13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Structure of micro-crack population and damage evolution in concrete Andrey P Jivkov1,* 1 School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK * Corresponding author: andrey.jivkov@manchester.ac.uk Abstract Tensile behaviour of concrete is controlled by the generation and growth of micro-cracks. A 3D lattice model is used in this work for generating micro-crack populations. In the model, lattice sites signify solid-phase grains and lattice bonds transmit forces and moments between adjacent sites. The meso-scale features generating micro-cracks are pores located at the interfaces between solid-phase grains. In the model these are allocated to the lattice bonds with sizes dictated by an experimentally determined pore size distribution. Micro-cracks are generated by removal of bonds when a criterion based on local forces and pore size is met. The growing population of micro-cracks results in a non-linear stress-strain response, which can be characterised by a standard damage parameter. This population is analysed using a graph-theoretical approach, where graph nodes represent failed bonds and graph edges connect neighbouring failed bonds, i.e. coalesced micro-cracks. The evolving structure of the graph components is presented and linked to the emergent non-linear behaviour and damage. The results provide new insights into the relation between the topological structure of the population of micro-cracks and the macroscopic response of concrete. They are applicable to a range of quasi-brittle materials with similar dominant damage mechanisms. Keywords Concrete porosity; Lattice model; Cracking graphs; Macroscopic damage 1. Introduction The mechanical behaviour of quasi-brittle materials, such as concrete, graphite, ceramics, or rock, emerges from underlying microstructure changes. At the engineering length scale it can be described with continuum constitutive laws of increasing complexity combining damage, plasticity and time-dependent effects [1-4]. In these phenomenological approaches the damage represents reduction of the material elastic constants. From the microstructure length scale perspective damage is introduced by the nucleation and evolution of micro-cracks. While the population of micro-cracks formed under loading could be sufficiently well captured by various continuum damage models, the latter cannot help to understand the effects of the population on other important physical properties of the material. In many applications the quasi-brittle materials have additional functions as barriers to fluid transport via convection/advection and/or diffusion. It is therefore important to take a mechanistic view on the development of damage by modelling the evolution of micro-crack population, which can inform us about changes in the transport properties. Such a mechanistic approach needs to account for the material microstructure in a way corresponding to the mechanism of micro-crack formation [5]. Micro-cracks typically emerge from pores in the interfacial transition zone between cement paste and aggregate in cement-based materials [6]. Discrete lattice representation of the material microstructure seems to offer the most appropriate modelling strategy for analysis of micro-crack populations. This is a meso-scale approach, where the material is appropriately subdivided into cells and lattice sites are placed at the centres of the cells. Discrete lattices allow for studies of distributed damage without constitutive assumptions about crack paths and coalescences that would be needed in a continuum finite element modelling. The deformation of the represented continuum arises from the interactions between the lattice sites. These involve forces resisting relative displacements and moments resisting relative rotations between sites. Two conceptually similar approaches have been proposed to link local interactions to continuum response. In the first one, the local forces are related to the stresses in the continuum cell, e.g. [7, 8]. In the second one, the interactions are represented by structural beam elements, the stiffness coefficients of which are determined by equating the strain energy in the discrete and the
RkJQdWJsaXNoZXIy MjM0NDE=