1.3. Factor de necrosis tumoral alfa (TNF- )
1.3.4. TNF- en el sistema nervioso central
Even before applying any load, a large number of micro-cracks, especially at the interface between aggregates/fibers and paste, already exist in concrete. Many of these micro- cracks are caused by segregation, shrinkage or thermal expansion of the mortar, etc. Propagation of these initial cracks can result in failure of a structure. The mechanism of crack formation and propagation or “fracture mechanism” is thereby employed to study the response and failure mechanism of structures, as a consequence of crack initiation and propagation.
Fig. 2.1- Basic modes of crack expansion (Hasanpour and Choupani 2009).
According to the fracture mechanism, a crack in a solid can occurr in three different modes, which are called “Opening Mode” or Mode I, “Sliding Mode” or mode II, and “Tearing Mode” or Mode III, as illustrated in Fig. 2.1. Mode I is one of the most common crack propagation modes, since it occurs in uniaxial, splitting and bending tensile failure. In Mode II, which receives the special attention in the present thesis, the displacement of crack surfaces is in the plain of the crack and perpendicular to the leading edge of the crack. In most of cases, the crack sliding is accompanied by crack opening due to the friction and asperities of the crack planes, resulting a mixed failure mode (Mode I and II). The Tearing Mode or out of plain shear (Mode III) is not so common like the previous failures modes, and occur in massive structures where 3D stress field can be developed (Ayatollahi et al. 2005), or in slab or shell type structures where punching failure mode is a concern (Ventura-Gouveira et al. 2011, Teixeira et al. 2015).
Fig. 2.2- Transferring stress from matrix to fiber by application of tensile load (löfgren
2005).
Mode I
When a tensile load is applied to a fiber reinforced composite, before initiation of any new crack, the matrix transfers some of the load to the fibers. Although the applied fibers generally have a higher elastic modulus compared to the matrix itself, they do not affect the tensile stiffness and strength of the elements before crack initiation. However, the fibers affect significantly the cracking process, and the failure mode of the FRC is highly influenced by the stress transfer between the fibers and the surrounding cementitious matrix. Thus, unlike plain concrete, which exhibits a brittle manner after initiation of the first crack, the FRC presents a relatively high toughness or fracture energy, i.e. the area under the stress-crack opening curve (Fig 2.3). In plain concrete, the pullout of aggregates bridging the crack is the main mechanism that causes the dissipation of energy, and the post-cracking tensile capacity decays towards zero for crack opening of about 0.3 mm. The combined crack bridging effect of aggregate and fibers is the main responsible for controlling the crack width (Fig. 2.3), which is very beneficial to increase the stress carried across the crack. In the following sections (Sec. 2.2.1 and .2.2.2) the effect of both aggregate bridging and fiber bridging on tensile behavior of FRC is discussed.
Fig. 2.3- Combined crack bridging effect of fibers and aggregate for the tensile capacity
2.2.1 Aggregate Bridging Action
Fig. 2.4 schematically represents stress-elongation relationship of plain concrete under uniaxial load. It shows that by applying a tensile load to a concrete element, initially micro-cracks start growing at the interface between the paste and the aggregates (A), and gradually propagate into the concrete (B). The crack localization occurs by reaching to the peak stress (C). This causes the initiation and propagation of the macro-cracks through the specimen, leading to the stress-drop (D). Crack bridging and crack branching is the principal mechanism responsible for the long softening tail (D-E) observed in experiments (see Fig. 2.4). However, depending on the aggregates and their bond to the matrix, the fracture process differs for high strength and normal strength concrete. For concretes with strong aggregate-paste bonds, or with weak aggregates, e.g. lightweight aggregates, the aggregate rupture may occur, losing its bridging effect, which results in a more brittle fracture process (Löfgren 2005).
Fig. 2.4- Schematic description of fracture process in uniaxial tension and the resulting
stress-crack opening relationship (Löfgren 2005).
Macro-cracks
Concrete fracture process zone Micro-crack growth
Macro-crack growth
Bridging and branching
Elongation,
l
ct f w Macro-cracks growth Traction free Bridging and branching Micro- cracking Bridging stress2.2.2 Fiber Bridging Action
According to the literature, fiber pull-out behavior, i.e. load-slip relationship has a significant influence on the mechanical behavior, especially in ductility of FRC (Cunha 2010). The principal bond mechanisms that contribute to improve the ductility of the composite material during the pullout of a fiber can be classified as chemical adhesion between fiber and matrix, frictional resistance, fiber-to-fiber interlock and mechanical component, arising from particular fiber geometry, e.g. deformed, crimped, or hooked- end fibers (Naaman 2003). Among all these factors, the mechanical component has proven to be the most effective one in improving the bond between fibers and surrounding matrix (Cunha et al. 2008, Cunha et al. 2010). Thus, for the deformed fibers (e.g. crimping, indenting or hooked end) the chemical bond can be neglected in favor of the mechanical bond between the fiber and the surrounding concrete (Robins et al. 2002), while the slip of smooth fibers mostly depends on the breakdown of chemical adhesion and the friction.
(a) (b) (c)
Fig. 2.5- (a) Pullout relationship between the load and the end-slip for (b) the smooth and
(c) the hooked end steel fibers (Cunha 2010).
Fig. 2.5 compares the pullout behavior of the smooth and hooked end steel fibers. This figure shows two distinct phases in the pre-peak branch of load-slip relationship for the
Hooked end fiber Smooth fiber
B C
smooth fibers (see Fig. 2.5(b)). The first phase, which is a linear ascending part (OA), is associated with the elastic bond. The second part (AB) corresponds to the initiation of the debonding process and starts with the micro-cracking of the interface transition zone between the fiber and matrix. After reaching to the maximum load, the load decreases with the increase of slip, resulting in an unstable interfacial crack growth on the post-peak behavior. Similar to the pull out behavior of smooth fibers, the pullout behavior of hooked end steel fibers consists of deboning and frictional pullout as well. However, the frictional pullout in the hooked end steel fibers is accompanied with a mechanical bond mechanism correspondent to the mechanical interlock and plastic deformation of the fiber hook (see Fig. 2.5(c)). Hence, after attaining the full debonding of the hooked end steel fibers (AB), the load still increases (BC) due to the mechanical anchorage provided by the hook of the fiber. By reaching the maximum pullout load (C), both curvatures 1 and 2 are deformed. Since the mechanical anchorage starts deforming progressively, the pullout load decreases (CD) after reaching the maximum load. However, at this stage the fiber is not fully straightened yet and, consequently another peak load is observed (DE), which coincide with the fiber (curvature 2) passing the last corner of the fiber imprint made in the matrix. After the fiber is fully straightened, likewise to the smooth fibers, the pullout action proceeds under frictional resistance (EF) (Cunha 2010). Orientation and dispersion of fibers are also factors that, together the fiber pullout mechanism, influence the mechanical behavior of FRC, as will be discussed in the following section.