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

Self-similar solutions for stress driven material dissolution

During corrosive dissolution of metal ions from a body surface, an oxide compound is produced. This compound forms a protective film that reduces the dissolution rate. When a fraction of a millimetre depth is dissolved the dissolution rate become insignificant. However, repeated loading will damage the film with continued dissolution as a result. In connection with this a threshold strain is assumed to exist. This paper proposes a model where electro- chemical processes and the mechanical load work together in forming a corrosion pit. The ratio between the threshold strain and the remotely applied strain is shown to control the shape of the pit. For small applied strains cracks are formed. A crack evolving from a surface irregularity is studied. The growth rate of the crack is determined by the dissolution rate at the crack tip. No crack growth criterion is needed. The growing crack is itself creating conditions for strain concentration, which leads to a high crack growth rate. The model simulates how dissolution forms a pit that grows to become a crack in a single continuous process. For small loads the crack growth rate is independent of applied load