Structure of micro-crack population and damage evolution in quasi-brittle media

AbstractMechanical behaviour of quasi-brittle materials, such as concrete and rock, 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 blocks and lattice bonds transmit forces and moments between adjacent sites. Micro-cracks are generated at the interfaces between solid-phase blocks, where initial defects are allocated according to given size distribution. This is represented by removal of bonds when a criterion based on local forces and defect 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 faces and graph edges connect neighbouring failed faces, 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 material macroscopic response. The study is focused on concrete, for which defect sizes were available, but the proposed methodology is applicable to a range of quasi-brittle materials with similar dominant damage mechanisms

Micromechanical modelling of deformation and fracture of hydrating cement paste using X-ray computed tomography characterisation

Cement paste is the basic but most complex component in cement composites, which are the dominant construction material in the world. Understanding and predicting elastic properties and fracture of hydrating cement paste are challenging tasks due to its complex microstructure, but important for durability assessments and life extension decisions. A recently proposed microstructure-informed site-bond model with elastic-brittle spring bundles is developed further to predict the evolution of elastic properties and fracture behaviour of cement paste. It is based on microstructural characteristics of hydrating cement paste obtained from X-ray computed microtomography (micro-CT) with a spatial resolution of 0.5 μm/voxel. Volume fraction and size distribution of anhydrous cement grains are used to determine the model length scale and pore-less elasticity. Porosity and pore size distribution are used for tuning elastic and failure properties of individual bonds. The fracture process is simulated by consecutive removal of bonds subjected to surface energy based failure criterion. The stress–strain response and elastic properties of hardened cement pastes with curing ages of 1, 7 and 28 days are obtained. The simulated Young's modulus and deformation response prior to peak stress agree very well with the experimental data. The proposed model provides an effective tool to evaluate time evolution of elastic properties and to simulate the initiation, propagation, coalescence and localisation of micro-cracks

Microstructure-informed modelling of damage evolution in cement paste

AbstractCement paste is a binder for cementitious materials and plays a critical role in their engineering-scale properties. Understanding fracture processes in such materials requires knowledge of damage evolution in cement paste. A site-bond model with elastic-brittle spring bundles is developed here for analysis of the mechanical behaviour of cement paste. It incorporates key microstructure information obtained from high resolution micro-CT. Volume fraction and size distribution of anhydrous cement grains are used for calculating model length scale and elasticity. Porosity and pore size distribution are used to allocate local failure energies. Macroscopic damage emerges from the generation of micro-crack population represented by bond removals. Effects of spatial distribution, porosity and sizes of pores on tensile strength and damage are investigated quantitatively. Results show a good agreement with experiment data, demonstrating that the proposed technology can predict mechanical and fracture behaviour of cementitious materials based exclusively on microstructure information