Abstract
In this study, the concrete fracture energy was obtained using the three point notched beam test method developed by Hillerborg et al. (Cem Concr Res 6(6):773–782, 1976). A total of 12 notched concrete beams were tested under two different loading conditions: constant stroke control and constant crack mouth opening displacement (CMOD) control. Despite individual fracture energies obtained from the two different loading conditions showing some variation, the average fracture energy from both loading conditions was very similar. Furthermore, the results obtained support the idea that a far tail constant “A” could change the true fracture energy by up to 11 %, if it is calculated using CMOD instead of LVDT. The far tail constant “A” is determined using a least squares fit onto a straight line according to Elices et al. (Mater Struct 25(148):212–218, 1992) and RILEM report (2007). It was also observed that the selection of the end point can produce variations of the true fracture energy. The end point indicates the point in the experiment at which to stop. An end point of 2 mm has been recommended, however, in this study other end points were also considered. The final form of the bilinear softening curve was determined based on Elices and Guinea’s methods (1992, 1994) and RILEM report (2007). This paper proposes a bilinear stress–crack opening displacement curve according to test results as well as the CEB-FIP model code.
Highlights
A few decades ago much research was undertaken to obtain the tensile properties of concrete using various methods such as a cohesive crack (Hillerborg et al 1976), crack band (Bazant 1976) or the damage process (Lubliner et al 1989)
The common feature of the aforementioned methods is their use of the concept of a softening curve to arrive at the concrete fracture energies GF and Gf
The tensile strength of the specimens was calculated using Rocco’s empirical equation (Eq 1), where B and D are the specimen dimensions, P is the load and b = b/D (5 %) which is the relative width of the bearing strips
Summary
A few decades ago much research was undertaken to obtain the tensile properties of concrete using various methods such as a cohesive crack (Hillerborg et al 1976), crack band (Bazant 1976) or the damage process (Lubliner et al 1989). The tensile strength (ft) can be obtained from a splitting tensile test (ASTM C496 2005; ACI 446 2009). The size effect fracture energy (Gf) and the true fracture energy (GF) can be found from a three point bending test of a notched concrete beam (Maturana et al 1990; Guinea et al 1994; Planas et al 1999; Kitsutaka et al 1998; Elices et al 2002; RILEM 2007; ACI 446 2009). The direct method of determining the tensile softening curve of concrete is a stable
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