PSI - Issue 17

Michal Vyhlídal et al. / Procedia Structural Integrity 17 (2019) 690–697 Vyhlídal et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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LEFM studies and describes behaviour of cracks in homogenous media. Generalized LEFM is able to describe also crack initiation in sharp notches, bi-material notches, bi-material inclusions etc. Knésl et al. (2007), Klusák et al. (2007), Náhlík et al. (2007) modified MTS criterion for general singular stress concentrators (bi-material notch, free edge singularity, etc.). The stability condition is related to the average stress σ̅ θθ (θ) calculated across a distance d ahead of the crack tip. The distance d is usually chosen in dependence on the mechanism of a rupture (dimension of a plastic zone or material grain size). The average stress σ̅ θθ (θ) ahead of the crack tip is given by expression: ̅ ( ) = 1 ∫ ( , ) 0 (4) The crack propagation direction is determined from the maximum of the average value of tangential stress, so the following conditions (5) have to be satisfied: ( ̅ ) 0 = 0 ∧ ( 2 ̅ 2 ) 0 < 0. (5) A crack propagation direction is clear. Now it is necessary to determine the critical value of tangential stress ̅ θθ,c corresponding to the crack initiation. For a crack in homogeneous material under fracture mode I we obtain equation (6). For more details, see also Klusák et al. (2013), Klusák et al. (2016), Knésl et al. (2007), Klusák et al. (2007) or Náhlík et al. (2007). ̅ , = 2 Ic √2 (6) The material ahead of the crack tip fractures when the mean value of tangential stress σ̅ θθ (θ 0 ) exceeds its critical value σ̅ θθ,c defined in (6): ̅ ≥ ̅ , (7) This generalized crack initiation criterion of average tangential stress (7) will be in the following used for complete study of crack propagation process from the initial notch ahead to the polygonal cavity and then for further crack propagation through the ligament of the specimen above the cavity. 3. Experimental part To determine the influence of polygonal cavity on the fracture behaviour of cement composite, fracture tests were conducted on specimens for three-point bending (3PB). These specimens, with the nominal dimensions 40×40×160 mm and an internal inclusion placed at midspan with the dimensions 8×8×40 mm, were provided with an initial central edge notch with a depth of 12 mm by diamond blade saw, see Fig. 1. Specimen geometry was designed according to the following recommendations – Karihaloo (1995) or Nallathambi and Karihaloo (1986): • The least dimension of specimen should be greater than 5g, where g is the maximum grain size of the aggregate, • Specimen’s width should be in the range of 40 – 100 mm, • Specimen’s length should be 4 times greater than specimen’s width,