Modeling of localized deformation in high and ultra-high performance fiber reinforced cementitious composites

Abstract

A low ratio between the compressive strength of concrete and its cost makes concrete one of the most widely used construction materials in civil engineering. Despite of a very good response to compressive stress, concrete exhibits a low tensile strength and limited tensile strain capacity. Adding short discrete fibers to a cementitious matrix can significantly improve its performance under tensile stress, thus ultimately exhibiting a ductile behavior. Nevertheless, in spite of their beneficial properties fiber reinforced cementitious composites remain underutilized in engineering practice. One of the main reasons for this is a lack of an adequate characterization of the tensile behavior as well as a lack of analysis methods that would allow engineers to incorporate fiber reinforced structural concrete elements into their design. Therefore, this dissertation has four key objectives: 1) to computationally model a stress-strain response of high performance fiber reinforced cementitious composites in uniaxial tension and uniaxial compression prior to macro-crack localization, 2) to develop and perform a diagnostic strain localization analysis for high performance fiber reinforced cementitious composites, the results of which can characterize effects of fibers on failure precursors, 3) to devise and perform an experimental program for characterization of ultra-high performance fiber reinforced cementitious composites, and 4) to characterize a full-fledged behavior including stress-strain and stress-crack opening displacement responses of ultra-high performance fiber reinforced cementitious composites in uniaxial tension. To quantify effects of fibers on onset of strain localization in fiber reinforced cementitious composites a combined computational/analytical models have been developed. To this end, linear-elastic multi-directional fibers were embedded into a cementitious matrix. The resulting composite was described by different types of two-invariant non-associated Drucker-Prager plasticity models. In order to investigate effects of a shape of a yield surface and hardening type linear and nonlinear yield surfaces, and linear and nonlinear hardening rules were considered. Diagnostic strain localization analyses were conducted for several plane stress uniaxial tension and uniaxial compression tests on non-reinforced cementitious composites as well as on high performance fiber-reinforced cementitious composites. It was found that presence of fibers delayed the inception of strain localization in all tests on fiber-reinforced composites. Furthermore, presence of fibers exerted a more significant effect on the strain localization direction and mode in uniaxial compression than in uniaxial tension. The main objective of experimental program was to facilitate characterization of the post-cracking tensile behavior of ultra-high performance fiber reinforced cementitious composites. To this end, five different mixes of fiber-reinforced cementitious composites were cast, whereby volumetric fiber content, fiber shape and water to binder ratio were the experimental variables. Two testing methods were adopted, a direct uniaxial tension test and four-point prism bending test. Two different post-cracking behaviors were observed in direct tension tests, softening and strain hardening accompanied with multiple cracking. On the other hand, the response from prism bending tests was less scattered. Several different inverse analyses were carried out to predict stress-strain and stress-crack opening displacement responses in uniaxial tension based on the prism bending tests. The analyses resulted in worthy correlations with the experimental data, thus suggesting that the prism bending test is a viable alternative to a much more challenging to perform direct tension test for ultra-high performance fiber reinforced composites.