13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A New LEFM Based Description of Concrete Fracture and Size Effects Kim Wallin VTT Materials and Built Environment, P.O. Box 1000, FI-02044 VTT, Espoo, Finland Kim.Wallin@vtt.fi Abstract 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. It has become increasingly popular to model the fracture process zone with different cohesive zone models. However, their use requires sophisticated finite element modeling and their success is directly related to the correctness of the assumed stress relaxation in the fracture process zone. An alternative is to use LEFM combined with an effective crack length. 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 but also the apparent fracture resistance increases since the fracture process zone effectively “blunts” the crack tip. This simple method, that does not require any finite element modeling, can be used as an aid to select the proper cohesive zone model for more sophisticated modeling. Keywords Concrete fracture, size effect, fracture toughness, quasi-brittle materials, K-R. 1. Introduction 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 (Fig. 1 [1]). 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. An excellent review of the physical fracture process of concrete has been given in e.g. [2] and need not be covered here in any more detail. Here, the focus is on the fracture mechanical description of the effect of the fracture process zone on the structural behavior of the test specimen and prediction of size effects. 0.0 0.1 0.2 0.3 0.4 0 1 2 3 4 5 Le Bellego et al. Concrete SE(B) a/W = 0.1 B = 40 mm, S/W = 3, W = 160 mm P [kN] Δ [mm] Figure 1. Example of a typical load-displacement relationship for concrete in a SE(B) fracture toughness test [1].
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