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    Continuous versus discontinuous bridged crack in the description of reinforced material flexural collapse

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    Two nonlinear bridged--crack models are formulated and proposed in order to explain and reproduce the constitutive flexural response of multiphase materials. The {\it{n--fibre discrete}} model applies to macrostructural studies of composites with brittle matrix and localized reinforcements or to microstructural analyses of fibrous composites. The {\it{continuous}} model applies to macrostructural analyses of brittle matrix composites with continuously distributed secondary phases such as fibre or particle reinforced materials. The two model formulations are briefly recalled and the resulting (moment versus rotation) constitutive relationships are explained and compared in the limit case of a composite with a high number of discontinuous reinforcements. The models both predict local discontinuities and a ductile--brittle transition in the global structural response when varying the mechanical and geometrical beam properties

    Reversal in the failure scaling transition of brittle matrix fibrous composites

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    A nonlinear fracture mechanics model is proposed for analysis of the flexural behavior of brittle-matrix composites with uniformly distributed secondary phases. In accordance with the Barenblatt-Dugdale model the bridging or cohesive zone of the material is replaced by a fictitious crack along which a closing traction distribution is applied. The dimensionless formulation brings out the parameters synthetically controlling the structural behavior and the size-scale effects. Different scaling transitions are predicted in the flexural behavior of the composite depending on different modeling of the toughening mechanisms. When a homogenized toughening mechanism for the whole composite is considered along with closing tractions as a linearly decreasing function of the crack opening displacement, a ductile to brittle transition is found as the beam depth increases. On the other hand, when the matrix toughness and the toughening mechanism of the reinforcements are separately modeled, and the closing tractions have a constant value until a critical track opening displacement, a double brittle-ductile-brittle transition is found. Experimental tests on fiber-reinforced mortar beams in bending are successfully simulated
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