Concrete is the most widely used construction material. Cracking is an important issue for concrete because cracks not only affect the mechanical behavior of concrete but also its serviceability. Moreover, large crack opening may lead to durability problems of reinforced concrete structures. To improve the toughness of concrete and to control the cracks, different types of fibers are employed to produce fiber reinforced concrete (FRC) or, more generally, fiber reinforced cementitious composite (FRCC).

In FRCC material, the main function of fiber is to bridge the cracks and to improve the post-cracking ductility of the material. Ideally, multiple cracking can be resulted so the opening of each crack under a certain deformation becomes smaller. When multiple cracks occur at small spacing...[ Read more ]

Concrete is the most widely used construction material. Cracking is an important issue for concrete because cracks not only affect the mechanical behavior of concrete but also its serviceability. Moreover, large crack opening may lead to durability problems of reinforced concrete structures. To improve the toughness of concrete and to control the cracks, different types of fibers are employed to produce fiber reinforced concrete (FRC) or, more generally, fiber reinforced cementitious composite (FRCC).

In FRCC material, the main function of fiber is to bridge the cracks and to improve the post-cracking ductility of the material. Ideally, multiple cracking can be resulted so the opening of each crack under a certain deformation becomes smaller. When multiple cracks occur at small spacing, they tend to interact with each other, and form complex crack patterns. With fiber incorporated to enhance the toughness of the composite material, cracks occur even closer to each other and interact more intensively, which is difficult to analyze. Moreover, the formation of multiple cracks in FRCC involves sophisticated stress transfer between fiber and matrix, which imposes additional challenge on the analysis.

In this thesis, the following key questions are addressed. What are the governing mechanisms in multiple cracking process of fiber reinforced cementitious materials? How can these mechanisms be considered in numerical models? How can the structural performance of FRCC under different loading conditions be assessed? For FRCC with strain-softening law, the mechanism of multiple crack interaction is being focused on. Based on the minimum energy principle, a method of energy minimization is developed and used to predict the multiple cracking pattern of quasi-brittle beam. The fracture behavior of the quasi-brittle material is simulated by cohesive zone model using the bilinear tension softening law. After appropriate normalization based on dimensional analysis, the multiple cracking process is found to be governed by only three parameters and their effects are systematically studied. Physically, the ratio between the “crack-tip toughness” and the “bridging toughness” is important for the crack pattern evolution. As a validation, the proposed method is used to predict the experimental crack pattern of fiber reinforced concrete beam and good agreement is achieved. The results of the study can provide material selection guidelines for crack control. In addition, by determining the crack pattern with a sound physical basis (which is the commonly adopted minimum energy criterion), the results can serve as a benchmark for checking the reliability of other methods for multiple cracking analysis

For strain-hardening materials, the mechanism of stress transfer between fiber and matrix is emphasized when analyzing their multiple cracking behavior. A new discrete model, with the matrix represented by continuum elements exhibiting smeared cracking behavior and the bridging effect of fiber represented by truss elements with proper constitutive law, is proposed. To explicitly account for the transfer of stress between fiber and matrix, the continuum element and the truss element are connected by an interface element that carries shear stress. Appropriate constitutive laws are assumed for these elements and the parameters for these constitutive laws are calibrated from the experimental stress vs. strain curve and crack spacing under direct tension. The validity of the model is shown by analyzing a tensile specimen with the proposed discrete model, and the stress-strain relationship and crack spacing are in good agreement with experimental results. The sequential formation of multiple cracks and fluctuations in the stress-strain curve of SHCC can also be captured. Moreover, the cracking condition including the average and maximum crack width vs. strain as well as the crack width distribution at different strain levels can be faithfully reproduced.

Further applications of the developed models are then being studied. The energy minimization method is employed for the multiple cracking analysis of a mortar overlay under shrinkage that is restrained by the concrete substrate below. The trend of crack pattern evolution in the overlay is in good qualitative agreement with other numerical studies in the literature. Quantitatively, the results are found to be very sensitive to the mode II interfacial interaction at the concrete/FRCC interface. This is a new discovery that warrants further study in the future. The proposed discrete model is used to study the multiple cracking process in components made with strain hardening FRCC under various loading conditions (bending, restrained shrinkage and reflective cracking). It is found that the crack pattern, failure mode and load-displacement response under these conditions can be well captured by the discrete model.

In summary, the work presented in this thesis can contribute to calculating the crack width in FRCC member and assessing the durability performance of the member. It can further contribute to the optimal design or selection of FRCC for the purpose of better controlling the crack width.