Meso-mechanical analysis of steel fiber reinforced cementitious composites

Abstract

The mechanical behavior of cement-based materials is greatly affected by crack propagation under general stress states. The presence of one or more dominant cracks in structural members modifies its response, possibly leading to brittle failure modes. The random dispersion of short steel fibers in cement materials is a new methodology used for enhancing the response in the post-cracking regime. The behavior of Fiber-Reinforced Cementitious Composite (FRCC), compared to conventional plain concrete, is characterized by several advantages, e.g., higher tensile and shear resistance, better post-cracking ductility, higher fracture energy, etc. In this framework, this thesis deals with both the experimental investigation and computational modeling of the mechanical behavior of FRCC. A great part of the work is intended at reporting the formulation and validation of a novel constitutive model aimed at simulating the stress-cracking response of FRCC and considering most complex fracture occurrences in mixed-modes of failure. Firstly, the results of an extensive experimental campaign, performed at the Laboratory of Materials testing and Structures (LMS) of the University of Salerno, is presented in which the possible influence of combining different fiber types on the resulting properties of Steel Fiber Reinforced Concrete (SFRC) is investigated. Particularly, the study concerns the four-point bending behavior of pre-notched SFRC beams where the influence of the amount of fibers and types on the first-crack strength and the whole post-cracking behavior is analyzed. After this, an innovative approach for reproducing the fiber effects on the cracking phenomena of the concrete/mortar matrix is proposed. The well-known discrete crack approach based on zerothickness interface elements is used to model the interaction between fibers and mortar as well as its degradation during fracture processes under mode I, II and/or mixed ones. The matrix degradation is modeled by means of a fracture energy-based softening law formulated in the framework of the flow theory of plasticity. Then, two fundamental aspects of the fiber-mortar interaction are considered in the model, i.e., the bond behavior of fibers bridging the crack opening and the dowel effect derived by possible relative transverse displacements of the two faces of the crack. The inclusion of fibers and the above two effects are taken into account by means of the well-known “Mixture Theory”. Particular emphasis and importance is dedicated to the description and modeling of the overall debonding behavior of fibers embedded in cementitious matrices. Actually, the adhesive interaction between fibers in concrete matrix is of key importance in controlling the postcracking response of FRCC. A unified formulation for simulating the overall bond behavior of fibers embedded in cementitious matrices is also presented. The proposed unified formulation is intended as a key element to be possibly employed in numerical models aimed at explicitly simulating the mechanical behavior of FRCC by taking into account the discrete nature of such materials and the contributions of the various constituents within the framework of the so-called meso-mechanical approach. The predictive capabilities of the aforementioned discontinuous approach for failure analyses of fiber reinforced cementitious composite are evaluated at different levels of observation. Particularly, the discrete crack formulation is employed and validated to simulate the fracture behavior of FRCC at constitutive, mesoscopic and macroscopic levels of observations. Several numerical results are performed to demonstrate if such proposal, based on the non-linear interface formulation, is capable to lead realistic predictions of failure processes of FRCC under different load scenarios and considering a wide spectrum of fiber contents and types. It is also analyzed if the proposed formulation is able to capture the significant influence of the fiber content on the maximum strength and post-peak ductility in mode I, II and mixed ones showing the capability of the cracking formulation to capture the complex interaction mechanisms between fibers and matrix. Furthermore, a simpler stress-crack opening model based on a hinge-crack approach, already available in the scientific literature, is proposed while the experimental results reported in this thesis are taken as reference for its validation. The model represents a reformulation of a fictitious crack model and is based on fracture mechanics concepts where the stress-crack opening relationship is accounted in a similar way obtainable by considering the pure “mode I” case of the discontinuous proposal formulated in general sense for mixed-modes of fracture. A closed-form solution for the stress-crack opening law with the explicit consideration of the fiber actions is considered for such a formulation. The model predictions, compared with the experimental measures, are performed to demonstrate the soundness of the model to reproduce the mechanical response of SFRC members in terms of Force-Crack Tip Opening Displacement (CTOD) curves. At last, both plain concrete and FRCC are analyzed and modeled by means of a novel microplanebased plasticity formulation. A continuum(smeared-crack) formulation, based on the non-linear microplane theory combined with the well-known “Mixture Theory”, is considered for describing the fiber effects on the failure behavior of FRCC. The constitutive formulation, failure analyses and the interactions between cementitious matrix and steel fibers are similarly approached as outlined for the discontinuous proposal. The capabilities of the microplane model to capture the significant enhancement in the post-cracking behavior of FRCC, with particular emphasis on the fracture and post-peak strengths, are finally evaluated by considering some experimental data available in scientific literature. [edited by author]