13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 0 50 100 150 200 250 300 0 20 40 60 80 100 W = 320 mm W = 80 mm W = 160 mm LeBellego SE(B) a/W = 0.1 B = 40 mm, S/W = 3 KIeff [N/mm3/2] Δa eff [mm] Pmax KIeff = 12.6⋅Δa0.36 eff [N/mm3/2] a) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 100 b) KIeff = 12.6⋅Δa0.36 eff [N/mm3/2] W = 80 mm W = 160 mm W = 320 mm LeBellego SE(B) a/W = 0.1 B = 40 mm, S/W = 3 KIeff [N/mm3/2] aeff/W Figure 8. Normalization of effective crack driving force versus effective crack growth for self-similar SE(B) specimens of different size. Data extracted from [1]. Fig. 8a shows the effective crack driving force versus absolute effective crack growth and Fig. 8b shows the effective crack driving force versus proportional crack growth. Also included in the plots is the effective K-R curve estimated for the maximum load values. The power law method contains similarities to an analytical cohesive zone method, which has been applied to describe the size effect in SE(B) specimens [14, 15]. The power law method is, however, much easier to use and provides an at least as good description of the size effect as can be seen by comparing Fig. (6) with Figs (4-6) in [15]. The advantage of the power law procedure lies in the very simple quantification of the fracture process zone development. A small power m indicates a brittle material, where the fracture process zone remains small throughout the fracture process. This is the case for m values of the order of 0.1 and below. The other extreme is a large m value in which case the material is crack insensitive and the damage comes mainly from the fracture process zone evolution. The method enables also the quantification of constraint in terms of the power m. The procedure results in the estimate of the effective stress intensity factor corresponding to 1 mm effective crack growth. 4. Summary and Conclusions Concrete is a so called quasi-brittle material which, despite predominantly elastic material response, exhibits in tension loading a stable non-linear fracture response, when tested under displacement control. The reason for the non-linearity is the development of a fracture process zone, in front of the crack, due to micro-cracking and crack bridging. The effect of the fracture process zone is to make the specimen sense the crack as being longer than a0+Δa. The fracture process zone causes thus an effective increase in the crack driving force and apparent fracture resistance. The fracture modeling of concrete has been considered a mature theory. However, Present state of the art testing and assessment methods are somewhat cumbersome to use. Here, a LEFM based estimate of the effective stress intensity factor and the effective crack growth at maximum load in a fracture mechanics test is used to obtain a simple power law approximation of the effective K-R curve. It is shown that it is applicable to the description of not only different size specimens, but also specimens with varying geometry. The method is based on a new theoretical estimate of the effective crack growth corresponding to maximum load. It can be concluded that:
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