Crack interlinking

The changes in Young s modulus can be explained in terms of crack development and interlinking, and these pre-existing cracks are assumed to be the result of thermal expansion mismatch between the MgO and MgAl204 phases.33 When the volume fraction of spinel increases, more microcracking occurs and lower Young s modulus values are obtained. 

From the mechanical standpoint, the particles have a density and are interlinked by contacts which are defined by their normal and tangential stiffnesses, a friction coefficient and a microscopic cohesion. A cohesive behaviour model serves to define a fracture threshold that determines the normal and tangential forces that can be withstood by the inter particle links. Hence, a micro crack appear when the contact between two adjacent particles is broken. When a connection between several micro cracks takes place, it can generate a new fracture in the model. 

The primary component of the tensile stress on an underground pipeline is in the hoop direction and results from the operating pressure. Residual stresses from fabrication, installation, and damage in service contribute to the total stress. Individual cracks initiate in the longitudinal direction on the outside surface of the pipe. The cracks typically occur in colonies that might contain hundreds or thousands of individual cracks. Over time, the cracks in the colonies interlink and may cause leaks or ruptures once a critical size flaw is achieved. 

From the liquid phase distribution, the capillary forces Fc on the individual gel particles are accessible, with one contribution from the bulk liquid and a second from the three-phase contact line. By use of the discrete element method (DEM), capillary forces can be loaded on the primary partides, which are connected by bonds as a result, micro-cracks - and also shrinkage -can be simulated (Kharaghani et al., 2011). The cracking criterion is, hence, set by the strength of the necks interlinking the primary partides. 

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