRST Doctoral Training Centre 2 Research Centre for Radwaste and Decommissioning 3 Modelling and Simulation Centre Dalton Nuclear Institute, The University of Manchester, Manchester, M13 9PL, UK * Corresponding author: craig.morrison-2@postgrad.manchester.ac.uk Abstract Generalized continuum theories such as couple stress theory have the potential to improve our understanding of material deformation and fracture behaviour in areas where classical continuum theory breaks down at, for example, the length scale of meso-scale features within the fracture process zone. The couple stress theory considers not only relative displacements between these features but also relative rotations, introducing a natural length scale. A model has been developed of a low stiffness matrix containing suitably situated high stiffness particles to simulate the presence of defects at the meso-scale. This has been used to assess the descriptive potential of a novel consistent couple stress theory. The model has been subjected to a set of displacement fields selected to produce strain energies with varying contributions from the coupled stresses. The results demonstrate the effect of particle size to spacing ratio on the elastic energies. These can be used to evaluate the couple stress constant as well as validate the constant experimentally for specific materials. Keywords: generalized continuum; meso-scale defects; FE analysis; strain-curvature energy; size effect 1. Introduction Analysis of materials at engineering length scales is based upon assumptions of classical continuum behaviour. This is adequate for most macro-scale analyses but, when considering smaller length scales where cracks, notches and defects introduce stress concentrations, the material microstructure is known to have a significant impact on material behaviour [1]. Local approaches, which incorporate mechanistic understanding of material failure behaviour at the length scale of their relevant features, are beneficial for linking microstructures to macroscopic responses [2]. However, the widely used weakest link (WL) assumption has been challenged as a realistic method of modelling size effects in cleavage [3] and quasi-brittle fracture [4] as a result of failing to account for the interaction processes during failure. Discrete methods have shown promise for modelling materials undergoing such fracture. Lattice models consist of nodes connected into a lattice via springs [5], beams [6] or other discrete elements with the properties of these connections allowing a micro structurally informed response. Lattice modelling differs in principle from previous local approach models by using a statistically parallel system, where loads are redistributed upon the breaking of a single bond, rather than the ultimate failure seen in WL systems. This is considered to be a closer representation of the interaction and coalescence of micro-cracks and flaws, which characterize quasi-brittle materials such as graphite [7] and cement-based materials [8]. The work presented here explores aspects of the site-bond model developed by Jivkov and Yates [9] and used for studies of damage evolution from distributed porosity in cements [10]. Work on this model has shown that evaluating the stiffness coefficients of the bonds using strain energy equivalence between the discrete model and a classical continuum creates an indeterminate problem. Use of a generalized continuum theory, such as couple stress theory, offers a possible solution to this indeterminacy.
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