Numerical study of microcracking coalescence in structural elements subjected to bending

Brittle and quasi-brittle materials are characterized by the presence of defects that can nucleate, grow, and coalesce, causing catastrophic failures in full-sized structural components. In this context, extensive research studies can be found in the current scientific literature due to the increasing interest in microcracks interaction and in its influence on the mechanical performance of cementitious materials. In the framework of Linear Elastic Fracture Mechanics, this Thesis aims to investigate the damage evolution in quasi-brittle solids characterized by a dominant macrocrack and a distribution of microcracks. Dual Boundary Element Method (DBEM) has been used to describe the propagation of a main crack and its interaction with surrounding microcracks in concrete beams subjected to tensile and flexural loadings. By using the macrocrack length as control parameter in the loading process, DBEM is able to perform a stress analysis, providing the external stress required to obtain crack propagation and the corresponding deformation. Following this route, it is possible to thoroughly describe the post-peak global and local response of the concrete element, including snap-back instabilities, which are due to the coalescence of the main crack with the surrounding microcracks. In both cases, i.e., tensile and flexural loadings, the phenomenon has been investigated by varying several parameters: (i) the relative length of the main edge crack (a0/b); (ii) the relative length of the collinear microcracks (a/b); the damage ratio, D, which synthetically describes the pre-existing damage. The comparison between the tensile and flexural loading case-studies is discussed pointing out the main analogies and differences concerning the local and the global structural behaviour. In addition, a remarkable analogy between cracking coalescence and fibre-reinforced brittle-matrix composites behaviour can be noticed. Let us consider a specimen with reinforcing fibres embedded in the brittle-matrix and a specimen containing a distribution of collinear microcracks, both subjected to a flexural loading process controlled by the monotonically increasing macrocrack length. The applied load produces the opening of the faces of an edge crack that propagates through the fibres or the collinear microcracks. Propagation will occur alternately within the matrix and through the heterogeneities. In both cases, the structural response presents a discrete number of snap-back instabilities with related peaks and valleys. After each single peak, the crack starts growing in the matrix. Thus, the descending branches after peaks describe the crack growth between a fibre and the next, or between a microcrack tip and the next. The crack arrests at the minimum of each valley, which represents the achievement of the next fibre or crack tip. The analogy between strengthened and weakened zones consists therefore in a multiple snap-back mechanical response, where descending branches of propagating cracks alternate with ascending (linear) branches of arrested cracks. Finally, the abovementioned analogy is investigated by making a comparison between DBEM numerical results, for the case of the microcracking coalescence, and those of the Bridged Crack Model, for the case of fibrous composites. Considering the equivalence of the emitted area, which is related to the multiple snap-back instabilities, a quantitative relationship between microcracks length and slippage force of the reinforcing fibres is found.