For beams made of quasi-brittle materials, the moment can increase after a crack starts to propagate so the formation of multiple cracks is possible. Here, an energy minimization based method is proposed to determine the pattern of multiple cracking in…
For beams made of quasi-brittle materials, the moment can increase after a crack starts to propagate so the formation of multiple cracks is possible. Here, an energy minimization based method is proposed to determine the pattern of multiple cracking in such beam under pure bending. The fracture behavior of quasi-brittle material is described through cohesive zone model (CZM) with a linear softening law. Assuming the presence of a periodic and parallel crack array in the beam, the effects of crack spacing and beam curvature on the total energy per unit length of the member is obtained through finite element (FE) analysis. In the FE model, only a representative segment of the beam with a single crack needs to be considered, so the modeling is simple and computationally efficient. After performing a series of analyses on a bending beam, the crack spacing corresponding to the lowest energy is found at different curvatures and the relation between this crack spacing and the curvature is used to describe the crack pattern evolution of the member. Normalization is conducted and the effect of various parameters (tension softening law, elastic modulus of material and height of beam) on the cracking process is also studied. The results indicate that multiple cracking behavior in beams made of a linear softening material is determined by only one dimensionless parameter-brittleness number. As the crack pattern derived from the proposed energy approach has a sound physical basis, it can potentially be used as a reference for checking if the multiple cracking pattern obtained by other computational methods is proper or not.