Three-point bend (TPB) and wedge splitting (WS) tests have been conducted on three different concretes and the specific fracture energy G F determined on the basis of the concept of local fracture energy. The latter is influenced by the free back surface of a notched test specimen, as explained by Hu and Wittmann. Tests on three or four specimen sizes with four notch to depth ratios confirm the idea of Hu and Wittmann that the size-independent specific fracture energy G F can be determined from measured fracture energy values that vary with the size of the specimen, W, and notch to depth ratio, a=W . More importantly, it is shown that the same size-independent G F can also be obtained by testing a single size specimen with only two notch to depth ratios, provided they are well separated (a=W ¼ 0·05 and 0·50 in TPB, and 0·2 and 0·5 in WS), thus greatly simplifying the determination of the size-dependent fracture energy G F .
IntroductionThe specific fracture energy G F is the most useful material parameter in the analysis of cracked concrete structures.1 The method of experimental determination of the fracture energy, G F , and even its definition has been a subject of debate among researchers because of its variability with the size and shape of the test specimen. Guinea et al. 2 identified several sources of energy dissipation that may influence the measurement of G F , for example the influence of curtailing the P-ä tail in a bend test. 3 They concluded that when all these sources are taken into account an almost size-independent specific fracture energy G F can be obtained. Hu and Wittmann 4 have addressed the possibility that the specific fracture energy itself may not be constant along the crack path in a test specimen.The recent model of Duan et al. 5 assumes that the fracture energy required to create a crack along the crack path is influenced by the size of the fracture process zone (FPZ) which in turn is influenced by the free boundary of the test specimen. To consider the boundary effect on the propagation of FPZ, they assumed a bilinear fracture energy distribution to explain the ligament effect on the fracture energy of concrete. When this effect is included, they obtain a size-independent fracture energy, which is needed for an accurate estimate of the load bearing capacity of cracked concrete structures. This is because only in this way can the spurious size dependency introduced by the size dependency of the fracture energy itself be avoided. The influence of curtailing the tail part of the loaddeflection (P-ä) diagram in a bend test studied by Elices et al.3 in fact gives an estimate of the energy dissipation when the load tends to zero i.e. the crack approaches the free surface of the test specimen. This is in principle similar to the boundary effect proposed by Duan et al. 5 which will be further explored below.In this paper, using the concept of 'boundary effect' and 'local fracture energy distribution', the boundary effect model of Duan et al.5 is subjected to additional verification using th...
In a recent paper, Abdalla and Karihaloo confirmed the boundary effect hypothesis of Hu and Wittmann and observed that a size-independent specific fracture energy G F of concrete could be obtained by testing three point bend (TPB) or wedge splitting (WS) specimens containing either a very shallow or a deep starter notch. This observation was based on TPB and WS tests on limited number of specimens. In this paper, we have re-evaluated 26 test data sets on specific fracture energy of concrete published in the literature to assess the validity of this observation. The re-evaluation is found to support this observation. The determination of the true specific fracture energy G F of concrete thus becomes a simple and straightforward task requiring very few specimens of the same dimensions and shape. This re-evaluation also provides guidance for the selection of the specimen dimensions depending on the maximum size of aggregate used in the concrete mix in order to obtain its true G F .
For the analysis of cracked concrete structures using the fictitious crack model two fracture properties of concrete are required, namely its true specific fracture energy G F and the corresponding tension softening relation ó(w). In a recent paper, the authors proposed a simple method for the determination of the true specific fracture energy of a concrete mix. In this paper a method is proposed based on the concept of a non-linear hinge for constructing a bilinear approximation of the tension softening relation consistent with the true specific fracture energy G F . The parameters of this bilinear approximation are inferred in an inverse manner. It is shown that this inverse identification procedure predicts accurate bilinear softening relations of concrete mixes tested in three-point bend and wedge-splitting modes.
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